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A TIME-DEPENDENT, T W O - D I M E N S I O N A L MATHEMATICAL MODEL

FOR S I M U L A T I N G THE HYDRAULIC, THERMAL, A N D WATER QUALITY CHARACTERISTICS

IN S H A L L O W WATER BODIES

Moshe Siman-Tov

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OAK RIDGE NATIONAL LABORATORY OPERATED BY UNION CARBIDE CORPORATION FOR THE U.S. ATOMIC ENfRGY COMMISSION

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ORNL-TM-4626

Contract No. W-7405-eng-26

ORNL ENGINEERING

A TIME-DEPENDENT, TWO-DIMENSIONAL MATHEMATICAL MODEL FOR SIMULATING THE HYDRAULIC, THERMAL, AND WATER QUALITY

CHARACTERISTICS IN SHALLOW WATER BODIES

Moshe Siman-Tov

Submitted as a dissertation to The University of Tennessee for the degree of Doctor of Philosophy.

AUGUST 1974

N O T I C E This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, uxpress or implied, or assumes any legal liability or responsibility for the accuracy, com-pleteness or usefulness of any informat ion, apparatus, product or proccss disclosed, or represents that Its use would not infringe privately owned rights.

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

for the U.S. ATOMIC ENERGY COMMISSION

0 ' 1 L '~J

FOREWORD

The objective of this study was to develop a time-dependent, two-

dimensional mathematical model for predicting the velocities, water

levels, temperature, and mass concentrations of various constituents in

shallow vertically mixed water bodies. The model developed and presented

here meets the basic objective, but still much remains to be done. A

general computer code of such a size and scope will necessarily have,

in its initial phases, some limitations and drawbacks. It cannot become

a truly reliable predictive tool unless evolutionalized through constant

use and experience. It will, no doubt, require future modifications,

capability improvements, verification with field data, and calibration

before becoming a productive computer program. It is hoped that this

computer model will indeed be used and adapted by careful thermal-

hydraulic analysts who are fully aware of its capabilities and, most

importantly, its limitations until it is proven to be completely reli-

able and productive.

Oak Ridge National Laboratory is providing technical assistance to

the U.S. Atomic Energy Commission Directorate of Licensing in its analy-

ses of the environmental impact of power reactors as required by the

National Environmental Policy Act. The assessment of the environmental

impact of a nuclear station has required the development of new analyti-

cal techniques and the expansion of many existing ones.

This document is one of the spin-off results of this effort by the

Commission and its National Laboratories to protect the environment.

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iv

Other documents of this series in the thermal-hydraulic area published by Oak Ridge National Laboratory are listed below.

1. L. Dresner, "Steady Temperature Distributions in the Far-Field Region Obtained by Solution of the Equation of Convective Diffusion in Two Dimensions," USAEC Report ORNL-TM-4119, Oak Ridge National Laboratory, April 1973.

2. D. A. Pilati, "Transient Cooling of a One-Dimensional Thermal Plume and its Application for Determining Cold Shock," USAEC Report ORNL-TM-4160, Oak Ridge National Laboratory, May 1973.

3. L. Dresner, V. R. Cain, and W. Davis, Jr., "INTAKE: A Numerical Program to Calculate Fluid Velocity Profiles Near a Rectangular Inlet in a Stream with Cross Flow," USAEC Report ORNL-TM-4185, Oak Ridge National Laboratory, July 1973.

4. L. Dresner, "One-Dimensional Analysis of Heat Dissipation in a Sidearm of a Cooling Lake," USAEC Report ORNL-TM-4287, Oak Ridge National Laboratory, October 1973.

5. D. A. Pilati, "Cold Shock: Biological Implications and a Method for Approximating Transient Environmental Temperatures in the Near-Field Region of a Thermal Discharge," USAEC Report ORNL-TM-4267, Oak Ridge National Laboratory, November 1973.

6. M. E. Mitchell, "The Prediction of the Temperature Distribution in an Irregularly Shaped, Partially Mixed, Closed-Cycle Cooling Reser-voir," USAEC Report ORNL-TM-4416, Oak Ridge National Laboratory fin press).

7. R. P. Wichner, "Program ESTU: A Method for Estimating Estuarine Temperature Distributions for Harleman's Closed-Form, One-Dimensional Model," USAEC Report ORNL-TM-4150, Oak Ridge National Laboratory, April 1974.

Internal Central Files memorandums which are not for external dis-

tribution are:

1. W. Davis, Jr., "Row of Buoyant Jets/Slot Jet Model for Koh and Fan on the IBM/360 Disk," USAEC Report ORNL-CF-72-11-36, Oak Ridge National Laboratory, November 22, 1972.

2. W. Davis, Jr., "Round Buoyant Jet Model of Hirst on the IBM/360 Disk," USAEC Report ORNL-CF-72-12-11, Oak Ridge National Laboratory, December 7, 1972.

V

3. W. Davis, Jr., "Three-Dimensional Heated Surface Discharge Model of Stolzenbach and Harleman on the IBM/360 Disk," USAEC Report ORNL-CF-73-2-39, Oak Ridge National Laboratory, February 27, 1973.

4. W. Davis, Jr., "Koh and Fan Model of Far-Field Heat Dissipation by Passive Turbulent Diffusion on the IBM/360 Disk," USAEC Report ORNL-CF-73-3-36, Oak Ridge National Laboratory, March 27, 1973.

5. V. R. Cain, "Interactive Access to the Thermal Modeling Computer Library," USAEC Report ORNL-CF-73-4-14, Oak Ridge National Labora-tory, April 9, 1973.

6. W. Davis, Jr., "Heated Surface Jet Discharged into a Flowing Ambient Stream-Model of Motz and Benedict on the IBM/360 Disk," USAEC Report ORNL-CF-73-4-23, Oak Ridge National Laboratory, April 9, 1973.

7. W. Davis, Jr., "Energy Dispersion in Vertical Thermal Plumes Dis-charged into Shallow Water-Model of Trent and Welty on the IBM/360 Disk," USAEC Report ORNL-CF-73-7-15, Oak Ridge National Laboratory, July 11, 1973.

8. W. Davis, Jr., and M. Siman-Tov, "Heat Dispersion in an Estuary— One-Dimensional, Time-Dependent Model of Siman-Tov on the IBM/360 Disk," USAEC Report ORNL-CF-73-7-49, Oak Ridge National Laboratory, July 26, 1973.

9. J. W. Roddy, "Entrainment Probabilities at Oceanic Sites," USAEC Report ORNL-CF-73-9-17, Oak Ridge National Laboratory, September 14, 1973.

10. Ben L. Sill, "A Two-Dimensional Thermal Plume Model for Injection Parallel to a Free Stream in a Bounded Channel," USAEC Report ORNL-CF-73-9-20, Oak Ridge National Laboratory, September 14, 1973.

11. Fred Vaslow, "Fog Probabilities, Plume Visibility, and Drift Deposi-tion from Mechanical and Natural Draft Wet Cooling Towers," USAEC Report ORNL-CF-73-10-7, Oak Ridge National Laboratory, October 4, 1973.

ABSTRACT

A time-dependent, two-dimensional model was developed to provide a

practical analytical tool for simulating the transient behavior of the

elevation, velocity, and temperature of water and the mass concentrations

of various soluble constituents in vertically mixed shallow water bodies.

The model is based on a time-dependent discrete element formulation of

the basic conservation equations for total mass, momentum, energy, and

mass concentration of soluble constituents. These equations are directly

formulated in an integral form over each discrete element and then

reduced to a set of initial-value ordinary differential equations with

respect to time. The equations are numerically integrated by the multi-

step explicit solution of the Runge-Kutta-Gill method. A stability

analysis is presented for evaluation of the time step to be used to avoid

computational instabilities.

The effects of bottom shear stresses, wind stresses, heat exchange

v/ith the atmosphere, Coriolis forces, seepage, evaporation, rain,

tributaries, power plant intake and discharge, and other possible contri-

butions are taken account of by the model. Internal normal anO shear

stresses are included fully in the momentum equations, and hydrostatic

pressure is also considered. Turbulent diffusion as well an the longi-

tudinal dispersion caused by vertical variations are taken account of

by the use of general functions and rinconstant diffusion coefficients.

Density and other physical properties san be expressed as functions of

vii

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temperature and constituent mass concentrations. Mesh size can be

variable, and irregular physical boundaries can be simulated on a rec-

tangular coordinate system.

The model is applicable to any natural water body wherein vertical

stratification is not of major importance. This includes many rivers,

estuaries, and coastal sites where the horizontal dimensions are usually

at least two orders of magnitude larger than the vertical (depth)

dimensions. The model is basically a far-field model, but because of the

incorporation of stresses in the momentum equations, it can also be used

for approximate simulation of the near field. The mutual effects of a

number of power plants sharing the same water body as well as the

recirculation of discharge water back into the intake structure can be

simulated. In a more restricted way, the model can also be used to simu-

late the entrainment of organisms into the intake structure of a power

plant as well as the cold shock effects on aquatic biota when sharp dis-

continuities in power plant operation occur. Because of the capability

to include any number of constituents, the model has the potential for

extension into a population distribution model for aquatic organisms.

TABLE OF CONTENTS

SECTION PAGE

1. INTRODUCTION 1

1.1. Current Mathematical Models 3

1.1.1. Near-Field Models 4

1.1.2. Far-Field Models 7

1.1.3. Intermediate Region 11

1.2. A Complete Model 12

1.3. Interim Model 17

2. FORMULATION OF THE MASS, MOMENTUM, AND ENERGY CONSERVATION

PRINCIPLES 19

2.1. General Discussion of the Physical Assumptions . . 19

2.2. General Discussion of the Numerical Method

Employed 20

2.3. The Integral Form of the Conservation

Principles 21

2.4. The Discrete Elements: Definitions and

Notation 28

2.5. The Discrete Element Formulation of the

Conservation Equation for Total Mass 34

2.6. The Discrete Element Formulation of the Mass

Conservation Equation for Constituent k 38

2.7. The Discrete Element Formulation of the Energy

Conservation Equation . . . * 42

i x

X

SECTION PAGE 2.8. The Discrete Element. Formulation of the Momentum Equation 49

2.9. The Half-Point Values on Discrete Element Surfaces and Comers 54

3. FORMULATION OF DIFFUSIVE AND OTHER NONCONVECTIVE INTERNAL FLUXES 58

3.1. The Gradient Law of Diffusion, Turbulent Diffusion, and Dispersion 58

3.2. Applicable Turbulent Transport Properties 69 3.3. Viscous and Hydrostatic Stresses 76 3.4. Energy Fluxes 81 3.5. Mass Diffusion Fluxes . 84

4. BOTTOM SURFACE, TOP SURFACE, AND VOLUMETRIC CONTRIBUTIONS 89 4.1. Shear Stresses at the Bottom 89

4.2. Wind Shear Stresses 92 4.3. Rain, Evaporation, and Other Mass Fluxes at the Bottom and Top 94

4.4. Heat Exchange with the Atmosphere and Other

Energy Fluxes at the Bottom and Top 96 4.4.1. General 96 4.4.2. Heat Exchange with the Atmosphere 97

4.5. Body Forces and Volumetric Heat and Mass Generation 103

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SECTION PAGE 4.6. Thermophysical Properties 104

5. FORMULATION OF INITIAL AND BOUNDARY CONDITIONS 108 5.1. Initial Conditions 108 5.2. General Discussion of Analytical and Numerical (Half Points) Boundary Conditions 109

5.3. Types of Boundary Conditions 112 5.4. Solid Wall, No-Slip, and Free-Slip Conditions . . . 116 5.5. Open Channel, Flow In . . . . 119 5.6. Open Channel, Flow Out 119 5.7. Ocean Opening in an Estuary 121 5.8. Summary of Boundary Conditions 122

6. THE NUMERICAL SOLUTION OF EQUATIONS AND STABILITY ANALYSIS 123 6.1. The Reduction of the Discrete Element Forms oF. the Conservation Equations to Their Classical Differential Form 123 6.1.1. The Total Mass Conservation Equation 123 6.1.2. The Mass Conservation Equation for Constituent k 124

6.1.3. Energy Conservation Equation 125 6.1.4. The Momentum Conservation Equations 126

6.2. The Numerical Solution of the Governing Equations . 127

6.3. The Donor Cell Differencing Method . 130

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SECTION PAGE 6.4. Stability Analysis of the Numerical Solution . . . 131

6.4.1. Stability Criteria for Calculating Temperature 135

6.4.2. Stability Criteria for Calculating Constituent Concentration C^ 139

6.4.3. Stability Criteria for Calculating Velocities 140

6.4.4. Stability Criteria for Calculating Water Elevation H 141

6.4.5. Total Time Step Limit Approximation 143 7. APPLICATION OF THE MODEL AND ITS COMPUTER PROGRAM 145

7.1. Applicability of the Model 146 7.1.1. Simulation of Power Plant Intake and Discharge . 146

7.1.2. Vertical Variations 148 7.1.3. Geometrical Considerations 149 7.1.4. Near- and Far-Field Modeling , . . 149 7.1.5. Recirculation, Interacting Power Plants, and Intake Entrainment 151

7.1.6. Multicomponent Analysis 153 7.2. The Computer Program 153 7.2.1. Program Structure and Condensed Flow Diagram 153

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SECTION PAGE

7.2.2. The Region Subdivision and the Flagging

Technique 156

7.2.3. Program Capabilities and Limitations 159 7.2.4. Brief Description of Input and Output 162

7.3. Application of the Model to Sample Problems . . . . 177 7.3.1. Sample Problem No. 1 . . . . . . 177 7.3.2. Sample Problem No. 2 181 7.3.3. Results and Discussion of Sample Problems . . . 209

8. SUMMARY AND CONCLUSIONS . . 259 LIST OF REFERENCES . . . . 267 APPENDIXES A. COMPLETE INPUT AND OUTPUT FOR THE SAMPLE PROBLEMS 279 B. COMPUTER PROGRAM NOMENCLATURE AND FORTRAN IV LISTING . . . . 339

LIST OF TABLES

TABLE PAGE

3.1. Averaging Levels of Transport Phenomena 68

4.1. Coefficients for Various Wind Function Correlations to be

Used in Equations 4.37 and 4.38 101

5.1. Types of Boundary Conditions 117

5.2. Some Examples of Possible Boundary Conditions and

Boundary Condition Types to be Used for Each Unknown

(see Table 5.1) 120

7.1. Summary of Input Variables and Their Format . . . . . . . . 163

A.l. Input Data for Sample Problem No. 1 280

A.2. Output Information for Sample Problem No. 1 at Time =

5.6 hr Using the Fall Version of the Program . . . . . . 293

A.3, Output Information for Sample Problem No. 1 at Time =

124.45 hr Using the Reduced Version of the Program . . . 301

A.4. Input Data for Sample Problem No. 2 309


0.61 hr Using the Full Version of the Program 323


37.205 hr Using the Reduced Version of the Program . . . 331

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LIST OP FIGURES

FIGURE PAGE

2.1. Arrangement of Discrete Elements 29

2.2. Top View Presentation of Properties and Fluxes in a

Discrete Element 31 2.3. X-Z Cross-Sectional Presentation of Fluxes in a Discrete

Element 32 2.4. Y-Z Cross-Sectional Presentation of Fluxes in a Discrete

Element . . ., 33

5.1. A Discrete Element with a Physical Boundary on Its Right Hand Side Ill

7.1. Simplified Flow Diagram for Computer Code 155 7.2. Regions and Boundary Conditions Arrangement ir Sample

Problem No. 1 179 7.3. Velocity Distribution (ft/hr) for Sample Problem No. 1

at Time = 2.050 hr 182 7.4. Velocity Distribution (ft/hr) for Sample Problem No. 1

at Time = 10.950 hr . 183 7.5. Velocity Distribution (ft/hr) for Sample Problem No. 1

at Time = 118.850 hr 184 7.b. Velocity Distribution (ft/hr) at the Zone of Discharge

for Sample Problem No. 1 at Time = 2,050 hT 185 7.7. Water Depth Distribution (ft) for Sample Problem No. 1

at Time = 2.050 hr 186

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xv i

FIGURE PAGO

7.8. Water Depth Distribution (ft) for Sample Problem No. 1

at Time » 3.050 hr 187


at Time a 4.050 hr 188


at Time a 5.050 hr 189


at Time «= 7.050 hr 190


at Time = 9.050 hr 191


at Time = 29.000 hr 192


at Time *> 41.7 hr 193


at Time = 118.85 hr 194

7.16. Water Depth Distribution (ft) at the Zone of Discharge

for Sample Problem No. 1 at Time = 2.050 hr 195







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FIGURE PAGE

;.20. Water Depth Distribution (ft) at the Zone of Discharge






7.23. Temperature Distribution (°F) for Sample Problem No. 1

at Time = 2.05 hr 202

7.24. Temperature Distribution (°F) at the Zone of Discharge

for Sample Problem No.- I at Time = 2.050 hr 203

7. 25. Temperature Distribution (°F) at the Zone of Discharge


7. 26. Temperature Distribution (°F) at the Zone of Discharge


7.27. Temperature distribution (°F) at the Zone of Discharge

for Sample Problem No. 1 at Time = 124.450 hr . . . . . 206

7. 28. Regions and Boundary Conditions Arrangement in Sample

Problem No. 2 207

7.29. Velocity Distribution (ft/hr) for Sample Problem No. 2

at Time = 25.435 hr and Period of Tidal of 2.051 . . . . 210 7. 30. Water Depth Distribution (ft) for Sample Problem No. 2

at Time = 25.435 hr and Period of Tidal of 2.051 . . . . 211 7.31. Temperature Distribution (°F) for Sample Problem No. 2

at Time = 25.435 hr and Period of Tidal of 2.051 . . . . 212

xviii

FIGURE PAGE



7. 33. Water Depth Distribution (ft) for Sample Problem No. 2

at Time =27.915 hr and Period of Tidal of 2.251 . . . . 214


at. Time = 27.97.5 hr and Period of Tidal of 2.251 . . . . 215

















7.43. Temperature Distribution ("l5) for Sample Problem No. 2


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FIGURE PAGE

"",44. Velocity Distribution (ft/hr) for Sample Problem No. 2












7.50. Velocity Distribution (ft/hr), at the Zone of Power Plant

Discharges, for Sample Problem No. 2 at Time =

25.435 hr and Period of Tidal of 2.051 231

7.51. Water Depth Distribution (ft), at the Zone of Power Plant



7.52. Temperature Distribution (°F), at the Zone of Power Plant






mccciii

FIGURE PAGE

7. 54. :» ; Depth Distribution (ft), at the Zone of Power Plant




Discharges, for Sample Problem No. 2 at Time a


7. 56. Velocity Distribution (ft/hr), at the Zone of Power Plant














31.635 hr and Period of Tidal of 2.551 . 241




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FIGURE PAGE















35.355 hr and Period of Tidal of 2,851 247


Discharges, for Sample Problem No. 2 at Time «

35.3S5 hr and Period of Tidal of 2.851 248



37.205 hr and Period of Tidal of 3.00



37.205 hr and Period of Tidal of 3.00 2S0

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FIGURE PAGE



37.205 hr and Period of Tidal of 3.00 . 251

LIST OF SYMBOLS

2 A Surface area enclosing the discrete element, L

a Radius of pipe in Eq. 3.17, L

b Width of a jet^s mixing zone in Prandtl's defect law (Eq. 3.12), L

C. Mass concentration of constituent k in the mixture, K Btu.M-lF-1

Cp Specific heat at constant pressure, Btu-M-^-F-l

Cy Specific heat at constant volume, Btu-M-lp-1

C2 Chezy resistance factor for bottom friction,

Overall diffusion coefficient combining the molecular, turbulent and shear effects, L2T~1

Dh Overall thermal diffusion coefficient, L2T_i

2 - 1 D Overall momentum diffusion coefficient, L T m * 2 - 1 Dm Overall binary mass diffusion coefficient, L T

dA Differential of surface area enclosing the discrete element, L2

dV- Differential of volume within a discrete element, L3

E Longitudinal diffusion coefficient which is caused by shear effects, L2T"1

E' See Table 3.1

E " See Table 3.1

e Specific internal energy, Btu>M-1

F Right-hand side of the basic differential equations of the model

°F Degrees Farenheit

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f(u>) Dimensionless function for turbulent velocity distribution along vertical direction, Eq. 3.19

? Depth mean average of f(w) - 2 2 f^ Body force per unit volume, ML T

- 2 - 2 fc Conolis force per unit volume, ML T _2 g Gravitational acceleration, LT r

-2 -1 g(X,Y,Z,t) Instantaneous mass flow rate per unit area, ML T _9 -1

g General instantaneous mass flux vector, ML T

h Specific enthalpy, Btu-M"1 h,. Film mass transfer coefficient across a boundary surface, M ML-2T-1 hM Film heat transfer coefficient across a boundary surface. H Btu.L-2T-lF-l

H(X,Y,Z,t) Instantaneous local total Water depth, L

K Heat exchange coefficient between the top water surface and the atmosphere, based on the equilibrium temperature con-cept, Btu/ft2«day.°F

kQ Von Karman's constant (Eq. 3.21)

a Prandtl's mixing length (Eq. 3.0), L

Taylor's mixing length (Eq. 3.10), L

(Le)e Turbulent Lewis number (Eq. 3.74) -1/3 n Manning roughness coefficient, TL

A

n Unit vector (outward positive) normal to surface area A

P(X,Y,Z,t) Represents in general any one of the basic unknowns of the model (H, U, V, T, or Ck)

P*(X,Y,t) Depth averaged and time averaged (over turbulent time scale) value of property P

-1 -2 Pr Local instantaneous pressure, ML T

XXV

- 1 - 2 * (P ) Local atmospheric pressure, ML T IT a

p'(X,Y,Z,t) Random turbulent fluctuations of property p compared to its time averaged value over turbulent time scale

p(X,Y,Z,t) Difference between local turbulent time scale mean value of property P and its depth averaged value

(PR)a Molecular Prandtl number (Eq. 3.55)

(PR)e Turbulent Prandtl number (Eq. 3.56)

(PR)e Longitudinal diffusion Prandtl number (Eq. 3.57)

(PR)D Total Prandtl number (Eq. 3.58) 2 Qs Gross solar radiation heat flux, Btu/ft -day

-*• -2-1 q General instantaneous heat flux vector, Btu*L T -3 -1

<ly Heat generation (or decay) per unit volume, Btu*L »T

RJi Hydraulic radius, L

Sg Slope of channel bottom

(Sc)a Molecular Schmidt number (Eq. 3.70)

(Sc)e Turbulent Schmidt number (Eq. 3.71)

(Sc)E Longitudinal diffusion Schmidt number (Eq. 3.72)

(Sc)D Total Schmidt number (Eq. 3.73)

T(X,Y,Z,t) Instantaneous local water temperature, °F

T^ Dew point temperature, °F

Tg Equilibrium temperature, °F

t time, T U(X,Y,Z,t) Instantaneous local horizontal velocity in X direction,

LT-1 U(X,Y,t) Depth averaged and time averaged (over turbulent time ,

scale) value o£ instantaneous velocity in X direction, LT

xxv i

U„(t) Freshwater velocity in oscillating water body (velocity averaged with respect to time over oscillating period time scale), LT"1

u'(X,Y,Z,t) Random turbulent fluctuations of velocity in X direction compared to its time averaged value over turbulent time scale, LT"1

u(X,Y,Z,t) Difference between local turbulent time scale mean value of velocity in X direction and its depth averaged value, LT_1

u T

Friction velocity in X direction (= A^/p), LT~* -1 u Internal energy, Btu»M

V(X,Y,Z,t) Instantaneous local horizontal velocity in Y direction, LT"1

V"(X,Y,t) Depth averaged and time averaged (over turbulent time scale) value of instantaneous velocity in Y direction, LT"1

^ Velocity of mixture, LT"*

^ Velocity of constituent k relative to the mixture velocity K V, LT-1

V^ Velocity (either U or V) normal to a boundary surface, LT"*

V Velocity (either U or V) tangent to a boundary sui-face, t LT_i 3 V- Volume of discrete element, L

> -1 v^ Friction velocity in Y direction (= /Ty/P), LT

W Wind velocity, miles/hr W,,(X,Y,t) Local instantaneous rate of change of water elevation

with time; that is, vertical velocity of the water top surface, LT"1

X Horizontal direction in the Cartesian coordinate system, L

Y Horizontal direction in the Cartesian coordinate system, L

Z Vertical direction in the Cartesian coordinate system, L

H 2 - 1 au Molecular thermal diffusion coefficient, L T

xxvii

2 -1 Molecular momentum diffusion coefficient, L T 2 - 1

Molecular binary mass diffusion coefficient, L T

Time step size used for numerical time integration, T

Smallest time step size required for numerical stability,, T

Size of a discrete element in X direction, L

Size of a discrete element in Y direction, L

Discrete perturbation error of numerical solution at time t Numerical error introduced in F(t) due to the discrete per-turbation error (t) Turbulent diffusion coefficient either mass, momentum, or heat, L2T-1

2 - 1 Turbulent thermal diffusion coefficient, L T 2 - 1 Turbulent momentum diffusion coefficient, L T

2 -1

Turbulent binary mass diffusion coefficient, L T

Dimensionless friction coefficient on a solid surface

Density, ML"3

Mass addition (or subtraction) of constituent k per unit volume and per unit time, ML'^T"1

- 1 - 2 Surface force vector per unit area, ML T -1 -2 Internal normal stresses in X direction, ML T

Internal shear stresses in X direction over a surface area directed in Y direction, ML_1T"2

Internal shear stresses in Y direction over a surface area directed in X direction, ML-1T"2

-1 -2 Internal normal stresses in Y direction, ML T -1 -2 Local shear stress on a solid surface, ML T

-1 -2 Local shear stress on side walls, ML T

xxviii

X Empirical dimensionless coefficient in Von Kantian*s similarity theory (Eq. 3.11)

X, Empirical dimensionless coefficient in Prandtl's defect 1 law (Eq. 3.12).

ip Coefficient of property P(H, U, V, T, or C^) in the right-hand side functions of the system differential equations (Eq. 6.18)

The term in the right-hand side functions of the system differential equations which is independent of P

a) Local dimensionless depth (Eq. 3.19)

Subscripts

A Identifies -the value to be per unit cross sectional area

a Identifies the value to be for ambient conditions

B Identifies the value to be for the bottom surface of the water body

b Identifies the value to be on a boundary surface

bf Identifies the value to be a flux (flow rate for unit area) across a boundary surface

bo Identifies the value to be for the outside the boundary surface and outside the boundary layer thickness

i Identifies the location of the center of a discrete element along X direction

i±l/2 Identifies the location of the half-point boundaries of a discrete element in X direction

ib Identifies the location of the half-point boundary of a discrete element in X direction when this element is next to a boundary

j Same as i but in Y direction

j+1/2 Same as (i±l/2) but in Y direction

k Identifies the value to be for a certain constituent k in the mixture

xxix

T Identifies the value to be for the top surface of the water body

W Identifies the value to be of the wind

WS Identifies the value to be for the water surface

X Identifies the value of a component in X direction

Y Identifies the value of a component in Y direction

Z Identifies the value of a component in vertical direction

0 Identifies the value to be evaluated at initial time (initial condition value)

Superscripts

Indicates a numerically computed value which includes the dis crefce perturbation error 6(Eq. 6.19)

— Indicates average value of either with respect to depth, or with respect to tuVbulent time scale or both

1. INTRODUCTION

During the past few years, considerable interest has arisen in

developing the capabilities for predicting temperature distributions

resulting from discharges of heated water from electric power plants

into rivers, lakes, estuaries, and coastal waters. This interest arose

because of a rapid growth in demand for electric power and an increased

awareness of the possible environmental impact of electric power gen-

erating plants. Much of the additional electric power demanded is

expected to be supplied by nuclear power plants, and these plants

reject about 7,500 Btu/hr for every kilowatt of power generation rather

than about 5,000 Btu/hr rejected by conventional steam plants. The

rejected hecit is transferred in one way or another to the natural

environment. Among the presently available methods of heat disposal,

the once-through cooling method, in which water is withdrawn from a

water body and returned to it after being heated, is the least expen-

sive1 and, therefore, the most attractive to the utilities. The main

disadvantage in this method is its possible destructive impact on aquatic

biota resulting from entrainment of organisms through the plant cooling

water intake and from elevation of the temperature of the water body to

undesirable levels.

To put the problem in somewhat better perspective, it must be

emphasized that the total cooling capacity of the earth still is far

greater than the total heat generation rate from power plants antici-

pated for the next few decades. It has been estimated that for the

1

BLANK PAGE

2

total annual heat generation rate of 1.2 million MW(t) anticipated by

the year 1990, the overall average water surface temperature will be 2

increased by only about 0.25°F. Unfortunately, the heat rejected from

power plants is not released uniformly throughout the total body of

water available. Instead, the heat is dumped locally to create large

concentrations of thermal energy that must be diluted and dissipated

to prevent local heat buildup.

Determination of the capability of a water body to dilute and

dissipate concentrated thermal discharges is a major thermal pollution

problem faced today. Estuaries and coastal waters are most effective

thermal sinks, but their capabilities in this respect are not as limit-

less as some may wish to believe. The situation is usually more severe

in rivers, lakes, and ponds. To evaluate properly the impact of thermal

discharges, the biologist must know, among other things, what portion

of the biota is affected by what levels of temperature increases and for

how long. To answer such broad questions, one must have detailed infor-

mation about the velocities, temperatures, and concentrations of dis-

solved substances as a function of three space dimensions and time.

Unfortunately, attainment of such information is not an easy task.

Various modeling methods have been used in attempts to determine

and predict the dilution and dissipation capabilities of specific water

bodies. Although useful in many applications, physical models cannot

simulate correctly many of the transport processes because of size

limitations and the need to distort the models greatly. Field measure-

ments are very expensive and are normally useful for "after-the-fact"

3

information and for supplementing the supporting theoretical models.

They cannot be used as predictive tools except for a very limited range

of conditions that have already been monitored. As predictive tools,

mathematical models are the most flexible and least expensive. Their

main limitations are directly related to our level of understanding of

the physical phenomena themselves. Many of these models suffer from

lack of verification by field and experimental data. Nevertheless,

their usefulness for predicting various possibilities and evaluating

alternative options is unmatched by other methods.

1.1. Current Mathematical Models

The mathematical models currently available for predicting the

effects of heat discharges into water bodies can be grouped in two major

categories: (1) near-field models, which are used primarily for model-

ing the thermal plume in the immediate vicinity of the discharge point,

and (2) far-field models, which are used to simulate the overall

behavior of the plume at some distance from the point of discharge after

it has lost its initial momentum. The distinction between the two

regions is based on the type of dominating mechanism involved in the

heat dissipation process. In the near-field region, the excess tempera-

ture of the jet is quite high and the jet has considerable momentum of

its own. Therefore, the main cooling process is by entrainment and

mixing with the ambient water. Buoyancy effects are of major importance

because of the high excess temperatures involved. In the far-field

region, the velocity of the jet is reduced in magnitude and is close to

4

that of the ambient, water. As a result, dilution by entrainment of

cooler water into the plume is very small, and the cooling process is

mainly by natural diffusion, convection, and heat transfer to the atmos-

phere. The zone where the near-field and far-field effects overlap is

usually teemed the intermediate zone.

1.1.1. Near-Field Models

General work related to near-field models (jets and plumes) has

been reported by Abramovitch,3 Pai,^ Schlichting,^ and Hinze.^ More

specific models for predicting the general behavior of submerged buoyant 7

jets in the near field have been developed by Fan (round buoyant jets), o

Fan and Brooks (round and slot buoyant jets in uniform and stratified 9 10 ambients), Koh and Fan (multiport submerged discharges), Ditmars

(buoyant jets in arbitrary stratified ambient), and Hirst** (three-

dimensional axisymmetric submerged jets in flowing and stratified

ambients). Both two- and three-dimensional models have been developed

for surface discharges in the near field. A two-dimensional surface dis-

charge model that includes both heat dissipation to the atmosphere and 12 wind shear stresses was developed by Zeller and his associates, and

two-dimensional models for surface discharges into cross-flow currents 1 3 14 have been developed by Carter and Motz and Benedict. A three-

dimensional surface discharge model that includes buoyancy and bottom-

slope effects was developed by Stolzenbach and Harleman,*^'*^ and Stefan 17

and his associates developed a three-dimensional surface discharge

model that includes the effects of weak cross currents and weak wind

velocities.

5

Most of the near-field jet models have common simplifications and

limitations. These include the assumption of steady-state conditions,

purely hydrostatic pressure variations, and axisymmetric flow within the

jet (or plume symmetrical flow in the case of slot jets). The jet is

assumed to be discharged into an ambient fluid of infinite extent, and

it is assumed that the velocity and temperature profiles along the axis

of the jet are similar. In most cases, these profiles axe assumed to be

Gaussian. Solution of these models is based on the radially integrated

form of the continuity, momentum, and energy equations, leaving the

distance along the axis of the jet as the only independent variable.

The similarity assumption and the integration and averaging

processes employed in these near-field models eliminate some of the

information related to local shear stresses and eddy dispersion that is

included basically in the partial differential equations. An empirical

entrainment coefficient, normally considered constant, is introduced in

the solution (together with the profiles assumed) to account for the

effects which cannot be derived from the solution because of the missing

shear stress terms. The intuitive judgment of the model user is relied

on considerably for application of the proper entrainment coefficient.

The effects of confining boundaries and recirculation cannot be included

in these models, and their validity with respect to ambient cross-flow

conditions is questionable.

The effects of limited depth (sL. iow water) on jet behavior have

been studied by Cederwall1,8 and Maxwell and Pazwash.*9 Some improved

entrainment functions, which relieve the model user to some extent from

6

making purely arbitrary selections of entrainment coefficients, have

been suggested by Hirsr"1 and Campbell and Schetz.20 However, these

models are based on the integrated approach, and the built-in coefficients

are largely empirical. The entrainment coefficient used by Hirst is a

combination of a number of empirical coefficients derived for more

restricted applications. Campbell and Schetz make use of the defect

law based on Prandtl's hypothesis, while relying on a constant rate of

jet spread for evaluation of the dimensionless constant.

It has become more and more evident that in order to overcome many

of the limitations inherent in these models, the problem must be

approached by employing the basic nonlinear partial differential

equations of motion, energy, and mass with the proper stress model

included. A model with such a finite difference approach has been 2 1 - 2 3

developed by Trent for the near-field behavior of a submerged

axisymmetric vertical thermal plume. This model, which is for steady-

state conditions, includes the effects of buoyancy, stratification, sur-

face spreading, and interaction with physical boundaries. The Prandtl

hypothesis (defect law) is used to simulate the eddy diffusivity, and no

empirical entrainment coefficient or similarity assumptions are used. A

similar but more general approach (exact numerical solution of the con-24

servation equations) has been taken by Chien and Schotz in their model

for a three-dimensional buoyant jet in a cross flow with confined

boundaries. These recent models are important contributions to the

analysis of submerged jets.

7

Despite the recent advances in near-field models, it should be

emphasized that n near-field model by itself is not adequate for complete

assessment of the temperature distribution expected in the vicinity of

a discharge. First, the zone analyzed by a near-field model is limited

in extent to the zone of jet mixing wherein the hydrodynamics are

dominated by the momentum of the jet, Second, jet cooling is dependent

on the entrainment of ambient water. The water in the near field inter-

acts directly with that in the so-called far field, and its temperature

is also affected by that of the far-field water. Therefore, it should

never be assumed that the temperature of the water entrained into the

jet is the same as that of ambient water in an unaffected area. Third,

a fact to be taken account of in the near-field model is that the con-

denser cooling water entering the intake structure is at some elevated

temperature because of recirculation from the far-field region. This

elevated temperature of the intake water is not necessarily the same as

that of the water entrained into the jet. Thus, it must be concluded

that a far-field analysis must precede any near-field analysis if these

analyses must of necessity be handled separately.

1.1.2. Far-Field Models

Heat dissipation in the far-field region takes place primarily by

natural turbulent diffusion and heat exchange with the atmosphere. In

this region, the behavior of the plume depends primarily on the ambient

conditions of the natural environment, and these conditions are often

very complex and irregular with time. Among the many factors contributing

8

to these conditions in a natural water body are tributary flows, rain,

wind, solar heat loads, atmospheric radiation, evaporation, density

variations, bottom and bank shear stresses, bottom seepage, Coriolis

forces, tidal forces, and physical boundaries. Among the man-made

factors contributing to these conditions are sewage, effluents from

chemical plants and electric power plants, and the effects of pumped

storage areas.

Simulation of these conditions by analytical models has been 25

attempted, but such models, like those proposed by Edinger and Polk 26

and by Csanady, are necessarily overly simplified and cannot simu-

late properly the actual conditions in most cases. A realization of the

limitations of analytical models and an appreciation of the potential

capabilities of modem computers for solving complex sets of partial

differential equations have led many investigators to shift their efforts

to numerical techniques. Such a solution for the behavior of a thermal 27

plume in shallow water was presented recently by Barry and Hoffman,

but their model is a simplified stead-state two-dimensional one that

does not take account of buoyancy, density variations, or physical

boundaries.

Because of the dynamics existing in estuaries, coastal regions, and

to a lesser extent in any other type of natural water body, a far-field

model that simulates actual conditions properly must be time dependent.

The major portion of available time-dependent far-field modes1 are one

dimensional, and a few are two dimensional. Hie state-of-the-art of

mathematical 'ling for thermal discharges in large lakes has been

9

28 reported by Policastro and Tokar, and that for estuaries has been 29

reported by TRACOR, Inc. Several one-dimensional time-dependent

investigations applicable primarily to estuaries have been performed

by Harleman and his colleagues at the Massachusetts Institute of Tech-

nology. A one-dimensional model for calculating tides and currents in estuaries was developed by Harleman and Lee." That model was extended

31 by Lee A for predicting the general water quality in estuaries, and 32 33

Thatcher and Harleman ' used it for predicting salt intrusion from

the ocean into estuaries. In this latter use, a method fox determining

the longitudinal dispersion coefficient was developed and incorporated 34 in tha model. Dailey and Harleman furthex developed the model into a

complete one-dimensional time-dependent water quality model that includes

water levels, water velocities, and multiple substance concentrations.

The basic one-dimensional model is used for geometrically complex

estuaries that can be simulated as a network of one-dimensional channels.

Other such one-dimensional models have been developed for channel

network simulation. They include the model developed by R. V. Thomann,

0. J. O'Connor, and associates in connection with a study of the Delaware

River Estuary, ~ the Bay Delta models developed by G. T. Orlob, R. P.

Shubinski, and associates in connection with studies of the Sacramento-36 37 38 San Joaquin Delta and San Francisco Bay, * and the QUAL-1 model

used by the Texas Water Development Board.

A general and flexible one-dimensional model developed recently by 39

Eraslan can alco take account of the effects of in-and-out flows from

storage areas, surface shear stresses (wind), seepage, evaporation, rain,

10

density variations, and river inclinations. The computer program is 11 1

kept flexible and general so that different expressions can be used for

turbulent dispersion and heat exchange with the atmosphere. The mathe-

matical solution is based on numerical integration with respect to time

of a system of nonlinear ordinary differential equations in which the

rate of change of each unknown is explicitly expressed in terms of all

the rest of the variables. The Runge-Kutta-Gill method is used for

that integration. No partial differential equations are derived.

Instead, the physical conservation principles are used directly for

numerical formulation.

Time-dependent models with two space dimensions expand greatly the

applicability of numerical models for simulation of natural water bodies.

A time-dependent two-dimensional model (TQPLYR-II) for thermal transport 40

in the far field has been developed by Kolesar and Sonnichsen. The

model is based on the implicit finite difference form of the convection-

diffusion equation for energy transport with specified velocity field.

Buoyancy and stratification are not simulated, but bottom contour

effects and heat exchange with the atmosphere are included. Eddy

thermal diffusivities must be read in as constant values. The develop-

ers of this model intend to expand their program to include the motion

equations within a three-dimensional model. Eraslan has used his numerical method for a time-dependent

41 tvjo-dimensional model fox predicting temperature distribution only. The model is very flexible and general. It accepts the velocity field

41 as input data and can handle, by using the improved FLIDE method,

11

variable mesh sizes in different regions as well as nonrectangui-a.

elements at the boundaries. A time-dependent two-dimensional hydrody-

namic model for shallow vertically mixed water bodies has been developed

by Masch and his colleagues.42'43 The solution applies an explicit

finite difference method in a completely rectangular coordinate system.

A number of models for various aspects of thermal discharges, including 44

the near-field area, have been developed by Wada. These models are

steady state in one, two, or three space dimensions, using constant

empirical eddy diffusivities. A time-dependent two-dimensional water

quality model was developed by Leendertse and his associat3s43-^ for

shallow, vertically mixed estuaries and coastal regions. The numerical

solution is based on a time-centered implicit difference scheme for the

continuity and momentum equations and an alternating implicit-explicit

scheme for the quality equations. The model is quite general, but it

does not explicitly include thermal diffusion considerations. The

developers intend to extend the model for prediction of temperature

distribution.

None of the previously discussed models include local viscous

stresses in their formulation of the momentum equations, and the two

most applicable two-dimensional water quality models do not include

temperature prediction as a part of their objectives.

1.1.3. Intermediate Region

Very few studies exist on the so-called intermediate region. As

previously discussed, such a region has no independent identity other

than as a zone wherein the effects of the near and far fieids overlap.

Analysis of this zone without its two bounding regions, the near and far

fields, appears unrealistic. The near-field analysis by itself is almost

of no value for complete assessment unless combined somehow with the

effects of the far field.

1.2. A Complete Model

It appears that unless one is interested only in long-term distant

effects, a proper thermal assessment calls for a complete model in which

the effects of both the near and far fields are combined. Such an

approach must definitely rely on the basic physical laws that are appli-

cable for both regions. The basic conservation principles of mass,

momentum, and energy constitute the common starting point, and because

of the complex mathematical and physical features of these principles,

a numerical approach of some kind seems to be required for their ^

solution.

The numerical approach used for solution of such a composite model

should be flexible enough to handle the characteristic features of both

the near- and far-field regions, which are quite different. A large

number of small-size elements are needed for the near-field region to

permit incorporation of the small-scale turbulence effects and the large

spatial gradients that exist in this region. On the other hand, large-

size elements are adequate for the far-field region because of the

relatively large-scale characteristics of thermal plume behavior in this

region. Use of the same resolution in both the near and far fields will

result in either meaningless near-field analysis or an impossible load

13

on computer memory and time. Some solution of this problem was proposed

by Eraslan^ and successfully used in a time-dependent two-dimensional

thermal model for the far-field region, and his approach can probably be

used in a general thermal-hydraulic model also.

A major obstacle to the development of such a complete model is

related to the type of turbulent diffusion model to be used for the

near-field and the far-field regions. At this point it should be

emphasized that formulation of a proper turbulent diffusion model for

either region is one of the most outstanding and difficult problems of

fluid mechanics in general and of natural water bodies specifically.

The various coefficients generally used in the diffusion terms of the

conservation equations are no more than compensation factors for the

inability to consider the convective phenomenon in its proper detail

and the averaging technique used as a result of this inability. The

gradient law for molecular diffusion (Fourier law for heat, Fick's law

for mass) is generally an acceptable approximation of the microscale

movements of molecular particles. Although successful in many specific

applications, the gradient formulation of turbulent diffusion (Boussinesq

approach) does not seem to be a universally correct representation of

turbulent behavior. The gradient formulation of the so-called dispersion

is even less substantiated.

The term "dispersion" created much confusion in the literature.

Basically, dispersion is the term normally used to express the phenomenon

of nonconvective transport of material in the direction of the main

stream in addition to normal molecular and turbulent diffusion. The

14

main reasons for such dispersion are the shear effects caused by

variations of velocities in directions perpendicular to those of .the

main stream. The so-called dispersion phenomenon is a result of spatial

averaging of those convective profiles that have an effect on the trans-

port mechanism along the main stream because of the shearing effects

between layers. A more detailed discussion of these terms is presented

in Section 3. However, to put the problem in perspective, it must be

remembered that molecular diffusion is in the order of about 10"^ to _7

10 smaller than turbulent diffusion, which is about one to two orders

of magnitude smaller than longitudinal dispersion.

The contribution of velocity variations in the radial direction on

the longitudinal transport mechanism in a pipe was studied by r 7 (• i C C

Taylor * . His approach was later expanded by Elder for flow in an

open channel. Both studies showed that the longitudinal dispersion

coefficient is about two orders of magnitude greater than the turbulent

diffusion coefficient in either the radial or the longitudinal direction.

Elder^ assumed that the vertical velocity variations have a dominant

effect on longitudinal dispersion, and he therefore neglected the lateral 56 57 effects. However, Fischer * showed that in natural streams the

lateral effects may be far more important and that inclusion of these

effects in the analysis can increase the longitudinal dispersion

coefficient by an additional one or two orders of magnitude. Fischer's

relationship is in better agreement with field observations of natural

streams than the correlations presented by Elder or Taylor. In addition

to velocity gradients, the longitudinal dispersion coefficient in natural

15

streams is affected by density variations, wind, wave motions, and other

factors.

In the near-field region (jet models), the turbulent diffusion

coefficients are dominated primarily by jet dynamics. Here, the scale

of turbulence is much smaller, and the applicable models rely mainly on

an empirical entrainment coefficient, on the Boussinesq assumption of 58

constant eddy viscosity, or on one of the more sophisticated (but still

gradient type by nature) turbulent models like those proposed by

P r a n d t l , v o n Karman,*'* and others. Application of these models to

jets and plumes results in much better agreement with field data than

their application in far-field regions. However, these correlations for

free turbulence are based on axisymmetrical geometry in which the plume

width is one of the major characteristic lengths, whereas most turbulent

models for the far field rely on overall channel dimensions and average

flow characteristics. This difference of approach in the applicable

existing correlations for turbulent diffusion coefficients in the near-

and far-field regions is another obstacle to the integration of the

effects of the two regions into one composite model.

A third difficulty in combining the near- and far-field models into

one is the fact that buoyancy effects are of major importance in the

near-field region of thermal discharges. A two-dimensional model in

which complete vertical mixing is assumed cannot be applied to a region

wherein buoyancy is of major importance and therefore cannot be used to

predict properly the effects of the near field. Expansion of the model

to take account of three space dimensions would help solve this

limitation.

16

A three-dimensional model is also very desirable for overcoming some

of the difficulties encountered in finding an effective turbulent

diffusion coefficient. Since the increase in the longitudinal dispersion

coefficient in a two-dimensional model is a result of the spatial

averaging procedure, a proper time-dependent three-dimensional model

should not require a dispersion coefficient that is two to three orders

of magnitude larger than the true turbulent diffusion coefficient. The

only coefficients required would then be those for molecular and turbu-

lent diffusion. Although the correct value of turbulent diffusivity to

be used in such a model is not yet known, the importance of using an

exact value will be reduced significantly since the relative importance

of diffusion transport with respect to convective transport is much

smaller in a time-dependent three-dimensional model. Of course, such a

model must include the normal and shear stresses as part of the momen-

tum equations, and an advanced locally evaluated function for turbulent

behavior must also be included. There is much hope that some of the

new and more sophisticated approaches to turbulent models taken recently 6 2 - 6 6

by many investigators ~ can bs successfully used for that purpose.

General time-dependent three-dimensional numerical solutions are

presently being attempted. Of particular importance is the work being 67-73 done at the Los Alamos Scientific Laboratory. ~ . The various computer 67 methods resulting from this work include the PIC method, the MAC

method,68 the FLIC method,69 and the SMAC method.7^ The work done in 74 75 simulating atmospheric behavior by Smagorinsky and by Skl&rew should

also be noted. However, these general numerical methods require very

17

large computer storage capabilities. Their ratio cf computer time to

actual time is very large, and they are too general in format to be used

directly for the thermal discharge problem at hand.

A time-dependent three-dimensional model designed primarily for 2

thermal discharges is being developed by Brady and Geyer. They have

developed very interesting techniques to reduce computer storage require-

ments, and they have demonstrated the feasibility of using three-

dimensional models for natural water bodies even with the presently

available computers. Although the viscous normal stress effects are

included in their model, the viscous shear stress effects are not

included. Their work is still under development, and hopefully it will

inspire other investigators to further contributions along those lines.

The development and operation of such models will be very costly. How-

ever, this cost is exceeded greatly by that of the tremendous personal

effort being expended to find larger and larger "diffusion" coefficients

to compensate for the information destroyed in the basic conservation

equations when they are averaged out over time and spatial dimensions.

1.3. Interim Model

This study was undertaken to develop a time-dependent two-dimensional

3odel for predicting water elevations, horizontal velocities, temperatures,

and dissolved substance concentrations. The model can be used to assess

the effects of thermal or other discharges into vertically mixed shallow

water bodies. The inclusion of the normal and shear stresses in the

momentum equations advances the presently available models one step

18

further toward a complete model that wi*1 in:lude both the near- and

far-field regions. This model cannot yet be used as a reliable near-

field jet model because of its lack of buoyancy effects and the

difficulty of incorporating a turbulent diffusivity model that can be

used in all regions evaluated locally. However, the model does have

the potential for such extension in the future.

2. FORMULATION OF THE MASS, MOMENTUM, AND

ENERGY CONSERVATION PRINCIPLES

2.1. General Discussion of the

Physical Assumptions

The model studied here is time-dependent and is based on two space

dimensions. As such, it is primarily applicable to shallow, vertically

mixed water bodies. Many estuaries and coastal regions and some natural

streams fall in this category. A typical depth in many such water

bodies will be in the order of 10 to 100 ft, while their width will fall

in the order of 500 to 5000 ft. Such a ratio of about two orders of

magnitude between horizontal and vertical dimensions can in many cases

be reliably approximated by a two-dimensional analysis. Bottom rough-

ness, wind stresses, and tidal motion considerably enhance the vertical i mixing in such water bodies. Thermal discharges, however, tend to

stratify vertically, especially in the near-field area, where the dis-

charged water is normally about 10 to 30°F above the ambient water. For

this and other reasons which will be discussed in subsequent sections,

the model will not be applicable as a reliable near-field thermal jet

analysis. However, a short distance from the discharge point the jet

loses its initial momentum and much of its excess temperature. The

behavior of the thermal plume from that point will depend primarily on

the ambient hydraulic conditions, and the present model will be much

more applicable for its analysis. In some cases that generally satisfy

the two-dimensional assumptions but still possess some weak vertical

19

20

variations, appropriate vertical distribution functions can be employed 41

as proposed by Eraslan. The model is not applicable to deep lakes and

ponds, where stratification is of major importance. In many cases in

such water bodies the time dependence is not of major concern, and some

form of steady-state three-dimensional models might better be applied.

In the present model the discrete elements are based on a rectangular

coordinate system, and this creates some difficulties in describing com-

plicated physical boundaries. The present model, however, does allow

for variable element sizing along each direction, which gives some

flexibility in this respect compared with other available models using

constant mesh spacings. Other aspects of the applicability of the model

are further discussed in subsequent sections.

2.2. General Discussion of the Numerical

Method Employed

The numerical method used in this study is based on the physical

conservation principles, which are expressed and applied directly in

their integral form over a control volume. The modeled region is

divided into variable-sized discrete elements. The integrated conserva-

tion principles are strictly enforced and satisfied over each discrete

element, thus approximating the physical reality over each discrete

element. The requirement that the dimensions of the elements approach

zero is never employed, and no partial differential equations are ever

formulated. Such an approach keeps a closer touch with the physical

world and is very helpful in formulating complex boundary conditions.

21

which are, after all, what distinguishes between various physical

situations. This simulative approach was used in the Los Alamos work

(FLIC69 and PIC67 methods), is very much emphasized by Cheng;76*'7 and 41

has been wised by others to various extents. Kraslan has used the

approach in his FLIDE method for treating vertical variation in a two-

dimensional formulation and for greater flexibility in discrete element

sizing. Excellent discussions of these and other methods can be found 72 in the general text-type report by Harlow and Amsden and in the more 78 recent computational fluid mechanics text by Roach.

2.3. The Integral Form of the

Conservation Principles

As discussed in Section 2.2, the integral forms of the physical

conservation principles will be employed. These principles will be

formulated first in a general form, and then each integral will be

evaluated on a typical discrete element. The general forms of these

equations aTe as follows.

a. Conservation equation for total mass

| r * P dA (2.1) " ¥• A

b. Conservation equation for mass of constituent k

~ f P k d* « (-n) dA • i pk d* (2.2)

22

c. Momentum equation (second law of motion)

IT- # (p\T) dV- + $ (n) dA = f d¥- + $ o. dA V A * D A A

( 2 . 3 )

This equation, which is in vectorial form, can be separated into X and Y

directions as

Is- j (pU) & * i (pu)V»n dA » 6 f. Y dV- • 6 av dA , (2.3a) V- A » A *

(pV) dV- + £ (pV)tf-n dA • j> ffay dV- + f ay dA . (2.3b) A ^ A

d. Energy conservation equation (first law of thermodynamics)

4 (pe)dV- - i I * * k=l (-n) dA + f I ((5ke.) + q v k=l v

dV-

K + i + f I < v V ^ '

A k=l (2.4)

In all these equations the area unit vector n is outward positive.

In the mass conservation equation for constituent k, the velocity

of the constituent, can be expressed as

(2.5)

where is the relative velocity (or diffusion velocity) of substance k

with respect to the overall mass-average flow velocity of the fluid, V.

Therefore, one can write

23

" A a Pktf+ ^ - * " A .

where is the relative flux of constituent k within the flow of the

mixture. This flux can, in part, be assumed to obey Fick's law for

binary diffusion between a constituent k and the rest of the mixture.

However, Fick's law may not always be the proper representation of this

flux, especially in turbulent flow. At this point the term pj.v£ will

be expressed as gk, and its evaluation will be left to later discussion

(Section 3).

Substituting Eq. 2.6 into Eq. 2.2 and using gk = gives

£ pk dV- = $ • gk) • (-n) dA • jS pk dV , (2.7) A

where

*k = V k ft (2.8)

and £k is mass generation of constituent k per unit volume and unit

time. It must be remembered that the summation of the mass conservation

equation (Eq. 2.2 or 2.7) for constituent k over all the constituents

should result in the conservation equation for total mass (Eq. 2.1).

While doing this summation process, the definitions

ck = P k / P

and K I Ck * 1 k=l K

must be extensively used.

24

In the momentum equations the only body forces explicitly considered

are the Coriolis forces caused by the rotation of the earth. These

forces are important in large shallow water bodies and should be taken

into account. The gravitational forces, which are also body forces, do

not appear explicitly in the two-dimensional formulation of the momentum

conservation equations. However, they appear implicitly in the normal

stress terms of these equations, as will be discussed in subsequent

sections.

The last two integrals in the energy equation are the flow work

done by the body forces and the surface stresses, respectively. In a

two-dimensional formulation the gravitational body force will produce

no flow work, since no vertical velocity is considered. The flow work

produced by the Coriolis forces can be neglected. For the velocities

of interest, the flow work produced by the viscous stresses can also

be neglected. The only flow work that must still be considered is the

work done by the fluid against the pressure. Therefore, the last two

integrals in Eq. 2.5 can be replaced by

^ I, dV- = 0 (2.9)

and K K

(2.10)

Substituting Eqs. 2.9 and 2.10 into Eq. 2.5 and rearranging gives

25

^ <£ (pe) dV- = K

J i p k ( e k + + ? C-n) dA

i v>

I (5kek ^ qv k=l dV (2.11)

The specific energy e consists of internal energy u, kinetic energy 2

V /2, and potential energy gZ, where the last two can be neglected in

comparison with the internal energy u. The same is true for the specific

energy e^ of constituent k. Combining the pressure flow work with the

internal energy gives the enthalpy h. Therefore ek = uk • (2.12)

K K , r „ ~ r h, = e, + — s u, + — , k k pk k pk ' (2.13)

K K e = T C, e, = y C, u, = u .

kii k k k=i k k (2.14)

Substituting Eqs. 2.12 to 2.14 into Eq, 2.11 and using from Eqs. 2.6 and

2.8 that

p A * ^ + pk% = ^ + 2k (2.15)

gives

J- f (pe) dV = dt V- A V i c * + «k> + « •(-n) dA

pkhk + (2.16)

26

Substituting

-*• -V qk = gkhk ' (2.17)

K

and

I p. = phtf k=l K K

M v) k - Pkhk

into Eq. 2.16 and rearranging gives

(2.18)

(2.18a)

f (pe) dV. = £ + q + K 2

k»l (-n) dA

+ # + I C U k=l \rk dV- , (2.19)

where the symbol e for specific energy is used for internal energy u,

based on Eq. 2.14.

The term q appearing inside the brackets of the fluxes includes the

nonconvective heat fluxes. These fluxes cannot always be represented as

purely diffusion but can include other effects like turbulent fluctuations

or contributions from shear effects. The detailed discussion on this

term is given in Section 3.

In summary, the integral forms of the physical conservation

equations that will be used in this study for an Eulerian control volume,

incompressible fluid, and nonconstant physical properties are as follows.

27

a. Conservation equation for total mass

Ir £ P dV- = f g-(-n) dA (2.20) dt V- A

b. Conservation equation for mass of constituent k

~ £ (pCk) dV- = $ (Ckg + gk)-(-^) dA + $ pk dV- (2.21) A ¥•

c. Energy conservation equation

rrr $ (pe) dV- » $ (gh + q * I q. ) • (-n) dA dt ¥- A k=l K

+ t + Jl CVk) * (2'22)

d. Momentum equations

In the X direction,

lr j (pU) dV- + $ f(U)g] • (n) dA = $ (£ ) dV- + j ax dA (2.23) V- A 1 V- ° * A *

In the Y direction,

i* $ (pV) dV- + £ f(V)g] • (n) dA = £ (f)Y dV- + <£ oY dA . (2.24) d t V- A I ' V- C Y A *

these equations,

g = PV , (2.25)

28

qk = Ikhk , (2.26)

q v - (lkhk , (2.27)

C k = p k / p . ( 2 . 2 8 )

The nonconvective fluxes gk and q and the stresses ax and will

be discussed in detail in Section 3. Those fluxes and stresses, however,

will be left in a general form for the discrete element formulation of

the conservation equations developed in the rest of this section.

2.4. The Discrete Elements:

Definitions and Notation

The discrete elements are defined by a net of grid lines in a

rectangular coordinate system. The grid lines along the X and Y

directions are marked successively by i and j indices, respectively, to

indicate full points at the centers of the elements and by i ± 1/2 and

j ± 1/2, respectively, to indicate half-value points on the boundaries

between them. Figure 2.1 shows the way those indices are marked on an

XY plane for a single discrete element.

The center of each discrete element is marked by (i, j), and its

boundaries along the X and Y directions are marked by i ±1/2 and

j ± 1/2, respectively. The space increments along the X and Y directions

are AX^ and AY^, respectively. These increments may or may not be equal,

and their sizes along each direction may vary. Each element will then

have the horizontal dimensions AX. and AY., which are constant, and the

29

CSS!. KG 74-1145

(M/2,j j+1/2-

( i - 1 , j )

J* 1/2 y

0-1/2,j-!/2)

i+1/2

Figure 2.1. Arrangement of discrete elements.

30

depth H. which may vary with time. All the properties are considered J

uniform along the depth as well as along AX. and AY.. Based on these

concepts, solid boundaries are defined by half points, so that all the

elements, including those attached to boundaries, have full size. All

the properties for both the center points and the half points are marked

with the corresponding indices showing the exact location they refer to.

Special effort is being made in the numerical formulation to evaluate

all the properties and their fluxes in their appropriate locations. The

properties in each discrete element are considered uniform throughout

its volume and are represented by center-point values located at the

centroid of the element volume. The fluxes into and out of each dis-

crete element are evaluated at the common boundaries between the elements

in terms of the average values in the neighboring elements. The program

calculates and stores all the center-point values. The values on the

common boundaries, termed half-point values, are recalculated at each

time step but are not stored. All the quantities involved are shown

schematically in three cross-sectional views (Figure- 2.2 to 2.4). The

volume of each element can be expressed as AX^ AY.. H^ the horizontal

top and bottom boundary areas as AX^ AY^ and the four vertical boundary areas as AY. H. . AY. H. .. AX. H. . . and AX. H. . . (see

J 1-1/2,j' j 1+1/2,2 i i.j-1/2' i i,J+l/2 Figs. 2.2-2.4). Since average fluxes are being assumed for either the

volume of each element or the area of each of its boundary surfaces, the

integrals in Eqs. 2.18 to 2,22 can be directly evaluated for each element.

The area unit vector n is considered to be positive outward. The

discrete element formulation of the conservation equations which were

given by Eqs. 2.18 to 2.22 will be derived in the following sections.

31

EVALUATED AT (i.j+i/2)

9y <*y Qky

ORNl OK 74-lue

(trxyVt/2,j H,U,V,I,Ck

fyMvk "Bx'^y ,0Tx' °Ty

EVALUATION AT (i,j)

9y S t y O y y Qy A t y

EVALUATED AT (i,y-«/2)

Figure 2.2. Top view presentation of properties and fluxes in a discrete element.

32

V i ATMOSPHERE ORNL O K 7 4 - 1 1 4 0

TOP SURFACE S L

j-1/2

Figure 2.3. X-Z cross-sectional presentation of fluxes in a discrete clement.

33

Figure 2.4. Y-Z cross-sectional presentation of fluxes in a discrete element.

34


Conservation Equation for Total Mass

The integral form of the conservation equation for total mass was

given in Eq. 2.20 as

~ f p dV- = j> g-(-n) dA . (2.29) d Z V- A

Considering the discrete element with constant horizontal dimensions

AX. and AY. (see Figs. 2.2 to 2.4), time-dependent depth H. ., and uniform 1 3 1 > J

density throughout the volume, the term on the left of Eq. 2.29 becomes

l ^ p d*=AX. AY. §- (P^H.^.) . (2.30)

The term on the right of Eq. 2.29 is a surface integral around the six

faces of the discrete element over the instantaneous mass flux g. The

unit area vector n being positive outward, one gets for this surface

integral (see Figs. 2.2-2.4)

"i-l/2,j "i+l/2,j i I (-n) dA . AY. / (gx)._1/2). dZ - AY. / C«x)i+1/2.j dZ

jj-1/2 "i,j+l/2 + AXi I î.j-1,2 ^ " / CSY>i,j+l/2 d Z

+ AXi + AX. AY. (gT)i)j , (2.31)

35

where is the mass flow rate coming from the bottom (seepage) per unit -2 -1 area (ML T ) and g^ is the mass flow zate coming from the top (precipi-

-2 - 1 tation, evaporation) per unit area (ML T ).

The instantaneous fluxes g^ and gy are defined as

gx = pU (2.32)

and

gy = pV , (2.33)

where U and V are the two instantaneous horizontal velocities in the X

and Y directions, respectively. These velocities are normally functions

of the depth Z, and,.in the case of turbulent flow, they also reflect

the random turbulent fluctuations. Each velocity can then be expressed

in three parts as

U. .(Z, t) = U .(t) + u. .(Z, t) - ur (Z, t) (2.34)

and the same for V or any other property P.

The part due to turbulent fluctuations, u' .(Z, t), vanishes when 1 > J time is averaged over a time scale larger than the turbulent fluctuations

(but smaller than the time scale of interest, in order to keep U^ ^(t)

time dependent). The vertical variation, u. .(Z, t), vanishes by 1»J definition when integrated over the depth. Therefore, the integrated

fluxes in Eq. 2.31 can be replaced by their depth-averaged counterparts

to give

36

i g.(-n) dA= AY. Cgx)i_i/2,jHi-i/2,j " ^Pi+l/ZJ^l/Z.j n

+ AX. C g y ) ^ . ^ ^ - ax. CiY)i,j+i/2Hi,j*l/2

+ AX. AY. CgB)i>;j + AX. AYj CgT)i>;j (2.35)

where the bar denotes average values over depth and turbulent time scale.

Substituting Eqs. 2.30 and 2.35 into Eq. 2.29 and dividing by AX. AY^

gives

3 i f , - - ] a t ^ i . A j ) = - s r iHi+l/2,jCgx)i+l/2,j • Hi-l/2,j(gX)i-l/2jJ

AY. l Hi,j+l/2(gY)iJj+l/2 " " i j - l ^ ^ i j - l ^ ,

+ + C&rîj (2.36)

Differentiating H^ ^p^ ^ gives

Substituting Eq. 2.37 into Eq. 2.36 and dividing by . gives

3H. . . _ _1 at p . .

-H. . (3p. ,/3t) J-ij X»J

" AX7 (Hi+l/2,jCSx)i+l/2,j " Hi-l/2,j(gX:ii-l/2,j]

37

" W T ( " i j + l ^ ^ i j - l ^ ' HiJ-l/2CgY)i,j-l/2j J

* &B>i,j + ter'ij (2.38)

which is the discrete element formulation of the total mass conservation

equation for variable water elevation H. Since the density is a function

of temperature and substance mass concentrations, one gets:

3p . . K - 5 7 ^ = ( 3 P / 3 T ) . . ( S T . . / a t ) + I c a p / a c . ) . . ( a c . . . / s t ) . ( 2 . 3 9 )

3p/3T and dp/dC^ are derivatives which can be evaluated once the equation

of state is known (see Section 4.6). ST. ./3t and 3C. . t are i»J * J- »j evaluated from the energy conservation equation and constituent mass con-

servation equation, respectively, both of which are numerically evaluated

before Eq. 2.38 is used. Equation 2.38 expresses explicitly the

instantaneous rate of change of water surface elevation with respect to

time and can be used with a proper integration routine to evaluate the

instantaneous water surface elevation itself. The rate of change of H

with respect to time actually gives the vertical velocity of the water

surface at any point, and, therefore,

( W - ) . . = 3H. . / 9 t . ( 2 . 4 0 ) 3 i»j J

The convective fluxes g"x and g"y are defined as pU and pV by Eqs. 2.32

and 2.33, and the bottom and top contributions gg and gT will be dis-

cussed in Section 4.

38

2.6. The Discrete Element Formulation of the Mess

Conservation Equation for Constituent k

The integral form of the mass conservation equation for constituent

k was given by Eq. 2.21 as

Using the same approach as for the total mass conservation equation,

the left-hand side of Eq. 2.41 for the discrete element formulation

becomes

and the last term on the right of Eq. 2.41 becomes

The first term on the right of Eq. 2.41 is the surface integral around

the six faces of the discrete element over the instantaneous mass fluxes

of constituent k. Using again the discrete element notation and the

schematic presentation of the fluxes in Figs. 2.2 to 2.4, pages 31 to 33,

one gets:

j CpCjP dY- = j, ((^g + gk)- c-i) dA + 9 pk dV- . (2.41)

(2.43)

H 'i-1/2, j # CgCk + g.) • (-n) dA = AY. J A K K 3 0

t(gX}i-1/2,jCCk}i-l/2,j CC,,) + CSkX}i-l/2,j JdZ

î+1/2,j - AYj I t(gx)i+1/2>jCck)i+1/2>j * Cgkx)i+1/2J]dZ

39

* *Xi I £(SY>iJ-l/2(Ck>iJ-l/2 + ^ i . j - l ^ 2

"i,j+l/2 - f ECg Y) i > j + 1 / 2CC k) i J + 1 / 2 «• CgkY)i>j+1/23dz

- AY j[(g r) i j j(C k T) i• C g k T ) M ] . (2.44)

where g^g is the nonconvective mass flow rate of constituent k coming -2 -1 from the bottom per unit area (ML T ) and g^T is the nonconvective mass

-2 -1

flow rate of constituent k coming from the top per unit area (ML T ).

As in the case of the total mass, each property may be a function of

the depth Z and of turbulent fluctuations; i.e., P. (Z, t) = P .(t) + p. . (Z, t) + pr .(Z, t) , (2.45)

where P designates any property (U, V, C^, T). Substituting Eq. 2.45

into Eq. 2.44 and then averaging with respect to the turbulent time

scale does not result in complete vanishing of the turbulent fluctuations,

pr .(Z, t). Nor does the vertical variation part, p. .(Z, t), vanish

when integrated over the depth. The reason for these nonvanishing terms

is that the average of a product does not equal the product of the

averages. This problem brings up the subject of the contributions of

turbulent and longitudinal dispersion (shear effects) to the overall

dispersion phenomenon. This subject will be discussed in detail in

40

Section 3. For the time being, the fluxes in each direction will be

separated into two parts. One part, which is purely convective, includes

only the averages over depth and time (over the turbulent time scale

only). The second part, which will be termed the nonconvective flux,

includes the contributions of both turbulence fluctuation and vertical

variations. This last part will be combined with the relative flux of

constituent k, designated in Eq. 2.8 as g^; that is, in general,

/ Âck + d z - Clft • ikA>H ' C2-46)

where the subscript A means flux over area, the bar means average over

depth and turbulent time scale, and g"^ represents the nonconvective mass

flux, which will be discussed in Section 3.

Using Eq. 2.46 for all the half points in Eq. 2.44 gives

* (gCk • g k W - n ) dA = AY.[(ix)i.1/2>jCCk)i.l/2,j + <%X>i-l/2.j]Hi-l/2J

" A Y j I ^ i + 1 / 2 J ( ^ ) i + 1 / 2 f j - Cskx)i+1/2jiHi+i/2,j

+ A X i I<«Y>iJ-l / 2 f l k > i . j - l / 2 + CSkY>i,j- l /2JHi,M/2

- AX 1Cti y) 1 J + 1 / 2(^) l f j + 1 / 2 + CgkY3i,j+l/2iHi,j+l/2

+ ax. AYJt(gB)i^cckB3i#J + ( g ^ . ^ l

+ AXk ^ j t ^ i j C V i j * C S k A j ] •

41

Substituting Eqs. 2.42, 2.43, and 2.47 into Eq. 2.41 and dividing by

AX._ AYj gives

It Ipi.JCCk)iJHi.j3 = " A3T Hi+l/2,j tCgX)i+l/2,j

+ (gkX)i-l/2,j] 1

AY. Hi,j+1/2 K ^ i J + l y ^ V i J + l ^

+ j+1/2^ " Hi,j-l/2 t(gY)i,j-l/2(Ck)i,j-l/2 + CgkY>ifj-l/2]

+ (gB>i,j((Wi,j + (gkB>i,j + ^ i . j f V i J + (gkT>i,j

* »k)if3Hi.5 ( 2' 4 8 )

Differentiating p. .H. A(C.). . gives

a 3(ckî i a It fpiJHi,j ( V i j J = ' i . P t . i - T T * ' ( V i j a t ^ i ^ i j )

(2.49) Substituting Eq. 2.36 for (3/8t)(p. .H. .) into Eq. 2.49 and then the

result into Eq. 2.48 gives, after rearranging terms,

X ac. at p. .h. .

1 S T Hi+l/2,j [CgX3i+l/2,j t V i + l / 2 J " K V i J

Y

+ CgkX3i+l72,ji - Hi-l/2,3 tCgX>i-l/2,j (((Vi-l/2,j " <Ck>i,j)

42

+

- cî>jj

'i-l/2,j]| " "TT |Hi,j+l/2 [CgY)i>j+l/2 (CCk>i,j+l/2

+ j+1/2^ " Hi,j-l/2 tCgY)i,j-l/2 [CCk)i,j-l/2

+ C8kB}i,j]

((ckT>i,j " C V i J + (gki>iji

+ (p.). .H. . (2.50)

which is the discrete element formulation of the mass conservation

equation for constituent k. The additional nonconvective mass fluxes

of constituent k, q ^ and qkY, will be discussed in Section 3.5, and the

bottom and top fluxes, gkB and g^T, in Section 4.6.


Energy Conservation Equation

The integral form of the energy conservation equation was given by

Eq. 2.22 as

K K fe i (pe) d* = $ (gh + q + I qk) • (-n) dA + $ + £ fty^] •

k=l k=l (2.51)

43

As in the case of total mass and mass of constituent k, the volume

integrals can be evaluated as

It I CP®) • AXi AYj > <2-52>

and, assuming uniform heat and mass generation rates per unit volume

throughout the discrete element i,j,

K K $ [Cqv) + I W V ) J dV-= AX. AY. + J 0 U J H i . , (2.53) ¥• k=l 1 J v k = 1 V K 1,J

where (qy)k was defined as P^h^ by Eq. 2.27.

The fi^st term on the right of Eq. 2.51 is the surface integral

around the six faces of the discrete element over the instantaneous

energy fluxes. Using again the discrete element notation and the

schematic presentation of the fluxes in Figs. 2.2-2.4, pages 31-33, one

gets:

^ K 4 (gh + q + I q. ) • (-n) dA • A k=l K

"i-1/2,j K AYj I i/2,jhi-i/2,j+ fcxW,:)i-1/2,j]dz

- AY. / Hi+l/2,j

3 0 H. .

tCSx)i+l/2,jhi+l/2,j + î+1/2,3 + J1CqkX)i+l/2,j3dZ

i.j-1/2 + *Xi / Cî,j-l / 2 hiJ-l / 2 + (Vi,j-l/2 + i,j-l/2]dZ

44

" AXj I ^ i , M / 2 h i , j + l / 2 + CVi, j +l/2 + k y ^ i J + l / 2 l d Z

+ A X i AY. [(gBDi#j BîJ + + J / W i j J

+ AX. AY. [ C g ^ O ^ * C V i J + j / ^ i j J C2.54)

As before, each property may be a function of depth 2 and of turbulent

fluctuations, as given by Eq. 2.45.

Substituting Eq. 2.45 into Eq. 2.54 and then averaging with respect

to time does not result in complete vanishing of the turbulent fluctuations

p^ .(Z, t). Nor do the contributions of the vertical variations, J

p. .(Z, t), vanish when integrated over the depth. The problem is the J

same as in the case of mass fluxes of constituent k except that here

there are the additional terms

? -k=l K

However, qk was defined by Eq. 2.26 as

= «khk '

and g^ was already discussed in Section 2.6. Then, using the same

approach as before, the total integration heat flux will be expressed in

three parts as

45

H K K / [gA)h + q A + I Cq^)] dZ = [g^ + q A + I C q ^ H . (2.55) 0 k=l k=X

where the subscript A means flux over area, the bar means average over

depth and turbulent time scale, and qA represents the nonconvective heat

flux, whivi may result from the contribution of molecular diffusion,

turbulent diffusion, and shear flow to the total dispersion phenomenon.

The evaluation of cfA will be more fully discussed in Section 3.

Evaluating Eq. 2.55 for all the half points in Eq. 2.54 gives

K -$ (gh + q + I qv) ' C-n) dA A k=l K

AYj [^1-1/2,^1-1/2,j + &X>i-l/2,j + 1Zlî-l/2,j3Hi-l/2.j

_ _ K _ - AYj t C g x ) i + 1 / 2 j X + 1 / 2 J + (q x) i + 1 / 2 J + kHWi +l/2,j3 Hi +l/2,j

_ _ K _ + A Xi + <Vi,j-l/2 +.Jl^kYJi,j-l/23Hi,j-l/2

_ _ K _ " AXi [fSYî,j+l/2Fi,j+l/2 + (Vi,j+l/2 + J/lkA,>1/2^1,j +l/2

K + AXi AYj K ^ i j f V i j + ( V i , j + J ^ W i j j

* AX, AYj [ ( g ^ . ^ ) . . . + (q,)^. + U % T ) i t j ] C2.56)

46

Substituting Eqs. 2.52, 2.53, and 2.56 into Eq. 2.51 and dividing by

AX^ AY^ gives

3t (pi,jei,jHi,j3 =

AX. l Hi+l/2,j tCgx)1+1/2,/i.i/z.j * î +l/2,j + J / ^ i + l ^ j 1

IV

Hi-l/2,j £<8x^-1/2,^-1/2,j + î-l/2,j + J 1C W i - l / 2 , j ^

AY. J Hi,j+l/2 [(SY3i,j+l/2hi,j+l/2 + CVi,j +l/2 + J ^ k X ^ . j + l ^

rw - Hi,j-i/2 Uhh.j-i/ih.j-i/i + (Vi,j-i/2 + J / W i j - i / 2 1

K + ^ i . j ^ V i J + + J ^ W i . j + + <Vi,j

K NK C2.57)

Differentiating p. .e. .H. . gives 1 »J 1 > J 1 a J

• °i,5Hi,3 W l > * e i J W j « l . j 3 • C2.58)

However, the internal energy e is a function of both the temperature and

the concentrations of the constituents, and its time derivative can be

evaluated by

47

W ^ . J 5 Be fdT. . K

* I k=l '3e '

3T i»J 3t k i

K * I k=l K J i.3 3 t

de 3T

3T. . K . X ( ek }ij i,j k=l *J 3t

3T\ . K i i r 3CCk3i • (2.59)

where use has been made of Eq. 2.14 (e ; u) and the thermodynamic

definition of the specific heat at constant volume.

Substituting Eq. 2.59 into Eq. 2.58, one gets

-(p. ,e. ,H. ,) = p. ,H, . (C.,). . 3T. .

3tv i,j i,j i,r i,j V'i.j 3t

K * cijHi.j J i ^ i>J 3t * ei,j Itî.î.J^ 2- 6 0)

Substituting Eq. 2.36 into Eq. 2.60 for eliminating (3/3t)(p. .H. .) and 1»J 1 ,J then substituting the result into Eq. 2.57 and rearranging terms gives

\ 3T. . 3t p. . (C,.). .H. . i»J V-'i.j 1,3

K -p. .H. . Y (ej. . 3t

1 X. Hi +l / 2,j [ ( g x W 2,j ( Fi+l / 2,j " ei,jD + ^ ^ 1 / 2 , j

+ J ^ ^ i + 1 / 2 , 3 1 " "i-1/2,j C(gX3i-l/2,j " i.j) + î-1/2,;

48

K _ 1 1 f - -+ J i ^ i - l / Z . j 3 ] " ATT [HiJ+l/2 j*l/2®i.M/2 • ®i J

K _ _ + CVi.j+l/2 + J ^ k A j + l ^ " HiJ-l/2 fî,3-1/2^1,3-1/2 -

K _ -j + (Vi,j-l/2 + J ^ i j - I / ^ J

+ [C*B>i,j

. * I V l J

^ i . j " eiJ

• f c V i i + I v l»J k=l \rk

+ ( q B ) i'j + J i ^ i J 1

K + C V i J * J x ^ i j j

/ J H. . (2,61)

The convective energy fluxes q^, qkB, and q^T are all evaluated on

the basis of the corresponding mass fluxes; i.e..

% = 8khk '

(qk)B - Cgk)BChk)B '

(qk)T - Cgk)T(hk)T .

(2.62)

(2.63)

(2.64)

The additional nonconvective heat fluxes q"x and qY will be discussed

in Section 3.4, and the bottom and top fluxes qfi and qT in Section 4.4.

The use of qv for the case of thermal discharge from a power plant will

be discussed in Section 7.1.

49

2.8. The Discrete Element Formulation

of the Momentum Equation

The integral forms of the momentum equations in the X and Y

directions are given by Eqs. 2.23 and 2.24, respectively, as:

!=• $ (pi?) dV- + j [(U)g]-(n) dA = i ( f L ( » + i e x dA , (2.65) 9t V- A V- c A A *

j (pV) dV- + $ [CV)g]-(n) dA = $ (f )Y d* * $ a dA . (2.66) « y, A v c 1 A Y

Referring to Fig. 2.2, page 31, it can be seen that, unlike other

vectorial surface fluxes, the stresses consist of normal stresses

°yy acting normal to a surface and shear stresses a^, aYX acting

parallel to the surface. The normal stresses are considered positive

when trying to stretch the element (tension), and the shear stresses

are considered positive when creating a positive angle of deformation.

Figures 2.2 to 2.4, pages 31 to 33, show all the stresses in their

positive direction. When evaluating the various components of the

integrals in Eqs. 2.65 and 2.66, one must suppose that the forces con-

tribute to the acceleration of the discrete element as a rigid unit

according to the second law of Newton and must keep in mind that force

and acceleration are considered positive when directed toward the

positive directions of the system coordinates.

As before, assuming uniform density (p) and Coriolis force per unit

volume (f ) within the volume of each discrete element, the volume

50

integrals of Eq. 2.65 can be evaluated for the discrete element

formulation as:

It I W ** - AX. AYj fcp^ftj (2^67)

and

The second term on the left of Eq. 2.65 is the surface integral

around the six faces of each discrete element over the instantaneous

momentum fluxes. Using the discrete element notation and the schematic

presentation of the fluxes in Figs. 2.2 to 2.4, pages 31 to 33, gives:

4 (U)l-Ci) dA= AY. rl/2'\feX3i.i/2.jUI-l/2.j3dZ

"i+l/2,j " *Y;j / [î +l/2. 3

Ui +l/2J ] d Z

"i.j-1/2

Hi,j+l/2 AXi / tî J +l/2 UiJ +l/2l d 2

• AX. AY.fgg)^.^).^ • AX. A Y . ^ . C U ^ . . £2.69)

51

The same is correct for the stress term on the right of Eq. 2.66; i.e.,

"i-l/2,j î+1/2,j £ ax dA = AY. / < - « x X > i - l / 2 . j d Z + AYj I Ca*xk+l/2,5 d Z

"i,j-l/2 "iJ+1/2 + AXi / (-°YX>i,j-l/2 d Z + AXi I <ffYX>i.j+l/2 d Z

+ AXi C ^ i J + AXi «>Txh,j ' C2-7°>

As explained before, the velocities may be a function of the depth

Z and also may include the turbulent fluctuations, as expressed by Eq.

2.45. Substituting Eq. 2.45 into Eqs. 2.69 and 2.70 results in non-

vanishing terms for those variations. As was done before, those

additional terms will be combined with the stress terms. In general,

then, a combined term will appear for these fluxes such that

H H - / [CgA)U] dZ * / (ax)A dZ = (gAU + a^H , (2.71)

where the subscript A means fluxes or stress over area, the bar means

value averaged over depth and turbulent time scale, &nd o^ represents

the combined effect of molecular stresses, turbulent stresses, and shear

effects because of velocity variations with depth. The evaluation of

o^, including the hydrostatic pressure effects involved, will be more

fully discussed in Section 3. Evaluating Eq. 2.71 for all the half

points in Eqs. 2.69 and 2.70 combined gives:

52

I Ug-W dA • $ ox dA = AY. [CgxJi.i/ajU..^^ - C«XX)i-i/2jJHi-l/2.j A

" AYj I 1+1/2.^1/2, j " (7XXJi+l/2,j3Hi+1/2jj

+ AXi ^Yh,3-1/2^1 ti-U2 - î,3-1/2^,j-1/2

- AX. [C8Y)ifj+1/2triJ+1/2 - (?YX)i.j-l/23l*l,j*l/2

• AX. AY. I t i t f ^ V J u •

• AX. AY. [ ( g ^ W ^ - • C2.72)

Substituting Eqs. 2.67, 2.68, and 2.72 into Eq. 2.65 and dividing by AX^ AYj gives:

It fri.j^.A.J3 = ' AT- Hi+l/2,j C(gX)i+l/2,jUi+l/2,j " (crXX)i+l/2,j]

1 AY. 3

Hi,j+l/2 ^YîJ+lî.j+l^ ~ ^YXîJ+l/21

• Hi,j-l/2 tCgY)i,j-l/2Ui,j-l/2 " ^YX^J-1/21

+ (f v). . H. . cX i > J 1,3 (2.73)

53

Differentiating (pHU). . gives: 1»J

Substituting Eq. 2.36 for (3/3t)(p. .H. .) into Eq. 2.74, then substituting the result into Eq. 2.73 and rearranging terms gives:

\

Hi+l/2,j t i+1/2,j C"i+l/2,"i,j3"^XX3i+1/2,j au. . .

= 1 at p. .h . . i.J 1.3 AX. i

" "i-1/2,j ffSx}i-l/2J«Ui-l/2,j " UiJ> " C*XX>i-l/2,j}

1 AY. Hi,j+l/2 [(SY}i,j+l/2Ciri,j+l/2 ~ Ui,j3 • (oYX3i,j+l/23

* t ( 8 B ) i J ( ( U B 5 i J - U . J ) . ( a B X ) i J ] + [ ( g T ) . J ( ( U ^ i ^ - T T ^ . ) + ( a T X ) .

•»• (f v). . H. . v cX'i,j 1,3 (2.75)

In a similar way the momentum equation in the Y direction, given in its integral form by Eq. 2.6£_ .;an be formulated for a discrete element to give:

\ 3V. . . -i±2.= 1 at p.^H. . 1.3 i»3 AX. i

54

' Hi-l/2,j[CgX3i-l/2,j(Vi-l/2,j ' Vi,j) " ^ i - l / Z . j 3

1 AY. J

HiJj+l/2[CgY)iJj+l/2(ViJj+l/2 " ' (0YY}i,j+l/23

" Hi,j-l/2tteY}i,3-1/2^1,j-1/2 " Vi,P " C a Y Y 3 i , M / 2 ]

• (f v). . H. . v cY i,j x,j (2.76)

The stresses o"yy» and °XY* include molecular stress,

turbulent stresses, and shear stresses because of velocity variations

with depth, will be discussed in Section 3. The Coriolis force per unit

volume, f , will be discussed in Section 4. c

2.9. The Half-Point Values on Discrete

Element Surfaces and Corners

In Section 2.4 the discrete element notation and representation

were discussed. However, as is seen from the discrete element formula-

tion of the conservation equations, all the fluxes and many of the

properties must be evaluated on the boundary faces between neighboring

55

discrete elements. The properties for each discrete element are

considered uniform along AX, and along AY^ and are represented at a point

(i, j) located at the center of each element. The properties on the

faces, located at half-point values, must be calculated by using some

extrapolation procedure. The first-order Taylor expansion approximation

is used in this study for that purpose; i.e., for any point, one can

write:

P(X + AX, Y + AY) = P(X, Y) + AX Y ) + AY Y ) . (2.77)

On the basis of Eq. 2.77, one gets the numerical approximation for

half-point values as

W . J * Pi.j + A Xi I X ^ / A X ^ ' <2-78>

After rearranging terms, Eq. 2.78, applied for the four faces of each

discrete element at th i -nters, gives (see Fig. 2.1, page 29):

AX. AX i + 1 Pi+l/2,j = AX. • AX.,]

Pi+1 , j + /J, ! A X . ~ Pi,j ' ( 2' 7 9 )

AX, i, | Pi-l/2,j = ""M. ' 1 - i , I AX,_7'J AKf ''i.l ' ( 2' 8 0 )

Pi,j+l/2 = W p T r f + A lii,j(] * A Y ^ r W ^ P i J '

56

'i,j-1/2 AY.^ + AY. Pi,j-1 + + AYj Pi,j ' C 2' 8 2 )

For the four corner points on each element, Eq. 2.77 gives:

P = P +AX Pi+14+l/2 " Pi>j+l/2 i+1/2,j+1/2 i , j i Aiii+1 + aJL

+ A Y . ! ™ i ± ( 2 . 8 3 )

p = P - AX Pi.3^1/2 " Pi-l,j+l/2 i-1/2,j+1/2 i, j i AXa + AXi_1

+ AY Pi-l/2.3+l " Pi-l/2,j ,2 8 4, A Y j A Y ^ j H- AY. ' C 2 - 8 4 ^

p = P + AX " P i J - V 2 i+1/2,j-1/2 ri,j AX i + 1 + AXi

AY i+1/2,3 i+1/2 j AY. + AY. , J 3 3-1

P = p - AX P i J - V 2 " Pi-1,3-1/2 i-1/2,j-1/2 *i,j a Ai AXi + AYi_1

. ^ Pi-l/2,3 " Pi-l/2.j-l j AY. + AY. , J 3 3-1

(2.85)

(2.86)

57

As an alternative to the above Taylor expansion for the average values

used in evaluating the fluxes on the discrete element faces, one can

define those values on the basis of physical arguments. One such method,

called the "donor cell" method, which is said to have good numerical

stabilizing effects, will be discussed in Section 6.3.

3. FORMULATION OF DIFFUSIVE AND OTHER

NONCONVECTIVE INTERNAL FLUXES

In Section 2 the discrete element fo:.*mulation of the conservation

equations has been developed. It was discussed there that since the

model is two dimensional, the effects of vertical variations cannot be

included directly in the model. However, in reality the vertical

variations of the various properties may have considerable effects on

the horizontal behavior of those properties. In addition, the random

fluctuations existing in turbulent flows were not explicitly formulated.

Instead, each flux was divided into two parts. The first part is

purely convective in nature and reflects the depth- and time-average

values of the corresponding fluxes (average over turbulent time scale

only). The second part, which is termed the nonconvective flux, includes

diffusive fluxes as well as the contributions of turbulent fluctuations

and vertical variations. The purely convective part was already properly

included in the discrete element equations developed in Section 2. The

nonconvective fluxes were left as general expressions. These fluxes

will be discussed in this section, first in a general form for all the

properties and then specifically for mass, momentum, and energy fluxes.

3.1. The Gradient Law of Diffusion, Turbulent

Diffusion, and Dispersion

The transport mechanism in turbulent flow and specifically in the

flow of natural streams is a very complicated phenomenon. As a result,

S8

59

there is a tendency among investigators in this field to apply simplified

and "easty-to-use" transport formulations in which all the transport

phenomena are lumped into a single term in the conservation equation,

using the gradient law of diffusion for that purpose. This law can be,

in general, expressed as

P A = - D vtpP) , C3.1)

where D is an overall effective coefficient that includes all

nonconvective effects.

An extreme example of such a case can be seen in the practice of

using a one-dimensional steady-state convection diffusion equation with

a huge

cons Lint "dispersion coefficient" to predict the transport

process in estuaries, i.e., 2

tfp S " D + K P = 0 •

where Up is the time-averagr r.ontidal fresh water flow velocity downstream

toward the ocean. Such an equation is the result of averaging over two-

space dimensions and time. The value of Tfp is a time average of the

instantaneous tidal velocity, which may be, at its peak, about 50 times

as large as Up itself. This means that the tidal movements, which are

the most powerful ones in estuaries, are not properly expressed in Eq. 3.2.

Instead, the diffusion-dispersion coefficient D is supposed to compen-

sate for those effects. However, experience with such an attempt shows

that there is no way to find a reliable value for such a coefficient

60

except, maybe, by field measurement for a specific location in a specific

water body and under a very specific set of conditions. Finding a

correct value for D in Eq. 3.2 almost means solving the whole problem.

Trying to separate the various effects included in such an overall

v efficient creates some difficulties because it is apparent that not

all those effects can be reliably expressed by the gradient law (Eq. 3.1).

Such a gradient law was proved to be very successful for expressing

molecular diffusion (Fourier law for heat and Fick's law for mass dif-

fusion). In a one-dimensional case and for a general property P, such a

law can be expressed as

P A = " °p r 1 • C 3- 3 )

2 -1

where dp expresses the molecular diffusivity (L T ) of a property P

and (PA)X is the flux in the X direction.

When convection and diffusion are combined, the flux of the

property can be expressed as

(?A)X = U(6P) (- otp I M l ] , (3.4)

where U is the velocity of the fluid in the X direction.

However, U represents the velocity when the fluid is considered to

be a continuum. The actual movements of the individual molecules are

in no way described in Eqs. 3.3 and 3.4. Looking at the problem from

this point of lew, one realizes that the diffusion terms in Eqs. 3.3

and 3.4 are time-average expressions for the molecular random motions.

61

In turbulent flow a similar phenomenon of random motions exists

except that in this case there are random motions of lumps of fluid

rather than molecules. The time and space scales involved in turbulent

fluctuations are much larger than those in molecular motions. Neverthe-

less, these motions are very complex for complete detection and

description. If one expresses the instantaneous velocities and proper-

ties as a superposition of a mean time-averaged value (indicated by a

bar) and an instantaneous random fluctuating value (indicated by a prime),

one gets

U = U + u' , (3.5)

P = P + p" .

Assuming that Eq. 3.4 is correct for turbulent flow as well as for

laminar flow if instantaneous values are used, one can substitute Eq.

3.5 into Eq. 3.4. If the interest is not focused on the fluctuating

terms themselves but rather on their overall effects on the mean flow,

one can time-average the equations over the appropriate scale (smaller

than the scale of interest but larger than the turbulent time scale) to

get

(PA)X • UCP) + (- o p §|) + SPp*" • (3.6)

The term u'p' is the only term left from the turbulent fluctuations,

because based on the Reynolds averaging principles, all the other terms

vanish on a time-average basis. Since in most cases the values of the

62

fluctuating quantities uf and pf are not known, great effort has been

made in the past 50 years to find a correlation that will relate the 58

turbulent effects to the mean flow parameters. Boussinesq has pro-

posed that the effective transport associated with the turbulent fluctua-

tion follows a gradient-type law and has represented the transport due

to random turbulent fluctuations as

u-p- - - E p , (3.7)

where ep is a constant termed the eddy viscosity (other names like

virtual, apparent, or turbulent viscosity are also used interchangeably

in the literature).

Substituting Eq. 3.7 into Eq. 3.6 gives

(PA)X = U(P) + - <°P+ ep> if) • v-v

Unfortunately, a relationship like the one given above, although

successful in some cases, is not universally correct for all turbulent

flow situations.

Other attempts to improve the relationship proposed by Boussinesq

were made by developing nonconstant formulations for the eddy viscosity

Without going into the details of those correlations, a number

of them will be mentioned here (see Refs. 79 and 80 for further

discussions).

Prandtl mixing length theory (Ref. 59) defines the eddy viscosity

as

e - ** , (3.9)

63

where A is a characteristic length, U is the velocity along the main

flow, and Y is perpendicular to the flow. The mixing length is inter-

preted as that length which fluid particles travel in the turbulent

mixing process before losing their identity. This is not an easy

parameter to evaluate and is definitely not universally constant. How-

ever, Prandtl's mixing length theory was successfully used in many

practical problems and is still considered one of the most helpful

correlations.

Taylor's vorticity transfer theory (Ref„ 81) states that

1 t 2 dU 37 (3.10)

where is also a characteristic mixing length but is larger than

Prandtl's mixing length i by a factor of /?. Taylor's vorticity transfer

theory finds its application mainly to problems of free turbulence and

does not agree well with experiments for turbulence along a solid surface.

Vop Karman's similarity hypothesis (Ref. 61) results in

. . x : . ( 3 .11 , cru/ry r

where x is an empirical dimensionless coefficient that must be determined

from experiments. Equation 3.11 is more general than Prandtl's mixing

length expression and has been especially useful in heat transfer

calculations.

64

Prandtl's new hypothesis for free turbulence (Ref. 60) lerds to the

defect law

where b is the width of the mixing zone and x^ again a dimensionless

coefficient that must be determined experimentally. The defect law is

actually a spccial application of Prandtl's mixing length theory. It

is a simpler relationship but is also more limited. It is primarily

used in free turbulence (jets and wakes) and has the advantage of not

vanishing at the center where dU/dY is zero as the expression in the

original Prandtl theory (Eq. 3.9) does. The relationship, however, is

not locally evaluated but is rather considered to be constant across the

area perpendicular to the flow.

It is apparent that there is no one locally dependent model for

turbulent shear stress that is capable of satisfactorily predicting the

entire range of turbulent flow. Serious doubts have recently been

raised as to the validity of the initial assumptions that turbulent

transport obeys the gradient-type relationship. The scope of this sub-

ject is far too wide and too complex to try to bring it to any kind of

final conclusion at the present time. It is by far the most formidable

problem in fluid mechanics, and in spite of major recent advances in

recent years, the task is still unresolved at the present time.

The availability of high-speed and large-memory computers has given

a new hope in this difficult field of fluid mechanics. Most of the new

methods are based on applying the conservation principles to the

65

turbulence parameters themselves. However, this approach created

difficulties in achieving closure to the system of equations derived.

These attempts are still in a state of flux, and their results are still

uncertain, but they seem to be very promising.

The above discussion emphasized two levels of averaging processes—

on a molecular scale and on a turbulent fluctuations scale. In both

cases, however, the resultant equations could still be time-dependent and

for three-dimensional space.

Let us now assume for the time being that our first two approximations

for molecular and turbulent time scale averaging are indeed successful

and that Eq. 3.8 is proper under those assumptions. Now using Eq. 3.8 in

a three-dimens^nal conservation equation will give

where a bar indicates a time average over a time scale greater than

turbulent fluctuations but smaller than the time scale of interest. Let

us assume now that for the practical problem at hand the interest is

focused only on the time-dependent two-dimensional behavior. However,

we cannot simply drop all the terms connected with the third dimension

First-order and second-order closures are presently being attempted. 62-66

(3.13)

66

(let us say Z), because their possible effects on the two dimensions of interest must be taken into account. Using the same technique used before for approximating turbulent characteristics, let

Ux - ux + u x ' •

UY * UY + UY' »

P = P + V " ,

(3.14)

where one bar indicates a time average over the turbulent time scale, and two bars indicate an average of the one-bar value over the third dimension (Z). Two primes indicate the deviation of the actual value along the third dimension (Z) from the two-bar value. Substituting Eq. 3.14 into Eq. 3.13 and performing the averaging operations as before gives

3P 3_ t 3X

3Y

UX(P) * (-Capx • epx) f ) +

Uy(P) r ^ 3P

PY CPY W , + U, = P (3.15)

To evaluate u^"p" and u^P", one needs a detailed knowledge of the variations along the third dimension, which are net known. If one takes the same approach as before and assumes that the contribution of verti-cal variation in the horizontal directions can be expressed by a gradient-type relationship, Eq. 3.15 can be rearranged to

67

3P 3 = = f , Jt + W ux PX

P, V (3.16)

and the flux in, let us say, the X direction can be expressed as

p r = u x C P ) + _(apj[ + PX £px E

This additional contribution of nonconvective transport in the X direction is a result of shear effects created between the layers because of the velocity variations along the dimensions that have been averaged out. In the literature, this transport phenomenon is often called "dispersion" or "longitudinal dispersion." "Virtual diffusion" or "longitudinal dif-fusion" may be a better term for that purpose.

This method of compensating for unknown convective transport by the use of ever-increasing "diffusion" coefficients is carried further by reducing the conservation equation from two-dimensional to one-dimensional (add another coefficient E^) and from transient to steady state in the case of periodic or tidal flow (add another coefficient E''). When the

A

problem of diffusion is viewed in this light, it seems that all those "diffusion" coefficients are nothing but good indicators of the level of our inability to express the actual transport phenomena in nature properly (see Table 3.1).

It must be emphasized at this point that molecular diffusion is normally very small compared with turbulent diffusion (ratio of about

Table 3-1. Averaging Levels of Transport Phenomena

Dimensionality Diffusion Coefficient Accumulated Level of Averaging of Model Used to Compensate Diffusion Coefficient

Average over all microscale details

(X, Y, t) a - molecular diffusivity D = a

Average over all details of turbulent fluctuations

Cx, Y, 2, t) £ - turbulent diffusivity

D = « + e

Average over all details of one direction

(X, Y, t) E - dispersion coefficient

D = a + e + E

Average over all details of two directions

(X, t) E' • - longitudinal dispersion coefficient

D = a + z + E + E'

Time average over cycle period in periodic flow

(X, t) E " - dispersion coefficient

D = a + £ + E + E' + E "

Note: One bar indicates average over turbulent scale fluctuations; two bars indicate average over time scale larger than cycle period but smaller than the time scale of interest.

6S

10" to 10" ). The contribution of molecular diffusivity is insignificant in turbulent flows except at the boundaries, where turbulent eddies are reduced to zero. The relative magnitude of dispersion in relation to the turbulent diffusion depends on the level of approximation made and the characteristics of the flow. The longitudinal dispersion in natural streams was found to be one or several orders of magnitude greater than turbulent diffusion. It is an unfortunate situation, then, that the level of confidence in the various "diffusion" coefficients used is inversely proportional to their relative magnitudes and importance.

It seems to the author that with the high-speed and large-memory computers available today, the time is right to eliminate at least part of those approximations. It seems unnecessary to get rid of the molecular diffusivity and hopeless at the present time to try to get rid of the turbulent diffusivity (which is indeed unfortunate). However, it seems certainly possible to get rid of the various dispersion coefficients, by investing most effort developing a workable time-dependent three-dimensional model in which convective movements are properly expressed. Such models are within our present technical capabilities. Of course, such models will be very costly both to develop and to use. However, when compared with the total cost being presently spent for not having such models, the balance will be in favor of developing them.

3.2. Applicable Turbulent Transport Properties

In the model developed in the present study, only one dimension is being averaged out (the vertical). The time-dependent momentum equations

70

include both normal and shear stresses in both horizontal directions. Therefore, in addition to the need for molecular and turbulent diffusion coefficients, there is a need for a virtual diffusion coefficient which will compensate for the transport caused in both the X and the Y direction because of the variations in velocity profiles in the vertical direction. Taylor^4 has developed an expression for this virtual dif-fusion coefficient for an instantaneous discharge in an axisymmetric flow in a long straight circular pipe and found that

Ex = 10.06auT , (3.17)

where a is the pipe radius, u^ is the shear velocity at the wall, /t~7p~, and E^ is the virtual diffusion coefficient in the flow direction X caused by shear effects from the velocity variations in the radial direction. This virtual diffusion coefficient in the flow direction is also called the longitudinal dispersion coefficient.

Elder^ has developed a similar expression for a two-dimensional open channel. Elder assumed that for this case the variations with depth are the main contributors to the horizontal longitudinal dispersion and has found, based on Taylor's approach, that

E = 5.86Hu , (3.18) A T

where H is the channel depth and u^ is the shear velocity at the br^ôm, /Tg/p. Other investigators have derived similar expressions based upon various assumptions (Refs. 82-84).

71

Field data collected and compared by a number of investigators have shown longitudinal dispersion coefficients many times those pre-

C C. C "7 dieted by Elder. Fischer ' has shown that lateral variations in velocity profile, which were neglected by Elder, were most important. He has followed Aris's85 and Taylor's54 methods and developed an expression for the longitudinal dispersion coefficient based on the velocity profile in a lateral direction. His correlations agreed better with measured values in actual streams and, therefore, gave a theoretical basis for the large discrepancies found in many cases between measured values and previously predicting models. However, Fischer has also shown that the longitudinal dispersion coefficient is extremely sensitive to the vertical velocity profile assumed and has suggested that successful prediction may have to be based upon detailed experimental knowledge of these profiles.

The compensation for the effects of lateral variations as proposed 56 5 7 by Fischer ' is not needed in the present two-dimensional model,

since those variations are incorporated and expressed in the model itself. 55 It seems, then, that the approach taken by Elder will be quite sufficient

for the model proposed here in the far-field regions. 55

Elder's basic expression for the longitudinal dispersion coefficient in an open channel where the effects of lateral variations are neglected can be expressed after some variations as:

E„ = - Hu / [f - fOO] A 0

l / w (df/du) / - f(w)] dtu 0 0

dw dw,(3.19)

72

where H is the channel depth, u a Z/H, u is the shear velocity at the

bottom, Ag/p, and f(w) is any function of w that specifies the vertical

velocity profile, so that

U = Umax " ux C3.20) and

U = U - u f . max T

If the vertical velocity profile is taken as logarithmic over the

whole depth, one gets:

£(«) = - (l/kQ) log (1 - a) , (3.21)

where kQ is the Von Karman constant and is equal to 0.41. Using this

velocity distribution in Eq. 3.19, as was done by Elder, the longitudinal

diffusion coefficient becomes

E x = 5.86HUt . (3.22)

Following Taylor's assumption of isotropic turbulence, Elder also

derived an expression for turbulent diffusivity, which is assumed to be

the same in any direction, and found

1 , E = Hu / u^df/dw)""1 du . (3.23)

T 0

With the velocity function f(o>) given in Eq. 3.21, one gets

ex = ey 5 0.07HUt . (3.24)

73

However, his experiments showed a value about 3 times as large, and he concluded that

This increase may be the result of the lateral contribution, which wad not included in Elder's analysis. However, the logarithmic vertical velocity profile is not always a good representation of the correct vertical velocity distribution. Other functions f(u>) can be assumed, and the proper coefficients can be evaluated based on Eqs. 3.19 and 3.23. The phenomenon of dispersion as investigated by Taylor and Elder is based on a Lagrangian frame of reference which is moving with the mean velocity of the fluid.

86 87 Bowden ' has derived similar expressions for the longitudinal

diffusion coefficient in an Eulerian frame of reference in alternating flow and for various assumptions of vertical velocity profiles. The results given in Table 1 of Ref. 87 may be useful for some corresponding situations. Since the assumption of isotropic turbulence was made, the turbulent diffusion coefficient is independent of direction. In a two-dimensional model, the shear velocity Ut in Eqs. 3.23 to 3.25 must be replaced by the total velocity, i.e.,

where is the shear velocity at the bottom in the X direction /OgX/p, and u Y is the shear velocity at the bottom in the Y direction /onv/p.

ev = ev = 0.23Hu . X Y T (3.25)

(3.26)

74

The assumption of isotropy cannot, however, be extended to the longitudinal dispersion coefficient E as well. Extension of Elder's approach for E^ and Ey may require replacing u . in Eq. 3.22 by u ^ and uTy, respectively, so that if the logarithmic velocity profile is assumed in both directions, one gets from Eq. 3.22 that

(3.27)

(3.28)

However, this type of extension from the one-dimensional to the two-dimensional case has not been verified.

In addition, most previous studies (Taylor, Elder, Bowden, Fischer, and others) have been performed and tested for instantaneous discharges only. The applicability of these derived correlations for continuous discharges was not verified and may be incorrect.

Effects of vertical stratification and density currents produced in estuaries complicate things even further. A proper formulation of the dispersion coefficient for such cases is presently not available, and, therefore, it is hoped that the model will not be used in its present form for regions where stratification is of major importance.

Because of the state of the art in this area, it was judged preferable at present to keep in the computer model a general expression composed of two parts. One part is based on a gradient-diffusion-type model, and the other can be any type of function. The overall effective diffusion coefficient appearing in the first part is not considered a

5.86Hu TX

E = 5.86HUw

75

a constant. It is always a function of the local flow characteristic. The computer program is constructed so that any such desirable function, if available, can be used.

In the near-field area, where the momentum of the jet creates most of the flow distribution around it, the turbulent eddy diffusivity is probably the most important part of the overall effective diffusion coefficient. One of the turbulent theories should be applied here. Prandtl's mixing length theory (Eq. 3.9) or Prandtl's hypothesis (Eq. 3.12) seems to be most effective for free turbulence of jets and plumes. However, a difficulty arises here as to the application of such corre-lations in a fixed rectangular XY coordinate system. This is indeed a difficult problem, which must be solved before the model can be used for transient two-dimensional near-field analysis. However, since, as dis-cussed in the introduction and in Section 7, there are other obstacles (stratification and element sizing) to achieving this goal, it will be assumed at the present time that the model will be used primarily as a far-field model with some approximation of the near field which is con-sidered to be part of it.

The discussion above on turbulent diffusion and longitudinal dispersion referred primarily to transport of dissolved substances. However, similar coefficients will exist also for momentum and energy transport.

In the rest of this chapter the nonconvective transport terms and their discrete element formulation for mass, momentum, and energy will be discussed.

76

3.3. Viscous and Hydrostatic Stresses

In Section 2.8 the discrete element formulation of the momentum equations has been derived (Eqs. 2.75 and 2.76). In Section 2.9 it was shown how to eliminate the half-point values in terms of the values in the center of each discrete element. In this section the internal viscous stresses as well as the effects of hydrostatic pressur ill be formulated so that the stress components o^, o^, °yx' and °XY ^rom

Eqs. 2.75 and 2.76 can be eliminated in terms of the appropriate basic

As indicated in Section 3.1, the gradient formulation will be basically assumed here to be valid for both laminar and turbulent viscous stresses. The momentum diffusivities used, however, are not constant but may themselves be complicated functions of the flow characteristics, as has already been discussed in Sections 3.1 and 3.2. With this approach, one gets for an incompressible flow that

values

(3.29)

a. YY -P + 2pD v ~ r K m Y 3Y (3.30)

cr XY = aYX = p DmX 3X + DmY 3Y (3.31)

The pressure Pr in Eqs. 3.29 and 3.30 can represent any pressure in the system and is considered always positive for compression. In the

77

case of natural water bodies the most significant pressures involved are atmospheric and hydrostatic pressures, which are the only ones considered in this study. The hydrostatic pressure can be derived from the momentum equation in the vertical direction, in which the vertical velocities and all derivatives in the vertical direction, except for pressure, are set equal to zero. In this case we get that

Integrating Eq. 3.32 with respect to depth and assigning the boundary condition that atmospheric pressure (P ) exists at the water surface elevation Z = H gives

where Hg is the total depth of water, Z is the vertical distance of the local point from the bottom, and (Pr)a is the atmospheric pressure.

Performing this integration along Z and assuming uniform water density along the depth, one gets

0 = -(9Pr/3Z) - pg . (3.32)

s

(3.33)

where

(3.34)

(3.35)

is the centroid of the height at each (X, Y) point. Therefore,

Pr(X, Y) = (Pr)a + (l/2)gp Hg . (3.36)

78

Substituting Eq. 3.36 into Eqs. 3.29 and 3.30 gives for the stress

components:

°XX = 2pDmX I T " < P A ' W W Hs ' <3-37>

r)V aYY = 2pDmY IT - <Va " (1/2)gp Hs ' (3'3S)

°XY = °YX = P n i l + n iM. mX 3X mY 8Y (3.39)

and DmY are the overall effective kinematic eddy viscosities and

are used for that part of the viscous stresses which can be expressed

with the gradient-type formulation. In this case, D ^ and D ^ can be

expressed as

DmX = % * em + EmX > C3"40^

DmY = \ + £m + EmY > <3-41>

where am is the molecular momentum diffusivity (or molecular kinematic

viscosity), which is independent of direction, and e^ is the turbulent

momentum diffusivity (or turbulent kinematic viscosity) which, for

isotropic turbulence, is also independent of direction. Em^ and EmY are

momentum longitudinal dispersion coefficients (or longitudinal eddy

kinematic viscosity) in the X and the Y direction which take into account

the effects on the stresses resulting from velocity variations along the

depth.

79

The discrete element formulation of the stress components can now

be developed based on Eqs. 3.37 to 3.39. Figures 2.2 to 2.4, pages 31

to 33, show the locations and directions of thoso stresses. All of the

stresses are evaluated at the half-point boundary values between the

discrete elements; for example,

ap ax

P, . - p. . » 1>3 f7 421

i+1/2, j ° ' 5 ( < 1 + ' C 3

Evaluating Eqs. 3,37 to 3.39 at the proper locations (see Figs. 2.2 to 2.4) and using the discrete element form of the derivatives (see Eq. 3.42) gives

Ui+1 j " Ui j C°XX)i+l/2,j = 2pi+l/2,j (IWi+l/2,j 0.5(AX. . + AX.) 1+1 1

T«pi+l/2.JHi+l/2.J " <Pr>a ' (3'43>

Ui j " Ui-1 j (crXX:)i-l/2,j = 2pi+l/2,j (IWi+1/2,j 0.5(AXj + AX.^)

• ^ > 1 / 2 / 1 . 1 / 2 , 3 ' ^ a ' C3'44>

Vi j+1 " Vi ' C°YY3i,j +1/2 = 2pi,j + l/2CDmY3i J + l/2 0.5(AXi+1 + AXR)

" I gpi,j+l/2Hi,j+l/2 " (Pr}a ' (3.45)

80

2pj YYi, j-1/2 Mi,j-l/2vmY;i,j-1/2 0.5(AX. + AX.^)

7gPi,j-l/2Hi,j-l/2 " ( P A ' (3.46)

(0XY)i,j+l/2 ° pi, j + 1/2 rU. . . - U. . I fD 1 i,3 l V i , j + 1/2 O.SXAYj J + AYj)

+ j+1/2 Vi+l/2,j+1/2 ~ Vi-l/2,j+l/2l

X. l , (3.47)

^XY^l,j-1/2 * Pi,j-1/2 ^mY^, j-1/2 "i.3 - UiJ-l

10-S(AY. + AY._X)

+ ^mXî, j-1/2 Vi+l/2,j-1/2 " Vi-l/2,j-l/2l

AX, (3.48)

^°XYî+l/2,j = pi+l/2,j (D 1 fUi+l/2,j+1/2 ~ Ui+l/2,j-l/2l tUmYJi+l/2,j [ W. J

V.+j . - V: + CDmX)i+l/2,j [o.S+(Ax,+1 +1A£.)< (3.49)

(°XY)i-l/2,j = Pi-l/2,j (DmY)i-l/2,j Ui-l/2,j+1/2 ' Ui-l/2,j-l/2j

AY. i

V - V. + CD ) , i»3 1-1'3 mX'i-1/2, j 0.5 (AX. + AY. .) 1 1" 1 (3.50)

81 i

The half-point values of the velocities both at the centers of the faces between the adjacent discrete elements and at the corners of those faces are all evaluated on the basis of the relations developed in Section 2.9.

3.4. Energy Fluxes

In Section 2.7 the discrete element formulation of the energy equation was derived (Eq. 2,61). The convective energy fluxes were for-mulated by Eqs. 2.62 to 2.64. In this section the internal energy fluxes qx and appearing in Eq. ?.61 will be formulated. As in the case of viscous stress, it will be assumed that part of these fluxes can be expressed with the gradient formulation and that other formulations can be added when they are available. With this assumption, one gets

q x = -pCpDHX(3T/3X) , (3.51)

qy = -pCpDHY(3T/3Y) , (3.52)

where D^x and D^y are the total effective thermal diffusivities in the X and the Y direction, respectively. As in the case of momentum fluxes, the total effective thermal diffusivities can be separated into three parts as

°HX = aH + eH + EHX ' <3'53>

°HY = aH + eH + EHY ' (3.54)

82

where a„ is the molecular thermal diffusivity, which is considered H independent of direction, and e^ is the turbulent thermal diffusivity, which, for isotropic turbulence, is also considered independent of direction. and EHy are the thermal longitudinal dispersion coefficients in the X and the Y direction, respectively.

The ratio between the momentum diffusivity (kinematic viscosity) and the thermal diffusivity is called the Prandtl number,

PRa = 0m/«H . (3.55)

Similarly, the turbulent Prandtl number is defined as

PRe - em/eH . (3.56)

On the same basis, one can also define the "longitudinal dispersion Prandtl number" as

PRe = Em/EH (3.57)

and an effective Prandtl number as

PRD = Dm/DH . (3.58)

The molecular Prandtl number, PR^, like the molecular momentum and thermal diffusivities, is characteristic of the material itself, whereas the rest of the Prandtl numbers, like the corresponding diffusivities, are mainly dominated by the flow characteristics. The Re>r.t Ids analogy states that the turbulent Prandtl number equals 1, and therefore eH = em-This assumption has been used very extensively in heat transfer analysis,

83

often with good results. Many studies show, however, that this assumption is not always correct and that the turbulent Prandtl number will vary for different flow conditions.

Vertical thermal stratification may be different from the vertical velocity variations, and each one of those vertical variations has its own effect on the corresponding dispersion coefficient. It is outside the scope of the present study to discuss this point properly. It will be assumed that the two-dimensional model proposed here will be used primarily in vertically mixed water bodies, and in this case the value of E„ will be conservatively neglected for environmental impact assessments. Any realistic analysis of a natural stream should, how-ever, try to look for the proper way to take the effect of vertical variations into account, since they always exist to some extent.

The discrete element formulation of the energy fluxes (Eqs. 3.51 and 3.52) can now be developed. Using Figs. 2.2 to 2.4, pages 31 to 33, and the proper notation as used for the stress components gives:

(qX}i+1/2,j = "Pi+l/2,j(Cp)i+l/2,j(DHX)i+l/2,j T. , . - T. . 1+1,3 i>3 0.5(AXi+1 + AXk) , (3.59)

= "pi-l/2,jCCp)i -l/2,j ( LWi T. . - T. , . 1,3 1-1,3

= "pi-l/2,jCCp)i -l/2,j ( LWi -1/2,3 0.5(AX. + AX. ,) v X l-l .

= -pi,j+l/2fCP3i ,j+l/2 C EWi

T - T i,j+l 1,3 = -pi,j+l/2fC

P3i ,j+l/2 C EWi ,3+1/2 0.5(AY.+1 + AY.)J

= " pi,j-l/2 (Vi ,j-l/2C°HX)i T. . - T. . . 1,3 1,3-1

= " pi,j-l/2 (Vi ,j-l/2C°HX)i ,3-1/2 0.5(AYj + AYj

, (3.60)

, (3.61)

(3.62)

84

Energy fluxes that cannot be expressed with the gradient formulation

can be added to Eqs. 3.59 to 3.62 when they are needed and are available.

The thermal fluxes from the bottom and top as well as the volumetric heat

generation (or decay) will be discussed in Section 4.

In Section 2.6 the discrete element formulation of the conservation

equation for the mass substance of k has been derived (Eq. 2.50). The

internal convective fluxes were already formulated explicitly in this

equation. In the present section the internal nonconvective mass fluxes

of substance k appearing in Eq. 2.50 will be formulated. In Section 2.3

the velocity of substance k was expressed in terms of the mixture

velocity V and the relative velocity of substance k with respect to

the mixture velocity V (Eq. 2.6). The relative velocity (also called

diffusive velocity) of substance k obeys the Fickian law for binary

diffusion in most cases. This law expresses the diffusion of one sub-

stance into the rest of the fluid mixture. Neglecting the effects of

pressure, temperature, and body forces, which are indeed negligible,

Fick's law for binary diffusion can be expressed as:

3.5. Mass Diffusion Fluxes

'M'k 1 C (3.63)

or, for a two-dimensional case

(3.64)

85

CV£)y = i- ( D M k) y . (3.65) k

^Mk-'x 311(1 ^Mk^Y a r e t h e t o t a l effective m a s s diffusivities of substance

k into the rest of the mixture in the X and the Y direction, respectively.

Since the mass flux of substance k was defined by Eq. 2.8 as g^ = p ^

and since C^ = Pj./P» Eqs. 3.64 and 3.65 can be written as:

9Ck g k x = - p ^ W x u r * C 3 , 6 6 )

9C

As in the case of the momentum and energy fluxes, (Dj^)^ and (Dîy

will be assumed to be composed of three parts, so that

(DMk>X " °Mk + eMk + (EMk>X • C 3' 6 8 )

V y " % k + GMk + (EMk>Y ' C3'693

where a ^ is the molecular mass diffusivity of substance k, which is

considered independent of direction, and e ^ is the turbulent mass

diffusivity of substance k, which, for isotropic turbulence, is also

considered independent of direction I E ^ X ^ ^Mk^Y a r e t*ie m a s s

longitudinal dispersion coefficients of substance k in the X and the Y

direction, respectively. The molecular binary diffusion coefficient

a ^ is a characteristic of the two materials involved. The turbulent

counterparts e ^ and E ^ , however, are mainly dominated by the flow

characteristics, e ^ and E ^ in Eqs. 3.68 and 3.69 can then be replaced

by e^ and E^, respectively.

86

The ratio between the momentum diffusivity and the mass diffusivity

is called the Schmidt number; i.e.,

< S C A - V a M k • (3-70>

Similarly, the turbulent Schmidt number is defined as

Sce a em/eM . (3.71)

On the same basis, one can also define a "longitudinal dispersion Schmidt

number" as

ScE = Em/EM (3.72)

and an effective Schmidt number as

<ScD>k " V D M k ' <3'73>

The ratio between the turbulent Prandtl number and the turbulent Schmidt

number is called the turbulent Lewis number; i.e.,

Le£ = PRe/Sce . (3.74)

The available experimental evidence shows that the turbulent Lewis

number in the boundary layer has the value 1. This may be true also in

free turbulence. However, in a large water body, thermal stratification

has considerable effect on the thermal longitudinal dispersion

coefficient E^ and probably also on the mass longitudinal dispersion

coefficient. As in the case of the momentum and the thermal dispersion

coefficient, it will be indicated here that it is outside the scope of

87

the present study to settle those difficult issues of turbulent diffusion and dispersion for mass, momentum, and energy as well as the interaction between them. The discussion in Sections 3,1 and 3.2 has emphasized these problems and some possible partial solutions. It is hoped, again, that the model will be used primarily in vertically mixed shallow water bodies, in which case the dispersion coefficients can be conservatively neglected for environmental impact assessments.

The discrete element formulation of the mass fluxes (Eqs. 3.66 and 3.67) can now be developed. Using Figs. 2.2 to 2.4. pages 31 to 33, and the proper notation as used for the momentum and energy fluxes gives:

CgkX5i+l/2,j = "pi+l/2fj^DMk^xU+l/2J

CgkX3i-l/2,j s ~pi-l/2,jt(DMk'Jx:ii-l/2,j

CgkYî, j+1/2 = "pi,j+l/2^DMkVi,j+l/2

CgkY)i,j-l/2 = "pi,j-l/2tCDMk)YIi,j-l/2

Additional mass fluxes that cannot be e:

formulation can be added to Eqs. 3.75 to 3.78 when they are indeed needed and are available.

By now, all the internal fluxes of mass, momentum, and energy have been formulated for each discrete element. The interaction of the water

<ck>i+l.j - tCk>i 0.5(AX.+1 + AX.) a' •

<Vi,i - Cck>i-1 »? 0.5(AXj +

ickh,j+i - J 0.5(AYj+1 + AY.) y »

CCk>i,i -l 0.5(AYj -

4

(3.75)

(3.76)

(3.77)

(3.78)

pressed by the gradient

88

body with its physical boundaries needs now to be discussed. This

discussion will be divided into two parts. The first (Section 4) will

discuss the interactions with the bottom and top surface as well as

volumetric heat itnd mass generation or decay. The second part (Section

S) will discuss the interaction with the side boundary conditions as

well as the initial conditions specified at a certain initial time.

Since no formal differential equations have been derived, there is no

need for "boundary conditions" in the classical sense. The purpose

of the formulation of boundary conditions in Section 5 is to eliminate

the half-point values on the boundaries from the basic numerical conser-

vation equations in terms of either internal or otherwise specified

values.

4. BOTTOM SURFACE, TOP SURFACE, AND

VOLUMETRIC CONTRIBUTIONS

In this section the mass, momentum, and energy fluxes from the

bottom and the surface of the water body will be discussed. This

includes the quantities gfi, gT, gkfi, g ^ , qfi, qT, qkfi, q k T, a g x, aBy,

and a^y appearing in the discrete element formulation of the con-

servation equations (Section 2.6). In addition, the body forces, the

mass and energy generation or decay per unit volume and unit time (i.e.,

fc, and the thermophysical properties involved (p, C^, e, h)

will be discussed.

4.1. Shear Stresses at the Bottom

The shear stresses at the bottom appear as (oBV.). . and (cDV). . in da or 1 ,3

Eqs. 2.75 and 2.76, respectively. With the signs notation discussed in

Section 2.5 and Figs. 2.2 to 2.4, pages 31 to 33, the bottom stresses

were considered positive in the positive direction of the corresponding

coordinates, and, therefore, the negative sign will be included in the

stress expressions themselves, so that the direction of the bottom

stresses is always opposite to that of the velocity.

The shear stresses over any solid surface are generally expresed

in the form

t = *pV2 , (4.1)

89

90

Similarly, the bottom shear stresses can be calculated in a modified form to suit a two-dimensional formulation (Ref. 88) and can be expressed as:

CBX = " V ^ 2 + y 2 U ' (4,2)

a f i Y = -XgP^/lJ2 + V 2 V , ( 4 . 3 )

where and tfgy are the bottom friction stresses in the X and the Y -1 -2

direction, respectively, (ML T ) and p is water density. The dimensionless constant Xg is mainly a function of Reynolds

number and the roughness of the surface. It is basically similar to the commonly used nondimensional friction factor f for flow in closed con-duits. Such a localized factor is very desirable for a two-dimensional model since the bottom shear stresses must be evaluated locally.

Bowden (Ref. 89) and others have evaluated, for the sea, a range of 2.4 x 10"3 <_ Ag <. 2.8 x 10"3 . (4.4)

In rivers and estuaries the value of Xg may be higher and its range wider, e.g.,

2.0 x 10"3 < Xg £ S x 10"3 . (4.5)

-3 -3

A value for Xg of about 3 x 10 to 4 x 10 seems to be reasonable for shallow water bodies. Most of the data available, however, are based on one-dimensional flow in open channels, in which cases it is common practice to use the Chezy formula in combination with the Manning coefficient. The Chezy formula can be expressed as:

91

U = Cz v^S^ , (4.6)

where U is the one-dimensional average velocity along the channel, R^ is the hydraulic radius, defined as the ratio between the cross-sectional area and its wetted perimeter, Sg is the slope of the channel bottom (tan 6), and Cz is the Chezy resistance factor, which can be related to XB by

Cz = gAB . (4.7)

1/2 -1 The dimensions of the Chezy resistance factor are L T , and one

should be careful in using the proper coefficient for the units in use. In practice the evaluation of the Chezy coefficient is based on empirical relationships which relate it to the effective roughness of the channel. The most widely accepted formula for determining the Chezy coefficient t

is the Manning formula,

C z - ( l - t M / n ) ^ 6 , ( 4 . U )

where n is the Manning roughness coefficient. Values of n are tabulated in various handbooks (Ref. 90). The dimensions of the Manning

-1/3 coefficient are TL . Again one should keep in mind the units involved when using this coefficient. For a two-dimensional model where it is assumed that the water depth is small, one can approximate the hydraulic radius by the depth and get:

Cz = (1.486/i.)H1/6 . (4.9)

Combining Eqs. 4.9 and 4.7, one gets:

92

XB = (gn2)/(2.208H1/3) , (4.10)

which can be used in Eqs. 4.2 and 4.3. The discrete element formulation of Eqs. 4.2 and 4.3 will be

Kv)^ i - -Cx, 'BViJ

where can be evaluated by Eq. 4.10 as:

2

P i j V Ui.3 2 + Vi>/ V U . (4.12)

c V i f j - r f w ^ H y - C4-13)

4.2. Wind Shear Stresses

The wind shear stresses appear as (aTY). . and (cr ). . in Eqs. 2.75 and 2.76, respectively. The direction of the stress caused by the wind will be the same as the wind direction itself (see Figs. 2.2 to 2.4, pages 31 to 33).

The shear stresses exerted by the wind on the free surface of a water body can be expressed (Ref. 88) for a two-dimensional formulation in a form similar to the expression for the bottom friction as:

a m = V \ / W x 2 + wY2 wx » ( 4 a 4 )

a m = x w p V V + wy2 WY ' (4-15)

93

where are the wind shear stresses in the X and the Y direction, -1 -2

respectively, (ML T ), p is the density of water, W^, are the wind velocities in the X and the Y direction, and Xw is a dimensionless con-stant, which must be empirically determined. Not all empirical studies result in correlations of the form expressed by Eqs. 4.14 and 4.15. In those correlations which do, A^ is normally based on the density of air rather than water, and its evaluation is not consistent in the open 91 literature. A summary of existing correlations is given by Hutchinson

88 92 93 and Dronkers. Ekman and Rosby obtained (in c.g.s.)

AWP = U2pa) = 3.2 x 10"6 . (4.16)-

94 Von Dom has given those values as functions of anemometer height, and for the height range of 25 cm to 1000 cm, he gets the range for as:

1.2 x 10"6 - X^ = X2Pa - 4.5 x 10"6 . (4.17)

Since the density of water p in cgs units is about 1.0, one gets a reasonable range for X^ as:

1.2 x 10"6 < Xw < 4.5 x 10"6 (dimensionless) . (4.18)

The discrete element formulation of Eqs. 4.14 and 4.15 will then be

<*TX>i§j " CVi,jpi,j i j + (WY^,j <"x>i.J > C4'19>

* CViJ pi,j "KîJ + "Vi.j C V i J » (4'20>

94

where W , Wy, and A^ are specified functions of time and must be given

for each case as discussed before.

4.3. Rain, Evaporation, and Other Mass Fluxes at the Bottom and Top

The mass fluxes to the water body from either the bottom (seepage) or the top surface (rain, evaporation, etc.) are considered in the con-

-2 -1 servation equations as CeB)±^j > Cft^ j» (SkBîJ' a n d ^kTî.j (ML T

The total mass fluxes gg and gj, must either be measured or calculated. In most cases, information on such fluxes as seepage or rain can be found from published meteorological data. Evaporation can sometimes be calculated on the basis of equations discussed in Section 4.4.

The quantities g^g and g ^ represent mass diffusion of substance k from the bottom and top, respectively. In a simplified form, such a mass diffusion can be expressed according to Fick's law for binary diffusion from one substance to the rest of the mixture as:

G - (D1 8 ( P ^ B ) kB " "luMJkB """an; B

(4.21)

2 - 1

where D^g is the mass diffusion coefficient (L T ) of substance k from the bottom (or top), n^ is the space direction perpendicular to the bottom (or top) surface, and C^g is the mass concentration of substance k at bottom (or top).

95

However, practical evaluation of such diffusion from outside will depend on empirical correlation which will normally be based on a formulation of the Nusselt number type, such as

where C^ is the mass concentration of substance k inside the control - 2 - 1

volume, Chjpkg is mass film diffusion coefficient (ML T ) of sub-stance k from the bottom (or top) to the control volume, and h^, like its equivalent for heat, is usually established empirically. The dis-crete element formulation of the mass flux from bottom will be

<*B>i.J = ^ i . j ^ l i j > C4"23>

and mass flux from the top

where |V| indicates the magnitude of the vector V. The mass fluxes of substance k by diffusion from the bottom and top using Eq. 4.22 are

&kB>i,j = - ^ W i j E C V i j - P W i j J ' C4-25)

<«kT>i.j - - ^ V k A j ^ i J " fWi.jJ > <4'26>

where (h ) g and (h^)are the mass film diffusion coefficients of substance k from the bottom and the top, respectively, to the discrete element (i,j).

96

4.4. Heat Exchange with the Atmosphere and Other

Energy Fluxes at the Bottom and Top

4.4.1. General

Energy fluxes are considered in the conservation equation as

<Vi,j> « W i , j ' •»* CBtu.L-V^F- 1).

The quantities qfi and qT are nonconvective energy fluxes from the

bottom (considered to be negligible) and the top surface (primarily by

heat exchange with the atmosphere). As in the case of mass diffusion,

these quantities can be expressed according to the Fourier law as

3(pReR) (Du) B B H-'B 3nfi (4.27)

B

where n g is the space direction perpendicular to the bottom (or top)

surface, efi is the energy per unit mass coming from the bottom (or top),

Pg is the density of mass coming from the bottom (or top), and (D^)g 2 -1

is the heat diffusion coefficient (L T ) from the bottom (or top).

Again, practical evaluation of such heat diffusion from outside the

boundaries will depend on empirical correlation and will normally be

based on the Nusselt number or the Newton law of cooling to give:

- t W " V » C 4- 2 8 )

where T is the temperature inside the control volume, Tfi is the tempera-

ture of the bottom (or top), and (hH)B is the film heat transfer -2 -1 -1

coefficient from the bottom (or top) to the control volume (Btu* L T F ),

which is usually established empirically.

97

The most important of this heat exchange takes place between the

water surface and the atmosphere above it.

4.2.2. Heat Exchange with the Atmosphere

The heat exchange of a given water body with the atmosphere above

it is a function of the particular meteorological conditions existing at

a particular time and location. The proper way to consider this heat

exchange is to sum up all the individual heat transfer rates due to the

various heat exchange mechanisms. Such a summation, although a function

of both surface water temperature and air temperature, cannot in general

be linearized into a direct proportionality with respect to the "tem-

perature drops" involved. Nevertheless, because of the simplicity

achieved by such linearizations, two approaches have become extremely 95-97

popular. One technique, recommended by Edinger et al., is based on

the concept of surface heat exchange coefficient and the equilibrium

temperature of the water body. Using these concepts the heat transfer

across the water surface can be expressed as:

q T • -K(TWS - Te> , (4.29)

where qT is the heat transfer rate, Btu/day, K is the heat exchange

coefficient, Btu/day-ft -°F, T w g is the water surface temperature, °F,

and Tg is the equilibrium temperature, °F. The equilibrium temperature

is the temperature to which a body of water would eventually come if it

were exposed constantly to the same meteorological conditions which

existed at the particular time and location. A body of water will con-

tinuously approach the equilibrium temperature but will always lag

98

behind it because of continuous changes in the meteorological conditions.

Both the equilibrium temperature and the heat exchange coefficient are

functions of the meteorological conditions and normally should not be 98

considered constant. However, it has been shown that in many cases

an approximate value for those parameters can be obtained by using the

following relationships:

TE a Td " » ( 4' 3 0 )

K = 15.7 + ($ + 0.26)(70 + 0.7 W2) , (4.31)

S * 0.255 - 0.0042(Twg + Tj) + 5.1 x 10"5(TWS + Tj)2 , (4.32)

where T^ is the dew-point temperature, °F, T^g is the surface water

temperature, °F, Q is the gross heat rate of solar radiation, &

2 2 Btu/day-ft , K is the heat exchange coefficient, Btu/day-ft-F, and

W is the wind speed, miles/hr.

Another approach becoming extremely popular because of its

simplicity is a technique based on what is called "excess temperature."

This method also is based on the concepts of equilibrium temperature and

heat /change coefficient, but it eliminates the need for calculating

the equilibrium temperature itself. This is achieved by using the

applicable energy balance equation twice—once for the water temperature

under no power plant thermal discharges and then for the water tempera-

ture under the specific thermal discharge analyzed, and subtracting the

first equation from the second. If the terms are indeed linear, the

equilibrium temperature drops out. The justification and advantage of

99

this method is that in many cases the main interest of the analyst is

to calculate the "excess temperature" created by the thermal discharge

rather than the actual water temperature.

Both methods are useful and can be used under a specific set of

conditions. However, neither will be correct as a general method. A

more proper way should be based on individual computation of each heat 99

exchange mechanism involved. Such an approach is used by Raphael and

was "computerized" by Tackston and Parker.1®0 This approach is much

more accurate than the previous two methods, has the advantage of being

more closely related to the individual meteorological effects, and is

adaptable to local and instantaneous time-dependent models. With the

computing capabilities presently available, there is no justification

for not applying such a method in a numerical model.

The equations used in the last approach and the parameters it

requires are summarized here, but the reader should refer to Ref. 100

for further details. The net heat exchange between the water surface

and its surrounding is

qT s qs + qa + qb + qe + qc ' C 4- 3 3 )

where q is the absorbed solar radiation (positive), q is the absorbed s a long-wave atmospheric radiation (positive), q^ is the long-wave back

radiation from the water body (negative), q is the heat lost by

evaporation (negative), and q is the heat lost by conduction (negative)

100

Solar Radiation.

qs » (1 - C.0071 C2)q0 , (4.34)

where

qQ a 2.044a + 0.1296a2 - 0.0019a3 + 0.0000076a4 , sin a = sin $ sin £ + cos $ cos £ cos h, <5 - -23.28 cos [2ir(d/36S) + 0.164],

c is the cloud cover in tenths of the sky, cf> is the latitude of the site, h is the hour angle of the sun, and d is the day of the year.

Long-Wave Atmospheric Radiation.

q = 1.66 X 10"9 $(T + 460)4 , (4.35) a cL

where 0 = A + Be ,

a

ea - exP t17'62 "

Twb = (0.655 + 0.36 R(Ta), T is the air temperature, °F, R is the relative humidity of the air, a and A, B are constants that depend on cloud cover c (see Table 2 in Ref. 100) .

Back Radiation.

qb = -1.668 x 10"9(Tws + 460)4 , (4.36)

where Tw<; is the surface water temperature, °F.

101

Evaporation Heat Loss.

% B -Ows " ea> f W • (4 '3?:>

where

eWS " e*P I17'62 " i ^ T O T ]

ea = exP [17.62 -

a and f(W) is a function for wind speed effect. There are a number of empirical correlations for f(W) which can be expressed as:

f(W) = a + bW , (4.38)

where W is wind speed in miles per hour. Table 4.1 summarizes three of those correlations.

Table 4.1. Coefficients for Various Wind Function Correlations to be Used in Equations 4.37 and 4.38

Correlation Coefficient a Coefficient b Lake Hafner 0 11.4 Lake Colorado City 0 16.8 Meyer 73 7.3

Heat Gain by Conduction.

qc = 0.00543 WP(Ta - Twg) , (4.39)

102

where P = 29.92

32.15E > exp 1545 (Ta + 4tI0f)l

E is the elevation of the site in feet, and W, T , and TWg are as defined before.

In conclusion, the input data required to compute the various heat exchanges between surface water and the atmosphere are:

1. cloud cover, c 2. latitude of the site, 3. hour angle of the sun, h (this parameter is not needed if daily

average calculations are desired) 4. elevation of the site, E 5. air temperature, 6. surface water temperature, T ^ 7. relative humidity or wet bulb temperature 8. wind speed 9. cloud cover function, 6 = A + Be 10. wind speed function, f(W) = a + bW The quantities q^g and q^T represent the energy convected to the

water body with the mass diffusion of substance k through the bottom and top surfaces, respectively. The discrete element formulation of those energy fluxes will be

» (4.40)

fouPi.j = ^ k T ^ . j ^ i J » (4.41)

103

wbare h k B and are the enthalpies of substance k coming from the

bottom and top surface, respectively. The nonconvective heat fluxes

from the bottom and top in a discrete element formulation will be

- - t W i J P i J - ( V i , j 3 ' C4.42J

where (hH)B and (hH)T are the film heat transfer coefficients from the

bottom and top, respectively, to the discrete element (i,j). (See dis-

cussion above on heat exchange with the atmosphere.)

4.5. Body Forces and Volumetric Heat

and Mass Generation

The conservation equations developed in Section 2.6 for a discrete

element include the effects of body forces (forces acting on the mass

itself rather than on its surfaces) and heat and mass generation or

decay per unit volume and time. In a two-dimensional model the gravita-

tional body forces have no effect except implicitly through the hydro-

static pressure (see Section 3.3). Other body forces do act, to various

degrees, in natural water bodies, but the most important is the Coriolis

force resulting from the rotation of the earth. This force is important

in large shallow water bodies and is the only body force considered in

the present model.

The Coriolis force is a function of the angular velocity of the

earth and the latitude of the site. For a two-dimensional model the -2 -2 88 101 Coriolis force per unit volume (ML T ) can be expressed as '

104

(fjx = pfiV , (4.44)

(fc)Y = - pS!U , . (4.45)

-4 where fi = 2u> sin iji, w is the angular velocity of the earth (0.73 x 10 radians/sec), and $ is the latitude of the site. It must be remembered that Eqs. 4.44 and 4.45 require that the coordinate system be rotating with the earth, that the XY plane be horizontal, and that the coordinate system be left-handed, with positve Z toward the center of the earth. The discrete element formulation of Eqs. 4.44 and 4.45 will be

( W i , i • "i./i.j v u • (4-47>

(fcY»iJ - - "i.A.j ui,i • «-4S>

The generation or decay of mass and of heat per unit volume and time are optional and are used for expressing chemical and thermal reactions. They can also be used to simulate intake and discharge operations, including thermal discharges, as will be discussed in Section 7.

4.6. Thermophysical Properties

The conservation equations developed in Section 2.6 include thermophysical properties which can be functions of temperature as well as substance concentrations. Although the model is not necessarily restricted to water, this is the material of interest in the present study. The following thermophysical properties are needed: P^CO,

105

the density of each substance k, as a function of temperature, and Cp^fT), tlie specific heat of each substance k as a function of tempera-ture. The total density and specific heat can then be calculated by

K P = I C.p. , (4.49)

k=l K K

c - I ckc . > p k pk

where C, is the concentration of substance k. k The formulation of the conservation equations also requires the

time derivatives of density and specific heat, which in turn must be expressed in terms of other derivatives as follows:

I F - If I f + X C3p/3Cv)OV3t) , (4.51) k= J

3C 3C ... K i f » + l=1 ( V 3 C i M 3 V 3 t 3 • (4.52)

The time derivatives of T and C^ are calculated in the corresponding conservation equations (see Section 2.6). The derivatives with respect to C^, using Eqs. 4.49 and 4.50, are

Op/aCj.) = pk , (4.53)

(3Cp/8Ck) - (Cp)k . (4.54)

106

The derivatives with respect to temperature must be derived from the corresponding functions Pk = f(T) and Cpk = f(T) and substituted in

K 3p/3T = I C. (3pk/3T) . (4.55)

k=l K K

K 3Cp/3T = J Ck(3Cpk/3T) . (4.56)

The demsity of saline water for the range of interest in this study can be expressed in practice as (Ref. 102)

p ~ 62.6651 + 46.013C - 0.00006238T2 , (4.58)

3 where p is the density lb/ft , C is the mass concentration of salt, and T is the temperature, °F„

Equation 4„S8 has a standard error of 0.1022 for the range

0.00 <_ C _< 0.1034 6 0 - T 1 2609F.

In order to bring Eq. 4.58 to a form which can be used in Eq. 4.49, the equation was broken into two parts:

Pk(salt) = 46.013 , (4.59)

p..(water) = (62.6651 - 0.00006238T2)/C, , (4.60) H. K

so that if Eq. 4.40 is used in the case of water and salt only, one gets

107

K 2 P = E c

kPk = Clpl * C2P2 = 62•6651 + 46'012Csalt " 0 0 0 0 6 2 3 8 1 » k=l which is Eq. 4.58.

2

As discussed in Section 2, the contributions of kinetic energy V /2 and potential energy gZ to the specific internal energy are negligible. Therefore, for each constituent we have

ek = CecPk + / C V k dT • C4-61)

hk " < V k * / <S}k d T ' (4'62)

0

where e^ and h^ are internal energy of formation and the enthalpy of formation for constituent k.

The internal energy and the enthalpy of the mixture must be calculated from

K I k=l

e = I Ckek , (4.63)

K h = I C.h, . (4.64)

k-1 K K

Expressions for ek and hk must be found in the literature for each constituent and combined by using Eqs. 4.63 and 4.64.

S. FORMULATION OF INITIAL AND BOUNDARY CONDITIONS

5.1. Initial Conditions

The mathematical formulation of a time-dependent model requires that all unknown values at certain time (t ) should be specified as a function of position. Such information must be either available or assumed. If the actual "history" of the case is not necessarily of interest, any set of initial conditions can be specified, and the problem must then be investigated for a sufficient length of time to let the existing external conditions dominate. In a case of an estuary, one may be interested in quasi-steady-state conditions. In this case, any set of initial conditions can be used, although a solution will be achieved sooner if those conditions are as close to the expected solution as possible. A quasi-steady state is assumed to be achieved, in an estuary case, when the results are practically repeating themselves every tidal cycle.

The discrate element formulation of the initial conditions can in general be expressed as

p i , j c t = V - f V i , j > C5-1)

where P is any property and Pq is the value of P at time tg, which can be a function of position.

108

109

5.2. General Discussion of Analytical and Numerical

(Half Points) Boundary Conditions

In a classical analytical formulation the boundary conditions can

be expressed by specifying the values of the unknowns themselves

(Dirichlet condition), the values of their derivatives (Neuman condition),

or the appropriate fluxes involved. For the numerical approach used in

this study, no partial differential equations have been derived, but

rather the conservation principles have been directly applied on each

discrete element. The method, therefore, does not call for boundary

conditions in the classical sense, which are applied in the process of

integrating the partial differential equations to retrieve back the

original integrated ones. Nevertheless, the discrete element formulation

of the conservation equations developed in Sections 2.5 to 2.8 does call

for half-point values, which are normally evaluated on an average basis,

as discussed in Section 2.9 for internal discrete elements. On the

boundaries, however, the elements do not have neighboring elements from

all sides, but rather some of their faces coincide with the physical

boundaries. The purpose of the "boundary conditions" from the discrete

element point of view is to allow the elimination of those half-point

values on the boundaries either in terms of specified values or in terms

of values of internal discrete elements. This section will discuss the

way this can be done for each type of physical boundary case on hand.

For the purpose of discussion, the classical analytical formulation of

the boundary conditions will be used, although the actual application of

110

those conditions will be only for deriving half-point value expressions.

The discussion here will be related to a discrete element with a single

side boundary, and the formulation for other situations can be similarly

derived. A corner element will be discussed later separately. Figure

5.1 shows such a discrete element with a physical boundary on its right-

hand side. The center of the element is located at (ib, j). The

boundary plane itself coincides with the half grid line, ib + 1/2. An

imaginary node is created outside of the boundary with an imaginary

grid line ib + 1 and with = AX^. The letter P will indicate any

one of the unknowns, that is, H, V, U, T, or C^. This imaginary element

is considered to have properties which are based on linear extrapolation

from the properties of its internal element counterpart, i.e.,

P.. . . = P., . + ^ l / H " ^ ^ AX., ; (5.2) ib+l,j ib,j 0.5 A X ^ lb v *

therefore,

Pib+l,j * 2Pib*l/2,j * Pib,j ' (5'3>

The half-point values in the center of each face of a discrete element

j 5.1), when this point falls on a boundary, will be

developed in Sections 5.4 to 5.7. For the boundary points in a corner

of a discrete element ( P i W / 2 > j + 1 / 2 o r pib+l/2,j-1/2 i n 5 > 1 ) a

linear averaging procedure is used based on its two neighboring face-

centered boundary points. In the sample shown in Fig. 5.1, this averaging

procedure can be expressed as:

Ill

J + V

AYi

-AXjb •

ib-!s, j + J j

2 V 't

0.5AXib—>

P gf-ib + Jj. j+jj

( i b . j )

I — 4 —

— j y k i-k^

i b + i . j

' I " ib-Jf. j-fc

PHYSICAL BOUNDARY-I I

Figure 5.1. A discrete element with a physical boundary on its right hand side.

112

AY. > = J p ib+l/2,j+l/2 AY. + AY. ib+l/2,j+l

AY AY. .

» (5.4) . * AY j + 1 ib+1/2,j '

AY. Pib+l/2,j-l/2 = AY., + AY. Pib+l/2,j-l

J J

AYj-l + AY^j + AY^ Pib+1/2,j ' C 5 , 5 )

The applicable boundary conditions, which will be considered in Sections

5.4 to 5.7, can be grouped into four types, which are discussed below.

5.3. Types of Boundary Conditions

Boundary condition type No. 1 represents the case where the value

of the unknown itself is specified, i.e.,

boundary * P b ^ ' <5-6>

This boundary condition is a Dirichlet condition type which specifies

the value of the unknown itself. The value can be a function of time

or constant, including zero. It is a most restricting specification,

and in order to be used, one must be sure that it does indeed reflect

the reality intended to be modeled. For discrete element formulation of

half-point values on the boundaries, this type of boundary condition is

simply defined by

113

Pib+1/2J ' (5*7>

where is a specified function of time for the property on the boundary surface.

Boundary condition type No. 2 represents the case where the first derivative of the unknown with respect to the direction perpendicular to the boundary surface is known, i.e.,

gp | 3n|boundary = Pbf°° ' (5,8)

This boundary condition is a Neuman condition type, and it specifies that the flux across the boundary is known. This is a definite specifi-cation of the boundary condition, although it is less restrictive than defining the value of the unknown itself. The specified flux can be a function of time or a constant (including zero). In order to use this type of condition, one must definitely know that it does reflect the reality intended to be modeled.

For discrete element formulation of half-point values on tht boundaries, this type of boundary condition is defined as

P i W i " "lb'j • • (S.W lb

Using Eq. 5.3 for Pib+1 j and rearranging, one gets

(AX)., Pib+l/2,j = Pib,j + Pbf C5'10)

114

The flux P^JJ of the pr vy at the boundary may, of course, also be

zero.

Boundary condition No. 3, which is equivalent to Newton's law of

cooling, represents a case where the conditions outside the modeled

boundaries rather than on the boundaries are known. The flux between

a boundary and its external surroundings is normally empirically corre-

lated as

Pbf = - V P b - pbo> ' ( 5 ' n )

where is the flux of the property across the boundary surface to the

surroundings, P^ is the value of the property at the boundary surface,

is the value of the property outside of the boundary, and h^ is the

film transfer coefficient, which defines the reciprocal of the resistance

to the flux of the property. On the basis of Eq. 5.11, if the flux Pfe£ and the outside value, of the property are known, the value at the

boundary surface, P^, can be evaluated. Here again, when using this type

of boundary condition, one must be sure that the value of the property

outside the boundaries is indeed independently known and that the flux

itself is indeed a forcing reality which must be satisfied by the

mathematical model.

Expressing this condition for discrete element half-point values and

rearranging gives

Pib+l/2,j - Pib,j + ^ V P b f • (5-12>

where is the flux through the boundary surface into the element and

1/h, is the "resistance" to this flux.

115

Boundary condition type No. 4 represents the case where the second

derivative of the unknown in the direction perpendicular to the boundary

surface equals zero, i.e.,

In (H) [boundary = 0 ' (5,135

or

3P W boundary = c o n s t a n t (unknown) . (5.14)

This type of boundary can be interpreted as specifying only that

the flux across the boundary is not a function of the directions perpen-

dicular to the boundary surface. It is a most unrestrictive condition

and practically leaves the condition unspecified in a second-order

differential equation. From an analytical formulation point of view,

there is no justification for this type of condition. The closest type

of analytical boundary condition that may have such unrestrictive

characteristics is the condition of specified ambient value at infinity.

However, such a condition is not available for finite difference

formulation, since an infinite space dimension is not realistically

possible. Nevertheless, the half-point value on the boundary must always

be specified, if not in terms of known values, at least in terms of

values of adjacent internal elements. This is the only purpose of

boundary condition type No. 4. Equation 5.14 can be expressed for dis-

crete element formulation as:

Pib+l/2,j " Pib-l/2,j _ Pib+l,j ' Pib,j r. AX AX ' la.iaj ib a*ib

116

Using Eq. 5.3 for P i b + 1 j and the half-point relationship for P ^ . j ^ J

given by Eq. 2.81, one gets, after reordering terras and spine algebraic

manipulation, that the property on the boundary itself, c a n b e

expressed in terms of known internal values as:

P = P + ib+1/2, j *ib,j AX., ib

AX., + AX., . lb ib-1 (pib,j - pib-lj3 •

A summary of the four types of boundary conditions and their

jphysical meaning as discussed above is given in Table 5.1. The classical

analytical formulation is used only for clarity, but, as said before, the

conditions are directly used for formulating half-point values of the

discrete elements.

In the next sections, various situations in reality that are of

interest in the present study will be discussed. The types of boundary

conditions to be used in each case for each unknown will also be

discussed.

5.4. Solid Wall, No-Slip, and Free-Slip Conditions

Any fluid that has a finite viscosity will have at the point of

contact with a solid boundary the same velocity as the boundary itself.

This means that both the relative normal and tangential velocities of

the fluid with respect to the solid boundaries must vanish at the points

of contact. Those are known as the ,;no slip" conditions, which are in

principle always correct and can be expressed as

117

Table 5.1. Types of Boundary Conditions

Boundary Condition Type

Mathematical Evaluation at the Boundary Surface Physical Meaning

1 P = PbCt) Property itself on the boundary surface is a known function of time which can also be constant or zero.

2 3P/3n a Pv£(t) Flux of property through boundary surface is a known function of time, which may also be constant or zero.

3 P 3 Pbo * tpbf/hb^ Flux of property on boundary sur-face and value of property itself outside of boundaries are known.

4 (a/3n)/(3P/3n) = 0 Flux of property through open boundary is undisturbed. A very unrestrictive boundary condition.

118

v R = 0 (boundary condition type No. 1) , (5.17)

vt = 0 (boundary condition type No. 1), at the boundary.

However, there are many situations under which the "free slip"

conditions are assumed to exist. In this case the relative normal

velocity vanishes at the solid surface (assuming no permeability), but

the tangential velocity is unaffected by it. This condition can be

expressed as follows. At the boundary,

v n = 0 (boundary condition type No. 1) , (5.18)

(3vt)/3n = 0 (boundary condition type No. 2).

Some examples of situations under which the "free slip" conditions

can be assumed are

1. ideal "nonviscous" fluid,

2. boundary represents an ideally smooth surface,

3. boundary represents a symmetry line,

4. zone of interest far from the physical boundaries,

5. in numerical solutions where the grid intervals are very large

compared with the thickness of the boundary layer.

A third possibility is that the tangential velocity will be left

undefined by using boundary condition type No. 4. In this way the

velocity is left to take its value under the constraints of the conserva-

tion equations themselves.

The boundary conditions to be imposed on water elevation, temperature,

and substance mass concentrations will depend again on the best boundary

condition type which can be chosen to reflect an existing reality. For

119

the case involving natural water bodies, it will be most common to use

boundary condition type No. 2 (flux assumed to be zero) for temperature

and mass concentration and boundary condition type No. 4 for water

elevation (since it is desired to allow the water elevation at the

boundary to find its position on the basis of the continuity equation).

5.5. Open Channel, Flow In

In the case of flow coming into the controlled volume through the

open channel, commonly all the unknowns are specified as boundary con-

dition type No. 1 (values specified based on the inlet conditions)

except water elevation, which is specified as boundary condition type

No. 4. Other situations are, of course, possible, and the appropriate

boundary conditions should then be used (see Table S.2).

5.6. Open Channel, Flow Out

In the case of flow leaving the control volume through an open

channel, all the fluxes are assumed to stay constant along the flow by

using boundary condition type No. 4. The values at the boundaries are

then functions of their corresponding internal values. The water level,

however, is specified by using boundary condition type No. 1. The

flow out can also be specified, but then the water level should be left

unspecified by using boundary condition type No. 4. Other situations are

possible, and the appropriate boundary conditions should be used on a

case-by-case basis.

120

Table 5.2. Some Examples of Possible Boundary Conditions and Boundary Condition Types to be Used for

Each Unknown (See Table 5.1)

Unknown Water Surface Normal Tangential Transported Property Elevation, H Velocity, Vp Velocity, Vj. Properties, T, C^

Solid wall, "no slip" condition

Solid wall, "free slip" conditions

1, V = 0 n

V = 0 n

1. v t - 0

2, 3P/3n = 0

2 4 2, 3V 3P/3n - 0 Iff"

Open channel, flow in (controlled by flow volume)

V n = (Vn)b(t) Vt P = Pbci)

Open channel, flow in (controlled by water level differential)

Vn " hCHfa-H) Vt ' Q r j b - 0 P = Pb(i)

Open channel, flow out

1 or 4 4 or 1

Flow out over a dam

Oceanic open-ing of an estuary (tidal)

Open channel, flow in (con-trolled by water level)

1, H = Hb

1,

H = H^t)

1,

4

4 Flood Ebb 4; 1,

P = pb(t)

1, P = Pb(t)

Note: Type 1

Type 2

Type 3

P - Pb(t) 3P/3n = Pb£(t).

P - Pbo + ^Pbf/hb3 2 2 Type 4: 3P/3n = const (or 3 P/3n = 0),

121

5.7. Ocean Opening in an Estuary

An estuary opening to the ocean is a special case and a very

complicated one. The dynamics in the estuary are mostly controlled by

the tidal movements in the ocean. In principle the zone being simulated

should include a large portion of the ocean itself, so that the con-

ditions at the model boundaries will be those of the unaffected ocean.

Such an attempt will, however, create major practical difficulties

because of the complicated conditions existing at the ocean itself. It

seems that a reasonable solution would be to limit the extent of an

estuary model to some location close to the ocean where conditions are

routinely monitored. Such a location is not always available, and the

issue must be settled on a case-by-case basis.

In many cases there are published data on the water elevation at

the estuary mouth as a function of time which can be used for specifying

water elevation at the boundary as boundary condition type No. 1. The

velocities, in this case, should be specified as boundary condition

type No. 4, so that their values will be established from internal

values which are calculated from the conservation equations. The trans-

ported values (temperature and substance mass concentrations) must also

be specified as boundary condition type No. 4 when the flow is leaving

the estuary. However, when the flow is reversed and is penetrating

back from the ocean into the estuary, the conditions are not well

defined. A large zone of the ocean itself was affected by dilution and

mixing with the discharge from the estuary at the previous ebb period;

and, therefore, one cannot specify the inlet conditions during the tide

122

period as being the same as for the unaffected ocean itself. This problem

cannot be solved correctly without analyzing av least part of the ocean

close to the estuary discharge point. A reasonable estimate may be to use

specified conditions (boundary condition type No. 1) for temperature and

mass concentration when flow is coming in (ebb period) and to express

their values as functions of either time or velocities. One possibility

of such a function, but speculative in nature, may be to assume an

exponential decay of the property with time immediately after the stage

of low slack water. The simplest possibility, although not accurate, is

to assume that the property transported into the estuary during the flood

period is constant and identical to the value in the ocean far from the

boundary point. Other possibilities exist, and much is left here to the

analyst's judgment of the specific case on hand.

5.8. Summary of Boundary Conditions

Table 5.2 gives a summary of various examples of interest in this

study. The boundary condition type suggested for each unknown in each

case is indicated. It must be remembered that this is not a complete

list of possible cases, nor are the boundary condition types recommended

the only ones that can be used for these cases. Hie boundary conditions

are the best chance for the analyst to integrate "reality" into his

mathematical model, and much professional judgment is required for taking

full advantage of this opportunity.

6. TOE NUMERICAL SOLUTION OF EQUATIONS AND

STABILITY ANALYSIS

The discrete element forms of the conservation equations have been

developed in Sections 2.5 to 2.8. The compatibility of this formulation

with the classical differential equations will be discussed in this

section, as well as the numerical solution of those equations and their

stability.

6.1. The Reduction of the Discrete Element Forms of the

Conservation Equations to Their

Classical Differential Form

As discussed in Section 2.2, the discrete element forms of the

conservation equations were derived directly from the corresponding con-

servation principles without taking the limiting procedure for deriving

the classical form of partial differential equations. This raises the

question of whether these equations will reduce to the classical

differential equations if the limits AX. . -*• 0, AY. . 0 are indeed

applied. This can be easily shown to be the case.

6.1.1. The Total Mass Conservation Equation

The discrete element form of this equation is given by Eq. 2.38.

Substituting backward Eq. 2.37 into Eq. 2.38, taking the limits AX. . + 0 , 1»J AY. . •*• 0, dropping the i, j notation of the properties to represent J local values, and rearranging gives

123

124

ft (PH) • ly (Hgx) + -L- Hgy) = gB + gT + pGH ; (6.1)

replacing g^ and gy by pU and pV, respectively,

k (PH) • (PHU) • (pHV) - gB + gy + pGH , 3X 3Y B (6.2)

which is the classical partial differential equation for the conservative

form of the total mass conservation in two space dimensions and variable

water depth. The right-hand side of Eq. 6.2 will, of course, be zero if

no external contributions are considered.

6.1.2. The Mass Conservation Equation for Constituent k

The discrete element form of the mass conservation equation for a

constituent k is given by Eq. 2.50. Substituting backward Eq. 2.49 into

Eq. 2.50, taking the limits AX. . 0, AY. . •*• 0, dropping the i, j

notation of the properties to represent local values, and rearranging

gives

It + h H C% Ck + gkX> + W H<gYCk + gkY>

= gBCkB + gkB + gTCkT + gkT + ^ k ' (6.3)

Substituting pU and pV for gx and gy and also p^ for pC , gives

It C<>kH> + h H<pkU + gkX> + W H(pkV + gkY^

s + gkB + gTCkT + gkT + pkHCk ' (6.4)

125


form of the mass conservation of constituent k in two space dimensions

and variable water depth. Equation 6.4 can be rearranged to a more

familiar form by moving the fluxes g k x and g k Y to the right side. If

those fluxes are considered to obey Fick's law, Eq. 6.4 can be rearranged

to

•iLcpHCk) • ^CpHUCk) • jyCpHVCfc)

a ack 3 3Ck = 3*cpDMk -BE5 + WcpDMk -373

+ gBCkB + gkB + gTCkT + gkT + pkHCk ' (6.5)

which may be a more familiar version.

6.1.3. Energy Conservation Equation

The discrete element form of the energy conservation equation is

given by Eq. 2.61. Substituting backward Eq. 2.60 into Eq. 2.61, taking

the limits AX. . ->-0, AY. 4 ->-0, dropping the i, j notation of the

properties to represent local values and rearranging gives:

+ w gxh + q x + K -J

i x ,kXJ 9Y gyh • qY • J q k y k=l

K NK = gBhB * %* X qkB + gThT * X qkT k=l k=l

q + K I k=l ttJ v'k H (6 .6 )

126

Substituting g x = pU, gy = pV gives:

f^pHe) • 3 "5x |H[ PUH + Q X • J I Q J J • |y H[pVh • qy + J ^ qkY)

K K

= SBhB • qB • I qkB + gThT + q r * I 1kT k=l k=l

K 4 + 1 (q

k=l H , (6.7)


form of the energy conservation in two space dimensions, variable water

depth, and multisubstance mixturet Equation 6.7 can be reduced to a

more familiar form if applied to a single constituent and by moving the

fluxes qx and qy to the right-hand side of the equation. If those fluxes

are also considered to be by diffusion only, Eq. 6.7 can be rearranged by

using the effective thermal conductivity k^ to give

^(PHC T) + f^CHpC UT) - (HpC VT) = f ^ fl) • fe ^ fl)

+ gghg + qB + gThT + q T + qyH , (6.8)

which may be a more familiar form.

6.1.4. The Momentum Conservation Equations

The discrete element form of the momentum equations in the X and Y

directions are given by Eqs. 2.75 and 2.76, respectively. Substituting

127

backward Eq. 2.74 into Eq. 2.75, taking the limits AX. . "»0, AY. . 0,

dropping the i, j notation of the properties to represent local valuos,

replacing g x and gy by pU and pV, respectively, and rearranging gives:

1-CpHU) • f^pHUU) • (pHVU) = lyCHoxx) + f^H

+ gBUB + °BX + STUT * ffTX + fbXH • (6'9)


form of the momentum equation in the X direction in two space dimensions

and variable water depth. A similar reduction can be accomplished for the

momentum equation in the Y direction.

The discrete element formulation is then competent with the classical

partial differential form but is not equivalent to it. The Taylor expan-

sion series normally used to get the finite difference equations from

the corresponding partial differential equations are not needed for

deriving the discrete element form of the conservation principles.

6.2. The Numerical Solution of the

Governing Equations

The system of equations presented by Eqs. 2.38, 2.50. 2.61, 2.75,

and 2.76 for the conservation of mass, momentum, and energy constitute

a set of nonlinear first-order simultaneous ordinary differential

equations with respect to time of the form

^ J i - FCa)[t, P^t), P2(t), ... P(N)(t)l (6.10)

128

with the initial conditions

P(J,)(t0) - P QW , (6.11)

where & » 1, 2, ... t N.

In order for this initial value problem to have a solution which is

both unique and continuous and also satisfies the initial conditions, the ful

functions F^ ' must have no singular points and may have only a finite

number of finite discontinuities in the neighborhood of the initial

point Fg, tQ. The system of equations on hand will satisfy these con-

ditions if the forcing functions involved (bottom, top, and volumetric

conditions) satisfy these conditions.

The conservation equations that were developed in Section 2.6 using

the discrete element approach do not involve a solution of nonlinear

second-order simultaneous partial differential equations with respect to

space and time but rather a set of ordinary differential equations with

respect to time which can be solved by numerical integration methods.

Because of the complexity of the problem, the number of unknowns and

equations involved, the complex and nonlinear boundary conditions which

must be handled, an explicit method of a matching computational technique

starting from a known set of initial conditions seems to be preferable.

Such a scheme will, of course, have stability limitations on the size of

time step used. Implicit schemes, which are known to be in most cases

unconditionally stable, may have some advantage over explicit, schemes

from the stability point of view. However, for such a complex system

as the one discussed here, the computational time which will be required

129

to achieve convergence of the matrix solution within each time step may

be very large, and, therefore, it is definitely not certain that the

choice of a larger time step will result in a net gain of computing

time. In addition, the stability of implicit methods is not actually

guaranteed for nonlinear simultaneous partial differential equations

with nonlinear boundary conditions, since there exists no rigorous

mathematical proof for such systems.

The discrete element system of Eqs. 2.38, 2.50, 2.61, 2.75, and

2.76 with the proper fluxes and volumetric generation have been inte-

grated by a forward marching technique. Both the simple Euler method

for one-time step integration and the more accurate modified fourth-

order Runge-Kutta method with Gill coefficients have been used. The

Runge-Kutta method is considerably more accurate than the Euler method

but requires about four times as much computing time for each complete

time step. One can also expect that the Runge-Kutta method will have

better stability characteristics compared with the Euler method. The

optimal trade-off between size of time step and computing time required

for each will depend on the case at hand. It may be desirable in many

cases to use the Eulerian method for one part of the problem and then

when closer to steady state or quasi steady state, to switch to the

Runge-Kutta method. This capability was included in the computer pro-

gram described in Section 7.

130

6.3. The Donor Cell Differencing Method

The donor cell differencing method has been used in this study

because of its improved stability effects on the convective terms of the 78 conservation equations. The method is known under various names

(upwind differencing, skew differencing, upstream differencing, and 69 others). In the Los Alamos FLIC method it is called the donor cell

78 method and by Roache the second upwind differencing method. It was 103

also used by Kurzrock for two-dimensional viscous compressible flow

and by many others with good success. Ths method is based on the

physical consideration that the property transported into a cell through

its edge should be always that of the cell "upstream" of it which

supplies the transported property, that is, of the "donor cell."

Therefore, the half-point values used in Section 2.9 and expressed

by Eqs. 2.79 and 2.86 will be altered for the density and the transport

properties as follows (see Fig. 2.2, page 31):

P. - . = P. . for U. , ,„ . > 0 1+1/2,3 1,3 i+l/2,g

" Pi+1,3 f 0 r Ui+l/2,j < 0

P. . y, . = P. . for U. , . < 0 1-1/2,3 i,j 1-1/2,3

" Pi-l,j £ 0 r Ui-1/2J " 0

Pi,3+1/2 " Pi,j f° r Vi,3*1/2 > 0

Pi,i+1 £ o r Vi,j+1/2 < ° <6-14>

131

= P. . for V i.J i.i-1/2 < 0

= P; for V i,j-l/2 > 0 (6.15)

where P denotes either density or any one of the transport properties.

For the cuse of zero velocity, no alteration of the usual equations

(Eqs. 2.79 to 2.86) is needed. It must be remembered that the donor

cell values are used only for the density and the transport properties

U, V, T, C^, and only in the convective terms of the conservation

equations. This means that in the case of velocities appearing in the

convective terms of the momentum equations, the velocities used for g^

and gy will not be donor cell values, since here the velocities are not

the transported properties but the transporting ones. The second

velocity appearing in those convective terms is a transported property

and will therefore be of the donor cell type.

The numerical solution employed for solving the governing equations

was discussed in Section 6.2. Any numerical solution will differ from

its exact counterpart because of both transaction errors (approximate

presentation of the exact equations) and round-off errors (computational

round-off errors). The difference between the computed value and its

exact counterpart can be defined as

6.4. Stability Analysis of the Numerical Solution

(6.16)

132

where P. . is the actual computed value of any unknown (H, U, V, T, C.)

at a discrete element i, j and P\ ^ is its exact counterpart.

In ordar to prevent computational instability, the error ^ must

die out or at least not grow unbounded. Therefore, one must require

that for any two successive steps

6. .(t + At) 6. . rt) < 1 . (6.17)

Each one of the discrete element conservation equations developed

in Sections 2.5 to 2.8 can be expressed in general in the form

3t ¥ L s Fi,j = Vl/2,jPi-l/2,j + î+1/2,jPi+l/2,j

+ î,j-l/2Pi,j-1/2 + î,j+l/2Pi,j+1/2

where p" indicates the value of any one of the unknowns (H, U, V, T, C^)

and the subscript indicates the location at which P is evaluated, ij;

indicates the corresponding coefficient of F in the proper location,

and »JJg is the term in Eq. 6.18 that is independent of F.

The stability analysis in this section will be developed for an

explicit single time step integration method like the classical Euler-

Cauchy explicit method. The stability criteria developed for this

method of solution should be sufficient for the stable solution of the

more accurate multistep integration method by Runge-Kutta with Gill

133

coefficients. It will also be assumed, for the purpose of the present

stability analysis, that the various equations are linear and noncoupled.

This is not an entirely correct assumption for the set of equations

developed in the present study. However, stability analysis for a set

of several coupled nonlinear equations does not exist and does not seem

to be possible at the present time. The stability conditions cfevelsped 134 1C5 here will be based cn the discrete perturbation stability analysis, *

which, although not as rigorous as the Von Neuman*^ and Hirt^^ analyses, 78

was successful in predicting the same criteria.

In the discrete perturbation stability analysis, it is assumed that

up to a certain time t the computed value P. .is exact everywhere and no error 6. . exists. Then a certain arbitrary error 6. . is induced l»j it] at only one arbitrary discrete element (i, j), so that

(6.19)

but

where the subscript i±, j± indicates any location other than i, j

itself. From Eq. 6.18 one gets

(6.20)

(6.21)

Substituting Eq. 6.19 into Eq. 6.21,

134

3P. . 36. . (6.22)

or

3 6 . . (6.23)

The stability condition expressed in Eq. 6.17 gives then

6. .(t • At) 36. .

* I T 1 1 V T i»3

i-2. At

or

At < 6. .

I > 3

WT7 i.J

1 1 »

(6.24)

(6.25)

From Eq. 6.18 one gets

Sr. . = F. . - F. . • , . (P. . . - P. .) i»J 1-1/2,1-1/2,j 1-1/2,y

* h*l/2,j (pi+l/2,j " pi+l/2,j5

* *i,j-l/2CPi,j-l/2 " Pi,j-l/2)

+ *i,j+l/2(Pi,j+l/2 " Pi,j+l/2)

+ . .(P. . - P. .) . i.J i»3 i»J (6.26)

However, based on the discrete perturbation error analysis, the

difference between computed and exact values is zero everywhere except

at i, j, where it equals $. .. Therefore, Eq. 6.26 reduces to i»3

135

(6F). . = y. .6. . , v Ji,j yi,2 1,3 *

or

T f f j f r - r r - C 6 - 2 7 )

Substituting Eq. 6.27 into the stability condition m Eq. 6.25 gives the desired stability condition

At < (6.28)

where .is the coefficient of P. .in the right-hand side of Eq. 6.18.

The separate stability criteria for each one of the discrete element

conservation equations will be based on Eq. 6.28, where the proper . J

is the sum of all the coefficients of the terms in which P. .is l» 3

involved.

6.4.1. Stability Criteria for Calculating Temperature

The basic discrete element equation to be solved is given by

Eq. 2.61, in which Eqs. 3.59 to 3.62 must be substituted for the non-

convective heat fluxes q^ and qy and Eqs. 4.42 and 4.43 for the bottom

and top heat fluxes q^ and q ,, respectively. Performing this substitu-

tion and then collecting all the coefficients of T. ., one gets

î,j^temp H. i-1/2,jPi-l/2,jUi-l/2,j _ Hi+l/2,jpi+l/2,jUi+l/2,j

pi,jHi,j *Xi AXi

+ Hi,j-I/2pi,j-l/2Vi,j-1/2 Hi,j+l/2pi,j+l/2Vi,j+l/2

AY. " AY. 3 3

136

Hi-l/2,j f Pi-1/2J ^ 1 - 1 / 2 ^ 1 " AX. [" O.S(AX. + AX.,) J

AY. J

AY.

+ pi+l/2>j(PHX)i+l/2>j "OTscax, • AXi+1)

px, j-1/2 (PHY:)itj-l/2l " O.&CAY. + AYj_J) J

«. Pi.j+1/2(PHY)i.j+l/2l 0.5(AY. + AY.+1) J

^ i j + T r p t 1 * fePi.j+ cc ] .

* H. ./5G i.r (6.29)

where q^ is the total heat flux to the atmosphere and can be calculated

from Eqs. 4.33 to 4.39. As an alternative, one can replace

J by K , T. .

where K is the heat exchange coefficient based on the equilibrium

temperature concept (Eq. 4.31). Substituting Eq. 6.29 into Eq. 6.28

and rearranging terms gives the stability condition for calculating

temperature as:

137

pi-l/2,j P- •

H i-l/2J H.

fUi-l/2,j + 2CDHX)i-l/2,j AXj " AXi(AXi + AXi_1J

i , j - l / 2

H-i+l/2,j H. . i.J

H. >3-1/2 H. .

X W 2

p. .H. .

f " ^ 1 / 2 , 3 , 2CPHX3i*l/2.j } [' AX. AX.(AX. + AXi+1)J

(Vi,3-l/2 , 2(DHY)i,j-1/2 /I { AY. AY. (AYj + A Y . ^ j J

f Vi,3 + l/2 , 2 ( V i , j + l / 2 I 1" AY. AY.(AY. i AYj+1)J

(hHR). . (qT)4 . + T T T ^ + ^ i j + (c) .i. • ,J K p i.j tJ p ifj.

H. i . W 2

H. .

(6.30)

The donor cell method discussed in Section 6.3 changes the stability

criteria of Eq. 6.30. Based on this method, the half values Pi+l/2 j +1/2 t*ie convective terms are replaced by center values of

the "donor cells" (see Section 6.3). When the values P..,,- .,, are ' i±1/2,3±1/2 replaced by P. ., the corresponding terms in Eq. 6.30 drop out. When

the values j+1/2 a r e rePlaceci by Pi+i j+i> there is no effect on

the stability criteria. Therefore, for the donor cell method, the con-

vective parts of the criteria will be effected as follows: Ui-l/2,3 > Pi-l/2,j = Pi-l,j e £ £ e C t (Ui-l/2,j > °)J

Ui-l/2 j < Pi-l/2 j = Pi j corresPondi«g term drops;

138

Ui+l/2 j < Pi+i/2 j ~ Pi j c o r r e sP o n d i ng t e r m drops;

Ui+l/2,j « Pi+l/2,j " Pi+l,j e f £ e C t (Ui+l/2,j < Vi,j-1/2 > Pi,j-1/2 " Pi,j-1 e f £ e C t <Vi,j-1/2 "

-5 I /O < a 1 n * a* corresponding term drops;

V. j + 1/ 2 > Pi j+1/2 B Pi j corresponding term drops;

V. . , < 0, P. = P. . . no effec- (V. . . /0 < 0). i,j+l/2 ' i,j+l/2 1,3+1 x,3+l/2

To be on the conservative side, one can leave all the convective

terms and always use the absolute value of the velocities to get:

( A t C R > T . t . 1 l /

Pi-l/2,j "i-1/2,j] H. .

1/2,3 AX.

2(DHX)i-l/2,j ) AX.cax. + AX;;^]

Pi+1/2,j i»3

H. i+1/2,j H. . 1,3

Pi.3-l/2 i »3

i,j+l/2 x»3 J

fH. i . j + 1 / 2 H. i»3

|Ui+l/2,ji + 2 ( V i + l / 2 , j 1

AX. " AX.fAX^^ + AX.^J

•v H i , j - 1 / 2

• H. .

J

f|Vitj-l/2l ^ i , j - 1 / 2 ) . AYj AY. (AY. + AY.^J

fiVitj+l/2l , 2^DHY)itj+1/2 I Y. Y.( Y. + Y T ~ T V 3 3 3 3+1

p . .H. . 1 , 3 1 , 3

(gB>isj * C V i , j + ( c ) h i . . P i,3 ,J P 1,3 1,3

(6.31)

139

Equation 6.31 establishes, then, a time step limit to avoid numerical

instability at discrete element i, j when calculating temperature. How-

ever, the actual time step to be used in the model will depend on the

time step criteria for the rest of the unknowns, which will be developed

next.

6.4.2. Stability Criteria for Calculating Constituent

Concentration C,

The basic discrete element equation to be solved is given by Eq.

2.50, in which Eqs. 3.75 to 3.78 must be substituted for the ncnconvective

mass fluxes g^ and gy and Eqs. 4.25 and 4.26 for the bottom and top mass

fluxes g^g and g^, respectively. Performing this substitution as in

the case of temperature gives an expression for stability criteria

similar to Eq. 6.31 except that some heat quantities are replaced by the

corresponding mass quantities. The result is:

^ ' ( V i j 1 "

P-kl/ld

1»3

H. 1-1/2,3 H.

,U. =JZLiL AX. l 2 ( IWi-l/2

AX.. (AX. zlIhLJ T i x r p - j

Pi+l/2,j "i+1/2,j Pi.3

Pi,3-1/2

H. . i>3

"i.j-l/^ . Pi.3

H. .

riui+i/2,ji , 2 (Vi+i/2.j i 1 AX. AX.(AX. + AX^pJ

1,3-1/2] AY. 3

2(DMY)i,j-1/2 1 AY. (AY. + A Y . ^ J

i,j,t-l/2 "i,3+1/2 f|Vi,j->-l/2l 2(DMY)i,j + l/2 ] p. . H. . AY. AY.(AY. + AY. .) I i»3 3 3 3 3+l

140

1>J x»3

(6.32)

6.4.3. Stability Criteria for Calculating Velocities

The basic discrete element equations to be solved are given by

Eqs. 2.75 and 2.76, in which Eqs. 3.42 to 3.50 must be substituted for

the stresses o^y, o y, and o^, Eqs. 4.11 and 4.12 for the bottom shear

stresses o^^ and c^, and Eqs. 4.19 and 4.20 for the wind shear stresses

cr^ and respectively. Performing this substitution and then

evaluating a. . as for temperature and mass concentration C. gives an 1,3 K

expression for stability criteria similar to Eqs. 6.31 and 6.32 except

that momentum quantities are used. The result for the U velocity is

C A t C R \ j i 1 7 fPi-l/2,j Hi-l/2,j

P i J H. . x>3 . f|Ui-l/2,j[ , 4 ( IWi-l/2,j 1 I AX. AX.(AX. + AX. .) l l i 1.-1 '

Pi+l/2,j Hi+l/2,j|f Pi.3 H. . 1

n U W 2 , j l + 4CDmX3i+l/2,j ]

. AX, AX(AX. + AX.+1)J

Pi i,j-1/2 P. . i.J

H. i,j-1/2 H. . 1,3 (J

V. i»j-1/21 + 2(DmY)i,j-l/2 AY.

3 AY.(AY. + AY. ,) 3 3 3-1

P. i,j+1/2 Pi,j

Hi,j+1/2 H. . i»3

rivi,j+i/2i. 2«W»i AY AY. 3

mYî,j+1/2 } .(AY. + AY. .)l 3 3 3+l

141

i ! < V i i + \<**h,i - - u r f 1 +

1,3 i,3 I ,J 1,3 'Jj ' ( 6 . 3 3 )

and the result for the V velocity is:

1,3 1-1/2,j

I i»3 "i-1/2,jlf|Ui-l/2,j| + 2CD

mx)j-l/2,j " AX. AXi(AXi + AXi_1). H. . i>3

pi+l/2,j 1,3

Pi,j-l/2 1,3

P, i,3+1/2 Pi,3

p. .H. . 1,3 1,3

H i+1/2,j H. . I 1,3

Hi,j-l/2

flUi+l/2,j[ , 2CDmX)i+l/2,j ] [ AX. AX. (AX. + AX.^J

H. . v 1,3 if i.j-l/21 , 4(DmY)i,j-l/2 W J AY.(AY. + AY. 3 3 3-1/2 ;

H. 1,3+1/2 H. . i,3

(gB>i,j

flVitj+l/2l , 4 ( IWi,3+1/2 AY3 AY.(AY. + AY.. , . , 7 3. 3 3 + 1/2

BY x»3 + fa 1 V, , gT i, j 1,3 (6.34)

where (a_v). . and (aBV). . can be calculated from Eqs. 4.11 to 4.13 to BX'1,3 ^ BY'1,3 n

get:

<°BX>l.j ' V u g°i,inj.i V"i . j 2 - Vx,j2 (6

Ji,j vi,j 2.208H. . 1 / 3 35)

2.208H. . 1,3

6.4.4. Stability Criteria for Calculating Water Elevation H

The basic discrete element equation to be solved is given by Eq.

2.38. Collecting the coefficients of H. ., one gets: 1,3

142

o. . = i>3 ij 9pi,j 3t ( 6 . 3 6 )

Substituting Eq. 6.29 into Eq. 6.28 and rearranging terms gives the

stability criterion for calculating H as

dp. . l»3 3t ( 6 . 3 7 )

The term 3p/3t is usually small or nonexisting. This will mean

that the time step stability limit for calculating H is very large.

However, combining Eqs. 6.23 and 6.27 gives

35. . 3t yi,j i,j ( 6 . 3 8 )

If . is zero, this will mean that any induced error 6. . will 3..J 3 1,3 not grow but will also not die out. Using the donor cell method for H

and replacing the half-point values by the corresponding center-point

values (see Section 6.4.1) in Eq. 2.38 changes tf. . by bringing in new 1 »3 terms involving P. .. Assuming, on the conservative side, that the 1 >3 velocity is always in the direction which requires P. . to be used, one i »3 gets:

O. i_ i,3 elev p,; • 3pi»j + Pi-l/2,jlVi-l/2,j' + pi+l/2,jlVi+l/2,jl "It AX. AX. l

, Pi,j-l/2'Vi,j-l/2< , pi,j+l/2iVi,j+I/2l' AY. AYj 3

( 6 . 3 9 )

143

Substituting Eq. 6.39 into Eq. 6.38 and rearranging terms gives the

stability criterion for calculating water elevation with the donor cell

method as:

<AtCR>H. • i 1 7 °i-l/2,j lUi-l/2,jl , Pi+l/2,j •Ui»l/2.jl p. . J X. i pi i I i»J J

X. 1

i,j-1/2 P. • AY. J

Pi,j+l/2 'VU+l/2i AY. J

3p. . lii at (6.40)

6.4.5. Total Time Step Limit Approximation

The final time step limit to avoid numerical instabilities will be

the smallest of (AtCR)T. (At£R) ( A t ^ , (AtCR)y, and (AtCR)H (given iv

by Eqs. 6.31, 6,32, 6.33, 6.34, and 6.40, respectively) when calculated

for each one of the discrete elements of i, j.

For a more simplified, but somewhat more conservative, expression

which combines all four conditions for all the elements, one can assume

the maximum or minimum values of the parameters which will give the

smallest time step. Such an expression will have the form

C A W t o t a l i U H max H . m m

max m m

max max AX . min AY . m m

+ 8 <D A a x , C V m a x

(AX)' m m m r m m

C*B>max + ^ m a x + L max p . H . m m m m

(6.41)

144

Snax i s t h e l a r? e s t tlie quantities

f HB r

qT + <rr

. P. max . p . • ^ J C B W + ^ k A a x ' ( " W W » max B' 'max

where * « - °B

» ' °BX °BY

V max " U max " V k 4 » <

S W ' m a x V ^ 2

max max max 2.208H . m m

1/3

(6.42)

and q^/T can be calculated from Eqs. 4.33 to 4.39 or replaced by the

heat exchange coefficient K.

7. APPLICATION OF THE MODEL AND ITS COMPUTER PROGRAM

The main purpose of this study is to solve for the water elevation,

temperature, and mass concentrations of all constituents k dissolved in

the water as functions of time and two horizontal space dimensions, X

and Y. As explained in Section 6.2, the Euler method and the modified

fourth-order Runge-Kutta formula with Gill coefficients have been

chosen for simultaneously integrating the equations expressing the time

derivatives of all the unknowns explicitly as function of known values

from the previous time step. A computer program was developed to handle

those solutions and to facilitate simulation of various complex

situations occurring in natural water bodies. However, when a computer

program of the type produced in this study is available, there always t

exists the risk that it will be used to model situations for which it is

not properly designed. It is important to recognize the capabilities of

the program as well as its limitations. These capabilities and

limitations will be described in this chapter to help the user to decide

if the program is applicable to a specific situation at hand. The

structure of the program is such that many modifications and additional

capabilities can be incorporated with no major effort. In some situations,

however, it may be uneconomical to try to modify the program to respond

to specific requirements. Some other available programs may be more

readily used for the case.

145

146

The computer program itself will be briefly described in Section

7.2. No attempt is being made to give a complete documentation of the

computer program. The complete listing of the program and its flow

diagram and nomenclature are a'-t cned in the appendices.

Two sample problems are described in Section 7.3, including their

full input and output informatics.

7.1. Applicability of the Model

A discussion of the applicability of the model to some situations

occurring in reality is given in this section. Additional capabilities

of the computer program itself are given in Section 7.2.3.

7.1.1. Simulation of Power Plant Intake and Discharge

There are a number of ways in which the intake and discharge

conditions can be modeled with the various terms available in the con-

servation equations developed in Sections 2.S to 2.8. Thermal discharges

or intakes which are located offshore can be simulated by the bottom or - 2 - 1

top heat fluxes qB> q^g, q ,, q ^ (Btu-L T ) or by the volumetric heat

generation qy (BtU'L'^-L"*). Since the model is two dimensional, it

makes no difference which method is used. If the effect of mass contri-

bution is of interest, the heat fluxes may be replaced by the mass - 2 - 1

fluxes gg, g^g, gT, g k T (ML T ) or volumetric mass generation - 3 - 1

p^ (ML T ) with the corresponding enthalpies specified for each. If

the intake or the discharge structures extend over a number of discrete

elements, they can be simulated correctly with corresponding portions on

147

each discrete element. All of the information can be supplied as time

dependent or if needed as a function of X, Y, or any other independent

variable (see Section 7.2.3).

If either the intake or the discharge is located along a shoreline

and it is desired to talce into account the correct contribution of momen-

tum (velocity), it must be simulated as a boundary condition. The

proper mass flow, heat, velocities, enthalpies, and other properties,

as the case may require, must be specified. It must be remembered, how-

ever, that in most cases the actual size of the structure is smaller

than the economically desirable size of the discrete elements. Using

a discrete element that is too small may require an undesirable time

step for stable solution. The user has here the choice of either accept-

ing this situation of smaller discrete elements and, therefore, smaller

time steps and specifying the boundary velocities in their correct

magnitudes and directions or choosing element sizes larger than the

actual size of the structure and then specifying a reduced velocity so

that the correct flow rate will be simulated. In the second case, how-

ever, the momentum effects will not be correctly simulated.

In the special case of power generating plant simulation, the intake

and discharge structures are coupled by the condenser installation, where

a certain heat load is transferred to the flow. A special handling of

the boundary conditions was incorporated in the program to account for

this situation. If a boundary simulates a power plant, the user

specifies, in addition to other regular information, the location (X, Y)

at which the power plant intake is located and the total condenser

148

temperature increase instead of the discharge temperature itself. The

program will then use the existing temperature at the specified intake

location as the current intake temperature, will add to it the tempera-

ture increase across the condenser, and will use the increased temperature

as the discharge temperature at the boundary condition. This procedure

is a means of accounting for recirculation of heated water between the

intake and discharge either of the same power plant or of neighboring

power plants mutually, affected (see Sections 7.1.4 and 7.1.5 for

discussion).

7.1.2. Vertical Variations

Since the model is based on two space dimensions only, it cannot be

used in deep water bodies or in other cases where vertical stratification

(thermal or otherwise) is significant. The program can be used in

shallow water bodies and cases where vertical mixing is significant.

Many estuaries, coastal regions, and some natural streams in the U.S.A.

will satisfy these conditions, but, on the other hand, many lakes and

ponds will not. Bottom roughness, wind stresses, and tidal motions may

considerably enhance the vertical mixing, whereas thermal discharges will

tend to stratify such water bodies. In some cases where vertical

variations do exist but are not considerable, some specified functions

which simulate those variations can be employed, as proposed by 41

Eraslan.

In some other situations where stratification is so strong that two

distinct layers can be detected, the model can be used by assuming the

149

depth of the layer of interest (usually the upper) as the effective depth

of the model. A corresponding adjustment must be made in this case to

other parameters such as velocities and others.

7.1.3. Geometrical Considerations

The geometry can be described in rectangular coordinates in the X

and Y directions only. Space increments can be varied along X and Y,

which gives some flexibility in describing irregular geometry. At the

present time, no partial elements are possible, nor is it possible to

use other than rectangular elements. This limitation is indeed impor-

tant when attempting to model a complex geometry. In addition, grid

lines cannot be stopped in the middle of the modeled zone. This limits

the flexibility in controlling the size of the elements in different

regions. Once a grid line is established, it must be extended all along

the model. This creates difficulty in using the program as a combined

near- and far-field model, as discussed in the next section. The method 41

used by Eraslan or another applicable method can be incorporated in

future versions of this model.

7.1.4. Near- and Far-Field Modeling

As discusr?4 in the introduction, most of the thermal hydraulic

models are either near-field or far-field oriented. By including the

viscous shear stresses in the present model, its potential capability

to analyze both the near field and the far field at the same time has

been greatly increased. However, there are three major drawbacks which

do not allow a full use of that potential.

150

1. The turbulent eddy diffusivity, as has been discussed in Sections

3.1 and 3,2, is a very difficult parameter to be correctly evaluated. As

discussed before, it depends primarily not only on the existing velocity

profiles in the directions modeled but also on the velocity profile in

the plane perpendicular to the main flow. In almost all cases, some

empirical constants are needed for its full evaluation. It is clear that

while in the far field the vertical velocity profile is the controlling

factor, in the near-field area the axisymmetric approach (defect law or

others) is the only one presently possible. To express this asisymmetri-

cal dependence for a jet, whose direction may be three dimensional and

probably in some curvilinear path, in a general far-field rectangular

coordinate system is a major difficulty.

2. Even if one could find a common way to express the eddy

diffusivities in both the far and near field, it is clear that the

near-field area will require a much finer grid line mesh than the far-

field area for proper description of the fluid dynamics. Since, as

was mentioned before, the program in its present form will not allow

complete flexibility in mesh sizing, a very large number of unnecessary

elements will be created in the far field, requiring an extensive

amount of machine calculation time as well as machine storage. This

problem, as was explained in Section 7.1.3, is technical and can be

corrected in future versions of the program.

3. Since one of the main purposes of this study is to analyze

thermal discharges, it is clear that a near field will involve a

buoyant plume, which, because of its buoyancy, will require the vertical

151

dimension for proper analysis. The same is true for the so-called

intermediate field, in which a stratified layer of heated water may be

stably created.

Because of the above drawbacks, it is recommended that the model

in its present form should be used primarily as a far-field model. The

near-field area can still be included in the model zone but should not

be looked upon for quantitative evaluations. After completing the

analysis based on the present model, an additional jet analysis should

be made for the near field using the results of this model as ambient or

background temperature distribution. In any case a near-field model

analysis should not stand alone. As has been already discussed in the

introduction, any near-field model calls for the ambient temperature

to be specified and uses this temperature for the fresh water entrained

into the jet. It must be remembered that the entrained water is not at

ambient temperature but rather is affected by its interaction with the

far ' 1 \ 'ones. This effect of the far field on the near field must

be analyzed by using a far-field model, or, if this is not possible, the

effect must be conservatively estimated.

7jJ:li- UeciiUlijuMtiit, itjtBJw:l iujj Power Plants, and Intake

Etttrainment

Tin. I niellii |,uu;.E: ul: tliu:;i- Uireo subjects iur proper assessment of

power plant environment: 111 iiiipnnl biiilhot lie nverempjias I <iu\, It h (}|e

tendency in many present thermal analyses to isolate the near-field

effect fioiti the far-field effects. This is a dangerous approach, since

152

intuition, which many times is being relied upon for that purpose, can

be very misleading. The feedback of thermal discharges through the

intake to the condenser system creates a closed loop which keeps heating

the same water until some thermal equilibrium is achieved. This partially

closed loop circulation results in localized temperatures which are much

higher than if recirculation does not exist. This is specifically true

if the intake structure is close to the discharge or, in estuaries,

when the distance between intake and discharge is less than a tidal

excursion length. When analytical studies are not possible, hydraulic

physical models and field dye studies should be performed. The method

indicated in Section 7.1.1 to simulate power plant intake and discharge

considers this recirculation effect to a certain degree. It must be

remembered, however, that this method of accounting for recirculation

suffers from the same three deficiencies mentioned before for the near-

field area.

Entrainment of passive aquatic species into the intake structure

is similar in nature to the problem of intake recirculation. It can

be simulated in the same fashion but will also have the same type of

limitations.

All these three cases—discharge jet, intake entrainment, and

intake recirculation--can be simulated in the model on an overall basis

but should be looked upon only for rough approximation of the near-field

area.

Mutual effects between power plants basically constitute a far-field

problem, since the distance between such power plants is normally greater

153

than the zone of the near field. The present model can then be

effectively used for proper assessment of interacting power plants by

specifying each power plant in its proper location in the model.

It must be remembered, however, that the model expresses only the

average properties in the vertical direction, and this must be taken

into account when the intake structure is built in such a way that it

withdraws water at conditions much different from the depth-averaged

conditions.

7.1.6. Multicomponent Analysis

The program is set to handle any number of dissolved substances,

although the interaction between them is handled in a simplified form

only, by using Fick's law of binary diffusion between one substance and

the rest of the mixture. The dimension statements in the program are

presently set to four dissolved substances, but this can be easily

increased if computer storage allows it.

7.2. The Computer Program

In this section the various features of the computer program itself

will be discussed. This includes the program's overall structure, its

various capabilities and limitations, the individual subroutines, and

some machine time and storage requirements.

7.2.1. Program Structure and Condensed Flow Diagram

The purpose of the computer program is to solve for the unknowns,

water elevation, velocities, temperature, and substance concentrations

154

as functions of time and the two horizontal space dimensions X and Y.

As discussed in Section 6.2, che initial value problem defined by Eqs.

2.38, 2.50, 2.61, 2.75, and 2.76 were integrated by using either Euler's

method or the Runge-Kutta method. A computer program was written to

facilitate the solution of these methods as well as the overall compu-

tational requirements for the system. The actual integration solutions

by either the Euler or the Runge-Kutta method were programmed under two

alternative subroutines: SOLEUL for the Euler method and SOLRKG for the

Runge-Kutta method with Gill cosfficients. The user, by means of a flag,

can choose the desired technique for the case at hand. Both subroutines

will be termed SOLVET in this section. The most important input data

required by SOLVET are time derivative functions of all the unknowns

(Eqs. 2.38, 2.50, 2.61, 2.75, and 2.76). These derivatives are evaluated

in a subroutine called SOLFNC. All the fluxes involved are calculated

in a subroutine FLXCON. The rest of the program is constructed around

these major subroutines. Figure 7.1 gives an overall flow diagram for

the various subroutines being used. In general the logic of the program

is as follows (see Fig. 7.1). The main program reads input information

from subroutines INPUT and GEOM. Based on this information, the number

of elements is calculated, the size of the vector array Z is defined, and

the storage requirements are established. It then calls subroutine DRIVE,

which does the monitoring of the rest of the subroutines and keeps track

of the time. DRIVE first calls practically all the subroutines from

which any input information must be read in. It then sets the counter

for time, time steps, and number of time steps (iterations) performed

155

( START )

MAIN SETZ INPUT GEOM

GEOHFE(E) DRIVE

r YES

OUTPRT RESTFL

END

^ YES

1 FILTER PLOT TAPE

t> CHEKED REGFLG PACFLG -) BSERCH -I

GENCNI > BNDCNI » BOTCNI

TOPCNI H H

* SQLFN I » FLXCNI -I * INTCON PLOT TAPE H

Figure 7.1. Simplified flow diagram for computer cade.

156

ind calls subroutine SOLVET in each time step. 'SOLVET is the program

that integrates the equations with respect to time, using the information

coming from subroutines BNDCCN and SOLFNC. BNDCON is an entry into

BNDCNI which updates the conditions on all the boundaries based on

functions specified by the user in GNRLFC and ANLFNC routines. SOLFNC

calculates the time derivatives of all the unknowns. For that purpose

it calls GTFLGS, which retrieves the boundary condition indices of each

element and its region number. MA.TPRP is called next to get the updated

information about the physical properties. GENCON brings in the updated

information about heat and mass generation (or decay) per unit volume.

FLXCON calculates the transport coefficients as well as all the fluxes

involved. For calculating the fluxes from bottom and top, FLXCON calls

subroutines BOTCON and TOPCON, which supply the updated conditions at

the bottom and top, respectively. Updating the conditions in all of

the above subroutines is done by using the functions specified by the

user in GNRLFC and ANLFNC routines. Those user functions can be either

analytical or tabulated and can be dependent on time, position (X, Y),

temperature, substance concentration, and other independent variables.

7.2.2. The Region Subdivision and the Flagging Technique

The zone modeled by the computer program is subdivided into

"regions." Each region is geometrically defined by two bounding planes

in the X direction and two in the Y direction. On each face bounding

the region, there is assigned a certain boundary condition identified

by a "boundary condition function number." If a face of a region has no

157

boundary (internal plane), it needs no such identification. The actual

data of the boundary conditions are given in each boundary condition

function number. In addition to the boundary conditions around it, each

region is also assigned the following.

1. Depth, which is the uniform depth of the region.

2. "Initial condition function number," which identifies a set of

initial conditions to be used for the region.

3. "Volumetric heat and mass generation (or decay) function

number," which specifies the heat and/or mass generation (or

decay) per unit volume in the region.

4. "Top conditions function number," which specifies a set of

conditions to which the top of the region is exposed.

5. "Bottom condition function number," which specifies a set of

conditions to which the bottom of the region is exposed.

Each one of these types of functions is separately documented with

identification numbers so that each function number readily identifies

the full set of conditions involved (see individual description). The

decision of the analyst on how to subdivide the modeled zone into regions

will depend largely on his judgment on what conditions can be considered

as uniform for a specific region. Once a function number is assigned

to a region, the conditions of this function are considered character-

istic for the whole region. In the present form of the program, each

region can be geometrically described by rectangular grid lines only.

A special flagging technique has been developed in this program for

identifying all the characteristics of a specific discrete element.

158

Before starting any time-dependent calculations, the program processes

the input information and files this information in an easy-to-access

compartment. An important tool in this procedure is the assignment of

a flag to each one of the discrete elements. The flag is an integer

variable dimensioned for the total number of elements in use. This

integer contains 32 hexadecimal bits which are subdivided into six

blocks. The first four blocks from the right have five bits each and

are used to identify the boundary function numbers on the four sides of

the element, one block for each side. If a block is empty (zero), the

face has no boundary and is assumed to be on an internal grid line. If

all four blocks are empty, the element is a completely internal node

(surrounded by water on all sides). The next four bits are presently

unused. The last block on the left, which has eight bits, identifies

the region number to which the element belongs. Once element region

number is identified, all the conditions of this element are clearly

specified, since each region number carries with it function numbers for

the initial conditions, heat and mass volumetric generation conditions,

top conditions, bottom conditions, and depth. A zero region number

indicates an element which is outside the modeled zone, that is, a land

element, which is for all purposes inactive. A special routine installs

those five identifying numbers in the flag, and smother two routines

retrieve them any time they are needed. This procedure is designed to

save storage, since six integers (or more) can be stored into one

variable. This is, of course, at the expense of machine time required

for retrieving those numbers each time they are needed. If storage is

159

not a restxicting problem and saving in machine calculation time is more

important, it is better to replace the flag by five integer variables.

Each one of those variables will have to be dimensioned for the total

number of elements in use.

7.2.3. Program Capabilities and Limitations

In Section 7.1 some application capabilities and limitations of the

model have been described. In this section some additional technical

features of the program as it presently exists will be described. Many

additional ones can be incorporated in the program if so desired. The

full listing which is given in the appendix can be of much help for that

purpose. Those features are as follows.

a. Bottom, top, and volumetric conditions. Natural phenomena like

wind, rain, evaporation, heat exchange with the atmosphere, seepage,

bottom shear stresses, and volumetric heat and mass generation or decay

can all be specified as functions of time, position, temperature, and

other parameters. Heat exchange with the atmosphere can be based on

either the equilibrium temperature concept or the actual balance of heat

fluxes across the water surface (see Section 4.4.2).

b. Transport properties. As discussed in Section 3.1 and 3.2, the

turbulent transport properties are difficult parameters to be evaluated.

Nevertheless, the program is set in such a form that each transport

property is a sum of molecular and turbulent parts. The molecular part

is specified by the user in INPUT as a constant, while the turbulent

part is calculated internally on the basis of the discussion in

160

Sections 3.1 and 3.2. Any one of the expressions for transport properties

can be easily modified with the program.

c. Boundary conditions. The program has extensive capabilities

for accepting almost any type of physical boundary condition. These

conditions can be technically imposed at any location along the "shore-

line" of the modeled zone and can simulate power plants, tributaries, or

any other intake or discharge points. All or part of the unknowns and

their fluxes can be specified as functions of time and other independent

parameters. The boundary conditions are discussed in detail in

Section 5.

d. Initial conditions. The initial conditions can be specified

for each region as functions of position (see Section 5.1 for discussion).

e. Analytical and tabulated functions. As was mentioned before,

most of the conditions can be set to be functions of time, position,

temperature, substance mass concentrations, and other parameters. This

is done by the use of subroutine GNRLFC, which multiplies the original

constant value, set by the user, by a proper function. This function

can be either in tabulated form, and therefore restricted to one

parameter at a time, or in a general analytical expression which is

almost unrestricted by either form or number and type of independent

parameters which can be used.

f. Control of time step. The program is set to evaluate the

minimum time step required for stability using for the time being a

simplified but conservative criterion. The program will evaluate the

required time step and use either this value or the value specified by

161

the user if indeed it is smaller. If the user's value is greater than

the time increment required for stability, it will be overridden and

the user will be notified. However, if the user's value is negative,

its positive value will be used in any case.

g. Restart file. The program can create, if so instructed, a file

that stores on disk all the values of the unknowns and other needed

values at the end of a computer run. This file can be used for restart-

ing the problem again from the exact point at which it has been stopped.

h. Monitoring points of temperatures in estuary. In cases of

periodic behavior as found in estuaries, the user can specify a number

of points in which he has special interest. The program will then keep

track of the temperature at these points and will print, at the end of

each cycle, the maximum, the minimum, and the average temperature at

each one of those points over a full cycle period. These values are

very helpful for testing if a quasi steady state has been indeed

achieved.

k. Program termination. The program will terminate the case when

the maximum value of either computer time or the problem (real) time

specified by the user has been exceeded. In both cases a restart file

will be created if requested by the user.

1. Plotting. Contour plotting for water elevations and temperature

and streak plotting for velocities can be generated by using the program

developed for that purpose.

162

7.2.4. Brief Description of Input and Output

The purpose of this section is to give a brief description of the

input and output of the computer program and give some instructions as

to how to prepare the input data required. It is not intended here to

give a full user manual.

Table 7.1 is a concentrated summary of the input variables, their

format, and some other information needed to prepare the input data.

The table is not self-explanatory but can be very helpful to the user

who is already familiar with the program. Columns 71-80 of each card

are reserved for card identification, but are not required by the pro-

gram. The first word in each box is the name of the variable. Then

its meaning is briefly indicated, and some limitations on its size if

any. The format is always either E10.3 for a real variable or 15 for an

integer one.

The input information is a good reflection of the various \

capabilities of the program. Many additional capabilities can be easily

incorporated. Table 7.1 represents the input required and possible at

the present time. The meaning of the input variables and some

explanation of their use will now be given in the order in which they

are being called for in the program.

Table 7.1. Summary of Input Variables and Their Format

COLMN* J 5 10 II 15 20 21 AS $Q }) JJ 40 41 4S SO 51 SS »0 61 TA 70 71 G Title Tit 1 r <Form*t 11*4) No. of NX {MX 41 NR£C (W* 25) NIMTLF (M* 25) NGENF «ux 25) *BNDF (US 25) NTOFF (•4* 25) NBOTF 25) NJWLFC KTBLFC (MX 10) NXCRL (ui SO) NTCM.

(MI SO) KTHU (MS 10) CARD 1 Control Flip ISTART IFIMJS 1 PLOT IVTRT CARD 2 T1M Control STM PRBTM CPUSEC DPRTTK TIDAL CARD 3 Ti»e Iacre»ent Control SOW raw OTNIT 1MTTH NDPC UJTHCR CARD 4 Tabulated Functions ITBLFC No. t miP(i)

CM* 25) TMAJtC(l.I) TABFNCU.I) TA6AA6(M> TABR)C(2,I) Cao continue up to 2S pairs TABU

Lattice tines XGHl(l) XGRL(2) XGM.<3) Can continue up to 50 points in I Subdivision IXFDj 1) | IXH>{2) IIFD(J) ) Can continue to 49 points LTD* V Grose Lattice tines YCJtLfl) YGRi.{2) YCS1(J) Can continue up to SO points LTY Y Subdivision JYF0(1) 1YFD(2) IYfD(J) Can continue up to 49 points LTDY Region Cards (Coupled Together)

1U6 No. 1 I!ftt(l) IGENF(I) DEPTH (I) UU(1) DNX(l) UPt(J) D«Y(1) RSI Region Cards (Coupled Together) ITOrf(I) lWTF{t) W»(f] jltMXB(I) 1UFYBO) | I0MYB(l) RC2 Monitoring Temperature XMACO nxiu(i) XTMAI(2) YTHAX(2) Can continue to 10 pairs TMAX Voluaetrlc Generation IGSNFC No. 1 QDV(I) IQDVF(I) CHDY(J.J) IGU)VF(1,I) aov(j,i) 1C1DVF(2,I) CN lomdary / Conditions (coupled together)

«

S

1B.WFC No. 1 mm? (1) MTTOTP(L) NVBDTP(J) NTBDTP(I) &MD1 lomdary / Conditions (coupled together) «

S

mso( i} FUBD(1 ) FVBO(I) FTI01U XIVT(t) TlNT(l) BX32

lomdary / Conditions (coupled together) «

S

FGBD(I) PQBO(I) FSBDN(l) FSBDSil(l) BNDJ


S

FCIBOfl,)) FCTBDfl.J) FCKBD(2,I) ffiXBPf2,l) BND4


S ]HJDF(J) SUiDF(J) JVBDFFL) | ITBOF(I) JGBDF(J) | IQBCF(I) ISNBOF(l) j ISHBOF(I) !CKB0F(1,I) |lCOCF(ltQ lCTBDF(2,I)|tGUDF(2,l) BSOS Bottc* / Conditions (coupled together)

s

I60TFC No. 1 0B(I) VB(l) NB(1) TB(I) Q»«O HCB(I) BTl Bottc* / Conditions (coupled together)

s

BKANGC(l) BT2

Bottc* / Conditions (coupled together)

s «B(1,1) DCKB(l.i) CKB(2,I) DCKB(2|1) BT3

Bottc* / Conditions (coupled together)

s mr(i) ivBrtn IKtF(t) j ITBFFN tQBF(t) 1 tHCBF(l) /aBF(j.i)} WOUFII.U 1CXBF(2,I) 11DCKB T(2,D BT4 Top f Conditions (coupled together)

\

ITOPfC No. 1 TRRU) VT(») TT(1) <TT(I) HCT(I) TPl Top f Conditions (coupled together)

\

TO(I) QS0L(1} MiDX(t) KNDY(I) TF2

Top f Conditions (coupled together)

\

cnji.n DCXT'1,1) CKT(2.1) Dcrru.n TT3

Top f Conditions (coupled together)

\ HJTF(l) j 1VTF(I) 1*TF(J) j JTTF(I) IQTF(I) | IHCTF(I) ITDF(I) ( IQSOU(f) icrrf(i,i) |iocrrr<',9 tCKTF(2,1) | Itxmii.n Transport ( Coefficient I (coupled 1 together) V

XKPC YtPC rrvsc YTVSC NSP] Transport ( Coefficient I (coupled 1 together) V 0KXC(1) EXTERN DKXC(2) D«C(2) 1SSP2 Initial r Conditions 'ecupled toiether)

V

INTFC No. 1 STM{ 1) STU(I) STV(l) STIS(l) STT(l) INI Initial r Conditions 'ecupled toiether)

V STCK(I.F) STT((Z,I) StCt(J.I) IN2

Initial r Conditions 'ecupled toiether)

V ISTWF(L) | ISTUF(I) I5TYF(I) | ISTVSF(I) ISTTF(I) I ISTCKF(I.I) ISTCKF(2,!)) 1N3 Restart File Presently read fro« retUrt (Jl« stored on disk IN binary character*. RE5TAKT

NOTE: The fomt is al-ays £10.3 for real variable JS for aa integer ucrpt the foraat of the title vhich It 1«A4.

164

Title

Card No. 1

NK

NREG

NINTLF

NGENF

NBNDF

NTOPF

NBOTF

NANLFC

NTBLFC

Title of the case in 72 alphanumerical characters.

Total number of constituents in the mixture. A maximum number of 4 can be presently specified.

Number of regions used (present limit, 25).

Number of initial condition functions used to specify the conditions existing at starting time of the case (STM) (present limit, 25).

Number of volumetric heat or mass generation functions used to specify heat or mass generation (or decay) per unit volume and time (present limit, 25),

Number of boundary condition functions used to specify the conditions on the physical boundaries of the model (present limit, 25).

Number of top condition functions used to specify the conditions on the top surface (present limit, 25).

Number of bottom condition functions used to specify the conditions at the bottom of the water body modeled (present limit, 25).

Number of analytical functions used as factors by which a corresponding variable is multiplied every time step. The functions can be any analytical expression and can involve almost any parameter like time, position (X, Y), temperature, constituent mass concentration, velocities, and others. The function is specified by the user in a FUNCTION routine named ANLFNC, which must be supplied by the user. There is no limit on the numbwr of functions that can be specified since this is controlled com-pletely by the user.

Number of tabulated functions used as factors by which a corresponding variable is multiplied every time step (present limit, 10). The tabulated functions are used in the same way as the analytical functions except that each function is specified in a tabulated form and therefore is limited to one parameter only. The index numbers for both analytical and tabulated functions are in one sequence, and the program distinguishes between the

165

NXGRL

NYGRL

NTMAX

two by the sign, Positive sign designates a tabulated function, and negative sign designates an analytical function.

Total number of gross lattice lines in the X direction normally used for defining the various regions (present limit, 50).

Total number of gross lattice lines in the Y direction (present limit, 50).

Number of points at which temperature will be monitored. The temperature monitoring is performed by detecting the minimum temperature and the maximum temperature occurring at the specified points during each tidal cycle. The average temperature during each tidal cycle is also calculated, and all three values are printed after each tidal cycle is completed.

Card No. 2

ISTART A restart flag for restarting and continuing a problem from a previous run. If nonzero (one), a restart information file is called for and must be available.

IFINIS

I PLOT

A flag for creating a restart file which can be used to continue the case if desired. If zero, no such file will be created.

A plotting flag for storing information required for contour plotting of water elevations, temperatures, and mass concentration of streak plotting ofl|/velocity vectors,

INTRT A numerical integration routine flag. Presently set to choose between Runge-Kutta method (INTRT « 1), Euler-Cauchy method (INTRT = 2).

Card No. 3

STM Starting time for the case. If a restart file is usedj the final time in the restart file will be used as STM.

PRBTM Span of actual time for which the case should be analyzed. Final time of the case will be STM plus PRBTM.

166

CPUSEC

DPRTTM

Computer time cutoff limit in seconds. The output will be printed and a restart file created if so specified.

Time increment for printing output information in addition to the output printed at both the beginning and the end of the case.

TIDAL Tidal period in the case of oscillating flow. Used for calculating tidal maximum, minimum, and average temperature during each tidal cycle.

Card No. 4

SDTM Initial time step used for the integration routines. If a restart file is used, the last time increment in the restart file will be used as SDTM unless SDTM is negative. If SDTM is negative, its positive value will be used, overriding the time step given in the restart file.

FDTM The largest time step permitted in the integration routines. The program will start the integration with a time step equal to SDTM. After INDTM time steps, using SDTM, the program will start multiplying the current time step by a factor DTMLT every NDTMC time steps until the largest time step allowed, FDTM, is achieved or the calculated time step is larger than the minimum time step required for maintaining numerical stability.

DTMLT See FDTM above.

INDTM See FDTM above.

NDTMC See FDTM above.

LDTMCR Stability criterion flag. If nonzero, the program will calculate a minimum time step required to main-tain numerical stability and will use this value whenever it is smaller than the value calculated by the basic procedure described under FDTM. The time step stability criterion used is presently simplified and temporary. If LDTMCR is zero, the option will not be activated at all.

167

Cards: TABL1 and TABL2

These cards are used to describe the tabulated functions by specifying the points of each such table.

ITBLFC Tabulated function number (I).

NTBLP(I) Number of pairs used to describe the tabulated function I (present limit, 25),

TABARG(K,I) Argument (independent value) K of tabulated function I.

TABFNC(K,I) Dependent value K of tabulated function I.

Cards: LTX, LTDX, LTY, LTDY

These cards are used to describe the geometrical grid lines creating the mesh of the model.

XGRL(I)

LTDX(I)

YGRL(I)

LTDY(I)

Gross lattice line I in the X direction. Those lines are used to describe the various regions.

Number of subdivisions between gross lattice line XGRL(I) and XGRL(I+1),

Gross lattice line I in the Y direction.

Number of subdivisions between gross lattice line YGRL(I) and YGRL(I+1).

Cards: RGl and RG2

These cards are used to first subdivide the zone modeled into regions. Then the various characteristics of each region, including boundary conditions, are defined by specifying a function number for each such characteristic. The actual specification of those functions is done in different cards (those which describe the functions themselves). There are two cards for each region.

IREG Region number (I).

INTF(I) Initial conditions function number for region I. This function specifies the initial conditions existing in region I at the time STM (see cards IN).

168

IGENF(I)

DEPTH(I)

UPX(I)

DNX(I)

UPY(I)

DNY(I)

ITOPF(I)

IBOTF(I)

IUPXB(I)

IDNXB(I)

IUPYB(I)

IDNYB(I)

Volumetric generation function number for region I. This function specifies the generation (or decay) of heat and/or mass per unit volume and unit time for region I (see card GN).

The depth of region I, Considered uniform throughout the region. The depth is measured from a constant arbitrary reference level.

Smallest X dimension (gross lattice line) bounding region I.

Largest X dimension (gross lattice line) bounding region I.

Smallest Y dimension (gross lattice line) bounding region I.

Largest Y dimension (gross lattice line) bounding region I.

Top conditions function number for region I. Specifies all the conditions on the top surface of the water in region I (see cards TP).

Bottom conditions function number for region I. Specifies all the conditions at the bottom of the water body in region I (see cards BT).

Boundary conditions function number existing on the smallest X lattice line, UPX(I), of region I. Describes all the conditions existing on this line if it constitutes a physical boundary. If it does not, the entry is left blank. A region with all its boundary entries blank is completely surrounded by water (see cards BND).

Same as IUPXB(I) but for DNX(I) line.

Same as IUPXB(I) but for UPY(I) line.

Same as IUPXB(I) but for DNY(I) line.

Card: TMAX

This card describes the points at which temperature monitoring is desired (see NTMAX).

XTMAX(I) X dimension of point I.

169

YTMAX(I) Y dimension of point I.

Card: GN

This card describes any heat and/or mass generation (or decay) per unit volume and time. There is one card for each set of such conditif (that is, for each volumetric function number).

IGENFC Volumetric generation function number (I).

QDV(I) Value of heat generation (or decay if negative) per unit time for function I.

IQDVF(I) Multiplier function number by which QDV(I) will be multiplied every time step. The function can be analytical (negative) or tabulated (positive). The function can include almost any number of parameters (see NANLFC and NTBLFC).

GKDV(K,I) Value of mass generation (or decay if negative) of constituent K per unit volume and unit time for function I.

IGKDV(K,I) Multiplier function number by which GKDV(K,I) will be multiplied every time step (see XQDVF(I)).

Cards: BN1 to BN5

These cards are used to specify the boundary conditions for each boundary conditions function. There are five cards for each such function. Card BN1 specifies the types of boundaries for H, U, V, and T, as discussed in Section 5.3, which are, in short:

B.C. type 1: P = P^ (value of property itself is specified).

B C £YD6 2 * 9P " * -jr- = Phffr) tthe property's normal derivative is specified).

B.C. type 3: P = P, + (Pbf^b^ ( f o r c e d f l u x f r o m outside is specified).

2 2 B.C. type 4: 3 P/3n = 0 (the property's second normal derivative

equals zero).

The boundary condition type specified for T is also used for C^.

IBNDFC Boundary conditions function number (I).

NHBQTP(I) Type of boundary condition specified for water elevation H.

170

NUBDTP(I)

NVBDTP(I)

NTBDTP(I)

FHBD(I)

FUBD(I)

FVBD(l)

FTBDCI)

XINT(I)

YINT(I)

Type of boundary condition specified for velocity in the X direction CU).

Type of boundary condition specified for velocity in the Y direction 00.

Type of boundary condition specified for temperature T or constituent mass concentration C ,.

The value specified (if required) for the water elevation at the boundary I. This value is multi-plied each time step by the factor specified in IHBDF(I).

The value specified Cif required) for the U velocity (X direction) at the boundary I. This value is multiplied each time step by the factor specified in IUBDFCI).

The value specified Cif required) for the V velocity (Y direction) at the boundary I. This value is multiplied each time step by the factor specified in IVBDFCI).

The value specified Cif required) for the temperature at the boundary I. If this.value is negative, then the boundary is assumed to simulate the heat dis-charge from a power plant. In this case the positive value of FTBDCI) is taken as the temperature increase across the condensers, and the discharge temperature is calculated as the sum of this temperature increase and the intake temperature. The intake temperature is the temperature existing at any time at the element simulating the intake structure, whose location is specified by the next two entries of this card. FTBD(I) is multiplied every time step by the factor specified in ITBDF(I).

X dimension of the intake structure location. Not required if FTBDCI). is positive.

Y dimension of the intake structure location, required if FTBDCI) is positive.

Not

Based on the above, the discharge temperature at boundary I at any time will be

discharge = TI* I N Td). YINT(I)] + jTBDCI) (7.1)

171

where TBD(I) is the updated value of the temperature increase across the condenser FTBD(I). This arrangement allows recirculation to be taken into account.

FGBD(I)

FQBD(I)

FSBDN(I)

FSBDSH(I)

FCKBD(K.I)

FGKBD(K,I)

IGBDF(I)

IUBDF(I)

The value specified (if required) for the mass flow (ML-2T-1) at boundary I, This value is multiplied every time step by the factor specified in IGBDF(I). Note that the total mass flux through the boundary will be the sum of GBD(I) and the density times velocity UBD(I) or VBD(I). FGBD(I) allows mass flux from the boundary without affecting momentum.

The value specified (if required) for the heat flux (Btu-L"2t~1) at the boundary I. This value is multiplied every time step by the factor specified in IQBD(I). Note that the total heat flux through the boundary will be the sum of QBD(I) and the convective heat flux specified by VBD(I) and TBD(I). FQBD(I) allows heat flux from the boundary without specifying ir.ass flow or velocity.

The value specified (if required) for the normal shear stresses (pressure) at the boundary I. This value is multiplied every time step by the factor specified in ISNBD(I).

The value specified (if required) for the shear stresses (friction forces per unit area) at boundary I. This value is multiplied every time step by the factor specified in ISHBDF(I).

The value specified (if required) for mass concentration of constituent k at boundary I. This value is multiplied each time step by the factor specified in ICKBDF(K,I).

The value specified (if required) for mass flow of constituent k at boundary I. This value is multi-plied each time step by the factor specified in IGKBDF(K,I). This mass flow of constituent k is in addition to the mass flow of constituent k con-vec.ted with the total mass flow (GBD(I)).

Multiplier function number for boundary water elevation (see FHBD).

Multiplier function number for boundary U velocity (see FUBD).

IVBDF(I) Multiplier function number for boundary V velocity (see FVBD).

172

ITBDF(I)

IGBDF(I)

IQBDF(I)

ISNBDF(I)

ISHBDF(I)

ICKBDF (K, I)

IGKBDF(K,I)

Multiplier function number for (see FTBD).

Multiplier function number for (see FGBD).

Multiplier function number for (see FQBD).

boundary temperature

boundary mass flux

boundary heat flux

Multiplier function number for boundary normal stresses (see FSBDN).

Multiplier function number for (see FSBDSH).

Multiplier function number for concentration of constituent k

Multiplier function number for constituent k (see FGKBD).

boundary shear stresses

boundary mass (see FCKBD).

boundary mass flux of

Cards: BT1 to BT4

These cards are used to specify the conditions at the bottom of the water body modeled. There are four cards for each such function.

IBOTFC UB(I)

VB(I)

Rottom conditions function number (I).

The value specified (if required) for the velocity in the X direction of the flow coming from the bottom. This value is multiplied each time step by the factor specified in IUBF(I).

The value specified (if required) for the velocity in the Y direction of the flow coming from the bottom. This value is multiplied each time step by the factor specified in IVBF(I).

WB(I) The value specified (if required) for the velocity in the vertical upward direction of the flow coming from the bottom. This value is multiplied eac!. time step by the factor specified in IWBF(I). WB(I) con-tributes to the total mass flow coming from the bottom but has no effect on the momentum. The total flow is calculated based on vectorial summation of UB, VB, and WB.

173

TB(I)

QB(I)

HCB(I)

BMANGC(I)

CKB(K,I)

DCKB(K,I)

IUBF(I)

IVBF(I)

IWBF(I)

ITBF(I)

The value specified (if required) for the temperature of the bottom for bottom conditions function I. This value is multiplied every time step by the factor specified in ITBF(I).

The value specified (if required) for the heat flux coming from the bottom. This value is multiplied each time step by the factor specified in IQB(l). This heat flux is in addition to the convective heat flux coming with the flow or the diffusive flux caused by temperature drop.

The value specified Cif required) for the film heat transfer coefficisnt between the bottom and the water for bottom conditions function I. This value is multiplied each time step by the factor specified in IHCBF(I). The heat flux will be calculated based on Eq. 4.42.

The value specified for the Manning roughness coefficient used to calculate the bottom shear stresses at bottom conditions function I. This value is not updatt-d each time step. The units of the Manning coefficient are hr/ft"*/^

The value specified for the mass concentration of constituent k at the bottom fox bottom conditions function I. This value is multiplied each time step by the factor specified in ICKBF(K,I).

The value specified for the film mass transfer coefficient between the bottom and the water for bottom conditions function I. This value is multi-plied every time step by the factor specified in IDCKBF(K>1). The mass flux will be calculated based on Eq. 4.25.

Multiplier function for the bottom velocity in the X direction Csee UB).

Multiplier function for the bottom velocity in the Y direction Csee VB).

Multiplier function for the bottom vertical velocity Csee WB).

Multiplier function for the bottom temperature Csee TB).

174

IQBF(I) Multiplier function for the bottom heat flux (see QB).

IHCBF(I) Multiplier function for the bottom film heat transfer coefficient (see HCB).

ICKBF(K,I) Multiplier function for the bottom mass concentration of constituent k (see CKB).

IDCKBF(K,I) Multiplier function for the bottom film mass transfer coefficient (see DCKB).

Cards; T1 to T4

These cards are used to specify the conditions on the top surface of the water body modeled. There are four cards for each such function. Most of the variables have meaning analogous to the corresponding bottom conditions variables with two differences. First, instead of the Manning coefficient, there is a need for a wind stress coefficient. How-ever, since no reliable values are given in the literature, a constant value (3.2 x 10-6) is used inside the program based on Section 4.2. Second, the film heat transfer coefficient between the top surface and the atmosphere above it is HCT(I). If HCT(I) 0, it is used as the heat exchange coefficient, and the equilibrium temperature is specified by TD(I) in card TP2 (see Section 4.4). If HCT < 0, the heat exchange coefficient is calculated based on Eqs. 4.31 and 4.32 in Section 4,.4, and the equilibrium temperature is calculated based on Eq. 4.30 in this section. The additional information required is specified in card TP2 as follows.

TD(I) Dew point temperature QSOL(I) Solar radiation heat flux WINDX(I) Wind velocity in the X direction WINDY(I) Wind velocity in the Y direction

Cards: TRSP1 and TRSP2

These cards are used to specify the transport properties of the fluid. For the present, only constant values are used from the input format. However, in the program itself, each transport property is the sum of the constant value specified in these cards and a built-in correspond-ing function for that property based on the discussion in Sections 3.1 and 3.2.

XKPC The constant part of the thermal conductivity of the fluid in the X direction (Btu.L-1T-1F-1).

175

YKPC

XTVSC

YTVSC

DKXC(K)

DKYC(K)

The constant part of the thermal conductivity of the fluid in the Y direction (BtU'L-lT-iF-l).

The constant part of the dynamic viscosity of the fluid in the X direction (ML-1!1-1;).

The constant part of the dynamic viscosity of the fluid in the Y direction (ML-lT-1).

The constant part of the mass diffusivity of constituent k into the rest of the mixture in the X direction (L2T-1).

The constant part of the mass diffusivity of constituent k into the rest of the mixture in the Y direction (L2T-1).

Cards: INI, IN2, and IN3

These cards are used to specify the initial conditions that exist at the starting time of the problem. There are three cards for each such function.

INTFC

STH(I)

STU(I)

STV(I)

STWS(I)

STT(I)

STCK(K,I)

Initial function number (I).

Initial water elevation for initial function I.

Initial velocity in the X direction for initial function I.

Initial velocity in the Y direction for initial function I.

Initial rate of change of water elevation for initial function I.

Initial temperature for initial function I.

Initial mass concentration of constituent k for initial function I.

Any one of the above values is multiplied by a factor specified in a corresponding multiplier function. These factors allow the initial conditions to be specified as functions of position (X, Y) within the same region. The functions are specified by the following.

ISTHF(I) Multiplier function for the initial water elevation (see STH).

176

ISTUF(I) Multiplier function for the initial velocity in the X direction (see STU).

ISTVF(I) Multiplier function for the initial velocity in the Y direction (see STV).

ISTWSF(I) Multiplier function for the initial rate of change of water elevation (see STWS).

ISTTF(I) Multiplier function for the initial temperature (see STT).

1STCKF(K,I) Multiplier function for the initial mass concentration of constituent k.

Card: RESTART These cards are used for restarting and continuing a problem from the point at which the previous case has been stopped (see ISTART and IFINIS). The cards (or file) are generated if IFINIS > 0 and are required only if ISTART > 0. The data in this card include the final time from the pre-vious case, the last time step used, and all the values of the unknowns. The program will continue calculations using those values and overriding any information specified by the initial conditions or by card 3 and card 4. If, however, the starting time step SDTM is negative, its positive value will be used, overriding the value given in the restart file.

177

7.3. Application of the Model to Sample Problems

Two sample problems have been shosen to demonstrate the workability of the model and its capabilities, The first problem is a very simplified case of flow of warm seawater (27 ppt salt concentration) into and out of a rectangular water body. The case demonstrates the symmetry of the flow and temperature distributions as well as the mass and heat balance achieved. The second problem represents two power plants located on two banks of the same water body. The flow in the water body is oscillating and can represent an estuary. There is an interaction between the flow and temperature distributions of the two power plants. The intake of each is located about 1,500 ft upstream of its discharge.

In order to save computer time, both sample problems have been run on a reduced version of the program which does not include constituent concentrations. However, a short-time run was made with the full version to demonstrate the capability of the program to calculate mass concentrations of a number of constituents in a water body.

7.3.1. Sample Problem No. 1 This case represents warm seawater (27 ppt salt concentration)

flowing into and out of a rectangular water body. The overall dimensions of the water body are 105,000 by 105,000 ft. Initially, the water body is filled with a 40-ft depth of pure water at 80°F and completely at rest. Then a 30,000-cfs flow of water enters at the center of one bank with a velocity of 0.15 ft/sec at a temperature of 95°F and salt con-centration of 27 ppt. At the center of the opposite bank there is an

178

opening 5,000 ft wide which is kept at a constant level at 40.0 ft. As a result, symmetrical flow is initiated within the water body. The water elevation adjusts itself correspondingly. Figure 7.2 shows a schematic presentation of the case, including the specification of both initial and boundary conditions.

The modeled water body is subdivided into nine regions (although three regions could be sufficient for this specific case). Each region is defined by its own dimensions, initial conditions, volumetric generation conditions, bottom conditions, top surface conditions, and boundary conditions on its four edges. Boundary conditions 1 and 4 represent solid walls. These are assumed to be impermeable to both heat and mass. The normal velocity, V , at the wall is set to zero, while free-slip conditions are assumed for the tangential velocity, V .. Water elevation is a free boundary and is specified as boundary condition type 4 (see Section 5). For the inlet (boundary condition 2) the values of velocities, temperature, and constituent mass concentrations are speci-fied, while the water elevation is again left as boundary condition type 4. At the outlet (boundary condition 3) the water elevation is specified to be constantly 40.0 ft, and the exit velocity is specified as having zero gradient along the flow. The rest of the unknowns are left as boundary condition type 4.

The bottom is considered impermeable to both mass and heat. A 1/3

Manning roughness coefficient of 0.03 sec/ft is assumed for calcu-lating the bottom shear stresses. On the top surface, rain and wind stresses are considered to be negligible. A constant value of

179

in x

I L<I ©

V

® B> I ® T>I

ja) fe

-21 X5000-

O REGION NO. \ 7 B C- NO-

INITIAL CONDITIONS B.C. 2 H0 = 40.0 ft Uo=0.0 v 0 = o . o T0=80.0°F Ck(1) = I.O CK(2) = 0.0

a2H/ax2= 0 U=540 ft/hr V=0.0 T= 95.0°F Ck< 0=0.973 Ck(2)= 0.027

B.C. 3 H =40.0 ft a2U/axz = 0 32V/ax*=0 azT/ax2 = 0 32Ck/ax2 = 0

B.C. 's 1 &4 d2Hy{?X2=0 Vn=0 dVt/an=0 aT/an=o aCk/an = 0

Figure 7.2. Regions and boundary conditions arrangement in sample problem No. 1.

180

2 5 Btu/ft -hr.°F is considered for the heat exchange coefficient between

the water surface and the atmosphere with-80.0°F equilibrium temperature.

The diffusion coefficients for mass, momentum, and heat were

considered as the sum of molecular and turbulent coefficients. The tur-

bulent diffusion coefficient was based on Elder's results55 for isotropic

turbulence. Evaluating the bottom shear stresses with a Manning

coefficient of 0.03 sec/ft1^3 gives (see Eq. 3.24)

£ = 0.07HuT = 0.0043H yju2 + V2 . (7.2)

The shear effects caused by velocity variations in the lateral 5 6 5 7

direction, which, as claimed by Fischer, ' are very important in one-

dimensional models, do not have to be considered here, since the model

is two dimensional and the velocity variations in the lateral direction

and the proper normal and shear stresses are properly included in the

model itself,

Some shear effects caused by velocity variations with depth must be

added to the above diffusion coefficient. However, since the correct

formulation for continuous discharges is not available, it was decided

to conservatively use Eq. 7.2 as it is.

An actual printout of the computer runs made for this sample problem,

with the full version and the reduced version, is given in Appendix A.

The input information is printed out in full, while the output results

are printed here only for two times—one for the full version and one

for the reduced version.

181

The results of the run were plotted for a number of successive timet,

and are shown in Figures 7.3 to 7.27. A discussion of these results is

given in Section 7.3.3.

7.3.2. Sample Problem No. 2

This case represents two power plants located on the same water body

where the flow is oscillating in nature. The overall dimensions of the

water body are 4,500 ft by 178,500 ft. Initially the water body is

filled with a 40-ft depth of water at 80°F and completely at rest. Then

a 4,000-cfs flow of water comes in at the center, of one narrow bank with

a velocity of 0.2 ft/sec and at a temperature of 80°F. At the opposite

bank the water elevation is oscillating sinusoidally as

H = 40 + 2.25 sin 2ir(t/T) , (7.3)

where t is the instantaneous time and T is the cycle period. This

behavior simulates the mouth of an estuary, with a tidal period of

12.4 hours. Figure 7.28 shows a schematic presentation of the case and

its initial and boundary conditions. Two power plants are simulated on

the two opposing longer banks of the water body. Each power plant dis-

charges about 2,480 cfs of water (7 ppt salt concentration) at a

velocity of about 0.125 ft/sec perpendicular to the shoreline and about q 8.33 x 10 Btu/hr of heat. The intake of each power plant is about

1,500 ft upstream of its discharge point. Recirculation is properly

taken into accour.si since the intake temperature is the actual temperature

existing at any time at the intake element. The discharge temperature

182

T I M E S 4 . 0 5 0 hr. VELOCITIES o

o o

8

o CO

o <o

o v>

o 3"

o cn

o CM

f / ^ / ^

N ^ I \

J I I I I I I I I I I I I I I I I I I L 10 20 30 40 50 60 70 80 90 100 110 FEET • 1.0E-03

Figure 7.3. Velocity distribution (ft/hr) for sample problem No. 1 at time =» 'c.050 hr.

183

T I M E 8 0 . 9 5 0 hr. VELOCITIES o

o o

8 -

o CO

o to

o to

a CO

a CM

* t f t r *

"•» N

N ^ * v

i I » 1 i I i I I I I I I I i I 1 I I I L 0 10 20 30 40 50 GO 70 80 90 100 110 FEET * !.0E-03

Figure 7.4. Velocity distribution (ft/hi") for sample problem No. 1 at time = 10.950 hr.

184

T I M E * 8 . 8 5 0 hr. VELOCITIES o

W o o ^

o on -

o CO

a r-

o to " t

V \ > s

80

\ § / f

o -

O C\J -

O -

1 1 1 1 1. I 1 1 1 1 1 1 1 1 1 1 0 10 20 30 W 50- 60 70 80 90 100 110 FEET « 0.1E-02

l-'igurc 7.5. Velocity distribution (ft/hr) for sample prohlem No. 1 at time = 118.850 hr.

185

TIME s 2 . 0 5 0 hr. VELOCITIES in.

t / / / S *

t / / s s * *

\ I / / - -

\ X / - - - - - -

: \ - - - - -

: \ \ N N. -

\ \ \ S s

1 \

i i • i i \ \

. . . 1 s • III • 1 • •

»»

1 1 1

o

in u>

o ui m o UJ YX Q lO

• V- SI u K

ITl a*

ui cn

10 IS 20 25 30 35 40 45 FEET • 1.0E-03

Figure 7.6. Velocity distribution (ft/hr) at the zone of discharge for sample problem No. 1 at time = 2.050 hr.

186

T I M E " 2 . 0 5 0 hr. DEPTH ( A H * 0 . 0 0 2 f t ) 4.0014E 01 ts

Figure 7.13. Water depth distribution (ft) for sample problem No. 1 at time = 29.000 hr.

187

T I M E - 3 . 0 5 0 hr DEPTH ( A H ' 0 . 0 0 2 f t ) U.0018E 01 ts


188

TIME =4 .050 hr. DEPTH I A H = 0 . 0 0 2 f t ) 4.0026E 01 ts

0 10 20 30 40 50 60 70 80 90 100 110 FEET » 1.0E-03


18!)

TI ME = 6 . 0 5 0 hr. DEPTH < ^ H = 0 .002 f t ) 4.0036E 01

o


11*0

D E P T H I A H = 0 . 0 0 2 f t ) 4.0042E 01

o


191

T I M E = 9 . 0 5 0 Q E P 7 H 0 . 0 0 2 f t ) 0 . U 0 0 S E 0 2

ts


192

TIME « 2 9 . 0 0 0 hr. DEPlh ( A H - 0 . 0 0 2 f t ) 0.M008E 02 ts


193

TIME = 4 I . 7 0 0 hr D E P T H < A H = 0 . 0 0 2 f t > 0 .4008E 02

o

Figure 7,14. Water depth distribution (ft) for sample problem No. 1 at time = 41.7 hr.

194

T I M E >118.850 hr. DEPTH ( A H « 0 . 0 0 2 f t ) 0.4003E 02 a


195

T I M E - 2 . 0 5 0 hr DEPTH ( A H » 0 . 0 0 2 ft > «I.001UE 01

Figure 7.16. Water depth distribution (ft) at the zone of discharge for sample problem No. 1 at time = 2.050 hr.

1 9 ( S

T I M E > 3 . 0 5 0 hr. D E P T H t A H » 0 . 0 0 2 f t ) U.0018E 01

Figure 7.17. Water depth distribution (ft) at the zone of discharge for sample problem No. 1 at time = 3.050 hr.

] 97

T IM E = 4 . 0 5 0 hr. DEPTH ( A H= 0 . 0 0 2 f * ) U.0026E 01

Figure 7.IS. Water depth distribution (ft) at the zone of discharg ?or sample problem No. 1 at time = 4.050 hr.

198

T I M E 8 5 . 0 5 0 hr. DEPTH ( A H « 0 . 0 0 2 f t ) 4.003IJE 01

Figure 7.22. Water depth distribution (ft) at the zone of discharge for sample problem No. 1 at time » 124.450 hr.

199

T I M E » 2 9 . 0 0 0 hr DEPTH ( A H = 0 . 0 0 2 hr) H .0080E 01

FEET « 1.0E-03


200

T I M E 4 1 . 7 0 0 hr D E P T H = 0 . 0 0 2 f») '4.00825 01


201

T I M E * 1 2 4 . 4 5 0 D E P T H < £ > H = o 0 0 2 f t ) y . o o e 2 E 0 1


202

T I M E * 2 . O 5 O HR TEMPERRTURE I ^ T - r n 7 .9000E 01 ts

§

8

f

o

o <fi>'

o in

o col

o i\i

a—J 1 I ( I 1 I 1 I 1 I 1 I 1 I 1 I 1 I L 0 10 20 30 40 50 60 70 80 90 100 110

FEET x 1.0E-03


203

TIME =2 .050 hr TEMPERATURE ( A T = I«FJ 8.0000E 01

Figure 7.24. Temperature distribution (°F) at the zone of discharge for sample problem No. 1 at time = 2.050 hr.

204

TIM E«21.000 hr TEMPERRTURE l °F) 8.0000E 01

Figure 7.25. Temperature distribution (°F) at the zone of discharge for sample problem No. 1 at time = 21.0 hr.

205

TIME 69.700 hr TEMPERATURE (ATH«F) S.IOOOE 01

15 20 25 30

FEET m 1.0E-03

Figure 7.26. Temperature distribution (°F) at the zone of discharge for sample problem No. 1 at time a 69.7 hr.

206

TIME <24,450 hr TEMPERATURE ( A T - m S.IOOOE 01

20 25

FEET • 1.0E-03

Figure 7.27. Temperature distribution (°F) at the zone of discharge for sample problem No. 1 at time » 124.4S0 hr.

VB.C. N O .

O R E G I O N N O .

INITIAL C O N D I T I O N S

H0-40 0 It Uo«0 0 Vq'0.0 To = BO. OOF CrU)H 0 Cj,(2)»0 0

B.C. 2

1 1 * 7 2 0 f t / h f V = 0 0 T = 8 0 0 n F Ck( t J = I 0 Ck121 = 0 0

B . C . 3

H = 4 0 + 2 2 5 SIN(2»-j-) a 2U/dX ? = 0

a ? V / a x ? = 0 0 a ? T / a x ? = o 0 [ 7 0 ° ] a?Ck/aK? = 0

[ 0 9 7 3 . 0 0 2 7 ]

B.C. 's j & 4 d?H/an' = 0 Vn=0 sVt/an-0 a T / a n = 0 sC|/an= 0

B . C . ' 5 5 g, 7

a7H/ayJ = 0 3?U/t>y? = 0 V = ± 4 4 6 5 8 f t / h r a ? W = o

B.C. '5 6 & B <j2U&y2 = 0 V = 0 . 0 i / = ± 4 4 6 5 8 f t / h r T - T , n i + I 5 » F Cfcf I ) = 0 9 9 3 Ck(2)=0 007

Figure 7.28. Regions and boundary conditions arrangement in sample problem^No. 2.

208

is calculated to be at any time 15°F above the intake temperature. The

two power plants are 20,500 ft apart along the main stream and are located

on two opposing banks of the water body. Interaction and recirculation

between the two power plants are properly considered.

The modeled water body is subdivided into 11 regions. Each region

is defined by its own dimensions, initial conditions, volumetric

generation conditions, bottom conditions, top surface conditions, and

boundary conditions on its four edges. Boundary conditions 1 and 4

represent solid walls with conditions the same as for sample problem

No. 1. The inlet conditions (boundary condition 2) and outlet conditions

(boundary condition 3) are also similar to those in sample problem No. 1

except that the water elevation is specified sinusoidally by Eq. 7.3

racher than being constant. This difference completely changes the

nature of the flow field in the water body. The temperature in boundary

condition 3 is specified as type 4. This imposes a constant temperature

gradient when the flow is positive (outward) and requires that the

temperature be equal to the outside temperature (70°F) when the flow is

negative (inlet). The same types of boundary conditions are used for

the mass concentration (ocean salt concentration of 27 ppt) as for the

temperature. Boundary conditions 5 and 6 simulate, respectively, the

intake and discharge structures of one power plant, while boundary

conditions 7 and 8 simulate the same for the second power plant. The

intake boundary conditions (5 and 7) have specified intake velocities,

and the rest of the properties are left as boundary condition type 4.

The discharge boundary conditions (6 and 8) have specified values for all

209

the properties except water elevation, which is left as boundary

condition type 4. In addition, each power plant discharge is coupled to

its own intake by way of temperature; that is, the discharge temperature

is always based on the current intake temperature plus the condenser

AT (15°F).

The conditions at the bottom surface and top surface as well as the

transport properties are the same as in sample problem No. 1.

An actual printout of the computer runs made for this sample problem,

both with the full version and the reduced version, is given in Appendix

A. The input information is printed out in full, while the output

results are printed here only for two times--one for the full version

and one for the reduced version.

The results of the run were plotted for a number of successive

times and cycle fractions and are shown in Figures 7.29 to 7.70. A dis-

cussion of these results is given in Section 7.3.3.

7.3.3. Results and Discussion of Sample Problems

Before discussing the actual results of the two sample problems

presented in Sections 7.3.1 and 7.3.2, it is worthwhile mentioning some

of the difficulties met before achieving them.

First, there was the problem of numerical instabilities. It was

found that the solution of the model, when used co predict temperatures

and mass concentrations only (that is, the water elevations and

velocities have been prespecified), was numerically much more stable

than when used as a full thermal-hydraulic model. It was possible to

run the model, for thermal prediction only, with time steps in the order

TIME = 25.435 HRS PERIOD = 0.2051E 01 | p p # ( | VELOCITIES

U J _ _ — 1

J I I I I . i i i I > « » J_ * 1 * •

40 60 j 80 100 IB P » 2 F F E E T • 0.1E-02

120 160

Figure 7.29. Velocity distribution (ft/hr) for sample problem No. 2 at time = 25.435 hr and period of tidal of 2.051.

TIME = 25.135 HAS PERIOD = 0.205IE 01 | p R # || DEPTH OH » 0.020 n 0.4048E 02

c\j 0 1 UJ

Hi LU

CM

I lo ®«o

o 6?

o 11> o' CM tn o v H X'

20 <10 > • » i I i i—I—i 1—<—i—i—i—

60 " » 80 n |PR »2HFFFT « 0.IE'

(0 OP o CM <0 00 in m m <0 (0 u> <0 <0 o o o o O o o o

• * * * U U H II II N II

X X X X X X X X

100 02

i.I i i 120 m o 160

-I—I—I u 180

u O M

Figure 7.30. Water depth distribution (ft) for sample problem No. 2 at time = 25.435 hr and period of tidal of 2.051.

TIME = 25.435 HRS


TIME = 27.915 HRS

PERIOD * 0.2251E 01 VELOCITIES

80 100 FEET n 0.1E-02

Figure 7.32. Velocity distribution (ft/hr) for sample problem No. 2 at time » 27.915 hr and period of tidal of 2.251.

TIME * 27.915 HRS PERIOO " 0.225IE 01 P.P.#1 DEPTH w - n 0.4230E 02

CVJ 0 1 UJ

UJ UJ u.

CM iD N CM * OJ

CM t-3

<M CM u-o CVJ

CO <q cvi <r

co <q cvi

20

I .l.i i • i * ' • i—i i—i—ii y 40 60 f

i «

[ RP. # 2 80

FEET n 100

0.1E-02 120

J_i

z a: u o

ts> M -U 140

-I L. 160 180

Figure 7.33. Water depth distribution (ft) for sample problem No. 2 at time » 27.915 hr and period of tidal of 2.251.

TIME = 27.915 HfiS

Figure 7.34. Temperature distribution (°F) for sample problem No. 2 at time = 27.915 hr and period of tidal of 2.251.

TIME = 29.155 HRS

PERIOD = 0.23S1E 01

CO

CM

|P.P. # I) VELOCITIES

• • ' I I I I I L. J l I I i—I—i—I—k—i—I—i—i—i—i I—i i i i I • • • » * » • • • ! • • • • 20 40

(E 60 t

». r * 2 r 80 100

FEET k 0.1E-02

120 140 160 180


TIME = 29.155 HRS PERIOD = 0.2351E 01 P. P. # 1 DEPTH 0.020 n 0.4186E 02

<o cO

II

x

rrf t cvi

CJ

CM

o cvi

00 ro cvi

<0 ro cvi

I t 20 40

I. I I L.—I 1 1-60 1 8 0 100 RP.#2|FEET „ Qi ,E.Q2

120 140 160 180


TIME = 29.155 HRS


TIME = 31.635 HRS PERIOD = 0.2551E 01 P.P.#1

to

(M

o _

VELOCITIES

n

i i.ii 20 -i t-H0 60 t 80 II

|P.P.#2|(tFFT . 0, IE i i J_

100 02

120 I , ... I

mo 160 I I

180


TIME = 31.635 HRS PERIOD = 0.2551E 01

CJ 0 1 UJ

UJ tu

ai

20

jP.P. *\\ DEPTH OH- 0.020 FT

<0 0> K)

" i Hi

i) (

CM/ <ol 0>! "i

0 <£> 01 IO

m

i a,! in! i • I

i i i i i <0! in I oil to

I

i : • i i i i i ! I »| 1 ml I I

40 60 1 P. P. # 2 ?_i—I i i i i L

80 10C FEET * 0.1E-( 100

02 120

I i I i _i i_

• i •

k ; at I fO i I i

0.3932E 02

140 160

z a: CJ o

i>J to o

180


TIME = 29.155 HRS


TIME = 34.115 HRS PERIOD = 0.2751E 01 VELOCITIES

40 60 Jf 80 100 lp.;R * 2 > FEET * 0.1E-02


TIME = 2 9 . 1 5 5 HRS

PERIOD = 0.275IE 01 P.P. # ! DEPTH OH-0.020 rr 0.3734E 0?

CM

i i i <D I ro i

Si ii

O l

ft i « I I I

_L_I I l_l

i ° ! £

i i i i i • i i i

i iSj ' I 1 1 i ! i i

' S 1 1 &I 1 I I

20 40 60 80 100 120 140 P.P.#2|feet „ o. 1E-02

160 180


TIME = 34.115 HRS

Figure 7.43. Temperature distribution (°F) for sample problem No, 2 at time = 34.115 hr and period of tidal of 2.751.

TIME = 35.355 HRS

PERIOD = 0.2851E 01 P. R # I

to

VELOCITIES

-

• »

• • i i I-.' • - - — — — — W. — _ • • • • • « , • • • » « .. • • « » « fc—

• * » » «

• • • * * " too

I 1 1 1 1 J 1 . ( . I 1 1 J 1 __!_ .1 1 1 1 1. 1 I , L t— 1 1 1 i -L a -L. I » t. 1 1 1 J 1 L_

CM

20 40 60 f P. » 2 ( — '

80 100 120 140 160 180 FEET • 0.1E-02

Figure 7.44. Velocity distribution (ft/hr) for sample problem No. 2 at time = 35,355 hr and period of tidal of 2.851.

TIME = 35.355 HAS PERIOD = 0.2851E 01 P.P.#1

zuz

DEPTH »o.ozo"

TTT i ! i I • • • I •

0.3744E 02

CM

^ I £ 1 lO I « I X i

I

20 40

I ooi ol <»-; <ni N'l Kl ro' toi I I i i l I ,i i i

i I .ll'l 60

-j, i i—J _f 80

P.P. # 2

»oJ , I 5 Oi • ool i ?o| I > i i : i <

100 -j—k_

i: : I i! lO & % 1 i I !

3 ! f*

120 140 160 FEET « 0.1E-02

180


TIME = 35.355 HRS


TIME = 37.205 HRS PERIOD = 0.3000E 01 VELOCITIES

z a LJ u o

100 FEET « 0.1E-02

to to 00

Figure 7.47. Velocity distribution (ft/hr) for sample problem No. 2 at time « 37.205 hr and period of tidal of 3.00.

TIME = 29.155 HRS

PERIOD =

CSJ

0.3000E 01 | p p . # i

20

(M 10 0> tO II X

40

JW I

s si

60

CM u> 2i K)

"I lis

DEPTH OH » 0.020 FT

<0 <ri to

<fi I <01 Si

pi 0>l ro<

o 00 a> to

•J L. 1—1 I L. 80

0.3960E 02

ft S' IOI

100 120 140 160 P.P. # 2 FEET * 0.1E-02

180


TIME = 37.205 HRS


TIME « 25.435 hr PERIOD" 2.051

4 P.P. # 4 VELOCITIES

<v _

i I I I I I I I I L I l I •I I. I L T P.P. # 2

J I I L H8 50 52 54 56 58 60 62 64 66 68 70

FEET « 1.0E-03

76 78 60

Figure 7.50. Velocity distribution (ft/hr), at the zone of power plant discharges, for sample problem No. 2 at time = 25.435 hr and period of tidal of 2.051.

TIME =25.435 hrs P E R I O D S . 0 5 1

P . R # I DEPTH (A H« 0.01 ft) 4.0460E 01

40.49 *

6 H

X

4 0 . 4 9

r . i i i i i i i • i i i i i i i i i i L 50 52 54 56 58 60 62 64 66

FEET a 1.0E-03 I l T * P.R#2

Figure 7.51. Water depth distribution (ft), at the zone of power plant discharges, for sample problem No. 2 at time = 25.435 hr and period of tidal of 2.051.

Figure 7.52. Temperature distribution (°F), at the zone of power plant discharges, for sample problem No. 2 at time = 25.435 hr and period of tidal of 2.051.

TIME * 27.915 hrs PERIOD = 2.251

P.P.#I VELOCITIES CO m

C\J

• ' I • I I 1 1 I 1 1 I I I I I ' ' I I I I I I I L_ I I I I I L . 48 50 52 54 56 58 60 62 64 66 68 70 72 |74 7S 78 80

FEET « 1.0E-03 P. P. # 2


T IME s 27.915 hrs PERIOD =2.251 P. P. # I DEPTH (AH«O.Ol f l ) 4.2660E 01

cn to 0 1

oj

UJ UJ

cvi o cvi "t

0) to cvi a>

ca'

i i I i I I 1 1 1 1 L J I I u

<0 <0 cvi

50 52 5H 56 58 60 62 6U 66 FEET m 1.0E-03

68 70 P. P. #2

J L

UJ a CO z < ut o o

IV) 04 tn 76 78

Figure 7.54. Water depth distribution (ft), at the zone of power plant discharges, for sample problem No. 2 at time = 27.915 hr and period of tidal of 2.251.

T I M E = 2 7 . 9 I 5 hrs PERIOD » 2 . 2 5 1

P.R # 1 r ~ l 8 7 °F

TEMPERATURE 7.9000E 01

FEET • 1.0E-03 P.P. # 2


TIME a 29J55 PERIOD • 2.351 __

- ™ * 1 VELOCITIES (O Q .

CO

I I I I—I I—I—I—I—I—I—I I I I I I I I I I I • I I I I I • 48 50 52 54 56 58 60 62 64 66 68 JO J 7 2 7 4 76 l l 80

FEE7 * 1, 0E-03 P . P # 2


TIME =29.155 hrs PERIOD^ 2.351

P. R # 1

CO CO o I UJ CJ

* h~ UJ UJ l i . —

o (si

J l L

DEPTH 4.2340E 01

0> rO cvi

J l L

CO ro cvi

N fO cvi

<0 fO csi *

J I I I I L — 1 — 1 I I L 50 52 54 56 58 60 62 64 66

FEET « l.CE-03

IO cvi *

in to d IO

cvi

70 ^2 | 74 P.P. # 2

j__l L 76 78

Ui Q tn z < bJ O O

K) W 00

F i g u r e 7 . 5 7 . W a t e r d e p t h d i s t r i b u t i o n (ft), a t t h e zone o f power p l a n t d i s c h a r g e s , f o r sample p r o b l e m No. 2 a t t i m e = 2 9 . 1 5 5 h r and p e r i o d o f t i d a l o f 2 . 3 5 1 .

TIME = 29.155 hr PERIOD = 2.351

Figure 7.58. Temperature distribution (°F), at the zone of power plant discharges, for sample problem No. 2 at time «* 34.115 hr and period of tidal of 2.751.

TI M E = 31.635 hrs PERIOD =2.551

P. R # t r - \

VELOCITIES

UJ o

z < UJ o o

IsJ o

J I I I I I L l i l t I 1,1 I I. I 46 50 52 54 56 58 60 62 64 66 68

FEET « 1.0E-03 70

I I I. I l I n P . R * 2

J 74 76- 78 80

F i g u r e 7 . 5 9 . V e l o c i t y d i s t r i b u t i o n ( f t / h r ) , a t t h e zone o f power p l a n t d i s c h a r g e s , f o r sample p r o b l e m No. 2 a t t i m e = 3 1 . 6 3 5 h r and p e r i o d o f t i d a l o f 2 . 5 5 1 .

TIME = 31.635 hr PERIOD = 2.551

P.P. # 1 DEPTH 3 . 9 5 8 0 E 01

FEET « 1.0E-03 RR # 2


TIME =31.635 hrs PERIOD =2.051

Figure 7.61. Temperature distribution (°F), at the zone of power plant dischai'ges, for sample problem No. 2 at time = 31.635 hr and period of tidal of 2.551.

TIME = 34.115 hr PERIOD = 2.751

P.P.#< VELOCITIES ID

tn o i UJ o

UJ UJ

J l L J ! L J I I L J I I I I L J l _ J L I I I I L 50 52 54 56 58 60 62 64 66 68

FEET « 1. QE-03

70 76 78

P .R#2

Figure 7.62. Temperature distribution ( ° F ) , at the zone of power plant discharges, for sample problem No. 2 at time «* 34.115 hr and period of tidal of 2.751.

T I M E S 3 4 . I I 5 hrs PERIOD® 2.751

P.R# I DEPTH 3.73l.'0E 01

11 11 i

in ro <T tn

i> rt N to

I I V <0 Hi N ro

i a Si • i

IO r-' m <70 «o N' to

• ' i I I L

10 IO

o

r» J I I i I I L

Oi

to1, i i i m \ S j •o , f\ I I » I * I I t

It K «o A

J I I L

rl rt"

J L 68 70 j72 T 76 78

P. P. # 2 50 52 54 56 58 60 62 64 66

FEET • 1.0E-03

F i g u r e 7 . 6 3 . W a t e r d e p t h d i s t r i b u t i o n ( f t ) , a t t h e zone o f power p l a n t d i s c h a r g e s , f o r sample p r o b l e m No. 2 a t t i m e = 3 4 . 1 1 5 h r and p e r i o d o f t i d a l o f 2 . 7 5 1 .

TIME » 34.115 PERIOD = 2.751


TIME * 35.355 hr PERIOD "2.851

P.P. # 1 VELOCITIES

m 0 1 U J o

CM

£ °

• ' ' ' ' » I I I I 1 I I I I » ' ' • • _J 1—1 L I I I I I L. TO 72 »74 76 76 80 rr

P.P. # 2

48 50 52 54 56 62 60 62 64 66 68 FEET « 1.0E-03


T I M S o 3c •p£3lT3CD»* L '5'i

P . P . * ! DEPTH 3.7460E 01

<n cn 0 1 UJ CD

fU

UJ UJ

to

COL

OH

I I

o m K ro

W in K to

IO » K «o

to K

tf> m; K K)

in

• \ • i «

<o 3 CO

to tn

f ' i

. i ». i > t j I l I I I l L

r-IO m

50 52 54 56 58 60 62 64 66 FEET u l.OE-03

J i I i—I i I i i i t .

UJ o

2 < UJ o o

ro -o

68 70 |72 > 74 "76 78 P. P.#2

F-rgirre 7 . 6 6 . Water d e p t h d i s t r i b u t i o n ( f t ) , a t t h e zone o f power p l a n t d i s c h a r g e s , f o r sample p r o b l e m No. 2 a t t i m e = 3 5 . 3 5 5 h r and p e r i o d o f t i d a l o f 2 . 8 5 1 .

T I M E - 3 5 . 3 5 5 hr» P E R I O D « 2 . 8 5 1 TEMPERATURE 7.9000E 01

CM

1 I I I I I I I I 1 I I I I I I I I I I I i92££_L E - p r P.R#2

50 52 51 56 58 60 62 64 66 FEET a 1.0E-03

68 70 76 78


TIME = 37.205 hr PERIOD = 3.0

r o o I

nj

UJ

P.P. # I n VELOCITIES

j I l L I ' ' I I ! I I I I I I I I I I I I J L- I I I • I • 48 50 52 54 56 58 60 62 64 66

FEET k 1.0E-03 68 70 72 74 76 78

P.P. # 2

F i g u r e 7 . 6 8 . V e l o c i t y d i s t r i b u t i o n ( f t / h r ) , a t t h e zone o f power p l a n t d i s c h a r g e s , f o r sample p r o b l e m No. 2 a t t i m e = 3 7 . 2 0 5 h r and p e r i o d o f t i d a l o f 3 . 0 0 .

TIME - 3 7 . 2 0 5 hr

PERIOD = 3 . 0

DEPTH 3.9800E 01

FEET 1.0E-03 P.P. # 2


Tl ME s 3 7 . 2 0 5 hrs P E R I 0 D « 3 . 0 p.r#i TEMPERATURE 7.9000E 01


252

of hours, which seemed to be limited mainly by the diffusive part of the stability criteria developed in Section 6. On the other hand, the stable time step for the full thermal-hydraulic model was much smaller and was restricted mainly by the convective part of the stability criteria.

After gaining confidence with the use of the time step required for numerical stability, it was apparent that even when the solution was completely stable, it demonstrated oscillations with space; that is, the values of both water elevations and velocities were alternating for successive discrete elements. A close insight into the actual calcu-lations performed by the computer program revealed that the problems come from the fact that both the water elevation (which is the driving force for the velocities) and the velocities (which are caused by water elevation differentials) are calculated at the same point (at the center of the discrete element). From the physical point of view the convecting fluxes must be evaluated on the half-point boundaries of each discrete element. This was indeed done, but the half-point values were based on linear interpolation between the two neighboring center values, which are the only ones calculated from the differential equations themselves. It seems more correct to evaluate the convective velocities at. the half-point boundaries of each discrete element based on the differential equations themselves rather than on linear interpolation. To do this will require a stagger d mesh, so that all the transported values will be calculated at the center point of each discrete element, while the convective velocities will be calculated (based on the actual differential equations and not linearly interpolated) at the half-point boundaries of

253

each such discrete element. The use of such a double staggered mesh system will complicate the numerical solution considerably.

It is also clear that if the mesh size is then small enough so that any disturbance is well distributed between a number of discrete elements, the oscillations will be eliminated or at least minimized. However, such a course will dramatically increase the ratio of computer time to real time because of the effects of both increase in number of elements and decrease in the size of the time step required for numerical stability.

As a temporary measure, those oscillations were successfully eliminated by the use of an averaging technique between each two successive discrete elements. These averaging calculations are performed at the end of each complete time in a special subroutine called FILTER. It is recommended that the filtering technique, the staggered mesh sys-tem, and the reduced mesh size, as well as other possible solutions, be investigated for the best way to eliminate those oscillations.

As was mentioned before, the size of the time step must satisfy the stability criteria devi'oped in Section 6. This, in addition to the fact that the computer time required for each time step for such an extensive model is understandably large, created a major financial obstacle to the ability to fully investigate the capabilities of the model by way of parametric studies under extensive sets of specified conditions. The two sample problems chosen here and presented in Sections 7.3.1 and 7.3.2 are designed to demonstrate the validity of the model (sample problem No. 1) and its capabilities (sample problem No. 2). Because of

254

computer cost and financial limitations, both sample problems were run on a reduced version of the model which does not include the calculations of constituent mass concentration, and both sample problems were stopped before complete steady-state equilibrium had been achieved.

Figures 7.3 to 7.27 pages 102 to 206, show the results of the computer run for sample problem No. 1 in the form of plots for velocities (Figs. 7.3 to 7.6), water elevations (Figs. 7.7 to 7.22), and tempera-tures (Figs. 7.23 to 7.27). The symmetry of the flow around the discharge and intake points can be very well seen in all the above figures and specifically in the streak plots for velocities. In some cases the con-tour plots did not come up very smooth and the symmetry is not perfect in spite of the fact that corresponding printed output shows complete symmetry. That may be a result of the interpolation technique used in the plotting routines and the number of points available for this interpolation. It can be seen from Figs. 7.3 to 7.6 that hydraulic equilibrium at the inlet point is achieved rather fast. At the outlet point, it takes a few hours to achieve hydraulic equilibrium. Figure 7.6 shows a blown-up plot of the velocities at the vicinity of the inlet.

The mass balance has been checked by calculating the mass flows in the X direction at corss sections near the inlet and outlet points and comparing them with the total mass flow supplied at the inlet. At time 124.45 hours after initial conditions, the inlet flow was 30,080 cfs. At that same time the total flow in the X direction at a cross section 7,500 ft from the inlet point was 30100.7 cfs, which is an excellent agreement of +0.07%. The total flow in the X direction at a

255

cross section 7,500 ft from the outlet point at the same time was 29,677.4 cfs which is also in a very good agreement of -1.3 percent, especially when the agreement might be further improved with time since complete hydrau-lic equilibrium was not yet achieved at the outlet.

Figures 7.7 to 7.15, pages 186 to 194, show the changes in water elevations with time over all the area modeled. Figures 7.16 to 7.22, pages 195 to 201, show a blown-up plot of the water elevations at the vicinity of the inlet. It is interesting in those plots to see the wave propagation and also the fact that the water elevations seem never to come to complete rest (at least not within the 124 hours of the run).

Figure 7.23 page 202, shows the temperature distribution and the spread of the heat around the discharge point. Since the farthest point to which change in temperature can be detected is less than 30,000 ft, Figures 7.24 to 7.27, pages 203 to 206, show blown-up plots of tempera-ture distribution within this area. Thermal equilibrium was definitely not achieved. It must take more than 1,300 hours for a particle to move from the inlet point to the outlet point. That means that convection cannot be relied on for fast distribution of the heat, and diffusion is even a slower process. However, the heat balance has been checked based on transient conditions by comparing the total heat dumped into the water body to the heat absorbed by the water plus the heat lost to the atmos-phere. The total heat dumped into the water body during the first 124.45 hours is

256

Q. = G. Cp. AT. At = (540 x 5000 x 40.08 x 62.2) x 1.0 x 15 Xxn m *in in v 1

x 124.45

= 6.731 x 109 x 1.0 x 15 x 124.45

= 12.565 x 1012 Btu/hr .

The total heat absorbed by the water during this period is

N N Q = I A.H.p.Cp. AT. = AH oCp 7 AT. xcap . I x a x avK * .L. x r i=l i=l

= 25 x 106 x 40.08 x 62.2 ;; 159.2 = 9.922 x 1012 Btu/hr ,

The total heat lost to the atmosphere must be calculated by increments

of time. However, approximating it by the heat loss at the time 124.45

hours, one gets

N N Q. = I h.A.(T. - T_) t = h-A- t V (T. - T_) uost ^ x xv x E' 1 E

= 5 x 25 x 106 x 124.45 x 159.2 = 2.477 x 1012 Btu/hr ,

which gives an error of

Qlost * Qcap 2.477 + 9.922 . Q.n = 127565 l l 3 % •

The heat lost to the atmosphere, however, is proportional to the

excess temperature which itself changes with time. Performing the same

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calculations by increments of time gives an error of about 10 percent. In any case the agreement seems to be good considering the crude way the heat balance was performed.

Figures 7.29 to 7.70, pages 210 to 250, show the results of the computer run for sample problem No. 2 in a form of plots for velocities, water elevations, and temperatures at seven successive fractions of the tidal periods. Figures 7.29 to 7.49, pages 210 to 229, show the full area of the estuary modeled, and Figures 7.50 to 7.70, pages 230 to 250, show blown-up plots of the area around the two power plants, giving the changes of water velocities and water elevations with the tidal period. The dashed lines indicate water elevation below 40 ft. Unfor-tunately, the scale of the velocity vectors does not allow the direction of the flow to be seen clearly near the intake and discharge points of each power plant, although this is apparent in the plots for water elevations, and also in the printout of the results (see Appendix A). The interaction between the two power plants can be clearly seen in the plots for temperature distributions in both the full-area plots and the blown-up plots. Also, the cooling effects of the ocean temperature, which was set to 70oF, can be seen very clearly. The maximum temperature occurs at each power plant after slack water at the beginning of the ebb period. The maximum temperature at power plant No. 2, which is about 5 miles downstream of power plant No. 1, is higher because of the effect of heat convected downstream. It can be seen very clearly that the intake temperature of each power plant is much above ambient temperature. Recir-culation of hot water from discharge to intake is properly taken into

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account. The full extent of the interaction between the two power plants may not yet have taken place, since the plots reflect only the third tidal cycle from the start of the problem. Quasi-steady-state conditions may not be achieved before at least 10 cycles. Nevertheless, most of the effects are already apparent. It is most satisfying to realize the capability of the model to handle such a complicated case of interacting power plants situated acorss from each other in an oscillating water body.

8. SUMMARY AND CONCLUSIONS

The objective of this study was to develop a time-dependent, two-dimensional mathematical model for predicting the velocities, water levels, temperature, and mass concentrations of various constituents in shallow vertically mixed water bodies. In order that such a model be useful, it must be capable of taking into account the very many complex contributors affecting the behavior and characteristics of such natural water bodies. Such a model must necessarily be highly nonlinear and is constrained by an extensive number of boundary conditions. For that reason the numerical approach is inescapable. In addition, it is recog-nized that for a prediction of various discharges into natural water bodies the model must incorporate both the immediate vicinity of the discharge point (nearfield) and the more distant zones (farfield), which are quite different in nature.

The model developed in this study meets most of those requirements although not all of them. The capability of the model to take into account complex factors affecting natural water bodies is almost unlimited. On the other hand, the use of the model for both the near field and the far field combined is limited mainly by our ability to understand and properly model the turbulent phenomena and the turbulent transport properties. The normal and shear stresses, which are properly included in the model, cannot be used to their full potential because of this basic limitation.

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The major conclusions which can be derived from the present study are as follows.

1. The discrete element method can be successfully used for simulating natural water bodies based directly on the basic conservation principles of mass, momentum, and energy. This direct application of the conservation principles eliminates the need for first deriving complex partial differential equations and then integrating them numerically, based on rigid rules of differential calculus. Such an approach is very helpful to the practical engineer and scientist because of the clear identification of the various physical 'phenomena as well as the physical constraints expressed by the model boundaries.

2. It was demonstrated that the discrete element formulation of the conservation principles of mass, momentum, and energy can be easily reduced to the classical finite difference formulation of those principles by taking the limits as AX -> 0, AY •*• 0, and At 0, as is nor-mally done in this formulation.

3. The time step criteria required to ensure numerical stability have been developed based on the discrete perturbation method for each one of the equations. These criteria include the effects of variable sizes of discrete elements, variable transport properties, convective effects, diffusion effects, surface heat and mass exchange on both bottom and top surfaces, and volumetric discharge and/or intake of both mass and heat. A more simplified but rather more conservative criterion commonly valid for all the equations has been developed for simpler and faster application.

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4. Very complex factors affecting natural water bodies, such as wind, rain, evaporation, heat exchange with the atmosphere, seepage, bottom shear stresses, tributaries, tidal oscillation, and others, have been taken into account in a two-dimensional model. These factors can be realistically specified as both functions of space and time (although the time scale is smaller than turbulent time scale fluctuations).

5. The full simulation of normal and shear viscous stresses (laminar and turbulent) has been included in the momentum conservation equations. This allows the model to be potentially valid for simulating both near- and far-field regions. Full utilization of that potential is limited, however, by the limited capability to properly simulate and model turbulent transport properties.

6. The model is capable of simulating the mass transport of any numbev of constituents in the water body and the interaction between them. Full utilization of this capability is also limited by our present ability to model turbulent transport properties, specifically for moê than two-component mixtures. However, used as such, the model can properly simulate salinity concentrations in salt intrusion zones in estuaries or mass concentrations of any number of noninteracting consti-tuents discharged into a water body.

7. The model is capable of simulating discharges from a number of sources, including power plants, and properly takes into account the interactions between them as well as the recirculation effects between the intake and discharge structures. This capability is most valuable for assessing the impact of discharges from power plants or other sources

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on the physical (and, therefore, also biological) environment of natural water bodies.

8. Because of its truly transient nature, the model is capable also of predicting rate of change of temperatures. Such information is very valuable for assessment of cold shock effects on aquatic biota when sharp discontinuities of start-up and shutdown in power plant operation occur.

9. Because of the inclusion of any number of constituents in the model and its capability to simulate intake structures, the model can potentially be extended to a full population distribution model for aquatic organisms in natural water bodies.

10. An extensive "decision making" network has been incorporated in the program for accepting the many possible physical boundary con-ditions. As can be imagined, with a minimum of six unknowns (assum-ing a mixture of two components only) and two space dimensions, such a logical network can be very complicated, and indeed it is. However, it allows the analyst to specify almost any realistic boundary con-ditions, which constitute, after all, the best chance to impose "reality" on a mathematical model.

11. The model was applied to two sample problems which demonstrated its workability and capabilities. The situation chosen in sample problem No. 2 is typical of realistic situations which are analyzed in environ-mental impact assessment and which definite]" all for a time-dependent model like the one developed in this study, i'he ability to take into account the effects of interaction between two power plants situated

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across from each other on the same water body under tidal conditions is most encouraging. Of course, a full verification of the validity of the model can be performed only by a very careful comparison with field data. Such a program is very strongly recommended for the future.

12. The application of the model with an extensive number of typical cases has shown that specification of a discontinuous function causes oscillations of the calculated velocities and water elevations with respect to space. These oscillations can be eliminated by the use

78 of a finer mesh size which satisfies the cell Reynolds number. However, satisfying this criterion requires the use of a very small grid mesh and, therefore, also a very small time step. The two requirements combined impose almost an impossible load on computer time. A temporary solution has been found by the use of the filtering subroutine, which eliminates these oscillations by an averaging technique. Another solution may be the use of a staggered mesh system. It is recommended that these and other methods be investigated to solve this problem.

13. Although the model is two dimensional and assumes vertically mixed conditions, this is not always the case found in reality. A three-dimensional model is very desirable from this point of view and will also reduce somewhat the necessity of using highly speculative shear flow dispersion coefficients to represent effects which are actually convective in nature. However, such models may be very costly to use, at least based on the presently available computing machines. Alternatively, an analytical method can be developed which will allow representation of vertical variations in a basically two-dimensional

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model. It is strongly recommended that this be done as the very next step to the present study, specifically for cases where stratification and vertical variations do exist but are not necessarily predominant.

14. A computer program of the size and nature developed in this study is expected to be costly to run. The computer time required will depend on factors like number of elements, size of elements, velocities, diffusion coefficients, and others. These factors also determine the minimum time step required for numerical stability. The basic computer time required for the reduced version is about 0.00295 second of the IBM 360/91 computer for each time step and element. The full version, with two constituents, requires almost twice as srijch. This is indeed an obstacle, since it makes it expensive to run parametric studies, trial and error solutions, and verifications. Since the program is still in its exploratory form and no serious attempt has been made to optimize it, there is room for sharply improving this computing time performance. It is recommended that this be done, and other methods should be investi-gated to reduce computer time. The storage requirements are reasonable and do not cause any special problems.

15. The most apparent limitation for realization of the potential capabilities of mathematical models (analytical and numerical) is the very limited ability pr&sently existing in realistically modeling tur-bulent transport properties. This fact is important especially when trying to simulate flow fields which are three dimensional in nature by two- or one-dimensional mclels. This limitation is a serious obstacle in a development of any model in fluid mechanics and seems to be the

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"bottle neck" for the progress in this area. There is a great need for research, both theoretical and experimental, in turbulent transport modeling and its application in computational fluid mechanics.

16. A general computer program of the size and scope presented here requires constant usage, verification with field data, calibration, modifications, and capability improvements. A computer code of that nature does not become a truly reliable predictive tool unless evolu-tionized through use and experience. It is hoped that this computer model will indeed be adapted and used by careful thermal-hydraulic analysts who are fully aware of its capabilities, and most importantly, its limitations, until it is proven to be completely reliable and productive.

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96. J. E. Edinger and J. C. Geyer, "Analyzing Steam Electric Power Plant Discharges," Proceedings of the American Society of Civil Engineers, Journal ol"the Sanitary Engineering Division, Vol. 94, pp. 61-623, August 1968.

97. J. E. Edinger, D. W. Duttweiler, and J. C. Geyer, "The Response of Water Temperatures to Meteorological Conditions," Water Resources Research, Vol. 4, p. 5, October 1968.

98. D. K. Brady, W. L. Graves, and J. C. Geyer, "Surface Heat Exchange at Power Plant Cooling Lakes," Johns Hopkins University, Depart-ment of Geography and Environmental Engineering, Report No. 5, November 1969.

99. J. M. Raphael, "Prediction of Temperature in Rivers and Reservoirs," Proceedings of the American Society of Civil Engineers, Journal of the Power Division, Vol. 88, pp. 157-181, July 1962.

100. E. L. Thackston and F. L. Parker, "Effect of Geographical Location on Cooling Pond Requirements and Performance," Project No. 16130 FDQ, March 1971, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

101. J. Proudman, Dynamical Oceanography, John Wiley and Sons, Inc., New York, 1953.

102. Saline Water Conversion Technical Data Book, Issue No. 2, prepared by the M. W. Kellogg Company for the Office of Saline Water, Data Sheet 0SW 11.60, March 1965.

103. J. W. Kurzrock and R. E. Mates, "Exact Numerical Solutions of the Time-Dependent Compressible Navier-Stokes Equations," AIAA Paper No. 66-30, 1966.

104. A. Thorn and C. J. Apelt, Field Computations in Engineering and Physics, D. Van Nostrand Co. Ltd., New York, 1961.

277

105. D. Thoman and A. A. Szewczyk, "Numerical Solutions of Time Dependent Two Dimensional Flow of a Viscous, Incompressible Fluid Over Stationary and Rotating Cylinders," Tech. Report No. 66-14, Heat Transfer and Fluid Mechanics Laboratory, Department of Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana, 1966.

106. G. G. O'Brien, M. A. Hyman, and S. Kaplan, "A Study of the Numerical Solution of Partial Differential Equations," Journal of Mathematics and Physics, Vol. 29, pp. 223-251, 1950.

107. C. W. Hirt, "Heuristic Stability Theory for Finite-Difference Equations," Journal of Computational Physics, Vol. 2, pp. 339-355, 1968.

APPENDIX A

COMPLETE INPUT AND OUTPUT FOR THE SAMPLE PROBLEMS

BLANK PAGE

Table A . l . Inpu t Data f o r Sample Problem No. 1

CASE T I T L P : T J S T P J P B I E B K O . I - s q u W E fQOL « I T H FLOU 1 » KT> 0 0 1

INPUT I N F O P I A T I O I P S o a S U B 9 0 U T I B E I B P ' ; T :

t«»D <0. I TOTAL MONTH OP CK. XL S P E C I E S CP CONSIBCTEO ( » * ) • 2

TOTAL (CU1BEP o r HEGIOBS ( l » E G ) > 1

TOTAL *UHBE» o r K I T I A L CdHDITIOHS FI1BCTI0IIS ( B I N I L F ) " 2

TOTAL H o n p c n o r »OLOBET«IC BEAT OH BASS G l a E B A T I O B POBCTIO«S IBqEBP) - 1

T n T » L « U 1 H [ » c f tOONDAIlT C O B P I T I O a S POBCTIOBS IBBBDF) • *

TOTAL HIHSFB cr TOP CONDITION MBCTIOBS <«TOPF>» 2

TnTAL a n i B H o r COTTON C O I D t T t O I S f l l » C T T 0 1 s t » » O T F ) • 2

TOTAL t a n ? * or ABALITICAL r o a c n c a s (BAILFC) - I

TOTAL I « O f TkBUUTCO r t l K C T I O M ( H T P t P C ) • t

TOTAL BUKBE* or caoss LATTICE LIBK IA I-OIBECTIOB (AICI I ) ' «

TOTAL BIHBE* o r GPOSS LATTICE L I B E S I « I - O I M C T I O B ( • T C I L | > <

TOTAL M H * M o r T E B P . IIOBITOalPG POINTS ( t T H A I ) • 1

CARD KO. 2

»ESTA»T PliO. ir EOOAL lEtO >0 FESTAKT HFOINATIO» IS ItgolAEC (ISTABTL • 0 'IBI5N riAG. IF tOOAL SSAO >0 StSTAPT FILE IS CBEATIO (IMaiS)' 0 P L O m a r . FLAG. TF EQUAL I E F O a o FLOTTIBC I«FOBNATIOB I S C E B I I A T E D . ( I P L O T ) • 0

rua ran SKPCTIIC THE yrniencn J»TECNTIO« FHOCEOOPF. I IBUT>I SELECTS JO»CE-KUTTA-CIIL RITH

I I I U ' J SEUCTS EOLE» ntuco. MTU'J SELECTS ADIK-EASBIIOHH KETHOD.) (I«T»T| . 1

CAPO W>. 1 STAMAS TINE or THIS CASE ts ini* o.o NOBLE* TF«E FOP THIS CASE <P*>T*)- 12B.0000

CONPBTEP T i n t CUIOFP L l f l l T l a S I C O I D S ( C P O S E C I « 2 9 5 . 0 0 TINE lacaemaT 'oa PBIBTEO OOTPDT |OP>TTH)> I.OOOO

T>I>Al p i a i o o t r AN ESTOA»F ( T I D A L ) » 1 . 0 0 0 0

C » » B 1 0 . •

K) co o

Table A..1 (continued)

I R I T I A L TIRE XRC1BRERT I S D t m • o.osooo LARGEST H R I T IO» TIKE I H C R M I R T (FDTm - 0 . 0 * 0 0 0

T I R E IRCRERERT I S K0LTIPLIED EVERT RDMC T I K I STEPS B I ( D I B I T ) » 1 . 0 0

RCRBER or Tint STEPS BEroRE PROCESS or I R C f t t l S E I t nut STEP SIZE BEG1IS (IHOTn) > to •ORBED OP T I R P STEPS BETVEER CHARGES I I T I R E STEP ( I D T K ) ' 5

CPITERIOR T I P E (IS OEPIRED I » SOBBOOTIRE CRROTR) TRAT SUCH OTR BILL BE REQUIRED TO SATISPT (LDTRCRI

TABOLATED PORCTIORS

TABLE < 0 . 1 TABARG TABPRC

0.0 0.0 1 . 0 0 0 0 D 0 0 a.OOOOD-OI 3 . 0 0 0 0 D 0 0 6 . 0 0 0 0 0 * 0 1 6 . 0 0 0 0 D 0 0 9 . 5 0 0 0 D - 0 1 8.00000 00 1.00000 00 1.00000 01 1.0000D 00 IRPOT IRPORRATIOR PROR SOBROOTtRt GEOR:

XGRL ( I ) - CROSS LATTICE LIRE I I B TRE X-BIRECTIOR

I«rO(H - RURBER OP SOBDITISIORS BETREER GPOSS LATTICl LIRES t G R L ( I ) IRD X C R L ( I » 1 ) .

T C P l ( I ) - CROSS LATTICE LIRE I IR T - D I R E C T I O R .

I I f D | I ) - R 0 R B I R OP S O B D I f I S I O R S BETVEER GROSS LATTICt LIRES 1 G B L I I I 1 R 0 T G R L ( I * 1 | .

T IGRL HPS 1 0.0 10 2 S.OOOOOD 00 1 3 5 . 5 0 0 0 0 0 on 10 o i.ofoooo o"; 1 TfiPL ITPD 1 0.0 10 2 5 . 0 0 0 0 0 0 OH 1 3 s.sonooo oo TO o l.osoono OS

NODAL UIOTR RODAL CERTER I «-DIRECTIOK Y-DIRECTIOR I-DIRECTIOR T-DIRECTIOR 1 5000. .00000 sooo. ,00000 2 .5000000 03 2. ,50 00 COD 03 2 sooo. .ooooo sooo. ,00000 7.SOOOOOD 03 7. .SOOOCOO 01 3 soon. .00000 sooo. ,00000 1, •2SOOOOD on 1. , 2500CQD on a 5000. ,00000 sooo. ,00000 1 .7500000 01 1. .7500 COD 0> 5 soon. ,00000 SOOO. ,00000 2 •250000D on 2. ,2500CCD 00 soon. .ooooo «000. 00000 2. .7SOOOOO OB 2. ,7«00C0B 00 7 sooo. ooooo sooo. ooooo 3. .2500000 oo 3. 2500CCD 00 8 soon. ooooo sooo. ooooo 3. •750000D on 3. 7500C0D 00


9 s o o o . . o o o o o s o o o . o o o o o u, . 2 5 0 0 0 0 0 OH n. .2SOOCOO 0 0 1 0 5 0 0 0 , . 0 0 0 0 0 • > 0 0 0 . o o o o o 1 . , 7 5 0 0 0 0 0 0 « . 7 5 0 0 C 0 0 0 0 1 1 s o o o , , 0 0 0 0 0 s o o o . . 0 0 0 0 0 5 . . 2 5 0 0 0 0 1 1 0 0 . 2 S C 0 C C 0 OH 1 2 s o o o . . 0 0 0 0 0 s o o o . o o o o o 5 . , 7 5 0 0 0 0 0 0 0 s , . 7 S 0 0 C 0 D 0 1 1 3 s o o o , . 0 0 0 0 0 s o o o . o o o o o 6 . 2 5 0 0 0 0 0 OH 6 . 3 5 0 0 0 0 0 DO 1 « s o o o . . 0 0 0 0 0 s o o o . o o o o o 6 . , 7 5 0 0 0 0 0 o n (. , 7 S 0 0 C 0 D 0 0 1 5 s o o o . , 0 0 0 0 0 s o o o . o o o o o 7 , , 2 5 0 0 0 0 0 o n 7 . , 2 5 0 0 1 0 0 0 0 1 6 5 0 0 0 , . 0 0 0 0 0 s o o o . o o o o o 7 . 7 5 0 0 0 0 0 o n 7 , , 7 S 0 0 C 0 D o n 1 7 5 0 0 0 . . 0 0 0 0 0 s o o o . o o o o o 8 , , 2 5 0 0 0 0 0 o n 8 . . 2 S 0 0 C 0 D OU 1 8 s o o o , . 0 0 0 0 0 SOOO. o o o o o a . . 7 5 0 0 0 0 0 0 0 e , . 7 S 0 0 C 0 D o n 1 9 5 0 0 0 , . 0 0 0 0 0 s o o o . o o o o o 5 , , 2 5 0 0 0 0 0 o n 9 , •2SOOCOO o n 2 0 5 0 0 0 , , 0 0 0 0 0 s o o o . o o o o o 9 . 7 5 0 0 0 0 0 o n 9 . , 7 « 0 0 C 0 D o n 2 1 s o o o , . 0 0 0 0 0 s o o o . o o o o o 1, , 0 2 5 0 0 0 0 OS 1 . 02SOCOD OS


GEonermc DESCRIPTIOH OF BEGIOHS IHDEXXCAL DESCRIPTION GIOH utx DUX opt OUT DEPTH ASEA I LOU IHIGH J LOW JHIGH HODES

i 0.0 50000.00 0.0 50000.00 UO.OOC 2 5000D 09 1 10 1 10 100 2 0.0 50000.00 50000.00 55000.00 10.000 2 5000D 08 1 10 11 11 10 3 0.0 50000.00 55CC0.00 105000.00 UO.OOC 2 5000D 09 1 10 12 21 100 u 50000.00 55000.00 0.0 50000.00 00.000 2 5000D on 11 11 1 10 10 S 50000.OD 55000.00 50000.00 55000.00 HO.000 2 5000D 07 11 11 11 11 1 6 50000.00 55000.00 55000.00 105000.00 no.ooo 2 5000D 08 11 11 12 21 10 7 55000.00 105000.00 0.0 50000.00 HO.000 2 5000D 09 12 21 1 10 100 8 55000.00 105000.00 50CQ0.00 55000.00 HO.000 2 5000D on 12 21 It 11 10 9 55000.00 105000.00 550C0.00 105000.00 no.ooo 2 5000D 09 12 21 12 21 100

TOTAL HO. o r BODES III (IHPOt) BEGTOHS" «<»1 HAX. HO. OF HODES IH GRID* ""I

POHCTinie ELECTION IHTF IGBKF ITOPF I F 0 1 I 0 0 0 0 0 0 0 0 0

BOOHBART SELECTIO« tOCUB JD»)><> WIS ! f t S

M 00

•0HBER OF ELEMENTS AVAILABLE III AHHAY t It 3AIN = 86CO

ANIIBEN op ELEHEITS NEEDED < e s n

COSITtOKS TO BQHI10B TEBrEBATOSE

II REQUESTED LOCATION X I

1 2 5 0 0 . 0 0 " 5 2 = 0 0 . 0 0 0 2 1 0 2 5 0 0 . M O 5 ? ' . 0 0 . 0 0 0 3 SZICU.AOO 2S00.00I>

SELECTED 1IODE I J

1 21

11 11

RODE L O C M O N X \

2 5 0 0 . 0 0 0 W O O . 0 0 0 10239C.OOO S J 5 0 0 . 0 0 0

5 2 5 0 C . 0 0 Q 2 5 0 0 . 0 0 0

NODE REGION

Table A.l (continued)

HO DA I. DISPLAY POS UPSTBBAH BOO>ir»BIES I B J - D I B E C H O I I,»ei ! l l

J= 21**1 1- 20««1 J - 1 9 « « 1 J = 1 8 » * t 0= 11**1 J = 1 M « 1

1 5 * « 1 J= IU**1 J = 1 3 * * 1 J= 12**1 ii**2 10*«1 J = 9 * * 1 j= 8*.1 J= 1»*1 J = 6 * * 1 J = 5 * » 1 3- U * « 1

3 * * 1 J = 2 » * 1 J « 1 * * 1

00 -f*


MODAL DISPLAY FOR DOIUSTBEAI1 BOUBDAPIES IH I-OIBECTION,DBXP

« 21»« - 20»«

• »8«» a 17** = »«•» = 15»« s m«» « 1 3 " I! 12«» • 11« » <(«» * R«* 5 7«« a 6«* = <;•* = a** S 3»« = 2«« = 1»»


»ODJL DISPLAY FOB UPSTBBAII BOUNDAFIES III Y-DIRECTIOH,«ETH

J = 2 1 " 3= 20" J= 19*. J= 18" 3- 17" J= 16" 3= 15" Js 1U" 13" J= 1 2 " J= 11" 3- 10" J= 9" J - 8 " 3= 7" J= f" J= 5" J= U" J= 3" J= 2" i««un>tuttubtiuiiuutiatm(iauuu


MODAL DISPLAY FOB DONNSTREAI1 BOUNDARIES IN I-DIRECTION,»BTP

j= 2i**uiiaubuaciaticiuc(uctii>iui£ua 2 0 "

J= 19"» 3= 1B»» J= J= 1 6 " J= 1 5 " J= 1U" J= 1 3 " J= 1 2 " J= I T " 3= 1 0 " 3= 9 " 3= 0 " J= 7 " J= f " J= « J= U " 0= 1" J= ?" J - 1 "


NOPfcl DISPLM POP BEGIOWS

= 21««33 « 20««33 S 19»«33 = 1B«»33 = 17«»33 * 16««33 » 15«33 = 1LL«»33 « 13»«33 E 1 2 " 33 » 1I««22 = 10«»11 * 9*»11 > 8««11 = 7»*1 I . 6"11 5 W»11 i lt«*U S 3»»11 = 2«M1

w«n

J3369999'99999 333€999q999999 33369999999999 333699999QQ99Q

33369999999999 333699999"9999 33369999999999 33369999999999 33369999999999 3336999999A9 99 22258B8FL89B38I> 11197777777777 11197777777777 11197777777777 >1197777777777 11197777777777 11197777777777 1110777777777'' 11107777777777 11107777777777 11107777777777

N) 00 00

T a b l e A . l ( c o n t i n u e d )

IBPOT i » r o p n » T i o K PPOH SOBBOOTIBI GEBCOH

IGEBPC - INTFBBAL GIBEBATIOB PUBCTIOB (A« IBOEI) QDV - VALOR OF HEAT GEBEBATIOB FER OBIT VOLOBT IB IBTIBBAL GEMBATIOB FOBCTIM IOOVF - GEMBBAL PURPOSE POKCTIOB TO ay ASEO on cor GKDV|Kk - VALUE OF BASS GEBEBATXON PKR OBIT VCLtME rCF SPECIE K IV INTERNAL GEBEFATIOB PUBCTIOB IGKOVF(K) - GEMEBAL POBPOSE IOBCTIOB TO Bf OSES OB GBCV(B)

IC rGEBPC QOt TOD VP CKtt(l) IGUCVFID GKDV (2) IGBCVP(2) 1 1 0.0 0 0.0 0 0.0 0

NI 00 lO


INPUT INFO«BATION M l . I I 3UBROI1TI HI BaDCON:

NBBDTP - » i p r o r BOUNDARY CONDITICF POR »ATIR m v n T t c i i « t « n e o T P ) HO - TYPE OF BOUNDARY COkDITION ICR YELOCIIY 0 |Kl)»DTtl » » - TYPE OF BOUNDARY CONDITION FCP YILOCITY V ( R » P n P ) NT - TYPE OF BOUNDARY CONDITION IOR T U P . OR S P I C 1 E S CONCENTRATION (NBTOTP) FH - VALUE Or BOUNDARY CONDITICN FOR WATER E L E U H C N (FHPDl FU - VAIOE OF BOUNDARY CONDITION FOR V H ITT U (FIIPC) FY - VALUE OF BOUNDARY C O N M I I O N (OR VELI--ITY 1 < M B O ( FT - VALOE OF BOUNDARY CONDITION TOR TPFLP. (FTBD) RO - TALUE OF BOUNDARY CONDITION RCR BASS FLUI (FGB0| FO - VALUE OF BOUNDARY CONDITION (OR BEAT FLUI (FCBt) rSBCN - VALUE o r BOUNDARY CONDITICN FCP NORSIAL STRESSFS FGR(1 | - VALUE OF BOUNDARY CONDITION FOR BASS FIIII CF SPECIE « (FCKBD) FCR " VAIUF. OF BOUNDARY CONDITICN FOP SPECIES CONCFMfATIO* (KKBC> IHFIDF BULTIPLIED FUNCTION FOR FNBD IU - MULTIPLIER FUNCTION FOR FUBD IF _ naiTirtlu FUNCTION FOR •HBO IT BULTIPTLER FUNCTION FOR FTBO 1G - M I L T I W ER FUNCTION (OR FGBD 10 • BULTIPLIER FUNCTION FOR ISN - BULTIPLIER FUNCTION (OR FSBDN ISH - BULTIPLIER FUNCTION FOR FSBDSB

BOUNDARY CONDITIONS AT STARTING T I N E NOD NHBOTP RO NF NT FH t « 1 2 2 0. ,0 2 it 1 1 1 0. ,0 3 1 U It a a, .0000000 a a 2 1 2 0 ,0 i b 1 1 1 0 .0

FU 0.0 S.UCCOOOB 02 0.0 0.0 0.0

»« 0.0 0.0 0 . 0 0.0 «.t65600» 02

FT 4.0000000 01 9.500000D 01 7.0C0000D 01 0.0000000 CI

-1.50000110 ftl

K) <o o

NBN FG FO FSBON PSPOSW FCIt(1| FGK(21 FCR (11 FCM2I • o.o o.o o.o o.o o.n o.o i.noo o.o 2 0.0 O.o 0.0 0.0 0.0 0.0 0.121 0.077 ) 0 .0 O.o 0 .0 0 .0 0 .0 0 .0 0.911 0.027 g O.o O.o 0.0 O.o 0.0 0.0 1.000 0.0 5 O.o 0.0 0.0 0.0 0.0 0.0 1.000 0.0 BUITIPLIER rUVCTIONS FOB BOUNDARY C O N D I T I O N NBN IBBDF 10 II IT IC IC ISN ISH 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0

POKER PLANT ON MUNDARt .

NBN DTPP(NRN) J I N T

5 1.500B 01 N.75000D Ok YINT I

2.S00C0D 03 10


R»p or Mrotmrrioi rtoi SOBPCOTINE tar com

oa - HEAT Conine riton TRE BCTTOR HCB - HEAT TRANSFER COEFFICIENT I CP THE BOTTOH OB - VELOCITY Or BASS CORING FPCR TNE BOTTON IN I-D1RICTION VB - VELOCITY OP HASS COSING PRCH THE BOTTOH IN Y - D 1 R K T I O N • B - VELOCITY OP HASS CONING FRCR TRE BOTTON IN I - D I R J C T I O N TB • TEHPEPATURE OP HASS COMING FROR THE BOTTOR BKANGC - BANNING COEr. ro» rPlCTICN »ITH THE BOTTO« DCKB - PASS DIFFUSION COEFFICIENT FOP SPECIE R FPOH BCTTOR CUB - HASS 1 ONCENTRATION OF S P E C K S CORING FPCR B O t l O P I0B - HtllTJniER FUNCTION FOR Of IHCB - HOLTlpLXSR FONCTION FOR «CC IUB - HULTIPLItR FUNCTION roR UP I»B - HBLTIPUER rORCTIO* FOR TE INB - RULTIPLIER FONCTION FOR HE ItR - HULTIPIIER PDRCTIOV FOR Tf IDCKB - H U 1 T I P U E R rUNCTION FOR OCRB ICRS - HOLTIPHFR PONCTION FOR CR8

BOTTOH CONDITIONS AT STAPHNG TIHP PCT. NO. 0 E HCB UB VP HP 1 0.0 0.0 0.0 0.0 0.0

2 0.0 0.0 0.0 0.0 0.0

TB NRANGC 8 . 0 0 D 0 1 4 . 3 3 3 - O b 8 . 0 C 9 0 1 8 . 3 1 D - 0 S

ROLTXPLIEN FUNCTION FOR BOTTcn CONDITIONS FCT.RO. I0E IHCB I0B IIP 1«B 1TB IDCKB(1) ICKI(1) 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0

DCKB [1) 0.0 0 . 0

;Ci.'»t(2| ICKB (21 0 0

CRB(1» 10.00 10.00

OC«B|2| 0.0 0 . 0

CRBI2) 0.0 0 .0

N) <o

INPUT INPOPRATtON PBOR SUBROUTINE TOPCON:

AT - HEAT COHINC. FROH THE TOP HCT - HEAT TRANSFER COErFICIERT FCR TOP OT - VELOCITT OF HASS CORING FROH THE TOP IH I - D I R I C 1 I 0 N VT - VELOCITY OF HASS COHING PBOR THE TOP IN Y-DIRECTION NT - VELOCITY OF HASS CORING FROH THt TOP IN E - 0 I R E C 1 I C N TT - TENPEPATOBE or HASS CORING FROH TR? TOP TO - DEN-POINT TEHPERATURE OSOL - SOLAR HEAT PLOI OCKT - PASS DIFFUSION COEFFICIENT TOR SPECIE ( FROH TCP CRT - HASS CONCENTRATION OF SPECIES CORING FROR THE TCP IQT - HOLTXPLIER FUNCTION FOR OT IHCT - HUlTIPirER PO»CTIOH P0» HCT IUT - HULTIPLIEP FUNCTION FOR OT IVT - MULTIPLIER FUNCTION FOB VI IDT - HULTIPLIEP FURCTIOR FOR NT ITT - HULTTPLIER FURCTION FOR TT ITD - HULTIPLISR FUNCTION TOR TC IOSOL - HULTIPLI5R FURCTION FOB OSOL InCKT " RULTIPLIER FUNCTION FOB DCRT ICRT - HOLTIPIIER PONCTIOR FOB CRT

TOP CONDITIONS AT STARTING TIRE FCT. NO. QT HCT UT VT NT TT TD flSOL DTRT(1 | CRTCU 0CRT(2I C R T ( 2 )


1 0 . 0 5 . 0 0 0 . 0 0 . 0 0 . 0 6 0 . 0 0 8 0 7 6 0 0 . 0 0 . 0 1 . 0 0 0 . 0 0 . 0 2 0 . 0 5 . 0 0 0 . 0 0 . 0 0 . 0 6 0 . 0 0 6 0 . 0 0 0 . 0 0 . 0 1 . 0 0 0 . 0 0 . 0

RULTIPLIER PORCTIOR POD TOP COBCITIORS r C T . RO. I Q T IHCT I U T I V T I 1 T I T T I T D I Q S O L I D C K T ( I ) I C K T ( I ) I D C K T ( 2 ) I C R T ( 2 ) 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0

2IPDT IRPOPJIATIOR FROR SOBFOOTIHB FLICOR: COEPPICIERT POR TOTAL EFFECTIVE TBIRRAL CORDOCTITITT IR X - D I R I C I I O R {IKPC) > 3 . 5 0 0 0 0 0 D - 0 1 COEFFICIERT FOB TOTAL EFFECTIVE THERRAL CORDOCTIVITT IR T-DIRECTIOR ( IKPC) = 3 . 5 0 0 0 0 0 D - 0 1 COEPFICIERT FOB TOBQOLEHT VISCOSITY I R X - D I R E C T I O R ( X T R S C ) ' 2 . 0 0 0 0 0 0 0 0 0 COEPFICIERT FOB TORBOLBIT P I S C O S I I l I I Y - D I B E C T I O R (T1VSC) •> 2 . 0 0 0 0 0 0 D 0 0

ORIC - COEPFICIERT FOR TOTAL BIRART EFFECTIVE DIFFOSICR COEPr iCIERT OP S P E C I E K I R X-OIRECTIOR DRTC - COBFFICIERT FOB TOTAL DIRABT I F P E C T I T E D I F F D S I C R COEFFICIERT OP S P E C I E I! I R t - D I B E C T I O l

DKXC(K)

5 . 2 2 0 0 0 0 0 - 0 5 5 . 2 2 0 0 0 0 0 - 0 5

5 . 2 2 0 0 0 0 D - 0 5 5 . 2 2 0 0 0 0 D - C 5 to CO fo

IRPOT IRFORRATIOR FBOH SOBRCOTIRE IRTCOI: STR - I N I T I A L VALOE FOR HATER SOIPACE ELEVATIOR. R, REASORED PROR THE BOTTOH s r o - I H I T I A L PALBE FOR RATER PELOCITF, 0 , I I X - D I R E C I I O R STT - I R I T I A L TALOE FOR VATER TELOCITT, P . I R T - D I R E C I I O R S T B S " I R I T I A I . TALOE FOR RATE OF CHARGE OF RATER ELETATIOR I I T B RESPECT TO T I R E STT - I R I T I A L TALOE FOR WATER TIRFEBATORB, T . S T C K ( I ) " I R I T I A L VALUE FOR RASS CORCERTRATIOR OF S P E C I E S ( I ) . I S T H P - ROLTIPLIER PORCTIOR FOB STR ISTOF - HOITIPLIER FOICTIOR FOR STO I S T f f - ROLTIPLIER FORCTIOR FOR STT 1 S T R S P - ROLTIPLIER FOICTIOR FOB STBS I S T T P - R O I T I P I I R R PORCTIOR POR STT I S T C K P ( I ) - R 0 L T I P L I 2 S FORCTIOR FOB S T C R ( I )

I R I T I A L CORDITIORS FORCTIOB RO. STR STO STT S T T S T C K ( 1 ) S T C ( ( 2 )

1 M>.00 0.0 0.0 80.00 1.00 0.0 2 00.00 0.0 0.0 80.00 1.00 0.0

ROLTIPLIER FORCTIOI EOS X I I T I A L CORDITIORS F C T . I O . I S T B I S T O I S T V I S T T ISTClt ( 1 ) I S T C R t f ) 1 0 0 0 0 0 0

2 0 0 0 0 0 0

Table A . 2 . O u t p u t I n f o r m a t i o n f o r Sample Prob lem No. 1 a t T ime = 5 . 6 h r U s i n g t h e F a l l V e r s i o n o f t h e Program

ITER.s 106 Tin3=5*3000000 00 pEBIODaS.300000o OO 71*?. mcRtHlMTB5.0O000DD-02 VELOCITT VELOCITT IATER ELEV.

I B D I - x - r - HATER I B IN P A T ! NODE CBS LOCATION LOCATION ELEVATION I - DIRECT. T - D I R I C T . OP CHANGE TEBP

1 1 2 * 0 0 0 0 2 5 0 0 0 0 1 0 1 0 6 0 D 0 1 2 2 3 7 0 0 1 - 2 . 1 5 0 D 0 1 5 . 8 1 9 0 - 0 3 8 0 0 0 0 0 1 2 2 5 0 0 0 0 7 5 0 0 0 0 II 0 1 0 6 1 0 0 1 2 2 5 1 0 0 1 - 6 . 5 0 5 D 0 1 1 . 1 1 3 0 - 0 2 8 0 0 0 0 0 1 3 2 5 0 0 0 0 1 2 5 0 0 0 0 1 0 1 0 6 1 9 0 1 2 11BD 0 1 - 1 . 1 1 1 0 0 2 2 . 1 0 0 0 - 0 2 9 0 0 0 0 0 1 i 2 5 0 0 0 0 1 7 5 0 0 0 0 1 0 1 0 6 2 0 0 1 3 2 1 1 0 0 1 - 1 . 6 3 9 D C2 1 . 7 9 7 0 - 0 2 8 0 0 0 0 0 1 5 2 5 0 0 0 0 2 2 5 0 0 0 0 It 0 1 0 6 9 D 0 1 5 072D 0 1 - 2 . 2 6 C D 0 2 - u . 2 6 5 0 - 0 2 8 OOOD 0 1 6 2 5 0 0 0 0 2 7 5 0 0 0 0 1 0 1 0 8 9 0 0 1 9 2 7 0 0 0 1 - 3 . 0 1 8 D 0 2 - 9 . 1 2 6 0 - 0 2 8 0 0 0 0 0 1 7 2 5 0 0 0 0 3 2 5 0 0 0 0 1 0 1 1 2 7 0 0 1 1 8 3 2 D 02 - 1 . 2 1 2 D 0 2 2 . 5 3 3 0 - 0 1 B 0 0 2 0 0 1 . 8 2 * 0 0 0 0 3 7 5 0 0 0 0 u 0 1 2 1 3 0 0 1 3 5 5 3 D 0 2 - 6 . 2 1 8 D 0 2 7 • 3 9 8 D - 0 1 8 0 1 2 0 0 1 9 2 5 0 0 0 0 1 2 5 0 0 0 0 1 0 ' 6 0 9 D 0 1 3 6 6 7 D 0 2 - 8 . 8 1 8 0 0 2 6 . 5 0 0 0 - 0 1 8 016D 0 1 1 0 2 5 0 0 0 0 0 7 5 0 0 0 0 1 0 3 1 0 1 0 0 1 - 7 . 1 6 7 0 0 2 - 8 . 0 0 8 0 02 - 1 • 1 6 3 D 0 0 e 110D 0 1 1 1 2 5 0 0 0 0 5 2 5 0 0 0 0 1 0 1 9 2 1 D 0 1 - 1 7 0 1 D 0 3 3 . 3 2 5 D - 12 3 . 7 0 6 0 0 0 8 313D 0 1 1 2 2 5 0 0 0 0 5 7 5 0 0 0 0 1 0 3 1 0 1 D 0 1 - 7 1 6 7 0 0 2 e.ooen 0 2 - 1 . 1 6 3 0 0 0 e 1 1 0 0 0 1 1 3 2 5 0 0 0 0 6 2 5 0 0 0 0 1 0 1 6 0 9 0 0 1 3 6 6 7 0 0 2 8 . 8 1 8 0 0 2 6 . 5 0 0 0 - 0 1 8 016D 0 1 1 1 2 * 0 0 0 0 6 7 5 0 0 0 0 1 0 1 2 1 3 0 0 1 3 5 5 3 D 0 2 6 . 2 1 8 D 02 7 . 3 9 8 0 - 0 1 8 0 1 2 0 0 1 1 5 2 5 0 0 0 0 7 2 5 0 0 0 0 1 0 1 1 2 7 0 0 1 1 B32D 0 2 1 . 2 1 2 0 0 2 2 . 5 3 3 D - 0 1 B 0 0 2 0 0 1 1 6 2 5 0 0 so 7 7 5 0 0 0 0 1 0 1 0 8 9 D 0 1 9 2 7 0 0 0 1 3 . 0 1 8 0 0 2 - 9 . 1 2 6 0 - 0 2 8 0 0 0 0 0 1 17 2 5 0 0 0 0 8 2 5 0 0 0 0 1 0 1 0 6 9D 0 1 5 0 7 2 D 0 1 2 . 2 6 0 D 0 2 - 1 • 2 6 5 D - 0 2 8 0 0 0 0 0 1 1 8 2 5 0 0 0 0 8 7 5 0 0 0 0 1 0 1 0 6 2 D 0 1 3 2 1 1 D 0 1 1 . 6 3 9 D 0 2 1 • 7 9 7 D - 0 2 8 OOOD 0 1 1 9 2 5 0 0 0 0 9 2 5 0 0 . 0 0 1 0 1 0 6 ID 0 1 2 U S D 0 1 1 . 1 1 1 D 0 2 2 . 1 0 0 D - 0 2 8 OOOD 0 1 2 0 2 5 0 0 00 9 7 5 0 0 CO 1 0 1 0 6 ID 0 1 2 2 5 1 0 0 1 6 . S 0 5 D 01 1 . 1 1 3 0 - 0 2 8 OOOD 0 1 2 1 2 5 0 0 00 1 0 2 5 0 0 0 0 1 0 1 0 6 0 0 0 1 2 2 3 7 0 0 1 2 . 1 5 0 0 01 5 . 8 1 9 0 - 0 3 8 0 0 0 0 0 2 1 7 * 0 0 0 0 2 5 0 0 . 0 0 1 0 1 0 5 7 0 0 1 6 250D 0 1 - . . 9 2 7 0 0 1 1 . 7 9 9 0 - 0 2 8 OOOD 0 2 2 7 5 0 0 0 0 7 5 0 0 0 0 1 0 1 0 5 9 0 0 1 6 16BD 0 1 - 5 - 7 1 C D 0 1 7 . 9 1 2 0 - 0 3 8 0 0 0 0 0 2 3 7 5 0 0 0 0 1 2 5 0 0 0 0 11 0 1 0 6 3 D 0 1 7 0 18D 0 1 - 9 . 7 2 1 D CI 5 . 2 2 2 0 - 0 3 8 OOOD 0 2 0 7 5 0 0 . 0 0 1 7 5 0 0 0 0 1 . 0 1 0 6 8 D 0 1 8 1 1 7 0 0 1 - 1 . 1 0 5 D 0 2 3 9 8 8 0 - 0 2 8 OOOD 0 2 5 7 * 0 0 0 0 2 2 5 0 0 0 0 1 0 1 0 7 IB 0 1 1 0 2 1 D 0 2 - 1 . B 9 0 D 0 2 1 . 0 6 6 0 - 0 1 B OOOD 0 2 6 7 5 0 0 00 2 7 5 0 0 0 0 1 0 1 0 7 7 D 0 1 1 3 7 5 0 0 2 - 2 . 1 1 8 D 02 1 . 3 3 3 0 - 0 1 B OOOD 0 2 7 7 5 0 0 0 0 3 2 5 0 0 . 0 0 1 0 1 1 1 1 D 0 1 1 B82D 0 2 - 2 . 8 1 1 0 0 2 - 3 . 9 5 1 0 - 0 1 8 OOOD 0 2 8 7 5 0 0 0 0 3 7 1 0 0 0 0 1 0 1 1 7 2 0 0 1 2 3 6 8 0 0 2 - 2 . 8 9 1 0 0 2 - 5 . 8 0 1 0 - 0 1 8 0 0 ID 0 2 9 7 5 0 0 0 0 1 2 * 0 0 0 0 1 0 1 1 7 5 D 0 1 1 6 7 9 D 0 2 - 2 . 1 2 2 D C2 - 1 . 6 6 9 0 - 0 1 8 006D 0 2 1 0 7 5 0 0 0 0 1 7 5 0 0 0 0 1 0 1 0 9 I D 0 1 - 2 3 2 8 D 0 2 - 1 . 2 9 6 D 0 2 5 . 5 1 1 0 - 0 1 8 OOOD 0 2 11 7 5 0 0 00 5 2 * 0 0 . CO 1 0 1 0 1 1 0 0 1 - 5 1 5 0 0 0 2 - 7 . 1 7 1 0 - 1 2 - 6 . 5 1 3 0 0 0 B OOOD 0 2 1 2 7 5 0 0 0 0 5 7 5 0 0 0 0 1 0 1 0 9 1 0 0 1 - 2 3 2 8 0 0 2 1 . 2 9 ( 0 0 2 5 . 5 1 1 0 - 0 1 8 OOOD 0 2 13 7 5 0 0 0 0 6 2 5 0 0 . 0 0 1 0 1 1 7 5 0 0 1 1 6 7 9 D 0 2 2 . 4 2 2 0 0 2 - 1 . 6 8 9 0 - 0 1 8 0 0 6 D 0 2 111 7 5 0 0 0 0 6 7 5 0 0 . 0 0 1 0 1 1 7 2 0 0 1 2 36BD 0 2 2 . 8 9 1 0 0 2 - 5 . 8 0 1 D - O 1 8 0 0 1 0 0 2 1 5 7 5 0 0 0 0 7 2 5 0 0 0 0 1 0 1 1 1 1 D 0 1 1 8 8 2 0 0 2 2 . 8 1 1 0 0 2 - 3 . 9 5 1 0 - 0 1 8 OOOD 0 2 16 7 5 0 0 . 0 0 7 7 5 0 0 . 0 0 1 0 1 0 7 7 D 0 1 1 3 7 5 D 0 2 2 . 1 1 8 0 0 2 1 3 3 3 0 - 0 1 8 OOOD 0 2 1 7 7 5 0 0 0 0 0 2 5 0 9 . 0 0 0 . 0 1 0 7 ID 0 1 1 0 2 1 D 0 2 1 . 8 9 0 D 0 2 1 . 0 6 6 0 - 0 1 8 OOOD 0 2 I B 7 5 0 0 0 0 8 7 5 0 0 0 0 1 0 1 0 6 8 D 0 1 e 1 I 7 D 0 1 1 . 1 0 5 0 0 2 3 . 9 B B D - 0 2 8 0 0 0 0 0 2 1 9 7 5 0 0 0 0 9 2 5 0 0 . 0 0 1 0 1 0 6 3 0 0 1 7 0 1 8 0 0 1 9 . 7 2 1 0 CI 5 . 2 2 2 0 - 0 3 8 OOOD 0 2 2 0 7 5 0 0 0 0 9 7 5 0 0 0 0 1 0 1 0 5 9 D 0 1 6 1 6 8 0 0 1 5 . 7 1 0 0 0 1 7 . 9 1 2 D - 0 3 8 0 0 0 0 0 2 2 1 7 5 0 0 0 0 1 0 2 5 0 0 0 0 1 0 1 0 5 7 0 0 1 6 2 5 0 0 0 1 1 . 9 2 7 D 0 1 1 . 7 9 9 0 - 0 2 B OOOD 0 3 1 1 2 5 0 0 0 0 2 5 0 0 0 0 1 0105OD 0 1 9 5 2 8 D 0 1 - 1 . 1 2 7 0 Ot 8 . 1 0 2 0 - 0 3 8 OOOD 0 3 2 1 2 5 0 0 0 0 7 5 0 0 0 0 u 0 1 0 5 ID 0 1 9 8 1 9 D 0 1 - 1 . 2 2 9 0 01 6 . 7 3 5 0 - 0 3 B OOOD 0 3 3 1 2 5 0 0 0 0 1 2 5 0 0 0 0 1 . 0 1 0 5 3 0 01 1 0 1 6 D 0 2 - 7 . 0 0 7 0 0 1 1 . 0 6 7 0 - 0 3 8 OOOS 0 3 1 1 2 5 0 0 . 0 0 1 7 5 0 0 0 0 1 0 1 0 5 6 0 0 1 1 1 5 3 0 0 2 - 9 . 6 5 6 D 01 -» . 0 8 0 0 - 0 2 8 OOOD 0 3 5 1 2 5 0 0 0 0 2 2 5 0 0 . 0 0 1 0 1 0 5 7 0 0 1 1 3 1 7 0 0 2 - 1 . 1 9 9 1 1 0 2 - 2 . 1 3 3 0 - 0 1 8 OOOD 0 3 6 1 2 5 0 9 0 0 2 7 5 0 0 0 0 1 0 1 0 5 3 0 0 1 1 5 1 5 0 01 - 1 . J 1 5 I 111 1 . 1 6 2 0 - 0 2 S 0 0 0 0 0 3 7 1 2 5 0 0 0 0 3 2 5 0 0 0 0 1 0 1 0 5 5 D 0 1 1 6 7 8 0 0 2 - 1 . 2 0 2 0 0 2 - 2 . 2 7 7 0 - 0 2 8 0 0 0 0 0 3 8 1 2 5 0 0 00 3 7 5 0 0 0 0 1 0 1 0 ( 6 0 0 1 1 MOD 0 2 - 1 . 6 5 1 0 0 1 - 2 . 6 6 1 0 - 0 1 8 OOOD 0 3 9 1 2 5 0 0 0 0 1 2 5 0 0 0 0 a 0 1 0 3 2 D 0 1 2 3 0 6 0 0 1 8 . 7 5 1 0 01 9 . 3 1 1 0 - 0 2 8 OOOO 0 3 10 1 2 5 0 0 0 0 1 7 5 0 0 00 1 0 0 7 8 1 D 0 1 - 1 6 6 1 0 0 2 I . 1 7 2 D 02 1 . 0 1 7 0 0 0 8 OOOD 0 3 1 1 1 2 * 0 0 0 0 5 2 5 0 0 0 0 1 0 0 5 7 5 0 01 - 2 6 9 0 0 0 2 • 1 . 0 9 7 0 - 12 2 . 2 1 6 0 0 0 8 OOOD 0 3 1 2 1 2 5 0 0 0 0 5 7 5 0 0 0 0 1 0 0 7 8 1 0 0 1 -1 6 6 1 D 0 2 - 1 . 1 7 2 0 02 1 . 0 1 7 0 0 0 8 OOOD 0 3 1 3 1 2 5 0 9 00 6 2 5 0 0 0 0 a 0 1 0 3 2 D 0 1 2 3 0 6 D 0 1 - 8 . 7 5 1 0 0 1 9 . 3 3 1 0 - 0 2 8 OOOD 0 3 i n 1 2 5 0 0 0 0 6 7 5 0 0 0 0 la 0 1 0 6 6 0 0 1 1 110D 0 2 1 . 6 5 1 0 CI -2 . 6 6 1 0 - 0 1 B OOOD 0

TEBP. 5D8STANCB BBSS C0BCI»IB»T10»S BUB OP CHARGE CB(1) CB(2) 1, .7600-12 1, ,0000 00 5, ,0910-15 8, .6790-10 1. oooo 00 1, ,0130-12 6. .8770-OB 1, ,0000 00 9, ,3950-11 3 .0350-06 1, .0000 00 1, ,8080-09 7. .880D-05 1. ,0000 00 1. .515D-07 1, .2270-03 1. .OOOD 00 2. ,9580-06 1, .1920-02 9.999L--01 3. ,1820-05 6. ,11170-02 9. ,993D-•01 2. .3180-01 1. .8310-01 9. 975D--01 8. ,7690-01 3, .2960-01 9. ,91 ID-•01 2. .0810-03 1. .2500-01 9. 8320-01 5, ,8860-03 3 .2960-01 9. ,9110-•01 2. .0810-03 1, .8310-01 9. .9750--01 8. ,7690-01 6, ,1170-02 9, .9930-•01 2. ,318D-0I 1, . 192D-02 9. ,9990--01 3, ,1820-05 1, ,2270-03 1, .0000 00 2. ,9580-06 7. .B80D-05 1. ,0000 00 1. ,5150-07 3i .0350-06 1, ,0000 00 a, .8080-09 6, ,8770-08 1. .0000 00 9, ,3950-11 8, ,6790-10 1. ,0000 00 1, .013D-12 1, ,7600-12 1. .0000 00 5. .0910-15 2. ,0010-13 1. 0000 00 1. ,8910-16 1. .036D-I1 1. OOOD 00 1, ,2870-11 3, ,5570-09 1. 0000 00 1. ,2930-12 1. ,7920-07 1. 0000 00 2. 1520-10 5, ,6330-06 1. .0000 00 8. ,6160-09 1, ,0980-01 1. .0000 00 1. ,9320-07 1, .1590-03 1. ,0000 00 2, ,7250-06 7. ,1160-03 9. 999D-•01 2. .36111-05 3. ,3130-02 9. ,9970-•01 1. ,0650-01 2. ,1160-03 1. OOOD 00 9. 2500-06 1, ,8360-01 1. OOOD 00 6, ,8110-07 2, ,1160-03 1, .OOOD 00 9. .2500-06 3. ,3130-02 9. ,9970--01 1. ,0650-01 .1160-03 9. 999C-•01 2. ,361D-05 V .1590-03 1. .OOOD 00 2. ,7350-06 1, ,0980-01 1. OOOD 00 1. 9320-07 5. ,6330-05 1. OOOD 00 8. 6160-09 1, ,7920-07 1. ,0000 00 2. .1520-10 3. 5570-09 1. OOOD 00 4, ,2930-12 1, .03SD-11 1, OOOD 00 1, .2870-11 2 .0010-13 1. ,0000 00 1, .891D-16 0. .1860-15 1. OOOO 00 3. ,69*0-18 9. ,5690-13 1. OOOD 00 9. ,1310-16 9, .1810-11 1. .0000 00 1. ,0070-13 5, ,3130-09 1. .0000 00 6, ,0190-12 1, ,8850-07 1. .0000 00 2, ,5780-10 u .3010-06 1, .4000 00 6, ,6630-09 6, ,0900-05 1. .0000 00 1, ,0850-07 5. ,0090-01 1. .0000 00 1. .0170-06 1, ,1980-03 1, .0000 00 2, ,9070-06 1, ,1110-05 1. oo or 00 7. .5160-08 1, ,1830-06 1. OOOD 00 1. ,9310-09 a, .1110-05 1. OOOD 00 7, ,5160-08 1. .1960-03 1. ,0000 00 2. ,9070-06 5. ,0090-01 1, .0000 00 1. .0170-06


I T E R . * 106 TIHE®5.300*000D 0 0 P E R I O D ' S . 3 0 0 0 0 0 0 0 0 TIRE I R C R E n E H T " 5 . 0 0 0 0 0 0 0 - 0 2

TELOCITY 1 E I O C I T J 4ATIR V . l l . TEBP. SUBSTARCE RAS5 C0MCEK1 1 R D I - X- 1 - RATER IR IR RATE RATE

RODE CES LOCATIOH LOCAT1OR UEPATIOR I - D I P E C T . T - D I ' E C T . OP CHARGE TEMP '.>» CHARGE C K ( I | CR (21

3 1 5 1 2 5 0 0 0 0 7 2 5 0 0 . 0 0 l l . 0 1 0 5 5D 0 1 . 6 7 B D 0 2 1 . 2 0 2 0 0 2 - t - 2 7 7 D - 0 2 8 GOOD 0 1 6 . 0 9 0 0 - 0 5 1 .OOOD 0 0 1 0 8 5 D - 0 7 3 16 1 2 5 0 0 0 0 7 7 5 0 0 . 0 0 0 . 0 1 1 ) 5 3D 0 1 . 5 2 5 D 0 2 1 3 4 90 0 2 1 . 1 8 2 D - 0 2 8 0 0 0 0 0 1 4 . 3 0 I D - 0 6 1 OOGD 0 0 6 6 6 3 0 - 0 9 3 1 1 1 2 5 0 0 0 0 6 2 5 0 0 . 0 0 0 . 0 1 0 5 7 0 0 1 . 3 1 7 0 0 2 1 199D 0 2 - 2 . 4 3 3 0 - 0 0 8 0 0 0 0 0 1 1 . 6 8 5 0 - 0 7 1 OOOD 0 0 2 5 7 8 0 - 1 0 3 1 8 1 2 5 0 0 0 0 8 7 5 0 0 . 0 0 4 . 0 1 0 5 6 D 0 1 . 1 5 3 0 0 2 9 6 5 6 0 CI - 1 . 0 8 0 0 - 0 2 8 0 0 0 0 0 1 5 . 3 4 3 D - 0 9 1 OOOP 0 0 6 . 4 » ? D - 1 2 J 1 9 1 2 5 0 0 0 0 9 2 5 0 0 . 0 0 0 . 0 1 0 5 3 0 0 1 . 0 9 6 0 0 2 7 0 0 7 D 0 1 4 . 0 6 7 0 - 0 3 8 OOOO 0 1 9 . 4 8 1 D - I t 1 OOOD 0 0 1 0 2 7 0 - 1 3 3 2 0 1 2 5 0 0 0 0 9 7 5 0 0 . 0 0 9 . 0 1 0 5 1 D 0 9 . 8 1 9 0 0 1 4 2 2 9 D 0 1 * . 7 3 5 0 - 0 3 B 0 0 0 0 0 1 9 . 5 6 9 0 - 1 1 1 OOOD 0 0 9 1 3 1 0 - 1 6 3 2 1 1 2 5 0 0 0 0 1 0 2 5 0 0 . 0 0 0 . 0 1 0 5 0 0 0 9 . 5 2 8 0 0 1 1 4 2 7 D 0 1 8 • 1 4 2 D - 0 3 a 0 0 0 0 0 1 4 . 1 8 6 D - 1 5 1 OOOD 0 0 3 . 6 9 5 0 - I B a 1 " 5 0 0 0 0 2 5 0 0 . 0 0 9 . 0 1 0 9 ID 0 1 . 1 6 3 0 0 2 - 8 38 sn 0 0 9 • 4 0 5 D - 0 3 8 OOOD 0 1 9 . 8 2 I D - 1 9 1 OOOD 0 0 5 0 3 7 D - 2 0 0 2 1 7 5 0 0 0 0 7 5 0 0 . 0 0 R . o i o m o 0 1 . 1 C 4 D 0 2 . 2 • 5 B D 0 1 1 . 4 5 8 0 - 0 2 8 OOOD 0 1 1 . 5 7 9 D - 1 4 1 OOOD 0 0 1 . 3 5 3 D - 1 7 a 3 1 7 5 0 0 0 0 1 2 5 0 0 . 0 0 9 . 0 1 0 0 IP 0 1 . 2 3 5 0 0 2 - 3 9 1 3 0 0 1 1 . 4 9 9 0 - 0 2 a 0 0 OP 0 1 1 . 7 2 7 0 - 1 2 1 OOOD 0 0 1 . 6 2 9 D - 1 5 a a 1 7 5 0 0 0 3 1 7 5 0 0 . 0 0 0 . 0 1 0 0 ID 0 1 . 2 8 4 f t 0 2 • 4 9&BD CI 1 • 1 5 8 P - 0 2 8 OOOD 0 1 1 . 0 8 9 0 - 1 0 1 OOOD 0 0 1 I4 3 D - 1 3 4 5 1 7 5 0 0 0 0 2 2 5 0 0 . 0 0 4 . 0 1 0 9 IP 0 1 . 3 4 2 D 0 2 - 5 1 7 9 0 0 1 - 8 . 5 6 7 0 - 0 3 8 OOOD 0 1 4 . 2 6 6 0 - 0 9 1 OOOO 0 0 5 . 0 8 2 D - I 2 4 6 1 7 5 0 0 0 0 2 7 5 0 0 . 0 0 0 . 0 1 0 3 8 D 0 1 . 3 5 B O 0 2 - 0 186D CI 3 • 9 6 1 D - 0 2 8 OOOD 0 1 1 . 0 8 5 0 - 0 7 1 OOOD 0 0 1 . 4 5 6 D - 1 0 « 7 1 7 5 0 0 0 0 3 2 5 0 0 . 0 0 0 . 0 1 0 2 6 5 9 1 . 2 2 9 0 0 2 - 1 4 5 5 ! ) 0 1 9 . 0 5 0 0 - 0 2 8 OOOD 0 1 1 . 7 4 0 0 - 0 * 1 OOOD 0 0 2 . 5 6 1 D - 0 9 9 8 1 7 5 0 0 0 0 3 7 5 0 0 . 0 0 4 , 0 1 0 1 I D 0 7 . 3 1 0 0 0 1 3 5 2 2 D 0 1 1 . 5 2 9 0 - 0 1 8 OOOD 0 1 1 . 3 5 1 D - 0 5 1 OOOP 0 0 2 . 0 9 9 D - 0 8 a 9 1 7 5 0 0 0 0 9 2 * 0 0 . 0 0 0 . 0 1 0 0 9 D 0 - 3 . 2 1 1 0 Ot 9 2 8 2 0 0 1 - 2 • 5 5 8 D - 0 1 8 OOOD 0 1 1 . 5 5 6 D - 0 7 1 OOOD 0 0 3 1 3 5 0 - 1 0 4 1 0 1 7 5 0 0 0 0 0 7 5 0 0 . O S 4 . 0 1 0 1 4 D 0 - 1 . 7 2 7 D 0 2 9 372D CI - 1 • 3 0 9 D - 0 1 8 0 0 OP 0 1 4 . 2 8 8 0 - 0 9 1 OOQD 0 0 4 . 9 B 4 D - 1 2 a 11 1 7 5 0 0 0 0 5 2 5 0 0 . 0 0 4 . 0 1 0 1 4 D 0 • 2 . 4 5 9 D 0 2 - 1 27 4D 12 - 0 •OOOD-01 a OOOD 0 1 8 . 1 2 9 D - 1 1 1 OOOD 0 0 9 . 8 8 1 D - 1 4 9 1 2 1 7 5 0 0 0 0 5 7 5 0 0 . 0 0 4 . 0 1 0 1 4 D 0 - 1 . 7 7 7 0 0 2 - 9 3 7 2 D 0 1 - 1 . 3 0 9 0 - 0 1 8 OOOD 0 1 4 . 2 8 8 0 - 0 9 1 OOOO 0 0 4 . 9 8 4 D - 1 2 < 1 3 1 7 5 0 0 0 0 < 2 5 0 0 . 0 0 4 . 0 1 0 0 9 D 0 - 3 . 2 1 1 0 0 1 - 9 2 8 2 0 CI - 2 . 5 5 9 0 - 0 1 8 OOOD 0 1 1 . 5 5 6 D - 0 7 1 0003 0 0 3 . 3 3 * 0 - 1 0 « 1a 1 7 5 0 0 0 0 6 7 5 0 0 . 0 0 4 . 0 1 0 1 1 0 0 7 . 3 1 4 D 0 1 - 3 5 2 2D 0 1 1 . 5 2 9 0 - 0 1 8 OOOD 0 1 1 . 3 5 1 0 - 0 5 1 OOOO 0 0 2 . 0 9 9 D - 0 B • 1 5 1 7 5 0 0 0 0 7 2 5 0 0 . 0 0 4 . 0 1 0 2 6 0 0 1 . 2 2 9 0 0 2 1 4 5 5 0 0 1 9 . 4 5 0 0 - 0 2 a OOOD 0 1 1 . 7 9 0 0 - 0 6 1 OOOO 0 0 2 . 5 6 1 D - 0 9 9 16 1 7 5 0 0 0 0 7 7 5 0 0 . 0 0 4 . 0 I 0 1 8 D 0 1 . 3 5 8 D 0 2 4 1 8 6 0 0 1 3 . 4 6 1 0 * 0 2 a OOOD 0 1 1 . 0 8 5 0 * 0 7 1 OOOD 0 0 1 . 4 5 6 0 - 1 0 • I T 1 7 5 0 0 0 0 B 2 5 0 0 . 0 0 4 . 0 1 0 4 ID 0 1 . 3 4 2 0 0 2 5 179D 0 1 - 8 . 5 6 7 0 - 0 3 8 OOOD 0 1 4 . 2 6 B D - 0 9 1 OOOD 0 0 5 . 0 8 2 D - 1 2 • 18 1 7 5 0 0 0 0 9 7 5 0 0 . 0 0 4 . 0 1 0 4 ID 0 1 . 2 B 4 B 0 2 4 9 4 8 D 0 1 1 . 1 5 8 0 - 0 2 a OOOD 0 1 1 . 0 8 9 0 - 1 0 1 OOCD 0 0 1 . 14 3 D - 1 3 4 1 9 1 7 5 0 0 0 0 9 2 5 0 0 . 0 0 4 . 0 1 0 4 ID 0 1 . 2 2 5 D 0 2 3 9 1 3 D 0 1 1 . 4 8 9 0 - 0 2 a OOOD 0 1 1 . 7 2 7 D - 1 2 1 OOOD 0 0 1 . 6 2 9 D - 1 5 * 2 0 1 7 5 0 0 0 0 97 5 0 0 . CO 4 . 0 1 0 4 ID 0 1 . 1 B 4 D 0 2 2 45BD 0 1 1 . 0 5 8 0 - 0 2 8 OOOD 0 1 1 . 5 7 9 0 - 1 4 1 OOOD 0 0 1 . 3 5 3 D - 1 7 4 2 1 1 7 5 0 0 . 0 0 1 0 2 5 0 0 . 0 0 4 . 0 1 0 4 1 0 0 1 . 16311 0 2 B 3»5t> 0 0 9 . 4 0 5 P - 0 J 8 OOOD 0 1 9 . 8 2 1 P - 1 9 1 OOOD 0 0 5 . 0 3 7 D - 2 0 5 1 2 2 5 0 0 0 0 2 5 0 0 . 0 0 4 . 0 1 0 3 ID 0 1 . 2 5 7 0 0 2 - 3 3 6 0 0 0 0 9 . 8 7 0 0 - 0 3 8 OOOO 0 1 - 1 . 1 2 4 D - 1 9 1 OOOD 0 0 5 . 2 2 0 0 - 2 2 5 2 2 2 5 0 0 0 0 7 5 0 0 . 0 0 4 . 0 1 0 3 1 0 0 1 . 2 6 2 0 0 2 - 5 1S1D 0 9 1 . 0 7 6 0 - 0 2 8 OOOD 0 1 6 . 9 4 6 D - 1 7 1 OOOD 0 0 1 . 5 1 2 0 - 1 9 5 3 2 2 5 0 0 0 0 1 2 5 0 0 . 0 0 4 . 0 1 0 3 ID 0 1 . 2 6 9 D 0 2 - 1 29CD CI 1 . 2 4 6 0 - 0 2 8 OOOD 0 1 2 . 3 0 7 0 - 1 4 1 OOOD 0 0 1 . 9 6 7 0 - 1 7 5 a 2 2 5 0 0 0 0 1 7 5 0 0 . 0 0 4 . 0 1 0 3 0 D 0 1 . 2 6 6 0 0 2 - 1 2 4 4 0 0 1 1 . 3 2 3 0 - 0 2 8 OOOD 0 1 1 . 5 8 6 D - 1 2 1 OOOO 0 0 1 . 4 B 5 D - I 5 5 5 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 4 . 0 1 0 2 9 0 0 1 . 2 2 ( 0 0 2 - 5 0 3 1 0 0 0 1 . 2 7 8 0 - 0 2 a 0 0 0 0 0 1 6 . 8 9 6 0 - 1 1 1 OOOO 0 0 7 . 1 6 3 0 - 1 4 5 6 2 2 5 0 0 0 0 2 7 5 0 0 . 0 C 4 . 0 1 0 2 7 D 0 1 . 1 0 2 0 0 2 1 165D 0 1 - 3 • 9 4 2 D - 0 3 a OOOD 0 1 1 . 8 B 4 D - 0 9 1 OOOD 0 0 2 . 1 9 5 0 - 1 2 5 1 2 2 5 0 0 0 0 1 2 5 0 0 . 0 0 4 . 0 1 0 2 2 0 0 ft.7860 0 1 3 . 7 6 3 0 0 1 1 . 1 4 7 0 - 0 2 a coot 01 2 . 7 4 3 0 - 0 8 1 OOOO 00 3 . 5 9 5 0 - 1 1 5 t 2 2 5 0 0 0 0 3 7 5 0 0 . 0 0 4 . 0 1 0 0 9 D 0 3 . 4 0 6 0 0 1 6 6 4 5 0 0 1 3 . 4 8 5 0 - 0 2 a OOOD 0 1 1 . 2 0 3 D - 0 ? 1 OOOD 0 0 1 . 6 1 0 D - 1 0 5 9 2 2 5 0 0 0 0 • 2 5 0 0 . 0 0 4 . 0 0 9 9 6 0 0 - 3 . 7 0 4 0 0 1 8 4 7 6 0 CI 6 • 4 5 6 D - 0 2 a OOOD 0 1 1 . 4 2 6 0 - 0 9 1 OOOD 0 0 1 . 8 9 7 0 - 1 2 5 10 2 2 5 0 0 . 0 0 9 7 5 0 0 . 0 0 4 . 0 0 9 B 5 P 0 - 1 . 1 2 7 0 0 2 6 6 6 2 0 01 - 1 . 9 0 4 0 * 0 2 a OOOD 0 1 1 . 6 4 2 0 * 1 1 1 OOOD 0 0 1 . 9 9 8 0 * 1 4 5 1 1 2 2 5 0 0 . 0 0 5 2 5 0 0 . 0 0 4 . 0 0 9 7 7 0 0 • 1 . 4 1 1 0 1)2 - a 5 4 3 0 - 12 2 . 7 9 3 D - 0 2 a OOOO 0 1 1 . 4 9 5 0 - 1 3 1 000(1 00 1. 6 6 9 0 - 1 6 S 1 2 2 2 5 0 0 0 0 5 7 5 0 0 . 0 0 4 . 0 0 9 8 5 0 0 - 1 . 1 2 7 0 0 2 6 6 2 0 0 1 - 1 . 9 0 4 0 - 0 2 a OOOD 0 1 1 . 6 4 2 P - 1 1 1 OOOD 0 0 1 . 9 9 8 0 - 1 4

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ITER.' ION TIH«5.IOOOOOD oo FRNIOD-S.IOOOOOO OO tine INCBEBNT'I.0000000-02 V E L C f I T f m o C l T I BATES BLEV. trap. SUBSTANCE BASS CCNCEN

XNDt - X- X- HATER I N I N BATE BATE •ODE CES LOCATION LOCATION ELEVATION X- 91BECT. X- J I R I C 1 . Of CHANGE 1 EBP OP CHANG? « ( l ) CB(2 )

9 1 1 2 * 0 0 00 2500 00 0 009950 0 9 9110 0 1 0 B85D CO 1 . 1 5 3 0 - 0 2 B 000l> 0 1 - 1 0 0 3 0 28 1 OOOD 00 1 37CD 30 q 2 CO 00 7 5 0 0 CO 1 0 0 9 9 5 0 0 9 . 6 * 7 0 01 1 1 5 1 0 01 1 . 1 6 9 0 - 0 2 8 0000 0 1 - 1 1610 25 1 , 0 0 0 0 00 1 9839 2P 9 I 0 2 1 0 0 00 12100 00 1 C09950 0 9 1270 0 1 2 1130 C I t . 1 2 1 0 - 0 2 8 0 0 0 0 O l - t * 7 5 D 21 I 1)000 00 7 73 60 26 9 1 0 2 1 0 0 00 17500 00 1 0 0 9 9 1 0 0 8 2 9 5 0 0 1 3 H B O 0 1 1 . 1 8 1 0 - 0 2 8 0009 0 1 - 1 ' . 010 ?1 1 OOOD 00 6 ) ISP 20 9 5 0 2 1 0 0 00 22500 00 0 00 99 I D 0 7 1 3 ' D 01 0 11 <0 0 1 1 . 6 1 5 0 - 0 2 8 0000 0 1 - 6 0 7 1 0 20 1 0009 00 2 17£D 22 9 6 0 2 1 0 0 00 27100 00 1 0 0 9 9 1 0 0 5 6560 0 1 1 6 8 1 0 CI 1 , 6 8 8 0 - 0 2 8 ocoo 0 1 - 1 0 5 2 0 17 1 OOOD 0 0 5 18S0 2 1 9 7 0 2 5 0 0 00 32500 00 1 0 0 9 9 3 0 0 1 9170 0 1 0 8 8 0 0 0 1 1 . 1 1 5 0 - 0 2 B OOOD 0 1 - 2 ) 9 7 D 17 1 OOOtl 00 2 2i;o 20 9 8 " 2 1 0 0 00 37500 0 0 0 0 0 9 9 3 0 0 2 0 7 3 0 01 1 5 5 3 0 C I 1 9 1 9 0 - 0 2 B 0000 0 1 - 2 2 7 5 0 19 1 OOOD 0 0 1 297P 21 9 9 0 2500 00 12500 00 1 0 0 9 9 2 0 0 3 8010 0 0 1 583P CI 2 0 2 2 0 - 0 2 8 0000 0 1 - 8 6 1 1 0 22 1 OOOD 0 9 7 3 390 2 " 9 10 0 2 1 0 0 00 17500 00 1 00 9110 0 • B 1 0 8 0 00 1 9 9 1 0 0 1 1 . 9 2 9 0 - 0 2 B OOOD 0 1 - 3 16 ID 21 1 0001) 00 7 2800 2b 9 11 'H ' . f tO 05 5 2 5 0 0 0 0 0 0 0 9 9 1 b 0 -1 2910 0 1 - 7 2210 12 1 . 9 9 1 0 - 0 2 8 OOOD 01 - 7 1810 27 1 OOOD 00 1 0 290 29 4 12 0 2 1 0 0 00 57500 00 1 009910 0 - B 10BD 00 -1 1710 0 1 1 . 9 2 9 0 - 0 2 8 OOOD 01 - 3 161D 2 1 1 OOOD 00 2 . 280D 2 f 9 13 0 2 5 0 0 00 6 2 5 0 0 0 0 1 009920 0 3 8010 00 - 3 5810 01 2 0 2 2 0 - 0 2 « 9 0 0 0 01 -B 631D 22 1 0900 00 7 )3 *D 2 1 9 IS 0 2 1 0 0 00 6 7 5 0 0 00 1 0 0 9 9 3 0 0 2 0710 01 -1 5 5 3 0 0 1 1 . 9 1 9 0 - 0 2 ^ OOOD 01 -2 . 2 7 5 0 19 1 .OOOD 00 1 2Y7D 21 9 1 1 0 2 5 0 0 00 72510 0 0 1 0 0 9 9 3 0 0 3 9170 0 1 -1 8800 C I 1 , f l 3 5 0 - 0 2 8 , 0 0 0 0 0 1 -2 3970 \ '7 1 0000 00 2 2 I ' D 20 9 1* 0210C 00 775 00 00 1 0 0 9 9 1 0 0 5 6 5 6 0 0 1 -1 6 8 3 0 01 1 • 6 B B 0 - 0 2 8 0000 0 1 - 3 os;.; . 1 1 .OOOD 00 5 1BPD 21 9 17 1 2 5 0 0 00 S2103 00 1 0 0 9 9 1 0 V 7 I 3 7 B 01 -1 1110 CI 1 , 6 1 1 0 - 0 2 8 OOOD 01 - 6 071D 20 1 OOOD 00 2 77»D 22 9 I S 0 2 5 0 0 00 87500 00 1 009910 0 P 2950 01 - 1 71BD 01 1 5 1 1 0 - 0 2 8 0000 01 - 1 5 0 1 0 21 1 OOOD 00 6 J3BD 2 1 9 19 1 2 1 0 0 00 9 2 5 0 0 00 1 0 0 9 9 5 0 0 9 1270 01 -2 1129 c« 1 . 1 2 1 0 - 0 2 8 OOOD 01 -1 975D 2 1 1 OOOD 09 7 7360 26 9 20 0 2 1 0 0 00 9T500 00 1 0 0 9 9 5 0 0 9 6 1 7 0 01 -1 1 5 7 0 01 1 1 6 9 0 - 0 2 a OOOD 01 -1 361D 2 1 1 OOOD 00 1 983D 28 9 2 1 1 2 5 0 0 00 102500 00 1 009950 0 9 0 11(1 01 - 1 885D 00 1 1 5 1 0 - 0 2 B OOOD 01 - 1 0 0 ) 0 2H 1 OOOD 00 1 )7CD 30

10 1 1 7 1 0 0 00 2100 00 1 0 0 9 8 7 0 0 8 711D 0 1 1 9110 00 1 . 5 2 5 0 - 0 2 8 OOOD 0 1 - 2 0 1 7 0 10 1 OOOD 00 f> 5100 33 10 7 1 7 5 0 0 00 7500 0 0 0 009870 0 8 506 <> 01 1 1 5 1 0 01 1 1 1 2 0 - 0 2 8 GOOD 01 - 7 216D 28 1 0)00 00 7 061D 10 10 1 1 7 1 0 0 00 12100 00 1 0 0 9 9 7 0 0 8 0290 01 2 3650 01 1 5 5 7 0 - 0 2 >1 OOOD 0 1 -1 062D 25 1 OOOD 0 0 3 e'jiD 28 10 a 1 7 1 0 0 00 17500 00 1 0 0 9 8 7 0 0 7 3070 01 3 1790 CI 1 6 3 8 0 - 0 2 8 OOOD 0 1 - 7 9 0 1 0 2 1 1 0000 00 ) 08(1) 26 10 5 1 7 5 0 0 00 22500 00 1 C09S70 0 6 3110 01 J B2C9 01 1 .6920-02 8 OOOD 0 1 -2 9860 22 1 OOOD 00 1 25PD 2 1 10 6 1710C 00 27100 00 1 009870 0 5 1630 01 1 2170 01 1 ,7770-02 8 OOOD 01 1 7 0 0 21 1 OOOD 00 2 0210 23 10 1 0 7 5 0 0 00 12100 00 1 0 0 9 8 7 0 0 1 8 0 3 0 0 1 0 :>!i> 01 1 . 8 2 7 0 - 0 2 0 OOOD 0 1 -1 36JD 20 1 • OOOo 00 6 6010 23 10 U 1 1 5 0 0 (10 17500 00 1 0 0 ) 8 7 0 0 2 5 0 7 0 01 3 8 1 2 0 01 I . 9 5 2 0 - 0 2 8 0000 0 1 - 5 0 8 5 0 22 1 0000 00 2 8B2D 2 1 10 9 0 7', 00 00 12100 00 1 0 0 9 8 7 0 a 1 3 320 01 2 92B0 CI 1 . 9 6 0 0 - 0 2 8 OOOD 01 -2 . 5 12i ' 2 1 1 OOOD 00 1 B92D 26 10 10 1 7 5 0 0 00 1 7 5 0 0 00 1 0 0 9 8 6 0 0 5 inn 00 1 5900 CI 2 . 0 6 2 0 - 0 2 8 OOOD ni -5 1100 27 1 0000 00 ) 1570 29

10 11 1 7 1 0 0 00 5 2 5 0 0 00 1 C09B6D 0 2 1900 00 - 6 1 7 1 0 12 1 . 9 5 6 0 - 0 2 8 OOOD 91 - 9 2 8 6 0 JO 1 OOOD 00 6 2 1 * 0 32 10 12 17' 00 00 5 7 5 0 0 on 1 0 0 9 8 6 0 0 1 1110 00 -1 5910 0 1 2 . 0 6 2 0 - 0 2 8 OOOD 0 1 - 1 . 1 1 0 0 27 1 0000 00 ) 157D 29 10 13 0 7 5 0 0 00 6 2 5 0 0 00 0 0 0 9 4 7 0 0 1 3 320 a-. • 2 «?BB 31 1 96110-0? 8 OOOD 01 - 2 5I2D 2 . 1 0000 00 1 )92D 2 * ! 0 11 0 7 1 0 0 00 67500 0 0 1 009870 0 2 1070 0 1 - 1 8)20 CI 1 8 0000 0 1 - 5 0 6 5 0 2; 1 0 0 0 9 00 2 882D 21 10 1 1 0 7 1 0 0 00 7 2 5 0 0 00 1 0 0 9 8 7 0 0 3 8130 01 - 1 2 1 9 0 01 1 , 8 2 7 0 - 0 2 8 liCOP 01 -1 1 6 ) 0 29 1 OOOD 00 6 601D 23 10 16 1 7 5 0 0 00 7 7 5 0 0 00 u 009370 0 5 1630 01 - 9 2110 01 1 7 7 7 0 - 0 2 B 0000 0 1 .4 1 7 0 0 21 1 0 0 0 9 OD 2 02OD 23 10 17 1 7 5 0 0 00 8 2 5 0 0 00 1 009870 0 « 1110 01 -3 8 2 6 0 01 1 . 6 9 2 0 - 0 2 8 OOOD 01 - 2 «* ,60 11 1 OOOD 00 1 2580 ?1 10 19 0 7 1 0 * 00 8 7 5 0 0 00 0 C09870 0 7 3070 01 - 3 1790 CI 1 , 6 3 9 0 - 0 2 8 0000 0 1 -7 901D 21 1 OOOD 00 3 OBf D 26 10 19 1 7 1 0 0 00 9 2 5 0 0 00 1 0 0 9 8 7 0 0 B 0290 01 -2 3650 0 1 1 . 5 5 7 0 - 0 2 8 COOO 0 1 -1 062D 25 1 OOOD 00 3 P570 2B 10 20 17500 00 97'00 00 1 00987D 0 8 5060 01 -1 1 5 1 0 CI 1 . 1 1 2 0 - 0 2 B OOOD 91 - 7 2 1 6 0 28 1 OOOD 00 2 0610 30 10 2 1 O7500 00 102500 on 1 0 0 9 8 7 0 0 8 7 1 1 0 0 1 - 0 9110 09 1 . 5 2 1 0 - 0 2 a OOOD 0 1 - 2 0 1 7 0 10 1 OOOD 0 0 I 511D ) ) 11 1 i?100 00 2 5 0 0 00 1 0 0 9 7 9 0 0 1 5 9 9 0 01 1 6*90 CO 1 ,111,0-02 B OOOD 0 1 - 8 5 6 3 0 IJ 1 OOOD 00 2 5 6 * 0 31 11 2 ijino 00 7 5 0 0 00 1 009790 0 7 1020 01 1 1720 CI 1 .1110-02 8 COQD 01 - 1 1 J 5 0 30 1 0000 00 9 96 20 33 II 3 5 2 5 0 0 00 12500 00 1 00979C 0 7 0100 01 2 2150 01 1 . 5 8 0 0 - 0 2 8 OOOD 0 1 • 1 . 6 3 8 0 28 1 OOOD 00 1 572D 30 11 1 12100 00 17100 00 1 . 0 0 9 9 0 0 0 6 1 2 9 0 01 2 inn 01 1 , 6 1 6 0 - 0 2 8 0000 01 -3 3 8 5 0 2* 1 0000 00 1 23 ID 28 11 6 5 2 5 0 0 00 22100 CO 1 0 0 9 8 0 0 0 5 6 7 8 0 01 3 1720 CI 1 , 7 1 B 0 - 0 2 B 0000 01 - 1 mo 21 1 0 9 0 9 00 1 727P 27 11 6 12100 00 2 7 5 0 0 00 1 0 0 9 8 0 0 0 0 7 9 5 0 01 3 750O 01 1 . 7 9 1 0 - 0 2 8 OOOD 01 -1 . 6 0 5 0 ?) 1 . 0 0 0 0 00 6 7 7 1 0 26 11 7 52«00 00 32100 0 0 1 0 0 9 ) 10 0 3 8120 01 1 6 9 9 0 01 1 . 8 6 0 0 - 0 2 8 OOOD 01 -1 010D 21 1 OOOD 00 I 810D 21 11 e 1 2 5 0 0 00 31500 s o 1 CO 9810 a ^ 9 1 1 0 0 1 1 270O 01 1 . 9 2 1 0 - 0 2 8 OOOD 0 1 -1 3)50 21 1 .0000 00 7 103D 27 11 9 • 2 1 0 0 00 1 2 1 0 0 00 1 0 0 9 8 1 0 0 2 1210 01 2 .1560 CI 1 • 9 8 2 D - 0 2 8 OOOD 01 - 7 .0130 27 1 .OOOD 00 ) 519P 29 11 10 5 2 5 0 0 00 1 7 5 0 0 00 0 0 0 9 8 1 0 0 1 5 8 9 0 ot 1 3220 ot 2 . 0 1 7 0 - 0 2 B OOOD 0 1 - 1 657D 29 1 OOOD 00 8 f.OOD 32 M 11 52500.00 52500 0 0 1 009810 0 1 39=0 01 - 3 , 7 0 5 9 12 2 , 0 2 6 0 - 0 2 8 OOOD 01 -2 5 9 9 0 12 1 OOOD 00 1 5 5 * 0 31 11 12 S2500 00 5 7 5 0 0 on 0 0098 ID 0 1 5890 ot -1 3220 01 2 . 0 1 7 0 - 0 2 8 Ot OD 0 1 -1 657D 29 1 .00(0 00 8 6010 32 11 13 5 2 1 0 0 00 6 2 1 0 0 00 0 0 0 9 8 1 0 0 2 12«0 Ot - 2 1 5 6 0 ct 1 9 8 2 P - 0 2 a 00/10 111 - 7 01 JO 21 1 0903 00 1 5U9D 29 11 11 5 2 5 0 0 00 6 7 5 0 0 CO 1 0 0 9 8 1 0 0 2,-9110 01 - 3 2700 CI 1 .9210-02 8 OOUD 01 -1 1)50 2 1 1 >0000 0 0 7 1010 27


R E D . ' 1 0 6 T I N E ' S . 3 0 0 0 0 0 D 0 0 P E R I O D ' S . 3 0 0 0 0 0 D 0 0 TIRE I E C I S 8 E H T ' 5 . 0 0 0 0 0 0 D - 0 2 VELOCITY VEL0CIT1 HATER ElEV. I R D I - r- T- HATER I B II RATE

BODE CBS LOCATIOB LOCATIOB ELRVATIOR I-DIRECT. 1-DIRIC1. OP CHARGE TEHP

11 15 SUM 0 0 72500. 00 a .0096 ID 0 3 ea2o 01 -3 69 9D 01 1 8600*02 6 0000 0 H 16 1J500 .00 11500 0 0 k •CSISOT 0 a 1 9 5 0 01 -3 15CD CI 1 ,7910-02 8 oo on 0 11 17 52500 .00 82500 00 a •C0980D 0 5 67BD 01 -3 «i:s 0 1 1 .7180-02 8 0 0 0 D 0 11 IB <2*00 .00 07 5 0 0 00 a . C 0 9 6 0 D 0 6 R29D 0 1 -2 937D 01 1 .6060-02 8 0 0 0 0 0 11 19 12500 00 92500 00 a .009790 0 7 0100 01 -2 2i;» CI 1 .1800-02 a 00 OD 0 11 20 52500 00 97500 00 • .009790 0 1 0020 01 - 1 3720 01 1 .5310-02 8 0000 0 11 21 12500 00 102500 00 ft . 0 0 9 7 9 0 0 1 599D 0 1 •a 6 6 9 D 00 1 .155D-U2 a OOOD 0 12 1 57500 00 2500 00 a .00972D 0 6 •m 01 a 128D 00 1 .5»aD-02 8 00 OD 0 12 2 57500 01) 7500 00 • • 0 0 9 7 2 D 0 6 3 7 0 0 01 1 2690 01 1 . 5 1 8 0 - 0 2 8 OOOD 0 12 3 57*00 00 12500 00 a .009720 0 6 0720 01 ? 039D 01 1 . 1 6 9 D - 0 2 8 OOOD 0 12 a 57500 00 17500 00 ft •00973D 0 5 6aio 01 ! »83D CI 1 .633D-02 8 OOOD 0 12 5 17500 00 22500 00 • •00974D 0 5 1020 S I 3 100D 01 1 6 9 0 D - 0 2 8 OOOD 0 12 6 17500 .00 27500 00 a .00970D 0 a 11920 01 3 362D 01 1 , 7 7 3 0 - 0 2 6 OOOD 0 12 7 17500.00 32500 00 u •009150 0 3 6620 0 1 3.2600 01 1 .6<30-02 e OOOD a 12 B 1 7 5 0 0 00 37500 00 a . 0 0 9 7 5 0 0 3 272b 0 1 2 S76D 01 1 .9130-02 9 OOOD 0 12 9 17500 00 K2500 00 a .009750 0 2 7 6 9 0 01 2 1 0 0 0 01 1 •9O1D-02 8 OOOD 0 12 10 57500 00 07500 00 a •00976D 0 2 0 7 1 0 01 1 10 8D 01 2 •003D-02 8 OOOD 0 12 1 1 17500 00 52500. 00 a .009160 0 2 3f 10 0 1 •3.0290 12 1 .978D-02 B OOOD 0 12 12 5 7 5 0 0 00 51500. 00 a • 0 0 9 7 6 D 0 2 0710 01 - 1 106D 01 2 ,0030-02 8 OOOD 0 12 13 57500 00 <2500. 00 a .00975D 0 2 7B9D 01 -2 loop 01 1 9 0 1 D - 0 2 8 OOOD 0 12 IB 17100.00 6 7 5 0 0 00 a • 0 0 9 7 5 D 0 3 2720 01 - 2 6 7 6 0 01 1 ,9130-02 8 OOOD 0 12 15 57500 00 7 2 5 0 0 . 00 b .00975D 0 J 8620 0 1 -3. 26 UD 01 1 833D-02 8 OOOD 0 12 1 6 57100 00 77500. 00 a .0Q910D 0 a 0920 01 - 3 . 3620 01 1 7 7 3 0 - 0 2 B OOOD 0 12 1 1 57500 00 82500 00 a .009111) 0 s 1020 01 -3 1S0D 01 1 . 6 9 0 0 - 0 2 8 OOOD 0 12 IB 57500 . 0 3 07500 00 a •00973D 0 5 6810 01 - 2 66 3!> 01 1 . 6 3 3 D - 0 2 8 OOOD 0 12 19 moo .00 92500 00 a • 0 0 9 7 2 D 0 6 0120 01 - 2 039D 01 1 . 1 6 9 0 - 0 2 0 0 0 OD 0 12 20 57100 00 97500 00 a .00972D 0 6 370D 01 - 1 26 9D 01 1 . 5 1 8 0 - 0 ? 8 OOOD 0 12 21 1 7 1 0 0 .00 102500 00 a .009720 0 6 5 1 2 3 01 -a 328D 6 0 1 , 5 0 0 D - * J 8 OOOD 0 13 1 62100 00 2500. on a .009650 0 5 5190 01 3 98 ID 00 1 .0910-02 8 XBB 0 13 2 6 2 5 0 0 00 7500 00 a . 0 0 9 6 6 0 0 1 a)2D 0! 1 169D 01 1 ,068D-'u.< a OOOD 0 13 3 «500 00 12500 00 « . 0 0 9 6 6 0 0 5 2 0 6 D 01 1 C-13 CI 1 •123D-01 » MOD 0 13 a 62500 00 17*30 00 u .009670 0 9 9 1 9 D 01 2 a88k 21 1 1823-0; <: ,<)00rv o 1.1 s 6 2 5 0 0 0 0 22500. 00 a •00967D 0 a 5770 CI 2 89 tO 01 1 S3BD-02 s o p , ' 0 13 s 12500 00 27500. 00 a •Q0966D 0 a 2160 01 3 09 3n 01 • 718D-02 OCSD 0 n 7 62 'inn 00 .i2sro. 0 0 b -CD9C9D 0 3 B73P 01 3 02«l> 01 1 7 7 9 0 - 0 2 .V OOOD 0 13 s 12500 00 3/1M. 00 a 009690 0 182B 01 2 . 6 5 1 0 01 1 H63P-02 e OOOD 0 13 9 62500 00 0250 C. 00 a .009700 0 3 3 6 8 0 01 1 9a en 01 1 873D-02 6 ooot a 13 10 62100 00 47500, 00 a •Q0970D 0 3.2010 0 1 1 0670 0 1 1 5510-01 e OOOD 0 13 11 62500 00 12500 00 a .009700 0 3 2 0 1 0 01 -6 867D 12 1 . 9 0 1 0 - 0 2 8 OOOD 0 13 12 62500 00 17500 00 a •00970D 0 3 201D 01 - 1 06 ID 01 1 9570-02 8 0000 0 13 13 62500 00 62500. 00 a .0097OD 0 3 368D 01 - 1 9 8 6D 01 1 8730-02 8 OOOD 0 13 la 62100 00 67100 00 0 .009690 0 3 5820 0 1 -2 6 5 5 D 01 1 8630-02 8 OOOD 0 13 15 62100 00 72500 00 a •00969D 0 3 873 D 01 -3 0200 01 1 7790-02 8 OOOD 0 13 16 62100 00 77500. 00 a .009660 0 a 2160 01 - 3 093D 01 1 7ISD-02 8 OOOD 0 13 17 62500 00 62500. 00 a .00967D 0 a 577D 01 -2 89 ID 01 1 63BD-02 e OOOD 0 13 16 62500 00 67500 00 a .009670 0 a 9190 01 - 2 a66D 01 1 5820-02 8 OOOD 0 13 19 62100 00 92500. 00 a , 0 0 9 u 6 D 0 5 . 2 0 6 D 0 1 - 1 . 87 7D C1 1 1 2 3 0 - 0 2 8 OOOD 0 13 20 62500 00 97500. 00 a .00966D 0 5 . 012 D 01 -1 169D 01 1 U6BD-02 8 OOOD 0 13 21 62500 00 102500. 00 a •00965D 0 5 5190 01 -3 98 ID 00 1 095D-02 8 OOOD 0 10 1 67500 00 2500. 00 a .009600 0 a . 5870 0 1 3. 67 ID CO 1 0130-02 8 0000 0 I t 2 67500 00 7500 00 a •00960D 0 a 5 2 0 D 01 1 06 OD 01 1 3800-02 8 OOOO 0 10 3 67500 00 12500 00 a .009600 0 a 3950 01 1 70 6D 01 1 039D-02 6 OOOD 0 10 a 67*00 00 17500 00 0 . 0 0 9 6 ID 0 a 2 3 5 D 01 2 309D 01 1 .0950-02 8 0000 0 in 5 67500 00 22500. oo a •00962D 0 « 0700 01 2 728D 01 1 551D-02 8 OOOD 0 1a 6 67500 00 27100 00 a .00962D 0 3 9 3 4 D 01 2 9520 01 1 ,6080-02 6 OOOD 0 ta 7 67500 00 32500. 00 a •00963D 0 3 8570 01 2 92 SD 01 1 .680D-02 0 OOOD 0

TBHP. SOBSTARCE KISS COBCERTRATIORS

OP CHARGE CR|1| CR(2| ,0300-23 t, .OOOD 00 1, ,8000-25 -1. .6010-13 1, .OOOD 00 6, ,1100-26 -1, ,2060-20 1, .OOOD 00 a, .727D-21 -3 ,3050-26 1, .OOOD 00 1 ,2310-26 -0 ,-ino-2a 1, .OOOD 00 1, .1720-30 -3. ,(350-30 1, .OOOD 00 9, .9620-33 -8, .563D-33 1, ,0009 00 2, ,5660-35 -2, .900D-31 1, .OOOD 00 8, ,1860-38 -1. •097D-32 1, .OOOD 00 3, .2180-35 -t, .6B3D-30 1, .OOOD 00 1, .2260-33 -1, ,1860-28 1, IOOOD 00 a, ,0060-31 •0, ,06«D-27 1, ,OOQD 00 1, ,0920-29 -5, .009D-26 1, .OOOD 00 1, ,9B6D-2e .1270-25 1, .0000 00 a, .8660-26 -3, ,7200-27 1, >0000 00 1, ,8560-29 -2, ,1270-29 1, .OOOD 00 1, .0600-31 -5, ,5050-J2 1 .OOOD 00 2, .9680-3* -1, ,0100-30 1, ,0009 00 lj< ,2600-37 -1.165D-12 1. • OOSD CO 2. ,9680-30 -2. ,127D-29 1. .OOOD oo 1. ,06CD-31 -J.120D-21 1, .OOOD 00 1, ,6160-29 -1, ,1270-25 1, >OOOD 00 a, ,86(0-28 -5, ,0090-26 1. ,0000 00 1. 986D-28 •0, ,0600-27 1, .OOOD 00 1. ,092D-29 -1, ,1860-28 1. .0000 00 a ,0060-31 -1, ,6030-30 1, .0000 00 1, ,2260-33 -1. ,0970 12 1, .oooo 00 3 ,270D-35 -2, .900D-J1 1, .COOD 00 8 .1860-38 -7, ,0810-38 1, ,3001) 00 2. ,109D-00 -3 .0870-35 1, .OOOD OS a, •726D-3B -a, .708D-33 1. .OOOD 00 1, ,010ll-3t 1, ,OOUD 00 1, ,«J J6D-33 -i, ,1J2D-J9 1. .00 0') 50 3, ,9910-32 -i. ,3770-28 1, , LUOD 00 5. ,1590-31 -2, ,9910-:H 1. OOOD 00 1. .2230-30 -1, ,96i0-29 1. ,Ol)"t> 30 s. ,0310-32 -7,0170-32 1. ,oocp 00 3. ,a5tD-30 -2, ,1910-40 1, .0000 00 1, .1890-36 -a. , B10D-17 1, .OOOD 6G 3. .02111-39 -2. ,191D-3a I. .0000 00 1. , 1890-36 -7, ,0570-32 1. .OOOD 00 3, .051C-30 -1. ,0650-29 1. ,0000 00 5. •03ID-32 -2.9950-28 1, ,0000 00 1, ,2230-30 -1, ,3770-28 1, .OOOD 00 5, . 159D-31 -1, ,1520-29 1, ,0000 00 3. .991D-32 -3: .U10D-31 1, , OOOD 00 1. •09BD-33 -a. 70SD-33 1. OOOD 00 1. ,0150-35 -3, ,087D-31 1. .OOOD 00 6. ,7260-30 -7. ,8830-38 1. .0000 OU 2. , 1090-00 -1, ,7030-00 1, .OOOD 00 0, 1060-03 -6, ,9230-38 1, , OOOD 00 1. ,D61P-00 -1, ,0850-35 1, .OOOD 00 3. .102D-3R -8. ,0160-30 1, .0000 00 2. ,0 55D-36 -2.750D-32 1, ,0000 00 9. . 009D-35 -3, ,3070-31 1, .OOOD 00 1, ,189D-33 -7, .5270-31 1, .OOOD 00 2. .9100-33


I T E R * • 106 T I H E a 5 . 300000D 00 PERIOD*5 .300000D 00 T IRE I I C R B H 8 N T " 5 . 0 0 0 0 0 0 D - 0 2

VELOCITT VELOCITT iATER ELEV. TEHP. SUBSTANCE BASS CONCEN I»0t- X- r - RATER I I I I N RATE RATE

RODE CES LOCATION LOCATION ELEVATION I - D T R 5 C T . Y - D I R I C 1 . OP CHANGE TEHF OP CHANGE CIC<1) CK<2)

l a 8 6 7 5 0 0 00 37500 00 9 009690 0 1 3 • 859D 0 2 .619D 01 1 . 7 8 7 0 - 0 2 8 OOOD 0 1 - 3 100D-32 1 .OOOD 0 0 1 395D-30 111 9 6 7 5 0 0 00 9 2 5 0 3 00 a 009690 0 1 3 -907D 0 I . 9 8 8 9 CI 1 . 7 0 2 0 - 0 2 8 OOOD 0 1 - 2 •510D-3U 1 .OOOD 00 1 2 0 6 0 - 3 6 l a 10 6 7 5 0 0 00 9 7 5 0 0 00 a . 0 0 9 6 9 0 0 1 3 . 9 7 9 0 0 1 0 8 0 0 01 1 . 9 I 6 D - 0 2 8 OOOD 0 1 - 9 . 7 9 8 D - 3 7 1 oooo 0 0 5 316D-39 1 a 11 67500 00 52500 00 9 . 0 0 9 6 9 D 0 1 9 • 015D 0 - 7 2 5 2 0 12 1 . 7 5 5 D - 0 2 8 OOOD 0 1 - 2 . 6 7 5 D - 3 9 1 .OOOD 00 1 6 2 0 D - 0 1 1a 12 6 7 5 0 0 00 5 7 5 0 0 00 9 . 0 0 9 6 9 0 0 1 3 • 979D 0 - 1 080D C1 1 . 9 1 6 0 - 0 2 8 OOOD 0 1 - 9 • 7 9 8 D - 3 7 1 OOOD 00 5 316D-39 1 U 13 6 7 5 0 0 00 62500 00 9 009690 0 1 3 . 907 D 0 - 1 9860 01 1 . 7 8 2 0 - 0 2 8 OOOD 0 1 - 2 . 5 1 0 D - 3 0 1 OOOD 00 1 206D-36 l a 10 6 7 5 0 0 00 6 7 5 0 0 00 9 00 9690 0 1 3 .85UD 0 - 2 . 61OD 01 1 . 7 8 7 0 - 0 2 8 OOOD 0 1 - 3 • 1 0 0 D - 3 2 1 . 0 0 0 0 00 1 3 9 5 0 - 3 0 l a 15 6 7 5 0 0 00 7 2 5 0 0 00 a 009630 O t 3 8 5 7 0 0 - 2 9 2 9 0 01 1 . 6 8 0 0 - 0 2 8 0000 0 1 - 7 • 5 2 7 D - 3 1 1 OOOD 00 2 9 1 0 0 - 3 3 l a 16 6 7 5 0 0 00 7 7 5 0 0 . 0 0 a 009620 0 1 3 9390 0 - 2 952D 01 1 • 6 9 8 D - 0 2 8 OOOD 0 1 - 3 . 3 0 7 D - 3 I 1 OOOD 00 1 189D-33 1a 17 6 7 5 0 0 00 82500 00 9 00962D 0 1 9 • 070D 0 - 2 7 2 8 0 01 1 551D-02 8 OOOD 0 1 - 2 . 7 5 0 0 - 3 2 1 OOOD 00 9 099D-35 l a 18 6 7 5 0 0 00 8 7 5 0 0 00 9 009610 0 1 a 235D 0 - 2 309D 0 1 1 . 9 9 5 0 - 0 2 8 OOOD 0 1 - 8 . 0 1 3 D - 3 0 1 OOOD 00 2 0 5 5 D - 3 6 i a 19 6 7 5 0 0 00 9 2 5 0 0 00 U 009600 0 1 9 • 395D 0 - 1 706D 01 1 . 4 3 9 D - 0 2 8 OOOD 0 1 - 1 0 8 5 D - 3 5 1 OOOD o o 3 102D-38 1a 20 6 7 5 0 0 00 97500 00 9 00 96 00 0 1 9 520D 0 - 1 089D 01 1 . 3 8 0 D - 0 2 8 OOOD 01 - 6 9 2 3 D - 3 8 1 OOOD 00 1 8 6 0 0 - 0 0 14 21 6 7 5 0 0 00 102500 00 a 009600 0 1 9 5B7D 0 - 3 671D 00 1 . 0 1 3 D - 0 2 8 OOOD 0 1 - 1 7 0 3 D - 0 0 1 OOOD 00 0 306D-03 15 1 7 2 5 0 0 00 2 5 0 0 . 0 0 9 009590 0 1 3 . 7 2 0 0 0 3 396D CO 1 • 3 0 0 D - 0 2 8 OOOD 0 1 - 2 8 8 2 D - U 3 1 OOOD 00 7 058D-U6 15 2 1 2 5 0 0 00 7 5 0 0 00 9 009550 01 3 . 6 8 9 0 0 1 011D 01 1 • 2 7 3 D - 0 2 8 OOOD 0 1 - 1 .220D-UO 1 OOOD 0 0 3 107D-03 15 3 7 2 5 0 0 00 12500 00 0 . 0 0 9 5 5 D 0 1 3 • 629D 0 1 69 ID 01 1 . 3 2 3 D - 0 2 8 OOOD 0 1 - 1 • 9 8 0 D - 3 8 1 OOOD 00 5 U32D-91 15 9 7 2 5 0 0 00 17500 00 9 009560 0 1 3 565U 0 ? 197D 01 1 • 3 8 8 D - 0 2 8 OOOU 0 1 - 1 5 2 6 D - 3 6 1 OOOD 00 0 060D-39 15 5 7 2 5 0 0 00 22500 00 9 009570 0 1 3 597D 0 2 602D 01 1 . 0 9 2 0 - 0 2 8 OOOD 0 1 - 5 0 89 D -35 1 OOOD 00 1 722D-37 15 6 7 2 5 0 0 00 2 7 5 0 0 00 a 00957D 0 1 3 611D 0 2 928D 01 1 5 9 8 D - 0 2 8 OOOD 0 1 - 7 1 3 3 0 - 3 0 1 DOOD 00 2 009D-36 15 7 7 2 5 0 0 00 32500 00 9 009580 0 1 3 790D 0 2 995D 01 1 . 5 1 9 D - 0 2 8 OOOD 0 1 - 1 7 7 2 D - 3 3 1 OOOD 00 6 090D-36 15 8 7 2 5 0 0 00 375C0 00 a 00959D 0 1 9 0B9D 0 2 763D 01 1 . 7 3 5 D - 0 2 8 OOOD 0 1 - 9 0 9 7 0 - 3 5 1 OOOD 00 3 896D-37 15 9 7 2 5 0 0 00 0 2 5 0 0 00 t 00959D 0 1 9 U51D 0 2 170D CI 1 . 5 1 1 D - 0 ? B OOOD 0 1 - 9 5 9 3 0 - 3 7 1 DOOD 00 0 515D-39 15 10 7 2 5 0 0 00 9 7 5 0 0 00 9 009590 01 9 771D 0 1 229D 01 1 . 9 6 0 0 - 0 2 8 OOOD 0 1 - 9 9 3 5 5 - 3 9 1 OOOD 0 0 2 6 2 2 D - 0 1 15 11 7 2 5 0 0 0 0 5 2 5 0 0 00 a 009590 0 1 a 909D 0 - 3 665D- 12 1 . 5 7 5 0 - 0 2 8 OOOD 0 » - 1 6 8 8 0 - 0 1 1 OOOD 0 0 9 533D-0O 15 12 7 2 5 0 0 0 0 5 7 5 0 0 00 a 009590 0 1 9 771D 0 - 1 229D 01 1 . 9 6 0 D - 0 2 8 OOOD 0 1 - 0 9 3 5 0 - 3 9 1 OOOD 00 2 6 2 2 D - 0 1 15 13 7 2 5 0 0 00 62500 00 9 009590 0 1 o a s m 0 - 2 1 7 0 D 0 1 1 • 5 1 1 D - 0 2 8 OOOD 0 1 - 9 5 9 7 0 - 3 7 1 OOOD 0 0 0 515D-39 15 19 7 2 5 0 0 00 6 7 5 0 0 00 a 009590 01 a 089D 0 - 2 7 6 3 0 01 1 . 7 3 5 0 - 0 2 B OOOD 0 1 - 9 0 9 7 D - 3 5 1 OOOD 0 0 3 896D-37 15 15 7 2 5 0 0 00 7 2 5 0 0 00 9 009580 0 1 3 790D 0 - 2 995D 01 1 . 5 1 9 0 - 0 2 8 OOOD 0 1 • l 7 7 2 D - 3 3 1 OOOD 0 0 6 090D-36 15 16 1 2 5 0 0 0 0 7 7 5 0 0 . 0 0 a 00957D 0 1 3 6110 0 - 2 9 2 8 0 01 1 • 5 U 8 D - 0 2 8 OOOD 0 1 - 7 1 3 3 D - 3 0 1 OOOD 00 2 009D-36 15 17 7 2 5 0 0 0 0 82500 00 9 009570 0 1 3 5U7D 0 - 2 692D 01 1 • 0 9 2 D - 0 2 8 OOOD 0 1 - 5 0 8 9 D - 3 5 1 OOOD o o 1 7 2 2 D - 3 7 15 18 7 2 5 0 0 0 0 87500 0 0 9 009560 0 1 1 565D 0 - 2 1970 Of 1 388D-02 8 0 0 0 0 0 1 -1 5 2 6 D - 3 6 1 o o o o 0 0 a 0 6 0 0 - 3 9 15 19 7 2 5 0 0 00 9 2 5 0 0 00 9 009550 0 1 3 629D 0 - 1 6 a ID 01 1 . 3 2 3 0 - 0 2 8 OOOD 0 1 -1 9 BOD-38 1 OOOD 0 0 5 0 3 2 D - 0 1 15 20 7 2 5 0 0 0 0 97500 00 0 00955D 0 1 3 6 B H D 0 - 1 0 1 1 D 01 1 2 7 3 D - 0 2 8 OOOD 0 1 -1 2 2 0 D - 0 0 1 OOOD 0 0 3 . 1 0 7 D - 0 3 15 2 1 7 2 5 0 0 0 0 102500 0 0 A 00959D 01 3 7 2 0 0 0 -3 3 9 6 0 00 1 .3000-02 8 . 0000 01 - 2 8 8 2 0 - 9 3 1 OOOD 0 0 7 . 0 5 8 0 - 0 6 16 1 7 7 5 0 0 0 0 2 5 0 0 . 00 9 00950D 0 1 2 915D 0 3 1210 00 1 162D-02 8 OOOD 0 1 - 3 7 3 1 D - 9 6 1 OOOD 0 0 8 B23D-99 16 2 7 7 5 0 0 00 7 5 0 0 . 0 0 9 009500 01 2 898D 0 9 389D 0 0 1 . i a o D - o 2 8 . OOOD 0 1 -1 6 5 0 D - 0 3 1 OOOD 0 0 9 . 105D-06 1 6 3 7 7 5 0 0 00 1 2 5 0 0 . 00 a 0095 ID 01 2 879D 0 1 590D 01 1 198D-02 8 . OOOD 0 1 - 2 8 1 2 D - 9 1 1 OOOD 0 0 7 . 009C-00 16 9 7 7 5 0 0 0 0 1 7 5 0 0 . 0 0 9 0095 ID 01 2 8 B 9 D 0 2 0 9 8 0 01 1 . 2 8 9 0 - 0 2 8 OOOD 0 1 - 2 2 9 1 D - 3 9 1 OOOD 0 0 6 035D-02 16 5 7 7 5 0 0 00 2 2 5 0 0 0 0 a 00952D 0 1 2 978 D 0 2 592D c » 1 . 2 9 2 0 - 0 2 8 OOOD 0 1 - 8 9 3 0 D - 3 8 1 OOOD 0 0 2 679D-00 16 6 7 7 5 0 0 0 0 2 7 5 0 0 00 a 0O953D 0 1 3 207D 0 2 979D 01 1 . 3 8 7 0 - 0 ! : 8 OOOD 0 1 - 1 3 0 3 D - 3 6 1 OOOD o c 0 190D-39 16 7 7 7 5 0 0 0 0 3 2 5 0 0 . 00 a 009500 01 3 629D 0 3 199D 01 1 783D-02 8 00 CD 0 1 - 3 8 3 9 5 - 3 6 1 OOOD 0 0 1 . 331D-38 16 8 7 7 5 0 0 0 0 37500 00 a 00959D 0 1 a 267D 0 3 108D 01 1 7 9 2 D - 0 2 8 . OOOD 0 1 - 2 6 0 8 D - 3 7 1 OOOD 0 0 1 . 075D-39 16 9 7 7 5 0 0 00 9 2 5 0 0 00 a 00959D 01 5 029 D 0 2 586D 01 1 2 5 0 D - 0 2 8 OOOD 0 1 - 3 9 2 5 0 - 3 9 1 OOOD 0 0 1 800D-01 16 10 7 7 5 0 0 00 97500 0 0 u 00953D 0 1 5 718D 0 1 5 3 f D 01 2 2 0 9 D - 0 ? 8 OOOD 01 - 2 7 8 0 D - 0 1 1 OOOD 00 1 015D-03 16 11 7 7 5 0 0 0 0 5 2 5 0 0 . 00 9 00953D 01 6 031D 0 - 2 9 9 9 D - 1 2 8 7 0 2 0 - 0 3 8 . OOOD 01 - 1 2 1 0 D - U 3 1 OOOD 0 0 6 . 2 6 5 0 - 0 6 16 12 7 7 5 0 0 00 57500 00 a 0 0 9 5 3 0 0 1 5 718D 0 - 1 536D C 1 2 . 2 9 9 0 - 0 2 8 . OOOD 0 1 - 2 7 8 0 0 - 0 1 1 OOOD o o 1 015D-03 16 13 7 7 5 0 0 00 6 2 5 0 0 . 00 a 00959D 01 5 020 D 0 - 2 586D 01 1 2 5 0 D - 0 ? 8 OOOD 01 - 3 9 2 5 0 - 3 9 1 OOOD 0 0 1 8 0 0 D - 0 1 16 1U 7 7 5 0 0 00 67500 0 0 a 009590 0 1 u 267D 0 - 3 108D 01 1 7920-02 8 OOOD 01 - 2 6 9 0 0 - 3 7 1 OOOD 0 0 1 075D-39 16 15 7 7 5 0 0 0 0 7 2 5 0 0 00 a 009590 0 1 3 629D 0 - 3 1 9 9 0 01 1 2 8 3 D - 0 2 8 OOOD 01 - 3 8 3 0 0 - 3 6 1 OOOD 0 0 1 . 3 3 1 D - 3 8 16 16 7 7 5 0 0 0 0 77500 00 a 009530 0 1 3 207D 0 - 2 9 7 9 0 01 1 3 8 7 0 - 0 2 8 . OOOD 01 -1 3 0 3 0 - 3 6 1 OOOD 0 0 0 . 190D-39 16 17 7 7 5 0 0 0 0 8 2 5 0 0 . 00 a 009520 0 1 2 978 D 0 - 2 5 9 2 D 01 1 2 9 2 D - 0 2 8 OOOD 0 1 -fl 9 3 0 D - 3 8 1 OOOD 0 0 2 . 679D-00 16 18 7 7 5 0 0 00 8 7 5 0 0 . 00 a 0095 ID 0 1 2 8 8 9 0 0 - 2 098D 01 1 2 8 0 D - 0 2 8 OOOD 0 1 - 2 2 9 1 D - 3 9 1 OOOD 0 0 6 . 035D-02 16 19 7 7 5 0 0 00 9 2 5 0 0 00 u 0095 ID 0 1 2 8 7 9 D 0 -1 5U0D 0 1 1 • 1 9 8 D - 0 2 8 OOOD 0 1 - 2 8 1 2 0 - 0 1 1 OOOD 0 0 7 U 0 9 D - 9 I I 16 20 7 7 5 0 0 0 0 9 7 5 0 0 00 a 00 95 0D 01 2 . 1 9 8 0 0 - 9 389D CO 1 . 19UD-02 8 OOOD 0 1 -1 6 5 0 D - 0 3 1 OOOD 00 0 105D-06 16 2 1 7 7 5 0 0 0 0 102500 00 a 00950D 0 1 2 915D 0 - 3 1 2 I D 0 0 1 1 6 2 D - 0 2 8 OCOO 0 1 - 3 7 3 1 0 - 0 6 1 OOOD 0 0 8 . 8 2 3 D - 0 9

K) to 00


ITEB.« 10S HBt'5.3000000 00 PMIOD-5.3000000 00 TIBE HICBSHEHT-5.0000000-02 VELOCITY VELOCITY 4ATEB ELEV. IIIDI- T- HATH in ID BATE •ODE OS LOCATIOH LOCATtO« ELEVATIOK I-DIBECT. t-DIBECT. OP CHIKCB TEHP

17 1 82500.00 2500 00 4 00946D 01 2 178D 01 2 7950 CO 1 0140-02 a 0000 0 17 2 82500.09 7500 00 0 .Q0946S 01 2 U9B 01 8 51 CO CO 1 .0160-02 8 0000 0 17 3 82500.00 12500 00 0 0094 70 01 2 164 0 01 1 4 120 01 1 0720-02 8 OOOO 0 17 4 82500.00 17500 00 4 .009480 01 2 201D 01 1 9650 01 1 .1340-02 B HOOD 0 17 5 82500.00 22500 00 0 .00949D 01 2 319D 01 2 5110 CI 1 .0530-02 3 OOOD 0 17 6 82500.00 27*00 00 4 009490 01 2 6730 01 3 019D 01 1 3850-02 8 OOOD 0 17 1 82*00.00 32500 00 <1 009500 01 3 2970 01 3 4060 01 1 0250-02 8 OOOO a 17 8 82500.00 17500 00 4 .00999D 01 4 3110 01 3 615D 01 2 105D-02 8 OOOD 0 17 9 82500.00 42500 00 4 .009490 01 5 610D 01 3 2910 01 7 819D-03 8 OOOi 0 17 10 82500.00 47500 00 4 009080 01 6 9500 01 2 1480 01 3 0790-02 8 OOOD 0 17 11 82500.00 52500 00 4 009460 01 7 6130 01 -3 7600 •12 - 1 0260-02 8 OOOO 0 17 12 82500.00 57500 00 0 009080 01 6 9500 01 -2 1060 01 3 0 7 9 0 - 0 2 8 OOOD 0 17 U 82500.00 62500 00 4 009490 01 5 6100 0 1 -3 2910 01 7 6 1 9 0 - 0 3 8 OOOD 0 17 14 62500.00 67500 00 11 009090 01 4 3110 0 1 -3.6150 01 2 1050-02 8 OOOD 0 17 15 82500.00 7 1 5 0 0 0 9 t .009500 01 3 2970 0 1 -3 00 6D 01 1 0250-03 8 OOOD 0 17 16 82*00.00 77500 00 4 009490 01 2 673D 0 1 -3 0190 01 1 3850-02 8 OOOD 0 17 17 82500.00 82500 00 4 009090 01 2 339D 01 - 2 5110 01 1 0530-02 8 OOOD 0 17 19 82500.00 87500 00 4 0 0 9 4 8 0 01 2. 2010 01 -1 9 6 * 0 01 1 1340-02 8 OOOO 0 17 19 62500.00 92500 00 4 00947D 01 2 1640 01 - 1 0120 01 1 0 7 2 0 - 0 2 8 OOOD 0 17 20 82500.00 97500 00 4 00946D 01 2 1690 01 -8 51C0 00 1 0 1 6 0 - 0 2 8 OOOD 0 17 21 © 2 5 0 0 . 0 0 102500 oo 4 0 0 9 4 6 0 01 2 178D 01 -2 7 9 * 0 00 1 0 1 4 0 - 0 2 8 OOOD 0 18 1 87500.00 2500 00 0 .009430 01 1 525D 01 2 370D 00 8 9480-03 8 OOOD 0 18 2 87500.00 7500 00 4 009430 01 1 5120 01 7 3000 00 9 1260-03 8 OOOD 0 18 3 8 7 5 0 0 . 0 0 12500 00 4 .009400 01 1 49BO 01 1 232D 01 9 3 0 8 D - 0 3 8 OOOD 0 18 4 87500.00 17500 00 4 009451) 01 1 5170 01 1 74 30 01 9 4 7 6 0 - 03 8 OOOO 0 16 5 87500.00 22500 00 4 00906D 01 1 6270 01 2 30CD 01 B ,8730-03 8 DOOD 0 18 6 87500.00 27500 00 4 009060 01 1 9500 01 2 8990 01 1 7 6 7 0 - 0 2 8 OOOD 0 IB 7 87500.00 32500 so 4 ,009470 01 2 67BD 01 3 5790 01 9 081D-03 » OOOD 0 18 8 67*00.00 37500 00 » 009460 01 4 0960 01 4 15 ID 01 2 3970-02 8 OOOO 0 18 9 87500.00 42500 00 4 .009473 01 6 1860 01 4 35 5D 01 -2 4020-02 8 OOOD 0 18 10 87500.00 47500 00 4 00946D 01 8 7590 01 3 3120 01 2 6 9 2 D - 0 2 8 OOOD 0 18 It 87500.00 52500. 00 4 009410 01 1 0180 02 - 4 674D •12 - 5 2810-02 8 OOOO 0 IB 12 B7500.00 57500 00 4 009460 01 8 759D 01 - 3 3120 01 2 8 9 2 D - 0 2 8 . OOOO 0 IB 13 87500.00 62500 00 4 009470 01 6 166D 01 - 4 3550 C-1 -2 9020-02 8 OOOD 0 18 14 87500.00 67500 00 4 00946D 01 0 0960 01 - 4 1510 01 2 3970-02 8 OOOO 0 18 15 87500.00 7 2 5 0 0 00 4 0 0 9 4 7 0 01 2 6780 01 -J 5790 0 1 9 0 8 1 0 - 0 3 8 OOOO 0 18 16 87500.00 71*00 00 4 .009460 01 1 954D 01 -2 89 SO 01 1 7670-02 6 OOOD 0 18 17 87*00.00 62500 00 4 009460 01 1 6270 01 -2 300D 01 B 8 7 3 D - 0 3 6 OOOD 0 18 18 87*00.00 87500 00 4 009050 01 1 5170 01 -1 70 30 01 9 4 7 6 0 - 0 3 8 OOOD 0 18 19 87500.00 92500 00 a 0094«D 01 1 4980 01 -1 232D 01 9 348D-03 8 OOOO 0 IB 20 87500.00 97500 00 4 .00943D 01 1 5120 01 -7 3440 QO 9 .1260-03 8 OOOD 0 18 21 87*00.00 102500 00 4 .009430 01 1 5250 01 -2 3740 00 6 . 9 4 8 0 - 0 3 8 OOOD 0 19 1 92500.00 2500 00 a 009410 01 9 7500 00 1 87 ID 00 7 9860-03 8 OOOD 0 19 2 92500.00 7500 00 4 00942D 01 9 5670 00 5 92BD 00 7 5420-03 a OOOD 0 19 3 92500.00 12500 00 4 009420 01 9 237D 00 9 9620 00 6 8860-03 8 OOOD 0 19 4 92500.00 17500 00 4 .00944D 0 1 8 972D 00 1 4040 01 9 5 4 0 0 - 0 3 8 OOOD 0 19 5 92500.00 22500 00 4 009450 Ot 9 1420 00 1 6720 01 6 2760-03 8 OOOD 0 19 6 92500.00 27590 00 a 00945D 01 I 1090 01 2 45 3D 01 1 4550-02 a OOOO 0 19 7 92500.00 32500 00 a 009080 01 1 709D 01 3 3800 01 - 7 5650-03 B OOOD 0 19 « 92500.00 37500 00 4 009460 01 3 313D 01 4 5050 01 4 .1470-02 e OOOD 0 19 9 92500.00 42500 00 a 009430 01 6 0860 01 5 8680 01 - 5 0880-02 6 OOOD 0 19 10 92500.00 4 7 5 0 0 00 4 00920D 0 1 1 0610 02 5 4950 01 2 3520-01 8 OOOD 0 19 11 92500.00 52500 00 4 00902D 01 1 3530 02 -1 1700 •12 1 982D-02 6 OOOD 0 19 12 92500.00 57500 00 a 00924D 01 1 061D 02 - S 4 9 5 0 01 2 .3520-01 8 OOOO 0 19 13 92500.00 6 2 5 0 0 00 4 009430 01 6 0860 01 -5 B88D CI -5 . 0 8 6 0 - 0 2 8 OOOD 0 19 14 92500.00 67500 00 4 009460 01 3 3130 01 -4 5050 01 4 ,1470-02 B OOOD 0

TKF1P. 50BSTAHCE FLASS COKCEBTRATIOPS BATE OP CflABGE CK(') CK (21 J.570D-09 •1.6520-06 •1.9650-00 •2.5940-02 •1.V28D-00 •1.947D-39 •7.3010-39 •7.4020-40 -1.7000-01 •1.7000-93 •I.0220-05 •1.700D-03 •1.7040-01 •7.0020-110 •7.3020-39 •1.9070-39 •1.1280-00 •2.594D-42 •2.9650-00 •1.6520-06 •3.5700-09 •2.000D-52 •1.1580-09 •2.1 B20-07 -2.0990-45 •1.0190-43 •2.1520-02 -1.1HSB-U1 1.8620-02 9.4350-00 •6.0 05D-00 3.7620-00 •6.0050-04 9.4350-40 •1.8620-02 •1.145D-01 •2.1520-42 •1.0100-43 -2.0090-45 •2.182D-47 •1.1580-09 •2.0000-52 •1.0550-55 •5.2550-53 •1.0(70-50 •9.9030-09 •5.0580-07 2.6780-06 2.B08D-01 8.7400-37 1.9420-32 -9,6640-33 •4.0840-19 •9,6600-33 1.9420-32 8.7400-37

1, ,0000 00 1, .0000 00 1, ,0000 00 1, .ODOD 00 1, .0000 00 1, ,0000 00 1. ,0000 00 1 ,0000 00 1, .0000 00 1, ,0000 00 1, , OOOD 00 1. .OOOD 00 1, ,0000 00 1, .0000 00 1, .0005 00 1, .0000 00 1, .0000 00 1, .OOOO 00 1, .OOOO Oil 1. .0000 00 1, .OOOD 00 1, .0000 DO 1, .OOOD 00 1, .0000 00 1, ,0000 00 1, .OOOO 00 1, i OOOD 00 A .OOOP 00 1, .0000 00 1, .oaoD 00 1. .oooo 00 1, .0000 00 1, ,0000 00 1, .OOOD 00 1, • OOOD 00 1, .OOOD 00 1, .OOOD 00 1, .0000 00 1, . OOOD 00 1, .0000 00 1 .OOOD DO 1, ,0000 00 1 ,000D 00 1, ,0000 00 1, ,0000 00 1 .0900 00 1, .0000 00 1, ,000D 00 1. .OOOD 00 1. .OOOD 00 1 .0000 00 1. . o o o o 00 1 .OOOD 00 1 .OOOD 00 1 .oaoD 00 1 .0000 00

B. 1970-S.i 3.9620-49 7.5500-47 7,0220-05 3.2060-43 5.9580-42 2.41CD-41 2.8310-42 7.5460-40 8.3040-46 4.7590-48 8.3440-06 7.5460-40 2.8310-42 2.4100-41 5.9580-42 3.2460-43 7.0220-45 7.5540-47 3.9820-49 8 . 1 9 7 0 - 5 2 5.3750-55 2.7190-52 5.3980-50 5.360P-48 2.7960-46 6.2770-45 3.5460-44 5.7I2D-45 1.0310-03 2.B30D-45 1.8050-40 2.6300-45 1.0310-43 6.7120-45 3.5460-40 6,2770-05 2.7960-06 5.3600-48 5.3960-50 2.7190-52 5.3790-55 2.3200-58 1.2090-55 2.0560-53 2.5200-51 2.2520-09 2.8980-05 3.0BB0-41 7.2280-37 1.0400-32 3.5B9D-34 5.0890-33 3.S99D-34 1.0400-32 7.228D-37

Table A.. 3 (continued)

ITER.. 106 TIRE'S.3000006 OO PERIOD*5.300000D 00 TIRE IRCREHBRT'S.0000000-03

TELOCITY TELOCITY RATER ELEY. TEHP. SOBSTARCE HASS C0RCEHT31TI0HS IRDI X- I - RATER 1R IR SATE BATE

RODE CES tOCATIOH LOCATJOH ELEYATIOR I-DISECT. 1-DIRIC1. OF CHARGE TERP. OF CHARGE CR(1| CR<2)

15 15 92SOO. .00 72500. 00 II, .0091.80 01 1, .1090 01 -3. .3840 01 -7, .5650-03 8. .OOOD 01 2. ,8080-01 1, .OOOD 00 3, .0880-01 19 16 92500. ,00 77500. ,00 a, •00905D 01 1 .1080 01 -2, .6531) 01 1 •U55D-02 a .OOOD 01 2. .6780-06 1. ,000D 00 2. .B9BD-05 19 17 92500, .00 82500, .00 Q .009D5D 01 9 .1020 00 -1, ,8720 01 6, ,2760-03 8, , OOOD 01 -5. ,0580-07 1. ,0000 00 2. ,2520-09 19 18 92500. ,00 87500. .00 II .009000 01 8 .9720 00 -1, .HOOD 01 9 ,5000-03 8. , OOOD 01 -9, .903D-09 1 .0000 00 2, ,5200-51 19 19 92500, ,00 92500. ,00 B .009020 01 9 .2370 00 -9, .9620 00 6 .8860-03 8, .OOOD 01 -1. .017D-50 1, .oooo 00 2. .056D-53 19 20 92500, ,00 97500. ,00 u .009U20 01 9 .5670 00 -5, .928D 00 7 . 5 - > 2 0 - 0 3 8. ,0000 01 -5, .2550-53 1, .0000 00 1. , 209D-55 19 21 92500, ,00 102500. .00 0 .0091110 01 9 .7500 00 -1, .8710 00 7 .V86D-03 8. ,0000 01 -1. .0550-55 1, .OOOD 00 2. ,3200-58 20 1 97500, ,ao 2500. .00 0, ,009900 01 5 .3670 00 1, .OOOD 00 7, . 3 32D-03 a, , OOOD 01 1. .8100-57 1, ,0000 00 1, , 570D-56 20 2 97500, .00 1500. .00 n .009000 01 5 .2000 00 0 .608D OO 6, ,5I9D-03 8. ,0000 01 1, .5070-52 1, ,000D 00 9. ,3500-52 20 3 97580, .00 12500. 00 0 .00992D 01 a. ,7860 00 1, .6120 CO 6 ,7290-03 a. OOOD 01 a, .001D-08 1. .OOOD 00 2. ,1820-07 20 0 97500, .00 17500. ,00 II .009030 01 0 .1270 00 1, .0350 01 1, ,0850-02 a. , 000? 01 7, . 8920-00 1. ,0000 00 J . 301D-03 20 5 97*00, .00 22500. 00 a, .009050 01 3 .2710 00 1, ,3310 01 8, .0 280-03 8. ,0000 01 9.B10D-00 1, , OOOD 00 3. ,7170-39 20 6 97*00,00 27500. .00 0 ,009060 01 3 .0203 00 1, ,663D 01 1 .0800-02 8. .OOOD 01 -6.255D-32 1. .OOOD 00 1. 2930-33 20 7 97500. ,00 32500. 00 o, ,009520 01 0 .6280 00 2, ,008D 01 -0, ,9270-02 a, .OOOD 01 -9. ,0580-28 1. ,0000 00 1. ,6000-29 20 8 97*00. .00 31500. 00 II .009000 01 1 .6690 01 3, .1030 01 * .1080-02 8. ,UOOD 01 -1. •030D-23 1. .OOOD 00 1. 6380-25 20 9 97500, .00 •2500. CO «, .009560 01 0 .6010 01 5. ,6610 01 -1, ,1910-01 a. , OOOD 01 -1, , 150D-25 1, .0000 00 1. .5520-26 20 10 97500, .00 17500. oo II, .009180 01 1 ,3520 02 7, .5910 01 3 .0020-01 a, .OOOD 01 -1. ,2050-18 1, .OOOD 00 1. , 1680-26 20 11 97500, .00 52500. oo o, .008550 01 2 .0570 02 3.9300-12 -6 . .3180-01 8, .OOOD 01 -1. .7200-10 1, .OOOD 00 9. .3750-22 20 12 97*00, ,00 57500. ,00 a .009180 01 1 .3520 02 -7 .5910 01 3 .B02D-01 a, , OOOD 01 -1, .2050-18 1, .OOOD 00 1. .I6BD-26 20 13 97500, .00 62500. 00 II ,009560 01 • .6070 01 -5. .6610 Of -1 .791D-01 a. , OOOD 01 -1. .1500-25 1. .OOOD 00 1. ,552D-26 20 in 97*00, .00 67500. ,00 a .009000 01 1 .6690 01 -3, .103D 01 5, .1080-02 a, , OOOD 01 -1. .0300-23 1, .0000 00 1, ,636D-25 20 IS 97500, .00 12500, ,00 0 ,009520 01 0, ,6280 00 -2.0080 01 - 1 .9270-02 a, , OOOD 01 -9. .0580-28 1. .0000 00 1. ,6000-29 20 16 97500. .00 77500. CO A, .00906D 01 3 .0200 00 -1. .6630 01 1 .08UD-02 8. ,0000 01 -6. .2550-32 1. .OOOD 00 1, . 293D-33 20 17 97500, .00 82500, CO 0 •00905D 01 3 • 271D 00 -1, .3310 01 8, .029D-03 8. ,0000 01 9, ,8100-00 1, .0000 00 3. 111D-39 20 18 97500. ,00 81500. ,00 II. ,009030 01 a, ,1270 00 -1, .0350 01 1 .0850-02 a, ,0000 01 7, .8920-00 1. .OOOD 00 3. .3010-03 20 19 97500, .00 92500. 00 0 .009>2D 01 II, .18(0 00 -7, .5120 00 6, .729D-03 8. OOOD 01 0. .0010-08 1. .OOOD 00 2. , 1B2D-07 2(1 20 97500. ,00 97500. ,00 0. ,009000 01 5, .200 0 00 -0, .60BD 00 6, ,5190-03 8. OOOD 01 1. .5070-52 1. .OOOD 00 9. ,3500-52 20 21 97500, .00 102500. 00 11 .009000 01 5. .3670 00 -1 .OOOD oo 7 ,3320-03 8. 0000 01 1. .8100-57 1. .OOOD 00 1. 570D-*6 21 1 102500, ,00 2500. 00 (1, .009390 01 1 .1820 00 1, .2510 00 6, .630D-03 8. OOOD 01 7. •110D-53 1, .OOOD 00 1. ,3970-51 21 2 102500, ,00 7500. .00 II, ,009000 01 1 .1170 00 3, .9730 00 8, .222D-03 a. . OO0D 01 6, . 112D-0B 1. ,0000 00 6. ,3370-07 21 3 102500, .00 12500. 00 «, .009010 01 1 .3500 00 6 .368D 00 7, ,6600-03 8. ,0000 01 1, .6200-03 1, .OOOD 00 1. , 250D-02 21 0 102500.00 11500. ,00 n ,009420 01 0 .8100-01 8, ,12CD 00 9 .S35D-03 8, ,0000 01 2. .OSDD-39 1. ,0000 00 1. 677D-38 21 5 102500.00 22500. 00 4 .009050 ot -1 .2180 00 9, .7210 00 -2, ,7050-03 8. .0000 01 2. .310D-35 1. .OOOD 00 1. .573D-30 21 6 102500. .00 27500. CO II .009080 01 - • .0370 00 9 •051D 00 3 ,1610-02 a, , OOOD 01 0, .901D-31 1, .OOOD 00 3. ,2'J5D-30 21 7 102500, .00 32500. 00 0, .009550 01 -9 .101D 00 1, ,1060 01 -3, ,3950-02 a, , OOOD 01 2, .762D-27 1. ,OOOD 00 3. 957D-26 21 8 102500, .00 37500. ,00 1 ,00903(r 01 -5 .9000 00 2, .0550 00 2 .8310-01 8. , OOOD 01 -1. •S55D-20 1. .OOOD 00 1. ,5170-22 21 9 102500, .00 42500. .00 •), ,010260 01 2 .3900 01 7. ,8810 01 .3810-01 a. , OOOD 01 -3. ,2350-19 1. >000D 00 3. ,0130-20 21 10 102500, .00 •7500, ,00 0 .0101*0 01 1 • 993D 02 8 .0010 01 2, .7500-01 a. , OOOD 01 -6, ,1620-10 1, ,0000 00 1. ,09*0-15 21 11 102500. .00 52500. 00 II .008980 01 3. ,5150 02 6, .0820-12 -1, .3930 00 8. , OOOD 01 0. •012D-09 1. ,0000 00 8. 029D-11 21 12 102*00. .00 51500. ,00 0, ,010100 01 1 .9930 02 -8, .0010 01 2 .750D-01 a. , OOOD 01 -6, ,1620-10 1. ,0000 00 1. 095D-1S 21 13 102500, ,00 62500. oo n ,010260 01 2, .3900 01 -3, ,8810 C1 ,3810-01 8. OOOD 01 -3. ,2350-19 1, .OOOD 00 3. 013D-20 21 It 102500, .00 61500. ,00 u, ,009030 01 -5 .9000 00 -2. .0550 09 2 •B31D-01 a. .OOOD 01 -1. •555D-20 1, ,0000 00 1. .517D-22 21 15 102500, .00 72500. ,00 0 ,009550 01 -9 • 101D 00 -1, .1060 01 -3, ,3950-02 8, , OOOD 01 2. ,7620-27 1, ,OOOD 00 3. ,9570-26 21 16 102500, .00 77500. .00 .009080 01 -0 .0310 00 -9 .0510 CO 3 >1610-02 a, ,0000 01 II, ,9010-31 1. ,0000 00 3. .2050-30 21 17 102*00, .00 82500. .00 • .009950 01 -1 .2180 00 -9.1210 oo -2, ,7050-03 a. , OOOD 01 2. .3100-35 1. .0000 00 1. .5730-30 21 18 102500.00 87500. ,00 g, .009020 01 0 .8100-01 - 8 .1200 00 9 .6 350-03 8, ,OOOD 01 2. .0800-39 1. .OOOD 00 1. ,677D-38 21 19 102500, .00 92500. .00 • .009010 01 1 .3500 00 -6 .3680 00 7 •660D-03 8. , OOOD 01 1, .620D-03 1. .OOOD 00 1. ,2500-02 21 20 102500,0(1 97500. .00 a, .009000 01 1 .1110 00 - 3 .9730 CO a .2220-03 8, ,0000 01 6, • 112D-08 1. > OOOD 00 6. •337D-U7 21 21 102*00, .00 102500. .00 0 .009390 01 1 .1820 00 -1 .251D 00 6 .6300-03 a. .OOOD 01 7. .770D-53 1. , OOOD 00 1. ,3970-51

IBC002I STOP 0

Table A.3. Output Information for Sample Problem No. 1 at Time = 124.45 hr Using the Reduced Version of the Program

m i . * 9 1 3 T IBI«1.2U500D C2 PEBI00-1.2(45000 02 TIKI I«CIMJMT"5.0000000-02

retocitt iHccitr «»TBB tttr. IBDI- I- 1 - u r n II IB BATE BATE

BOOB CIS locmoB LOCATIOC flTIOB I-DIBECT. T-OIBECT. or CBAIGZ or CBABGB I 1 2500. 00 2500.00 •.006910 01 8.0790 •C1 -7.e68t-01 3 .0(40-05 8.OOOD 01 1.1630-12 1 2 2500. 00 7500.00 •.00891D Ol 8.6520- CI -2.518C 00 7 .1550-05 8 0000 01 2.5300-10 1 3 2500. 00 12500.00 •.00890D 01 9.66W CI -4.404C 00 -3 .1280-05 e OOOD 01 2.33(0-08 1 * 2500. 00 17500.00 •.00890D 01 1.0920 00 -6.606C 00 -1 .7(40-04 8 OOOD 01 1.171D-06 1 5 2500. so 22500.00 (.000890 01 1.1900 CO -9.3610 00 6 .72(0-04 8 OOOD 01 3.(470-05 1 6 2500. oo 27500.00 O.006B8D 01 1*4500 CO -1.304C 01 6 .9120-04 e 0020 01 5.9890-04 1 7 2500. 00 32500.00 • .008850 01 2.2870 cc -1.8580 01 1 .5220-03 8 0230 01 5.7890-03 1 1 2500. oo 37500.00 ••008950 01 7.9410 00 -2.239C 01 -1 .0280-01 8 1730 01 1.7660-02 1 9 2500. 00 •2500. 00 ••00820D 01 2.9060 C1 -S.744D 01 4 .31(0-01 8 7290 01 6.429D-02 1 10 2500. oo 17500.00 ••009010 01 1*2370 02 -0.727C 01 - ( .7530-01 9 1130 01 (.7170-02 1 11 2500. 00 52500.40 (.010690 01 2.1230 02 -6.839C-12 2 .8970-01 9 •73D 01 2.3(80-05 1 12 2500. 00 57500.00 ••00901D 01 1.237D C2 8.727C 01 -4 .7530-01 9 1130 01 (.7170-02 1 13 2500. 00 €2500.00 •-00B20D 01 2.4060 01 5.74(0 01 ( .31(0-01 E 7290 01 6.(290-02 1 1* 2500. 00 67500.00 O.00895D 01 7.9*10 00 2.239C 01 -1 .0280-01 8 1730 01 1.7660-02 1 15 2500. 00 72500.00 •.ooeasD 01 2.2870 CC 1.8580 01 1 .5220-03 8 0230 01 5.7B9D-03 1 16 2500. 00 77500.00 •.00888D 01 1.«50D CO 1.394C 01 6 .912D-0( 8 0020 01 5.989D-09 1 17 2500. 00 02500.00 •.008890 01 1.1900 00 9.3610 00 6 .72(0-04 e OOOD 01 3.(470-05 i ia 2500. 00 07500.00 ••00B90D 01 1.0920 00 6.606C 00 -1 .7490-09 a OOOD 01 1.171D-06 1 19 2509, 00 92500.00 ••000900 01 9.66«0-01 (.40(0 00 -3 .1280-05 8 OOOD 01 2.33(0-08 1 20 2500. 00 97500.00 •.OOB9IO 01 8*6520-01 2.518C 00 7 .1550-05 8 0000 01 2.5309-10 1 21 2500. 00 102500.00 ••000910 01 8.0790-01 7.(680-01 3 .0440-05 8 0000 01 1.163D-12 2 1 7500. 00 2500.00 •.000910 01 2.5070 00 •a.oaat-oi •8 .6210-05 8 0000 01 7.132D-13 2 2 7500. 00 7500.00 •.063910 01 2.69BD CO -2.5890 00 -1 .8050-05 8 OOOD 01 1.6270-10 2 3 7500. 00 12500.00 4.000900 01 3.0970 CO -(.5(3C 00 -1 .9360-04 E OOOD 01 1.5810-00 2 • 7500. 00 17500.00 •.00890D 01 3.7610 00 -6.(650 00 -3 .6580-04 8 OOOD 01 8.(0(0-07 I s 7500. 00 22300.00 •.008900 01 ••836D 00 -9.018C 00 -6 .6680-04 8 OOOD 01 2.603D-05 2 6 7500. 00 27500.00 «.008890 01 6*8010 00 -1.3920 01 2 .3160-03 e 0010 01 4.7770-04 2 7 7500. 00 32500.00 •.008870 01 1*0800 01 -2.008C 01 6 .6040-03 8 0160 01 4.923D-03 2 » 7500. 00 37500.00 •.0089(0 01 2.0160 C1 -2.6520 01 -2.7600-02 8 1180 01 2.4080-02 2 f 7500. 00 <2500.00 ••008720 01 3.7380 01 -•.727C 0 1 9 .9910-02 8 4880 01 5.7070-02 2 10 7500. so •7500.00 •.009010 01 1.0110 02 -5.7770 01 -2 .5430-01 E. 9260 01 4.068D-02 2 It 7500. CO 52500.00 ••00960D 01 1 • 54 30 C2 -5.536C-12 3 .5260-01 9. 414D 01 8.511D-03 2 12 7500. so 57500.00 ••00901D 01 1.0110 02 5.7770 01 -2 .5430-01 8 9260 01 4.0680-02 2 13 7500. 00 62500.00 ••008720 01 3.7380 01 4.727C 01 9 .9910-02 8 4880 01 5.7070-02 2 t« 7500. 00 67500.00 •.0089«D 01 2.0160 C1 2.6520 01 -2 .7600-02 8 1180 01 2.4080-02 2 IS 7500. 00 72500.00 ••008870 01 1.0000 01 2.008C 01 6 .6040-03 8 0160 01 4.9230-03 2 It 7500. 00 77500.00 ••00889D 01 6.8010 00 1.3920 01 2 .3160-03 8 0010 01 4.777D-04 2 17 7500. 00 02500.00 (.000900 01 •.8360 00 9.818C 00 -6 .6680-04 8 0000 01 2.6030-05 2 If 7500. 00 87500.00 •.00090D 0' 3*7010 00 6.(650 00 -3 .6580-04 8 OOOD 01 8.4040-07 2 19 7500. 00 92500.00 •.00090D 01 3.0970 00 4.543C 00 -1 •936D-0( 8 OOOD 01 1.5810-08 2 20 7500. 00 97500.00 •.00891D 01 2.6900 00 2.5B90 00 -1 .8050-05 8 OOOD 01 1.6270-10 2 21 7500. 00 102500.00 ••008910 01 2.507il 00 8.C88C-01 -8 .6210-05 8 OOOD 01 7.1320-13 3 1 12500. 00 2500.00 ••00891D 01 ••2560 CO -B.((3C-01 6 .1250-05 8 OOOD 01 2.5030-13 3 2 12500. 00 7500.00 «.00691!) 01 ».S92B 00 -2.692C 00 9 .2030-05 8 OOOD 01 S.8530-11 J J 12500. 00 12500.00 •.008910 01 5.305D CO -(.73(0 00 1 .2310-04 8 OOOD Ot 5.8820-09 1 » 12500. 00 17500.00 ••008900 01 6.5170 00 -7.179E 00 1 .6130-04 8 0000 01 3.2FT70-07 3 S 12500. 00 22500.00 ••000900 01 8*5000 00 -1.0270 01 1 .7860-04 8 OOOD 01 1.0550-05 3 < 12500. 00 27500.00 ••008900 01 1.1070 CI -1.M0C 01 3 .2990-04 a OOOD 01 2.0320-04 3 7 12500. 00 32500.00 ••00889P 01 1.7960 01 -2.01CD 01 ( .8980-03 a 0060 01 Z. 29 00-03 3 a 12500. 00 37500.00 (.008930 01 2.9170 01 -2.6310 01 -1 .5050-02 a 0510 01 1.3760-02 3 9 12500. 00 •2500.00 •.000900 01 •.6370 01 -3.(910 01 3 .1560-02 8 24 8D 01 4.5120-02 1 10 12500. 00 •7500.00 •.009000 01 8.1990 01 -3.293C 01 - t .(340-01 8.6270 01 5.7080-02 3 11 12509. 00 52500.00 • .009191) 01 1.0770 C2 -5.2750-12 2 .(090-01 9 2700 01 2.0200-02 ] 12 12500. OS 57500.00 •.009000 01 8.1940 01 3.2B3C 0 1 -1 .«3«0-01 a 6270 01 5.7080-02 3 13 12500. 00 62500.00 ••00890D 01 4.6370 CI 3.(910 01 3 .1560-02 B 24 AO 01 4.5120-02 3 IB 12500. 00 67500.00 ••00893D 01 2.9170 01 Z.tllC 01 -1 .5050-02 8 0510 01 1.3760-02

w o


M l . " 9 1 } T I B E M . 5 4 4 5 C 0 D CJ r i l I 0 9 > 1 . 2 * * 5 9 0 9 C2 T l l l l I I C B E 8 E I T - S . 0 0 0 0 0 0 9 - 0 2

XI9I* I -«OOt CIS LOCATION 1 2 9 0 0 . 0 0 1 2 5 0 0 . 0 0 1 2 5 0 0 . 0 0 1 2 5 0 0 . 0 0 1 2 5 0 0 . 0 0 1 2 S 0 0 . 0 0 12500.09 I 7 5 P 0 . 0 0 1 7 5 0 0 . C O 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 1 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 9 . 0 9 1 7 5 0 0 . 0 0 1 7 5 0 0 . 9 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 1 5 9 9 . 0 0 1 7 5 0 0 . 0 9 1 1 5 9 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 0 . 0 0 1 7 5 0 9 . 0 9 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 9 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 9 0 . 0 9 2 2 5 9 9 . 9 9 2 2 5 9 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 9 9 . 9 0 2 2 5 0 9 . 9 0 2 2 5 9 0 . 9 0 2 2 5 9 0 . 0 0 2 2 5 9 0 . 0 0 2 2 5 0 0 . 0 0 2 2 5 0 9 . 0 0 2 2 5 0 0 . 0 0 2 1 5 9 0 . 9 0 2 1 5 9 9 . 9 9 2 7 5 0 0 . 0 0 2 1 5 0 9 . 0 9 2 7 5 9 9 . 0 0 2 1 S 0 0 . 0 0 2 7 5 0 0 . 0 9 2 1 5 0 9 . 0 0

3 I S 3 I t 3 1 7 3 1 1 3 1 9 3 2 9 3 2 1 * 1 4 2 4 1 4 4 4 s 4 ( 4 7 4 • 4 9 4 1 0 • 1 1 4 1 2 4 1 1 4 1 4 4 I S 4 I t 4 1 7 4 1 9 1 1 9 4 2 9 • 2 1 5 1 S 2 S 3 s 4 s S 5 f 5 7 5 • 5 9 S 1 9 S 1 1 5 1 2 5 1 3 5 1 4 S I S S I t s 1 7 s 1 « s 1 9 5 2 9 s 2 1 6 1 6 2 6 3 6 4 6 S 6 t 6 7

I-tOClTIOB 7 2 5 0 0 . 0 0 7 1 5 0 9 . 9 0 6 2 * 1 0 . 0 9 8 1 5 0 0 . 0 0 9 2 5 0 0 . 9 9 9 7 5 0 ; . 0 0

1 0 2 5 0 9 . 9 0 2 5 0 0 . 9 0 7 5 0 0 . 0 0

1 2 5 9 0 . 0 9 1 1 5 0 0 . 0 0 3 2 5 0 9 . 9 9 3 7 5 9 9 . 9 0 3 2 5 0 0 . 0 0 3 1 5 9 9 . 0 9 < 2 5 0 0 . 0 0 < 1 5 0 0 . 0 0 5 2 5 0 9 . 9 0 S 7 S 0 9 . 9 0 8 2 5 0 9 . 0 0 6 7 5 0 0 . 0 0 7 2 5 0 0 . 0 0 7 1 5 0 9 . 9 9 8 2 5 9 9 . 0 0 9 7 5 9 0 . 0 0 9 2 5 0 0 . 9 0 9 1 5 0 0 . 0 0

1 9 2 5 9 9 . 9 0 2 5 0 0 . 9 0 1 5 9 9 . 0 0

1 2 5 0 0 . 0 9 1 7 S 0 0 . 0 0 2 2 5 9 9 . 9 0 2 1 5 0 0 . 9 9 3 2 5 0 0 . 0 0 3 1 5 0 0 . 0 0 < 2 5 9 9 . 9 9 • 7 5 9 9 . 9 0 5 2 5 9 0 . 9 9 5 7 5 0 C . 0 0 6 2 5 0 0 . 9 0 6 7 5 9 9 . 9 9 7 2 5 9 9 . 9 0 7 7 5 9 0 . 0 0 6 2 5 0 0 . 0 0 6 7 5 0 0 . 0 0 9 2 5 9 9 . 0 9 9 1 5 0 0 . 0 0

1 9 2 5 9 0 . 0 0 2 5 0 9 . 9 9 7 5 9 9 . 9 9

1 2 5 9 9 . 9 9 1 7 5 0 0 . 0 V 2 2 5 9 0 . 0 0 2 7 5 0 9 . 9 9 3 2 5 9 9 . 9 0

•ini E L E T I T I 0 1

• . 9 0 6 6 9 0 0 1 • • 0 9 6 9 0 D 9 1 • . 0 9 6 9 0 0 9 1 • • 0 0 8 9 0 D 0 1 • . 9 9 6 9 1 0 0 1 • . 0 9 6 9 1 0 0 1 • • 9 0 6 9 1 D 9 1 • . 9 9 6 9 1 0 0 1 • • 0 0 8 9 1 D 9 1 • • 9 0 3 9 1 9 0 1 • . 0 0 6 9 1 0 0 1 • • 0 0 6 9 1 0 9 1 • . 9 0 6 9 1 0 0 1 • . C 9 8 9 1 0 0 1 • • 9 9 6 9 3 D 0 1 • • 0 9 8 9 1 0 0 1 • . 0 0 8 9 9 9 0 1 • . 9 9 9 9 9 9 9 1 • . 9 9 6 9 9 0 9 1 • . 9 0 6 9 1 0 0 1 • . 9 9 6 9 3 0 0 1 a . 0 0 6 9 1 9 91 • . 0 9 6 9 1 9 0 1 • • 0 0 8 9 1 D 0 1 • • 9 0 6 9 I B 9 1 « . 0 9 6 9 1 9 0 1 • . 0 0 8 9 1 0 0 1 • . 9 0 6 9 1 9 0 1 • . 9 9 B 9 1 9 0 1 •.008110 01 • . 9 0 B 9 1 0 0 1 • . 9 0 6 9 1 9 0 1 • . 0 0 8 9 2 0 0 1 4 . 9 9 6 9 2 9 9 1 • . 0 0 6 9 2 0 0 1 • - 0 0 8 9 1 0 9 1 • . 0 0 6 9 3 9 9 1 • • 9 9 6 9 7 b 0 1 • • 0 9 9 0 1 D 0 1 • . 9 0 6 9 7 9 0 1 • • 0 0 6 9 3 D 9 1 4 . 9 9 6 9 3 9 9 1 4 . 0 9 8 9 2 D 9 1 • . 9 9 6 9 2 9 0 1 • . 0 0 6 9 2 9 9 1 • . 9 9 6 9 1 9 0 1 • . 9 9 6 9 1 9 0 1 4 . 0 0 9 9 1 B 9 1 • • 0 0 6 9 1 9 0 1 • • 9 9 6 9 2 9 9 1 • . 9 0 6 9 2 9 0 1 4 . 0 0 6 9 2 9 0 1 • . 0 9 6 9 2 9 0 1 • • 9 0 S 9 2 D 0 1 • • 9 9 6 9 2 D 9 1 • • 9 0 6 9 2 9 0 1

9EL0CXT1 I B i-rtiicT.

1 . 7 9 ( 9 CI 1 . 1 6 1 0 CI 8 . 5 9 0 0 CO 6 . 5 1 1 0 CO 5 . 3 9 5 9 CO • . 5 9 2 0 CO • . 2 5 6 9 C9 6 . 0 6 7 D CO 6 . 5 5 ) 9 0 9 1 . 5 6 3 0 CO 9 . 3 9 5 C CC 1 . 2 9 3 9 9 1 1 . 6 3 0 9 CI 2 . 3 9 8 9 0 1 1 . 3 7 3 9 CI

• . B U D 0 1 6 . 7 1 3 9 0 1 7 , 9 5 6 9 9 1 6 . 7 ( 3 9 C t •.61)0 01 1 . 3 7 ) 9 CI 2 . 3 9 6 9 0 1 1 . 6 3 0 0 CI 1 . 2 0 1 9 0 1 9 . 3 0 5 9 CC 7 . 5 6 3 9 CO C . S S 3 B CO 6 . 0 6 7 9 C9 7 . 6 6 1 9 9 9 • . 4 9 0 0 CO 9 . 7 6 8 9 0 9 1 . 1 9 1 9 0 1 t.SIOD 01 1 . 9 7 3 9 9 1 2 . 6 3 1 9 0 1 3 . S 2 8 D 9 1 4 . S 9 6 9 9 1 5 . 7 6 5 9 0 1 6 . 4 1 5 9 9 1 S . 7 6 S D 9 1 • • 5 9 9 9 9 1 3 . 5 2 6 9 0 1 2 . 6 3 1 9 0 1 1 . 9 7 ) 9 9 1 1 . 5 1 0 9 9 1 1 . 1 9 1 9 0 1 9 . 7 6 6 9 CO

• . 4 9 0 9 CO 7 . 8 6 6 9 9 9 9 . 5 4 6 9 9 9 1 . 9 2 1 C 0 1 1 . 1 7 6 9 9 1 1 . 4 1 ) 9 0 1 1 . 7 5 2 9 CI 2 . 2 1 * 9 9 1 2 . 9 1 4 9 0 1

PELCCI1T II T - 9 X I I C T .

2 . 0 1 0 C 0 1 1 . M C D 9 1 1 . 0 2 7 C 9 1 7 . 1 7 9 0 9 9 4 . 7 3 * C 9 0 2 . 6 9 2 C 0 9 6 . M 3 C - 9 1

' 9 . 6 3 6 9 * 0 1 2 . 7 3 2 C 9 9 • . 7 9 0 9 Ou

• 7 . 3 2 1 9 0 0 > 1 . 0 1 B C 9 1 - 1 . 3 6 1 9 0 1 • 1 . 6 1 2 9 0 1 • 2 . 2 9 1 9 9 1 • 2 . 4 9 1 C 9 1 ' 2 . 0 1 C 9 9 1 • . 1 2 3 1 - - 1 2 2 . 9 1 0 9 0 1 2 . 4 6 1 C 0 1 2 . 3 9 1 9 9 1 1 . 6 1 2 C 0 1 1 . 3 6 1 0 9 1 1 . 9 1 6 C 9 1 7 . 2 2 1 9 9 9 4 . 7 9 C 9 9 9 2 . 7 3 3 C 0 0 S . 6 3 6 C - 0 1

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11 is S2500. 00 72500.00 ft 008930 01 2.9870 CI -1.15(0 00 3.4*80 06 8 0000 01 1.1780-10 11 16 52500 00 77500.00 ft 008930 01 2.5580 CI -1.7391 00 1.0680 06 B 0000 01 2.*76D-12 11 17 52500. 00 02500.00 ft 008910 01 2.1620 01 .«7*c 00 1.2370 06 8 0090 01 3.3030-lft 11 18 52500. 00 87500.00 ft 008910 01 1.8250 01 -1.306C 00 2.1960 06 6.0900 01 2.8(70-16 11 19 52500, 00 92500.00 ft 008930 01 1.5610 CI -9.700C-01 -5.9290 06 8 0090 01 0.0 20 52500. 00 97500.00 ft 008930 01 1.1660 CI -5.953C-0I 6.657D 06 8 0000 01 0.0 II 21 52500. 00 102500.00 ft 008930 01 1.2960 01 -2.0*60-01 -2.9250 06 8 0000 01 0.0 12 1 57500. 00 2500.00 ft .000930 01 1.21 so TL «.2ftSt-D1 -9.431B 06 8 OOOD 01 0.0 12 2 57500 00 7500.00 ft 008930 01 i.«*o CI 1.259C 00 8.8150 06 8 0000 01 0.0 12 1 57500 00 12500.00 ft .008930 01 1.5050 01 2.CB7C 00 -6.8890 06 8 0000 01 0.0 12 ft 57500. 00 17500.00 ft .008930 01 1.7710 (1 2.(6 CO 00 2.8000 06 8 OOOP 01 9.9(20-22 12 S 57500 00 22500.00 ft .008910 01 2.1210 NI 3. 58 IE 00 2.2920 06 B 0000 01 1.10(0-15 12 6 57500. 00 27500.00 ft .008930 01 2.5170 01 ft.09(0 00 1.8860 06 B 0000 01 1.0550-11 12 7 57500. 00 32500.00 ft 008910 01 2.9910 ot 4.295C 00 1.9(00 06 8 0000 01 6.3220-12 12 8 57500. 00 37500.00 ft 008920 01 3.4500 ti ft.0320 00 2.2960 OS B 0000 01 2.1310-10 12 9 57500. 00 92500.00 ft 008920 01 3.B500 CI 3.203C 00 -4.8(10 05 8 OOOD 01 5.1930-09 12 10 57500. 00 07500.00 ft 008920 01 (.1320 CI 1.601D 00 1.2760 04 8 OOOD 01 6.86(0-08 12 11 57500. 00 52500.00 ft 008920 01 (.2360 01 1.C63C-I2 -2.0600 Oft 8 0000 01 7.75 90- 07 12 12 57500. 00 57500.00 ft 008920 01 4.1320 01 -1.C0ID 00 1.2760 04 8 OOOD 01 6.86(0-08 12 13 57500. 00 62500.00 ft 008920 01 3.8500 01 -3.203C 00 -4.8470 05 8 OOOD 01 5.1930-09 12 11 57500. 00 67500.00 ft 008920 01 3.4500 CI -*.032C 00 2.2960 OS 8 OOOD 01 2.3310-10 12 IS 57500. 00 77500.00 008910 01 2.9930 01 -ft.295C 00 1.9400 06 6 OOOD 01 6.122D-12 12 16 57500. 00 77500.00 ft 008910 01 2.5370 01 -ft.C9C0 00 1.8B6D 06 8 0000 01 1.0550-13 12 17 57500. 00 82500.00 ft 008910 01 2.1210 01 -3.581C 00 2.2920 06 8 OOOD 01 1.10(0-15 12 IB 57500. 00 87500.00 ft 00891D 01 1.7730 CI -2.BB0C 00 2.8000 06 8 0090 01 9.9«2D-22 12 19 57500 00 92500.00 ft 008910 01 1.5050 01 -2.0B7C 00 -6.6890 06 B OOOD 01 0.0 12 20 S7500. 00 97500.00 ft 008910 01 1.32(0 CI -1.2550 00 8.8 ISO 06 8 OOOD 01 0.0 12 21 57500. 00 102500.00 ft 006910 01 1.2330 01 -FT.2*SC-01 -9.4310 06 8 0000 01 0.0 1) 1 62500. 00 2500.00 ft 008910 ot 1.1280 01 6.21(0-01 -1.8010 OS 6 0000 01 0.0 11 2 62500. 00 7500.00 ft 0089(0 01 1.2190 01 1.I62C 00 1.0190 05 8 oooo 01 0.0 11 3 62500. 00 12500.00 ft 008930 01 1.(010 CI 3.1170 00 -5.9790 06 e 0001 01 0.0 11 • 62500. 00 17500.00 ft 008910 01 1.6750 01 4.365E 00 1.9630 06 B 0000 01 0.0 11 S 62500. 00 22500.00 a 008910 01 2.0(00 CI 5.5290 00 1.0*00 06 8 0000 01 2.9«6D-17 11 6 62500. 00 27500.00 « 008910 01 2.4870 C1 6.462C 00 3.9020 06 6 OOOD 01 ft.1190-15 11 7 6T500. 00 32500.00 * .008910 01 2.9930 CI 6.9350 00 2.7110 06 e 0000 01 3.1420-13 11 8 6.1500. 00 37500.00 « .0GS92D 01 j.5170 01 6.673C 00 6.6990 05 8 OOOD 01 1.4(60-11 11 9 62500. 00 42500.00 « 008920 01 3.9950 CI 5.4280 00 -1.9060 04 B OOOD 01 3.9190-10 11 10 62S00. 00 >7500.00 « 008910 01 (.3440 01 3.1161 00 3.8660 04 8 0000 01 6.0950-09 11 11 62500. 00 52500.00 • 008910 01 4.(760 CI 2.3520-12 -6.0610 Oft 8 OOOD 01 7.82*0-08 11 12 62500. 00 57500.00 • 006910 01 n.3((0 01 -3.116C 00 3.8660 04 8 0000 01 6.09SD-09 11 13 62500. 00 62500.00 ft 008920 01 3.99S0 01 -5.4260 00 -1.(060 04 8 OOOD 01 3.9190-10 11 1ft 62500. 00 67500.00 • C06920 01 3.5170 01 -6.671C 00 6.6990 05 6 OOOD 01 1.4460-11 11 IS 62500. 00 72500.00 • .008930 01 2.9930 CI -6.9350 00 2.7110 06 8 OOOD 01 1.142D-13 11 16 62500. 00 77500.00 • 006910 01 2.(070 01 -6.4620 00 3.9020 06 8 OOOD 01 4.1190-15 11 17 62500. 00 112500.00 • 008930 01 2.0(00 CI -5.S29C 00 1.0(00 OS 8 OOOD 01 2.9460-17 11 18 62500. 00 87500.00 • 006910 01 1.6750 CI -4.365C 00 1.9630 06 8 OOOD 01 0.0 13 19 62500. 00 92500.00 • 00693D 01 1.4010 01 -3.1170 00 -5.9790 06 8 OOOD 01 0.0 11 20 62500. 00 97S00.00 « 0089(0 01 1.2190 01 -1.862C 00 1.0T90 OS 8 0000 01 0.0 11 21 62500. 00 102500.00 « 0069110 01 1.1280 01 -6.21(0-01 -1.8010 05 8 OOOD 01 0.0 1( 1 67500. 00 2500.00 « 008990 01 9.8S70 CC 7.766[-01 -2.6650 05 8 OOOD 01 0.0 1* 2 67500. 00 7500.00 • 006940 01 1.07»0 CI 2.15(0 00 1.0000 OS 8 OOOD 01 0.0 It 3 67500. 00 12500.00 « .0089*0 01 1.25*0 01 3.9B(C 00 -2.1310 06 8 OOOD 01 0.0 It ft 67500. 00 17500.00 « 0089(0 01 1.5310 CI 5.67IC 00 -*.533D 06 6 0000 01 0.0 in 5 67500. 00 22500.00 n 008910 01 1.9120 01 7.339C 00 t.sito 06 B OOOD 01 0.0 1* 6 67500. 00 27500.00 « 008930 01 2.3960 C1 8.(020 00 1.1*20 05 8 OOOD 01 1.5570-16 1* 7 67500. 00 32500.00 • 008930 01 2.9720 01 9.7330 00 2.157D 05 e.ooon oi 1.(50D-1«


ITER.- M TRAE* i . 2 4 4 5 o o o C2 PFRTOD*I .244500D C2 T i n t IRCBEBERT«S.OOOOOOD-O2

VEIOCITT VELCCITT HATER ELIV. TERR MRP. IRDI- «- 1- HATIR IB IR BATE RATE •ODE CES LOCATION LOCATIOR ELEVATION I-OIBECT. 1-DIRICT. OF CHARGE or CHARGE 14 8 67500. 00 37500.00 4.0C892D 01 3.6010 01 9. >656C 00 1 .3370-04 8 .OOOD 01 8.4730-13 14 9 67S00. .00 42500.00 4.00691D 01 4.2050 CI e, .113C 00 -4 .152D-C4 8 .0000 01 2.8370-11 It 10 67500. 00 47500.00 4.008910 01 4.6750 01 4. , 795C 00 9 .3330-04 8 .OOOD 01 5.2420-10 14 11 67500. 00 52500.00 4.008900 01 4.8620 «1 1, .9019-11 -1 .5490-03 B .OOOD 01 7.6440-09 14 12 67500. 00 57500.00 4.008910 01 4.675C CI -4. 795C 00 9 •3330-04 a .0000 01 5.242D-10 14 13 67500. 00 62500.00 4.008910 01 4.2050 CI -8. >113C 00 -4 .1520-04 8 .0000 01 2.8370-11 It 14 67500. 00 67500.00 4.00892D 01 3.6010 01 -9. >656t 00 1 •337D-04 8 .OOOD 01 8.473D-13 11 15 67500. 00 72500.00 4.00693D 01 2.9720 CI -9. ,733C 00 2 .1570-05 8, ,0000 01 1.4500-14 la 16 61500. 00 17S00.00 4.00893D 01 2.3960 01 -8. E02C 00 1 .1420-05 8, ,0000 01 1.5570-16 14 11 67500. 00 82500.00 4.008930 01 1.9120 Ct -7. 339E OU 4 .5140-06 8, .0000 01 0.0 16 14 18 67500. 00 81500.00 4.00B94D 01 1.5310 01 -5. ,6711 00 -4 .5330-06 8, .OOOD 01 0.0 14 19 67500. 00 92500.00 4.00 894 0 01 1.2540 CI -3. ,S84C 00 -2 ,1310-06 8. .OOOD 01 0.0 14 20 67500. 00 97500.00 4.008940 01 1.014D 01 -2. 354C 00 1 ,0000-05 8 .OOOD 01 0.0 14 21 67500. 00 1025CO.OO 4.0D894D 01 9.8570 to -7. 766C-0I -2 .8650-05 8. .0000 01 0.0 IS 1 72500. 00 2500.00 4.00894D 01 8.1540 00 a. ,7111-01 -3 .9960-05 8, .OOOD 01 0.0 IS 2 72500. 00 7500.00 4.00894D 01 3.9640 CO 2. ,6770 00 7 .2220-06 8, .OOOD 01 0.0 15 3 72500. 00 12500.00 4.008940 01 1.0690 01 4. , 592C 00 2 ,1410-07 8 .0000 01 0.0 IS 4 72500. 00 17500.00 4.008940 01 1.340D (1 6, .668C 00 -6 .8380-06 8 .OOOD 01 0.0 15 5 72500. 00 22500.00 4.00894D 01 1.7270 CI 8. ,8651 00 B •40BD-06 8, .0000 01 0.0 15 6 72500. 00 27500.00 4.00893D 01 2.2470 CI 1. >10CD 01 1 .7850-05 a, .0000 01 7.1580-22 15 7 72500. 00 32500.00 4.008930 01 2.906D CI 1, ,265G 01 •6 .0300-05 8 • OOOD 01 6.D93D-16 IS 8 72SOO. 00 37S0S.00 4.00892D 01 3.681D CI 1. • 310C 01 3 .07*0-04 a .OOOD 01 4.721D-14 15 9 72500. 00 42500.00 4.008910 01 4.478D 01 1. 1S4C Ot -1 .1920-03 8.0000 01 2.0080-12 15 10 72500. 00 47500.00 4.908909 01 S.154D CI 7. ,1310 00 2 .7870-03 8, .OOOD 01 4.4950-11 15 11 72500. ,00 52500.00 4.008890 01 5.4420 01 1. 303C-12 -3 .4010-03 8, .OOOO 01 7.521D-10 IS 12 72500. 00 57500.00 4.00890D 01 5.1540 CI -7. •131C 00 2 .7870-03 8, ,0000 01 4.49SD-11 15 13 72500. ,00 62500.00 4.00891D 01 4.4780 CI -1. 154C 01 -1 .1920-03 8, .OOOD 01 2.008D-12 IS 14 72500. 00 67500.00 4.008920 01 3,6810 01 -1. 31CC 01 3 .0750-04 8, .OOOD 01 4.71D-14 IS IS 72500. 00 72500.00 4.008930 01 2.906D 01 -1, ,26511 01 -6 .0300-05 0, .OOOD 01 6.093D-16 IS 16 72500. 00 77500.00 4.00893D 01 2.2470 CI -1. ,109C 01 1 .7850-05 8, .0000 01 7.15BD-22 1S 11 72S00. ,00 82500.00 4.008990 01 1,7270 01 -8, ,S65C 00 8 .4080-06 8 .OOOD 01 0.0 15 18 72500. 00 87500.00 4.008940 01 1.3400 CI -6. ,6680 00 -6 .8380-06 8, .OOOD 01 0.0 15 19 72500. ,00 92500.00 4.00694 0 01 1.0690 ot -4. ,592C 00 2 .1410-07 8 .OOOD 01 0.0 15 20 72500. 00 97500.00 4.00894D 01 8.9840 CO -2. ,677C 00 7 .2220-06 8, .OOOD 01 0.0 15 21 72500. 00 102500.00 4.008940 01 B.1540 cc -B. ,7111-01 -3 .9960-05 8, .0000 91 0.9 16 1 77500. 00 2500.00 4.008950 01 6.3010 cc 8. 8750-01 -4 .787D-0S 8, .0000 01 0.9 16 2 77500. 00 7500.00 4.008950 01 7.0320 00 2. 174C 00 -2 .5400-06 8, .OOOD 01 9.9 16 3 77500. 00 12500.00 4.008950 01 8.5520 CO 4. 8320 00 1, .1270-05 8, iOOOD 01 0.0 16 4 77500. 00 17500.00 4.008940 01 1.1040 ct 7. 188C 00 -7, .4480-06 8, .OOOD 01 0.0 16 5 77500. 00 22500.00 4.00894D 01 1.4790 CI 9. 68C9 00 3 •075D-0S 8. .OOOD 01 0.0 16 6 77500. 00 27500.00 4.008940 01 2.0180 G1 1. 280C 01 -7 .0870-05 8. .0000 01 0.0 16 1 77S00. CD 32S00.00 4.008910 01 2.7600 CI 1. 5530 01 -1 .7280-04 a. .0000 01 2.0020-17 16 8 77500. 00 37500.00 4.008920 01 3.71S0 01 1. 704C 01 8 .2080-04 8, ,0000 01 2.4760-15 16 9 77500. 00 4250C.00 4.008910 01 4.7940 01 1. ,6060 01 -2 .2300-03 8. .OOOD 01 1.409D-13 16 10 77500. 00 47500.00 4.008B8D 01 S.823D CI 1. 059C 01 7 .4610-0] S. .OOOD 01 3.9410-12 16 11 77500. 00 52SOO.OO 4.008860 01 6.3040 01 1. .6191-12 -1 .0470-02 8. .OOOD 01 7.7620-11 16 12 77500. 00 57500.00 4.008880 01 5.8230 CI -1. 059: 01 7 .4670-03 8, .GOOD 01 3.9410-12 16 13 77500. 00 62500.00 4.00891D 01 4.7940 01 -1. ,6060 01 -2 .2300-03 8.OOOD 01 1.409D-13 16 14 77500. 00 67500.00 4.008920 01 3.715C 01 -1. 704E 01 8 .2080-04 a, .0000 01 2.4760-IS 16 IS 77500. 00 72300.00 4.00893D 01 2.7600 CI -1. 552C 01 -1 •728D-04 8.0000 01 2.002D-17 16 16 77500. .00 77500.00 4.0Q894D 01 2.0180 ot -1. ,3B0t 01 -7 .8870-05 8, .OOOD 01 9.9 16 17 77500. 00 82500.00 4.00894D 01 1.4790 Ct -9. E8CC 00 3, .0750-05 8. ,0000 01 0.0 16 18 77500. 00 87500.00 4. 00 894 0 01 1.1040 01 -7. 18BC 00 -7 .4480-06 8. .OOOD 01 0.0 16 19 77500.00 92S00.00 4.00895D 01 8.552D CO -4. ,G32C 00 1, >1270-05 e. ,0000 01 0.0 16 20 77500. 00 97500.30 4.00B9SD 01 7.032D CO -2. 174C 00 -2 .5400-06 9, ,OOOD 01 C.O 16 21 77500. 00 102500.00 4.008950 01 6.3070 CO -8. 8750-01 -4, .7870-05 0, 01 0.i>


ITM.« <>13 TIRE-1.2495000 C2 PERIOO-1.2445009 02 TXHf I«Cflet!E*T-5. 0000000-02 91L0CIT1 4ILCCI1X «AtER ELM. TEBP t cap. IIDI- I- T- IU1I in II BITE RATE HOPE CIS tOCATJOI L0CAT10R umixoi »-CTD1C1. 1-DIBICT. or CHARGE OF CHARGE

17 1 62500.00 2500.00 «.008950 01 9 9860 CO 8.1799 •01 -5 .5060-05 8 OOOD 01 0 .0 17 2 82500.00 7500.00 9.006959 01 S .0560 00 2.605C 00 -1 .7420-05 8 0009 01 0 .0 17 3 82500.00 12500.00 9.008959 01 6 .2790 CO 4.617C 00 1 .0020-05 8 0009 01 0 .0 17 a 82500.00 17500.00 9.008959 01 8 3539 CO 7.0S6C 00 •9 ,250?-05 8 0009 01 0 .0 17 5 82500.00 22500.00 9.00895D 01 1 1679 01 1.C05D 01 •1 :SJ9-04 8 0009 01 0 .0 17 6 82500.00 27500.00 9.006950 01 1 6350 CI 1.377C 01 -1 393&-C4 8 OOOO 01 0 .0 17 7 82500.00 32500.00 9.008999 01 2 .9770 CI 1.789C 01 -3 .42B9-04 8 CdOD 01 0 .0 16 17 8 82500.00 37500.00 9.008929 01 3 6319 01 2.122C 01 : .8690-9? P OOOD 01 1 .2970-16 17 9 82500.00 92500.00 9.008910 01 5 0969 01 2.2129 01 •6 .1050-di 8 OOOD 01 9 .7930-15 t7 10 »2i00.00 97500.00 4.O08R6D 01 6 7969 01 1.607C 01 1 .8639-02 8 0009 01 3 •607D-13 17 11 82500.00 52500.00 9.008819 01 7 .6079 CI 1.7191 •13 -2 .7105-02 9 .0009 01 a .8369-12 17 12 82500.00 575OC.00 «. 008869 01 6 7060 CI -1.607C 01 1 .8 630-02 b 0009 01 3 .6070-13 17 13 82500.00 62500.00 9.00891b 01 5 0969 CI •2.2129 01 •6 .1050-03 a 0009 01 9 .79JD-15 17 1» 82500.00 67500.00 9.008929 01 3 6319 21 -2.122t 01 2 .8690-03 B 0009 01 1 .2970-16 17 IS 82500.00 72500.00 9.006999 01 2 .9779 CI •1.789D 01 -3 .9280-09 8 0009 01 0 .0 17 16 82500.00 77500.00 9.008950 01 1 6850 CI -1.377C ot • 1 .3930-09 8 OOOD 01 0 .0 17 17 82500.00 82500.00 9.008959 01 1 1679 CI -1.C09C 01 -1 140D-09 8 OOOD 01 0 .0 fT If 02500. 00 <7500.00 <•008950 or a 3530 CO -7.05 « 00 •9 .2500-05 S OOOO 01 0 .0 17 19 82500.00 92500.00 9.008959 01 6 2799 CO -9.61711 00 1 002D-05 8 oooo 01 0 0 17 20 62500.00 97500.00 9.008959 01 5 0589 CC •2.605C 00 -1 .7429-05 8 0009 01 0 .0 17 21 62500.00 102500.00 9.008950 01 « .9669 CO -a.nnc •01 -5 .5069-05 a OOOD 01 0 .0 IB 1 87500.00 2500.00 9.00896 0 01 2 8689 00 6.700C •01 -3 1480-06 8 0009 01 0 .0 1S 2 87500.00 7500.00 9.00896D 01 3 2580 CO 2.1B9C 00 2 1829-05 a 0009 01 0 0 18 3 87500.00 12*00.00 9.008969 01 9 0939 00 3.939C 00 1 .1079-09 8 OOOD 01 0 .0 IS « 87500.00 17500.00 9.008969 01 S .5700 CO 6.176C OS 1 .8530-05 8 OOOD 01 0 .0 18 S 87500.00 22500.00 «.008960 01 8 0669 00 9.197C 00 2 .2179-04 8 0009 01 0 .0 1* 6 87500.00 275CO.O0 9.008969 01 1 .2379 01 1.1330 01 6 •274D-09 8 0009 01 0 .0 IS 7 87500.00 32500.00 9.008959 01 1 9969 01 1.88CC 01 9 .8560-09 a 0009 01 0 .0 21 18 8 B7«00.00 37500.00 9.008939 01 3 .3229 01 2.5780 01 9 ,7050-03 8 0009 01 1 2B5D-21 IS 9 87500.00 92500.00 9.0O899D 01 5 3169 01 7.9991 01 -2 .7320-02 a 0009 01 6 .7600-16 IS 10 87500.00 97500.00 1.008369 01 8 .1209 CI 2.500D 01 2 3280-02 8 OOOD 01 3 .4900-14 18 11 87500.00 52500.00 9.008759 01 9 7700 01 -9.605C-11 -8 9149-02 a OOOO Of 1 1690-12 18 12 87500.00 57500.00 • .008861) 01 8 1209 01 •2.50CD 01 2 3269-02 a 0009 01 3 .4900-14 IB 13 67500.00 62500.00 9.00899D 01 5 3169 01 •2.999C 01 -2 .7320-02 8 OOOD 01 6 .760D-16 IB 19 87500.00 67500.00 9.008930 01 3 3229 01 -2.9789 01 9 7059-03 8.0009 01 1 2850-21 IB 15 87500.00 72500.00 *.008950 01 1 9969 01 -1.B86I 01 9 .8569-09 a. OOQD 01 0 .0 18 16 87500.00 77500.CO 9.008960 01 1 2379 01 -1.113D 01 6 2749-04 a. OOOO 01 0 0 18 17 87500.00 82500.es 9.008969 01 8.0669 00 -9.197C 00 2 2179-04 a 0009 01 0 0 It IS 87500.00 67SOO.OO 9.006960 01 5 5709 00 •6.1769 00 1 B53D-&5 a OOOD 01 0 0 IS 19 87500.00 92500.00 9.006960 01 9 .0989 00 -3.934C 00 1 .1070-04 8 OOOD 01 0 .0 18 20 87500.00 97500.00 9.038969 01 3 2569 CO -2.1849 00 2 .1820-05 8. ooort ot 0 .0 18 21 87500.00 102500.00 9.008960 01 2 8689 00 -6.7001 •01 -3 1480-06 8 0001' 01 0 .0 19 1 92509.00 2500.00 9.008969 01 1 6129 CO 9.7769 01 -1 0189-04 8 0009 01 0 0 19 J! 92500.00 7500.00 9.068969 01 1 .8319 OC 1.60 It 00 -1 .6779-04 a 00 09 01 0 .0 19 3 42560.00 12500.00 9 0Q696D 01 2 .2969 CO 2.9139 00 _2 .1580-04 a OOOO 01 0 .0 19 a 92SCO.00 17500.UO 9.008979 01 3 1109 CO 9.65CC 00 •ii .6849-04 8 0009 01 0 .0 19 5 92500.00 22500.00 9.006979 01 « 5329 CO 7.1379 00 -7 2729-04 a 0009 01 0 b 19 6 9250.1. 00 27500.00 9.008979 01 7 .2589 CC 1.09SI 01 -1 1900*03 a OOOO 01 0 .0 19 7 92500.00 32500.00 9.006989 01 1 .3069 01 1.7329 01 -5 .2970-03 a OOOD 01 0 .0 19 » 92S00. 00 37500.00 4.OO095S 01 2 609 C 01 2. 6091 01 1 0590-02 8 OOOD 01 0 0 19 9 92500.00 92500.00 «.008970 01 9 9139 01 3.9990 01 -3 6840-02 a OOOD 01 3 7130-17 19 10 92500.00 97500.00 9.008709 01 9.9309 01 ». out 01 2 ,1019-01 8 0009 01 3.6269-IS 19 11 92509.00 52500.00 9.0081X9 01 1 .2539 C2 -9.357D-13 -5 5610-02 a 0009 01 1 •94BD-13 19 12 92 SCO. 00 57500.00 9.008700 01 9.9309 01 -9.0111 01 2 .1019-01 a OOOD 01 3 .6260-15 19 13 92500.00 62500.00 9.008979 01 9 9139 01 -3.999C 01 -3 6899*02 8 OOOD 01 3 713D-17 19 1* 92500.00 67500.00 4.0089SD 01 2 6099 01 -2.6091 01 1 0549*02 a 0009 01 0 .0


IT EN." 013 TItlt» 1 •2445C0D l C2 9EBIOD.1i .244500D C2 7381 INC»IJI«»I»5.000000D-02

VILOC.IT r n o c m IITEB ELEV. TEHP. TEnp. m i I- T- •ATEN IN IN BATE BATE

•ODE crs LOCUTION LOCATION ELEVATION i-tiatci 1-0IFICT. OP CHANCE OF CHAISE 19 15 92500.00 72500.00 0089BD 01 1.308D 01 -1. 732C 01 -5.2970-03 8.OOOD 01 0 .0 14 It 92500.00 77500.00 00B97D 01 7.2560 CC -1. 09(0 01 -1.1900-03 S.OOOS 01 0 .0 1« 11 92500.00 82500.00 9. ,008970 01 4.532C 00 -1. 137c 00 -7.2720-04 8.OOOD 01 0 .0 19 18 92500.00 87500.00 >006970 01 3.1100 CO -a. 65CC 00 -4.684D-09 a.OOOD 01 0 .0 19 19 92S0C.00 92500.00 a. 008960 01 2.2960 CO -2. 913c 00 -2.1580-04 8.OOOD 01 0 .0 19 20 92500.00 97500.00 ,008960 01 1.8310 CO -1. 6010 00 -1.6770-09 B.OOOD 01 0 .0 19 21 92500.00 102500.00 .00896 0 01 1.612D 00 776C-01 -1.0180-09 B.OOOD 01 0, .0 20 1 97500.00 2500.00 00B96S OI 7.627D-C1 3. 017C-01 1.7510-04 8.0000 01 c, .0 20 2 97500.00 7500.00 a, 008970 01 8.619D-C1 1. 0S1C 00 7.9670-05 6.00CD 01 0 .0 20 J 97500.00 12500.00 008970 01 1.0580 CO 1. 5110 00 3.021D-09 a.oooo 01 0. .0 20 • 97500.00 17500.00 00B97D 01 1.351C CO 3. 021C 00 6.4210-04 a.oooo 01 0, .0 20 5 47500.00 22500.00 •.006980 01 1.762D OO 9. 6i;c oo 1.5230-03 8.0000 01 0, .0 20 6 97500.00 27500.00 009000 01 2.S7SB co 7. 203C 00 -4.3590-09 8.OOOD 01 0 .0 20 7 97500.00 32500.00 9. ,009030 01 9.919D 00 1. 52 ID 01 -1.1590-02 8.OOOD 01 0, .0 20 8 97500.00 37500.00 00896D 01 1.348B 01 1. 649C 01 1.4540-02 a.OOOD 01 0, .0 20 9 97500.00 92500.00 009170 01 3.441D CI 9. 1460 01 -1.1340-01 B.OOOD 01 0, .0 20 10 97500.00 •7500.00 4. 008670 01 1.1480 02 5. 586C 01 1.0890-01 8.OOOD 01 3 .7450-16 20 11 97500.00 52500.00 4. ,007890 01 1.8110 C2 -1. ,72et-13 -6.SS60-01 B.OOOD 01 3, .9470-14 20 12 47500.00 57500.00 4, .008670 01 1.148C CI -5. 586c 01 3.0890-01 B.OOOD 01 3, .7450-16 20 1] 47500.00 62500.00 00917D 01 3.49 ID CI -4. 1460 01 -1.9340-01 B.OOOD 01 0. .0 20 It 47500.00 67500.00 008960 01 1.3«8D CI -1. B49C 01 1.9590*02 8.00OD 01 0, .0 20 15 97500.00 7250C.00 00903D 01 •.9190 CO -1. 2210 01 -T.1540-02 8.0000 01 0, .0 20 16 97500.00 77500.00 0)9000 01 2.S75D 00 -7. 203C 00 -4.3590-04 8.0000 01 0. ,0 20 17 4TMJ.00 82500.00 4. 008980 01 1.7620 00 -4. 615C 00 1.5230-03 8.0000 01 0. .0 20 IB *7S00.00 87500.00 «. 00897D 01 1.351D CO -3. 027C 00 6.4210-04 e.oooD 01 0, .0 19 t» 97500.00 92500.00 4. 008970 01 1.0S8D CC -1. 51IC 00 3.0230*04 8.0000 01 0, .0 So 20 97500.00 97500.00 4. 00 897 D 01 8.619 C-01 -1. 05IC 00 7.9870-05 8.0000 01 0. .0 20 21 97500.00 102500.00 >. ,0089611 01 7.627C-01 -3. 011C-01 1.7510-09 a. oooo 01 0, .0 21 1 102500.00 2500.00 4. 008970 01 1.722D-61 2. 038C-01 1.0640-05 6.OOOD 01 0, .0 21 2 102500.00 7500.00 4. 00897D 01 1.9830" 'CI 1, .3690-01 -4.5410-05 e.ooos 01 0 .0 21 3 102500.00 1250C.00 ,00 897 0 01 2.200-01 1. ,33(C 00 1.1400-05 8.0000 01 0, .0 21 • 102500.00 17500.00 a. > 00B97D 01 1.580D-C1 2. C5SC 00 2.3I3D-04 8.00 OP 01 0. .0 Zt 5 102500.00 22500.00 4.008981! 01 -2.770B-C1 2. 911C 00 -1.7590-Ot 8.OOOD 01 0, .0 21 6 102500.00 27500.00 a. .G0900D 01 -I.999D 00 4. ,12CD 00 -3.1860*09 8.OOOD 01 0, .0 21 7 102500.00 32500.00 ,009050 01 -3.742C CO 6. S5JC 00 -5.4910-03 B.OOOD 01 0, .0 21 a 102500.00 31500.00 •.006970 01 -2.692D CO 4. 19«0 00 1.2*90-01 8.OOOD 01 0, ,0 21 9 102500.00 •2500.00 4. 009830 01 1.4890 01 3. 025C 01 -3.6«7D-01 8.OOOD 01 -1, .7620-20 21 10 102500.00 •7500.00 4. 00950D 01 1.6360 C2 6. 2030 01 3.5110-01 a.oooo 01 9. .5400-16 21 11 102500.00 52500.00 4. 00818D 01 2.972D C2 -8. 544C-13 -1.337D 00 8.OOOD 01 1. . U1D-13 21 12 102500.00 S7500.00 4. 009500 01 1.6KD 02 -6. 20 Jt 01 3.5310-01 8.0000 01 9, ,5400-16 21 13 102500.00 62500.00 4. 00983D 01 1.489D 01 -3. 025C 01 >3.6470*01 a.oooo 01 -1, .7620-20 21 14 102500.00 67500.00 4. ,008970 01 -2.6920 £0 - a . ,19!C 00 1.2490-01 8.0000 01 0, .0 21 IS 102500.00 72500.00 4, 009050 01 -3.742D 00 -6. 252C 00 -5.4910-03 8.OOOD 01 0. ,0 21 16 102500.00 77500.00 4. 009000 01 -1.444C CO -4. 12CC 00 •3.1860-04 a.OOOD 01 0. .0 21 17 102500.00 a2500.00 4, ,0089BD 01 -2.770D-•01 •2. 971C 00 -3.7590-09 B.OOOD 01 0. .0 Z1 IB 102900.00 87500.00 a. 008970 01 1.580B-0t -2. C550 00 2.3130s04 8.OOOD 01 0. .0 21 19 102500.30 42500.00 «. ,036970 01 2.2430*01 -1. 33tt 00 3.1900-05 B.OOOD 01 0. .0 21 20 102500.00 97500.00 4, ,006970 01 1.98J0" •CI -1, , 386C-01 •9.5610*05 B.OOOD 01 0, .0 21 21 102500.00 102500.00 4, .00 897 0 01 1.7220->01 -2. oiec-oi 1.6640-05 tt.OOOD 01 0 .0

IBC0021 STOP 0

Table A.4. Input Data for S&raple Problem No. 2

c»sr Tm»: FRIT BO.?: TWO PM'P PinTr. TII curs; r.T«r»>! •!.<•». liPW l«m»n»-'ic* r»o* sustooTiir WOT:

c»»o «o. « Tt/t'L »tn«r» or rntftctL setcits c» coBsroneo <«n • l writ «iimir.» if ..cioas iit>s|' 11 T"T«t «'!•»»» or uirm rnBDITlnBS PIIH(TIO.<IS i«r«TLH • ? * n m HIBHM rr joioiemc n*»T of tins-. np.»rp»Tl<'» »ii»crto«s (":r.i>yi- t w«L Bin»t» 'ir pod»d»m co«oiTtc«r. 'ovtiobs m w n • » tot»L « I « I I sr p>t r o o m c m iu«ctin«s utn»«»' i

TOT»l »*i|!l»r W »ott™ CultITIOW rUBCTWBS (Hi'OTH ' 3 TOTBL »nn»r« or «»»l»Tlc»t m«citc»s (U«l 'CI • 1

TnT«t »0»Br» op t»BHWt> ro»CTIO»5 IKTBIPCI. 1 TTTIL ••>»«•• or n»oss imjcr n»is in » - M W T W » t«>n»M> n TD O T O M «N»N» or CPNII nmcr u«fs t« »-®nrctir« IUCPI I . » ^

TR.Tit. «IIIT»R» OP TENP. HOUTOBIBC points M U N • '

ci«r «o. i •rsT«»r rt»c. ir coon it»n >o MSTBBT IBPOBHTIOB is »n<»i"rn (ISTHTI' MMSH n»«. ir noiut. mo no nfsuir nw is rwvw urii'st* o T;OTTIHi 'lit. rr TOntt W.PO no ptorrii«: T«'<JMTIN« !s «E«IBBTCT. Actori • N

run ro» SUICTIM THE «0BCBte»i IBT'SUTIOB p«orii>«R>. ( I I I I T I SPUCTS »u«nr-r"TT«-r.IIL HETHOO. L » W ? SBL'CT* EBUF BFTHOIL. IBTBT" I SBIECT5 «0»F-F«5««N«TH IIITTIOO.1 ( I1THI - I

C»B® «0. 1

STI'THfi -IBf /!» THIS C«SE (5TH(. 0.0 "BOBIEB TIHE P0» TBI? C»SE (PUMBI- »J,«000 roBHITPB T I " CUTOIP LIBIT |B stO'BOS (CPUSEH' 7»'>.00

TIN* I»RPB»P«R PPXREO O N M (OPBTTBI • o. mco TIOM WMOT IR »» PSTIUHT IH IUU • 'I.«ooo

CABD >0. •


Uttttn IHCHM'HT IS0TH1 • U.OQ'.OCI

upcrsT urn p»» TI«E IBCREBBBI irnT»|. D.OO-PU

Tint urarKCiT 11 BiiiTiPtur PVERT at>1v TIBP SIPPS BY C'T«ITI. 1 . 0 9

»»*PW or TI»I AM-"- irrour PWTISS OP i»c»usr •« W *T»I I M (I«NT«LS to ewiiw op STPPS BPTUEEB CHtnr.rt ia rr»r srFP («r>T«ri .

CBITEPloa TTPE IAS OErlB'O 1» Sl'BRrtlTIar CHR!>T»I TIUT IM'H CTI IIIL! FIT RRO'II>• *t* SAIUP* (L»H!' P) « 0 TAB'ILATPO poact!oas

»A»L» an, 1 TAB«R« TABHC 0.0 0.0 1.00009 oo a.ooono-ot 1,09999 09 B.OOOOti-OI 6.00900 09 9.50000-01 a.oooon on i.cooon oo 1,00900 01 1.10900 on

iiptir IBPOPIITIOB HOB ciiotn«TI«R FIEOH: OJ O

IOSL(L> - r.RNSS IMIRT U»» 1 1* THC L-TIINCTINX 1IPo<H - aiUBER OP S'lPOMlSIORS BEWfB CROSS 1ATT1CI pars «ii»l('| ABO mat (1»1| . YGBLOI - OBOSS LATTICE LIRE I 1* T-OIPPrTIOa. irpoin - BOPBFR PP SOBOI'ISIOBS »ET«t» caoss IATTKI lwti loutu »»n torlimi).

1 IrtM mo 1 0. 0 r 2 5. .0009' 0 oa 2 1 s, . 10C00D <<a 1 a 5, ,150900 04 2 * 5. .2*0900 oa 1 5. , JConoo 9a 5 7 5. ,5*0900 04 15 B 7, .050000 2 4 7, . 150il0t> oa 1 10 7 .200009 oa 2 1 [ 7, ,100907 na 1 12 7. , 150000 04 10 tl 7. .8*0000 la 10 ia 1. ,785000 05

I TfiPl ITPO 1 9.0 u ? j,oooort> oi i 1 2.5000ro 93 2 a a.ioooon 0)


»nn»i »fr>T» noon rr»T»» 1 I-DIfCTIOl T-PVFrCTtnO 1- DIRECT 1**9 r-oioprnoo 1 ipnon. ninnc r.-.,, ponon ' .ooooion 11 7 '001(11 o> i 10000 onoon ' 10 i.nor..' ooooo r* no 7 '.noofni 07 1 10000 onno' '0(1 noi:oo 2,'ononnu 09 1 j'nnci'n 0 I o 11)000 onoon «nn o no o.i i.« nooonn 00 1. •"noro p i 5 moon .OHIO" '10 oonno o,inooP!. 09 7 2'onoi'ii n 1 (. 5 00 001)01 inn i noonn 5.0," 000|l 09 l norofnp i I 7 '00 onion tooo 00001 •.f710000 (10 0 oon.jrnr n i fl 509 .onion '.1250000 110 1 «.pn oonon '.175(1001 «» 10 '•90 oonon '.2250000 10 u •09 onooo *,?75000n no 1? 500 onion '•• 12500011 no ' ) 'on onnon '..••7'.onop no in 500 nnoon ' .92'.oonp no 1-1 501) nnnon 5.97500011 no 16 tO" 00101 '..'250901 no 17 18

1000 1001) onoon or.non 5.r,ooooon 5.7000001 no no iq 10 01 onoon '.wnoonnn no 20 inon onoc 'i.iononni no 71 loon onoon *.nononnp no 2 i 10 on onoon 6. 1010001 00 21 mon nan or ( .7000001 no 24 loon onoor i. , jonnonp no 25 1000 nnoon i .udooon no ?6 toon onnon ft.'.onoo'tr. no 27 iaon oonon fi.'OOOOOP no 20 loon onnoi 6.7000001 30 29 mon nnoor f..nonr.onn 10 IO 1001) onooo I..900000P no n man noocr 7.000000P no »i)P onooo 7.0750001 no JI •no onnoo 7,12'0nnp no 10 'OO onoon 7.175000P no 15 ••on nnnon 7.225000P no 36 '.on 00000 •>.?750I)np no 17 '00 nnoon 7.125000P no 16 '00 oonoo 7.1750001 no '9 'on ODOtn 7.U2r00rill no uo 5 00 nonon 7.9750000 no UI 500 oooon 7.5250001 no "2 500 onoon J.575000P no uj *00 onooo 7.A75000P no UK ••no oonon 7.6750000 oo U5 «oo oonon 7.725000P nu oft 500 onnoo 7,7750000 »7 ••on oooon 7,B250n0P no U8 10000 onnon 9.3500000 00 OS 100&0 oonoo 9.150000P no 50 10000 onoon 1.0350001 05 51 10000 oooon 1.1150000 05 52 looon ooooo 1.2J5000P 05 51 10000 oooon 1.1150001) 05 50 10000 ooooo 1.935000n 05 5 5 10000 oooon 1.5 350000 05 56 10000 90009 1.61501)01 05 57 10000 oooon 1.735000 0 P5

Table A.4 (continued)

GEOHETRTC DESCRIPTION OP RECTORS ONI DPI DNT 1NDEXICAL nESCRIPTIOR LOR I HIGH J LOU .THIGH 1 0 0 •51 OOO 00 0 0 2 0 0 0 OS 0 0 ooo 1 0 2 0 0 0 0 5 1 7 1 0 28 2 0 0 5 1 0 0 0 00 2000 0 0 2 5 0 0 00 0 0 O0C 2 5 5 0 0 0 07 1 7 * 5 7 3 0 0 siooo 00 2500 0 0 0 5 0 0 00 00 0 0 0 1 0 7 0 0 D 0 8 1 7 6 7 10 0 5 1 0 0 0 00 5 1 5 0 0 CO 0 0 0 500 CO 0 0 0 0 0 2 2 5 0 0 0 06 B 8 1 7 7

5 5 1 * 0 0 00 1 2 5 0 0 CO 0 0 0 5 0 0 00 00 0 0 0 0 «0 00D 06 9 10 1 7 10 6 5 2 5 0 0 00 5 3 0 0 0 00 0 0 0 5 0 0 00 00 0 0 0 2 2S00D 06 11 11 1 T 7 7 5 1 0 0 0 00 7 1 5 0 0 00 0 0 0 5 0 0 00 00 ooo 8 3 2 * 0 D 07 12 13 1 7 150 0 7 1 5 0 0 oo 7 2 0 0 0 00 0 0 U500 00 0 0 0 0 0 2 25001) 06 30 30 1 7 7 9 7 2 0 0 0 00 7 3 0 0 0 00 0 0 0 5 0 0 00 00 ooo 0 5 0 0 0 D 0 1 3 * 36 1 7 10

10 7 3 0 0 0 OP 7 3 5 0 0 00 0 0 0 5 0 3 00 00 0 0 0 2 2 1 0 0 0 P6 37 37 1 7 7 11 7 1 5 0 0 oo 1 7 8 5 0 0 00 0 0 U500 CO 00 ooo 0 7 2 5 0 0 06 3B 5 7 1 7 100

TOTAL 10. or RODES IR (IHPUTI REGIONS" HAH. RO. or NODES IN GRfO" 399 399

PUBCTIOR SELECTION BOUNDARY SELECTION REGION I N T r IGERP ITOPP I B O T r I H P I B I D H I B IOPTB IDHTB

1 - 1 0 1 1 1 0 0 0 2 1 0 1 1 2 0 0 0 3 1 0 1 ' 1 1 0 0 0 0 1 0 1 1 0 0 0 • 5 1 0 1 1 0 0 0 0 6 1 0 1 1 0 0 a f 7 1 0 1 1 0 0 0 0 8 1 0 1 1 0 0 7 0 9 1 0 1 1 0 0 0 0

10 1 0 1 1 0 0 8 0 11 1 0 1 1 0 3 It 0

RUHBER OP RLEHEHTS AVAILABLE IR ARRAT Z IN HAIR = B600 ROHBER OP ELEHERTS HEEDED " 7B3?

POSITIOkS TO HONITOP TEHPEBATURE REQUESTED LCCATIOH

* T

1 73250.000 2 73J50.000 3 73250.000 250.000 2250.000 3000.000

SELECTED RODE I J 37 37 37

RflDE LOCATIOH I T 7325C.000 7125C.000 7325C.000

250.000 2250.000 3000.000

BODE REGION '0 10 10


HODAL DISPLAY FOB OPSTBEAH B00BDA8IES III X-DJ OH,BEX*

B *r««i * 6 » « 1 = 5*»2 « tt%»i = 3»«1 = 2**1

Table A. 4 (continued)

hodtL o r s p u r rcn DOVHSTEZAB BOUHDARIBS I» i - n i s e r n o H , i i B r p

Ja 3 J* 3 J> 3 J* *

J« 3»« J* 2«« J*


w o r n DISFUY POR UPSTWIN "OUWDMRS IS R-M*RCTJO«,M«

a T» • i *,•» a a«* • • 2**


HOD?'. f.75PL«T FOB DOUNSTBEAH BOOHDABIES IH T-OIBECIIOH,HBrP

js 7«*uauutiiiui0u6ti(iutiatitiui|iitiiibtiti(iiiiiaijiitt<juiiaiibtiiiubuuiiu<iuuatiiiutiijii j= 6»» u- •>•• Js U»» J= 3»» J= 2 «

CM I—1 Ov

Table A.4 (continued.)

NODAL DISPLAY FOB BEGIOBS

J = 7 * * 3 3 3 3 3 3 3 U 5 5 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 9 9 A B B B B B B B B B B P 8 B P B B E P B B J * « » « 3 3 3 3 3 3 3 » 5 5 S 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 9 9 A B B B B B B B B B B E B B B B B B B B B J = < 5 * * 2 2 2 2 2 2 2 0 5 5 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 7 7 7 7 7 B 9 9 A B B B B B B B B B B E B B B B B B P B B

» * * 1 1 1 1 1 1 1 0 5 5 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 9 9 A B B B P E B B B B B E B B B B B B B B B J * 3 * • 1 1 1 1 1 1 1 1 5 5 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 9 9 A D B B B B B B B E B E B B B B B B B E E 3 = 2 * » 1 1 1 1 1 1 1 1 5 5 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 9 9 A B B B B B B B B B B B B B B B B B B B B J « 1 * « 1 1 1 1 1 1 1 U 5 S 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 7 7 7 7 7 B 9 9 A B B B B B B B B B B E B B E B E B B E B


input INFOPHITIPN ppn* SIJEIOUTIRE GENCON:

IGENFC - INTERNAL GENERATION FUNCTION (SN INDEII - VALUE OF HEAT GENERATION PF.R U « " YOU1BF in INTERNAL GENERATION FUNCTION

10DVF - GFN5PAL PURPOSE FUNCTION TO Bt ISED ON OPV GKDV(M - VALUE OF HASS GENERATION PER UNIT VnmfE FOP SPECIE K IN INTERNAL GEHEPATION FORCTIO" IGKDVF(K) - GENERAL PURPOSE FUNCTION TO BE USED OH GKCV(K)

r IGEHFC QDV IQDVF GKDV<1) IGKDVF(1 | GKDV(2) IGKDVP(2 I 1 1 0.0 0 0.0 0 0.0 0


INPUT INFORH«TION PROH SUBPOOTIHE BNDCO":

NBH - B011KDAPY COHDTTIOI NUHBER NHROTP - T I P E OF BOURIIARY COHDITIOR FOR WATER ELPVATICN H (HHEDTP) HO - T I P E OF BOUNDARY COHDITIOH FOR VELOCITY » (RUBDTF) «V - TTPE Of BOUHDART CONDITION FOR VELOCITT V ( NVBD1P) «T - TTPE OF BOtlHOAPT CONDITION FOR TEHP. OR SPECIES CORCENTRAl lnV ( N B T I T P I FH - VALUE OP BOUNDARY CONDIT ION FOB RATER ELFVATION (FHBD) »l) - VALUE OF BOUNDARY CORBIT IOR FOR VELOCITT U (PUBO) FV - VALUE OF BOUNDART COHDITIOR "OR V E L O C I T I V (FVSDJ FT - VALOE OP BOUNDARY CORDITIOR FOR TEHP. (PTPD) FS - VALUE OP BOUNDARY CORDIT IOR FOR RASS F L U I |»GBD) FQ - VALOE OF BOUNDARY CORDITIOR FOR HEAT F L U I (POBD) FSBDN - VALUE CP BOUNDARY C O N D I T I O * FOR NOPHAL S T B E S S I S PGK(1 | - VALOR OP BOUNDARY CONDIT ION FOR HASS F L U ! OP S P F C I E R (PGItBD) PCK - VALUE OP BOUNDARY CONDIT ION FOR SPECIES CONCENTRATION (FCKIOI I H 8 D F - H O L T I P L I K R FONCTION FOR FHBD I U - H t ' L T I PLIER FURCTION FOR FUBD I V - HULTIPLTER FUNCTION FOR FVBD I T - H U L T I P L t E R FUNCTION FOR FTED 10 - H 0 L T 5 P L I E S FUNCTION FOR FHBD IQ - H I 1 L T I P I I E R FURCTICH FOR FQBD I S * - H U L T I P L I E R FURCTION FOR FSBDN I S H - H U L T I P L I E R FURCTION FOP FS1DSH

BOURDART COHDITIORS AT STARTING T I H E HBH NHBDTP NO RV N 1 (1 1 2 2 2 tt 1 1 1 3 1 g u a u (1 2 1 2 •i 11 a 1 u 6 U i 1 1 7 a g 1 a 8 u 1 1 1

FH PU FV FT 0. . 0 0, . 0 0. , 0 8, .OOOOOOD 0 1 0. . 0 7 . 2 0 0 0 0 0 D 0 2 0. . 0 n . 0 0 0 0 0 0 " 0 1 1, .OOOOOOD 00 0 . 0 0, . 0 7 . 0 0 0 0 0 0 0 0 1 0. . 0 0 . 0 0, . 0 8 . 0 0 0 0 0 0 0 0 1 0 . 0 0, . 0 a . UPS800D 02 6 , .OOOOOOD 0 1 0 . 0 0 , . 0 - g . • 1 6 5 8 0 0 D 02 - 1 . • 5 0 0 0 0 0 D 0 1 0. 0 0 , , 0 - g . , t t f i ?800D 02 8 , . 0 0 0 0 0 0 D 0 1 0. .0 0 , .0 g. 0 6 5 8 0 0 D 0 2 -1 . .sooooon 0 1

Oi vo

KBH FS PO FSBDK PSEDSH 1 0.0 0.0 0.0 0.0 2 0.0 0.0 0.0 0.0 3 0 . 0 0 . 0 0 . 0 0 . 0 u 0 .0 0 .0 0 .0 0 .0 •5 0.0 0.0 0.0 0.0 6 0.0 0.0 0.0 0.0 7 0.0 0.0 0.0 0.0 B 0 . 0 0 . 0 0 . 0 O . D

PGR (1) PGR (2) FCEOJ F C K ( 2 | 0. . 0 0. . 0 1 . 0 0 0 0 . 0 0. . 0 0, . 0 1 . 0 0 0 0 . 0 0. . 0 0 , . 0 0 . 9 7 3 0 . 0 2 7 0. 0 0, . 0 1 . 0 0 0 0 . 0 0. 0 0. . 0 0 . 9 9 3 0 . 0 0 7 0. 0 0 . , 0 0 . 9 9 3 0 . 0 0 7 0. 0 0. , 0 0 . 9 9 3 0 . 0 0 7 0. 0 0. . 0 0 . 9 9 3 0 . 0 0 7

H U L T I P L I E R PUHCTIOHS FOR BOUHDART COHDIT IORS NBff IHBDP 10 r v IT IG I f l ISH rsH 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 - 2 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 ' 0 0 0 0 0 0 0 0

Table A.4 (continued.)

POWER PLART OR BOUNDARY.

IBR DTPP(RBH) T I N T

6 1 . 5 0 0 D 0 1 5 . 1 2 5 0 0 0 8 1 . 5 0 0 0 0 1 7 . 1 7 5 0 0 0

t I R T T J

00 0.2SOOOD 03 8 7 00 2 . 5 0 0 0 0 0 02 30 1

IRPOT IRPORHITIOR FROR SUBROUTINE BOICON:

QB - HEAT COHIUG PBOn THE BOTTOR HCB - HEAT TRARSPER COEFFICIENT POR THE BOTTOR TO - tBLOCTTT OT K»SS COSIfS FRO! TUB BOTtOB M X-DltHCTIO* 7B - TELOCITY OF HASS CORIHG PROH THE BOTTOR I H Y - O I R I C T I O N RB - T E L O C I T I OF HASS COHIRG FROH THE BOTTOH I N Z -DIRECTIOR TB - TBHPERATOBE OP HASS COHIRG FROR THE BOTTOR BHARGC " HAUNIRG COEP. FOR FRICTION WITH THE BOTTON DCItO - RASS DIFPOSIOH COEFFICIERT FOR SPECIE K FROH BCTTOH CltB - HASS CONCERT RATION OP SPECIES CORING FROR BOTTOR IQB - H B L T I T L I S R PORCTIOR POR QE IHCB - ROLTIPLIER FUNCTION FOB SCB IOB - HOLTIPLIER FORCTIOR FOB OE I V B - H B L T I P L I E B FORCTION POR VE I R S - HOLTIPLIER FORCTION POR RE I T B - ROi .T IPI . IEH FORCTIOR FOR TE IDCICB - HOLTIPLIER PORCTIOR TOR OCKB ICKB - MULTIPLIER FORCTIOR FOR CltB

BOTTOR CONDITIONS AT STARTIRG T I R E »CT. NO. OB HCB OB VB RB TB BHARGC ECKB (1)

1 0 .0 0.0 0.0 0.0 0.0 e.OOD OI B. 310-06 0.0 2 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 8 . 0 0 0 0 1 8 . 3 3 D - 0 6 0 . 0

HOLTIPLTEP FORCTIOR FOR BOTTOR CONDITIONS FCT.RO. I D B IHCB IUB I V B I B B I T B I D C K B ( I ) ICICB(1) IDCKB(2) ICKR(2 ) 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0

IRPOT IUFORRATIOR FEOR SUBROUTINE TOPCON:

QT - HEAT COHIRG FHOR THE TOP HCT - HEAT TRARSPER COEFPICIEBT POR TOP OT - VELOCITY OP HASS COHIRG FSOH THE TOP I N I - D I R E C T I O N VT - VELOCITY OP HASS COHIES FROR THE TOP I H Y-DIRECTION RT - VELOCITY OP RASS COHIHG FROR THE TOP I R Z-DIRECTION TT " TEHPPSATORE OP HASS COHIRG FROR THE TOP TO - DEW-POINT TEHPBRATDBB QSOL - SOLAR HEAT F L O ! DCUT - RASS DIFFUSION COEFFICIENT POB SPBCIB R PROH TOP CRT " RASS CONCENTRATION OF SPECIES COniHG FROH THE TOP I Q T - HOLTIPLIER PORCTIOR FOR QT IHCT - HOLTIPLIER PDRCTIOR FOR HCT IOT - H O L T I P L I M FDNCTFOR POR OT I V T - HOLTIPL IEB F0RC?) "R POR VT

w NJ o

CKB(1> OCKB(2) C K B ( J ) 10.00 0 .0 0 . 0 10.00 0.0 0.0


m - n U L T l P L i m TOUCH OH FOB » T I T T - NULTIPLIER PONCTION POB TT ITO - N U I T I P I I E " FONCTION FOB To TQSOL - HULTIPLIER FUHCTIOB FOB 0S01. IPCHT - BHLTIPL7ER FUNCTION "OB OCKT ICKT - H O f l P L I E P FUNCTION POB CHT

TOP CONDITIONS \ T STARTING TINE FCT. HO. OT HCT OT »T HT TT TO OSOL 0 C K T ( 1 | C K T ( l ) OCI tT(2 | C K T H l

1 0 . 0 5 . 0 0 0 . 0 0 . 0 0 . 0 8 0 . 0 0 BO.00 0 . 0 0 . 0 1 . 0 0 0 . 0 0 . 0 2 0 . 0 5 . 0 0 0 . 0 0.0 0.0 8 0 . 0 0 60.00 0.0 0.0 1 . 0 0 0 . 0 0 . 0

BULTIPLIER FUNCTION FOB TCP C09DIT I0NS PCT. NO. I 0 T IBCT IOT I V T INT I T T TTD IOSOL I D C E T ( I ) I C K T ( 1 | I D C R f < 2 | I C K T ( 2 I 1 0 0 0 0 0 0 0 0 0 0 0 0 2 O O O O O O O O O 0 0 0

INPUT INPORHATION FROH SOBROIITINE FLXCON:

COEFFICIENT VOR TOTAL EFFECTIVE 1BERHAL CONDUCTIVITY IN X - D I R f C T t O N (XHPC) •= 3.*OOOOOD-O1 COEFFICIENT FOB TOTAL EFFECTIVE THERHAL COHOOCTIVITT I H T - D I R t C T I O N (XKPCI = i . * 0 0 0 0 0 0 - 0 1 c o e f f i c i e n t f o b t u r b u l e n t v i s c o s i t x i n x - d i r e c t i o h ( x t v s c ) » 2 . 0 0 0 0 0 0 0 00 COEFFICIENT FOR TURBOLPUT VISCOS1TX I B T -D IBBCTIOH ( I I V S C ) - 2 . 0 0 0 0 0 0 0 00

Ul N> DKXC - COEFFICIENT POB TOTAL BINARY BFPECTIVE MFFCS1CN COEFFICIENT OP SPECIE OFTC - COEFFICIENT FOR TOTAL BIHART EFFECTIVE OIFFOSICN COEfPICIBNT OP SPECIE

-DIRECTIOH - DIRECTION

DKXC ( M

1 5 . 2 2 0 0 0 0 0 - 0 5 2 5 . 2 2 0 0 0 0 D - 0 5

O M C I B )

5 . 2 2 0 0 0 0 D - 0 5 5 . 7 2 0 0 0 0 D - 0 5

INPUT INPO»BATIOH FBOB SUBBOOTINE INTCON:

S IH - I N I T I A L VALOE FOR BATER SURFACE E l E V A T I O N , B , HXASUBED PR0H THE BOTTOH STO - I N I T I A L VALOE FOB HATER VELOCITT, U, I N X-DIRECTION STV - I N I T I A L VALOE FOB HATER V U O C I T T , V , I H T-DTRECI ION STBS - W T r A L VALOE FOB BATE OF CHANGE OF HATEB ELEVATION WITH RESPECT TO T IHE STT - I N I T I A L VALOE FOB N A U R TtBPEBATORB, T . S T C K ( I ) - I N I T I A L VALOE FOB BASS CONCENTRATION OF S P E C I E S ( I ) . TSTHP - BOLTIPLIER PONCTION FOB STH ISTOP - H O L T I P I I B R PONCTION FOB STU ISTVP - HtJLTIPLIER FONCTION POB STV ISTHSF - HULTIPL IEB "OBCTION FOB STBS TSTTF - B U L T I ' L I E R PONCTIOB FOR STT TSTCKP( I ) - n U L T I P L I E R FUNCTION FOB STCK( I )

I N I T I A L CONDITIONS FUNCTION NO. STH STU 1 HO.00 0.0 2 ao.oo 0.0

STV STT STCX(11 STCK(2! 0.0 BO.00 1.00 0.1) 0.0 BO.00 1.00 0.0


MULTIPLIER PIJBCTIOH FOB I N I T I A L CONDITIONS p e r . B O . I S T B I5TU JSTV ISTT J S T C K ( 1 ) I S T C K I 2 l 1 0 0 0 0 0 0

2 0 0 0 0 0 0

Table A.5. Output Information for Sample Problem No. 2 at Time = 0.61 hr Using the Full Version of the Program

I T E P . * 1 1 0 T I R E - 5 . 9 0 0 0 0 0 0 - 0 1 P E R I O D " 0 . 7 5 8 0 6 5 0 - 9 2 H U E I 4 C B t H E I 1 T « 5 . 0 0 0 0 0 0 D - P 3

VELOCITf VELOCITT 1ATER ELEV. TPHP. SU9STANCE RAI CONCEN I N D I - I - I - WATEF I N III «ATU RATE

MODE CES LOCATION LOCATION ELEVATION I - DIRECT* l - DIRECT. o r CHANGE TEHP D p CHANGE C M ' l C R I 2 I

1 1 5 0 0 0 0 0 2 5 0 0 0 9 0 0 1 3 1 0 0 1 1 . 0 6 7 0 0 2 - 1 5 8 2 0 0 0 - 1 . 6 6 5 0 - 0 2 8 OOOD 0 1 - 2 . 8 2 1 0 - 7 1 1 .GOOD 0 0 2 1 9 5 0 - 7 9 1 2 5 0 0 0 0 0 7 5 0 0 0 II 0 0 1 3 9 0 0 1 1 . 0 7 7 D 0 2 - 6 6 5 8 0 0 0 - 2 . 2 9 0 0 - 0 1 8 OOOD 0 1 - 2 . 5 5 6 9 - 6 8 1 0 0 0 1 0 0 2 7 0 6 0 - 7 1 1 3 5 0 0 0 0 0 1 2 5 0 0 0 II 0 0 1 3 9 D 0 1 1 .OOOD 0 2 - 1 . 2 5 2 D 0 1 3 . 7 8 2 0 - 0 1 8 OOOD 0 1 - 1 . 3 7 1 9 - 6 5 1 . 0 0 0 0 0 0 1 5 H D - 6 8 1 II 5 0 0 0 0 0 1 7 5 0 0 0 a 0 0 1 9 3 0 0 1 1 . 5 1 6 0 0 2 - 1 6 6 7 D 0 1 - 5 . 7 2 7 0 - 0 1 8 0 0 0 0 0 1 - 2 . 6 1 0 9 - 6 3 1 .OOOD 0 0 1 9 2 0 0 - 6 6 1 5 0 0 0 0 0 2 2 5 0 0 0 9 0 0 1 5 8 D 0 1 1 . 5 2 8 0 0 2 - 8 . 5 3 5 0 0 0 2 . 1 7 3 0 - 0 1 8 OOOD 0 1 4 . 3 8 5 9 - 6 ) 1 OOOO 0 0 7 ( - 1 ) 0 - 6 4 1 6 5 0 0 0 0 0 3 0 0 0 0 0 9 0 0 1 2 5 D 0 1 1 . 5 1 0 0 0 2 8 2 3 ID 0 0 - 9 . 9 ) 7 0 - 0 1 8 0 0 0 0 0 1 1 . 1 5 1 9 - 6 0 1 o o o n 0 0 3 . 1 1 C D - 6 0 1 7 5 0 0 0 0 0 a 000 0 0 9 0 0 0 9 9 D 0 1 1 . 0 8 5 D 0 2 - 1 5 0 8 0 - CI 1 . 0 0 5 0 - 0 1 8 0 0 9 9 0 1 2 . 2 5 9 0 - 5 6 1 OOOD 0 0 1 7 7 9 0 - 5 6 2 1 1 5 0 0 0 0 0 2 5 0 0 0 9 0 0 1 9 0 D 0 1 1 . 2 2 9 0 0 2 - 7 5 9 1 0 - 01 1 . 8 3 2 0 - 0 1 8 OOOO 0 1 - 5 . 1 6 2 9 - 6 1 1 OOOD 0 0 f 1 1 9 9 - 6 4 2 2 1 5 0 0 0 0 0 7 5 0 0 0 9 CO190D 0 1 1 . 2 2 8 0 0 2 - 2 . 6 8 7 0 0 0 1 • 2 6 6 D - 0 1 8 OOOD 0 1 - 1 . 9 2 4 9 - 5 7 1 . o o o n 0 0 3 OOOD- tO 2 3 1 5 0 0 0 00 1 2 5 0 0 0 9 0 0 1 B 8 D 0 1 1 2 3 3 D 0 2 - a 7 2 J n 00 1 . 2 2 7 0 - 0 1 8 OOOD 0 1 - 1 . 9 6 7 9 - 5 0 1 o o o n 0 0 6 • 2 9 9 - 5 7 2 9 1 5 0 0 0 00 1 7 5 0 0 0 9 0 0 1 8 7 0 0 1 1 . 2 3 8 0 0 2 - 6 . 0 0 0 0 00 0 . 6 2 3 0 - 0 2 8 OOOD 0 1 - 1 . 1 1 3 9 - 5 1 1 o o o o 0 0 7 7 0 t 0 * 5 9 2 5 1 5 0 0 0 00 2 2 5 0 0 0 9 0 0 1 8 8 D 0 1 1 • 2 3 7 D 0 2 - 1 9151) 0 0 - 8 . 3 7 0 0 - 0 2 8 OOOD 0 1 9 • B 9 5 9 - 5 1 1 0 0 0 9 0 0 R 8 8 1 0 - 5 1 2 6 1 5 0 0 0 00 3 0 0 0 0 0 9 0 0 1 8 0 D 0 1 1 . 2 1 6 0 0 2 3 5 3 9D 00 8 . 1 9 2 0 - 0 2 8 OOOD 0 1 1 . 9 8 0 9 - 4 7 1 .OOOD 0 0 1. 2 4 2 D - 4 7 2 7 1 5 0 0 0 00 9 0 0 0 0 0 CI 0 0 1 7 9 D 0 1 1 . 199D 0 2 3 767D- 0 3 2 . 2 2 3 0 - 0 1 8 OOOD 1)1 1 . 7 1 6 9 - 9 1 1 o o o n 0 0 1 3 4 0 9 - 4 3 3 1 2 5 0 0 0 00 2 5 0 0 0 a 0 0 2 1 9 0 0 1 9 . 6 2 2 0 0 1 - 1 5 9 5 0 0 1 1 . 0 2 3 0 - 0 1 8 OOOD 0 1 • . 0 8 5 0 - 5 0 1 0 0 0 9 0 0 4 6 M 1 0 - 5 4 3 2 2 5 0 0 0 00 7 5 0 0 0 9 0 0 2 1 9 0 0 1 9 . 6 0 2 0 0 1 - 2 860D- 0 1 1 . 0 0 6 0 - 0 1 8 OOOD 0 1 1 . 0 5 4 0 - 4 9 1 OOOD 0 0 1 . 1 7 5 D - 9 9 3 3 2 5 0 0 0 00 1 2 5 0 0 0 U 00213D 0 1 9 5 5 3 0 0 1 - 3 5 1 6 0 - 0 1 1 0 8 3 0 - 0 1 8 OOOD 0 1 1 • 1 2 9 - 9 5 1 OOOD 0 0 I . 5 M 0 - 9 5 3 11 2 5 0 0 0 00 1 7 5 0 0 0 II 0 0 2 1 2 D 0 1 9 . U 6 3 D 0 1 - 9 0 1 6 0 - 0 1 1 . 9 2 2 D - 0 1 8 OOOD 0 1 1 2 4 5 9 * 9 1 1 OOOD 0 0 1 . 1 3 J D - 0 1 3 5 2 5 0 0 0 00 2 2 5 0 0 0 II 0 0 2 1 ID 0 1 9 . 3 1 9 0 0 1 - 2 2 6 1 D - 0 1 1 5 0 1 0 - 0 1 8 OOOD 0 1 - 8 7 2 2 9 - 3 6 1 0 0 DO 0 0 (., 9 6 1 0 - 1 8 3 2 5 0 0 0 00 3 0 0 0 0 0 9 0 0 2 1 2 D 0 1 9 0 0 8 D 0 1 - 1 6 2 0 D - 0 1 1 U 7 5 D - 0 I 8 OOOD 0 1 - 2 7 2 9 0 - 1 2 1 OOOD 0 0 2 . 1 7 2 9 - 3 4 3 7 2 5 0 0 0 00 9 0 0 0 0 0 u 0 0 2 1 3 D 0 1 8 . 7 9 0 D 0 1 - B 109D- 0 1 1 . 0 8 0 0 - 0 1 8 OOOD 0 1 9 2 1 3 0 - 3 1 1 OOOD 0 0 5 , 0 6 1 9 - ) ! o 1 3 5 0 0 0 00 2 5 0 0 0 9 00 2 000 0 1 6 5 6 0 0 0 1 1 0 2 3 0 - 0 1 1 . 9 8 9 0 - 0 1 8 OOOD 0 1 - 6 5 8 8 0 - 4 2 1 OOOD 0 0 5 . 7 S P » - « 0 3 5 0 0 0 00 7 5 0 0 0 9 0 0 2 0 1 D 0 1 6 098D 0 1 9 6 9 2 0 - CI 1 0 9 0 0 - 0 1 8 OOOD 0 1 - 2 6 1 1 0 - 1 7 1 OOOO 0 0 2 . 2 7 9 9 - 4 0 9 3 3 5 0 0 0 00 1 2 5 0 0 0 u 0 0 2 0 2 0 0 1 6 . 3 6 9 0 0 1 7 2 1 9 0 - 0 1 1 6 2 9 D - 0 1 8 OOOD 0 1 - 5 1 1 4 0 - ) ) 1 OOOD 0 0 0 , 6 9 9 D - 1 6 a 3 5 0 0 0 00 1 7 5 0 00 II 0 0 2 0 3 D 0 1 6 168D 0 1 8 0 0 ID- 01 1 . 7 1 3 D - 0 1 B OOOD 0 1 - 4 2 6 9 D - 2 9 1 OOOO 0 0 4 . 8 9 7 0 - 1 2 a 3 5 0 0 0 00 2 2 5 0 0 0 9 0 0 2 0 5 D 0 1 5 . 8 9 7 0 0 1 7 7CCD- CI 1 . 7 8 3 0 - 0 1 8 OOOD 0 1 - 1 5 1 5 9 - 2 5 1 OOOD 0 0 2 . • 2 ' 0 - 2 » 0 3 5 0 0 0 0 0 3 0 0 0 0 0 II 0 0 2 0 9 D 0 1 5 . 9 0 9 0 0 1 9 1 0 6 D - 01 1 . 7 7 1 0 - 0 1 B OOOD 0 1 - 2 0 0 2 0 - 2 2 1 OOOn 0 0 6 . 8 2 1 0 - 2 5 o 7 7 5 0 0 0 00 UOOO 0 0 u 0 0 2 1 6 0 0 1 5 0 2 3 D 0 1 - 1 9 0 7 D - 0 2 9 9 7 2 0 - 0 2 6. uOOD 0 1 1 (19 1 0 - 1 9 1 o o o o 0 0 1 . H R P - 2 1

1 " 5 0 0 0 00 2 5 0 0 0 a 0 0 1 6 3 D 0 1 2 7 9 8 D 0 1 8 8 1 C D - 0 1 9 5 8 6 0 - 0 2 8 . 0001) 0 1 6 1 8 6 9 - 4 9 1 0 0 0 0 0 0 1 . M 5 D - 0 1 5 2 U 5 0 0 0 00 7 5 0 0 0 a 0 0 1 6 3 D 0 1 2 7 0 3 D 0 1 3 0 2 2 0 00 5 . 1 2 5 0 - 0 2 8 OOOD 0 1 3 2 7 7 0 - 3 9 1 o o o n 0 0 5 . 1 6 6 0 * 1 9 5 9 5 0 0 0 00 1 2 5 0 0 0 9 0 0 1 6 9 D 0 1 2 5 1 1 0 0 1 4 9 9 B n 0 0 6 8 9 9 D - 0 2 8 OOOD 0 1 9 2 5 8 9 - 1 5 1 OOOD 0 0 1. 1 1 4 9 - 3 4 5 9 9 5 0 0 0 00 1 7 5 0 00 9 0 0 1 6 6 D 0 1 2 2 1 5 0 0 1 6 8 6 9 D 00 7 5 9 9 9 - 0 2 8 OOOD 0 1 1 8 2 2 9 - 3 0 1 OOOD 0 0 1 . 7 8 7 9 - 3 0 5 5 U 5 0 0 0 00 2 2 5 0 0 0 9 00167D 0 1 1 • R18D 0 1 B 2 1 ID 00 1 . 5 5 3 0 - 0 1 B OOOD 1)1 • 1 2 1 6 0 - 2 3 1 OOOD 0 0 5 . 6 ( 2 9 * 2 t

9 5 0 0 0 00 3 0 0 0 0 0 9 0 0 I 6 9 D 0 1 1 0 1 1 D 0 1 9 5 0 9 0 0 0 2 1 1 6 0 - 0 1 8 OOOD 0 1 1 • 1 7 9 - 1 6 1 OOOD 0 0 8 . 0 8 6 0 - 2 1 5 7 U 5 0 0 0 o o 9 0 0 0 0 0 9 0 0 1 7 5 D 0 1 7 6 0 7 D - 0 1 1 1 0 1 0 0 1 9 4 6 0 0 - 0 1 8 . OOOD 0 1 1 7 8 2 0 - 1 1 1 0 0 OD 0 0 1 . 5 5 1 0 - 1 5 6 1 5 0 2 5 0 00 2 5 0 0 0 II 0 0 1 9 I D 0 1 5 . 2 5 8 0 0 0 1 6 b 9 D 00 2 . 5 1 0 : 1 - 0 2 8 OOOD 0 1 2 8 2 5 0 - 1 9 1 OOOD 0 0 2 3 8 ( 9 - 1 9 6 5 0 2 5 0 o r 7 5 0 0 0 II 0 0 1 9 2 0 0 1 9 . 2 2 8 0 0 0 5 4 3 3 0 00 1 . 9 8 6 0 - 0 2 8 OOOO 0 1 1 1 0 9 9 * 3 9 1 OOOD 0 0 7 . 0 5 7 0 - 3 5 6 3 5 0 2 5 0 00 1 2 5 0 00 U 0 0 1 9 3 D 0 1 2 1B2D 0 0 9 0 5 7 0 00 - 2 1 7 9 9 - 0 2 8 OOOO 0 1 2 1 9 9 9 - 1 0 1 OOOD 0 0 1 . 2 2 2 1 1 - 1 0 f ' 9 5 0 2 5 0 0 1 1 7 ' 0 0 0 9 0 0 1 4 9 0 0 1 - 8 6 0 2 0 - 0 1 1 2 5 9 0 0 1 - 2 , 0 6 7 0 - 0 2 8 OOOO 0 1 - 1 8 1 7 0 - 2 4 1 0 0 0 0 0 0 1 . 9 9 9 0 - 2 6 6 5 5 0 2 5 0 o u 2 2 5 0 0 0 u 0 0 1 9 5 0 0 1 • 0 . 7 0 2 0 0 0 1 0 2 9 0 0 1 - 7 0 5 1 D - 0 2 8 OCOD 0 1 8 5 7 8 9 * 1 9 1 0 0 0 9 0 0 3 . 6 5 2 9 * 2 2 e 5 0 2 5 0 0 0 3 0 0 0 0 0 9 0 0 1 5 5 0 0 1 - 9 9 8 5 D 0 0 1 R92D 0 1 - 3 2 1 0 0 - 0 1 8 . OOOD 0 1 1 5 9 5 9 - 1 2 1 0 0 0 0 0 0 4 . 2 7 2 9 - 1 7

7 5 0 2 5 0 00 9 0 0 0 0 0 9 0 0 1 BOD 0 1 - 1 9 33D 0 1 2 56811 0 1 - 2 0 2 1 9 0 0 8 o o o n 0 1 - 2 B 4 0 9 - 1 I 1 0 0 0 9 0 0 2 . 5 0 9 0 - 1 2 7 1 5 0 7 5 0 00 2 5 0 00 u 0 0 1 U 4 D 0 1 0 3 6 1 D 0 1 2 2 9 8 D 00 1 2 9 0 0 - 0 1 8 OOOD 0 1 - 1 8 0 1 0 - 3 4 1 OOOD 0 0 1 . ) 7 1 0 - ) f 7 5 0 7 5 0 00 7 5 0 0 0 9 0 0 1 0 9 0 0 1 - 5 93BO 0 1 7 0 8 4 D 00 1 2 9 9 0 - 0 1 S OOOD 0 1 - 6 6 6 9 D - 3 0 1 OOOD 0 0 3 . 6 9 6 9 - 3 7 7 5 0 7 5 0 0 0 1 2 5 0 0 0 9 00195D 0 1 - 2 7 10D 0 0 1 212D CI 1 . 7 7 B D - 0 I 8 OOOD 0 1 - 1 5 2 3 D - 2 5 1 OOOD 0 0 5 . 6 1 4 9 - 7 8 7 9 5 0 7 5 0 00 1 7 5 0 00 9 0 0 1 9 9 D 0 1 - 5 . 9 6 2 0 0 0 1 7 5 3 0 0 1 2 7 9 5 0 - 0 1 8 OCOD 0 1 - 2 1 1 2 0 - 2 1 1 0 0 0 9 0 0 5 , 5 4 2 0 - 2 4 7 5 0 7 5 0 0 0 2 2 5 0 0 0 9 0 0 1 9 5 D 0 1 - 1 0 2 0 D 0 1 2 0 6 2 D 0 1 5 . 5 9 5 9 - 0 1 8 o o o n 0 1 5 3 6 6 D - 1 5 1 OOOD 0 0 1. 4 f C 9 * t n 7 5 0 7 5 0 00 3 0 0 0 00 9 0 0 1 0 9 0 0 1 - 1 2 8 0 D 0 1 9 304D 0 1 8 . 7 9 2 9 - 0 1 8 OOOD 0 1 9 1 2 3 9 - 1 0 1 OOOD 0 0 1. 7 5 1 0 - 1 4 7 7 5 0 7 5 0 00 9 0 0 0 0 0 9 001U8D 0 1 - 1 2 6 6 D 0 1 7 3 1 ID 0 1 2 8 0 9 9 0 0 B OOCD 0 1 2 3 4 5 9 - 0 5 1 0 0 0 1 0 0 2 . 0 1 0 9 - 0 9 8 1 c 1 2 * 0 00 250 0 0 9 0 0 1 0 7 0 0 1 - 5 9 0 8 0 0 0 2 8 8 8 0 00 - a . 0 1 9 0 - 0 1 8 OOOD 0 1 - 1 • 1 5 9 - 3 1 1 0 0 3 0 0 0 5 . O'MO- 3 4 8 2 5 1 2 5 0 0 0 7 5 0 0 0 9 0 0 1 9 7 0 0 1 - 7 3 1 3 D 00 B 6 3 8 D 00 2 0 1 5 0 - 0 2 8 . OOOD 0 1 - 3 8 0 0 9 - 2 7 1 0 0 0 9 0 0 1. 2 4 0 P - 2 9 fl 3 = 1 2 ^ 0 o o 1 2 5 0 0 0 9 0 0 1 0 6 0 0 1 - 1 0 3 1 0 0 1 1 9B3D C I - 8 2 8 1 9 - 0 2 8 OOOD 0 1 - 6 0 0 9 0 - 2 3 1 OOOD 0 0 1 . 7 ) 5 9 - 2 5 8 u 5 1 2 5 0 0 0 1 7 5 0 0 0 9 00190D 0 1 - 1 . 5 6 8 0 0 1 2 1 7 0 0 0 1 - 3 2 9 1 D - 0 2 8 OOOD 0 1 4 0 1 0 0 - 1 0 1 OOOD 0 0 1 . 4 1 2 D - 2 1 e 5 5 1 2 5 0 00 2 2 5 0 0 0 9 0 0 1 0 3 D 0 1 - 2 050D 0 1 3 2 2 1 0 0 1 - 8 1 8 6 9 - 0 1 8. OOOD 0 1 1 • 8 1 9 - 1 2 1 o o o o 0 0 3 . 0 7 * 0 - 1 7 8 f> " 5 1 2 5 0 00 3 0 0 0 0 0 11 0 0 1 3 0 D 0 1 - 0 509D 0 1 6 1 9 f D CI - 8 • 2 6 1 D - 0 1 8 OOOO 0 1 1 7 9 1 0 - 0 7 1 OOOD 0 0 6 601)11-17 8 7 5 1 2 5 0 00 9 0 0 0 0 0 9 0 0 0 7 8 D 0 1 - 7 2 9 6 0 0 1 1 0 9 0 0 0 2 - 2 . 1 9 4 0 0 0 B OOOD 0 1 3 8 7 2 9 - 0 3 1 OOOD 0 0 2 9 0 0 9 - 0 7

W N> W


I T E R . a 1IR TIHE'5.900000r-ni PEBIOD'O.758065D -02 TIDE i a c p s « E » T > 5 . 0 0 0 0 0 0 0 - 0 3

I»DT- I-RODE CES 1.0CATI9N

I-LOCATIOH

VATER ELEVATION VELOCITY

I I I J - D I R E C T .

1 H O C IT t IK I-ETRSCT.

HATER ELEV. RATE

OP CHANGE

TPHP. RATE

OP CHANGE

9 1 5 1 7 5 0 . , 0 0 2 5 0 . . 0 0 4 , . 0 0 1 5 1 D 0 1 - 1 , , 2 6 5 D 0 1 2, ,B0 6D 0 0 1 . 0 8 1 0 - 0 1 8 . o o o o 0 1 - 2 , . 2 6 6 0 - 2 9 9 2 l i n o , . 0 0 7 5 0 . , 0 0 0 . . 0 0 1 5 1 0 0 1 - 1 , . 0 2 6 0 0 1 8 . 0 5 1 0 0 0 1 . 4 5 0 0 - 0 1 8 .OOOD 0 1 - 5 . 2 3 3 0 - 2 5 4 3 5 1 7 5 0 . . 0 0 1 2 5 0 . . 0 0 0 , , 0 0 1 5 1 0 0 1 - 1 , , 7 7 9 0 0 1 1, , 3 2 6 0 0 1 2 . 3 4 3 0 - 0 1 8 .OOOD 0 1 . 3 4 2 0 - 2 1 9 1 5 1 7 5 0 , . 0 0 1 7 5 0 , , 0 0 0 , . C 0 1 5 0 D 0 1 - 2 , , 0 5 8 0 0 1 1, . 8 3 6 0 0 1 2 . 3 8 7 0 - 0 1 8 .OOOD 0 1 1 . 8 4 2 D - I 5 9 5 5 1 7 * 0 , . 0 0 2 2 5 0 , . 0 0 0 , . 0 0 1 5 0 0 0 1 - 3 , , 6 9 0 0 0 1 2, . 3 1 2 0 0 1 6 . 6 6 2 0 - 0 1 8 . 0 0 0 0 0 1 1, . 9 5 8 9 - 1 0 4 6 5 1 7 5 0 , . 0 0 3 0 0 0 . . o c 0 . , 0 0 1 5 0 0 0 1 - 7 , . 8 7 9 0 0 1 3 . 3 1 9 0 0 1 8 . 1 0 B D - 0 1 8 .OCOD 0 1 1, . 2 5 2 0 - 0 5 9 7 5 1 7 5 0 . , 0 0 <1000. .00 <1. . 0 0 1 5 6 0 0 1 - 1 , . 3 9 5 0 0 2 5 . 2 0 0 0 0 1 u . 1 9 6 D 0 0 8 . 0 0 2 0 0 1 1, , 2 a a o - 0 2

10 1 5 2 2 5 0 , . 0 0 2 * 0 . 00 4 . , 0 0 1 * 6 0 0 1 - 1 , , 0 6 1 0 01 2. .3000 00 6 . . 7 0 2 0 - 0 2 8, . 0 0 0 0 0 1 - 1 , , 1 5 7 0 - 2 7 10 2 5 2 2 5 0 , , 0 0 7 5 0 , . 0 0 1., . 0 0 1 5 6 0 0 1 - 1 , . 9 9 0 0 0 1 6 . 2 2 9 0 0 0 5 . 5 6 7 0 - 0 2 8. .OOOD 0 1 - 2 . 2 1 4 0 - 2 ) 10 3 5 2 2 5 0 , , 0 0 1 2 5 0 , , 0 0 4 , . 0 0 1 5 5 0 0 1 - 2 , . 2 6 7 0 0 1 9 . 7 8 0 0 CO - 0 . 8 9 2 0 - 0 2 9 . .0000 01 a , .010 0 - 19 10 a 5 2 2 5 0 , , 0 0 1 7 5 0 . 0 0 0 . 0 0 1 5 7 D 0 1 - 2 . 7 8 3 0 0 1 1, . 2 i a n 0 1 - 1 , . 7 3 6 0 - 0 1 8, .OOOD 0 1 8 . , 0 8 5 0 - 1 1 10 5 5 2 2 5 0 . . 0 0 2 2 5 0 . 0 0 0 , . 0 0 1 5 ID 01 - 3 , , 69BD 0 1 9 , , 1 5 6 0 AO 6 . 7 3 4 0 - 0 2 8, . o o o n 0 1 5, , 1 2 2 0 - 0 8 10 6 5 2 2 5 0 , , 0 0 3 0 0 0 . , 0 0 0, .OîBBO 0 1 - 7 . . 2 3 0 0 0 1 3 . 7 8 1 0 CO - 1 . 3 5 3 0 0 0 8 , . 0 0 3 0 0 1 3, , S 3 6 D - 0 * 10 7 5 2 2 5 0 , , 0 0 4 0 0 0 . . 0 0 0. . 0 0 3 6 4 D 0 1 - 1 . . 2 5 1 D 0 2 2 . 6 7 5 0 Ot - 6 , , 3 6 t o 00 fl. . 0 2 1 0 0 1 6 . , 9 6 4 0 - 0 1 11 1 5 2 7 * 0 , , 0 0 2 5 0 . 0 0 4 . , 0 0 1 6 1 0 0 1 - 2 . . 3 2 9 0 0 1 1 . .53CO CO 1, . 0 8 1 0 - 0 1 8 , . 0 0 0 0 0 1 - 1 , , 1 2 5 0 - 2 5 11 2 5 2 7 * 0 , , 0 0 7 * 0 . . 0 0 0 . , 0 0 1 6 ID 0 1 - 2 . . 39BD 0 1 3. . 7 2 8 0 00 5 • 1 5 6 D - 0 2 8 . , 0 0 0 0 0 1 - 6 , . 2 2 0 0 - 2 2 11 3 5 2 7 5 0 . . 0 0 1 2 5 0 . , 0 0 0 , , 0 0 1 6 0 0 0 1 - 2 . . 5 3 0 D 0 1 5 . . 0 0 8 0 0 0 1. , 5 1 6 0 - 0 1 8 , . o o o o 0 1 2 . , 6 6 0 0 - 1 6 11 a * 2 7 * 0 , ,00 1 7 * 0 . ,00 0. 00163D 0 1 - 2 . , 7 3 1 0 0 1 6 . . 6150 0 0 - 1 , , 2 0 2 0 - 0 1 e , , 0 0 0 0 0 1 2 . , 0 9 6 0 - 1 1 11 5 5 2 7 5 0 , . 0 0 2 2 5 0 . . 0 0 4 . . 0 0 1 5 1 D 0 1 - 2 , , 9 5 1 0 0 1 - 1 , . 3 8 0 0 CO 1 . 5 1 5 0 0 0 6, , 0 0 0 0 0 1 2 . 0 0 6 0 - 9 5 11 6 5 2 7 5 0 , . 0 0 3 0 0 0 . 0 0 0 . , 0 0 2 1 3 0 0 1 - 3 . . 1 2 3 0 0 1 - 6 . . 3 6 2 0 0 0 - 3 , , 0 1 1 0 00 8 , , 0 0 0 0 0 1 7 , , 8 9 3 0 - 0 6 11 7 * 2 7 * 0 . 0 0 4 0 0 0 . ,00 0 , . 0 0 5 1 ID 0 1 - 3 , , 1 3 6 0 0 1 0, , 3 5 0 0 0 1 5 . , 8 1 1 0 OO B, , 3 1 3 9 9 1 5 , . 1 2 5 0 0 0 12 1 5 3 2 5 0 , ,00 2 5 0 . , 0 0 0 , , 001670 0 1 - 2 . . 608D 0 1 0 . , 4 4 0 0 ' •01 8 6 5 0 D - 0 2 8 . , 0 0 0 0 9 1 - B , , 5 9 8 0 - 2 3 12 2 5 3 2 5 0 . ,00 7 5 0 , .00 4 . . 0 0 1 6 7 0 0 1 - 2 , , 6 0 8 0 0 1 3 . , 8 0 3 0 - • 0 1 9 , . 2 3 1 0 - 0 2 8, .OOOD 9 1 - 3 . . ) 9 6 D - 1 9 12 3 5 3 2 5 0 , . 0 0 1 2 5 0 . , 0 0 0, • 0 0 1 6 6 D 0 1 - 2 , . 6 0 0 0 0 1 - 3 , , 1 0 6 0 - 0 1 1, , 1 2 0 0 - 0 2 8 , , 0 0 0 0 9 1 1, , 5 1 2 1 1 - 1 0 1 2 u 5 3 2 50 .CO 1 7 5 0 . . 0 0 4 . 00166D 0 1 - 2 , , 0 9 8 0 0 1 - 1 . , 9 6 5 0 0 0 - 8 , . 6 9 4 D - 0 2 8 , . OOOl) 0 1 9 , , 5 9 1 0 - 1 6 12 5 5 3 2 5 0 , . 0 0 2 2 5 0 . . 0 0 4 , , 0 0 1 6 2 0 0 1 - 2 . , 1 1 7 0 0 1 - 9 . , 8 « 9 0 0 1, . 8 6 5 0 - 0 1 8 , .OOOD 0 1 4 , . 2 1 8 0 - 0 6 12 6 5 3 2 5 0 . 0 0 3 0 0 0 . , 0 0 4 , • 0 0 1 9 2 D 0 1 5 . . 1 2 6 0 0 0 - 1 , . 9070 0 1 - 9 . 3 0 2 1 , - 0 1 8 , , 0 0 0 0 0 1 1, , 9 5 6 0 - 0 1 12 7 5 3 2 5 0 , 00 UOOO. . 0 0 4 . .003UUO 0 1 1 . 8 6 1 0 0 1 - 1 , . 4 7 7 0 0 0 - 0 . 5 5 6 0 0 0 8, , OOBD 0 1 3. , 1 1 2 0 - 0 1 11 1 5 3 7 5 0 . 0 0 2 5 0 , . 0 0 0 , . 0 0 1 7 0 0 0 1 - 2 , 0 1 - 7 , . 5 8 1 0 - -CI 1, , 0 1 0 0 - 0 1 8, , 0 0 0 0 0 1 - 2 . , 6 0 7 0 - 2 0 13 2 5 3 7 50 .00 7 * 0 . , 00 0 , .00170D 0 1 - 2 , . 5810 0 1 - 3 , .OBfD c o 1 . . 2 8 0 0 - 0 1 B, . 0 0 0 0 0 1 2, , 5 0 9 0 - 1 ' ' 13 3 5 3 7 5 0 . 0 0 1 2 * 0 , , 0 0 4 , , 0 0 1 7 4 0 0 1 - 2 , , 0 3 6 0 0 1 - 6 , , 2 3 2 b 0 0 1 , 6 5 5 0 - 0 1 8, ,00011 1)1 3. . J 1 4 9 - 1 2 13 a 5 3 7 5 0 . 0 0 1 7 5 0 , , 0 0 0 , . 0 0 1 7 4 0 0 1 - 3 , .10OD 0 1 - 1 . , 0 * 3 0 0 1 1, . 0 1 2 0 - 0 1 8 , , 0 0 0 0 0 1 2 , , o a 6 c - 9 4 13 5 5 3 7 5 0 . . 0 0 2 2 5 0 . 00 «. .001750 0 1 - 1 . . 4 0 0 0 0 1 - 1 , , 7810 0 1 2, , 1 9 0 0 - 0 1 8 , .OOOD 0 1 6 . . 1 0 9 0 - 9 7 13 6 5 3 7 5 0 , ,00 3 0 0 0 , ,00 4 , . 001760 0 1 1, , 317D 0 1 - 2 . , 9 7 1 0 0 1 9 • M B D - O I 8 . 0 0 0 0 0 1 1, , 9 1 8 0 - 0 1 13 7 5 3 7 5 0 , . 0 0 0 0 0 0 . .00 4 . > 0 0 1 0 7 0 0 1 5, 2 1 9 0 01 - 4 , . 2 2 1 0 0 1 1. , 7 2 4 0 00 8 , . 8 0 0 0 0 1 1. , 3 8 6 0 - 0 7 14 1 5 4 2 5 5 . 0 0 2 5 0 . ,00 4 , . 0 0 1 8 0 0 0 1 - 2 , , 0 6 6 0 0 1 - 1 , ,707D 0 0 t , , 0 7 9 D - 0 1 8 , . 0 0 0 0 0 1 - 1 . , 0 8 9 0 - 2 1 14 2 54250 , .00 7 5 0 . ,00 4 , . 0 0 1 8 0 0 0 1 - 2 , , 3 5 0 0 0 1 - 5 . .456D 0 0 1. , 0 9 2 0 - 0 1 8 . .OOOD 0 1 5 . , 5 5 1 0 - 1 7 11 3 5 8 2 5 0 . , 0 0 1 2 5 0 . , 0 0 4 , . 0 0 1 8 1 0 0 1 - 2 . , 0 8 7 0 0 1 - 9 , . 9 2 9 0 0 0 1, , 0 7 5 0 - 0 1 8 . . 0 0 0 0 0 1 5 , , 9 1 9 0 - 1 1 14 4 5 4 2 5 0 , , 0 0 1 7 * 0 . ,00 0 , . 0 0 1 8 2 0 0 1 - 1 , , 6 0 6 0 0 1 - 1 . . 5 6 9 0 ' 0 1 1, , 6 8 3 0 - 0 1 8 . . 0 0 0 0 0 1 3, , 1 0 8 0 - 1 1 14 5 5 4 2 5 0 . . 0 0 2 2 5 0 . .00 4 . . 001B40 0 1 - 8 . . 101D 0 0 - 2 , . 2 1 7 0 0 1 a. , 2 6 6 0 - 0 2 8 , ,0000 o t 8 . , 7 6 2 0 - 0 9 1U 6 5 4 2 5 0 . 00 3 0 0 0 . . 0 0 0 . , 0 0 1 9 1 0 0 1 1, , 0060 0 1 - 2 . , 9 2 5 0 0 1 1, , 3 6 3 0 - 0 2 B, , 0 0 0 0 0 1 1. , 2 2 8 0 - 0 6 l a 7 5 0 2 5 0 , . 0 0 0 0 0 0 . . 0 0 0 , . 0 0 1 9 7 0 0 1 3 , . 0 7 9 0 0 1 - 3 . . 5760 C I 8 . . 2 1 2 D - 0 1 8 . .OOOD 0 1 2. , 0 6 0 0 - 0 1 1 5 1 5 4 7 5 0 . 0 0 2 5 0 . .00 0 , , 0 0 1 6 6 0 0 1 - 2 , . 1 9 7 0 0 1 - 2 , , 0 5 0 0 00 1, , 1 5 7 0 - 0 1 8, , 0 0 0 0 01 - 3 , , 1 2 2 0 - 2 1 1 5 2 5 4 1 5 0 , , 0 0 7 5 0 . . 00 4 , . 001860 0 1 - 2 . , 0 1 6 0 01 - 6 . , 0560 CO 1. , 0 6 7 0 - 0 1 8 , . 0 0 0 0 0 1 - B , , 0 6 1 0 - 2 1 15 3 5 4 7 5 0 . , 0 0 1 2 5 0 , . 0 0 4 , •001B7D 0 1 - 1 , . 7 2 5 0 0 1 - 1 , , 0300 0 1 1, . 0 2 6 0 - 0 1 8 , OOOD 0 1 1, , 1 2 6 0 - 1 6 15 u 5 0 7 5 0 , , 0 0 1750 . .00 4 , , 0 0 1 8 7 0 0 1 - 1 , . 2 0 1 0 0 1 - 1 , . 5 0 5 0 0 1 1, , 1 1 1 0 - 0 1 8, .OOOD 0 1 1, , 1 0 8 0 - 1 ) 15 5 5 4 7 5 0 , , 0 0 2 2 5 0 . . 0 0 4 , . 0 0 1 8 8 0 0 1 - 4 , , 6 3 0 0 0 0 - 1 . . 9 0 20 o t 1, . 0 7 9 0 - 0 1 8 , , 0009 0 1 4, , 1 5 7 0 - 1 1 15 6 5 4 7 5 0 . 0 0 3 0 0 0 . , 00 4 , , 0 0 1 9 1 0 01 7, . 9500 00 - 2 , .1330 0 1 1, , 2 5 1 0 - 0 1 8 , , 0 0 0 9 0 1 8 . , 5 0 2 0 - 0 9 15 7 5 4 7 5 0 . .00 OOOO. ,00 4 . , 0 0 1 9 0 0 0 1 2 . , 0 0 8 0 0 1 - 2 . .0330 o t t . , 5 2 7 0 - 0 1 8 . , 0 0 0 0 0 1 1. , 8 8 1 0 - 0 6 16 1 5 5 2 5 0 , . 0 0 2 5 0 . . 0 0 0 , , 0 0 1 9 2 0 0 1 - 1 , , 9 0 8 0 0 1 - 1 , .90CD 0 0 1, , 2 2 8 0 - 0 1 8, , 0 0 0 0 0 1 - 3 , , 9 3 8 0 - 2 7 16 2 5 5 2 5 0 . . 0 0 7 * 0 . .00 4 . . 0 0 1 9 2 0 0 1 - 1 , . 7 9 3 0 0 1 - 5 , . 5 0 1 0 CO 1 , 2 3 0 0 - 0 1 8 . . 0 0 0 9 0 1 - 1 . , 2 8 9 0 - 2 3 16 3 5 5 2 5 0 . 0 0 1 2 5 0 . ,00 4 , . 0 0 1 9 2 0 0 1 - 1 . , 0 7 7 0 01 - 9 . . 0 2 5 0 0 0 1, . 1 1 0 0 - 0 1 8. • OOOD 0 1 - 1 . 7 1 3 0 - 2 0 16 4 5 5 2 50 , . 0 0 1 7 5 0 , ,00 0 . . 0 0 1 9 3 0 0 1 - 1 , . 0 0 5 0 01 - 1 , . 2 3 2 0 0 1 1. , 1 5 9 0 - 0 1 8 , . 0 0 0 9 0 1 2 , , 1 1 1 0 - 1 6 16 5 5 5 2 5 0 . 0 0 2 2 5 0 . , 00 4 . . 0 0 1 9 3 0 0 1 - 4 , . 0 7 7 0 0 0 - 1 , , 0 6 7 0 o t t , . 1 0 5 0 - 0 1 8 , .OOOD 0 1 1 . , 2 2 1 0 - 1 1 IS 6 5 5 2 5 0 , , 0 0 3 0 0 0 , , 00 0 , . 0 0 1 9 3 0 0 1 4 , , 5 3 6 0 0 0 - 1 , , 4 1 5 0 0 1 1, , 8 5 0 0 - 0 1 S. .0000 o t 3 , , 1 6 3 0 - I t 16 7 55350 , . 00 0 0 0 0 . ,00 4 , . 0 0 1 9 ID 0 1 1, . 190D 0 1 - 1 . , 0 6 1 0 0 1 1 , 4 1 0 0 - 0 1 8, . 0 0 0 9 o t 9 . , 2 8 1 0 - 0 9

SUBSTANCE BASS CCNCEHTRUI0N3

C N | 1 ) CK (21

1 . 0 0 0 9 0 0 1 . 0 0 0 0 - 31 1 .OOOD 0 0 2, , 2 7 6 0 - 27 1 . 0 0 0 0 0 0 2, , 7 1 6 0 - 2 3 1 .0000 0 0 1, . 5 * 7 0 - 19 1 . o a on 0 0 3 . 7 8 2 0 - 1 5 t .OOOD 0 0 5, . 9 * 0 9 - i n 1 . o o o o 0 0 7, . 1 0 1 9 - 0 6 1 .0000 0 0 9 . , 2 2 0 0 - 10 1 .OOOD o o 1 , 9 1 9 D * J 5 1, , 0 9 0 9 0 0 1, , 9 7 9 0 - 2 1 1, . 0 9 0 9 0 0 1, , 2 2 9 0 - 17 1 .OOOD 0 0 7, , 7 5 7 0 - IJ 1 .OOOD 0 0 0 , , 2 5 6 0 - 0 8 9. . 9 9 9 0 ' • 0 1 9 . , 7 0 5 0 - 0 * 1 . 0 0 0 9 0 0 1, , 5 2 6 0 - 2 8 1, .OOOD 0 0 6 . 5 0 9 D - 2 4 1, .OOOD 0 0 6 , , 0 1 3 0 - 2 0 1, . 0 0 0 9 0 0 5 , ,B1RP- 15 1 . 0 0 0 9 0 0 3, , 2 0 1 0 - 10 1, . 0 0 0 9 0 0 2 . , 2 2 5 0 - 0 7 9, . 9B1D-• 0 1 I , 6 0 3 0 - 0 3 1, .OOOD 0 0 1, , 5 7 1 0 - 2 3 1, . 0 0 0 9 0 0 1. , 5 9 3 0 - 2 2 1, . 0 9 0 9 0 0 1, 2 9 5 0 - 10 1, , 0 9 0 0 0 0 5 . 3B9D- 11 1, .OOOn 0 0 t , BJCD- 10 1, . 0 0 0 9 0 0 9 , , 1 3 * 0 " o a 1, . OOOD 0 0 3, , 6 6 1 0 - 0 5 1, . 0 0 0 9 9 0 1, 997D- 2 3 1, . 0 0 0 9 0 0 7 , , 9 6 8 9 - 2 0 1 .OOOD 0 0 1, , 1 S « D - l « 1, • OOOD 0 0 B. , 193D- 14 1, . 0 0 0 0 0 0 2 . , 9 B P 0 - 11 1 .OOOD 0 0 tj , 9 9 2 0 - 04 t .00011 00 1. 0 4 7 0 -Of 1, , 0 0 0 0 0 0 7 , , 9 3 1 0 - 2 5 1, , 0 0 0 0 0 0 1. , 1 9 5 0 - 2 1 1, , 0 0 0 9 0 0 1, 8 0 I P - i a 1. , 9 0 0 9 00 1, , 0 2 6 0 * 15 1. . 0 9 0 9 00 3, 1 8 3 0 - 13 1, . 0 9 0 9 oa 7 , , 1 5 6 0 - 11 1. . 0 0 0 9 0 0 1 . , 1 7 9 0 - OB 1, , 0 0 0 9 00 1, , 6 7 0 0 - 2 7 1. . o o o n uo 1 . , 6 6 3 0 - 2 1 1, , 0 0 0 0 00 5. 912D- 2 1 1, ,0009 0 0 1 , ,2800- IB 1, , 0 0 0 9 0 0 1, 8 I 9 D - 15 1. .OOOD o o 1 . 8 9 1 0 - 13 1, .OOOD 00 1. , 2 2 5 0 - 10 1, .OOOD 00 1. , 7 1 0 0 - 30 t, . 0 0 0 9 00 6 . 6 0 0 0 - 2 7 1, . 0 0 0 9 0 0 1. , 0 9 2 0 - 2 3 1, . 0 0 0 9 0 0 1. , 0 0 5 0 - 2 0 1 .OOOD 0 0 5 , 18 1, , 0 0 0 9 00 1, 0)7(1-15 1 .OOOD 0 0 f , , 1 7 1 0 - 13


l i e T IHC- 1 ) . 9 0 0 0 0 0 0 - 0 1 PBRXOD-4.75a06SD-02 7XHt Z»C*&nEKT-5. 0000000 -03

PElOCIJlr f B I O C I T I RATER E I E » . SOBSTARCf IIASS CORCERTRATJORS IRDI- I- T- RATER III II RATE RITE

BODE CBS IOCATIOR 10CATI0R LLEHTIOR X-DIBECT. I- DIRECT. OP CHARGE 1ERP OP CHAHIIE C«I1> CR 12) 17 1 5(000.00 250 00 11 00200D 01 -1 7319 01 -1 05CD 00 1 .3080-01 8 OOOD 01 -1 1070-10 1 .OOOD 00 4 B20D-34 17 2 56000.00 750 00 0 00200D 01 -1 .6010 01 -0 1700 00 1 .3300-01 8 OOOO 01 -0 791D-27 1 .0030 00 2 M 2 D - 3 0 17 3 •<6000.00 1250 00 0 00 2000 01 -1 3060 31 -6 6050 00 1 ,2660-01 8 OOOO 01 -8 296D-24 1 OOOD 00 5 59'0-27 17 4 16000.00 1750 00 0 002000 01 -9 8570 00 -8 60 20 00 1 3060-01 B OOOD 01 -7 049D-21 1 OOCD 00 6 9770-24 17 5 M000.00 2250 00 0 00200D 01 -5 7010 00 -9 7390 00 1 .2190-01 8 OOOD 01 6 1130-17 1 OOOD 00 5 2420-21 17 6 ••6000.00 3000 00 0 00200D 01 -3 069D 01 -8 5950 DO 0190-01 8 OOOD 01 2 .9980-10 1 OOOD 00 2 0490-18 17 7 56000.00 0000 00 0 .001980 01 U 107D 00 -5 200D CO 1 .0370-01 8 OOOO 01 1 3060-11 1 OOOD 00 1 0280-15 18 1 57000.00 260 00 0 .0G21CD 01 -1 6270 01 -9 2390- 01 1 3690-01 8 OOOD 01 -1 6230- 10 1 OOOD 00 B 4940-38 IB P7000.00 750 00 0 002100 01 - 1 S36D 01 -2 (380 00 1 .3920-01 8 OOOO 01 -9 2680- I t 1 3000 00 S 9100-30 18 3 57000.00 1250 00 0 002100 01 - 1 3620 01 -4 10111 CO 1 .3620-01 8 OOOD 0 1 -7.03)0-17 1 9008 03 1 1650-10 IB 57000.00 1750 00 0 002100 01 -1 1310 01 -5 1250 CO 1 .0310-01 8 0030 01 -2 1510-20 1 0030 30 2 9310-27 18 t 17000.00 2250 0 0 0 002100 31 -8 8760 00 - S 5190 00 1 395D-01 8 O M O 01 -1 3749-21 1 3330 03 2 87J0-24 18 57000.00 3000 00 0 002103 01 - 6 315D 30 - a 5720 CO 1 .5010-01 8 OOOD 0 1 -2 1310-19 1 3000 00 t 6980-21 IS 7 57000.00 OOOO 00 0 002090 31 -3 7 6 7 c 33 •2 3330 03 1 5000-31 8 0030 0 1 7 9750-16 I OOOO 00 9 2110-19 19 1 58000.00 250 03 0 002220 01 - 1 725 D 31 - 5 6310- 01 1 1570-01 8 0030 31 -1 6600-18 t.OAOD 3 3 1 l a J D - * 1 19 5 6 0 0 0 . 0 0 750 03 0 002220 01 - 1 6650 01 -1 5 8 fD 00 1 1710-01 8 1)000 01 -1 1950-IA 1 OOOD 0 0 1 0D5D-37 19 3 68000 .00 1250 0 3 II 302220 3 1 - 1 550 D Ot -2 0260 00 1 5620-31 8 0030 01 -3 3510-11 1 OOOD 00 3 8350-34 19 58000.00 1750. 03 e 002210 01 - 1 013B Ot -2 9600 00 1 199D-01 8 OOOO 01 - « 6160-28 1 0300 00 B M6P-31 19 9 5 8 0 0 0 . 0 0 2 2 5 0 . 00 II 002210 01 - 1 2 7 3 0 01 - 3 11 CD 00 1 189D-01 8 OOOD 01 -1 2400-21 1 OOOD 00 9. 925D-2B 19 58000.00 3000 00 II 002210 01 - 1 1170 0 1 -2 5390 00 1 6390-01 8 OOOD 01 -6,6690-23 1 OOOD 00 7 LB'D-25 19 7 58000.00 0 0 0 0 00 4 0 0 2 2 1 0 01 -9 9720 00 -1 1910 30 1 6210-01 8 0001) 01 0 7750-22 1 0000 00 0 7 4 8 0 - 2 2 20 1 59000.00 250 0 0 a 0 0 2 3 0 0 01 - 1 9770 01 - 3 302D- 01 1 716D-01 8 0000 01 -1 096D-42 1 OOOD 0 0 1 0 6 5 0 - 4 5 20 19000,00 750 0 0 0 .002300 01 - 1 938D 31 -9 192D-C1 1 , 7 2 5 0 - 0 1 8 0300 01 -9.7399-19 1 OOOK 30 1 10(0-41 20 3 59000.00 1250 0 0 0 002300 01 - 1 8690 01 -1 3890 00 1 7210-01 8 OCOD 01 - 1 1500-15 1 ooor> on 1 453D-3B 20 59000,00 1 7 5 0 0 0 0 00 2 3 0 0 01 - 1 .7830 01 - 1 6680 00 1 7020-01 8 OOOD 01 -5 5740-12 1 OOi i) "'u 1 431D-34 30 19000.00 2250 00 0 302340 01 - 1 7010 01 -1 725D CO 1 ,7010-01 8 OOOD 0 1 - a 7260-19 1 2 1570-31 20 59000.00 3000 00 0 002340 01 - 1 613D Ot - 1 37 5D 00 1 .770D-01 8 OOOO 01 -1 1510-26 1 no-.:- 1 9110-28 20 7 19000.00 9000 0 0 0 002300 01 - 1 500 0 01 -6 4170- 01 1 7660-01 9 oooo 01 7 1860-21 )' oot,y 0 0 1 £220-25 31 1 60000.00 210 0 0 0 002070 01 - 2 3360 01 - 1 82 30- CI 1 8720-01 8 oooo 01 -7 9850-42 1 HOOn t>i ~ 49»D-A6 21 60000.00 750 00 0 002070 01 -2 311D 31 - 5 0350- 01 1 878D-01 8 0030 01 - 5 216D-43 1 OD in 00 8 0840-16 21 3 60000 .00 1250. 00 D 00201D 01 -2 267 D 01 -7 508D- o t 1 8 7 8 0 - 0 1 8 OOOO 01 - 1 915D-19 1 OOOO 09 4 7160-42 21 n 60000,06 1750 00 0 <102410 01 -2 / n o 01 -B 965D- 01 1 8910-01 6 OOOD 01 -1 90SL>-IX 1 UQOD 0 0 T 5110-33 21 60000.00 2250. 00 b 002070 0 1 -2 1600 01 -9 n » D - 01 1 8950-01 8 OOOD 01 -0 0070-13 1 oooo 00 2 8450-35 21 60000,00 3000. 00 0 002070 0 1 -2 1 1 1 0 01 -7 262D- 01 1 9120-01 8 0300 01 - 1 1390-10 1 3300 00 1 0840-32 i l 7 60000.00 4C00 00 c 002073 01 -2 0710 CI J 5 « 0 - 01 1 9150-01 * OOOD 01 5 4600-29 1 3000 39 2.9160-29 22 1 61000.00 250 00 0 002610 01 -2 777D 01 -8 65 20- 02 3 0320-01 e OOOO 01 -0 17 ID-JB 1 3030 00 1 9250-42 22 61000.00 750 00 0 002610 01 -2 760D 31 -2 387D- 01 2 0360-01 8 OOOD 01 -3 7460-00 t 11300 30 3 1990-44 22 3 61000 .00 1250 00 It 002610 01 -2 7310 31 - 3 5590- 01 2 0 370-01 8 3030 01 -2 0370-42 1 OOOD 00 3 7250-46 32 61000.00 1750 00 0 00261D 01 -2 6950 0« - 0 1 4 5 0 - 01 2 0060-91 6 3030 31 - 1 2960-40 t OOOD 0 0 8 90/0-43 22 61000.00 2210 00 0 002610 01 - 2 6620 91 - a 274D- 01 2 0510-31 t 11000 OT - t 6230-17 t 9000 00 2 0540-39 22 61000.00 3000 00 0 00 2610 at - 2 &28B 01 - 3 367D-* 01 2 0610-31 8 C03D 31 -5 2010-15 t 0300 00 2 7050-)6 22 7 6 1 0 0 0 . 0 0 0030 00 0 302610 31 -7 6020 3 1 - 1 52 RO- 01 3 .0660-31 8 OOOO 0 1 7 152P-11 1 OOOD 00 3 12 ID-33 23 1 62000.00 2 5 0 . 00 0 002760 or -3 2870 01 - 1 SS 2 0 - 02 2 1950-01 « OOOD „» -1 606P-34 1 0000 00 I 8050-38 23 2 62000.00 750 0 3 0 002760 01 -3 270 0 Ot - 5 4110- 02 2 197D-01 B OOOO .11 -1 5490-16 1 0300 00 1. 55BD-40 23 3 62300.00 1250 00 II 332760 01 -3 2100 31 -8 0S6D- 02 2 199D-0I 8 OOOD 01 -9 0670-)9 1 .OOOD 00 N 3 3 J D - 4 3 23 62000.03 1750 03 0 302760 01 -3 2220 31 -9 5I5D- 02 2 2050-01 8 0030 01 -I 8020-01 1 OBOD 03 1 5370-45 23 62000.00 2250 0 0 0 002760 01 -3 1960 01 - 9 7800- 02 2 2130-01 8 OOOD 01 - 1 1 1 1 0 - 4 2 t ooon 0 0 6 4210 -aa 23 62000.00 3000 00 a 002760 01 -3 1700 01 -7 6800-02 2 2150-01 8 OOOD 01 -2 877P-00 t OOOD 00 1 1140-40 2 3 7 6 2 0 0 0 . 0 0 0 0 0 0 . 00 0 002760 01 -3 1500 01 -3 9630- 02 2 2220-31 8 OOOD 01 a 2250-17 1 0300 90 1 54J0-37 aa 1 6 7 0 0 0 . 0 0 310 00 0 0 0 2 9 2 0 01 - 3 860 D 01 3 B12R-02 7 3600-01 B OOOD 01 - a 603D-11 1 OOOD 00 5 1180-15 29 2 6 3 0 0 0 . 0 0 750 00 a ,002920 ot -3 806D 01 9 9070-02 2 ,3610-01 S OOOO 01 - a 6490-1) 1 OOOD 00 5 460D-17 21 3 6 3 0 0 0 . 0 0 1250 00 a 00292D 01 -3 822 D 01 1 4580- 01 2 3630-01 8 OOOD 01 -3 0 3 B D - 3 5 1 0030 33 3 2170-39 29 63000.00 1 7 1 0 0 0 a 00292D 01 -3 793D 01 1 68 ( 0 - 01 2 1670-01 8 aooo 01 - 6 6940-IB 1 OOOD 30 6 4030-42 2° 63000.00 2250 00 0 002930 01 -3 767 D 01 1 6630- 01 2 3720-01 8 OOOD 01 - 1 3320-40 1 .OOOD 00 1 1910-40 29 6 63000.00 3 0 0 0 0 0 0 0 0 2 9 2 0 01 -3 7010 01 1 2920-C1 2 .3730-01 8 OOOD 01 -5 8230-44 1 OOOD 00 1 2750-45 24 7 63000.00 OOOO 00 a 002930 01 -3 .7220 01 6 7190-02 2 .1820-01 8 OOOD 01 7 .2580-02 1 ooon 0 0 i 2580-42

KJ VI


ITPR.» UX TI»»»C. <51100000-01 prMr)\>.li.7S8D6'D-02 IIPE IHCR1HEHT" ..OOOOOOD'Ol fELOCITY VElOrlTY ES LnrATl flK

6 0 0 0 0 . 0 0 10000.00 60000.00 60000.00 6 0 0 0 0 . 0 0 unoo.oo '0000.00 61000.00 1*0C0.00 61000.oo imoo.oo (-1000.00 61000.00 sioto.oo 16000.00 11000.00 66100.00 Si-000.00 6*000.00 66COO.00 6 6 0 0 0 . 0 0 67000.00 67000.00 67000.00 67000.00 17000.00 67000.00 67000.00 68000.00 6 6 0 0 0 . 0 0 60000.00 18000.00 68000.00 6 8 0 0 0 . 0 0 6 8 0 0 0 . 0 0 69000.00 MO 00,00 69000.00 19000.00 69000.00 69000.00 19000.00 70000.00 70000.00 70000.00 70000.00 70000.00 70000.00 70000.00 70710.00 70710.00 70710.00 70710.00 70710.00 707*0.00 70710.00

Y-10CATICH 2 5 0 . 0 0 7 1 0 . 0 0

1210.00 1 7 1 0 . 0 0 2 2 * 0 . 0 0 1000.00 O000.00

2 * 0 . 0 0 7 1 0 . C j

1 2 1 0 . 0 0 1 7 * 0 . 0 0 2 2 5 0 . 0 0 1 0 0 0 . 0 0 0 0 0 0 , 0 0

2 1 0 . 0 0 7 * 0 . 0 0 1210.00

1 7 * 0 . 0 0 2 2 * 0 . 0 0 3 0 0 0 . 0 0 0000.00

2 1 0 . 0 0 7 1 0 . 0 0 1210.00

1 7 1 0 . 0 0 2 2 * 0 . 0 0 3 0 0 0 . 0 0 0000.00

2 * 0 . 0 0 7 5 0 . 0 0

1 2 * 0 . 0 0 1 7 * 0 . 0 0 2210.00 3 0 0 0 . 0 0 0 0 0 0 . 0 0

2 1 0 . 0 0 7 * 0 . 0 0

1 2 5 0 . 0 0 1 7 5 0 . 0 0 2 2 * 0 . 0 0 3 0 0 0 . 0 0 0000.00

2 1 0 . 0 0 7 1 0 . 0 0

1 2 1 0 . 0 0 1 7 5 0 . 0 0 27 .50 .00 3 0 0 0 . 0 0 0000.00

2 1 0 . 0 0 7 1 0 . 0 0

1210.00 1 7 * 0 . 0 0 2 2 5 0 . 0 0 3 0 0 0 . 0 0 0000.00

MATER ELEVATION 0,00 3080 0.CO 1080 0.001080 0.0030BD 0.001081) u.ooioeo O.C0109D 0.00321D 0.003310 0.00125II 0.001J10 0.001210 0,003210 U.C03250 0.003000 0.00100(1 0.00103D 0.00 3030 0.00303D 0 . 0 0 1 0 30 0.001010 0.003630 0.001630 0,00 3620 0.0(11620 0,001621) 0,003620 0.0036 ID 0.003800 0.00 IBID

WATER .LEV. MVT T1HP. RATE SOBSTARCE HASS CORCERTRATIORS

0.003831) 0 0.00382D 0,00 3820 0 0.0038 ID 0 0.00380D 0 0.00UQ7D 0 0.000070 0 0.000060 0 0.000030 0 0.00001D 0 0.000000 0 0.001990 0 0.00018D 0 0.000190 0 0.000300 0 0,0002ID 0 o,00019D 0 0.00018D 0 0.000170 0 0,000950 0 0.00007D 0 0,000350 0 U.000181) 0 o,000]6D 0 0.000330 0 0.00032D 0

« - JISFC' T-DIPfCI. nr CHARGE TEHP OP CHARGE CRM) CK (?) -0 11930 01 9 69eD-02 .5260-0 I 9 OOOD 01 -9 .3I1D-28 1 ,0000 00 1 390D-31 -0 0 7*0 01 2 1100-01 2 1260-01 8 oooo 01 -1 012D-29 1 OOOD 00 1 001D-33 -0 0010 01 1 701D-C1 2 12BD-0I 8 OOOD 01 -7 61OD-12 1 OOOD 00 9 210D-36 -0 ,U0P0 01 u 1010-01 2 .111(1-01 8 .OOOD 01 -1 B66D-10 1 .00 CD 00 2 OOOD-36 -0 17*D 01 0 21*0-01 2 1360-01 8 000.1 01 -0 022D*37 1 OOOD 00 0 098D-01 -0 1000 CI 3 2610-01 2 1100-01 8 OOOD 01 -2 012D-00 1 OOOD 00 1 929D-0O -0 321D 01 1 578D-01 2 1010-01 8 0000 01 -0 2100-011 1 0000 00 5 002D-08 -1 1010 01 1 6900-01 2 69OD-0I 8 OOOD 01 -1 197D-20 I OOOD 00 J 012D-2/I 1650 01 0 383D-01 2 6920-01 8 OOOD 01 -1 7310-26 1 0001) 00 2 681D-30 -1 i?on 01 6 301D-C1 2 .69011-01 8.OOOD 01 -1 007D-2B 1 ooon 00 1 99 3D-32 -5 0680 01 7 19SD-01 2 699D-0I tl OOOD 01 -3 916D-11 1 oooc 00 0 921D-31 -1 0220 01 6 O89D-01 2 .700D-01 8 OOOD 01 -9 2210-30 1 ooon 00 1 069D-37 -0 .9790 01 1 3020-01 2 .6 190-01 8 OOOD 01 - « 9020-17 1 .ooon 00 1 1170-01 -0 9o7D 01 2 078D-C1 2 ! 120-01 8 OOOD 01 -1 0900-00 1 OOOD 00 1 136D-OU -5 9180 01 2 627D-01 2 P600-01 8 OOflD 01 -1 62ID-21 1 OOOD 00 3 102D-2S -1 9170 01 6 122D-C1 2 8710-01 8 OOOD 01 -2 230D-21 1 OOOD 00 3 9110-37 -1 SoBD 01 9 1O7D-01 2 867D-01 B OOOu 01 -2 1120-21 1 0000 00 3 302D-29 -1 1701) 01 1 0110 CO 2 870D-D1 B OOOD 01 -6 032D-28 1 OOOD 00 9 100D-32 - * 70°D 01 9 5*10-C1 2 8760- 01 8 OOOD 01 -1 6210-30 1 oooo 00 2 143D-30 -1 600 0 01 7 0670-01 / P6RD-01 8 OOOD 01 -9 .1310-10 1 OOOD 00 1 150D-17 -1 601D 01 3 1900-01 2 881D-01 8 OOOD 01 -2 179D-37 1 OOOD 00 2 162D-01 -6 79flD 01 3 OlgD-OI 3 0100-01 8 OOOD 01 -1 1060-18 1 OOOD 00 1 1820-22 -6 7 33 D 01 8 39DD-01 3 051D-01 8 OOOO 01 -2 2000-20 1 OOOD 00 0 011(1-20 -6 620D 01 1 13 ID 00 1 .0190-01 8 OOOD 01 -2 1770-23 1 OOOD 00 0 232D-26 -6 506D 01 1 1660 00 3 0030-01 B OOOD 01 -8 0500-21 1 OOOD 00 1 3020-26 -6 0 16D 01 1 023D 00 1 037D-01 8 OOOD 01 -2 195D-27 1 OOOD 00 3 320D-31 -6 3000 01 7 110D-01 1 .02BD-01 8 OOOD 01 -1 161D-.10 1 OOOn 00 1 921D-30 -6 208D 01 3 129D-C1 3 011D-01 8 OOOD 01 -3 3720-30 1 OOOD 00 0 096D-38 -7 6830 01 0 070D-C1 3 1210-01 8 OOOD 01 1 021D-10 1 OOOD 00 2 1970-19 -7 5720 01 7 627D-01 2 R90D-01 B OOOD 01 2 661D-16 1 OOOD 00 3 9020-21 -7 0090 01 8 9720-01 J 0233-01 8 OOOD 01 -2 0620-19 1 0000 00 u 2220-23 -7 2*8D 01 7 110D-C1 3 199D-01 B OOOD 01 -7 T7ID-22 1 OOOD 00 1 0090-25 -7 1110 01 0 1250-01 3 2000-0' 8 OOOD 01 -2 290D-20 1 OOOD 00 u 0110-28 -7 07*D 01 1 7O2D-01 3 176D-01 8 OOOD 01 -1 5070-27 1 OOOD 00 2 500D-31 -7 078D 01 8 1610-02 3 2010-01 8 OOOD 01 -4 0800-11 1 OOOD 00 6 190D-31 -R 580D 01 1 0300 00 3 0170-01 a OOOD 01 1 86 ID-11 1 OOOD 00 1 706D-16 -8 1190 01 -1 1290-01 3 1800-01 8 OOOD 01 2.8920-1) 1 OOOD 00 2 706D-18 -8 1510 01 -1 6230 00 3 0700-01 a 0000 01 3 3590-15 1 ooon 00 3 3030-20 -8 0050 01 -2 k 0 2 o 01) 3 507D-01 8 OOOD 01 -1 700D-19 1 OOOD 00 1 263D-22 -7 9 30 0 01 -2 363D 00 3 177D-01 a nooD 01 -1 8070-21 1 OOOD 00 3 787D-35 -7 9050 01 - » 8850 00 3 5360-01 a 0000 0 1 -1 360D-20 1 OOOD 00 2 567D-2P -7 8960 01 -6 91eD-C1 1 1030-01 a OOOD 01 -3 8830-20 1 OOOD 00 6 789D-32 -9 8690 01 -1 633D 00 8 1295-01 8 ooon 01 9 1760-09 1 OOOD 00 9. 09BD-10 -9 355B 01 -6 673D 00 8 121D-01 H OOOD 01 1 3670' 10 1 OOOD 00 1 5JOD-11 -B 980D 01 -1 0160 01 1 lf.OD-01 u OOOD 01 1 891D-12 1 OOOD 00 2 029D-17 -8 8B9D 01 -1 1070 01 3 .6880-01 a OOOD 01 8 J82D-15 1 ooon 00 a 603D-20 - 8 916D 01 -1 OOOD 01 3 .9080-01 8 OOOD 01 -1 10CD-18 1 OOOD 00 2 7730-22 -0 983D 01 -6 90 ID 00 3 7270-01 a OOOD 01 -9 3870-32 1 0900 00 2 0500-25 -9 0320 0( - 2 1990 00 3 6000-01 a 0000 01 -2. 8800-25 1 OOOD 00 5. 7970-29 - 8 «81D 01 -7 817D 00 - 2 .9100 00 8 OOOD 01 2 0170-06 1 OOOD 00 3 951D-11 -8 9100 01 -1 5670 01 -6 0070-01 8 OOOD 01 0 5370-00 1 OOOD 00 6 6010-13 -9 2620 01 - 2 10 ID 01 6 1B9D-02 a OOOD 01 6 H31D-10 1 OOOD 00 9 305D-15 -9 1610 01 - 2 21BD 01 2 0280-01 a OOOD 01 3 600D-12 1 OOOD 00 0 392D-17 -9 8100 01 -1 926D 01 2 .2100-01 B OOOD 01 1 370D-10 1 OOOD 00 1 10BD-19 -9 9990 01 -1 277® 01 1 03)0-01 a 0000 01 -0 7610-19 1 OOOD 00 1 321D-22 -1 ,011D 02 -3 593D 00 3 .123J-01 B OOOD 01 -1 197D-22 1 OOOD DO 3 1100-26


ITER** l i e TIRE'S.9000000-01 PERIOD*".7500650-02 TIRE I0CRERENT-5.OOOOOOD-Oi

PI- 1 -f. S LOCATION

T-LOC1TION

NATER ELEVATION

VELOCITY TN

J-DIBECT.

VELOCITY I» I-PIRIC1.

WATER ELEV. RATE

OP CHANGE

13 1 7 1 2 5 0 00 250 0 0 9 00097P 0 1 - 7 6 2 8 0 0 1 - 1 0 1 ( 0 02 2 759D 00 33 2 7 1 2 5 0 00 750 00 9 0 0 9 3 9 0 0 1 - 8 95111 0 1 - 7 6 0 * 0 01 7 706P 00 33 3 7 1 2 5 0 00 1250 00 9 0CB3B0 0 1 - 1 0 0 9 0 02 - 5 5210 01 2 0 2 0 0 00 33 a 7 1 2 5 0 00 1750 00 0 009000 0 1 - 1 0 6 2 0 02 - 9 0 6 1 0 01 1 01811 00 33 5 7 1 2 5 0 00 2 2 5 0 0 0 11 0 0 ( 9 2 0 0 1 - 1 OBRO 02 - J 015D 01 7 OOOD-O1 33 6 7 1 2 5 0 00 3 0 0 0 00 9 0000 30 0 1 - 1 1020 02 - 1 8 3 9 0 01 0 3 1 ) 0 - 0 1 31 7 7 1 2 * 0 00 9 0 0 0 00 9 0 0 ( 9 30 0 1 - 1 109P 02 - 9 7 5 6 0 00 0 7 8 9 D - 0 1 30 1 7 1 7 5 0 . 0 0 2 5 0 00 9 00326P 0 1 - 1 5210 02 - 1 8320 02 8 2 1 9 0 - 0 1 19 2 7 1 7 5 0 00 750 00 9 0 0 0 1 3 0 0 1 - 1 o o o o 02 - 1 2 6 7 0 02 - 3 9790 00 39 3 7 1 7 5 0 00 1250 00 a 0 0 ( 3 8 0 0 1 - 1 3720 02 - 7 96811 01 - 2 6180 OO 39 9 V1750 00 1750 00 0 00939P 0 1 - 1 3 IP D 02 - 5 . 0 1 9 0 01 - 0 I 7 I D - 0 I i « 5 7 1 7 5 0 OO 2 2 5 0 00 9 0 0 0 0 6 0 0 1 - 1 2770 02 - 1 3680 01 - 0 2 7 8 0 - 0 2 39 6 7 1 7 5 0 00 1000 00 9 009520 0 1 - 1 2060 02 - 1 90 10 01 1 2 8 0 0 - 0 1 39 7 7 1 7 5 0 00 9 0 0 0 00 9 C005UO 0 1 - 1 . 2 2 6 0 02 - 5 0970 00 1 1 0 1 0 - 0 1 35 1 7 2 2 5 0 00 250 00 9 0 0 9 1 5 0 n i - 2 09BD 02 - 6 8 0 0 0 01 5 I 51P 00 35 2 7 2 2 5 0 00 ••50 00 9 0 0 9 5 3 0 0 1 - 2 o a i o 02 - 5 1B7P 01 1 99RD 00 35 3 7 2 2 5 0 . 0 0 1250 00 9 009600 0 1 - 1 7090 02 - 3 7109 01 2 ) ' I9D 00 35 9 7 2 2 5 0 00 1750 00 9 000620 0 1 - 1 5630 02 - 2 0B7[> 01 7 8 0 2 0 - 0 1 15 5 7 2 2 5 0 00 2 2 5 0 00 9 001-600 0 1 - 1 0 5 2 0 02 - 1 6 5 0 0 01 n 6 1 0 R - 0 I 35 6 7 2 7 5 0 00 3000 00 0 0 0 0 6 6 0 0 1 - 1 3780 02 - 9 758D 00 5 152D-01 35 7 7 2 2 5 0 00 OOOO 00 9 00067D 0 1 - 1 310P 02 - 3 o n o n 00 0 5 2 1 0 - 8 1 36 1 7 2 7 5 0 00 250 00 9 00712D 0 1 - 2 966D 02 5 6 5 2 0 01 - 9 B9an oo 36 2 7 2 7 5 0 . 0 0 750 00 a 005170 0 1 - 2 0 6 2 0 02 5 8 7 r p C1 - 1 2 8 2 0 00 36 1 7 2 7 5 0 00 1250 00 a 0 0 0 8 1 0 0 1 - 1 751P 02 3 3650 01 - 1 8 5 0 0 - 0 1 16 9 7 2 7 5 0 oo 1750 00 9 009910 0 1 - 1 597D 02 1 079D 01 - 5 l o i n - n i 36 5 7 2 7 5 0 oo 2250 00 a 009B50 0 1 - 1 0 9 m 02 8 6HC1) CO - 1 o o t n - o i 16 6 7 2 7 5 0 00 1000 00 0 0098 IP 0 1 - 1 0 35P 02 3 BR90 00 3 1 5 0 D - 0 I 16 7 7 2 7 5 0 00 ODOO 00 9 00079P 0 1 - 1 390P 02 9 3580 02 3 738P-0I 37 1 7 3 2 5 0 00 250 00 9 009150 0 1 - 1 0 3R0 02 7 7670 01 8 8510 00 37 2 7 1 2 5 0 00 750 00 9 005600 0 1 - 1 . 0 6 0 0 02 1 052D 02 - 1 2600 00 37 1 7 3 2 5 0 00 1250 00 0 0 0 0 9 2 0 0 1 - 1 069P 02 7 190D 01 1 B65P 00 3 / 9 7 1 2 5 0 00 1750 00 a 00511D 0 1 - 1 9 r -60 02 3 6H50 CI 1 010D 00 37 5 7 3 2 5 0 00 2250 00 9 005010 0 1 - 1 OIBD 02 2 5120 01 1 I70D 00 37 6 7 3 2 5 0 00 1 0 0 0 00 0 00095P 0 1 - 1 9 2 0 0 02 t 32in 01 7 5 2 5 H - 0 I 37 7 7 3 2 5 0 00 OOOO 00 a 00 0920 0 1 - 1 007P 02 2 0270 00 0 B1BD-01 38 1 71750 oo 250 00 0 006720 0 1 - 6 202P 01 6 555n 01 - 7 2170 00 38 2 7 1 7 5 0 00 750 00 0 005290 0 1 -9 8190 0 1 7 59RP 0 1 - 8 9 1 5 0 - 0 2 3R 1 71750 00 1250 00 9 005070 01 -1 2250 02 5 5290 01 2 0 3 7 D - 0 1 38 a 7 1 7 5 0 00 1750 00 a 005150 0 1 - 1 1180 02 l 629P C1 - 0 7060-01 38 5 7 3 7 5 0 00 2 2 5 0 00 a 005090 0 1 - 1 1660 02 2 7150 01 0 O82D-07 38 6 7 3 7 5 0 00 3000 00 9 005070 0 1 - 1 1090 02 1 .600D 01 0 2080-01 18 7 71750 0 0 6000 00 a 0O50»J> 0 1 - 1 005D 02 1 56CI) 00 0 0 9 2 0 - 0 1 19 1 7 9 2 5 0 00 250 00 9 00969P 0 1 -7 7010 0 1 3 5 7.ID C1 2 929D 00 39 2 7 9 ? 5 0 00 750 00 9 005100 0 1 -1 0 2 2 0 02 3 219P 01 1 5260 00 39 3 7 9 2 * 0 on 1250 00 a 0 0 5 2 ) 0 0 1 -1 2 0 5 0 02 ? P06P 01 7 6 R I D - 0 I 39 a 7 0 2 5 0 00 1750 00 9 00519D 0 1 - 1 2900 02 2 562n 01 1 7 1 8 0 - 0 1 39 5 7 8 2 5 0 00 2250 00 9 0 0 5 1 8 0 0 1 - 1 3060 02 2 189P 01 5 6 2 2 0 - 0 1 19 5 7 9 2 5 0 00 3000 00 0 0 0 5 1 9 0 0 1 - 1 3890 02 1 0 220 01 0 8 6 0 D - 0 I 39 7 7 0 2 5 0 on 9 0 0 0 00 9 005190 0 1 - 1 0090 02 3 8730 00 0 0 9 8 0 - 0 1 90 1 7 9 7 * 0 00 2 * 0 CO a 005170 0 1 - 1 1920 02 1 1710 01 8 2 3 1 D - 0 1 90 2 7 0 7 5 0 00 750 00 9 0050 00 0 1 - 1 1980 02 1 6810 0 1 - 3 5 7 6 0 - 0 1 90 1 7 9 7 5 0 00 1250 00 9 005170 0 1 - 1 2670 02 2 01 1 0 9 0 D - 0 1 90 9 70 750 00 1750 00 a 00519P 0 1 - 1 1220 02 1 •V. . t 01 6 1 3 7 0 - 0 1 »0 5 7 9 7 5 0 00 2250 00 a 005100 0 1 - 1 1660 02 1 6 5 ID 01 0 8 6 2 0 - 0 1 90 6 7 9 7 5 0 00 3000 00 a 0 0 5 1 9 0 0 1 - 1 ooon 02 1 11511 01 0 2 5 1 D - 0 1 90 7 7 9 7 5 0 00 9 0 0 0 PO a 00 5 3 or, 0 1 - 1 0 2 2 0 02 3 B120 00 0 1 6 9 0 - 0 1

IE IIP. RATE

SUBSTANCE HAS5 C0NCENTRAT1ONS

TEnPi o r CHANGE CR(1 | CR (2)

8 , , 0000 0 1 2, , 9 3 9 0 - 00 1, , ooon 00 9. ,207D- 09 a, > OOOD 0 1 5, . 8 2 2 0 - 05 1, , o o o n 00 1, , 292P- 10 8, , OOOD 0 1 9 , 1 7 1 0 - 08 1. .OOOD 00 1, , 7 0 6 0 - 12 8. , 0000 0 1 5, , 6 6 2 0 - 10 1 .OOOD 00 P, , 6 0 6 0 - 15 B, , OOOD 0 1 2, ,U19D- 12 1. . OOOD 00 1. , 198D- 17 fl, , OOOD 0 1 1 , 9 2 6 0 - 15 1 .OUOP 00 7, ,R61D- 20 8, , OOOD 0 1 -3, .076D- 20 1, .OGOD 00 9, ,085D- 20 A .OOOD 0 1 1 . 8 0 1 0 - 02 1, , 0 0 0 0 00 6, I895D-07 8. , OOOP 0 1 1, , 9 3 7 0 - ON 1, .OOOD 0 0 1. ,3I3D- OA n, , OOOD 0 1 7 , 0 0 2 0 - 05 1, , 0 0 0 0 00 1, , 966P- 10 B. .OOOD 0 1 5 . 9 7 0 0 - 08 1, ,OOOD 00 1, ,1S1D- 12 A, , OOOD 9 1 2, , 9 8 9 0 - 10 1, , 0 0 0 0 00 0, ,R60D- 15 8, , OOOD 0 1 1 , 6 0 6 0 - 11 1, , OOOD oo K l ,035D- 18 N , OOOD 0 1 - 5 . 5 1 5 0 - 18 1, , 0 0 0 0 00 i, ,B77D- 21 H ,0000 0 1 1, , 0 1 2 0 - 01 1, .000D 00 2. D36P- 05 8. .OOOD 0 1 1 • 2 7 0 D - 02 1, . 0 0 0 0 00 5, , 27 7P-07 8, , OOOD 01 3, , 5 7 9 D - 00 1, • 0000 00 1, ,159P-OR a. , 0000 0 1 1, , 8 6 0 0 - Of 1, 0300 00 9 . , 58 f t p - 11 8, , 0000 0 1 2, , 9 7 7 D - 09 1, ,ooon 00 5 . 0920- 13 8, ,0000 0 1 1, , 7 5 7 p - 11 1, . o o o n on 6. , 097D-16 a, , OOOD 0 1 1, , 7 6 6 0 - 19 1, , 0 0 0 0 00 2, , 8 3 1 0 - 19 8. , 050P 01 2, ,06BD 00 9. ,9970* •01 2. 5 1 2 0 - 00 9, , 003P 0 1 2, , 1 3 8 0 - 01 1, .ooon 00 1. , 3 6 2 0 - 05 8 .OOOD 0 1 9 , 5 7 0 0 - 01 1, ,00011 00 0, , 6 1 7 0 - 07 8, ,000P 0 1 1 .5000- 00 1, .ooon 00 5. ,701P- 00 8, ,0000 01 1, , JO f lp - 06 1. .0000 00 1. ,8880-11 R , OOOD 0 1 2 . 6 8 8 0 - 09 1. .ooon 00 6. , 205P- 10 B. , OOOP 0 1 1 • 619D-12 1, . o c o n 00 3, , 2 0 1 0 - 17 8, , 602D 0 1 7, , 2 9 5 0 00 9, .9720-•01 7. Bonc-03 8, , 0 5 1 0 0 1 1 .166D 00 9 .998D* •01 2, , 0 0 0 0 - 00 8. , 003D 0 1 1, . 5 0 8 D - 01 I , . 0 0 0 0 00 1. ,189D-05 8, , OOOD 0 1 1, ,O90D- 01 1, , 0000 00 2 . 10BD- 07 8, .OOOD 0 1 a, ,0090- 05 1, .OOOD 00 1, , 8 6 0 0 - OO 8. ,0001) 01 fl, ,5780-08 1, , 0 0 0 0 00 3, ,561D- 12 8. OOOP 0 1 7, , 9 3 0 0 - 11 1, , OOOD 00 2 . 3560- 15 3, , 010D 0 1 - 5 , •600D- 0 1 1, ,OOOD 00 9. ,553D- 05 8, , OOOD 0 1 i. , 079D-02 1. . o o o n 00 1. 7100- 06 a. OOOD 0 1 1. , 1 9 9 0 - 00 1, ooon 00 3 . 167D- 08 B, .OOOD 0 1 o, , 1 2 0 0 - 06 1. ,oo on 00 2. , B60D-10 a, ,oooo 0 1 1. , 0 7 7 0 - 08 1, ,onon 00 1. 530D- 12 N , OOOD 0 1 7, , 7 9 0 0 - 11 1, .OOOD 00 2. , 606P- 15 8, , 0 0 0 0 0 1 5 . 5 8 0 0 - 19 1, .OOOD 00 1, , 57BD-18 H. , OOOD 0 1 - 6 . . 7 0 7 0 - 00 t . ,0000 00 1. 50 5 0 -Of 8, , OOOD 0 1 2, . 0 2 2 0 - 09 1. .ooon 00 1. 173D- 08 8, , OOOD 0 1 1 , 5 2 2 0 - 06 1, .ooon 00 1, , 26 *D - 10 8, OOOD 0 1 1, , 6 8 5 0 - 08 1. .OOOD 00 2. , 302P-12 3, , 0 0 0 0 0 1 2, , 9 9 2 0 - 10 1, .OOOD 00 1. 110D- 10 8. , OOOD 0 1 0, . 6 9 0 D - 11 1, .ooon 00 1, , 702D- 17 8, , OOOD 0 1 ), , 0 7 0 0 - 16 1, .OOOD 00 1. 117P- 20 8, , OOOD 0 1 - 1 , , 1 6 2 0 - 06 1, ,OOOP 00 6, ,536P-09 A. OOOO 01 2, ,133D- 07 1, , OOOD oo 7. , 353P- 11 8 , OOOD 0 1 r, t ,B 1 9 0 - 09 1, .0000 00 5, R03P- 13 8, , OOOD 0 1 5, , 2 7 5 0 - 11 1, , 0000 00 3. , 36BD- 1* 8 , ,0000 0 1 2. , 5 8 2 0 - 13 1, .OOOD 00 1. 372P- 17 A. .OOOD 0 1 1, , 6 0 1 0 - 16 1, .ooon 00 1, 87BP- 20 9, , OOOD 0 1 - 1 . 1 I S D - 20 1 .OOOP 00 1, ,1030- 23

W to


R R " . ' TIN TII»«5.ooooo9n-ni rrBTOD"u.7*iot,o-')2 TINE I»CB"IIR*R«'. .000h ion-c 1 VFICCITY V F t n C l T Y NAT « 5 I F » .

1 7 1 - 1- 1- NATFP I N IN 1ATE NODE ES i n r A T i m i UICAT10H ILTVAIION 1 - 0 1 F * C T . r - r m n . OF r M * i ' . s 7F1P

UL 7 5 2 5 0 . 0 0 2 * 0 00 A CC5509 0 1 - 1 2619 02 3 00 it 1U«| i -01 B 0099 0 OI 7 * 2 * 0 00 750 00 0 0 0 5 0 6 0 01 -1 7P7P 02 9 1 * 7 0 on 2 . 0 1 * 0 - 0 1 8 o n o n 0 h i 752*0 00 1210 110 u 005U7D 01 -1 1760 02 1 ? « w 01 a . 9 1 . 1 9 - 0 1 B OCOP 0 m 7*7'0 .00 1710 00 0 005U70 01 -1 3f ° 9 02 1 29«n 01 1 ,I28'-0I •1 0(109 n u i 7*2*0 00 2 7 * 0 00 0 0 0 5 0 8 9 0 1 -1 0010 02 T N * N 0 1 U . M o r - o i H c o o n 0 OI 7 * 7 5 0 00 l o o n o n 0 a o s u p o 0 1 - 1 0 279 07 B ORen CO 0 .7070-01 rt 0009 11 01 7 5 2 ' 0 0 0 u n o o o n a C0518P 01 -1 0 0 * 0 0: 1 21'T> CO U . ' U 9 - 0 I fl o o n n 0 02 7 5 7 5 0 00 2 * 0 00 u 0 0 5 6 2 9 0 1 - 1 l " . p 02 2 1810 CO 1 ,7711-01 H COOP .7 02 75">50 00 7 * 0 00 0 0 0 5 6 1 9 0 1 - 1 3769 02 5 * 1 i n on 5 6 * ID - f l 1 B C19D 0 02 7 1 7 * 0 00 1 2 * 0 0 0 0 005610 01 -1 1999 0 7 7 a p * p 00 a .00111-01 II o o o n 0 <•2 7 * 7 * 0 00 1750 09 0 0 0 5 6 2 0 01 -1 171 0 01 n 0 )»0 00 4 .4 1*0 - 0 1 8 o c o n 0 at 7 * 7 * 0 00 2 7 5 0 0 0 0 0 0 5 6 2 9 01 -1 0079 02 7 * 5 1 9 00 0 0 1 6 9 - 0 t 4 c o o n 0 112 7 * 7 * 0 0 0 1000 0 0 0 0 0 * 6 2 9 01 -1 06 * 0 0 7 * " 1 1 1 c n 0 , r (17 0 - 01 N o n o n 0 12 7 * 7 * 0 0 0 1 0 0 0 no 0 0 0 5 * 2 0 01 -1 U 700 n2 2 1621) 00 4 ' . a u o - O l R 00011 9 N 7 1 7 * 0 00 250 00 0 00 5769 01 -1 U 0 0 1 0 2 1 o o u n c n u f 5 0 9 - 0 1 B 0909 0 U) 7 6 7 * 0 0 0 7 * 0 00 0 0 0 5 7 6 9 01 -1 0 * 7 1 02 1 i f l f n CO U l u t m - o t B o n n p 9 03 76 2 * 0 0 0 1210 0 0 u 005760 01 -1 0700 02 0 0 2 * 0 00 0 6 6 6 D - 0 1 rt o o o n 9 1 ) 7 6 7 * 0 00 1750 00 0 005760 01 - 1 0B6B 02 0 97S9 09 0 * ' , 2 0 - 0 1 8 0099 0 43 1T?10 0 0 7 2 5 0 00 U 0 0 5 7 6 9 0 1 -1 0 9O0 02 u B * c n 00 II .( 110-0 1 8 o o o n 9 13 7 6 2 * 0 00 3000 00 u 00576 0 01 -1 * t i n 0 2 3 6 * 7 0 0 9 It M . u n - 0 1 1 o o o p 9 a i 7 * 2 * 0 00 0 0 0 0 00 0 0 0 5 7 6 9 01 - 1 *?10 n7 1 *B8D 00 II 6 7 0 9 - 0 1 B 0C09 9 t i l 767S0 00 2 5 0 00 U 0 0 5 9 0 9 0 1 - 1 * 2 u o 02 6 027D- 0 1 0 I 2 i n - f l i A 0090 0 lib 7 6 7 * 0 00 7 * 0 00 0 9 0 5 9 1 9 0 1 - 1 * 2 8 n 02 1 7730 CO a . 7 4 1 0 - 0 1 tl o n o o 0 ab 7 * 7 * 0 0 0 12*0 00 0 0059171 0 1 -1 1 i 7 r 02 2 * f l 10 09 0 7100-01 8 OG'.'P 9 1 1 7 6 7 * 0 00 1 7 * 0 00 u 0 0 5 9 1 9 0 1 - 1 5060 C2 2 Q7cn CO u 7 5 0 9 - 0 1 9 o n o n 9 au 7 6 7 * 0 00 2 2 * 0 00 0 0 0 5 9 1 9 0 1 -1 1159 02 2 9269 00 0 7 7 8 9 - 0 1 B o o o o 0 an 7 6 7 * 0 00 i n n o n o 0 0 0 * 9 1 9 a t -1 5600 02 2 2329 09 u 756D-01 B OOOD 9 on 7 1 7 * 0 00 UOOO 00 u 0 0 5 9 1 9 0 1 -1 *70D 02 a 9 0 1 0 . 01 0 71BD-01 a OOOD 0 a s 7 7 7 * 0 00 2 * 0 00 a 0 0 6 0 * 9 0 1 -1 *9?D n 2 ) 2120- 01 0 B 7 3 9 - 0 1 8 o o o o 0 a s 7 7 2 * 0 00 7*0 oa U 0 0 6 0 * 9 0 1 -1 5»*I> n2 9 Ofl t o - 0 1 It 1 1 1 0 - 0 1 G o o o o 0 a s 7 7 7 * 0 0 0 1 2 * 0 00 0 0 0 6 0 * 9 01 -1 6010 02 1 OL 09 00 u 8 1 9 9 - 0 1 B 0900 0 a s 7 7 2 5 0 0 0 1 7 * 0 00 0 0 0 6 0 * 9 0 1 -1 6070 02 1 6379 09 * . B 5 5 1 - 0 1 B o o o o 0 US 7 7 7 5 0 00 2 2 5 0 00 0 0 0 6 0 5 9 01 - 1 6 1 3 0 02 1 6 2 0 9 00 0 •B52D-0I 8 OOOD 0 a s 7 7 2 ' f l •Oil i o n o 00 0 . 0 0 6 0 * 9 0 1 -1 . 6 2 0 9 02 1 2 1 1 9 00 0 . B 3 0 D - 0 1 9 0 0 0 0 0 05 7 7 7 * 0 .00 UOOO 00 a 00605D CL -L . 6 2 0 0 02 5 6 7 2 D - C 1 0 .B11D-0I 8 o o o o 0 46 7 7 7 * 0 Off 2 5 0 00 JI 00620O o t - 1 6 5 0 9 02 1 0 5 0 9 - 0 1 0 9 5 O : i - 0 l n oooo 0 16 7 7 7 5 0 00 7 * 0 00 0 00620D 0 1 -1 6 6 9 0 02 0 * o 7 n - 01 •0 . 9 1 7 0 - 0 1 8 oooo 0 06 7 7 7 5 0 00 1750 n o 0 006201) 0 1 . 1 6600 02 6 91 1 9 - 0 1 It 9 5 1 D - 0 1 B o o o o 9 a* 7 7 7 * 0 00 1 7 * 0 00 u 0 0 6 2 0 0 0 1 ' i «690 02 fl 0 7 * 9 - CI 0 , 0 0 8 0 - 0 1 B oooo 0 06 7 7 7 5 0 n o 2250 00 0 0 0 6 2 0 9 0 1 - 1 6 7 0 0 02 8 02C9- 01 0 9129-01 8 o o o n 0 06 7 7 7 5 0 00 1000 00 0 0 0 6 2 0 0 0 1 - 1 6 7 9 9 07 6 2 0 0 9 - 0 1 <1 <1319-01 B 0 0 0 0 0 16 7 7 7 * 0 00 0 0 0 0 00 0 00 6 209 0 1 • 1 6820 02 2 RO'O- 01 II 9 1 6 0 - 0 1 8 o o o o 0 a ? 7 8 2 5 0 00 2 * 0 00 0 0 0 6 3 5 9 0 1 - 1 7 2 2 9 02 7 0 2 6 9 - 02 5 0 2 1 D - 0 1 8 OOOP 0 07 7 8 2 5 0 00 750 00 0 0C61SD 0 1 - 1 7 2 0 0 02 2 1 5 2 n - 0 1 5 0 2 7 0 - 0 1 8 OOOO 0 07 7 8 1 * 0 0 0 1210 00 0 00635B 0 1 • 1 727D 02 1 71C9- CI 5 0 2 9 0 - 0 1 8 ooon 0 07 7 8 2 5 0 00 1 7 * 0 00 u 0 0 6 3 5 0 0 1 • 1 7310 02 3 7 1 2 9 - 0 1 5 0 2 1 D - 0 1 B o o o o 0 07 7 8 7 5 0 00 7 2 1 0 00 0 0 0 6 1 5 9 0 1 • 1 73*0 02 1 8 0 0 9 - 01 1 0 2 3 0 - 0 1 8 OOOP 0 07 7 8 2 5 0 00 3000 00 0 0 0 6 3 5 0 0 1 - 1 7 0 0 0 02 2 9 1 6 9 - 01 5 0 2 ) 0-01 B OOOD 9 07 7 8 2 5 0 00 u o n o n o 0 0 0 6 3 5 0 0 1 - 1 7030 0 2 1 2 6 0 9 - 01 5 n 2 i D - 0 1 a 0 0 9 9 9 08 81 * 0 0 00 2 * 0 00 u 0 0 7 9 * 9 0 1 - 2 . 3 8 1 0 02 2 7 8 8 0 - 02 r, . 0 4 1 0 - 0 1 8 0000 0 as 8 ) 5 0 0 . 0 0 750 00 u 0 0 7 9 5 0 0 1 - 2 3B10 02 8 36SD- 02 1 . 0 4 1 0 - 0 1 8 o o o o 9 08 8 3 1 0 0 . 0 0 1250 00 0 . 0 0 7 9 5 0 0 1 -2 .3880 02 1 2U09-01 5 . 0 1 1 9 - 0 1 8 OOOD 9 08 8 ) 1 0 0 00 17 *0 00 0 0 0 7 9 * 0 0 1 - 2 1910 02 1 0 5 5 9 - 0 1 5 . 0 1 1 0 - 0 1 8 o o o o 0 08 8 1 1 0 0 . 0 0 2250 00 0 0 0 7 9 * 9 0 1 - 2 390D 02 1 5 0 1 9 - C I 1 . 0 1 1 9 - 0 1 8 OOOD 0 08 B H O O 00 3000 00 0 0 0 7 9 5 0 0 1 - 2 . 3 9 7 0 02 1 1639-CI r, . 0 1 6 0 - 0 1 8 OOOP 9 0 9 8 1 1 0 0 . 0 0 OOOO 00 0 0 0 7 9 5 0 0 1 - 2 OOOD 02 0 6 1 7 9 - 0 2 * , 0 1 5 0 - 0 1 8 o o o n n

TCBP. SUBSTANCE nASS CONCENTRATIONS RATE

0 ? rHANOB c K i n r i m

- 1 0 0 0 0 - 0 0 1 0 0 0 9 0 0 p 7 9 0 D 12 7 0 7 7 9 - 19 1 OOOn 0 0 7 MOD 10 1 2 2 ) 0 - 12 1 9 0 0 9 0 0 0 11PD 16 2 0 2 5 9 - lu 1 0 0 0 9 0 0 2 1 0 5 0 IP ft 2 I 2 H - 17 1 0 1 0 9 0 0 6 9 6 0 9 21

- 1 o o 19 2 1 1 9 9 0 9 0 0 7 7 7 9 0 20 - 1 0 H 7 P - 2 0 1 0 0 0 9 0 0 1 0 6 5 0 2 7 - u 6 0 9 9 - 12 1 0 0 0 9 0 0 1 0 1 2 D 10

1 6 5 9 9 - I I 1 OOOD OA 5 7 0 0 P 17 1 6 2 2 0 - 1* 1 0 JOII 0 0 7 6 0 ID 19

6 3 9 1 0 - 2 9 1 0 0 0 9 0 0 ti 9 9 0 0 7 2 - 1 n s 2 o - 7 1 1 0 0 0 9 0 0 2 2 7 7 0 7 0 - 1 19 1 0 - 70 1 0 0 0 9 0 0 1 . 9 0 ID 27 - 5 H 9 0 9 - 2» 1 o o o n 0 0 7 6 0 1 0 3 1 - 7 1 3 6 0 - 15 1 o o o n 0 0 8 B37D IB

7 7 9 5 9 - 17 1 0 0 0 9 0 0 3 18BP 2 0 - 1 ROOD- 7 9 1 0 0 0 9 0 0 1 123D 2 2 - 7 f . 7 1 9 - 7 1 1 0 0 0 9 ( 1 0 2 7 0 0 9 2 5 - 1 9 8 1 9 - 2* ' 1 0 0 0 9 0 0 0 7 8 8 9 2B - 1 6 2 6 9 - 2 H 1 o o o o n o 7 065D 31 - 5 9 7 9 9 - 12 1 0 0 0 9 0 0 B 6960 i r

2 0 0 9 9 - IB 1 OOOIl n o 5 3 9 7 9 21 - 5 0 6 8 9 - 22 1 o n o o 0 0 1 6 1 1 P 2 3 - 0 1 9 5 9 - 7 1 1 0 9 0 9 0 0 1 516D 26 - 1 1 0 1 9 - 2 B 1 OOOD 0 0 5 9 1 2 0 20 - 2 1 1 8 9 - 2 9 1 OOOD 0 0 7 2 9 0 0 32 - 9 7 1 B 9 - 12 1 0 0 0 9 0 0 0 . 15t!> 3 1 - H J 8 9 9 - 17 1 0 9 0 0 0 0 1 t l 3 ID .15

6 6 6 9 9 - 7 ) 1 0 0 0 9 0 0 2 566D 2 0 - 9 2 5 2 9 - 26 1 o o o n CO * 776P 27 -B 1 5 5 9 - 2 8 1 0 0 0 9 0 0 9 0 0 8 0 10 - 2 539D- 2 9 1 o n o n 0 0 1 311C 32 - 2 ) 7 2 9 - 2 9 1 OOOD 0 0 1 226P 31 - 2 1 0 0 0 - 7 9 1 0 0 0 9 0 0 1 2 6 0 0 33 - 2 122D- 29 1 0 0 0 9 0 0 3 292P 3 1

2 1669 - 2 « 1 oooo 00 1 0170 27 - 1 9 2 1 D - 11 1 OOOP 0 0 2 7 0 1 P 30 - 5 8 6 7 9 - 27 1 o o o o 0 0 a 020D 31 - 5 0 1 1 9 - 27 1 OOOD 0 0 B 979D 31 - 5 9 1 7 9 - 27 1 0009 0 0 9 0 5 2 P 31 - 6 0 0 2 0 - >7 1 OOOD 0 0 9 12BP 31 -r, 0 ) 7 0 - 27 1 o o o n 0 0 9 187P 31 - 1 7 5 2 9 - 7 1 1 OOOP 0 0 2 1 6 1 0 78 - 1 2 5 5 9 - 2 1 1 OOOD 0 0 2 , I62D 28 - 1 7 5 9 9 - 2 1 t 0000 0 0 2 . 171(1 7 8 - 1 2 6 5 9 - 2 1 1 0 0 0 9 0 9 2 183P 28 - 1 2 7 9 9 - 2 0 1 0 0 0 9 0 0 2 . 19 31) 2 8 - 1 2 7 6 9 - 2 1 1 OOOP 0 0 2 . 2010 28 - t 2B0D- 2 1 1 o o o n 0 0 2 2 I 2 P 2fl - 2 2 1 1 9 - 2 2 1 0 0 0 9 0 0 1 1861) 26 - 2 205D- 1> 1 0 0 0 9 0 0 1 090P 2 6 - 2 70BD- 2 2 1 OOOP 0 0 1 19BD 26 • 2 2 5 ) 0 - il 1 0 0 0 9 0 0 0 5089 26 - 2 2 5 7 0 - 2 2 1 . 0 0 0 9 0 0 1 5 170 2 6 - 2 2 6 1 9 - 2 2 t OOOD 0 . 1 5 2 5 9 26 - 2 2 6 0 9 - 2 7 1 0009 0 0 1 5 ) 2 D 26


ITER.- LID THE"5.9100000-01 PFBLRI)»».7SR0»,D-0J TIBE I»{R1!HEHT"1.N0()10L)D-C" V E i o r i T r VFI0C1TT NAIF" ELFV. TF *P . suusrAwce M.1;:; c r m r *

INDT- * - T- WATER IN IH RATE »»TF KODe CES LOCATION LOCATION ELEVATION X-DIPECT. T-CIP1C1. OF f-HMt'.s 1ENP o» chanf;* CK|1) CR (2)

go 1 93500 00 210 00 0 011110 0 - 3 6810 02 0 11CD-03 5. n<>o-oi 8 OOOD 01 - 1 11JD-16 1.00CD 00 0 lC*r-23 09 93«00 00 710 00 li 011110 0 - 1 6860 02 1 1690-02 * 1990-01 9 0100 01 -1 1*10-16 i 0J01 00 9 3tr .0-73 09 3 9 3500 00 1250 00 0 .011110 0 - 3 6080 02 1 7 H O - 0 2 r, 19*0 -01 a 0001' (11 - 1 ID-1* i 0003 00 * 11 70- 7 ) 09 03500 00 1750 00 0 0111 to 0 - 3 6930 02 7 OOin.l77 1 1920-31 H noon n t - I SuD- 1» t OOCO CO •t 1210-7.1 09 5 93500 00 2250 00 0 011110 0 - 1 692D 07 2 0670-02 1 1885-01 H 0001 91 -1 1 *00 -16 i noon 00 Q n o r - 2 ) 09 93100 00 3000 00 II 011110 0 - 3 6900 02 1 7670-02 1 1B10-01 8 oooo 01 -1 ' 1 * 0 - 1 6 1 ooor> 00 •1 > o i r - 7 ) 09 7 91100 01) 0000 00 0 011110 0 - 3 691D 02 1 00 1D-02 1 1B70-01 H OOOP 01 - 1 I'.IO" 1< i n.ion 00 9 lb9t i -7 1 50 1 103100 00 210 00 0 010570 0 - 1 icon 02 0 9 2 1 0 - C ' 6 0200-01 8 0000 01 -2 110 21)-11 i moo 00 1 117C-19 50 103500 00 710 00 0 010570 0 - 1 1010 02 7 3261-0) 6 0220-01 8 oooo 01 -2 0020-1* l oooo 00 1 1520-10 50 3 1031P0 .00 1210 00 0 010570 0 - 1 1060 07 t 0260-02 6 (1200-31 8 OOOD 31 -2 IIU2D-11 1 oooo 00 t 15)0-19 50 it 103500 00 17*0 00 0 010570 0 - 1 1370 02 1 176D-02 6 0200-01 8 oooo 01 -7 oniD-1* i 0300 00 1 111D-19 50 103500 00 2250 00 0 010170 0 - 5 1080 02 1 12*D-07 h M 9 0 - 0 1 8 OOOD 01 -2 OHO-11 1 0009 00 1 l l b t l - 1 9 50 103100 00 3000 00 0 010170 0 - 1 1090 02 1 O'IBn-c? 6 0110-01 fl OOOD 1)1 -2 1)000-1* l OOOD oo 1 r.OD- 19 50 7 103500 00 0000 00 0 010570 0 - 5 1100 01 1 3210-02 6 0ISD-01 8 OOOP 01 -7 c o o p - 1 * i 0300 00 1 15*0-19 51 1 113100 00 250 00 0 oinooo 0 -6 7050 02 5 55 10-CI 6 HBon-01 8 OOOD 01 - 1 2910-12 1 0300 00 9 C6 2r-17 51 2 113100 00 710 00 0 01 ROOD 0 -6 7010 02 9 ooon-c) r. 88*0-01 8 OOOO 01 - 1 2nn-12 i 0000 00 9 06 10-17 51 3 113500 00 1250 on o 0181100 0 - 6 7060 02 t )16n-02 k 980 0-01 8 3030 01 - 1 29 10-12 t <1000 00 9 P6UC-17 51 0 113100 00 1710 00 0 OISOOD 0 -6 7070 02 1 10911-0? 6 BB1D-01 8 OOOD 01 -1 7 '10 0 - 12 1 noon 1)0 q 06 6r-17 51 5 113500 00 2210 00 0 018000 0 - 6 707D 02 1 iisn-o? 6 H860*0 * 8 OOOD 01 - 1 2900-12 t OOOD 00 9 06HD-17 51 113500 00 3000 00 0 oieooo 0 -6 70"D 02 1 O2?1-07 6 9800-01 8 0030 01 - 1 2°0D-12 1 oooo OO 9 07CI'- 17 51 7 113*00 00 OOOO 00 0 016000 0 -6 7090 02 1 17CD-02 1 HNBD-01 8 oooo 01 - 1 2900-12 i oooo 00 9 077P-17 52 1 123500 00 250 00 0 022770 0 -R 5000 02 0 502D-01 7 9 01D-01 U OOOD 01 -5 0110-10 I 0007 00 0 179 f -10 52 123100 00 750 00 0 022770 0 - 8 5010 02 7 1160-03 7 9060-01 8 OOOD 31 - 1 0 110-10 i 0900 00 0 6 7 * C - l o 02 3 123500 00 1210 00 0 022770 0 - 8 1010 02 1 11fD-02 7 " 0 1 0 - 0 1 B oooo 01 - 1 0120-10 i ooon 00 0. 6790-10 52 U 123500 00 1710 00 0 022770 0 - 9 502D 02 1 311D-02 1 9060-01 8 OOOD 01 - 1 0170->0 i ooon 09 0 . 6300-10 5? 5 123100 00 2210 00 0 072770 0 -8 1020 02 1 32CO-C2 7 9070-01 8 oooo 01 -1 U110-10 1 OOOD CO b 630D-1U 52 6 123500 00 3000 00 0 022770 0 - 8 1020 32 1 2390-02 7 9010-01 8 OOOD 01 -1 01 ID-Io 1 oooo co 0 6110-10 52 7 123500 00 0000 00 0 022770 0 -a 5030 02 1 311D-02 7 909D-01 8 0030 01 -1 01140-10 l OOOD 00 It 6 310-10 53 1 133100 00 210 00 0 027110 0 - i 0610 31 3 319n-0 ) 9 1110-01 8 oooo 01 - 1 0 29(1- 07 1 oooo 00 1 119(1-11 53 133500 00 750 00 0 077550 3 - 1 065D 33 1 3600-03 9 150D-01 P OOOD 01 -1 0 29D-07 i DO on OD 1. 139P-11 53 3 133SOO 00 1210 00 a 027 55D 0 - i 06*0 03 7 9360-03 9 1100-01 8 oooo 01 - 1 0 290-07 i OOOD oo 1 1110-11 53 133500 00 1710 00 0 02750D 0 - i 0610 03 9 10c.0-01 9 111D-01 8 OOOD 01 - 1 0290-07 i 3000 00 1 * i « n - i i 53 5 133500 00 2 210 00 0 027500 0 - l 065D 01 9 00 10-01 9 1110-01 8 oooo 01 -1 o 29 0-07 i ooon 00 1 rJl"ll).1l 53 6 133100 00 3000 00 u 027100 3 -i 065D 03 9 0170 -01 9 1100-01 8 oooo 01 -1 029 0-07 1 OuOli 00 1 5390-11 53 7 133100 00 0000 00 0 027100 9 0610 01 1 0110-02 9 1170-01 8 OOOD 01 - 1 0 2911-07 i OOOP on 1 H o p - 1 1 50 1 1035 00 00 250 00 0 032710 0 3070 03 2 3710-01 1 006D 00 8 OOOD 01 -2 I2JD-01 1 OOOD 00 1 280P-00 50 2 103500 00 750 00 0 032710 0 - I )07D 03 1 6700-03 1 0060 00 8 OOOP 01 - 2 12)0-01 i 30GD 00 ) 7B9P-09 50 3 103500 00 1253 00 0 032710 0 -t 3070 0) c O7BD-0* t oo6n on 8 OOOD 01 -2 121D-01 i OOOD oo 3. 2900-09 50 0 •03100 00 1750 oo 0 032710 3 3070 01 6 1110-03 1 no6P oo 8 OOOD 01 -2 H I D " 01 1 3300 00 3 79011-09 50 5 103100 00 2210 00 u .032710 0 -i 3C7D 01 6 n l i O - 0 3 1 0060 00 B OOOD 01 -2 )?in-ni 1 OOOD 00 ) 2900-09 50 103500 00 3000 00 0 032710 3 -i 3070 03 6 2900-03 1 006D 00 H OOOD 01 -2 1730-01 i OOOD 00 3 7900-09 50 7 103100 00 0000 00 0 032710 0 -i 307D 01 7 1 6 ) 0 - 0 1 1 0U6D 00 9 OOOD 01 - 2 3330-01 i ooon 00 1 2900-0* 55 1 153100 00 210 00 0 038180 0 -i 580O 03 1 16 90-03 1 178D 00 a OOOD 01 -2 710D-01 1.3300 00 0 0010-07 55 2 153100 CO 750 00 0 038170 0 -1 580D 3 ) 2 OO0D-C1 1 1780 03 8 3000 01 -2 2100-01 1 OOOD 00 0 001D-0 1

55 3 n:*oo 00 1210 00 0 038I7D 3 -l 5800 33 1 600O-0) 1 178D 00 8 ooon 01 -2 2100-01 1 ooon no 0 001P-07 55 113100 00 1710 00 0 03817n 0 -i 5P0D 03 0 3160-01 1 1780 00 8 ooon 01 -2 7100-31 1 0B0O oo 0 0010-07 55 5 113100 00 2250 00 0 038170 0 -1 5800 03 0 272n-0) 1 1780 00 8 0030 01 -2 2100-31 1 OOOD 00 0 OC2P-07 5* 6 113100 00 1000 00 0 038170 3 -i 1800 0 ) 0 1760-C1 t 1780 00 8 ooon 01 -2 7100-31 1 ooon OD 0 0020-07 55 7 153100 00 OOOO 00 u 03817D 0 -i 580D 03 5 0650-03 1 1780 00 8 OOOD 01 - 2 7100-03 1 OOOD 00 0 0020-07 56 1 161*00 00 2*0 00 11 0033 ID 0 -i 8«*D 03 8 9100-00 1 3090 00 7 9990 01 - 1 1100-01 1 oooi) 00 3 103D-0* 56 1 163100 00 7*0 00 0 00 38 ID 0 -1 881D 03 1 09{n-C1 1 1090 00 7 9990 01 -1 1100-01 1 OOOD 00 3 1030-01 56 3 163500 00 1210 00 0 003810 0 -i 8850 03 2 121D-03 1 1090 00 7 0990 01 - 1 1100-01 1 oonn oo ) 10)0-01 *6 0 163100 00 1710 00 0 003810 0 -i 89*0 01 2 5 2 l n - 0 ) 1 1090 00 7 9" 90 01 -1.1100-01 1 ooon CO ).1030-05 56 5 163100 00 2250 00 0 00 38 ID 3 -1 0650 03 2 0660-01 1 309D 00 7 999D 01 - 1 uon-oi 1 OOOD 00 1 1010-0* 56 6 163100 00 3000 00 0 00 38 ID 0 -i 8850 01 2 3580-03 1 109P 00 7 9990 01 -1 1100-01 1 ooon 00 1 1030-01 56 7 163500 00 OOOO 00 b 003810 3 -i 8B5D 03 2 6680-03 1 1090 00 7 99 9p 01 -1 .1100-01 1 ooon 00 1 1030-01

w t\J I D


ITER - 11F TIHB»5 9000001 -01 PERIOD* It. 7580650-02 TIHE 1NCRBBBNT*5.0000000 -03 VELOCITT VELOCITY VATER ELEV. H H P . SOBSTANCE BASS CONCENT

INOT- X- Y- RATER IN IH RATE RATE HODE CES LOCATION LOCATION ELEVATION X-DIFECT. I-DIRICT. OP CHAHOE TEflP OF CHARGE CR(1) CKI2)

57 1 73500.00 250 00 11 CU950D 01 -2.2100 03 2.36CD-00 1.0010 00 7. 9000 01 -2.2060 00 9 9850-01 1. 5000-03 5? 2 73500.00 750 o o li 01I950D 01 -2.211D 03 5.5550-00 1.0010 00 7. 900 D 01 -2.2U6D 00 9 9850-01 1. 5000-03 57 3 73500.00 1250 00 11 0U950D 01 -2.210D 03 7.9010-00 1.001D 00 7. 900D 01 -2.206D 00 9 985D-01 1. 500D-03 57 u 73500.00 1750 00 Ij CO950D 01 -2.2100 03 B.920D-00 1.001D 00 7 9000 01 -2.2U6D 00 9 985D-01 1 5000-03 57 5 7 3 1 0 0 .00 22*0. 0 0 0 0 0 9 1 0 0 01 -2.2100 03 e.eaio-ou I.'OIO 00 7. 9UVD 01 -2.206D 0 0 9 9850-01 1 5000-03 57 fi 73500.00 3000 0 0 9 00950D 01 -2.2100 03 6.5850-00 1.00111 00 7 . 9000 01 -2.2060 0 0 9 9850-01 1. 500D-03 57 7 73500.00 UOOO 00 11 C0950D 0 1 -2.210D 03 3.071D-00 i . o o i o o o 7 90110 01 -2.2060 0 0 9 9850-01 1 5000-03

I H C 0 0 2 I STOP 0

Table A. 6. Output Information for Sample Problem No. 2 at Time = 37.205 hr the Reduced Version of the Program

I T E R . > 2 4 7 9 T I H E = 3 . 7 2 0 5 0 0 0 01 P E R I O C « 3 . 0 0 0 4 0 3 D CO I I H t I N C R B H E N T = S . 0 0 0 0 0 0 0 - 0 3

VELOCITY VELCCI1T OUTER ELEV. TEHP. T E n P . I N D I - X - V - RATER I R IR RATE RATE

RODE CES LOCATION LOCATION ELEVATION I - DIRECT • 1 - DIRECT. OP CHARGE OP CHARGE

1 1 SOOO. 00 2 5 0 . 00 3 9 6 3 1 0 D 0 1 - 5 . 1 7 6 0 01 - 2 . 6 8 5 0 00 1 4 5 7 0 00 8 . 0 0 0 0 0 1 3 8 6 1 0 - 0 8 1 SOOO. 00 7 5 0 00 3 96314D 0 1 - 5 • 0 1 4 0 0 1 - 7 . 26SC 00 1 347D 00 8 .0000 0 1 2 6 9 3 0 - 0 8 1 3 sooo. 00 1250 0 0 3 96314D 0 1 -11 . 7 2 6 0 C I - 1 . 3 4 4 0 0 1 1 7 7 6 D 00 8 .OOOD 0 1 1 9 7 3 0 - 0 7 1 sooo. 00 1750 00 3 96 332 D 0 1 —4 . 3 6 1 0 0 1 -1 • 6 8 0 c 0 1 7 9 8 5 D 0 1 8 .OOOD 0 1 1 4 7 9 0 - 0 6 1 5 5 0 0 0 . 00 2 2 5 0 00 3 9 6 3 5 4 0 0 1 - 4 . 1 3 3 0 CI - 9 • 781C 00 2 0 8 5 0 0 0 8 .OOOD 0 1 8 6 6 5 D - 0 6 1 5 0 0 0 . 00 3 0 0 0 0 0 3 9 6 3 1 0 D 0 1 - 4 • 3 2 4 C C I 6 • 579C 00 3 . 4 2 1 0 01 8 .0000 0 1 8 6 0 5 0 - 0 5 1 7 5 0 0 0 . 00 4 0 0 0 00 3 96269D 0 1 - 4 . 6 2 7 0 0 1 6 941C 00 1 54 3D 00 8 .0000 0 1 6 3 3 1 0 - 0 4 2 1 1 5 0 0 0 . 00 2 5 0 0 0 3 9 6 3 1 5 D 0 1 - 0 . 2 9 2 0 02 - 1 • 30EE 00 1 639D 00 8 .0000 0 1 2 0 3 3 0 - 0 6 2 15000 00 7 5 0 00 3 963 ' . 5D 0 1 - 4 . 2 7 9 0 C2 - 3 .4640 00 1 • 6 1 0 D 0 0 8 .0000 0 1 6 4 7 1 0 - 0 7 2 3 1 5 0 0 0 00 1 2 5 0 0 0 3 9 6 3 1 3 0 01 -4 . 2 5 6 D C2 - 6 • C57C 00 1 . 5 8 9 D 00 8 .0000 0 1 1 3 6 5 D - 0 6 2 4 1 5 0 0 0 00 1750 00 3 96 312D 0 1 • 4 .2280 0 2 - 7 181C 00 1 . 4 0 2 0 00 8 .OOOD 0 1 1 8 5 8 0 - 0 5 2 5 1 5 0 0 0 00 2250 00 3 9 6 3 1 4 D 0 1 - 4 .2080 02 - 3 229C 00 1 . 2 3 4 0 0 0 8 .OOOD 0 1 1 . 9 3 9 0 - 0 4 2 15000. 00 3 0 0 0 0 0 3 9 6 3 0 2 0 0 1 - 4 . 2 1 1 0 02 2 7860 00 1 .3730 00 .0000 01 1 6 3 2 0 - 0 3 2 7 1 5 0 0 0 . 00 4 0 0 0 0 0 3 96294 0 0 1 - 4 • 222C 02 3 . 3 3 EC 00 1 6 2 5 D 00 a .0030 01 1 1 1 1 0 - 0 2 3 1 2 5 0 0 0 . 00 250 00 3 96292D 01 - 8 . 0 8 7 0 02 -1 . 7 9 7 0 0 1 1 5 0 9 0 00 8 .OOOD 0 1 3 0 1 8 0 - 0 5 3 2 5 0 0 0 . 00 7 5 0 0 0 3 9 6 2 9 2 D 0 1 - 8 . 0 7 5 0 02 - 4 . 16 IE 0 1 1 5 1 1 0 00 8 .OOOD 0 1 9 4 4 8 0 - 0 6 3 3 2 5 0 0 0 . 00 1 2 5 0 . 0 0 3 96290D 0 1 - 8 . 0 5 5 D C2 - 6 . 5 9 6 C 0 1 1 513D 00 8 .0000 0 1 9 S 1 0 D - 0 6 3 . 4 2 5 0 0 0 . 00 1750 00 3 9 6 2 8 8 D 0 1 -8 . 0 2 9 D 02 - 7 325C 0 1 1 5 3 0 0 0 0 8 .OOOD 0 1 1 1 8 0 0 - 0 4 3 2 5 0 0 0 . 00 2 2 5 0 00 3 9 6 2 8 7 D 0 1 • 8 . 0 0 6 0 02 - 4 . 3 0 20 0 1 1 534D 00 8 .0000 0 1 1 2 0 S D - 0 3 3 2 5 0 0 0 . 0 0 3 0 0 0 00 3 9 6 2 9 0 D 0 1 - 7 . 9 9 1 0 02 - 7 33CC •02 1 5 1 3 0 00 8 . 0 0 3 0 0 1 9 4 6 7 0 - 0 3 3 7 2 5 0 0 0 00 4 0 0 0 00 3 9 6 2 9 6 D 0 1 - 7 . 9 8 2 0 C2 - 2 . 2 0 2 0 - 0 1 1 • 446D 00 8 • 021D 0 1 S 9 1 2 0 - 0 2 a 1 3 5 0 0 0 00 2 5 0 0 0 3 9 6 2 4 4 D 0 1 - 1 • 193C 0 3 4 .S5CC • 0 1 1 4 8 8 0 0 0 8 .0000 0 1 1 6 4 6 0 - 0 4 4 3 5 0 0 0 00 7 5 0 0 0 3 96245D 0 1 - 1 . 1 9 2 0 0 3 1 • 438C 00 1 492D 00 8 . 0 0 0 0 0 1 5 2 5 5 0 - 0 5 4 3 3 5 0 0 0 0 0 1 2 5 0 0 0 3 . 9 6 2 4 6 0 0 1 . 1 8 9 0 C3 2 . 2 5 5 C 00 1 . 5 1 8 0 0 0 a .OOOD 0 1 4 4 5 1 0 - 0 5 4 4 3 5 0 0 0 00 1750 0 0 3 . 9 6 2 4 8 D 0 1 - 1 . 1 8 6 0 03 2 . 7 6 6 0 00 1 . 5 5 2 0 0 0 8 . 0 0 0 0 0 1 4 5 7 1 0 - 0 4 4 5 3 5 0 0 0 00 2 2 5 0 00 3 9 6 2 5 I D 0 1 - 1 . 1 8 2 0 03 2 • 789C 00 1 . S 8 3 D 00 8 . 0 0 2 0 0 1 4 1 3 1 D - 0 3 4 3 5 0 0 0 0 0 3 0 0 0 0 0 3 9 6 2 6 1 D 0 1 - 1 . 1 7 8 0 03 2 398C 0 0 1 • 556D 00 8 . 0 1 3 0 0 1 2 9 2 3 0 - 0 2 4 7 3 5 0 0 0 00 4 0 0 0 0 0 3 9 6 2 8 1 0 0 1 - 1 . 1 7 5 0 03 2 . 2 0 0 1 0 0 1 4 4 1 0 0 0 8 . 0 8 2 0 0 1 1 5 9 5 D - 0 1

5 1 4 5 0 0 0 . 00 250 0 0 3 9 6 1 8 8 0 0 1 - 1 . 5 8 4 0 0 3 1 . 4 2 5 C 00 1 3 5 2 0 00 8 . 0 0 0 0 0 1 5 8 2 7 0 - 0 4 5 4 5 0 0 0 . 00 7 5 0 00 3 96188 0 0 1 - 1 • 5 8 3 0 0 3 4 345C 00 1 . 3 5 6 0 00 8 .OOOD 0 1 1 7 1 2 0 - 0 4 5 3 45000. 00 1 2 5 0 0 0 3 9 6 1 8 9 0 0 1 - 1 . s a io C3 7 , 3 1 2 c 00 1 3701) 0 0 a .OOOs 0 1 2 1 1 2 D - 0 4 5 4 4 5 0 0 0 . 0 0 1750 0 0 3 9 6 1 9 0 0 0 1 - 1 . 5 7 6 0 0 3 1 • C29C 0 1 1 3 9 4 0 00 a .0000 0 1 2 3 2 9 0 - 0 3 5 115000 00 2 2 5 0 0 0 3 9 6 1 9 1 D 0 1 - 1 •5700 03 1 • 2 9 1 0 0 1 1 . 4 8 3 0 00 a , 0 0 5 0 0 1 2 0060-02 5 4 5 0 0 0 00 3 0 0 0 00 3 9 6 2 0 1 D 0 1 - 1 . 5 6 0 C 0 3 1 . 6 6 5 C 0 1 1 . 4 6 6 D 0 0 a . 0 3 3 0 0 1 1 1 4 6 0 - 0 1 5 7 4 5 0 0 0 . 00 4 0 0 0 00 3 96 224 D 0 1 - 1 . 5 5 2 0 C3 2 25ED 0 1 1 972D 0 0 8 • 200D 0 1 5 7 1 2 0 - 0 1 6 1 5 0 2 5 0 00 2 5 0 00 3 961611) 0 1 - 1 . 7 9 3 D 03 1 • 989C 00 1 . 3 6 7 0 0 0 8 .OOOD 01 8 B 9 8 D - 0 3 e 2 5 0 2 5 0 00 7 5 0 00 3 96161D 9 1 - 1 . 7 9 2 0 03 6 • C640 0 0 1 3 7 2 0 00 8 .OOOD 0 1 2 4 6 9 0 - 0 3 6 3 5 0 2 5 0 00 1250 0 0 3 9 6 1 6 0 D 0 1 - 1 . 7 8 9 0 0 3 1 • 05 3C 01 1 3 4 9 0 0 0 a .OOOD 0 1 1 7 6 8 0 - 0 3 6 4 5 0 2 5 0 0 0 1750 0 0 3 9 6 1 6 0 D 0 1 - 1 . 7 8 4 0 C3 1 • 562C 0 1 1 3 5 9 0 00 a . 0 0 2 0 0 1 1 5 7 6 D - 0 2 6 5 0 2 5 0 00 2 2 5 0 0 0 3 9 6 1 6 0 0 0 1 - 1 . 7 7 6 0 03 2 • 107C 0 1 1 3 2 5 0 0 0 8 • 016D 0 1 1 1 2 4 0 - 0 1 6 S0250. 00 3 0 0 0 0 0 3 9 6 1 7 4 0 0 1 - 1 . 7 5 6 0 C3 3 . C55D 01 1 0200 oo 8 .1010 01 4 9 5 9 D - 0 1 6 7 5 0 2 5 0 0 0 4 0 0 0 00 3 9 6 2 1 5 D 0 1 - 1 . 7 3 4 0 0 3 4 .52CC 0 1 -6 0 2 7 0 - 0 1 8 • 543D 0 1 2 188D 0 0 7 1 5 0 7 5 0 . 0 0 2 5 0 0 0 3 0 6 1 6 5 0 0 1 - 1 . 8 1 5 0 03 1 . 6 5 8 0 00 1 439D 00 8 . 0 0 1 0 0 1 1 4 3 0 0 - 0 2 7 5 0 7 5 0 . 00 7 5 0 . 00 3. 9 6 1 6 4 0 0 1 - 1 . 8 1 4 0 0 3 S 275C oo 1 4 4 6 0 00 8 .0000 01 3 9 2 8 0 - 0 3 7 3 5 0 7 5 0 00 1 2 5 0 0 0 3 9 6 1 6 4 D 0 1 - 1 . 8 1 3 0 0 3 9 . 6 7 30 0 0 1 4 6 3 0 0 0 6 .OOOD 0 1 2 0 4 2 0 - 0 3 7 4 5 0 7 5 0 0 0 1750 0 0 3 9 6 1 6 3 0 0 1 - 1 .8080 0 3 1 , : s3c 01 1 . 5 1 5 0 0 0 8 • 0 0 2 0 0 1 1 5 0 5 0 - 0 2 7 5 0 7 5 0 00 2 2 5 0 00 3 9 6 1 6 3 D 0 1 - 1 . 8 0 1 0 C3 2 . 4 4 9 0 0 1 1 65BD 0 0 8 . 0 2 0 0 0 1 9 3 1 3 0 - 0 2 7 5 0 7 5 0 00 3 0 0 0 0 0 3 9 6 1 6 3 0 0 1 - 1 . 7 7 7 0 03 4 . 6 3 9 1 0 1 1 9 9 4 D 0 0 8 • 116D 01 3 2 4 4 0 - 0 1 7 7 5 0 7 5 0 . 00 4 0 0 0 00 j 96153D 0 1 - 1 . 7 4 4 0 C3 8 . C310 0 1 4 5H1D 00 8 . 6 1 1 0 0 1 1 243D 0 0

8 1 5 1 2 5 0 oo 250 00 3 9 6 1 6 9 0 0 1 - 1 . 8 3 6 C 03 9 • 305C- 0 1 1 3 7 8 0 0 0 8 . 0 0 1 0 0 1 2 1 9 4 D - 0 2 8 5 1 2 5 0 00 7 5 0 00 3 96169D 0 1 - 1 . 8 3 6 0 0 3 3 . 2 0 8 C 0 0 1 3 BOD 0 0 a . 0 0 0 0 0 1 S 9 8 3 0 - 0 3 8 3 5 1 2 5 0 00 1 2 5 0 0 0 3 9 6 1 6 8 D 01 - 1 .8 350 0 3 6 • 471C 00 1 3 3 2 0 0 0 8 .OOOD 0 1 2 2 9 3 0 - 0 3 8 4 5 1 2 5 0 . 0 0 1750 00 3 96166D 0 1 - 1 . 8 3 5 0 0 3 1 . 1 6 5 0 0 1 1 3 7 3 0 00 8 . 0 0 3 0 0 1 1 3 2 0 D - 0 2 8 5 5 1 2 5 0 . 0 0 2 2 5 0 . 0 0 3 9 6 1 6 5 0 0 1 - 1 . 8 3 3 0 0 3 2 .22CC 0 1 8 2 2 8 0 - 01 8 . 0 2 2 0 0 1 6 9 8 8 D - 0 2 8 6 5 1 2 5 0 . 00 3 0 0 0 . 00 3 96142D 0 1 - 1 . 8 2 8 0 03 5 . 2 7 1 0 0 1 1 320D 0 0 8 . 1 2 5 0 0 1 1 7 1 1 0 - 0 1 8 7 5 1 2 5 0 . 00 4 0 0 0 00 3 96 058 D 0 1 - 1 . 8 1 9 D 03 9 . 9 9 6 C 0 1 - 2 032D 0 0 8 . 6 5 4 0 0 1 4 2 B 7 D - 0 1


I T E R • • 2 0 7 9 T I H E " 3 . 7 2 0 5 C O D CI P I R I O D . 3 . O O U O O I D CO IIRE I H C R E N E N T » 5 . 0 0 0 0 0 0 D - 0 3

V E L 0 C I T 1 V E L C C I 1 1 RATER E L E V . T E B P T i n p . I N 0 I - * - T - H A T t R i n i n R A T I RATE

RODE CES L O C A T I O N L O C A T I O N E L E V A T I O N J - C I R E C T . 1 - D J R t C T . OP CHANCE OP CHANCE

9 1 5 1 7 5 0 . 0 0 2 5 0 . , 0 0 3 , , 9 6 1 7 0 9 0 1 - 1 . 8 5 0 0 C3 - 1 . 6 1 3 C - - 0 1 1 . 0 11D 0 0 6, . 0 0 2 0 0 1 3 . 1 9 9 D - 0 2 9 2 5 1 7 5 0 . 0 0 7 5 0 . . 0 0 3 , , 9 6 1 7 0 0 0 1 - 1 . 8 5 5 0 0 3 - 2 . 7 2 C C -• 0 1 1 . 0 16D 0 0 9. • OOOD 0 1 8 . 6 9 6 D - 0 3 9 3 5 1 7 5 0 . 00 1 2 5 0 , . 0 0 3 , 9 6 1 7 3 0 0 1 - 1 • 8 5 6 0 0 3 1 • 026C-• 0 1 1 • 9 5 0 0 0 0 9 .OOOD 0 1 2 . 5 7 7 D - 0 3 9 0 5 1 7 5 0 . 0 0 1 7 5 0 . , 0 0 3. , 9 6 1 7 2 0 0 1 - 1 . 8 5 9 0 0 3 1, . 0 5 2 C 0 0 1 • 5 1 5 D 0 0 8 . . 0 0 3 D 0 1 1, . 1 2 1 0 - 0 2 9 5 5 1 7 5 0 . 0 0 2 2 5 0 , , 0 0 3 , , 9 6 1 7 2 0 0 1 - 1 . 8 6 9 0 0 3 5 . 6 9 1 C 0 0 1 . 6 9 0 0 0 0 8 , > 0 2 9 0 0 1 5 . 9 9 9 0 - 0 2 9 6 5 1 7 5 0 . 0 0 3 0 0 0 , . 0 0 3, , 9 6 1 6 1 0 0 1 - 1 . 8 8 3 0 C3 1 . 5 9 6 0 0 1 2 • 3 6 6 D 0 0 8 . , 1 3 1 0 0 1 1 . 1 7 1 D - 0 1 9 7 5 1 7 5 6 . 0 0 0 0 0 0 , . 0 0 3 , . 9 6 1 1 6 9 0 1 - 1 • 9 IOC 0 3 0, , 2 5 J E 0 1 6, . 5 1 0 D 0 0 8 , , 6 9 3 D 0 1 3 . 2 6 6 D - 0 1

10 1 5 2 2 5 0 . 0 0 2 5 0 . , 0 0 3 . , 9 6 1 7 9 9 0 1 - 1 . 8 7 1 9 C3 - 1 , • 35CC 0 9 1, , 3 9 0 0 0 0 8 . , 0 0 3 D 0 1 4 , , 9 3 6 D - 0 2 10 2 5 2 2 5 0 . 0 0 7 5 0 . . 0 0 3 . , 9 6 1 7 9 0 0 1 - 1 . 9 7 I D C3 - 9 . , 1 9 9 C 0 9 1, . 3 8 9 D 00 8 . 0 0 1 0 0 1 1, . 2 0 6 0 - 0 2

10 3 5 2 2 5 0 . 0 0 1 2 5 0 , , 0 0 3 , , 9 6 1 7 9 0 0 1 - 1 . 8 7 2 0 C ) - 7 , . 9 0 1 0 0 0 1 . 3 5 2 0 0 0 8 , , 0 0 0 9 0 1 2 . 9 5 0 0 - 0 3 1 0 0 5 2 2 5 0 . 0 0 1 7 5 0 . . 0 0 3 , 9 6 1 8 1 D 0 1 - 1 . 8 7 5 0 C I - 1 , . 1 3 0 9 0 1 1, . 2 9 0 0 OC 8 . . 0 0 3 9 0 1 9 . , 3 1 5 0 - 0 3 10 5 5 2 2 5 0 . 0 0 2 2 5 0 , , 0 0 3 . , 9 6 1 6 1 9 0 1 - 1 »BB1D 0 3 - 1 , , 7 2 0 t 0 1 1, , 0 9 3 0 0 0 8 . , 0 2 6 0 0 1 9 , , 9 0 3 D - 0 2 1 0 6 5 2 2 5 0 . 0 0 3 0 0 0 . , 0 0 3 . , 9 6 1 9 1 9 0 1 - 1 . 9 0 ID 0 3 - 3 , . 1 5 5 9 0 1 0 , , 9 2 3 0 - • 0 1 8 . , 1 3 4 0 0 1 1, . 0 3 9 D - 0 1 10 7 5 2 2 5 0 . 0 0 0 0 0 0 . , 3 0 3 . , 9 6 2 2 9 0 0 1 - 1 . 9 2 9 0 0 3 - 5 , . 2 9 8 c 0 1 - 3 , , 7 9 7 0 0 0 9 . 6 9 0 0 0 1 3 , . 7 7 8 0 - 0 1 11 1 5 2 7 5 0 . 0 0 2 5 0 . 0 0 3 . , 9 6 1 8 0 9 0 1 - 1 . 8 8 0 0 0 3 - 2 , , 2 3 3 C 0 0 1, , 9 1 0 D 0 0 B, , 0 0 0 9 0 1 5 , , 8 7 7 D - 0 2 1 1 2 5 2 7 5 0 . 0 0 7 5 0 . . 0 0 3 . . 9 6 1 6 4 D 0 1 - 1 . 9 8 0 0 0 3 - 7 . 0 7 7 C 0 0 1, , 0 1 2 0 0 0 8 . 0 0 1 0 0 1 1 , . 6 1 0 0 - 0 2 11 3 5 2 7 5 0 . 0 0 1 2 5 0 . 0 0 3 . 9 6 1 8 5 1 0 1 - 1 . 8 8 0 0 C3 - 1 , . 2 8 1 9 0 1 1 , . 0 5 6 0 0 0 8 . OOOD 0 1 3 . , 9 9 3 0 - 0 3 1 1 0 5 2 7 5 0 . 0 0 1 7 5 0 . . 0 0 3 . , 9 6 1 8 9 9 0 1 - 1 . 8 8 0 D 0 3 - 2 , . 0 1 C C 0 1 1, . 0 30D 0 0 8 . , 0 0 3 9 0 1 8 , . 1 7 0 0 - 0 3 11 5 5 2 7 5 0 . 0 0 2 2 5 0 . 0 9 3 . 9 6 1 8 9 9 0 1 - 1 • 8 0 5 C 0 3 - 3 . , 2 3 7 C 0 1 t , , 9 5 3 0 0 0 8 . , 0 2 6 0 01 5 . ,2310-01 11 6 5 2 7 5 0 . 0 0 3 0 0 0 . 0 0 3 . 9 6 2 1 0 D 0 1 - 1 . 8 8 2 0 0 3 - 6 , . 2 6 0 1 0 1 1 , . 5 5 0 0 0 0 8 . , 1 3 3 0 0 1 2 . . 4 5 8 D - 0 1 1 1 1 5 2 7 5 0 . 0 0 4 0 0 0 . . 0 0 3 . , 9 6 2 9 9 9 0 1 - 1 . 8 7 7 0 C3 - 1 . 0 7 9 1 0 2 4 . 9 1 5 0 0 0 8 . , 7 0 9 9 0 1 4 , . 9 6 9 0 - 0 1 1 2 1 5 3 2 5 0 . 0 0 2 5 0 , , 0 0 3 . , 9 6 1 8 8 0 0 1 - 1 . 8 9 7 0 0 3 - 2 , • 5 5 9 C 0 0 1 . 3 9 6 0 0 0 8 , , 0 0 5 0 0 1 7 . , 5 0 0 0 - 0 2 1 2 2 5 3 2 5 0 . 0 0 7 5 0 . . 0 0 3 . 9 6 1 8 8 D 0 1 - 1 . 8 9 6 0 0 3 - 8 • OOCC 0 0 1 . 3 9 1 0 0 0 8 . . 0 0 1 0 0 1 2 . . 0 7 0 0 - 0 2 1 2 3 5 3 2 5 0 . 0 0 1 2 5 0 , , 0 0 3 . . 9 6 1 8 9 9 0 1 - 1 • B 9 9 D 0 3 - 1 , • 9 2 0 C 0 1 1 >369D 0 0 8 . , 0 0 1 0 0 1 3 , , 9 4 7 0 - 0 3 12 • 5 3 2 5 0 . 0 0 1 7 5 0 . , 0 0 3 . , 9 6 1 9 0 0 0 1 - 1 . 8 9 2 0 0 3 - 2 . 1 7 6 9 0 1 1 • 3 3 3 D 0 0 8 . , 0 0 3 D 0 1 5 • 5 0 6 D - 0 3 1 2 5 5 3 2 5 0 . 0 0 2 2 5 0 . , 0 0 3 , , 9 6 1 9 2 0 0 1 - 1 . 8 8 7 0 0 3 - 3 . 19CC 0 1 1 . 1 5 , 3 0 0 0 8 . , 0 2 9 D 0 1 3 > 0 0 6 0 - 0 2 1 2 6 5 3 2 5 0 . 0 0 3 0 0 0 . , 0 0 3 . , 9 6 1 9 9 0 0 1 - 1 . 8 6 9 0 0 3 - 5 . . 2 7 7 0 0 1 8 , , 3 1 8 0 - • 0 1 8 . . 1 2 0 0 0 1 1. , 1 0 7 0 - 0 1 1 2 7 5 3 2 5 0 . >00 0 0 0 0 . , 0 0 3 , , 9 6 2 1 9 0 0 1 - 1 . 8 9 2 0 0 3 -8 . 3 1 9 C 0 1 - 1 . 7 1 5 D 0 0 a. , 5 9 1 0 0 1 3 . 9 1 3 0 - 0 1 13 1 5 3 7 5 0 . 0 0 2 5 0 , , 0 0 3 , , 9 6 1 9 2 D 0 1 - 1 . 9 0 9 9 0 3 - 2 . 0 0 5 9 0 0 1 .OOOD 0 0 8 . , 0 0 7 0 0 1 9 . . 3 1 2 0 - 0 2 1 3 2 5 3 7 5 0 . , 0 0 7 5 0 , . 0 0 3 , . 9 6 1 9 2 9 0 1 - 1 • 9 0 8 C 0 3 - 7 • 3 3 8 C 0 0 1 • 9 0 2 D 0 0 8 . . 0 0 2 D 0 1 2, > 6 0 5 0 - 0 2 13 3 5 3 7 5 0 . 0 0 1 2 5 0 , , 0 0 J, , 9 6 1 9 2 0 0 1 - 1 . 9 0 6 9 03 - 1 .25911 0 1 1 , 4 1 6 0 0 0 8 . , 0 0 1 0 0 1 9 , . 6 4 0 0 - 0 3 13 U 5 3 7 5 0 . 0 0 1 7 5 0 . . 0 0 3 . 9 6 1 9 1 D 0 1 - 1 . 9 0 2 0 03 - 1 . , 8 3 9 C 0 1 1 . 9 3 9 0 0 0 8 . 0 0 3 0 0 1 3 > 0 4 0 0 - 0 3 13 5 5 3 7 5 0 . 0 0 2 2 5 0 , , 0 0 3 , , 9 6 1 9 0 0 0 1 - 1 • 8 9 7 0 C3 - 2 . 3 9 1 0 0 1 1 . 9 9 7 0 0 0 8 , >023D 0 1 1, . 6 7 0 D - 0 2 1 3 6 5 3 7 5 0 . 0 0 3 0 0 0 , . 0 0 3 , , 9 6 1 8 9 9 0 1 - 1 . 8 8 4 0 0 3 - 3 . 0 1 5 C 0 1 1 . 7 6 7 0 0 0 9 . , 1 1 7 0 0 1 6 , . 0 2 0 D - 0 2 13 7 5 3 7 5 0 . 0 0 > 0 0 0 , , 0 0 3 , , 9 6 1 6 3 0 0 1 - 1 . 8 6 9 0 0 } - 3 , .else oi 3 , , 3 5 9 0 0 0 8 . 5 5 2 0 0 1 9 , . 7 5 9 0 - 0 2 10 1 5 0 2 5 0 . 0 0 2 5 0 . . 0 0 3 . . 9 6 1 9 5 0 0 1 - 1 . 9 2 2 9 C3 - 1 . , 9 8 1 c 0 0 1, , 3 9 9 0 0 0 8 . , 0 1 0 D 0 1 1 1 3 7 0 - 0 1 10 2 5 0 2 5 0 . 0 0 7 5 0 . , 0 0 3 . 9 6 1 9 6 0 0 1 - 1 . 9 2 1 D 03 - 5 , , 6 9 7 9 0 0 1, , 3 9 / 0 0 0 8 . , 0 0 1 0 0 1 3 . , 2 2 3 0 - 0 2 10 3 5 0 2 5 0 . 0 0 1 2 5 0 . . 0 0 3 . , 9 6 1 9 6 0 0 1 - 1 . 9 1 9 C 0 3 - 9 , . 7 9 9 C 0 0 1, • 3 9 1 D 0 0 8 . , 0 0 1 0 0 1 5 . . 5 0 0 9 - 0 3 10 0 5 0 2 5 0 . 0 0 1 7 5 0 . 0 0 3 . 9 6 1 9 6 0 0 1 - 1 • 9 1 5 C 0 3 - 1 . , 369C- 0 1 1, , 9 1 1 0 0 0 e . , 0 0 3 D 0 1 9 . 1 6 9 9 - 0 4 10 5 5 0 2 5 0 . 0 0 2 2 5 0 , , 0 0 3 , 9 6 1 9 7 0 0 1 - 1 . 9 1 1 0 C3 • 1 , . 6 9 9 1 0 1 1, , 3 9 1 0 0 0 9 . 0 2 JD 0 1 - 2 , , 2 3 2 0 - 0 3 10 6 5 0 2 5 0 . 0 0 3 0 0 0 . , 0 0 3 . , 9 6 1 9 9 9 0 1 - 1 . 9 0 6 9 0 3 - 1 , . 7 6 0 D 0 1 1, , 9 0 6 0 0 0 8 . . 1 1 5 0 0 1 - 2 . , 3 9 7 0 - 0 2 1« 7 5 0 2 5 0 . 0 0 0 0 0 0 . , 0 0 3 . , 9 6 1 9 9 9 0 1 -1 . 9 0 3 0 0 3 -1. , 7 3 IC 01 9 , . 6 3 5 0 -• 0 1 8 . . 5 5 5 0 0 1 - 2 , , 5 6 5 0 - 0 1 1 5 1 5 0 7 5 0 . 0 0 2 5 0 . . 0 0 3 . 9 6 1 9 9 9 0 1 -1 . 9 3 6 0 C3 -1, . 0 5 8 C 0 0 1, , 3 9 9 0 0 0 8 . .013 J (It 1, , 3 7 0 0 - 0 1 15 2 5 0 7 5 0 . 0 0 7 5 0 , . 0 0 3 . 9 6 1 9 9 9 0 1 -1 . 9 3 5 0 C3 -4, , 2 9 3 C 0 0 1, , 3 9 9 0 0 0 8 . o c « , i 0 1 3 , , 9 0 8 0 - 0 2 15 3 5 0 1 5 0 . , 0 0 1 2 5 0 , , 0 0 3 , . 9 6 1 9 9 0 0 1 -1 . 9 3 3 0 0 3 - 6 . I 0 6 D 0 0 1 . 3 9 8 0 0 0 8 . . 0 0 I V , i n 6 , . 7 3 9 0 - 0 3 15 a 5 0 7 5 0 . , 0 0 1 7 5 0 . , 0 0 3 . . 9 6 1 9 9 9 0 1 -1 . 9 3 1 0 0 3 - B . 9 1 9 C 0 9 1 . 9 0 5 0 0 0 8 . , 0 0 3 0 01 •1. , 7 1 5 0 - 0 3 15 5 5 0 7 5 0 . 0 0 2 2 5 0 . , 0 0 3 , 9 6 1 9 9 9 0 1 -1 • 9 2 8 D 0 3 -1 . O O I C 0 1 1 . 3 9 4 0 0 0 8, . 0 2 2 0 0 1 -1. , 9 3 6 0 - 0 2 15 6 5 0 7 5 0 . . 0 0 3 0 0 0 . , 3 0 3 . . 9 6 1 9 8 9 0 1 -1 . 9 2 5 0 C3 - B . 9 5 1 C 0 0 1 . 4 5 0 0 0 0 8 . , 1 1 2 0 0 1 -1 . 0 3 3 D - 0 1 1 5 7 5 0 7 5 0 . 0 0 4 0 0 0 , , 0 0 3 , , 9 6 1 9 2 9 0 1 -1 . 9 2 0 0 0 3 - 6 • C99D 0 0 1 . 4 5 9 0 0 0 8 . , 5 4 3 0 0 1 - 5 , . 9 9 5 D - 0 1 1 6 1 5 5 2 5 0 . . 0 0 2 5 0 . , 0 0 3 . . 9 6 2 0 1 9 0 1 -1 . 9 5 2 9 0 3 -1, ,oi:c 0 0 1 , 3 9 7 0 0 0 8. .0160 0 1 1, , 6 4 9 0 - 0 1 1 6 2 5 5 2 5 0 . 0 0 7 5 0 , , 0 0 3 . , 9 6 2 0 3 0 0 1 -1 • 9 5 1 0 0 3 - 2 • 9 0 I C 0 0 1 , 3 9 9 0 0 0 8 , , 0 0 5 9 0 1 4 , . 8 0 1 0 - 0 2 16 3 5 5 2 5 0 . 0 0 1 2 5 0 . , 0 0 3 . , 9 6 2 0 3 0 0 1 -1 • 9 9 9 D C I - 0 . 5 0 1 C 0 0 1 . 3 9 6 0 0 0 8 . , 0 0 1 D 0 1 8 . 2 6 3 D - 0 3 16 0 5 5 2 5 0 . 0 0 1 7 5 0 . . 0 0 3. . 9 6 2 0 2 0 0 1 -1 • 9 4 7 D 03 - 5 . 6 0 0 0 0 9 1 • 4 0 2 0 0 0 8 . , 0 0 3 » 0 1 - 3 , . 2 9 9 0 - 0 3 1 6 5 5 5 2 5 0 . 0 0 2 2 5 0 . , 0 0 3 . , 9 6 2 0 2 0 o t -1 • 9 9 6 C 0 3 - 5 . , e 7 9 C 0 9 1 . 3 9 2 0 0 0 8 . . 0 2 1 0 01 - 3 , . 3 0 6 0 - 0 2 1 6 6 5 5 2 5 0 . 0 0 3 0 0 0 , . 0 0 3 , . 9 6 2 0 1 9 01 -1 • 9 4 4 9 0 3 -4 . 5 9 1 C 0 0 1 • 4 3 6 D 0 0 8 , , 1 0 9 0 0 1 - 1 , , 7 2 0 0 - 0 1 1 6 7 5 5 2 5 0 . , 0 0 4 0 0 0 , ,00 3 . , 9 6 1 9 8 0 01 -1 . 9 9 9 0 C3 -1 • 6 5 5 C 0 0 1 . 4 0 0 0 0 0 8 , , 5 3 3 0 0 1 - 8 , . 9 2 0 0 - 0 1


I T E R • • 2 4 7 9 T l f lE*3*7205C0D 01 PERIOD-1.01.0403D 00 T I B f KCBEHENT 'S .0000000 -03

VELOCITT VELCCI11 HATER ELEV. TEBP TEBP. INDI- I- T- HATEH IN IN BATE BATE

RODE CES LOCATIOB LOCATION ELEVATION 1-TIRECT. T-OIBICT. OP CHANCE OP CHANCE

17 1 56000 00 250 00 3 96208D 01 -1.976D 03 -6.235C-01 1 . 392D 00 8 .0210 01 1 .9630-01 17 2 SCOOO 00 750 00 3 962080 01 -1.9150 C3 -1.7720 00 1 .3930 00 8 0060 01 5 •795D-02 17 3 50000 00 12S0 00 3 962070 01 -1,9750 03 -2.(BSC 00 1 • 391D 00 B .0010 01 1 .0140-02 17 4 56000 00 1750 00 3 962070 01 -1.9730 03 -3.2050 00 1 .3920 00 8 .0030 01 -4 .2800-03 17 56000 00 2250 00 3 96206D 01 -1.9720 03 -3.21IC 00 1 .3880 00 8 .0200 01 -4 .3510-02 17 56000 00 3000 00 3 96206D 01 -1.9720 C3 -2.25CC 00 1 .3900 00 8 100D 01 -2 .2670-01 17 7 56000 00 4000 00 3 96 204 D 01 -1.972E 03 -4.571C-01 1 .3990 00 8 51 ID 01 -1 ,1220 00 IB 1 57000 00 250 00 3 962150 01 -2,0100 03 -3.CB20-01 1 .3910 00 8 0300 01 2 ,6770-01 IB 57000 00 750 00 3 96215D 01 -2.O09O 03 -8.6B6C-01 1 • 3930 00 a .0090 01 8 .0750-02 18 3 57000 00 1250 00 3 962140 01 -2.0090 03 -1.2B10 00 1 .3920 00 a .0020 01 1 .4620-02 18 4 57000.00 1750 00 3 962140 01 -2.0080 03 -1.4680 00 1 .3900 00 a 002D 01 -5 4870-03 18 57000 00 2250 00 3 962140 01 -2.0080 03 -1.4100 00 1 .3950 00 a 0I7D 01 -5 B46D-Q2 18 57000 00 3000 00 3 962130 01 -2.0060 03 -9.3230-01 1 .3950 00 8 0930 01 -3 0650-01 18 7 57000 00 4000 00 3 962130 01 -2.0080 03 -8.6B1E-02 1 • 3980 00 a 055D 01 -1 4S6D 00 19 1 58000 00 250 00 * 962220 01 -2.0440 03 -1.395C-01 1 .3930 00 8 OOOD 01 3 5790-01 19 58000 00 750 00 3 962220 01 -2.0440 C3 -3.S82C-01 1 • 393D 00 8 0130 01 1 .101D-01 19 3 58000 00 1250 00 3 962220 01 -2.0440 03 -5.5980-01 1 .3930 00 8 0020 01 2 ,0680-02 19 4 50000 00 1750 00 3. 962220 01 •2.0430 03 -6.205C-01 1 .3900 00 8 002D 01 -5 1620-03 19 5 58000 00 2250 00 3. 962220 01 -2.0430 C3 -5.7BSC-01 1 .3940 00 8 0140 01 -6 203D-02 19 58000 00 3000 00 3 962220 01 -2.0430 03 -3.733C-01 1 .3920 00 8 078D 01 -3 3180-01 19 7 58000 00 4000 00 3 962210 01 -2.04 30 03 -2.2260-02 1 .391,0 00 8 3830 01 -1 .5580 OD 20 1 59000 00 250 00 3 962300 01 -2.0790 03 -5.2B3E-02 1 .3920 00 a 0610 01 4 68SD-01 20 59000 00 750 00 3 962300 01 -2.079E 03 -1.46LD-01 1 .3920 00 8 0180 01 1 0660-01 20 3 59000 00 1250 00 3 962300 01 -2.0790 03 -2.049C-01 1 .3920 00 8 0030 01 2 .6460-02 20 4 59000 30 1750 00 3 962300 01 -2.0780 03 -2.1780-01 1 .3920 00 8 0020 01 -3 .5530-0} 20 S9000 0' 2250 00 3 962300 01 -2.0780 03 -1.949C-01 1 .3920 00 B .0110 01 -5 BSQD-02 20 6 59000 00 3000 00 3 962300 01 -2.0780 C3 -1.2060-01 1 • 391D 00 8 0610 01 -3 1160-01 20 7 59000 00 4000 00 3 962300 01 -2.0780 03 2.0S5C-03 1 .3920 00 8 3080 01 -1 .4670 00 21 1 60000 00 250 00 3. 962390 01 -2.1140 03 -9.6500-03 1 .3910 00 8 OBOD 01 5 9B2D-01 21 60000 00 750 00 3 96239D 01 -2.1140 03 -2.153C-02 1 .3910 00 8 025D 01 1 6960-01 21 3 60000 00 1250 00 3. 96239D 01 •2.1140 03 -3.0010-02 1 .3910 00 8 0050 31 3 7B4D-02 21 4 60000 00 1750 00 3 962390 01 -2.1140 03 -2.617C-02 1 .3410 00 A 0020 01 -1 .0920-03 21 60000 00 2250 00 3 962390 01 -2.113D C3 -1.720D-02 1 .3910 00 8 0080 01 -4 91S3-02 21 60000 00 3000 00 3 962390 01 -2.1130 03 -1.297C-03 •1 .3910 00 a 0470 01 -2 6520-01 21 7 60000 00 4000 00 3. 962390 01 -2.1130 03 2.2060-02 1 .3910 00 8 2390 01 -1 263D 00 22 1 61000 00 250 00 3 962480 01 -2.1490 03 1.196C-02 1 .3890 OO 8 1I2D 01 7 .4020-01 22 2 61000 00 750 00 3 96243D 01 -2.149D 03 3.0790-02 1 .3900 00 8 0340 01 2 .3700-01 22 3 61000 00 1250 00 3. 96248D 01 -2.1490 03 4.904C-02 1 .3900 00 6 0070 01 4 6400-02 22 4 61000 00 1750 00 3 96246D 01 -2.1490 03 6.5810-02 1 .3900 00 8 0010 01 1 781D-03 22 5 61000 00 2250 00 J. 962480 01 -2.1490 03 6.743C-02 1 .3900 00 8 006D 01 -3 8000-02 22 61000. 00 3000 00 3. 96 248 D 01 - 2 . H 9 D 03 5.7390-02 1 .3890 00 8 0340 01 -2 .0990-01 22 7 61000 00 9000 00 3 96248D 01 -2.1480 03 3.756C-02 1 .3900 00 8 180D 01 -1 .0210 00 23 1 62000 00 250 00 3. 96 257 D 01 -2.1B4D 03 2.3310-02 1 .388D 00 B 1460 01 0 6340-01 23 62000. 00 750. 00 3. 962570 01 -2.1840 C3 5.998E-02 1 388D 00 B 045D 01 2 .8600-01 23 3 62000. 00 1250 00 3. 962570 01 -2.1840 C3 8.9890-02 1 • 388D 00 A 0090 01 5 9760-02 23 4 62000 00 1750 00 3. 96 257 D 01 -2.1840 03 1.065C-01 1 • 3B8D 00 a 002D 01 4 7800-0) 23 5 62000 00 2250 00 3. 96 257 D 01 -2.1B0D 03 1.0700-01 1 .3880 00 8 004 D 01 -2.7520-02 23 62000 00 3000 on 3. 962570 01 -2.1830 03 8.479C-02 1 .3880 00 a 025D 01 -1 .5770-01 23 7 62000. 00 4000 00 3. 962570 01 -2.1630 C3 4.6870-02 1 .3880 00 a 133D 01 -7 .912D-01 29 1 63000 00 250 00 3 96266D 01 -2.219C 03 2.B19C-02 1 .3870 00 a 1860 01 1 .0210 00 29 2 63000 00 750. 00 3. 962660 01 -2.2190 03 6.941C-02 1 .387D 00 8 0580 01 3 3820-01 24 3 63000 00 1250 00 3. 96266D 01 -2.219D 03 1.006C-01 1 .3871) 00 8 0110 01 7 .3010-02 24 4 63000. 00 1750 00 3. 96266D 01 -2.2190 03 1.1420-01 1 .3870 00 a 0020 01 7 .9820-03 24 5 63000 00 2250 00 3 962660 01 -2.2180 03 1.091C-01 1 • 3870 00 8 0030 01 -1 ,871D-02 24 6 63000. 00 3000. 00 3. 962660 01 -2.2180 03 8.282C-02 1 • 3870 00 8 0170 01 -1 1440-01 24 7 63000. 00 oooo 00 3. 962660 01 -2.21BD 03 4.499E-02 1 .3870 00 a 0970 01 -5 .9760-01


I T E R . - 2 0 7 9 TIHC'3. 7 2 0 5 C 0 D 0 1 P E R I O D » 3 . 0 0 0 1 0 3 0 CO T I I U INCH B R E N T ' S . 0 0 0 0 0 0 0 - 0 3

V E L O C I T T V E L C C I I T HATER ELEV. T E R P . T E H P . 1 S D I - T _ T - HATER IR IN RATE S A T E

H O D E C E S L O C A T I O N L O C A T I O N E L E V A T I O N 1-1 DIRECT. T- DIRICT. or CHANGE o r CHANGE

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APPENDIX B

COMPUTER PROGRAM NOMENCLATURE AND FORTRAN IV LISTING

0S/360 TORTBU H COBPI1ER OPTIONS - NABE» BAIH,0PT=02.LINECST«60,SIZI«0000K,

SOURCE, EBCDIC, NOHST,NODICK,LO AD, NORAP,*OEDIT,HOID,NOXREF C* » • • * • * * » » * * * * • » • » • » • » « * • » » » » • » • » » » * • to c N O T A I I O D S » » 20 C • • 30 C C O N T E N T I O N U S E D • » 40 C THE INDICES I , a ARE USED TO LOCATE It POUT I * SHE AREA IT BT * * 50 C INDICATING THE I IID J GRID IINES SiUCH CROSS EACH OTHER AT THAT » • 60 C POINT. HID POINTS ARE INDICATED El IRE USE OF * • 70 C I • OR - 1/2 AND J * OS - 1 /2 INDICES. HOST VARIABLE BABES THEN • » 80 C HAVE A BASIC PART HARKED HEBE BT XIX AND AN INDEX PART BHICH • * 90 C HAVE THE FOLLOWING HEARING * * 100 C XXXIJ VM.0F AT ( I , J ) IOCATION • • 110 C XXXIHJ VALDE AT ( I - 1 / 2 , J ) I0CATICN « » 120 C XXTIPJ VALUE AT {1*1/2,0) ICCATICN * • 130 C XXXI3B VALUE AT ( I . J - 1 / 2 ) LOCATICN * • 140 C XXXIJP VALOE AT (I,-1*1/2) L0CATIC3 • • 150 C XXIBJH VALOE AT ( 1 - 1 / 2 , J - 1 / 2 ) LOCATION * * 160 C XXIPJB VALOE AT ( 1 * 1 / 2 , J - 1 / 2 ) LOCATION • • 170 C XXIBJP---VALUE AT ( I - 1 / 2 , J * 1 / 2 ) LOCATION » » 180 C XXIPJP—VALUE AT (1*1/2 , J*1/2) LOCATION • » "(90 C » • 200 C HALFVALOES OF THE ABOVE ARE NAHED ACCORDING TO THE I , J INDICES * • 210 C CONCEPT EXPLAINED ABOVE. THE! ARE NOT DIMENSIONED FOR I AND J • « 220 C SINCE THEI ARE BEING HE-CALCULATED FOF EVERT POINT ANC EVERT TIRE * • 230 C STEP. FOR INSTANCE, THE TEMPERATURE AT TOINT I * 1 / 2 , J IS HARKED * * 240 C TIPJ(NON-DIHESSIONA^) ADC BASS CONCEN1RA1ICN AT POINT * » 250 C I , J - 1 / 2 IS HARKED CKIJH(X) IDIHENSICRED CNIT FOP K BUT NOT ?OR I , J ) . « • 260 C * • 270 C I SOBSCRIPT IN X DIRECTION FOR GRID LINE I (X=0 AT 1 = 1*1/2 * • 280 C AND X=LX AT I=NX*1/2). • • 290 C J SOBSCRIPT IN 7 DIRECTION FCR GIIC LINE J (1=0 AT J=1*1/2 * * 300 C AND T=LY AT J=NY*1/2). * " 310 C K INDEX FOR THE SPECIFIC CHEHICAI SPECIES CK (K=1.. .NK). =» « 320 C * • 330 C » « 340 C BKIJ CONSTANT BASED ON THE SLOPE OT TBS ECTTOB. (SEE NOTES) » • 350 C *EHAHGC(B) BANNING COEF. »OR FRICTION IN THE BOTTOJI.-INPOT » • 360 C BHDIJ BASS FLUX BATE COBING FRCB THE BCTICH. * • 370 C CIJ CHEZT COEFFICIENT FOR BOTTOB FRICTION CALCULATIONS • « 380 C CK(K,I,J) SPECIES BASS CONCENTRATION * * 390 C» CKTIJ(K) BASS CONCENTRATION OF SPECIES CCHING FROH THE TOP * « U00 C* CKBIJ(K) HASS CONCENTRATION OF SPECIES CCHIMG FROB THE BOTTOH. * • 410 C CKT3D(K,I,J) TIME DERIVIATIVE OF SPECI'S BASS CONCENTRATION. » » 420 C CP MIXTURE SPECIFIC HEAT * • 430 C CPK (K) SPECIFIC HEAT * * 440 C «CPUSEC COMPUTER TIHE COT-OTP LIBIT IN SIC.-INPUT » » 450 C *DCKB (1.B) BOSS COEFFICIENT FOR SPECIES K EHOH BOTTOB.-INPUT * • 460 C *FCKT <K,B) -—HASS COEFFICIENT FOR SPECIES K FROB TOP.-INPOT * * 470 C *DEPTH(I) THE UNIFORB DEPTH OF REGION I . • « 480 C *DKXC COEFFICIENT FOR DFXIJ-INPDT * * 490 C DKXIJ(K) TCTM. BINAflY EFFECTIVE DIFFUSION COEFFICIENT FOR « « 500 C SPECIES K IN X-DIRECTIOt. * » 510 C *DKYC—COEFFICIENT FOR DKYIJ-INPUT • • 520 C DKYTJ(K) TOTAL BINARY EFFECTIVE tIFFOSION COEFFICIENT FOR * * 530 C SPECIES K IN Y-DIRECTIOK. * • 540 C *DNX(I) DONNSTBEAB GROSS LATTICE USE BCURLING REGION I IN » » 550 C X DIRECTION. • • 560

340

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C *P*Y(I) -"-DOBRSTREAH GROSS LATTICE U K ECOAEIIG S'SIOH I III • • 570 C T D7RICTICR. • • 5B0 C •PPBTTH TIHE ISCREBEflt POB PBHTIFG OOTFOI H A3DI7IOR TO IK9TIAL • • 590 C AID TIDAL PRISTCOTS.-IRFOT * * SCO C PTB TIRE IRC:*EHERT FOB RIISERTC»L CALCOtATICRS. • » 610 C «PTBLT TIBE IRCRERERT IS HOLTIPLIEC BT ETEII EPERY • • 620 C ROTHC TISE STEFS.-IRFOT • * 630 C DX(TJ EISTARCP IRCREHERT III X OIFFCTIOI AT GRID LIRE I . » • 610 C DY(J)---DISTICE IRCBEBIRT I I t DIBECTIOS AT GRID LIRE J . • • 650 C •rcKBD(K.H)—-TAtOE 0» BOOIDAPI CCRtlTIOR »CB SPECIES CORCERTRATIO*. • • 660 C «F3TR LARGEST LIBIT TOP TIHI IRCBEEEIiT.-IHECT • • 670 C 'PGBD (I) VALUE C» BOURDART CORDITICR POR EEECIES BASS PLljX * • 680 C *FGKBD(R.R) VALUE OP B03RDAFY CCREITIOR PCR BASS ELSE OF SPECIE X. * • 690 C *PHBD (B) "--VALUE CP BODRDART COIDITICI POF S»TER ELEVAYIOR. • • 700 C »FQBDCH)—VALUE CP BOORCART COREITiCR FOE SEAT PLUX * • 710 C *PSBDV(B) VALOE OP BOUPCAR? COJCITICR PCB I0RHAL STRESSES • • 720 C *PSBDSK(fl) VALUE CP BOURDAFT COBC1TIOR EOF SHEAS STRESSES • • 730 C •PTBDCBJ PA IDE CP BOUNDARY eORMTICR PCS TEHP. • • 7«0 C * m PIXiL TIBE OP THE CASP • • 750 C •FUBDrR)—VALUE OP BOURDARY COROITICR POR 0 VELOCITTY • • 760 C *PVBD(H) VALUE CP EOURDARY COROITICR EOF V VEJ.JCITY * • 770 C GKBIJ BASS DIPPDSIOR OP SPECIES R TPOB BCTTOH • • 780 C •GKOT(K.I) VALUE CP BASS GEREBATIC* FEB OUT VOLUBE TOR SPECIE K • • 790 C IR IITERRAL GERPBATIOR PDRCTIOI R1RBER I . • • 800 C GKTIJ HASS riFFDSIOl OP SPECIES K EBOH TCP. • • 810 C GKTTJ(K) HASS PLDX OP SPHCIES K I I X-DIBECTIGR. • • 820 C GKTIJ (R)—RASS EWX OP SPECIES R IR Y-DIRECTIO*. • • P30 C GR EARTH'S GRAVITY, 32.2 ET-SQ/SEC • • 8&0 C SBC CGHVERSICR OBIT. 32.2 LB-BASS IT/LB-ECBCB SSC-SQ. • • 850 C H | I . J ) SATEK SURFACE ELEVATICK REASUBEt EBOH THE BOTTOH. • • 860 C PBfT,J) ELEVATIOR OP BOTTOR PRCB A BEPEBZICE DATUH. • • 870 C RC(T.J) ELFVATIOR OP THE CERTBCIt OP THE ELEHERT PROH A . • • 880 C BEEEBERCE DATUB * • 890 C *HCB(H)—HEAT COE»PICiERT PCP BOTTCH.-IRFDT « • 900 C «HCT(B) HEAT COEPFICIERT POB TOP.-IRPOT • » 910 C HS(T,J) EIFVATIOR OP BATEB SORFACE FBOB A BEPEBERCE DATOH. • » 920 C HT—SIXTORE ERTHAtPT • • 930 C» HTBIJ-—ENTHALPY OP PLUIC COHIlff? PFCH BCITCH. • • 9»0 C HTK(IC) SPECIES ERTHALPT * « 9S0 C HTHD(T.J) TIRE DERIVIATIVE OP HATER SUFFACE ELEVATIOH * • 960 C* HTTIJ ERTHALPT OP PLOIt CORIRG PFCE THE TCF. » • 970 C »IBRDPC»— BOURDABT CORDITIORS PDRCTIOB RORBES (AH I*0EX> • • 980 C •IBOTPJI) BOTTOS CORDITIOBS PORCTIOR ROBBER BSICH BILL SI OSSD • « 990 C POP THE BEGIOR I . • • 1000 C •IBOTPC BOTTCH CORDITIOIS FDRCTIOI ROHBtR |AR IRDEX) • •» 1010 C •ICKBDT(K,H)—BOLTIPLIEB PORCTIOR EOB FCRBC (R> R) » • 1020 C 'ICK8P(K,HJ—HOLTIPLER rOSCTIOR EOF CKB<K,H) « • 1030 C •ICKTPJR.H) BOLTIPLEB POECTIOR POB CKT(R.S) • • 10U0 C »IDCKB<R,B) HOLTIFLIEB PORCTIOR PCB DCXE(R,H) • • 1050 C *ZDCKT(X,H) HOLTIPLIEB EORCTIOR FCB tCKT(K.B) • * t060 C »IDRXB|I)—BCORDAB? COHDITIORS PORCTIORS ROEEEB TO BE IRPOSED CB • • 1070 C PACE CHX(I) CE BEGIOR I . • • 1080 C »IDRYB(I) BOOHDAR? COHDITIORS PORCTIORS ROBBER TO BE IHPOSED OB • • 1090 C P»CE CRY (I) OP REGIOR I . • • 1100 C » I P I R I S — I P EQUAL IEFO RC RESTART EIIE IS CSEAT^'-- - I" /OT • • 1110 C •IGERP(I) — IRTEBRAL GEHERATICR PURCTICR ROBEEit SBtCH RILL BE USED * • 1120 C POB THE BEGIOR I . » • 1130 C •IGBDP(H) nULTIPLIER PORCTIOH EOB EGED(I) • • 1100

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C •IGKBDP(K,N)---NOLTIPLIER FUNCTION JCR FGKBC(*,1) SPE^9£ Kt • » 1150 C •IG!CDVP(!C,T) GFNEFAL PURPOSE FOSCIION TC EE USED CK GKDV(K.I) • » 1160 C 'IC^NFC INTERNAL GENFPATI01 FDNCTICN NDPBER {AN INDEX) • • 1110 C •IHBDPJH— SCITIPLISR FONCTICN TCS FHED(N) • • 1190 C •IHCB(B) NUITIPLIER FUNCTION FOP ECB (S) « « 11«0 C •THCT(SJ SnlTIPLIEP FUNCTION FOB BCTIN) • • 1200 C •INDTR SIBBER OF TINE STEPS BIFCSE EPOCESS OF INCREASE I* TINE STEP* • 1210 C SIZE EFGINS.-INPOT • « 1220 C «INTF(I)---INITIAL CONDITION FONCTICN NUSBES SHICH BILL BE USED FOR • • 1230 C TBI SECTOR I.-INPUT • • 1390 C «TNTFC INITIAL CONDITIONS PONCTICH RUBBER (MB INDEX) • « 1250 C •TNTPT NDBERICAL INTEGRATION PROCEDURE SEIECT10N • • 1260 C (1) SFLFCTS RUNGF-NUTTA-GIII KTHOt • • 1270 C (2) SELFCT5 SULER BETHOD • « 1280 C (3) SELECTS ADAB-BAStORTH AFTHOD • • 1290 C "IPLOT—TP EQUAL ZERO NO PLOTTING INFORBATION IS GENERATED.-INPUT • « 1300 C •lOBDF(B) — BUITIPLIER FUNCTION »S5 FCBD(N) • • 1310 C *TQBF(N| BUITIPLIER FORCTICN FOB CE «H) * * 1320 C •IQDVF(I) GENERAL PUREOSE 'OtiCTIOll TC BE USED ON QDT(I) • • 1330 C *IQTF(N) BUITIPLIER F05CTICN FOE CT(B) • • 13110 C •TRSG REGION RUBBER (AN INDEX)-I*PUT' • • 1350 C •ISBBDF(B) BOVTIPLIER FUNCTION FOP PSBDSB(H) • * 1360 C •I5NBDF(B) BDITIPIIER EDUCTION EOF FSBDI(R) • • 1370 C •ISTART IF EQUAL ZERO NO RESTART INFORHATICN IS REUOIRED.-INPUT • • 1380 C •ISTCKP (K.H) ---BUITIPLIER FOSCTION ICR STCK H. B)-INPUT • « 1390 C •ISTHF(B) BOLTIPLIER FONCTICN »CR STH(B)-INPUT • • 1900 C »ISTTF(B)— BCLTIPLIER 'UNCTION FCR STT(B)-INPUT • • 1910 C •ISTDF(B)-"BUtTIPLIER FUNCTION FOR ST0(K)-1NPUI • • 1920 C •ISTVF(B) BOITIPLIER FUNCTION FOR SIV(B)-1»PUT • • 1930 C «ISTBSF(B) BOITIPLIEP FOSCTION FOS STBS (B)-INPOT • • 1490 C •ITBDF(B) BOITIPLIER FONCTICN FOB ETED(K) • • 1950 C •ITBF(B) — BUITIPIER FUNCTION FOB TI(H) • • 1960 C •ITOPF (I) - -TCP CONDITIONS PONCTICH NCBBER BBICH BILL BE USED FOR • • 1970 C TSE FFGIO* I . • • 1980 C "ITOPFC—-TOP CONDITIONS FONCTTO'S NtflBFR (AN INDEX) • » 1B90 C "ITTF (»)---BOITIPIES FONCTICN P-R TI(H) • • 1500 C •IU8F(B) — BUITXPLER FUNCTION FOB OE(H) • • 1510 C *IUBDP(B) BOtTIFLIER PONCTION FOR EUBD(ft) • • 1520 C •lOPXB(I) BOUNDARY CONDITIONS FDNCTIONS NOBBER TO BE IBPOSED ON • * 1530 C PACE UPX(I) OF REGION I . » • 1590 O •I0PTB(7) BOONDART CONDITIONS FUNCTIONS ROBBER TO BE IRPOSED ON • • 1550 C FACE OPY(I) OF RFGICN I . • • 1560 C •I0TF(N)—HOITIPtEB FfTNCTION FOR 01(11) • • 1570 C •IVBDP(B) BDITIFLIER FONCTICN FOR f?»8<«) • » 1580 C •IFBF(B) BOITIPLER FUNCTION »OR »E(!1) • • 1590 C »IVTF(S) BDl IPLBR FUNCTICN FOR V1(«) • • 1600 C •I«BF(B)— BBVrrpiER FONCITON FOR HE (B) » » 1610 C • m r ( B ) HOIT!i>lER FUNCTION FOR «I(N) • * 1620 C •IZPD(I) NUnBER OF SUBDIVISIONS BITNEEH GROSS LATTICE LINES XGRl(I)* • If,30 C ANt XGxL<I»1) .-INPUT • % 1640 C *IYPD(I)--"NOBBER OF SUBDIVISIONS 7ITREEN GROSS LATTICE LINES YGRL(X)* • 1650 C AND YGRl (1*1) .-INPUT • • 1660 C •LOTHCR—SELECTS THE DESIRED CRITESICR TC DETEPNINE TRE SU7TABILITY • • 1670 C CF THE FRCPOSED tTB.-INPOl • • 1690 C •NANLFC---TOTAL NOBBER OP ANAIYTICAI FUNCTIONS - INPUT • • 1690 C •NBN-—BOUNDARY CONDITION NOBBER • • 1700 C *NBNDF TOTAL NDKBER OF BOONCARY CCNBITICNS FUNCTIONS.-INPOT • • 1710 C »NB0TF—TOTAL NUHBER OF BOYTCH CONtlllONS FUNCTIONS.-INPOT • • 1720

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C BBXH BODAL EISPLAY FOB OPSTJtEAR ECOBEABIES I* X-DIBECTIOB. • • 1730 C WB*P— BODAL EISPLAY FOB D0HB5TREAB ECOBCABIES I * X-DI9ECTI0B. • * 1780 C BBYB BODAL DISPLAY FCB OPSTREAB EOOBEABIES IB Y-DIBECTIOB. " • 1750 C BBYP---BODAL EISFLAY FOR DOBBSTREAB BCOBEABIES III T-DIRECTIOB. • • 17G0 C •HDTHC-—BOHBER OF TIRE STEPS BETCEEB CRABGES IB TIRE STEP SIZE.-IBPO* • 1770 C «BGEBF---T0TA1 SOMBIF OF VOLOHETBIC HEAT CB BASS GEBERATIOB • * 1780 C FOBCTICBS•-IBPOT • • 1790 C •RRBDTP(R) TYf'E OF BOOBCABT COBCITIO* F "EVATIOH • « 1800 C •BISTLF—IOTAI BOBEEB OF IBITIAL CCBCIT" • »BBCTIOBS.-IHPDT • « 1810 C *HK TOTAL BOREER OF CBEBICA1 SPECIES Cli ...BStDEBED.-IBPOT • « 1820 C •BFEG TOTAL BOH EE F OF REGIOBS.-IBE. • • 1830 C •HTBDTP(R) TYPE OF BOOBDABY CON CI HOB FCB TEW. OB . • T.CIES • * 1880 C COBCEUTRATIOB. • • 1850 C • BTBLFC—TOTAL BOHBEB OF TA60LATEB FOBCTIOBS - : VPDT » • 1860 C •HTflAI TOTAI BOHBEB Or TERPEB ATCBE HOBITOBIBG POIBTS.-IBPOT • • 1870 C BTOPF—--TOTAL ROBBER OF TOP CO*DIIICRS FDBCTIOBS.-1HPOT • « 18B0 C *BOBDTP(BJ TYPE OF BOOBtABY COBOITICB FCB VET.OCITY 0 • • 1890 C 'BVBDTP(B) TYPE CF BOOBSARY COBCITIOB FCB VELOCITY V • • 1900 C • BIGRL TOTAI BOBBER OF GROSS LATTICE LIBES I t I DIRECTXOB.-IBPOT • • 1910 C •BYGPL—TOTAI B09BEF OF GBOSS LATTICE LII»S I* Y DIBECTIOB.-IBPOT • • 1920 C •PB9TR PROBLFH TIRE FOB TBiS CASJ.-IKPOT • • 1930 C *CB(B) HEAT COBIBC FBOH THE BCTICR. • • 1980 C •Q«>W(T) VALOE OF HEAT GEBEBATIOB FEB OBIT VOLME IB IETEBBAL • • 1950 C GEBEBATXOB FOBCTIOB BOSEEf I • * 1960 C QKBIJ HEAT COHIBG FBOH EOTTOS BECAOSE CF RASS DI'FOSIOB. • • 1970 C OSTIJ —HEAT COHIBC FROH TOP BECAUSE CF FASS DIFFOSIOB. • • 1980 C *QSOL SOLAS BEAT FLUX-IBPUT • • 1990 C *0T(HJ HEAT COBIBG FROM THE TOP. • • 2000 C 0XIJ---HEAT FLOX IB X-DIBECTIOB. • • 2010 C 0TIJ HEAT FLOX IB Y-MRECTIOB. • • 2020 C BO HIXTORE BESSITY • 2030 C FOR(K) SPECIES OEBSITY • • 2080 C B0KT9—TF1PEFAT0BI DEBIVIATIVE OF THE SPECIES OEBSITY. « • 2050 C BOTD TIRPEFATOBE DEBIVIATIVE OF THE RIITIIFE DEBSITY. • • 2060 C SEXIJ—S-BIES Al THE BCT10B III B-IIFECTIOB. • • 2070 C SBYTJ---STBESS AT THE BOTTOI IB Y-CISECTIC*. • • 2080 C SDTB-—IBITIAL TTBl IBCBEHEBT-IBPOT • • 2090 C •STCB(B,S) IBITIAl VALUE FOB CE |K,I,JJ-IMFOT • » 2100 C »STHCB) IBITIAL VALOE FOB B |I,J»-1BF0T • • 2110 C •STB STABTISG TIRE OF THIS CASI.-1BF0T • • 2120 C •srr<q) IBITIAL VALUE FOB T(I,J»-1BF0T • • 2130 C *STO (H) IBITIAL VALOE FOR 0 ,.1|-IBPOT • » 2180 C *STV INITIAL VAinE TO* VJI.J»-l«FOT • • 2150 C •ST»S|B)-«IBITIAL TALIIE FOB HSfl.JJ-tKFtJT • • 2160 C STXIJ STRESS AT THE TOP IB X-L-IBICTIOB. • • 2170 C STYXJ STRESS AT THE TOP IB X-OIBICTIOB. • • 2180 C SXXTJ— BCBBAL STBtSS IS X-tlBECTICB. • • 21S0 C SXTIJ—SHEAF STSESS IB X- OK Y-OIUCTIOB. • • 2200 C SYYIJ BOBHAL STRESS I * T-DIBECTIC*. • • 2210 C TABABG • • 2220 C TABFBC " • 2230 C T|T.J)---BATBR TFIHEFATOBE. • • 2 2 8 0 C '7D|H) TE1PEFATBBE OF RASS COhlBG FBOR TH* BOTTOI. • • 2250 C •Tr-'-ftEB-POIBT TtBI.-IHPOT • • 2260 I t T! 1' ^ I " " T j n K t EEBIOO IF AB ESTOABY. • • 2270 j TjUj---C0H3TAHT BASED OB TBE SLOPE OF THE TCP HATER SOPFACE. • • 22B0

IH COBBEBT TIRE • • 2290 '«1>T.1—B»S!= Ftox BATE rnHIBG FRCB THE TCP. • • JJOO

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C »TT(H) — TERPEFATORE OP MASS CONING FBOH IHS TOP. * » 2310 C TTRD(I.J) TIBE DEBIVIATIVE OP BA1EB TEnPEBHTOBZ. » • 2320 C 0 | I , J | BATES VELOCITT IB X DIRECTION. » » 2330 C »DB(B) VELOCITT OP HASS COHING FBOH THE BCTTOB IK X-DIBECTIOH-INPDT* « 23U0 C *0PX(I)—OPSTBEAH GROSS IATTICE LIFE BOUNDING REGION I IH * « 2350 C X DIRECTION. • • 2360 C •DPY(I>—OPSTFBA"l GROSS LATTICE LIRE BOOSDING REGION I IR « • 2370 C T DIRECTION. » » 2380 C «DT(H) VELOCITY OP BASS CODING FBCfl TBE TCF IN X-DIRECTION.-INEOT • » 2390 C DTHD(I.J) TIHE DERIVIMIVE OP VEICCITY IB X-DIRECTION. • « 2100 C V(I,J)™«ATER VELOCITY IN Y DIRECTION. * » 2110 C »VB(B) VELOCITY OP HASS CORING ERCH THE BOITOB IN Y-DIBECTION-INPOT» * 2120 C »VT(H) VELOCITY OP HASS COHING ERCH TBI TCE IN Y-DIRECTION.-INPOT « « 2130 C VTHD(I.J) TIBE DESIVIATIVE OF VEICCITY I I Y-DISECTION. * « 21M0 C »BF(B) VELOCITY OP HASS COHING FRCH THE BOTTOH IN Z-DIRECTION-IHPOT* » 2H50 C BS(I.3) RATE OF CHANGE OP BATER ELEVATION BITH RESPECT TO • « 2060 C TIBE. THAT IS ALSO RATER VIRTICAI VELOCITY AT THE SORPACE. » » 2070 C »BT(S) VELOCITY OP HASS COHING ERCH THE TCE IN E-DIBECTION.-INPOT » • 2080 C XGRL(I» AND XGRL(I-O) . -IKOT * « 2M90 C X(I) DISTANCE IR X DIRECTION OP TO THE I GRID tINE. • * 2500 C *XCBL(I) BRCSS LATTICE HHP I I V I DIREC.-INPDT » » 2510 C XGRL<I) AND XGRL(I*1) ,-IFFDT « • 2520 C *XKPC CONSTANT PA FT OP THERHAL CONDUCTIVITY IN • « 2530 C X DIRECTION -INPUT » * 2500 C XXPIJ TOTAL EFFECTIVE BEAT DISFEFSICN COEFFICIENT IN X-DIRECTIOH. • • 2550 C *XTBAX(I) X LOCATION OI POIBT AT SHICH HEAL HADE AVERAGE AND » • 2560 C HIRIBDB TEBPERATOBE SHOULD BE CIICOL&TED * * 2570 C •XTVSC— COBSTANT PAST OP DY3A3IC VISCOSITY IN » » 25S0 C X DIRECTION -INPOT * * 2590 C XTVSIJ TURBULENT VISCOSITY IN X-CIFC * • 2600 C Y(J| DISTABCE IR Y DIRECTICB OP TO THE 3 GRID LINE » • 2610 C •YGRLfll GROSS LATTICE LINE I IN Y DIFEC.-INPOT * * 2620 C »YKPC CONSTANT FAFT OF THEBHAL CORtCCTIVITY IN • * 2630 C T DIRECTION -TBFOT » » 26H0 C YKPIJ-—TOTAL EFFECTIVE HEAT DISPEBSICN COEIPICIEB? Ill Y-DIBECTION. » » 2650 C «YTBAX|I) Y LOCATION OP ABOVE POINT. • » 2660 C XTVS---TURBOLENT VISCOSITY IN I-CIRECTIOK. * « 2670 C •YTVSC—CONSTANT PART OF DYNAMIC VISCQSIIY IN • « 2680 C Y DIRECTION -INPOT * » 2690 C * « 2700 c * . a . . » . . . « * • • • • * • * * • * « » * * • « * • • • • » • • » » 2710 C • * 2720 C • * 2730 C • * 2700

ISN 0002 IHPLICIT BEAL»e (A-H.O-Z) * « 2750 ISN 0003 COHHON/COHBIN/ ANL,AT«PfCFIJ,CKrO(a) ,CFIFJ(«) rCKIBJ(4) ,CKIJP(«) , • « 2760

> CXI JB (0) .DXBVDXP.DYB.EYP.CXIP1tCY3P1»CXII.DXBI.DXLI1« DXR11«DYLJ ,» • 2770 V DTB3,DTtJ1,DTBJ1,RBIJ,GKEIJ(0'/ ,CEIJrQ*BIJ<0) ,SBXIJ,SBYIJ,GXIMJ , * « 2780 > GXIPJ,GYIJB.GYIOP,GTIJ,GKTIJ ,CTIJ,CKTIJ(II) ,STXIJ,STYIJ,QDVIJ ,» » 2790 > QXI(UrQIIPJ,OYIJB.QYTOP,GRTlBJt") ,GKTIPJt«) ,GXYIJH(«) ,GKYIJP(0) .* • 2600 > HTKIJ (0) .HTRIJfl (0) #HTKIP0{4> ,HTRIHJ(ft) .HTKIJP (ft) VHIJVHIJH*HIPJ , * * 2B10 > HIBJ,HIJP.OIO,DIJH.DIPJ.aiHJ.OIJE,VIJ,VIJH.VIPJ,VIHO,VI3P»Tla , • * 2820 > TMR,TIPJ.TIBJ,TIJF.ROICTPC(<l| ,BCIJ,ROIJH,ROIPJ,ROIHJ.BOIJP , » « 2B30 > SHKTPD(»),SHTCKD{0».SHTTPt,SXXIHJ,SXXIPJ,SYYIJH,SYYIJP,SXYIJN , * * 2B00 > SXYIPa.SXYIHJ.SXYIJP.BOIHJD.BCIIJE.ROIJHt.flOiaPD.BQTBP.TDia , * * 2850 > HCIHJ,HCIPJ,HCIJH,HCIJP,GR,HOCKE(ll),SEflTll(0),DENSK(ll),R0OKIJ(O) • 2B60 > GKDVIJ(S» ,DXI,DYJ ,QDV(25),HBD125).UB£(25).VBD(25),TBD(25). • * 2870 > CKBD(«,25),TBIJ,HCBIJ .DCKBIJ(ft).HTKBIJ(ft).BNIJ.UBIJ.VBIJ,«BIJ. • • 2880

345

> B0BIJ.HTB3J.CRBIJ(«) .TTIJ.HCTIJ ,CCKTIJ (H) .HTKTIJ (») ,OTIJ,VTIJ, » « 2390 > STIJ.BOTIJ.HTTIJ.CKTIJJll) ,QBD (2SJ ,GBt (IS) ,GKBD (1.25) ,SBDN(25) , * « 2900 > SBDSH (25) .NIND.WNDX,WINDY , IJ , IR1J. I11 J,IJS1,1JP1,INTRT,KOIJ. » » 2910 > KQIR1J,K0IP1J,K0TJR1,K0IJP1 .NBXR.NBXF.HEYR.NBYP,KSEGIN.SBNDF , * « 2320 > IXQV(25) ,JYQV (25) ,NHBDIP(25) ,N0EBTP(25) ,NVBDTP(25) ,NTBDTP(25) , « » 2930 > NXGSL,NYGFI,NREG,NINTLF,NT0PF,NECTF,N'IEIFC.NTHAX,NGEN1> * • 29(10

ISN OOOt COHHON/Z/NZSP, NDDR, Z (1) * « 2950 ISN 0005 CORHCN/DROO/TIR,DTR,TR,PERIOD,IT.SHOVE,LRCVE.N » « 2960 ISN 0006 CORHO!!/ODT/NK.![X.KY,!IKI(X,IX0.IYO.IH0,IB0.IV0,IS50,IT0,ITTHD0,ICK0 • * 2970 ISN 0007 BIBENSION IXT(10],JYT(10) • » 2980 ISN OOOR CALL 5ETZ « • 2990

C*«* SBBR.SETZ DEFINES FOLLY THE SIZE OF Z ABEAY AND THE YALOE » » 3000 C OF NZSP. « * 3010

ISN 0009 CALL INPBT (NK) « « 3020 ISN 0010 CALL GEOH(KX,KY,Z,Z(2000),Z(HOOO),2(6000),IXT,JYT) • » 3030

C Z=DX.Z(2000) »DY,Z(«000)=X.Z(6000) = Y * * 3010 C »•• PARTITION 1-BIR. ARRAY Z INTO SOEARRAYS CF THE » « 3050 C •» • CORRECT SIZE FOR THE ASSOCIATED 1- , 2", 3- * * 3060 C ««« BIHENSIONAI APRAY. « * 3070

ISN 0011 N=KX«KY • » 3080 ISN 0012 R=NK*N » » 3090

C »»• THE DIMENSIONED ARRAYS A(ICX,KT) ASD B(NK,XX,KT) CONTAIN N AND • • 3100 C R ELERENTS RESPECTIVELY. • » 3110

ISN 0013 I® (KX. IE. 1999. AND.KY.LE. 1999. ARE. NZSP.GE.HAXO(6000*KY-1,N*«*(KX* » * 3120 > KY))) GO 1C 10 » » 3130

ISN 0015 PRINT 1000 ,KX,KY,NZSP • • 3110 ISN 0016 CALL EXIT * • 3150 IS» 0017 10 IDX=1 » » 3160 ISN 001B IDY=KX*1 » » 3170 ISN 0019 IX=IBY*KY • • 3180 •CSN 0020 IY=IX*KX » • 3190 ISN 0021 BO 12 1-1,KY • • 3200 ISN 0022 12 Z (IDY-1*1) =Z (1999*1) » » 3210 ISN 0023 BO 11 1=1,KX » * 3220 ISN 002H 1i» Z(IX-1*I)=Z (3999*1) « • 3230 ISN 0025 BO 16 1=1,KY » * 3210 ISN 0026 16 Z(IY-1*I)-7(5999*1) • « 3250 ISN 0027 LROVE= (tt*NK)»N * • 3260

C •»* HAVE LHOVE ONKNOBNS » « 3270 ISN 0028 GO TO (18,20,18),ISTRT » * 3280 ISN 0029 18 NROVE=IROVE*LROVE • • 3290

C » • • SAVE HEANS SAVING IN A RESTART F l i t AT IKB OF THIS RON • « 3300 C »«• SAVE UNKNOWNS AND ROUNDING ERR.EST., 0. R-K-G. * « 3310 C »»• * • 3320 C * •» SAVE BNKNONHS ANO DERIVATIVES AT PREVICOS TIRE STEP (DER. IN Q). » » 3330 C *»» ADAHS-EASHFCRTH • • 33H0

ISN 0030 GO TO 22 • » 3350 ISN 0031 20 NROVE=I.KOVE » » 3360

C •» • SAVE ONKNONNS ONLY, EOIER. • « 3370 ISN 0032 22 CONTINUE • « 3380 IS7 0033 IDXL-IYfKY » « 3390 ISK 00311 IDXfl=>IDXl*KX * • 3U00 TSN 0035 IDYL=IDXR*KX « » 3»10 ISH 0036 IDYR-IDY1+KY • • 3H20

C «»• DXL ( I *1)-DX(I ) / (DX(I ) +DX (1+1) ) I - 1 , . . . , K X - 1 • » 3H30 C «•» DXR(I*1)=DX(I*1)/(DX(I)4DX(I*1)) 1=1 KI-1 » « 3«»0 C * • » BYL (I*1)=DY (I) / (DY(I) *DY (1*1)) I=1 , . . . ,KY-1 • • 3U50 C *»* DYR(I*1)»DY(I*1)/(DY(I)*D1 (1*1)) I=1 , . . . ,KY-1 * • 3H60

346

ISN 0037 KXN1=KX-1 * * 3470 ISH 0038 DO 24 I=1.K*ai » « 3480 ISN 003C D=Z(IDX«-I) •Z(I0X-1*I) * » 3490 ISN 0040 Z(IDXt«-I)=Z(IDX-1»I)/r « « 3500 IS* 0041 24 Z(IDXB*I) = Z(IDX4I)/D * • 3510 ISH 0042 KYB1=KY-1 * * 3520 ISH 0043 DO 26 I=1,RYH1 » • 3530 ISH 0044 D*ZriDT»I|*Z(IDT-1*I) • * 35U0 ISH 0045 Z(IOYl*I)=Z(IDY-1*I)/D » • 3550 ISH 0046 26 Z(IDYB»I)=2(IDY*I)/D * « 3560 ISH 00U7 IHF1G=IMR<XI * * 3570 ISS 0048 IH=THFLG*H * * 3580 ISH 0049 in=IH+R * * 3590 ISH 0050 IV*IO*N * * 3600 ISH 0051 IT=I?*R • * * 3610 ISH 0052 ICK=IT»N » * 3620 ISH 0053 IEHS5=ICK*fl • * 3630 ISR 005U IEDFI=IEHSF*N * * 3640 ISN 0055 IE7Fl=IE0FI*N * « 3650 ISH 0056 IETHP-IEYFI*N • « 3660 ISH 0057 I5CSK=IETHE*N * » 3670 ISR 005R IBTRD"IECS*»H * • 3680 ISH 0059 I0THD=IHT3D*N » * 3690 ISH 0060 IVTHD=IOTSD*N * « 3700 ISN 0061 ITTF!D=ITTHC+N « * 3710 ISH 0062 ICKTHD-ITTBD»N » * 3720 ISH 0063 KSPACE=ICKT!tD+H-1 » * 3730 ISN 0064 CALL GEOHFG(Z (INFLG) ,KX,KY,S (IDX) ,Z (IDT) ,Z (IX) .2 (IT) ,IXT,JYT, * • 3740

> NCHECK.NZSE.NSPACEj * * 3750 C ••» SET CONSTANTS NEEDED IN SOBR.OtJTFRT. * * 3760

ISH 0065 NKKX=NK»KX » * 3770 ISN 0066 IX0=IX-1 * * 3780 ISN 0067 IY0=IY-1 » • 3790 ISN 0068 IR0=IB-1 * * 3800 ISN 0069 IDOsIO-1 • « 3810 ISN 0070 IV0=IV-1 » * 3820 ISH 0071 IBS0=IHTND-1 * * 3830 ISN 0072 IT0=IT-1 * * 3840 ISN 0073 ITTHD0=ITTHE-1 * » 3850 isr 007tt ICK0=ICX-1 « » 3860 ISN 0075 IF (NSPACE.GT.NZSP) HCBECK=NCBECM10000 * * 3870 ISN 0077 CALL DRIVE (NX, KY.HR.Z (IX) ,Z (IY) , Z (IDX) ,Z (IDY) , Z (IDXL) , Z (IDXR) , * * 3B80

> Z(IDYL) ,Z(IDYR) .Z(IH) ,Z(IO) .2(17) ,Z(IT) ,7(ICK) ,Z(IEHSB) ,Z(IHTHD) , * * 3890 > Z(IOTHB) ,Z (I»THD| ,Z(ITTBE) ,3(ICRTHD) ,Z (INl'lG) ,IXT,JYT,NCHECKi- • * 3900 > Z (IH) ) * * 3910

ISN 0078 RETURN * * 3920 ISN 0079 1000 FORMAT (MEITHER KX.GT. 1999 ' /8X, ' JY .GT. 1999'/ ,5X, * « 3930

> 'OB NZSP.IT.HAX(6000»KY-1,N*4(KX*KY))'/// ' KX=' , I4 / ' KY=', I4/ * « 3940 > ' HZSP=>,I6//' N=KX*KI'//' CF.SOBR.HAIN') • * 3950

ISN 0080 BHD * * 3960 •OPTIONS IH EFFECT* NAHE= BAIR,OPT=02.1ItlECllT=60,SIZE=OOOOK.

• OPTIONS IH EFFECT* SOOBCB, EECDICrHOLIST,BODECK,LCAD,NOI!AI,NOEDIT,NOID,NOXREP

•STATISTICS* SOOBCE STATEBENTS = 79 .PBOGEAH SIZE = 2526

•STATISTICS* NO DIAGNOSTICS GEHIBATEC

1660

• •* • • • EHD OF COHPIIATTOH •«•• •» 105K BYTES OF COBB BOT DSED

348

OS/360 FORTRAB H COHPILER OPTIOBS - BAHE= HAtK,OPT=02,LINECi:T=60,SIEE=0000!(,

SOORCE.EECDIC.BOLIST,NODECK,LOUD,BOHAP,BOEDIT,MOID,HOXREP ISS 0002 SOBROOTIBE IBPOT (BE) ISPtJ 10 ISK 0003 IHPLICIT BEAL»B (A-H.O-Z) INPO 20 ISB 0009 EH«t»0 TODBT.TITIE IHPO 30 ISH 0005 COBHOB/COHEIB/ ANL, ATHP,CPIJ,CFIO (8) ,C«I E3 (8) , CKI1U (U) .CKIJP («) , IHPO 00

> CKIJR(8),EEH,0XP.BIB,BTP,EXIP1,tT0P1,t*II,D*SI.DXlI1.DXRI1.DIIJ .1BPB 50 > DIEJ.DHJ1,BIHJ1,GBIJ,GBEIJ (0) , CEIOtQEBIJ (8) ,SBXia,SBYIJ,GXIH3 , l»PO GO > GXIPJ.GTIOB.GYIOP.GTIJ.GKTIJ (8) ,QTIJ,0RIIJ(<I) .SltflJ.STTIJ.QDVIJ ,INPO 70 > QXIBJ,QXXEJ,QYIJn,QYIJP,GKXXH3|8),GKXIPJ|B) ,GKYIJH(8) ,GKYIJP(8) ,INPO 80 > HTKIJ(«),BTKIJH(8) ,HTHIPJJO),HTEIHJ(8),HTEIJP(8),HIO,HIJH.HIPJ , INPB 90 > HIBa.HiaP.OM.OIJM.DIPJ.OIBO.DIOF.flJ.VIJH.VIPJ.ylBJ.VIJP.TIJ , IBPO 100 > TIJHrTIPa,TIBJ,TIJP,BCKTEB(aj,BCI3,9013F,BOIPJ,R0IR3,80IJP , IBPO 110 > SHKTPO(8),SHTCKD(8),SHTTPt,SXXIHJ.SXXIPJ,SYYIJH.SYTIJP,SXTIJH , XKPO 120 > SXTIP3,SXYIH0,S)(YiaP,BOTHJD,BCItJr,ROUSE,ROIJPD.EQTHP.TCIJ , INPO 130 > HCHJJ,HCIPJ,BCIJ8,HCIJP,GR,ROCKO(8) ,SSHTK(») ,DEBSK(ll) ,»0D*I3(8) ,3NP0 180 > GKDVIJ(«) ,CXI,OYJ .QD7(25) ,HB0(25) ,OBD(:S) ,VBD(25) ,T6D(25), INPO 150 > CrBD(8,25).TBI3.HCBI3 .SCKBI318).BTKBIJ («).BKIJ.OBIJ.VBIJ.BBIJ, IBPO 160 > H&BIJ,HTBIJ,C!tBIJ(B).TTIJ.HCTIJ.DCKTIJ(8),RTKTI3(8),0TIJ,VTI3, IBPO 170 > «Tla,30TIJ,HTTIJ.CKTIJ(II) ,OBD (25) ,GBC (25) , GICBD <4, 25) ,5BDN (25) , INPO 180 > SBDSH<25),«IHD,SIBDX.«IBDI ,13.IH10,1113,IJH1,1JP1,IBTRT.KOIJ. INPO 190 > K0IH1J, KOIP13.K0IJH1rR0IJP1 ,BBXB,1IBXE,HETH,NBYP,HHEGIB,SBBDF , IBPO 700 > IXQ7(25) ,JYQV(25) ,BHBCTP(25) ,B0EDTP(2S) ,BVBDTP(2S) ,NTBDTP(25) , INPB 210 > BXGRL,HIGtL,BREG,BIBTLF,HTOPF,HEOTF,BlBIPC,BTRAX, NGENF INPB 220

TSB 0006 DIHEBSIOB TITLE(18).TODAY(2),BCB(2) IBPO 230 ISB 0007 COHBOB/IBDBIT/DTHLT.STH,SD''H,PBBTH,CPBTTB ,CPOSEC,TItAL,FDTH, IBPO 280

> IHDTR.HDTBC,IPIBIS,l.DTHCB,ISTABT,ISL<3T,«CPO INPO 250 ISB 0008 C03HOB/TABLE/BTBLP(10) .TABABG (25,10) ,TABFBC(25, 10) INPO 260 ISB 0009 COHHOH/SCR1TH/BTAB(10) INPO 270 ISB 0010 READ(5Q,100C) TITLE IBPO 280

C « * • THESE CALLS GET THE DATE ABO TIHE ABE FRIBT THEH « » « * « « INPO 290 ISB 0011 CALL IDAT(TCBAY) IHPO 300 ISB 0012 CALL TIHE(BCB) IBPO 310 ISB 0013 PRINT 1010, (TITLE ( I ) , I«1, 18) , (TCDAX ( I ) , 1=1, 2) , (NOW (I) ,1=1, 2) IBPO 320

c * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * INPO 330 ISB 0018 PRIST 1020 IBPO 380 •ISB 0015 BEAD(50, 1030) HK,NKBGrHIHlir,NGE»F,HBHCP,8T0PP,BB0TF,NABLFC, INPD 350

> NT3LFC,BXGBL,NYGRL,BTBAX IBPO 360 ISB 0016 BEAD(SO,1030) ISTART.IFIBIS .IPICT.INTBT IBPO 370 ISH 0017 READ(5Q,10QO) STH,PRET1,CP0SEC,DEBTIB,TIDAL INPO 3B0 ISK 0018 BEAD(50,1050) SDTB,PDTH,BTHLT.IBtTH.BDTHC.LDTHCR IBPO 390 ISB 0019 PRINT 1060, HK,RBEG,NIBTIF,HGE«F,BBNDF.BTCPP,HEOTP.HANLFC. BTBLFC.IHPO 800

> BXGRL,*"GBL,BTHAX IBPO 810 ISB 0020 PRIHT 1070, I5TABT,IEIBIS .IPLOT.IBTRT IBPO 820 ISB 0021 PRINT 1080, STB,PRBT«,CP0SEC,DPR7TB,TIEAI INPO 830 ISB 0022 ORIST 1090, SDTH,FDTR,DTBLT,IBETE,BDTBC,IETHCB IBPO 880 ISH 0023 IP (BTBLFC.LE.0) GO TO 22 IBPO 850 ISB 0025 I» (BTELFC.LE.10) GO TO 10 IBPO 860 ISB 0027 PRIHT 1100,BTBLFC IBPO 870 ISK 0029 GO TO 18 IBPO 880 ISH 0029 10 DO 12 3=1,BTBLFC IHPO 890 ISB 0030 12 !tTAB(J)=-1 IBPO 500 ISH 0031 PRIST 1110 IBPO 510 ISB 0032 DO 18 I=1,BT8IFC IBPO 520 ISH 0033 BEAD (50, 112C) ITBLFC.BTEHP. (TABABG (J.ITBLfC) .TABFBC (J.ITBLK) , 0= IBPO 530

> 1.BTEHP) IBPO 580 ISB 0038 HTBLP(ITBLTC)»BTEBP IBPO 550 ISB 0035 IE (1•LF.ITBLFC.AHD.IT3LFC.LE.BTGLFC) GO TO 16 IBPO 560

349

IS* 0037 IS* 0038 I SB 0039 ISS 0041 ISB 0042 ISB 0 043 ISB 0044 ISB 0045 ISN 0046 IS* 0047 ISN 0048 ISR 0049 ISN 0050

ISN 0051 ISN 0052 IS* 0053 ISN 0054

ISN 0055

ISN 0056

ISN 0057

ISN 0058 ISN 0059 ISN 0060 ISN 0061 ISN 0062

PSIHT 1130,ITBLFC,BTBLEC INPO 570 14 CALL EXIT INPB 580 16 IT (KTAB(ITSLFC) .EO.-1) CO TO IB IBPO 590

PHIRI 1140,ITBLFC INPO 600 60 TO 14 INPO 610

18 KTAB (IIBLFC)-ilBXEC IBPO 620 DO 20 I'l.BTBLFC INPO 630 RTEHF*NTBLF (I) INPO 640

20 PRINT 1150,1, (TABARG (3,1) ,TABFNC (J , I ) ,0=1,BTEBf) INPO 650 22 8ET0RN INPO 660

1000 FORNAT(18A4) INPO 670 1010 FORBAT(1R1,' CASE TITLES »,18A4,i3X,2A4,4X,2A4/1K, • '/)INPB 680 1020 FORBAT(1X,' INPOT INFORMATION FBCB SDBBOCTINE IHPaT: ' /1I , INPO 690

> t . . . . . . . . . . . . . . . . . . . . . . . . — —1) ISPO 700 1030 *OBNAT(14IS) INPO 710 1040 FORHAT (8E10.2) INPO 720 1050 FORMAT (3E10,2,315) INPD 730 1060 FORBAT ( / ' 0« ,1X, 'CARD *0. 1</ IHPO 7<I0

>'0',IX.'TOTAL FORBES OF CBF1SICAL SFEcHS CK CONSIDERED (*K)» ' . 1 3 INPO 750 > / ' O S IX,'TOTAL 103BER OF REGIONS (RREG)* ' INPB 760 >,I3/'9«,1X,'TOTAL NOBBER OF INITIAI COXDIIIONS FONCTIONS (BINTLF) INPO 770 >• ' , l 3 / ' 0« ,IX,'TOTAL BOBBER OF TCLOBETSIC HEAT OB BASS GENERATION INPO 780 > FONCTIONS (NGENF)« ' , 1 3 / ' 0',1X'TOTAL BOBBER OF BOONDARX CONDITIONINPO 790 >S FBNCTIONS (NBN DP)» ' ,13/'0',IX,'TOTAL NDBBEB OF TOP CONDITIONS FINPO 800 >BNCTIONS (BTOPF) » ' ,I3/'OMX,'TCIAI BOBBER OF BOTTOB CONDITIONS FDINPO 810 >NCTI0NS (NEOTF)» «,13/'0',IX,•TOTAL NDBBEB OF ANALYTICAL FONCTIONSINPO 820 > <NANLFC)« ' .M/'O'.IX. 'TCTAL ROBBER OE TABULATED FONCTIONS (NTBLPINPO 830 >C)» • , 13/ ' 0 ' ,1X, 'TOTAL BOBBER CF GROSS LATTICE LINES IB X-DIRECTIOINPO 840 >N (NXGBL)- ' , I3/ '0 ' , IX, 'TOTAL NOBBER Ot GROSS LATTICE LINES IH Y-DINPO 850 >1RECTIOB (*YGRL)« •,T3/»0',1X.'TCTAL BQNEEB OF TEBP. BONITORING POINPH 860 >INTS (BTBAX) = ' ,13) INPD 870

1070 FOHHAT (// '0 ' ,IX, 'CARD NO. 2 ' . INPO 880 > /»0',IX,'RESTART FLAG. IF IQOAL 2EBC NO RESTART INFOBBATION IRPO 890 >IS REQD1RED (ISTART)' ' , 13 / ' 0 ' . IX, "FINISH FLAG. IF EQDAL ZERO NO RISPO 900 >ESTART FILE IS CREATED (IPINISI- ' .13/ '0 ' , IXPLOTTING FLAG. IF EQINPU 910 >0AL ZEBO NC PLOTTING INFOBBATIOB IS GEREBATED. (IPLOT) - ' , 1 3 / INPD 920 >'0 FLAG FOR SELECTING TBE NOBEBICAL IBTEGBATION PBOCEDORE. (INTHT»IHPO 930 >1 SELECTS BONGE-KOTTA-GILL BETHOC. «/1H ,3X.'INTRT»2 SELECTS EOLER INPO 940 > BETBOD. IBXRT»3 SELECTS ADAR-BASRROBTH BETHOD.) (1RTRT) «='.I1) IHPO 950

1080 P0RBAT(///02X,'CABD NO. 3 ' / ' 0 ' , 1 X . INPB 960 > 'STARTING TIBE OF TBIS CASE (STB)" ' ,F8 .4 /<0 ' ,1X, IHPO 970 > 'fROBLEB TIRE FOB THIS CASE (PBEIR)» ' , F 8 . 4 / ' 0 ' , 1 X , IHPO 980 > 'CORPOTER TIBE COTOFF LIBIT I* SECONDS (CPBSEC) » ' ,F7 .2 /»0 ' ,1X, IHPO 990 > 'TINE INCRIRENT FOB IBINTED 0STE5T ;DfSlTB)= ' , F 9 . 4 / 'O ' . IX, IHP01000 > 'TIDAL PERIOD IF AN ESTOABT (TICAI) « ' .E8.4) INP01010

1090 »OBBAT{//'0«,IX,'CARD BO. 4 ' / ' 0 ' , ' INITIAL TIBE INCBEBENT (SDTH) >INP01020 >• ,F8.5/'0*,1X,'LARGEST LIBIT FOS TIBE INCREBERT (FDTB) = »,F8.5/'0INP01030 >*,IX,'TINE INCBEBENT IS BDLTIPLIED E7ERT BCTBC TISE STEPS BX (DTHJ.IHP<J1040 >T) • ',F6.2/'0*,IX,'BOBBER OF IIBI STEPS EE»0RE PROCESS 0* INCREASINP01050 >E IN TIBE STIP SIZE BEGINS (IHBTB)» ',I3/«0«,1X,'NOBBER OF TINE STINPO1060 >EPS BETBEEN CHANGES IN TIRE STEP SIZE (BtTBC) » ',I3/«0',1X,'CRITEINPB1070 >RION TIPE (AS DEFINED IN SUBROUTINE CBRD1B) THAT EACH OTN BIM BE INP01080 >RSQOIRED TO SATISFY (LDTBCF)" «,I3) INP01090

1100 FOHBAT(• NTBLFC«'I2,1X'IS GREilER TF^N BAX.ALLONED VALOE OF 10. ' ) IHP01100 1110 FORBAT (//2X,'TAB0LATED FONCTIONS') IHP01110 1120 FORBAT(215,6E10« 5.10X/(10X,6E10.S,10X)) IHP01120 1130 FOBBAT (* ITBLFC»'I2,1X'IS NOT I* TBE BANGE 1 10 NTBLFC»'I2) IRP01130 1140 FORBAT ( ' TABLE NC. - ITELFC > 1 J2,1X'BAS ALREADY BEEN OSED.') INP01140

350

ISB 0053 1150 FOEB»T(//7x'l»BtS »0.'I3/llX'T»BiBG ,8*'I»E?»C»/C1PB12 .ll r3X,I11.»)) INPB1150 ISB 0064 BID INP01160

•OPTIONS I * EFFECT* NABE= HAIN,OPT*02,1IHECNT*60,SIZE*OOCOK,

•OPTIONS IN EFFECT* SOOBCB, EECDIC,N01.IST,N0DECK,I,CXD(N0RAE,N0EDIT,H0ID,N0XREF

•STATISTICS* SOOBCE STATEBERTS = 63 .PBOGBAB SIZE = 4236

•STATISTICS* NO DIAGNOSTICS GENERATED

****** -ekd OF COBPHATION •*»»•• 105K BITES OF COBB NOT OSED

351

CS/360 FCFTRAN H

COHPIIER OPTIONS - RAHE» HAIB.OPT«02,LINTCi:T«60,SIZS*OOOOK. SOORCE, EBCDIC, NOLIST.BODECK.LCAD.RCHAP.NOEDIT.HOID.NOXBEP

ISM 0002 SUBROUTINE GEOB(FX,KY,DX,DY,X,Y.IXI,JYT] ISN 0003 IHPLICIT REAL*8 (A-H.O-Z) ISN 0004 COHHON/REGICN/DEFTB (25) ,SH (25) ,IIBEG(2E) ,IRREG(25) ,<** REG (25) ,

> JHBEG (25) ,INTP(25) ,IGENP (25) ,ITCPF(2£) ,IE0TF<25) ISN 0005 IHTEGES*2 IIREG.IBBEG.OIREG.JRFEC ISS 0006 INTEGER»2 INTF,IGENP,ITOPP,IBOTF ISN 0007 COHRON/CONBIN/ ANI, ATHP.CPIJ ,CKI J (1) ,CKIF J («) , CKIH J («) ,CNIJP (») ,

> CKIJB(t),EXR,DXP,DIN,DIP,DXIP1,rTJP1,CXII,DXBI,DXLI1,DXSI1,DTlJ , > D T R J , D T I J 1 , D r R 3 1 # G B I J , G K B I J ( H ) , C B I J , Q N B T 3 ( « ) , S B T I J , 5 B T T J , G I I f ! J , > GXIPJ,GYIJH,GYIJP.GTIJ,GRTI.I (4) ,QTIJ,CXTIJ(4) .STXTJ.STYIJ.QDVIJ , > 0XIRa,QXIFJ.QYI0H.QYi;)P,GKXIHJ|4) ,GKSIPJ(») ,GKYIJH(4) ,GKYIJP(4) . > HTKIJ(<!) .HTKIJH ( 4 ) .HTKIPJ(U) , H I F I H J ( 4 ) , EIKIJP («) ,HIJ ,HIJH .HIPJ , > H I N J , H I J P . D I J r O I J B . D I F J , O I B J , D I J P , V I J , T i a ! , V I P J . T l n j r T I J P . T I J , > TIJ«,TIP3,Tlm,IHP,aOKTPE(») ,RC13,POIJ*,BOIPJ,BOIBa,POIJP , > SHKTPO(*),SHTCKD(4),SBITPD,SXXIEJ,SXXIPJ.ST7IJN,STIIJP,SXIIJR , > SXYIPJ.SXYISJ.SXYiaP.ROIBOD,RCIEOD.RCTJEC.ROIJPD,EOYHP.-TDIJ , > BCI(l3,BCIPJ,BCiaR,RCI3E.GB,BOCFC(<l) .SERIF (0) ,DENSK(4) .B0DKI3J4) , > GfCDVTJ(4) ,CXI,DYJ .QDY(25),H3D(2S) .OBCCE) ,VBD(25) ,TBD(2S) , > CRBD(4,25),TBIJ,BCBIJ ,DCKBIJ (4) .BTKBIJ (4),BNIJ,OBIJ.VBIJ,BBIJ. > ROBIJ,BTBIJ,CKBU(4) ,TTIJ,HCTla,ECKTIO (4) ,HTKTIJ(4) . B T I J . t T I J , > RTI J,ROTIJ,HTTIJ,CRTIJ(4) ,0BD(Z5) ,GBC(2°) ,GKB0(4.25) ,SBDR(25) . > SBDSH(25).BIND,BINDX,HINDI , I J , IB1J , IElJ . I JH1, IJP1 , INTBI ,KOIJ , > K 0 I R 1 J , K 0 I F 1 J , K 0 I J H 1 , K 0 I J P 1 . R B J H . N B X F . N E Y H . B B Y P . N B E G I N . B B N D P , > IXQY (25) * JYQY (25) , NBBDTP (25) ,H0EDTP(25) ,NYBDTP(25) ,NTBDTP(25) , > NIGRL,NTGFI.NREG,PINTLE,RT0PP,Nf01F,NTEIFC,BTBAX,BGENF

LOGICAI*1 TABLE (32) .STRING (132) INTEGER»4 NCB (£) ,KFLG (5) BEAL*4 F1AC«5J,XNANE,YNXNE EQUIVALENCE (TABIS(H ,T»B (1) ) DinERSION EX(1),DT(1) ,J,M) ,V(1) C0HHON/SCB>TB/ZGBL(50) ,IGRlt5C} < tBAREG (25) ,0PX (25) ,DRX(25) ,OPT (25)

> ,DNT (2S) , IXFD (49) ,ITPE(49),IXGR1 ISO] .JTGFL(50) ,NODBEG(25) > IOPXB(25) ,IDNXB (25) ,ICPYE(25) ,ItNYB{25) ,r?1C(25)

INTEGEB*2 IXED,IYFD.IXGRL,JYGRl,IOEREG INTEGERS IUPXB,IDNXB,Tt)PYB,IDH3E, NPEG DIREBS10R IXT(1) ,OYT(1> DIHERSION 1TRAX (10) ,YTHAX(10) .THE (4) DATA XNAHE/' X •/,YNAHE/• T ' / DATA NSCALE/2010000 00/ OATA TAB/' 1234567'.'89ABCDEF','GHIJICLHH','OPQBSTBY'/ DATA PIAB/'BBXB','HBIP', 'BETH',«»BTF«,'BEG.'/

ISN 0008 ISN 0009 ISN 0010 ISN 0011 ISN 0012 ISN 0013

ISN 0014 ISN 0015 ISB 0016 ISN 0017 ISN 0018 ISN 0019 ISN 0020 ISB 0021

ISH 0022 ISN 0023 ISN 0024 ISN 0025 ISN 0026 ISR 0027 ISB 0028 ISN 0029 ISN 0030 ISN 0031 ISN 0032 ISS 0033 ISN 0034

10 20 30 DO 50 60 70 80 90

BEAD(50,1000) (XGPL(H),H»1,NXGSL) NXL«HXGBL-1 BEAD(50, 1010) (IxrD(H) ,H«1,NXL) PRINT 1020 PRINT 1030 TRIBT 1040,(H,XGFL(H) ,IXrD(N) ,B«1,NXl) PBIBT 1040,BXGRL,XGBI(NXGB1) BEAD(50,10GO) (TGBL (H) ,K*1,NYGRL) HYL-HYGRL-1 BEAD (50, 10 10) (IXFD (HI ,H«1,NYL) PRINT 1050 PRINT 1040, (B,YGBL(N) ,ITFD(H) ,R>1,RYL) PRIBT 1040,RIGRL,YGRI(BYGBI)

GEOH GEOH GEOR GEOH GEOH GEOR GEOH GEOR GEOH GEOH 100 GEOH 110 GEOH 120 GEOH 150 GEOH 140 GEOH ISO GEOR 160 GEOH 170 GEOH 180 GEOH 190 GEOH 200 GEOH 210 GEOH 220 GEOH 230 GEOH 240 GEON 250 GEOR 260 GEOH 270 GEOH 280 GEOH 290 GEOH 300 GROH 310 GEOH 320 GEOH 330 GEOH 340 GPOH 350 GEOH 360 GEOH 370 GEOH 380 OEOH 390 GEO?: 400 GEOH m o GEOH 420 GEOH 430 GEOH 440 GEOH 450 GEOH 460 GEOH 470 GEOH 480 GEOH 490 GEOH 500 GEOH 510 GEOH 520 GEOH 530 GEON 540 GEOH 550 GEOH 560

352

I S O 0 0 3 5 I S N 0 0 3 S I S N 0 0 3 7 I S N Q03R XSN 0 0 3 9 I S N 0 0 4 0 I S N 0 0 4 1 I S N 0 0 4 2 I S B O 0 » 3 I S N OOHU ISN ooas I S N 0 0 4 6 I S N 0 0 4 7

ISN scaa I S * 0 0 0 1 I S N 0 0 5 0 TSB 0 0 5 1 • SB 0 0 5 2 I S N 0 0 5 3 TSB 0 0 5 4 I S N 0 0 5 5 I S N 0 0 5 S I S N 0 0 5 7 I S N 0 0 5 B I S N 0 0 5 9 I S 4 0 0 6 0 I S N 0 0 6 1 I S N 0 0 6 2 ISM 1/063

C • •• c »»»

c " 10 c» C» 11 c» C» 12 c» c» C» 13 c«

I SB 0064 ISB 0065 ISB 0067 ISB 0068 ISB 0070 ZSB 0072 ISN 00?3 IS« 0074 18 IS* 0075 ISB 0076 20 ISB 0077

c 22

mmm I SB 0078

c * • • ISB 0079

c ISB 0080 I SB 0081

LASTI=0 GECB 570 BO 12 B=1,BXl GEOR 580 IBTI»LASTI-f1 GEOR 590 LASTI=tASTl4lX?B(Rl GEOB 600 NH>TH=(XGRI(!l»1>-XG8L<81|/im(«l GEOR 610 XL*IGRHH)-.5»«IMH GEOR 620 ITGai(R)»I»TI GSOH 630 00 10 I ' lBTI. lASTI GEOR 640 BX(I1=BIBTR GEOR 650 IC=Xt*BIDTB GEOS 660 ' (IJ»Xl GEOR 670 COBTINBE GEOB 680 IXGRI.(NIGB11»LASTI*1 GEOR 690 IXCEL(R) IS THE 1ST I SOSSCBIPT 10 THE RIGHT OP THE X-GSOSS GEOR 700 LATTICE LI BE. XGRL(B) . GEOR 710 LASTJ-0 GEOR 720 DO 16 R»1,BYI GEOR 730 IBTJ»1AST0*1 GEOR 740 LASTJ-riSTJUTfD (H| GEOR 750 SIDTH«(TGBt(B*1>-YGBL(H))/ITFD{H> GEOR 760 Yl«YGRt(B)-.S»BItTH GEOR 770 JYGBL(B)>IBTJ GEOR 780 DO IB J«IBTJ,L»SIJ GEOS 790 BY(J|«BIDTH GEOR 800 Y1»YL*BIDTH GEOR 910 T(J)«Tt GEOR 820 COBTXNQE GEOR 830 JTGRl(3TGBI)«LASTJ*1 GEOR 940 KX»I»STI GEOR 950 KY-LASTJ SEOR 860 PBIHT 1060 GMR 870 •OP.RAT ( / / • «,7X«B0!)E VIDTB'3X'BOEAL CEBTEI") GEOB 880 PRINT 11 GEOR 890 FORRATI4X'I12X'X-BXBICTIOB'3X'X-CIRECTXOB'/) GEOR 900 PBIBT 12.(X,BX(X),X(X),I»1,LASIX) GEOR 910 FOSRAT(I5.0PF13.5.1PE15.6) GSOR 920 PRINT 10 GEOB 930 PRINT 15 GEOR 940 FORaaT(l»X'J'2X'T-BIRHCTI0B>3X'»-tIRECT10B«/J GEOB 950 PRINT 12, (J,BY(-1),Y(J) ,J»1,LASTJ) GEOR 960 LASTK-IASTI GEON 970 IF (LASTJ.GT.IASTI) lASTR'IASTJ GEOR 980 BO 22 K«1,tASTK GEOR 990 i r (K.GT.IASTI) GO TO 18 GEORIOOO TF (K.GT.LASTJ) GO TO 20 GEORIOIO PBIBT 107a,B,0I<K),DY(K) ,X(K) ,Y(t) GEOR1020 GO TO 22 GEOR1030 PRINT 10BO,K,OI(K).Y(IC) GEOH10UO GO TO 32 GEORIOSO PRINT 1090 vK.DX (K) « X (B) GEOR 1060 COBT1BBE GEOH1370 ASSORE XGR1 ABB YGRl ABE CEDZRIO IB ASCEBIXNG ORBER. GEOR1080 PRINT 1100 GEOS1090 BOBBXP«TOTAl BOBBER OF BODES BEIIRHIBEB BY THE BECTABGDLAB GRID GEOB1100 »ODEXP»IASTI»LAStJ GEOB1110 B09T0T«=T0TAL BOBBER OF B0BE5 IN IHZ DESCRIBES REGIONS. GEOR 1120 MODTOT'O GEOB1130 HSKaO GEOB 1110

353

ISN 0082 ISN 0083 ISI 008« ISN 0085 ISN 0086 ISN 0088 ISN 0089 ISR 0090 ISR 0092 ISH 0093 ISN 0094 ISN 0095 ISR 0097 ISN 0098

ISR 0099 ISB 0100 TSN 0101 IS* 0102 ISB 0103 ISN 0104 ISN 0105 ISN 0106 ISN 0107 ISN 0108 ISN 0109 ISN 0110 isit mil ISB 0113 ISR 0114 I SB 0115 ISB (1116 ISB 0117

ISB 0118 ISB 0119 ISB 0120 IS* 0122 ISB 0123 IS* 0124 ISB 0125 ISB 0127 ISR 0129

C »«• NSK SET TO 1 IP A REGIOB EEGE DOESN'T HE CLOSE EBOOGB TO A GROSS GEOR1150 C •»• LATTICE LTBE. THIS INDICATES THAT A RISSAGE HAS BEEN PRINTED. GE091160 DO 24 8*1, BRIG GEO* 117 0 24 KPEG(B)=-1 GS0S1180 C ••• INITIALIZATION OF 1CREG. BILL CHICK THAT SINE 8EGIOB BOBBER ISN'T GE081190 C »•• ASSIGNED HOSE THAN OBCE. GEOS1200 DO 3« R=1,BREG GEOR1210 READ(50,1110) IfiEG,IBTF(IREG) .IGJBMIRIG) ,DEPT': 1 IREtJ) .UPX(IREG) , GEOR122C > DBX(IBEG) ,BPT(IREG),9BY(ISEG) ,IT0PP{IIEG1 - ?*RIG) .IDPXB (IREGJ GEOR1230 > «IDBXB IIREG),IOPYB (XREG),XBNYE(IREG) GE081240 IF t1.IE.IBIG.ABD.IREG.IE.25) (10 To 28 GEOH12SO PRIBT 1120,XREG GEOR1260 26 CALL EXIT GEON1270 28 IF (KREG(ISZG) .EQ.-1) GO IC 30 GEOR12SO PRIBT 1130,IREG 15108 1 290 CO TO 26 GEOR1300 30 KREG(ISF.6)«IREG GEOR 13 10 IF (0PX(IJ>IG).L?.B3IX(ISEG),*51Klij»(IRIG) . LT. B»Y(IREG> ) GO TO 32 GEOR1320 PBINT 1140,IREG, BPX (IREG) ,LBX(18EG) ,t)?1<lEEG) ,BB7(IREG) GEOR1330 GO TO 26 GS081340 C •»» A BECIOB EDGE SHOULD LIE CB A GBCSS LATTICE LIRE. TBIS IS GEOB13SO C *»• CHECKED IB SBBB.CHEKIB (CHECK EDGE) GEOH1360 C «•• OPOB EXIT FBOH SBBR.CBEKEG, THE VA1BE CF TBS REGIOB EDGE GEOH1370 C ••• BILL CORRESPOND SXACTVY BIIH THE GROSS LATTICE LINE BEAREST GEOR13SO C *»» THE REGION EEGE OPON EBTRl. GEOR1390 32 CALL CREKED (BPX (IREG), XGRL.NXGRL.NSB,' BEX', RC.IREG) GEOB1400 ILREG (IREG) *IXGRl(flC) GEOR1410 CALL CHEXEB(BBX(IREG),XGR1.NEGRI,NSK.* Oil',RC,IREG) GEON1420 IHBEG(IREG)»IXGRL(HC)-1 GE081430 CALL CHEKED(BPT(IREG).TGRL.MTGRL,BSK,' DEI'.RC.IkfiG) GEOS10HO JIHEGIIRBG)»JTGRI(HC) GEOR 14 50 CALL CHEKEB(BRY (IREG), YGR1.BYGBL. NSK, > D NY' , RC.IEEG) GEOR1460 JRREG(IREG)*JYGBL(RC)-1 GE0R1470 ARAREG(IReG)>(DBX (IREG) -OPX (IREG) ) • (BN1 (IBEG)-SPY (IREG)) GEOH14BO NODREG(IREG)s(IBBEG(IREG)-XLREG(IREG)*1) • (JHHEG(IBEG) -JLBEG(IREG) GE081490 > »1) GEOR1500 ROOIOT««OBTCT*BOBBEG(IREG) GEOR1510 34 COBTIBOE GE081520 IF (BSK.EQ.1) PRINT 1100 GEQR1530 PRINT 1150 GEOB1500 PRINt 1160, (I,BPX (I) ,DNX (I) , BPY (I) ,DBY (T) .DEPTH (I) , ARAREG (I) , GEOR15SO > XLREG(I).IRKEG(I),3LREGtD.JBREG(I).NC0FIG(I) ,I=1.BREG) GEOR1560 PRINT 1170,BODTOT,NODEXP GE0R1570 PRINT 1180 GEOH1580 PRINT 1190, (I.IHTFd) ,IGENF<I) .ITOPF (I) . IEOTF(I) .lOPXB(I) , GEOR1590 > IBBXB (I),IOPYB(l) ,IBBYB(I) ,I«1,KRIG) GEORI6OO C ••• CHECK THAT THE BEGIOBS ASI PAMB1SE DISJOINT. SE0H161D C ••• BHEN PAIBTIBG OF ONE REGIOB UPON ANOTHER IS ALLOWED,THIS GEOR1620 C «•• DISJOIBTBESS TEST HOST BE ALIESEE. GEOH163D BDISJT-0 GEOH1640 BREGH1>BREG-1 GEOR1650 IF (NREGR1.EQ.0) GO TO 40 GEOH1660 DO 38 I>1,BBEGB1 GEOH1670 IM«I»1 GEOB1680 DO 36 J*XP1,NBEG GEOR1690 IF (IHBEG(3) .LT.ILREG(I)) GO TO 36 GE081700 IF (ILREG(J) .GT.IRREG(I)) CO TO 36 GEOR1710 IF (JRREG(J) .Ll.JLREG(I)) GO TO 56 GEOR1720

354

ISM 0131

ISH 0133 TSK 0135 ISH 0136 ISH 0137 ISH 0138 ISN 0139 ISN 0190

ISH 0141

ISH 0112 ISN 0143 ISH 014H ISH 0145 ISN 0146 ISM 0147

ISH 0148 ISN 0149 ISH 0150 ISH 0151 ISN 0152

ISH 0153 ISN 0154 ISH 0155 ISN 0156 ISN 0157 ISN 0158 ISH 0154 ISH 0160 ISN 0161 ISH 0162 ISN 0163 ISN 0164 ISN 0165 ISN 0166 ISN 0167 ISN 0169

ISH 0171 ISN 0172 ISN 0173

IP (JLREG(J) .GT.JHPEG(I)) GO TO 36 C »»» IV HERE 2 REGIONS OVERLAF.

IP (NDISJT.EQ.O) PRINT 1100 NDISJT=1 PRINT 1200,1,0 COHTIHOE CONTINOE CONTINUE RPTORH

36 38 40

C »•* C *»« c »«» c ***

ENTRI GEOHFG[NFLG,KX,KY, DX,DY,X,7,IXT,OYT,NCHECK,N3SPf NSPACE)

DIMENSION NFIG(KX,1) PRINT 1210,NZSP,NSPACE

C •»* 1SI ZEFO AIL FLAGS DO 44 1=1,KX DO 42 J=1,NY

42 NPLG(I,J)«0 44 CONTINOE

C •*• A HPLG NORD IS PARTITIOHED AS FOIIONS. THE 1ST 8 BITS (FROM LEFT) C •** CONTAIN THE REGION NUMBER. THE HEXT 4 B U S ARE UNUSED. THE NEXT C •»» ARE N3YP, NEXT 5 NBYB, NEXT 5 NBXE, NEXT E N8XM

00 52 M=1,NFEG IL=tLREG(N) IH=IHREG(M) JL=JLREG |M) JH=JRRFG(H)

C •»« SM USED IH SDBR.CHKDTH TO ASSESS CR DETERMINE THE TIHE STEP, DTM. SH (N) =DMIN1 (EX (II) ,DY (JL)) DO 46 I=IL,IH DO 1)6 J = JL.Jfl

C »** SET THE REGION FLAG IH NPtG(I,J) TC BE H CALL REGPLG (HFLG (I, J) , H)

46 CONTINUE DO 46 I=IL,IH

C ««» SET Y- BCONEAFY FOR REGION N (DPY) CALL PACPLG (NFLG (I, JL) ,IUPYB(M) , 3)

C *»* SET Y* BOOHEARY FOR REGION M (ENY) 48 CALL PACPLC(HFLG(I,3N) ,IDNYB(M), 4)

DO 50 J^JL.JB C »»» SET X- BOUNEARY FOR REGION N (OPX)

CALL PACPLG (HFLG (IL , J) ,IUPXB(M) , 1) C *»» SET X* EOONEARY FOR REGION M (IHX)

50 CALL PACPLG(HFLG(IH, J).IDNXB(M), 2) 5? CONTIHUE

NLAND-0 HTEM=0 IF (NTMAX.LE.O) GO TO 70 IP (NTMAX. IE.10) GO TO 54

C »*» NTMAX IS RESTRICTED BY THE DIMENSIONING CF THE ARRAYS IXT AND JYT C *«* IH SUBR. HAIN. AND THE ABBAY XTBAX AHD YIBAX IN THIS SUBR. C •«• AND ARRAYS THAX.laiH.SHIDTM IH SCBB.DBTV6.

PRINT 1220.NTHAX CALL EXIT

54 READ(50,1230) (XTNAX(M),YIBAX(M),H=1,NIMAX) C *»* DETERMINE NCPES AT NHICH TEMPERATURE HILL BE MONITORED.

GEOM1730 GP.OM174Q GOTH1750 GEQN1760 GEOM1770 GEON1780 GEOH1790 GTOH1800 GEOM1810 GEOM 18 20 GEON1830 GEON1840 GEOM1850 GEOM1860 GEON1870 GEOM1880 GEOM1890 GEOM1900 GEOH1910 GEOH1920 GEOM 19 30 GEOH1940

5GEON1950 GEOM1960 GEOM1970 GE0M19B0 GEOM1990 GEOM2000 GEON2010 GEOB2020 GEOH2030 GEDH2040 GEOM2050 GEON2060 GEOM2070 GEON2080 GEON2090 GEOH2100 GEOM2HO GE0H2120 GEOH2130 GEOM2140 GE0M2150 GEQM2160 GEOM2170 GEOH2180 GEOM2190 GE0112200 GEOH2210 G50H2220 GEOM2230 GEOM2240 GEOM2250 GEOH2260 GEOM 2270 GEOH2280 GEOM2290 GEQH2300

355

i s s a m ISH 0175 ISH 0176 ISH 0177 ISN 0178 ISH 0179 ISN 0180 ISH 0181 ISH 0182 ISH 0183 ISH 018ft

ISH 0186 ISH 0188 ISH 0189 ISH 0191 ISH 0192 ISH 0193 ISH 0194 ISH 0196 ISH 0197 ISH 0199 ISH 0200 ISS 0201 ISM 0202 ISN 020« ISH 0205 ISH 0207 ISH 0208 ISH 0209 ISH 0210 ISH 0212 ISH 0213 ISH 0215 ISH 0216 ISH 0'.17 ISH 0218 ISH 0219 ISH 0220 ISH 0221

ISH 0222

ISH 0223 ISH 0221 IS* 0225 ISH 0226 ISH 0227 ISN 0228 ISH 0229 ISH 0230 ISH 0231 ISH 0232 ISH 0233 ISH 0234

58

c *** c »«*

C •** CP. SOBR.DBIVE. GEOH2310 00 56 W,H«H GEOS2320 CALL BSERCFL(IXT(H),XTHAX(H),X,LASTI,DX ,XBAHE,H,NTEH,0) GE0112330 CALL BSERCH(JYT(R) ,YTHAX(M) ,Y,LASTa.DY.YBABE,R,BTEB,0) GE0B2340

56 COHTIHOE GEDH2350 PRIST 1240 GEOM2360 DO 68 H=1vBTHAX GE0H2370 IXT1=IXT(H) GEOH2380 JYTH=3YT(B) GEOH2390 LREG=BPLG(IXTB.JTTH)/NSCALE GEOM2HOO PRINT 1250,B,XTMAX(H) ,YTHAX(B) , I JTB.3YTB, X (IXTB) ,T (JYTB) ,LBEG GEOB2410 I P (LFEG.G1.C) GO TO 68 GE0B2U20 IF BODE OH LABD, CHECK BEIGHBOBIBG (IH IBEEXICAL SENSE) BODES TO GEON2430 SEE IF OBE I S IH SATER. I F TBEBE IS, OSE I T . GEOH2UaO IF (IXTH .EC.1) GO TO 60 GEOB2450 LREG=RPIG(IXIW-1,JYTH|/HSCALE GE0H2U60 IF (LBEG.EC.O) GC TO 60 GEOM2470 IXTH=IXTH-1 GE0H2480 IXT(H)=IXTB GE0H2490 GO TO 58 GEOH2SOO

60 IP (IXTH.EC.LASTI) GO TO 62 GEOH2S10 LBEG=HFLG{IXTH*1,3YTH)/BSCALE GEON2520 IF (LREG.EQ.O) GO TO 62 GEOH2530 IXTH=IXTH»1 GEOH2540 IXT(H)=IXTH GEOH2550 CO TO 58 GEOM2560

62 IF (aETW.EC.1J GO TO 64 GEOM2570 LREG"BFLG(IX1R ,JYTB~1)/BSCALE GEOH2580 IF (LREG.EQ.O) GO TO 64 BEOB2590 JYTH»JYTH-1 GEOM2600 JYT(H)=JITB GEOH2610 GO TO 58 GEO!)2820

64 IF (JYTM.EQ.IASTJ) GC TO 66 GEOB2630 LREG«BTIG(1XTH,JTTH+1)/NSCAL2 GEOW2640 IF (LREG.EQ.O) GO TO 66 GEOM2650 JYTH=JYTM+1 GEOM 2660 JYT(H)=3YTH GEOH2670 GO TO 58 GEOH26flO

66 BLABD=1 GEOM2690 PRIBT 1260 GEOM2700

63 CONTIHOF GEOM2710 70 CONTIHOE GE0H272D

C »»» VISOAL DISPLAY OF BOONtART FLAGS ABO REGICN IDENTIFIERS. GEOH2730 DO 90 KO-1,5 GE012740

CM PRINT 601,FLAG(KO) GEOH2750 CB601 FORHAT{'1'///' NODAL DISPLAY FOB *A4//| GEOB2160

GO TO (72,74,76,78,80),RO GEOH2770 72 PRIBT 1270,FIAG(1) GEOH2780

GO TO 82 GEOM2790 74 PRINT 1280,FLAG(2) GEOB2800

GO TO 82 GEOM2810 76 PRINT 1290,FLAG(3) GEOM2820

GO TO 82 GE0M2B30 78 PRINT 1300,FLAG(4) GEOM2BUO

GO TO 82 GEOH2850 BO PBIHT 1310 GEOM2860 82 fH=0 GEOH2870 84 IL=IH+1 GEOB2880

356

ISN 0235 ISH 0236 ISH 0237 ISH 0 238 ISH 0231 ISH 0210 ISH 0211 ISH 0212 ISH 0213 ISH 0211 ISH 0215 TSH 0216 ISH 0217 ISH 0219 ISH 0250 ISH 0251 ISH 0252 ISH 0253 ISH 0251

ISH 0255 ISH 0256 ISN 0257 ISN 0258


ISH 0265 ISN 0266 ISN 0267

ISN 0268 ISN 0269

ISN 0270


IH=HIN0(LASTI,IH*122) GEOM2890 DO 88 JR=1,LASTJ GEOM2900 J=(LASTJ4 1)-JR GEOM2910 IS=0 GEOM2920 DO 86 I«IL,IH GEOH2930 IS=IS*1 GEOM2910 CALL GTFLGS(JIOR,N?LG(I,J)) G80M2950 SIRING (IS)*TABIE(NOR(KC)»1> GEW12960

86 COHTJNDE GEOM2970 PRINT 1320,J,(STBING(I),I«1,IS) GEON29BO

86 CONTIHOE GEOH2990 PRINT 1330 GT30M3000 IP (IH.LT.IASTI) GO TO 81 G80M3010

90 CONTINUE GEOH3020 NCRFCN=NDISJT*1O»NSKHO0»HlEH«-10CO»NIAND GEOM3030 BETORH GEOM3010

1000 FORMAT(7E10.2.10X) GEOM3050 1010 PORNAT(14I5,10X) GEDM3060 1020 FORMAT(//'0',IX,'INPUT INFCRHATICN FROM SUBROUTINE 0E0H:*/1X, GEOM3070

>. ... V'O'.H,' TGRL(I) - GROSS GEOM 3 080 > LATTICE LIRE I IN THE X-DTRECTICN'/'01,1J,'IXFD(I) - ROMBEB OF SUGEON3090 >BDIYISIONS B1TNEEH GROSS LATTICE LINES XGBL(I) AHD XGRL(I*1).' GEOM3100 >/'0',1X,'YGRL(I) - GROSS LATTICE IIHE I IS T-DIRECTIOH.•/'0*,1X, C?0M3110 >'IYFD(I) - HOMBES OF SOBCIVISIONS BETWEFE GROSS LAT1ICE LINES YGRLGEOM3120 X I ) AND YGBL (1 + 1) .') GEOH313D

1030 POBHAT (//'01,1X'I*6X'XGRL'7X'IXFEI) GE0M3110 1040 FOBMAT(T3,1FI14,5,I6) GEOM3150 1050 F0BMAT(///2X»I,6X'YGRL»7X'IYFD') GEOM3160 1060 FORHAT (//* *,13X, 'NODAL WIDTH', 17X,' NOEAL CENT EB '/IX, * I' ,2X, GEOM3170

> 'X-DIRECTICN*,3X,'Y-DI4ECTI0N1,3X,'X-DIFICTION',3X,'Y-DIRECTION1)GEOH3180 1070 FORMAT (15, OP 2F 13. 5,1P2E15,6) GEOH3190 1080 PORHAT(I5,13X,OPF13.5,15X,1PE15.6) GEOM3200 1090 FORMAT(15,0PF13.S,13X,1PF15. 6) GEON3210 1100 FORMAT ('1') GEOH 3220 1110 FORWAT(3I5.5X,5E10. 2/215,2OX,4 (5X.I5)) GE0H3230 1120 FORHATC 1REGI0N NOHBEB IS OOTSIDE THE FAfGE OF 1 TO 25',IX GEOH3240

> 'IFEG»'I2) GEOH3250 1130 FORMAT(•1REGION NO.=IBEG»•13,1X'RAS ALFBADY BEEN DEFINED.') GE0N3260 1140 FORMAT('1THI OP- AND CONN-STRFAH VALCES ABE INCORRECTLY ORDERED INGEOH3270

> REGION '12/' UPX='P11.5/' DNX«'F11.5/' UEY»'P11.5/' DNY«'F11.5> GE0H3280 1150 FORHAT I///19X'GEOMETRIC DESCRIPTION OF REGIONS',36X, GEOM3290

> 'IHDEXICAL DESCRIPTION'/' REGION'6X'UFX'8X'CNX'8X'DPY>8X*DNY'8X GP.On3300 > 'DEPTH18X'AREA' 7X'I LON'2X«IHIGH'2X'J LCH'2X'JHIOH'3X 'NODES'//) GE0M3310

1160 FOBMAT(I5,OPF13.2,3F11.2,F11.3,1EE13.4,3X,4I7,I8) GEOH3320 1170 FOBHATC ' ,68X, GEOH3310

> '/ GEOH3340 > 68X'TCTAL NC. OE HODES IH (IHFOI) REG30NS»'I8/ GEOH3350 > 68X* HAX. NO. OF NODES IN GRID*'12X.I8) GEOH3360

1180 FOBMAT(//////I3XfFUNCTION SELECTION113X'BCUKDARY SELECTION'/ GE013370 > 1 REGION'3X'TNTF,2X'IGENF'2X'ITCFF,2X,IECTP'5X'I0PXB'2X'ICNXB' GE0H3380 > 2X'IOPYB'2X'IDNYB') GSON3390

1190 FOBMAT(I5,18,16,217,110,317) GSOM34QO 1200 FOB MAT (///' THE REGIONS '12,1X'ANC'13,1X'CVBRLAP.') GEOM3410 1210 FORM AT(//////• NOKBER 07 FLEHENT* AVAILABLE IN ARRAY Z IN MAIN «',GEOH3420

> 17//' NOBEEF OF ELEMENTS HEEDED «',I7) GE0H3430 1220 FORMAT (MNTHAX EXCEEDS 10. CF.SUEB GECK. RTHAX»'I3) GEOH3440 1230 FORMAT (6E10. 2, 20X) GEON3450 1240 FORMAT(//'0',T23,'POSITIONS TC HCNITOB TEMPERATURE' // GEON3460

357

> 3X'M'2X'REQUESTED 1.0CATT0H'9X'SflECTFE > T76,"N0DEV11X' XMIX'Y' 12X'I'7X 'J'lOX'X

ISN 0277 1250 FnRtlAT(IU,:T13.3,5X,Itt,UX,IU.3X,;P12.3,T ISN 0278 1260 FORMAT(/• LAND MODE SELECTED. H U D ONI TSH 0279 1270 FORMAT ('1*///

> • NODAL DISPLAY FOR 0PSTREAH BCONDABIES ISH 0280 12B0 FORMAT(#1'///' NCCA L DISPLAY fOR CCWNSTR

>ION,',*«//» ISH 0281 1290 FORMAT('I1///

> • NODAI DISPLAY FOP OPSTREAft EOONEAPItS ISN 0282 1300 FORMAT ('1'///' HODAL DISPLAY FOR D0HNS1R

>10(1. < ,AU//) rSN 028.1 1310 "ORMAT ('1'///' NODAL DISPLAY "OR RFGICHS TSH 029» 13J0 POFMAT(1 J='13,'•*'122A1J ISB 0285 1330 FORMAT(//) ISB 0286 END

NCBS'OX'NODE LOCATION', GEOH3170 11X,y,7X'REGION'/) GEOMJUBO

7) GE0M3«90 IN WATER.'/) GEON3500

GEOH3510 IN X-HIRECIION,',>«//) GEOM3520 EA1 BOUNDARIES IN X-DIPECTGEOB3530

GEOM35UO GEOH3550

IN Y-OTRECTTON,',AU//) GEOM35fcO EAN BOUNDARIES IN Y-DIRECTGEOM3570

GÔM 3580 //) GE0113590

GEON36DO GEOM3610 GEOM 3620

•OPTION'S IH EFF7CT* HAHE= MAIN,OPT=02,LINECNT=60,«IZF=0000K, •OPTIONS IN ''."ECT* SOOPCE, EBCDIC ,NOLIST, NOCECB , ICAt,NCEAE .NOEDIT .NOItl.NOXREF •STATISTICS* SOtlRC. STATEMENTS = 285 ,PRCGPAM SIZ» = 9180 •STATISTICS* NO DIAGNOSTICS GENERATED ****** END 0» COMPILATION **«**» 53K BYTES OF CORE NOT OSED

358

OS/360 FORTPAN H COMPILER OPTIONS - BAHE» (1AIH,OPT=02,LINECST«60,SIZE»0000K,

SOBBCE,EBCDIC,NOLIST,NODECK,LC»D,HOHAP,HOEB1T,NOID.NOXREF ISH 0002 SBBROBTINE SOLRKG(KX,KY,NK,Y,Q,E,H,U,V,T,CK,HTMB,UTMD, VTHD.TTBD,

> CKTHD,DX,tY,DXl,tlXR,DYL,DYR,NFLG) C »•* C *•» C *•* NBHERICAL IRTEGRATION OP THE SYS1EH OP DIFFERENTIAL EQUATIONS. C •** VIA RDHBE-KBTTA-GILL'S BETHOD. C •*» C *** C *** R-K-G METHOD COMPUTATIONALLY EXECUTES AS BESCRIBKB BY C •»* ROBERT J.THCHPSON IN VOL.12/NUMEER 12/ CECEBBER, 1970 OP THE C •»« COBHOBICATICNS OP THE ACM. C »»* c •» •

ISA 0003 IHPLICIT REAL'S (A-H.0-3) ISN 0004 COnnON/COnBID/ ANL.ATHP.CPIJ.CKIJW.CKIFJW.CF.IHJ^) ,CKIJP(4) ,

> CKIjn (4),EXB,DXF,DYn,BYP, CXl'PI, EYJP1,DXII,DXPI,DXLI1,BXRI1 jDYLJ > DTHJ,DI1J1,DYHJ1,GBIJ,GKEIJ (U),CEIJ.QKBIJ(4),SBXIJ,SBYIJ,GXIMJ , > GXIPJ,GYIJH,GYIJP,GTIJ,GKTIJ(i|| ,0TIJ,0K7IJ(4) ,STXIJ,STYIJ,QDVIJ > QXIHJ,QXIrJ,QYIdH,QYIJP,GKXIHJ(4) ,GKXIPJ It) ,GKYIJH(4) ,GKYIJP(«) > HTKIJ(U) ,HH(IJH(4) ,HTKIPJ (4) ,HTKIHJ(4),HTKIJP (4) , HIJ , IIIJ fl , IIIP J , > Hinj,HiJP,oiJ,uijn,nipj,oiNj,Dijp,vij,vijn,vipj,vinj,vijp,Tij , > TUn.TIPJ.Tir J,TIJP,ROKTPC(U) ,RCIJ,ROIJB,ROIPJ, ROII1J,ROUP , > SHfTPD(4) .SHTCKD(lt) ,SHTTPr,SXXIBJ,SXXIPO,SYYIJH,SYYIJP,SXYIJN , > SXYIPJ,SXYina.SXYIJP,ROIHOD,RCIEJO,RCIJI!B,ROIjrB,EQTnP,TBIJ , > HCIHJ,HCIPJ,HCIJH,HCIJP,GR,ROCKE (<4) .SFHTIi (1) , BENSK (4) ,ROBKIJ(4) > GKBVIJ (1) .BXI.DYJ ,0BV(25),HBB{25) ,BBD(J5) ,VBD(25) ,TBB<25) , > CKBB(<I,2S) ,TBIJ,HCBIJ , DCKDIJ(H) ,HTKBIJ(4) ,BNIJ,UBIJ,VBIJ,NBIJ, > ROBIJ,HTBIJ,CKBIJ(4),TTIJ,HCTIJ,CCKT1J(1).HTKTIJ(4).UTIJ.VTIJ, > NTIJ,ROTIJ, HTTIJ,CKTIJ (4) ,QBB(2S) ,GFC(25) ,GKBD (4,25) ,SBBN(2S) , > SBBSH (25) ,NIND,SINDX,»INBY ,IJ ,IH 1J, IE1 J ,1.111 ,IJP1, INTRT, KOI 3 , > KOin1J,KOIP1J,KOIJni,KOIJPl ,NBXn,NBXE,mn,NBYP.NREGIN.NBNDP , > IXQV (25) , JYQV (25) ,NHBDTP(25) ,B0EBTP(25) .NVBDTP (25) , NTBDTP (25) , > NXGBL,HYGFl,HBEC,NINTLP,NTOPr,NECTF,NIElFC.NTNAX,NGENr

ISN 0005 CONHOB/BROE/TIH,LfH,TH,PER10B,IT,NHCVE,LPCV^,N ISN 0006 DIBENSION Y (1) , Q (1) , E (1) ISN 0007 01HENSION H (1) ,0 (1) . V (1) ,T (1) .CK (1) .ERFHSF (1) , HTHD ( 1) , OTHD (1) ,

> VTHD (1) ,TTRC( 1) ,CKTHD(1) , EX < 1) , CY (1) ,DXI(1) ,DXR (1) ,DYL(1) ,DIH(1) > RPLG (1)

C •«* 404AFB0CCC06219B » 1-1/SORT(2) IN H^XADBCIHAL C ••• 411BS04P333E5DE6 = 1»1/SQRI(2) IB HEXABECIBAL

ISH 0008

ISN 0009 ISN 0010

ISK 0012 ISW 0013 ISN 0014 ISN 0015 ISN 0017 ISH 001R

SOLR SOLR SOLR SOLR SOLR SOLR SOLR SOLR SOLR

10 2fl 30 40 50 6 0 70 80 90

A 1 A2 A 3 • »• 402AAAAAAAAAAAAB « 1/6 IN REXAOECINAL

DATA A1/Z40I|».FBOCCC06219B/,A2/Z411B504»333F9DE6/ ,A3/ > Z402AAAAAAAAAAAAB/.NSB/V

•»» BOUNDARY CONDITIONS HAY VARY NITB TIHI. ••* HOREOVER, ECONDARY CONDITIONS BAY DEPEND ON Y (I.E., CURRENT »»* VALUES OF VARIABLES).

ODDTH*1•BO/BTH IF (NSV.EQ.O) GO TO 14

••« THE VERY 1ST CALL TO SOLVET IS SEECIAL. SPECIAL IN ORDER TO ««* OBTAIB WS AS BE tO. 10 TIH=TH

GO TO 28 12 NSB»0

IF (IT.EQ.C) CALL OUTPBT 1'! DO 16 Ka 1, LBCVE

TEBP=. 5D0* (F (K) -2.D0»O (K) )

SOLR 100 SOLR 110 SOLR 120 SOLR 130 SOLR 140 SOLR 150

,SOLE 160 SOLR 170

,SOLR 180 ,SOLR 190 SOLR 200 SOLR 210 SOL7I 220 SOLB 230 SOLR 240 .SOLR 2 50 SOLR 26 0 SOLR 270 SOLR 280 SOLR 290 SOLR 300 SOLR 310 SOLD 320 SOLR 330 SOLR 340 SOLR 350 SOLR 360

,SOLR 370 SOLR 380 SOLR 390 SOLR 400 SOLR 410 SOLR 4 20 SOLR 430 SOLR 440 SOLR 450 SOLR 460 SOLR 470 SOLR 480 SOLR 490 SOLR 500 SOLR 510 SOLP 520 SOLR 530 SOLR 540 SOLR 550 SOLR 560

359

ISN 0019 SA*E«Y(K) SOLR ISN 0020 K M »T (M •D1B*TEB? SOLR ISN 0021 TENP*(Y <M-SAVE)«ODDTH SOLR ISN 0022 16 Q(K)«Q (It) «3.r.0*TENP-.5D0»F(N) SOLR TSN 0023 TIB*T«».5D0*DTH SOLR ISN 0024 CALL BNDCON(KX,NK,T,CK) SOLR ISN 0025 CALL SOIPNC( HT«D,UTND,VTHC,TTHD ,CKf|1D ,H ,0,V .T ,CK, DX, DY ,DXl, DXR, SOLR

> OYL.DYR.NEIG) SOLR ISN 0026 DO 10 K»1,lNOVE SOLR ISN 0027 TEIIP*A1^ (P IK)-Q(ff)) SOLR ISN 0028 SAVE** (K) SOLR ISM 0029 Y(K)"T(M*CTN^TBHP SOLR ISN 0030 TEltP* <Y(K) -SAVE) *OPDTM SOLR ISN 0031 18 Q(lt)«Q(K)«3.D0*TEtfP-A1»F(K) SOLR TSN 0032 CALL BNDCON(KX,NK,T,CK) SOLR ISN 0033 CALL SOLPHC( HTHD.UTND.VTHC.TTHD .CKTHD .H ,T ,CK, OX, DY ,DXL, OXR , SOLR

> DYL,DYR,HPIG) SOLR ISN 0034 20 DO 22 K'L.LDOVE SOLR ISH 0035 TEnP*A2*(F(K)-0(K)) SOLR ISN 0036 SAVE-Y(K) SOLR ISN 0037 Y(K)*Y{X) •CTB*TEHP SOLR ISN 0038 TRIP" (Y (K) -SAVE) »00!>TM SOLR ISN 0039 22 Q<K )"Q(*)»3 .D0»TI«r-A2»F(X) SOLR TSN 0040 24 TIH*1N*DTH SOLR ISN 0041 CALL BNDCON(KX,NK,T,CK) SOLR ISN 0042 CALL SCLFNC( HTND,UTHO,VTMC,TTHD ,C*THD ,H ,T!,V .T ,CK, DX, IT ,0X1, DXR, SOLR

> OYL.DYR.NPIO) SOLR ISN 004 3 DO 26 K»1,LHOVE SOLR ISN 0044 TEHP"A3# IF (A) -2. D0*Q(K)) SOLR ISN 0045 SAVE«Y(R) SOLR ISN 0046 Y <lt) -T (K) •C1B*TE«P SOLfl ISN 0047 TENP*(Y(K)-SAVE)*ODDTN SOLR ISN 0048 26 Q(K)*Q(K) • 3 .T0*TENP- .5D0*P<K) SOLR ISN 0049 28 CONTINOF SOLR ISN 0050 CALL BHDCON(KX,NK,T,CK) SOLR ISN 0051 CALL SOLFNC( HTND,UTND,VTND,TTND ,CKTND ,D,V .T ,CK, DX, DY • DXL, DXR, SOLR

> DYL,DYR,NIIO) SOLR ISN 0052 IF (NSV.EQ.1) GO TO 12 SOLR ISN 0054 TB*Tin SOLR ISN 0 0 5 5 30 RETORN SOLR ISN 0056 END SOLR

•OPTIONS IN EPPECT* NANE" HAIN,OPT-0<,LINECNT»60 ,SIZE»' OOCCK,

570 580 590 600 610 620 630 640 650 6 6 0 670 6 8 0 690 700 710 720 730 740 750 760 770 780 790 0U0 8 1 0 820 830 840 850 8 6 0 870 8 8 0 890 900 910 920 930 940 950 960 970

• OPTIONS IN EFFECT* SOURCE,EBCDIC,HOLIST,NOtECK,LCAD,HOEAl,NOBDIT,NOID,ltOXREP

•STATISTICS* SOORCE STATEHENTS • 55 ,PSOOSAH SIZE • 2056

•STATISTICS* NO DIAGNOSTICS GEKEPATED

•*»«•• END Of COMPILATION •••••• 105K BITES OP CORE NOT USED

360

CS/360 FORTBAB H COBPIL3R OPTIONS - NAHY* RAIB ,0PT«02 ,LIHEC«T»60 ,STTS«OMOK,

SOOBCE,EBCDIC,HOLISTf H0DECK,L0 AO ,NOBAP ,NOEDIT,BOID ,NOXREF ISH 0002 SBBROOTINE SOLEOL(KX,KY,NN,Y,Q,F,H,C,VfT,CK,HTHD,BTI1D, VIHD.TTHD,

> CKTHD,DX,EY ,DXL,DXR,E1L,BYR,NFLG)

ISH 0003 ISH 0004

ISN 0005 ISN 0006

ISN 0007 ISN 0009 IS* 0010 ISH 0011

ISN 0012 ISH 0013 ISB 0014 ISN 0015 ISH 0016 TSH 0017 ISH 0018 ISN 0019 ISN 0020

C C C c »• c c *» c »• c **

HOREBICAL INTEGRATION OF THE SYSTEH OP DIFFERENTIAL EQOATIOHS. VIA EULER'S BETHCD*

X(TH+DTfl) • r(TB) • DTH«X'(t(H

10 20 30 40 50 60 70 80 90

IMPLICIT REAL*8 (A-H.O-Z) COHHOM/COHEIN/ ANL,ATHP,CPIJ,Cr;lJ(«) .CKItJ(«),CKIHJ (4) ,CIU3P(4) ,

> CKIJH(«),CXB,DXF,DTn,tTP,C(IP1,[EJP1,CXII,[)XRX.DXLI1,DXRI1,DTLJ . > DYRJ,OYLJ1,DYB31,GBIJ,GKEIJ (4).CBIJ.OKBIJ(U),SBXIJ,SBYIJ.GXIBJ , > GXIPJ,GtIOH,GYIJP,OTI3,Gr.TXO(4) ,0TIJ, CKTIJ (4) ,STXIJ,STYIJ,QDVIJ , > QXIHJ,QXIPJ.QYZJR,gTIJP,eBXIBJ<4) ,GKXIPJ(4) .GKTIJH (4) ,GKYIJP(U) , > HTICI.7 (4) , HTKIJH (4) .RTRIPJ (4) ,HTBIHJ (4) , BTRIJP (4) ,HI3,HIJB,HIPJ , > HIIIJ.HIJP.OIJ.DIJII.OIPJ.UIBJ.UIOP.VIJ.VIJB.VIPJ.VKIJ.VIJP.TIJ , > TIJ», TIPJ, TIHJ. TUP, ROBTFC(4| .BC > J.BOIO !! ,ROIP3, BOIH3, ROIJP , > SHKTPD (4) ,SHTCKD(«) ,SHTTPD,SXXIPJ,SXXIPa,S*TI3H,ST*I3P,SXtIJR , > SXYIPO,SIIIBJ,SXTIJP,ROI(1JD,ROIfJD.nOIJI1C,ROIJPD,EQTnP,TDlJ , > HCIflJ, HCX?J,HCIJK, HCIJP,GflfROCKE (4),SEHTR(U), P'r'NSK(4) .BODKIJ(4) , > OKDVI3 !•») ,DXI,DYJ ,QDV(25) ,HBD (25) .ODD (2!) ,VSD(25) ,TBD(25) , > CKBD(4,25) ,TBI3,HCBI3 ,DCRBIJ (4) .BTKHJ (4) ,BNIJ,UBIJ,VBIJ,WBId, > ROBIJ,HTBIJfCKBIJ(4) ,TTIO,HC*IJ,DCRTIJ(») ,KTKTIJ(lt) ,0TIJ,VTIJ, > HTIJ,R0TIJ,HTTI3,CKTIJ(») ,0BD(J5) .GtC (25) ,GKBD (4 , 25) ,SBDN(25) , > SBDSH (25) ,NIND,HIBDX,«INCY , 13 , 1H1 J , 1H J.IJH1,1JP1,INTBT.KOIJ, > frOIH1J,MIF1J,KOIJM,KOIJP1 ,NBXB,NBXP, *MH,NBYP,HREOIH, BBNDF , > IXQV(25),JY0V(25).BHBDTP(25),N<JEDTP(25) .BVBDTP (25) ,NTBDTP (75) , > NXGBL,NYGBL,BRKG,BXB?L*,BTOPP,HEOTF,NIBXFCr NTHAXfNGEHF CO!IHOH/BROt/TIH,OTH.TH,PIBIOC,IT,»HOVE,LBCVE,H DIflEBSION Y |1) ,Q (1) ,F(1) ,H (1) ,0 (1) ,V (1) ,T (1| ,CK(1) ,HTRD<1) ,UTRD(1)

> , VTRC (1) ,TTBD (1) ,CKTHD(1) ,DX(1) ,BY(1) ,DXt (1) , DXB(1) ,DYt(1) ,OTB(1) > ,HF.:.(1)

IF (IT.GT.O) GO TO 10 TIH-TB CALL BNDCOH(RX*HK,T,CK) CALL SOLFNC(nTflD,OTHD,VTND,TTHO,CKTHD,»,0,V,T,CK,DX,DY,DXL, DXR,

•> DYL,DYB,BFIG) CALL OOTPBT

10 DO 12 B'l.LBOVE 12 Y(K)-ttB) • DTB«F(K)

TB"TR*DTH TIR-TB CALL BBDCOB (KX,NK,T,CK) CALL SOLFHC ((1THD,1ITnD,VTED,TT1D,C1tTHD,H, 0«V,T,CK,DX,DY,9XL, DXR,

> DYL,DYR,NFLG) RETOBN END

SOLE SOLE SOLE SOLE SOLE SOLE SOLE SOLE SOLE SOLE 100 SOLE 110 SOLE 120 SOLE 130 SOLE 140 SOLE 150 SOLE 160 SOLE 170 SOLE 180 SOLE 190 SOLE 200 SOLE 210 SOLE 220 SOLE 230 SOLE 240 SOLE 250 SOLE 260 SOLE 270 SOLE 280 SOLE 290 SOLE 300 SOLE 310 SOLE 320 SOLE 3 30 SOLE 340 SOLE 350 SOLE 360 SOLE 370 SOLE 380 SOLE 390 SOLE 400 SOLE 410 SOLE 420 SOLE 430 SOLE 440 SOLE 450 SOLE 460 SOLE 470 SOLE 480 SOLE 490

•OPTIONS IN EFFECT* NAME* f!«IN,0PT»02.LZNECNT«60,fI2E«OOOOK,

•OPTIONS IN EFFECT* SOBBCJ.*ECDIC,NOLIST,BOEECK.LCAD,HOEAF,«OEOIT,NOIO,BOXHFF

•STATISTICS* SOOBCE S'fATEHEBTS - 19 ,»S06BAB SIZE - 1252

•STATISTICS* BO DIAONOSTICS W S i i l L

361

eon OP caHPTmTios 121«, BYTES OP COEE SOT USED

362

OS/360 FORTBAN H

COHPILER OPTIONS - NAME" HAIN,OPT*02,LINECST=60,SIZE=0000K, SOURCE,EBCDIC, NOLIST, NODICK,LOUD ,NOfl»P , NOEDIT, MOID, NOXREF ISH 0002 SUBROOTIHP SCLFNI(NK,KX,KY) ISN 0003 IHPLICIT BEAI*8 (A-H,0-Z) ISN 0004 COHHON/COHBIH/ »NL, ATHP,CPIJ,CKIJ (It) ,CKIE3 (1) , CKIH J (4) .CKTJP (4) ,

ISN 0005 ISN 0006 ISN 0007 ISM 000ft TSN 0009 ISN 0010 ISN 0011 ISN 0012 ISN 0013 ISN 00It ISN 0015 ISN 0016 ISN 0017 ISN 0011 ISN 0019 TSN 0020 ISN 0021 ISN 0022 tSK 0021 ISN 0021 ISN 0025 ISN 0026 ISN 0027 ISN 0028 TSN 0029 TSN 0030

DYRJ»DriJ1,DYi1J1.GBIJ.GKBI.J(4J ,CEIJ,QI1BIJ(1( ,SBXIJ.SBYIJ,GXIMJ QXIHa.QXIPJ.OYIJn.OTIJP.GEXinJIII) fGKXIPi] (1) .GKYIJHO) ,GKYIJP(I») HTKIJ(U) ,HiriJB(U) .HTNIPJ(U) , HT Fill J (4) . HTKIJP 1<I) ,HIJ,HIJH,HIPJ , HIHa,BIJP,UIO,UTJH,OIPJ,UIHJ,OIJP,VIJ,VIJH.VIPJ,YII1J,»IJP,TIJ , TIJH.TIPJ,TIHJ,TIJP,F0KTFD(4) ,RCIJ,BOIJH,HOIPJ,ROIHJ,ROIJP , SHKTPD(4) fSHTCKD(U) ,SHTTPD,SXXIHJ,SXXIPJ,SYYIJN.SYYIJP,SXYIJH . SXYIPJ,SXYIHJ,SXYIJP,R0IHJC,B0II3D,P0IJBD,R0IJPD,EOTHP,TDIJ , HCIHJ ,HCIPJ,HCIJN,HCI<)P,GIt,POCKE (1) , SPHTR (4) , CEHSK (4) .RODKIJ(U) GKDVIJ(4) ,CXI,DYJ ,QD»(25),HBD(Z5) ,UBD(2S) ,YBD(25) ,TBD(25), CKBD(4,25).TUIJ.HCBIJ ,CCKBIJ(tt) .HTKBIJ(4),BHIJ,UBIO,VBIJ,VBI3, ROBIJ,HTBW,C BIJ(U) ,TTI J.HCTIJ ,"CKTIJ (0) ,HTKTIJ(4) ,UTIJ,VTIJ, NTIJ,ROTIJ,HTTIJ,CKTIJ(4) ,QBD(25),GBD(2E),GKED(4,25) ,SBDN(25), SBDSH (25) ,BIND,HINDX,HINDI ,IJ,IH1J.I11J.IJH1,I3P1,tNTBT,KOIJ, K0IH1J,K0IP1J,K0IJH1,K0IJP1 ,NDXH,NBXF,SEI/1, NBYP, HREGIN, NBNDP , IXQV (25) , JYQV (25) ,NHBDTP (25) ,NUEDTP(?5) , NVBDTP(25) ,NTBDTP(25) , NXGRL,NYGFL,NREG,NINTLF,NTOPF,NEOTF,NTBIEC* RTHAX,NQEMF DIHENSION CKIHJD(t) .CRIPJD(II) ,CKIJHD(4) .CKIJPD (4) C **• INSERT 9/12/73 COHHON/DROC/TIH,DTH,TH,PERIOD, IT,!. ROVE,LRCVE.N C0HH0N/INDRIT/DTHLT,STH,SDTH,PRB1H,DPRTTH,CPUSEC,TIDAL,PDTH, > IHBTH,NDTKC,IFINIS,LDTHCR,ISTART,IFLOT,KCPU C *«» END INSERT DATA HASK/IOOOPPPPP/ DATA HASK/TO00FFPFP/ ATHP«2116.224D0«GR I'S III NASK COVER TOTHLLY SPACE TOR »B*H,HBXP, HBYH,HBYP IN PLUG, N»LG. DENS>62.2DC SPHT«1.D0 KXNK-KX*NK XXNK'KX*NK CALL FIXCNI(NK) RETURN ENTRY SOLPNCI HTHD,UTHD,VTHD.TTHE.CKTHt,H,0,V,T,CK,DX,D*,DXL, DXF > DYL,DYR,NFLG) DIHPNSION KTHD (1) ,UTHD(1) ,»THD(1) ,1TH0(1) ,CKTHD(1) ,H(1),U(1) ,V(1) > T(1),CK(1) ,DX<1) ,DY (1) ,DX1 (1) ,DXR (1) ,CYI (1) ,DYR (1) ,NPLG(1) KOIJS'O 00 282 I»1,XX IJ-I DXLI'DXL(I) DXRI-DXR(I) OXRI1*BXR (1*1) DXLI1-DXL(I*1) * DXHU (DXPO) NOT USED HREN • 0Y10 (DTPO) NOT DSED WHEN DXHU-OXOO DXI-DX (I) DXPQ'DX (I) *0X(I*1) KOIJ'irOIJS DO 280 J«1,KY

1-1 J«1 •KX) •KT)

SOL" 10 SOW 20 SOL" 30 SOL" uo SO LP 50 SO LP 60 SOLE 70 SOLE BO SOLP 90 SOLP 100 SOLP 110 SOLP 120 SOLF 130 SOL" m o SOLP 150 SOLP 160 SOLP 170 SOLP 180 SOLP 190 SOLP 200 SOLP 210 SOLF 220 SOLP 230 SOL" 240 SOLP 250 SOLP 260 SOLP 270 SOL" 280 SOLP 290 SOL" 300 SO LP 310 SOL" 320 SOLP 330 SO LP 340 SOLP 150 SOLF 360 SOLP 370 SOLP 180 ,SOIF 190 SOt." 400 iSOLP 410 SOLP 420 SOLP 430 SOL" 440 SOL" 450 SOLP 460 SOL" 470 SOLP 4 BO SOL" 490 SOL" 500 SOLF 510 SOL" 520 SOL" 530 S"LP 540 SG'.F 550 SOL" 560

363

ISH 0031 ISK 0032 ISN 0033

ISN 003® ISN 0035 ISH 0036

ISH 003*7 ISN 0039 ISN 0040 ISN 001(1 ISN 0042

ISN 00U3 ISN 0044 ISK 0045 ISH 0046 ISN 0047 ISN 0048 ISH 0049 ISN 0050 ISN 0051 ISN 0052

ISN 0053 ISN 0054 ISN 4055 ISN 0056 ISN 0057 13* 0058

DYH0«PYP0 DYJ=DY (J) DYPU»DY|J)*DY(J»1)

C • •» OFTENTIMES HI VIE* 2- AND 3- DIBTNSIONAL ARRAYS AS 1- DIBENSIONAL C »»* ARRAYS. THIS OFTEN EXPEDITES THI BACHIWl EXECOTION OF THS PROG. C •*» SUPPOSE DIMENSION A(RX.KY),C<NK,»X,KY) A»E C *** SDPPOSE EQUIVALENCE <3 (1) , A ( 1, 1) ,C (1, 1,1) ) . C *»» THEN C •** A(I,J)=B((J-1(*KX*I) C *** C(K,Ir0)»D((J-1)»NK*KX»Ct-1> *NK*K)

I J P I = I J * K X K0IJP1»KOIJ*KXNK CALL GTFLG S (NBXH,NFLG (IJ) )

C ALL FLAGS ARE OBTAINED WITH CALL TO GTFLGS. TREY ARE STORED IN C NBXt<1), NEXH(2) r NBXH(3) ,...NBXE(5} C NOTE THAT CCHHON/COHBIH/ IS ARRAKGEC SC THAT C NBXR(2)cNBXP, NBXM (3) =NBYB, NBXH <4) =11BYE , NBXH (5) =NREGIN C NREGIH»REGICB BOBBER FOR (I,J)-NCDI C NREGINaO IHPLIES NODE <I,J) IS A MOHWATSS NODE

I " (NREGIN.EQ.O) CO TO 278 DYLJ»DYLfJ) OYRJ=DYR(J) DTLJ1=DYL(J*1) DYRJ1»DYR(J*1)

C *«* A(IJ)cA(I,J) C *** A(IH1J)=A(I-1,J) C «•» A(IP1J)»A(I*1,J) C *** AfIJB1)=A(I,J"1> C »•» A(I,1P1)«A(I,0*1) C *•* C(KOIJ*K)«C(K,1,0) C • • • C(K0IM1J*K|«C(K.X-1 ,0) C »»» C(K0IP1J*K|«C(K,I*1,J) C »•» C(K0IJH1«K)'C(K,I,J-1) C »*» C(K0I3P1*K)»CtK,I,a*1)

KOIB1J»KOJJ-BK KOIP1J«KOJO**K KOIJHI'KOIJ-KXNX IH1J-IJ-1 IP I J s I J H IJH1»IJ-KX DX»!«DXHD OXP»DXPO DYI1-DYMO DYP«DYP0

I J = ( J - 1 ) * K X * I I M 1 J = I J - 1 I P 1 J » I J * 1 I JB1= IJ -KX IJE1=IJ*KX KOTJAFJ- 1)*NK*KX«( I -1) *NK K0IH13-KCIJ-NK KOIPU»KOIJ*NK K0 IJB1»KCIJ - ( * * *»»> K0IJB1»K0IJ* (BK*KX)

(O.I .J)

c DXH»DX(I-1)*DX (I) IF (MEXB.EQ .0) c DXB«2*rX(I) IF (NBXK.GT .0) c * * • DXP»DX(I)*CX(I*1) IF (NBXF. EQ .0) c • * * DXP»2«DX (I) IF (NBXP.GT .0) c * • * OYH-DY (J-1)*DYtJ) TF (NEYH, EQ .0) c DYB«2»0Y(J) I * tNBYB.GT .0) c • * • DYP-DY (J)*CY(J*I) IF (NEYP. EQ .0) c • • • OYP»2«0Y(J) IF (NBYP. GT .0> • Hrj»H(U) 0IJ«0(IJ) YIJ»V(IJ) tn«nm DO 10 K>1,KK

10 CKTJ(K)«CMK0IJ*K)

SOLF 570 SOLF 580 SOLF 590 SOLF 600 SOLF 610 SOLF 620 SOLF 630 SOLF 64 0 SOLF 650 SOLF 660 SOLF 670 SOLF 680 SOLF 690 SOLF 700 SOLF 710 SOLF 720 SOLF 7 30 SOLF 740 SOLF 750 SOLF 760 SOLF 770 SOLF 780 SOLF 790 SOLF 800 SOLF 810 SOLF 820 SOLF 830 SOLF 840 SOLF 850 SOLF 860 SOLF 870 SOLF 880 SOLF 890 SOLF 900 SOLF 910 SOLF 920 SOLF 930 SOL? 940 SOLF 950 SOLF 960 SOLF 970 SOLF 980 SOLF 990 SOLFIOOO SOLFIOIO SOLF1020 SOLF1030 SOLF1040 SOLF1050 SOL»1060 SOLIM070 SOL»1080 SOLF1090 SOLFHOO SOLF 1110 SOL»1120 SOLF1130 SOLF1140

364

c IF HBXH=NBXP=NBTH=NBYP=0, THEN GC TO 440 (UN INTERIOR NODE) SOLF11SO ISH 0059 IHSIDE=I»HE (HASK.NFLG<IJ|) SOLF1160 ISN 0060 IF (INSIDE.EQ. 0) GO TO 200 SOLF1170 ISN 0062 IF (NBXH) 12.12,16 SOLF118 0 ISH 0063 12 HIHJ=HIJ •» DXR I* (H (IH1 J) -HIJ) SOLF1190 ISH 006a 0IH0=0IJ • DJtBI«(0(IH13J-0IJ) SOLF1200 ISN 0065 VIHJ=VIJ • DXRI«(V(IH1J)-VIJ) SOLF1210 ISN 0066 TIHJ=TIJ • nXHI*(T(IH1J)-TIJ) SOLF1220 ISN 0067 DO 14 K=1,NK SOLF1230 ISH 0 068 14 CKIHJ(K)=CK(KOIO*K) • DXFI* (CK (K01H1J* -CMKOIJ+K)) SOLF 1240 ISN 0069 GO TO 58 SOLF1250 ISN 0070 16 HH-NHBDTP(NBXB) SOLF1260 ISN 0071 DXH=DXI»DXI SOLF1270 ISN 0072 GOTO (22,20,284,18),HH SOLP1280 ISN 0073 GO TO 284 SOLF1290 ISN 0074 18 HIH0=HI3»DXII1*(HIJ-H (IP 10)) SOLF1300 ISN 0075 GO TO 24 SOLF1310 ISN 0076 20 HIHJ=HIJ SGLF1320 ISN 0077 GO TO 24 SOLF1330 ISH 0078 22 HIHJ"HBD (NBXH) SOLF1340 ISN 0079 24 ND=H0BD7P(NEXH) SOLF1350 ISH 0080 GOTO (30,28,284,26),NO S0LF1360 ISN 0081 GO TO 284 SOLF1370 ISN 0082 26 OIH.1=OIJ*DXII1 * (OIJ-O (IP13)) SOL»1380 ISN 0083 GO TO 32 SOL*1390 ISN 0084 28 OIHJ-OIO F0LF1400 ISN 0085 GO TO 32 SOLF1410 ISN 0086 30 OIHJaOBD (NBXH) SQLF1420 ISN 0087 32 NV»NVBDTP(NBXH) SQLF1430 ISN 0088 GO TO (38, 36,284,34) .,HF SOLF1440 ISN 0089 GO TO 284 SOLF1450 ISH 0090 34 VIHJ»VIJ*DXII1*(VIJ-V(IP10)) S0LF1460 ISN 0091 GO TO 40 SOLF1470 ISN 0092 36 VTHJs'VIO SOr,F14BO ISN 0093 GO TO 40 SOLF1490 ISN 0094 38 VIH0»7BD(HBXH) SOLF1500 ISN 0095 U0 NTaNTBDTP(NEXH) S0LF1510 ISN 0096 GO TO (52, 48,284,42),NT SOLF1520 ISN 0097 GO TO 284 S0LF1530 ISN 009B 42 IF (tllHJ) 44,44,52 SOLF1540 ISH 0099 44 TIHJ=TIJ»DXII1»(TIJ-T(IP10)) 30LF1550 ISH 0100 DO 46 K°1,NK SOLF1560 ISN 0101 46 CKIHJ(K)=CK(KOIJ*K) «DXLI1« (CK (KOIJ+K) -CK iOIP1J*K) ) SOLF1570 ISN 0102 GO TO 56 SOLF1580 ISN 0103 48 TIHJ=TIJ SOLF1590 ISH 0104 DO 50 K«1, NK SOLFI6OO ISN 0105 50 CKIHJ (K) =CK (KOIJ+K) SO LF1610 ISN 0106 GO TO 56 SOLF1620 ISN 0107 52 TIHJ=TBD(NBXH) SOLF1630 ISH 0108 DO 54 Ka1,RK SOLP1640 ISN 0109 54 CKIHJ (K) *CFBD (K, NBXH) SOLF1650 ISH 0110 56 CONTINOE SOLF1660 ISH 0111 58 IF (NBXP) 60,60,64 SOLF1670 ISN 0112 60 HIPJ=HIJ+0*LI1»(H(IP1J)-HIJ) SOLF'Ce" ISN 0113 OIPJ»BIJ+DXL11*(0(IP1J)-Old) SOLrieOO ISH 0114 7IPJ»FIJ*DXLI1 * (7 (IV1 J) -910) SCLF170C1 ISN 0115 TIPJ=TIJ*DXLI1»(T(IP1J)-7IJ) SOLF 1710 ISN 0116 DO 62 K»1,NK SOLP1720

355

ISH 0117 62 CKIPJ (K) =CK (K0TJ*K) +EXLT1" (CF (KOLPIJ + FJ-CCFK^TJ^K) ) TSH 0119 GO 10 106 ISH 0119 6« NH«NHBDTP(NEXP) ISH 0120 DXP=BXI«!)XI ISH 0121 GO 70 (70.6fl.284 ,66) ,HH ISH 0122 GO TO 281 ISH 0123 66 HIPJ=HIJ*DXTI* (HIJ-H 1IH1J)) ISH 0124 GO TO 72 ISH 0125 68 HTP.1=HIJ ISH 0126 GO TO 72 ISH 0127 10 HIP.T=HBD (NEXP) ISH 0128 72 ««=H0B0TP(»EXP) ISH 0129 JO TO (78,76 ,284 .74) ,»0 ISH 0130 GO TO 2fl» ISN 0131 7ft 0IPJ=UIJ»DXH*(MIJ-0(IS1J)) ISN 0132 GO TO 80 ISN 0133 76 NIPJ=0IJ 7SN 0134 GO TO BO ISK 0135 78 UIPJ=BBD(NEXP) ISN 0136 80 NV NVBDTP(NSXP) ISN 0137 GO TO (86,e«,284,B2) ,NV ISN 0138 GO TO 294 TSH 0139 82 VIPJ=VIJ»DXSI«(VIJ-V(IH1J) ) ISN 0140 GO TC 8fl ISN 0141 84 VIPJ=VTJ ISN 0142 GO TO EE ISH 0143 86 VIPJ=VED(NBXP) ISN 0144 88 HTaNTEDTP(NEXP) ISN 0145 GO TO (100.96.284.90),NI ISH 0146 GO TO 284 ISN 0147 90 IF (OIPJ) 100.92,92 ISN 0148 92 TIPJ=TI.7*DXFI» (IIJ-T(THU)) ISN 0149 On 94 K= 1, NK ISH 0150 94 CKIPJ (K) *CK (KOIJ+K) +DX8I* (CK (K0IJ4K) -CK (KCIH 1J*K)) ISH 0151 GO TO 104 ISN 0152 96 TIPJ=TIJ ISH 0153 00 98 K= 1, NK ISN 0154 98 CKIPJ (K) »CK(K0IJ+K) ISH 0155 GO TO 104 ISN 0156 100 TTP.T=TBI)(NBXP) ISN 0157 DO 102 K=*1,»K ISN 0158 102 CKIPJ (K)=CKBD(K,HBXP) ISN 0159 104 CONTINUE ISN 0160 106 IF (NBYH) 108,108,112 ISN 0161 108 HIJB=RIJ • D*PJ*(H(IJH1)-HIJ) TSH 0162 OTJH=OIJ • D7RJ*(0(IJH1)-0I.1) ISH 0163 VIJH=VIJ • T7PJ*(V(IJH1)-VIJ) ISl< 0164 TIJH=TIJ • DYRJ* (T(IJH1) -TIJ) ISN 0165 DO 110 K=1,NK ISN 0166 110 CKIJH(K)=CK(KCIJ+K) + EYBJ» (CK (KOI JFLU K)-CK (KOIJ+K) ) ISN 0167 GO TO 154 ISN 0168 112 HH=NHBDTP(NBYM) ISN 0169 DYH=ETJ«DYJ ISN 0170 GOTO (118,116,284,114),HH ISH 0171 GO TO 284 ISH 0172 114 HIJH»HIJ»DY1J1«(HTJ-H(IJP1)) ISN 0173 GO TO 120 ISN 0174 116 HIJtfsHIJ

50LR1730 SOLF1740 SOLF1750 SOLF1760 SOL*1770 SOL»1780 SOL"1790 SOLF1800 SOLF1110 SDL'1820 SOLÎ8 30 S0LP1840 SOLF1B50 SOL** 18 60 SOL»1B70 SOLF18BO SOLF1890 SOLF1900 SOLF1910 SOLF1920 SOLF1930 SOLF194 0 SOLF1950 50LF1960 S0LP1970 SOLP19BO SOL"1°90 SOL"2000 SOLF2010 SOL*2020 SOLF2030 SOLF2040 50LF2050 50LF2060 SOLL'207 0 SOLF2080 SOLT2090 S0LF2100 SOLF 2110 SOLF2120 S0LF2130 SO LV 21 4 0 S0LF215C-SOLF2160 SOLF2170 S0LP2180 S0LF219D S0LF2200 S0LF2210 S0LF2220 S0LF2230 S0LF2240 S0LF2250 SOLF2260 30LF2270 SOLF2280 SOLT2290 S7LF2300

366

ISH 0175 GO TO 120 ISH 0176 118 BIJH=H9D (NBYH) ISN 0177 120 NO=NOBDTP(BEIH) ISN 0178 GO TO (126.124,284,122).NO ISH 0179 GO TO 284 ISN 0180 122 0IJH=0IJ+DILJ1«(Dia-0(I3Pl)) ISN 0181 GO TO 128 ISN 0182 124 0IJn=0IJ ISN 0183 GO TO 128 ISN 0184 126 UIJ!i=DED(NETN) ISH 0185 128 N7=NVBDTPt*E1H) ISN 0186 GO TO (134,132,284,130),N9 ISN 0187 GO TO 280 ISN 0188 130 TIJN=VIJ*l)TIJ1 • («J-f (IJP1) ) ISH 0189 GO TO 136 ISN 0190 132 »IJH=9I3 ISN 0191 GO TO 136 ISH 0192 134 VIJH=VBD (NETH) TSN 0193 136 NT=HT8DTP(NEYH) ISN 01911 GO TO (148,144,2B4,133).NT ISN 0195 GO TO 28» ISN 0196 138 IF (FIJN) 140, 140,148 ISN 0197 140 TIJN=TIJ*DUJ1»(IIO-T(IOP1)) ISN 0198 DO 142 R=1,NF ISN 0199 142 CKI3H (*)=CF(NOIO*N) VDYLJI*(CKI ISN 0200 GO TO 152 ISN 0 201 14q TIJH=TIJ ISN 0202 DO 146 K»1,NK ISN 0203 146 CltTJH(K) =CK (KOIJ+KJ ISH 0204 GO TO 152 ISH 0205 148 TIJH=TBD(NBYK) ISN 0206 DO 150 !t=1,NK ISN 0207 150 CKUS(K)=CFEC(K,NBYN) ISN 0208 152 CONTINUE ISN 0209 154 IF (NBIP) 156,156,160 ISN 0210 156 HIJP=HIJ»DYLJ1»(B(IJP1)-HIJ) ISH 0211 0IJP=0IJ*D S L J 1 » (0 (I JP1) -O I J ) ISH 0212 VIJP=VIJ*DIIJ1» (V ; .-JP1) -VI0) ISN 0213 TIJP=Tia»DILJ1»(T(lJP1) -TIJ) ISN 0214 00 158 K*1,HK ISN 0215 158 CICTJP (K) =CK (NCI3+K) •DILJ1* (CN ISN 0216 GO TO 204 IS* 0217 180 HH=NH3DTP(NE7P) ISN 0218 DIP—DYJ*DTJ ISN 0219 GO TO (166,164,284,162),NH ISH 0220 GO TO 284 IS'i 0221 162 HIJP=HIJ*DYSJ»(HIJ-H(IJH1)) ISN 0222 GO TO 168 ISN 0223 164 HIJP=HIJ ISN 0224 GO TO 168 ISH 0225 166 KTJP=HBD(NEYP) ISN 0226 168 ND-NDBDTF(NBYP) IS* 0227 GO TO (174,172,2811,170) ,HD ISN 0228 GO TO 284 ISN 0229 170 OIJP=01J+DYBJ*(013-0(I0H1)) ISH 0230 GO TO 176 ISN 0231 172 OIJP=OIJ ISH 0232 GO TO 576

S0LF2310 SOL? 2 3 20 SOLF2330 SOLF2340 SOLF2350 SOLF2360 SDLF2370 S0LF2380 SQLP2390 SOLF2400 SOLF2410 SOLF242C SOLF2430 SOLP2BUO SOLF2450 SOLF2USO SOI.F2U70 SOLF2480 SOLF249C SOLF2500 SOLF2510 SOLF2520 SOLF2530 SOLF2540 SOLF2550 SOLF2560 SOLF2570 SOLF25SO SOLF2590 SOLF2600 SOLF 2610 SOLF262C S0LF2630 SOLF26UO SOLF2650 SOL"2660 SOLF2670 SOV26BO S0LF2690 SOLF 27 00 S0LF2710 SOLP2720 S0LF273C SOLF 27 UO 50LF2750 S0LF2760 50I.F2770 S01/"2780 S0LF2790 SOL"2800 S0LF2810 S01,l»2820 SQLF2830 SQLF2840 S0LF2950 S0LF2860 SOLF2870 SQLF2880

367

ISH 0233 174 OIJP=OBD(NBYF) SOL»2890 ISN 0230 176 NV=NVBDTP(NBYP) SOLF2900 ISN 0235 G O T O (182,180,284,178),NV SOIT29TO ISN 0236 GO TO 284 SOLF2920 ISN 0237 178 VIJP=VIJ*DYEJ* (VIJ-V (IJfll) ) SOLF293C ISN 0238 GO TO 184 S0LF2940 ISN 0239 180 VIJP=VIJ SOLF29SO ISN 0210 GO TO 184 SOLF2960 ISH 0211 182 VIJP«YBD (NEYP) S0LF2970 ISN 0242 184 NT=NTB0TP(NEYP) SOLF2980 ISN 0243 GO TO (196,192,284,186),NT SOLP2990 I SB 0244 GO TO 284 SQLV3000 ISN 0245 186 IF (VIJP) 156,188,188 50LF3010 ISN 0?46 188 TIJP=TIJ»DYBJ»(IIJ-T(IJH1) ) SCLF3020 ISH 0247 00 190 K=1,NK SOLF3030 ISN 0248 190 CKIJP (K)=CK(K0IJ*K)•DTB3«(CK(KOIJ*K)-CK(KCIJH1*K) ) SOLF 30 40 ISN 0249 GO TO 204 SOLF30 50 ISN 0250 192 TIJpsTIJ SGLF3060 ISN 0251 DO 194 K=1,NK SOLF3070 ISH 0252 194 CKIJP (K) -CK (KOI J+K) SOLF3080 ISN 0253 GO TO 204 SOLF3090 ISN 0254 196 ?IJP«TED (HEYP) SOLF3100 ISN 0255 DO 198 K*1,HK SOLF3HO ISN 0256 198 CKIJP (K) =CKBD (K, NBYP) SOLF3120 ISN 0257 GO TO 204 SOLF3130

C «•» BEGIN CAtCtJIATION POS INTIBIOB NCBE. SOLF3140 ISN 025A 200 DO 202 K=1,NK SOLF31SO ISN 0259 CKIJ (K) *CK (KCXd+K) SOLF3160 ISN 0260 CKIBJ(K)»CKIJ(K) • DYE I * (CK (KOI H1J+K) -CKIJ (K) ) 30LF3-.70 ISN 0261 CKIPJ (K)=CKIJ(K) • DXLI1* (CK(K0IE1J*K) -CKIJ (K) ) SOL»3180 ISN 0262 CKIJH(K)«CKIJ(K) * DYBJ * (CK (KOI JB1«K) "CPU (K) ) SOLF3190 ISN 0263 CKIJP (K)=CKIJ(K) • DYIJ1*(CK(K0IJP1*K) -CPU(K) ) SOLF3200 ISN 0261 202 CONTINOE SOLF3210 ISN 0265 HIHJ«HIJ • DXBI »(H (IHIJ)-HIJ) 50LF3220 ISN 0266 HIPJ=HIJ • DXLI1*(H(TP1J)-HIJ) SOLF3230 ISH 0267 HIJB-KIJ • DYBJ *(H (IJB1) -BXJ) SOLF3240 ISN 0 26B HIJP-HIJ • DYIJ1*(H (IJPI)-HIJ) 50LF3250 ISH 0269 OIHJ»OIJ • CXBI »(0(IH1J)-0IJ) SOLF3260 ISN 0270 OIFJsOIJ • DXLI1 * (0 (XF1 J) -OI J) SOLF3270 ISN 0271 OIJB=OIJ • EYBJ » (0 (IJHI)-OIO) SOLF32SO ISN 0272 0IJP=0IJ • DYtJ1*(D(IJP1)-DIJ) SOLF3290 ISN 0273 VIHJ=VIJ • DXEI »(V (IB1J)-VIJ) SOLF3300 ISN 0274 VIPJ»VIJ • DX1I1*(V(IP1J)-VIJ) SOLF3310 ISN 0275 VIJB=VIJ DYBJ *(V (IJBI)-VIJ) SOLF3320 ISN 0276 VIJP=VIJ • EYIJ1*(V(IJP1)-VIJ) SOLP3330 ISN 0277 TIHJ=TIJ • DXBI •(T(IHU)-TIJ) SOL"3340 ISH 0278 TIPJ=TIJ • EX1I1»(T(IP1J)-TIJ) SOLF33SO ISN 0279 TIJH=TIJ • DYBJ •(T(IJH1)-TIJ) SOL" 3 3 60 ISH 0280 TIJP=TIJ • EYLJ1* (T (IJP1) -TIJ) SOLF3370

C •»» END CAICOIATIOB FOB IBTEHICB NODE. SQLF3380 ISH 0281 204 CONTTNOE SOLP3390 ISN 0282 IF (OIBJ) 206,210,214 50LF3400 ISN 0283 206 OXBJD=OIJ SOLF3410 ISN 0284 VIHJD=VIJ SOLF3420 ISN 0285 TI!1.1D=TIJ SOLF3430 ISN 0286 HIHJD=HIJ SOLF3440 ISH 0 287 DO 208 K«1.NK SOLF3450 ISN 0 288 208 CKIHJD (K) -CSIJ (K) SQLF3460

368

IS* 0239 GO TO 218 SOLP3470 ISN 0290 210 OIHJDsDIHJ SOLF3480 ISN 0291 VIHJD=TIHJ SOLP3490 ISN 0292 TIHJD=TIHJ SOLP3SOO ISN 0293 HIHJD=HIHJ SOLP3510 ISN 0298 T)0 212 K=1,HK S0LP3520 ISH 0295 212 CKIHJD(X) =CKIHJ(K) SOLP3530 ISH 0296 GO TO 218 SOLP3540 ISN 0297 214 IF (NBXH.GT.O) GO TO 210 SOLP 3 5 50 ISN 0299 0IHJD=O(IHV1) SOLP3560 ISN 0300 VIHJD=P(IHTJ) SOLP3570 ISN 0301 TIHJD=T(IH1J) SOLr3580 ISN 0302 HIHJD'R(IHIJ) SOLF3590 ISN 0303 00 216 Ke1,RK SOLP3600 ISN 0300 216 CKIHJD <K> =CR (KUIH1J+K) SOLP3610 ISN 0305 218 IF (BIPJ) 128,224,220 SOLF3620 ISN 030G 220 OIPJD=OIJ 50LP3630 ISN 0307 VIPJD=FIJ SOLP3640 ISN 0308 TIPJB'TIJ SOLT3650 ISN 0 309 HIPJ0=BIJ SOL1*3660 ISH 0 310 10 222 K»1,HK 50LF3670 ISN 0311 222 CKIPJD (K)=CRIJ(K) SOLK36BO ISN 0 312 GO TO 232 SOLP3690 ISN 0313 224 OIPJO=BIPJ SOLF37DO ISN 0310 VIPJD=TIPJ SOLP371C ISN 0315 TIPJD=TIBJ SOLP 37 20 ISN 0316 HIPJD=HIBJ S0LP3730 ISN 0317 DO 226 K=1.N!t SOLP37 40 ISN 0318 226 CKIPJD (K)=CKIPJ (K| SOLP 37 50 ISN 0319 GO TO 232 S0LP3760 ISN 0320 228 IF (NBXP.GT.O) GO TO 224 SOLP3770 ISN 0322 0IPJD=D(IP1J) SOLP37BO ISN 0323 VIPJD-V(IP1J) 50LF3790 ISN 03211 TIPJD-T(IP1J) SOLP3800 ISN 0325 HIP3D»H(IP1J) SOLF3810 ISN 0 326 DO 230 K=1 ,NK SOLP3820 ISN 0327 230 CKIPJD (K) =CK (K0IF1 J*K) SOLF3830 ISN 0328 232 IP (VIJHJ 234.238,242 SOLP3B4D ISN 0 329 234 BIJND=DIJ SOLF38SO ISH 0330 VIJPD-PU SDLP3860 ISN 0331 TIJHO=TIJ SOLP3870 ISN 0 332 BIJHD=HIJ SQLF3880 ISN 0 333 DO 236 K=1,NK SOLP3890 ISN 0334 236 CKIJHD (K)=CFIO (K) SOLP3900 ISN 0335 GO TO 246 S0LF3910 ISN 0336 238 0IJI>0=DIJH S0LP3920 ISN 0 337 VIJ«D=7IJB SOLP39 30 ISN 0338 TIJHD=TIJfl SOLP394D ISR 0339 HIJHD=BIJH SOLP395D ISN 0340 HO 240 F=1,8* 50LP3960 ISH 03U1 240 CKIJHD (K) =CKIJH (F) SQLP3970 ISN 0 342 GO TO 246 S0L"398B ISN 0343 242 IP (HBIH.GT.O) GC TO 238 SOLP3990 ISN 0345 BIJHD=0(13H1) SOLPKOOO ISN 0346 VIJHDuVdJHI) SOLPOOIO ISH 0347 TIJHD=T(1JB1) SOLF4020 ISN 034B HIJHD=H(IJH1) SOLP40 30 ISH 0349 DO 244 K=1,NK SOLP4040

369

ISN 0350 ISN 0351 TSN 0352 ISN 0353 TSN 035U ISN 0355 ISN 0356 ISH 0357 ISH 0358 ISN 0359 ISN 0360 ISH 0361 TSN 0362 ISH 0363 ISN 0364 ISN 0365 'ISN 03o6 ISN 0368 ISN 0369 ISN 0370 ISH 0371 ISH l»„72 ISN 0373 ISN 0374

ISN 0375 ISN 0376 ISN 0377 ISN 0378

ISH 0379 ISH 0380 ISN 0381

ISN 0382 ISK 0383 ISH 0384

ISN 0385 ISH 0386 ISN 0387

ISN 0388 ISN 0389

244 CKIJHD (K)*CK (K0IJH1+K) 246 IT (TIJP) 256,252.248 248 OIJPD-OIJ

VIJPD-TIJ TIJPD-1IJ HIJPD-HIJ DO 250 K«1 ,NK

250 CKIJPD (KJ « C K U (K) GO TO 260

252 OIJPD-OIJP VIJPD-TIJP TIJPD-TIJP HIJPD-HIJP DO 254 K»1,NK

254 CKIJPD (N)«CKIJP(K) GO TO 260

256 IP (NB7P.GT.C) GO TO 252 OIJPD»0(IJP1) VIJPD»V(IJP1) TIJPD«T(IJF1) HIJPD«H(IJP1) DO 258 K»1,NK

258 CKIJPD (K)»CK(K0IJP1+K) 260 COHT1NOB

THE CENTROIDAL ELETATION HC CAN Br! CALCULATED PON THE TIME BEING PCB ONIPOBH DEPTH AS

HCIPJ«0.5D0*HIPJ HCIHJ«0.5D0*HIHJ HCIJP»0.5DO»BIJP HCIJH-0.5D0»HMH

EPALOATE PHTSICAI PROPERTIES BT CAIIINS THE NATPR SBBROOTIHE NITB THE APPROPRIATE ANG0EEN7S

AT P01HT I+1/2,«I

CALL HATPRP( CKIFJ.TIPJ,DE«S,SFHT.ROTPE) HOIPJODENS HTIPJ»SPHT»TIPJ

AT POIHT 1-1/2,J

CALL HATPRP( CKIHJ,TIHJ,DEHS,SEH1,R0TPDJ HOIHJ-DEHS nTIHJ«SPHT*TIHJ

AT POIHT I , J + 1 / 2

CALL HATPRP( CKIJP,TIJP,DINS,SPHI.BOTPD) ROIJP-DENS HTIJP*SPHT»TIJP

AT POINT I,J-1/2

CALL HATPRP ( CKIJH,TUB.DENS,SFHI.FOTPC) BOIJH-DEHS

SOLP4050 SOLP4060 SOLP4070 SOLP4080 30LP4090 SOLP4100 S0LP4110 SOLF4120 SOLP4130 SOLP4140 SOLP4150 SOLP4160 SOLF4170 SOLP4180 SOLP4190 50LP4200 SOLP4210 SOLF4220 S0tLP4230 SOLP4240 SOLP4250 SOLF4260 SOLP4270 SOLF4280 SOLP4290 SOLP 4 300 SOLP4310 SOLP4320 SOLP4330 SOL»4 340 SOLP4 350 SOLP4360 SOLP437Q SOir43B0 30LP4390 SOLP4400 SOLP4410 SOLT4 420 SCLF4430 30LP44 40 SOLPW4SO 50LF4460 SQLF4470 SOLF4480 SOLF4490 3OLF4500 SOLF4510 SQLP4520 SOLF45 30 SOLF4540 SQLF4550 SOLF4560 SOLF4570 SOLP4580 SOLF4590 SOLF4600 SOLF4610 SOLF462Q

370

ISN 0390

ISO 0391 ISN 0392 ISN 0393

ISN 0394 ISN 0395 ISN 0396

ISN 0397 ISN 0398 TSK 0399

ISN 0400 ISN 0401 ISN 0402

ISN 0*03 ISN 0*04 ISN 0405 ISN 0406 ISN 0407 ISN 0400

ISN 0009 ISH 0411 ISN 0412 ISN 0413 ISN 0414 ISN 0415 ISN 0*16 ISN 0417

ISN 0418

l!IIJ«»aPHT«TiaH XT POINT 1*1/2,J

262 CULL t1»TPSP( CKTWD,TIPJD,DENS,SmT,«MPD) ROIPJD'DENS HTIPJD-SPflT»TIPJD

AT POINT 1-1/2.J CAM. NATPRP ( CKIMD,TIHJD,DENS(SIHT,POTPC) NOIHJD«DZNS IITIHJD»SPHT»T1MJD

AT POINT I . J41 /2

CALL RATPRP ( CKIJPD.TIJPD,DENS,SUIT,ROTPt) R0IJPD«DlNS H*tJtO-SP«T«TIOTll

AT POINT I . J - 1 / 2

CALL HATPRP( CNIJ1D,TIJH0,t^NS,5IHI,R0TPCl NOIJBD-DINS HTIJHD'SPHT*TIJND

C AT POINT I , J C

264 CALL IIAIPNP( CHI J.TIJ,BENS,SfNT, IOTPD) ROIJ-BIKS CPIJ-3PHT HTIJ«SPHT»TIJ DO 266 K"1,NR

266 nTHIJ(KfStRIMK)«TIJ C C CALCOLATIS VOIORITBIC HEAT GENERATION AND MECIES 1ASS C GENERATION I I NZEOID.

I* (lOlNT.IQ.O) 00 TO 268 CALL GBNCON GO TO 272

26B CONTINUE QDVIJ-C.ODO DO 270 N>1,NN

270 o*n»ij(*j-e.ODO 272 CONTINUE

C C C

CALL rLXCON(CK,0,V,T,NFLG> C FLXCON CALLS TCPCOI AND 10TC0N SOBfOOTINIS C C*«***THIS TS A BOAT PROCEDOAE FC* TfSIING SOLVIT C»*»» C* DO 206 Ka1,NK C*206 CKTHD(K0IJ«K)-.001 C» TTRD(IJ)"10,

SOLF4630 SOL»4640 SOLF4630 30LF4660 30LF4670 SQLF4680 30LF4690 30LF4700 S0LF4710 SOLF4720 SOLF4730 30LF4740 30LF4750 SQLF4760 80LF4770 SOLF47BO S0LF4790 SOLO4800 SOLE4910 SOLP4820 3OLF4830 SOLF4B40 30L»4950 30LF4860 SOLP4870 SOLF48SO SOLF4990 30LF4900 SOLF4910 SOLF4920 30LF4930 SOL*4940 50LF4950 SOLF4960 30LF4970 80LP4960 SOLF4990 SOLF5000 SOLESO10 30LF5020 30LF5030 SOLF5040 30LF5050 SOLF5060 SOLF5070 SOLPSOSO 80LF5090 SOLF5100 SOLF5HO SOLP5120 S0LF5130 SOLF5140 SOLF5150 SOLFS160 30LF5170 30LF5180 50LP5190 80LF5200

371

ISR o m i ISN 0420 ISN 0421 ISN 0422 ISN 0423 IS* 0424 ISN 0425 ISN 0426

IE* 0427

ISN 0428 JSN 0429 ISN 0430

ISN 0431

ISN 0432 IS* 0433 ISN 0»3« ISN 0435 ISN 0436 IS* 0437 IS* 0438 ISN 0439 ISN 0440 ISN 0441 ISN 0442 ISN 0443 ISN 0444 ISN 0445 ISN 0446

C• HTHN<IJ)«1P. c« *Ttin(M)» c.ro C UTBD(IJ)»0.CD0 C• 00 "o J11

SKXIflJ«0. SXXIPJ»O. STTIJB-O. STYTJP-O. 3XIIHJ-0. 3XTIPJ.0. SXTIJH«0. SXTTJP-O. ir (IJ.FQ. H9.0H.IJ.EQ.201.0R.ia.EQ.241.CB.IJ.!Q.243)GBIJ"233 = IN (IJ.EQ.200.0R.IJ.EQ.220.0n.ia.IC.222.CS.IJ.EQ.242) GBIJ-233. IP(IJ.EQ.211)OBIJ"179.13SD0 IF(IJ.EQ.211)OBIJ.333.333CO IP(IJ.IQ. 145) GBIJ-80.44600 IPCIJ.EQ.73) QBT3.748.43B0

CALCULATE IRE 71 BE DERITUTIfS Of A U TBI ONKNOWNS BT OSINS THE MAJOR EQOATIOHS

BASIC CONTINOITI E30ATION

HROTHD •GBIJ4GTIJ -(HIPJD*GXXPJ-HIWJD»GXIHJ)/DXI -(HIJP0»GTIJP > HIJSD«OTIJH)/DTJ

C* C* C• c« c* C» c C C c c c

SPECIES HASS CONCENTRATION EQOATION SOHK-O.ODO DO 274 K«1,*K CKTBD(K0XJ+K)« GKDVIJ(K)/ROIJH - (•HIPO« (GXT»J» (CKIPJD (K) -CKIJ > »0KXIPJ(K)) -HIHJ«<6XIHJ«(CKIHJt(K)-CKIJ(K))»GKXIHJ(K)))/EXI > HIJP* <GTIJP*<CKIJP9(B)-CRIJ (X) MONTIJt(«() -HUH* (GTI.1H* > (CKIJHD(K)-CKIJ(K)]«GKTIJH(K|))/CIJ •GBXJ* (CKBIJ (N) -CKIJ (K) ) • > OX BIO (X) «GTIJ*(CKTIJ(K)-CKIJ(K))*GKTIJ(K) )/(ROIJ»HIJ)

274 saHK»SOHK»RCCKD|R)»CKTHD(KOIJ*K)

ENERGT EQOATIO* SQCRON-O.OCO SQKXIP'O.OCO SQXXIfl«O.ODO SQKTJP»O.ODO SQKTJH-O.OEO SQKBIJaO.ODO SQKTIJ«O.ODO DO 276 K»1,HN SQCKG»"SQCKGN*HTKIJ (It) *CKTHD (KOIJ+K) SQMIJ"SQKBIJ*QKBIJ (X) SQKTIO*SQXTIJ»QXTIJ(K) SOKXIP-SCNIIF»GKXIPJ(R>»(HTRIO (K)) SQKXIB«SQKXIH»GKXIBJ(K)•(HTKIJ(X)) SQKTJP-SOKIJF+OKTXJP (II) • (HTKIJ (K) )

276 SQKTJB'SQKYJB+GKTIJH (K) • (HTKIJ (K»

S0LF5210 S0LP5220 S0LP5230 S0t*5240 SOLP5250 30LF5260 S0L*5270 SOLP52BO SOLF5290 SOU'S 300 SOLF5310 SOLP5320 50LF5330 S0LF5340 SOL»5350 SOLP5360 SOLP5370 SOLF53BO SOLF5390 50LF5409 SOL»5410 50LP5420 SOLP54 30 50LF5440 SOLP 54 50 SOLP5460 50LP5470 SOLP5480 50LP5490 50LP5500 S0LP5510 SOL»5520

(K))S0LP553D -(• SOLF5540

S0LP555Q SOIP556D SOLF5570 SOLF5580 SOLP5*90 50LF5600 SOLF5610 SOLP5620 SOLF5630 SOL"S640 SOL"5650 SOLP5660 S0LF567C SOLP56SO SOL"5690 SOLF570O SOLP5710 SOL"5720 SOLP5730 SOL"5740 SOL"5750 SOL"5760 S0L»5770 SOLF5780

372

TSN null?

TSN 9HUB TSN 1UU0

ISN 1450 IS* 0451 ISN 145? ISN 0451

ISN 0454

ISN 0455

ISN 045(1

ISN 0457 ISN 045fl

TSN 0459 ISN OUfift TSN 0461 ISN 1462

TT«n (T.1) "-SCCK1N/CPIJ • ( - (•HIPJ* (GXIPJ* (BTIPJD-HTIJ) +QXIPJ+ » SQKXIF) -DTM»{CXI,!3«(BTT«JE-HT13>*QXIflJ«S0KXm))/DXI -(•HIJP* > (GTIJP»(HIIJPC-HTIJ)•<)YIJr*SQI<YOE) -HIJN*(1YIJH*(BTIJBD-HTIJ)• > OXIJItSQKYJH)J/EYJ •GEIO* (HTBIJ-BTIJ)«QEIJ*SQKBIJ •GTIJ*(HTTIJ-> HTIJ) •QTI3»S0*TI3 )/tS0I0*CPI3«FI3) «QD» 13/ (ROIJ*CFIJ)

CONTINUITY F.CWIOR TOP UATFR I i m U O * B POTPlD«SOIPI!*lTNn (TJ) +S0KK

HT«n ( I JJ « ( - H rJ»R0T.H>*HR0TRl> /SCIO

N0»FNTU1 FCURTIOH TN X-HRFCTICN

BYPTP,1=fSR»FCIPJ* (HTPJ-BCTFO) HYPIJP=f5R«FCIJP*(HTJP-HCTJE) HYPIHJ=GR«5CINJ*(HIHJ-HCIRO) HYPI.7P=na»FCION» (HIJH-BCTJH)

OT*D(I,1)=-(HIPJ«H*PIPJ-RIRJ*HYPI!!J)/(DXI»EOIJ»HI3)+ ( - (tHIPJ* > (GXIP.l* tUIF30-0I.l) -SXXTFJ) -HIRJ* (GXItlJ» (OIHJD-OIJ) -SXXIHJ) l/DXI > - (+BTJO« 10 F» (111 JPD-0T3) -SXYIJP) -RIJB»<GYIJH«{BIJ(ID-DIJ) -> SXYIJM) )/EYJ •GBM«<CIBIJ-0IJ)*SEXI0*GIIJ*J0TIJ-0IJ)*STXI3 )/ > (ROIJ*HIJ)

CW » » « » • » CP' I" (I.TO-I-HN":. J-FQ. 1) PBINT 10,I,3.0THC(IJ) ,OIJ.BROTIID, CN 1tUP3,GXTP3,tlP3r,5XXIP3,RYPIP3,nltJ,GXI!1J,0IH.JD,SXXTH3,BYPIHJ, CN 2nTI.HIJF,GYI3P,ai.TP0,SXYIJP. RIJ(1,GYI3N,0IJHB,SXYIJH,DY3,GBIJ, C» JITBT.T.SBXIJ,G7ia,OTIJ,STXIO,ROIJ.BI3 C» 10 P 0 B 1 * T ( W B> • |I,3) ,I»'»I3,3X,' J»',I3/(13Z10>) CV I» (I,EC.1.ABC.J.EQ.1| PSTNT 11 ,CCOT , M « CN 11 FORHAT(IOZIO) CI C C c c

EEBOflGING

N0HERT0J1 BCCWION I. Y-BIBICTICH VTtin (13) «- (HIJP*HYPIJP-RIJ»»RYPIJ?I>/(I>M»E0I3*HIJ) • ( -(•HIPJ*

> (GXIP3»(»IFJH-»IJ) -SXYIF3) -HIH3* (GXIM» (VIB3D-YI3) -SXYIH3) )/BXI > -(•BI3P«(fiY:3P*(VI3Pt-YI3)-SYYI3t*HYPTJI) -BI3«»(GYI3R«(YI3M0-> VIJ)-S»YIJE»PYPIJH))/BYJ •GBIJ«(1EIJ-VIJ)•SBYIJ+GTIJ*(VTIJ-FIJJ• > STYIJ )/(FOJJ»HIJ)

27P CONTINOF C C

I.1=T.1P1 K0IJ=K0IJE1

CN • » • DEBUGGING » • * C I TF( I .BQ.1.»NE.J.EQ.1.ABC.NC01)NT.EC<3) CAll EXIT CN * » * OEBBGGIRG • * •

280 CONTTNOE KOLJS=KNI.JS*HF

282 CONTIHOE GO TO 286

SOLP5790 SOLP5BOO SOLF5810 SOLP5820 SOLP5830 S01.P5840 SOLP5850 SOLV5860 SOIP5BTO SOLP5880 SOLPS890 SOLP5900 SOLF5910 SOLP5920 SOl»5930 S01P5940 SOLP59SO S01.P5960 S0t»59?0 SOLF5980 SDLP5990 SOLP6000 SOLP6OIO SOLP6020 SOLP6030 SOLP6040 SOIF6050 SOLF6O6O SOLP6070 SOLP6O8O SOLP6090 SOLP6IOO SOIF6110 SOLP6120 50LF6130 SOLP6140 SOLP6150 SOLP6160 SOIP6170 SOLP61BO 50LF6190 SOL76200 SOLP6210 SOIP6220 S01P6230 SOLP6240 SOLP6250 SOIP6260 SOLF6270 SOLP6280 SOLP6290 SOLP6300 S01P6310 SOLF6320 S0W6330 SOLP63UO SOLF6350 SOLP6360

373

191V 0<I63 20b PRINT 1000 SOL»63?0 ISN 0064 STOP 2 SOLF630O ISN 0465 286 RETURN SOL»«390 ISN 0066 1000 TORI AT ( / / ' ®**•••••••****•••••••••*******11**1******'/ , SOLF6'lOO

> '0 PROORAN IS NOT SET 10 RANCH THIS TYU OF BCUNDART' , 9OLF6110 > ' CONDITION V/# '0** •*•••*•*•*•••*• •••Ml****************1*'/) SOLV6U20

ISN 0067 END 9Ot»6»30 •OPTIONS IN EFFECT* BANE" tlXIN,OIT>02.LINECNT'60,!m*OOOQK.

•OPTIONS IN EFFECT* SOORCE.IECDIC.NOLIRT.NODECN.tCAE.NOIAt.NOEST'O.IIOID.NOXREF

•STATISTICS* SOURCE STATEHENTS > 166 ,PROGRAM 5IZF • 10062

•STATISTICS* NO DIAGNOSTICS GENERATED

•••«»* END OF COMPILATION »•••»» 2 IK BYTES 0* CORE NOT DS»t>

374

CS/V," FCPTM M cntpmp OTot»3 - NAFF* t«T(.0PT»p?,t;<r»c»''.«u,fT?«»)0ifi», inr(lCK,fCn7C,HOT1ST,ll0nfCli,T.r»n,ll01»p,H0'-DT''.S')Tl),',0*',rF TIM 0002 1UP50IITTN* 'TM'MKK.KX.FY) 1C

7SN 0001 IMPLICIT BT«I-•» (A-M.O-Z) RU- if *5N noon comoN/conur/ m.ATnr.efi,I,cKT0(4) ,C*T«J(«) ,CKMI (U) , 'ir 10 > CKTJH(«),t»i',u r.D»«,CTP,R*TPI,TYJPI,cxti.IXPT,OXIII,oxpn,iirr,.» , tjt" (10 > nri»j,rTi.ii,nTii.ii,'iBi.i,f)rfi,i(»i ,<»:J,OKBTJ(«| ,SBUJ,SBRU,NTTTI.I , •TIT 6C > 1XTPJ,NYTOB,OYTJP,OTTJ,RTK1TI1|4) .CTT.I.CKT M (4) .•MTJ.ITYJJ.'INVM ,'TL- 60 > oxTiJ,o*7u,or:.i«,oTTjp,nrx:tj<'i|,rKxipJtin ,OK*I.II(4) ,OK*T,IP(U) ,FTL- 7C > H-KIJ<4),HTKTJ1<4) ,IPKTPJ (4) , n't Mi l (4) ,BT«T.»P (M) ,NJJ,HI.1I',II'P.) , FT?.- PC > IIT!1J,MI3P,u:J,UIJ«,OIta,UIH3,OXOf,VIO,tlJ'»,tHiJ,*T1J,*IJR,TTLJ , FTLT 90 > TTJ1,TIPJ,UKJ,TIJP,P0KTPt»ll) ,BtIJ,POI.lf,«OIP.l, B0T1J,N0IJ« , FTt.T 100 > SH»TPD(4),SHTC*C(»).SMTTTt,SXXIFJ,SXXTPJ,SVTTJ1.SYYIJP,*XYTJN , •TI.T 110 > SXYTPJ,3XY?1.1,nx»rjr,»OTNJD,»CTfJI),PO'JI't,«OT.»Pn,»OT1P.TOTJ , FT!," 12" > HCTl».1,MCTPJ,HC»J,",HCY.1P,e»,)'0CKE(l() ,SFHTD(l|) , BM3* (4) ,BODK:j(U) .FILT 110 > flFD»I.1(4| ,0X1,DYJ ,0n»(25).HBB«;5).UBr(3!>,Vni)(25),TPB(25», FILT 140 > CKPD(»,25|.TBTJ,HCPTJ . rCFETJ (4) IJ (»| , DtTJ,UDTJ, YDTJ A'PIJ, m- 15C > »OBI.>,HffiTJ,CI'Ot.1<4),TrrJ,HC"IJ,t'CKTIJ«4|,HTKT»J<4) ,UT!J,»T!J, PTLT UP > VTIi],BOTIJ,KTTTJ,CXTli1 (4) ,3BB (25) ,OI>r (55) ,<irnn(4,25) ,!S0BN(25) , FIL* 170 > SB9.1ff(25| ,«IHB,«I*../,»rNrT ,TJ, T11J, IP» J,TJH1,1JP1, I1TRT, ROM, FILT ISO > K0IB1J,K0IP1i1,K0IJH1,RDTJP1 , NBXB.NBXt, »m,MBr ?, NP»3IH,IIBSDF , FILT |AN > ItO»(25),JYO»|25),HHBCP(75),»UirTP(2;) .N»BB»P(25) .NTDPTIZS) , FTLT 700 > NXOBl,NYOft,HSEO,l»TNTLP,NTOP»,»inF,HYEI«C,NTB»X,NO? P •ILT 210 ISH onoi niB'S-SION CX1KOT|«) ,CK7PJB(4) .CKIJBB(4) ,<.<1JPI>(4) FILT 220 ISH 0006 COB!10N/npoO/IIH,tIH,TH.PFRIOB,TT,»lieVF.I.*C»t,N »rr,-2J0

N» 00O7 C01aON/INBHVCTHlT,»TI1.Sr7n.PB81I',CP1IIT"',Cit)S«C,TIri«l,FCT>), «TLT 240 > INCTH.NrTHC.TFTNTS.lBTNCP.ISTtBl.mOT.NCPII FILT 250 ISH O'JOR OATA 1ASK/2COOFFF"/ FILT 260 c • •• 1'S IN BASK COYEP TOTALLY SPACE »0P NEXH.NBXP, NBYS.BBYP IN FLA (*, •ILT 270 c ••• NFLO, FILT 280 TSH oooo PETiJBB FILT 290 ISN oom FNTBY FILTEN ( HTHB,0TBt,»THB,TT«t,C*THC,H,0,»,T,Clt,BX,BY,BXL, BXS ,»ILT 100 0011 > BYL,BYP,BEIG) FILT 310 TSN 0011 WHEBSION HTBDJ1) ,DTBB (1) ,VTBD(1) ,TTBD (1) ,«TB0(1) ,H(1) ,0 (1) ,T (1) , FTLT 120 > T(1).CK(1).BX|1),DY(1) ,BXI(1) ,DXR (1) ,tYl (1) ,BYR (1) ,NFLG(1) FILT 110 ISN 9012 10 DO 94 1*1, KX FILT 140 ISN 0O11 IJ»I FTL" 150 ISN 0011 DXHI.DIB(T) FTLT 360 ISN 0015 DZLT1«B(t(I*1) FTLT 170 ISH 0016 DO 92 J-1.KY •TLT ine UN 0017 DYBJ«DYB(J) •ILT 19P TSN oom BYtJ1»DYL(J«1) •TI- 400 tSH on 19 CALL OTTLGI(BBX«,NFLO(IJ)) FT LT 410 TSN 0020 IF (BRraiH.EC.O) GO TO 90 FILT 4? 0 ISN 0022 IP1J-IJM FILT 4 3C TSN 0023 TJP1-IJ*KX FIL* 440 c« IF(T.GE.1.ANC.T.LE.5.AND.J.GE. 1. ANB. J.t» .«. ANB.TT.L*. 3) FILT 450 c» 1PRINT 20,I,J,IJ,HTHD(IJ),H(IJ) ,HIB0 .H1PJ .HIJB ,HIJP , pri' 46(< c» 20T(!D(IJ),VTBD(IJ),O(IJ),»(IJ),0lrJ ,VIHJ ,0IPJ ,»IPJ , PUT 470 c« 30IJH ,YIJN ,OIJP ,TTJP FT IT 480 ISH 0024 HIJ«H(I.l) •IV 490 ISN 0025 OIJ-O(TJ) FTLT 500 ISN 0026 »IJ»T(T.l) FTLT 510 ISN 0027 TIJ«T(IO) F:V 520 c ' ••• IF NBXM»NBXF'NBYH«NBYP>O, THEN at TO 440 (*-I INTSSTO" 'IOIE) FTLT 51C ISN 002* INSIDT.-lANt (RASK,»»lO(I3)) FIL- 540 ISN 0029 IF (INSIDE.EC.0) GO TO 86 FILT 550 ISN 0031 IF (NBYB) 12,12,14 FTLT "60

375

•SI "IV 12 H-J»»«|T,|1>>C Til iMI tr."i-'"".irrc T*H inn VMH».»',ir?C rn» iris »t.iir«"*.ii>»c Tfi* ami in if run mi1 m MM.Him-ii nY'i) rs» ooin nn "> ( 2 0 , n , H H no-io op "o i"i T<m nr«i ir MI.»'«F>M:.I«PYI.II»(HIJ-II(Y.I»1)J TRW O W IN TO 2? tin nou? in '!t.in»«"rj i»s o w i io TO ??. 'SN 0044 20 HI.li»«HrT(ilIIY1> IBM ooii ?•» *ti«riifr"P(KfY>i) TSM 1C16 10 TO (24, 36,IRC ,24) ,<10 TBI 0047 fin TO 110 Tit» HIM 2" nrJi»»iTJ«rifiJt»(w.j-ri(tJPiM iou9 nn "0 isn oo*i ui.i«p»n*.i TRW 01*1 W 70 IT TSN 005 ' »R IJTJ"»»I>RI (UPTH) JSII 0051 WV«l)VPfi-?(»IT!tt) T N 00111 FIL "1 06.14.H9.32) ,NV ISK now no TO 1®<> IS1 0«56 3? VI,inf«»7J»CYIJ1«(»IJ-V(TJP1) ) T5H oon 150 TO I" TSN OOlfl in VIJ*»«»-.1 JSN no '0 !» T S N 0 0 6 0 V T . 1 1 » « V ' j 1 ( K P * R ) T S H 1 0 6 1 r " , » F ' T r ' n ® ( S f Y « l | U N 0062 GO 70 (46.44.1*0,40).SI ISN 0061 GO TO TSN 0064 Of I? (7T.V1F) 47,42,46 TSN •7061 47 rMH»«TT.l*r»lJM* (TJ-T (T0°1) ) TSN 106* GO 4R tsn 0167 uu '•r.r»»'«TTJ TSN 006A GO '0 on TFK OOf 4f TTJRPwT1T) (NPYR) ISN 007O «( CPNTIHO'1 TSN 0071 TF ( 1 P Y P )

C0.»C,52 TSN 007? »TJ',FC«l»IJ»nY[J1«(H(T.lP1)-HI.l) TSN 0071 HTJn»"',TJPTC TSN 0074 i"jP»r«fM*r*l,.l1»(P (IJpi)-0T.1) TSN 107 UIJP*»"-.)r7C T*5H 00"»« V\'?T{»VT.T»tYl,11"(V (I.1P1)-VT J) TSW 007T VT.TPF»V:.1P*C TSM 0 0 7 R T T J n r C « " , : . T * r Y I . J 1 » ( " , ( T , l c i ) - T T - l ) TSN 0r**1 T"Ja»""TJpTC TSN noni no 'O "q TSN 0CB1 52 NH«NH'""'=1NEYP) TSN 00R7 GO ~0 c6,18C, 54) TSN 1081 no TO 1J>1 TSN 00R4 HTlPF'HM+rYP.1* (ft.1-flTJ11) T S N O O P ' . T O m t> 6 0 is* ow- 56 »rj»p»«rj TSN 0M7 00 "0 6" - S I l O f l B 5 P , H I J " » » ! l 3 3 ( N r » P ) I S N 0 0 « 9 fic N n « N n r r > T p ( N P Y r )

FILT 570 FIL* 580 PUT 590 FILT 609 FILT 610 »UT 620 F U T 630 »ILT 64 0 •TIT 650 FILT 660 Fur 6 re »ILT 68ft FILT 69C FILT 700 »TV 71? FILT 720 Fit- 71C TILT 74C »IL- 76C »ivr

«TL-PTT.T

r7'.~

76C 770 7BC 710 V 4 10

I'.f net. TTL- «7f

FT'." MO 100 01C

Til," TIL"

r:it 02c fl" <>10 TL1" 940 F'.L? 950 TTL" 960 TILT 970 "JLT 98f FTLT 09C "7LT1C00 FTLTIIIC FTLT1020 FTLTln10 *IV104C "ILT1050 "IL71060 FTLT1070 FILHflO FILT1090 FILT11Q0 FILT1110 FTLT1120 FTLT1130 FILT1140

376

0090 SO TO (66, (H. 100,62), NO FILT11S0 19* 0091 no 10 100 FH.T1160 HI 0092 62 oz.ipi»oiJ*cT*j*(siJ-oijni) FILT1 HO ISB 009) 00 TO 6f PHTM0O TSN 0091 6* OIJPMUIJ FtLTI190 ISN 0095 00 TO 60 FIIT1100 ISN 0096 66 OZJPF«O0»(NHP) PILT1210 ISN 0097 60 ilV«N!>BCTP(NMF) FILT1220 ISN 009ft GO TO (7*,72,180,70) ,N» FILT1210 ISN 0049 00 TO 100 FILT1240 ISN 0100 70 tijPF fijtctNatiwa-Nnni) FILT12S0 ISN 0101 00 TO 76 FILT1260 ISN 0102 72 VI3PT-VIJ FIIT1270 ISN 0> >} GO TO 76 FILT12S0 ISN 010* 7* FIJPP*FBD(NB1P) PILT1290 ISN 01C.9 76 NTMTIBTP (N8YF) F1LT1300 ISN 0106 00 TO (0«,e2,1«O,7B),NT PUT 1310 ISN 0107 GO TO 100 FILT1320 TSN 010« 78 IP (BIJPF) 0*,80,00 FILT13J0 ISN 0109 80 FILT1JQO ISN 0110 no TO 01 FILT1350 ISN 0111 02 TIJPP-TM FILT1360 ISN 0112 00 TO 00 PUT 1370 ISN 0113 0* TIJP«-TBD(NB1F) FILT1100 ISN 0119 no TO 88 FllT1196 C ••• BEGIN CALCOtAIION PON INTfBIOR NCOI. FILT1*00 ISN 0115 0J COBTIDOE FILT1*10 ISN 0116 BIJNP-HIJPRC PUT 1*20 ISN 0117 WIOPFC-HIJ • DLTJ1««H<IJP1|-HIJ) FILT1930 ISN 011ft nijpP'Rijprc FILT1**0 ISN 0119 OIJBF»OIJPIC PILT1450 ISN 0120 0I3PFC-0I3 * DTLJIMO(IJPI)-OIJ) FILT1460 ISN 0121 oupE-ouprc FILT1*70 ISN 0122 njiir-Nijprc TILT1*00 ISN 0121 »MPPC-»IJ • MU1*(f(XJ»1)<FID) FILT 1*90 ISN 012* »I«P«WJP*C HIT 1580 ISN 0125 TIJBP-TIMC PXLT1510 ISN 0126 TIJPFC-TIJ » DTLJ1*(T(IJP1)-TI3) PILT152C ISN 0127 TIJPP-TIJPPC FILT 1510 C ••• END CFTLCOLLTION TON INTEIICR NOCF. FILT15*0 ISN 0128 80 CONTIN00 FILT1550 ISN 0129 HIJFL1>IIIJ FILT1560 ISN 9130 OUBI-DIJ FILT1570 ISN 0131 YIJB1-NIJ FILT1580 ISN 0132 TI3B1»TIJ FILT1590 ISN 0133 R(13)>0.SDO*(HIJBP»NI3PF) FILT1600 ISN 013* c« 0(IJ)-0.5DO«(OI3BE»NI3PFJ

IF (OABS (0(13)) .LT.1.00-19)0(13) -C.0 FILT1610 FILT1620 ISN 0135 c» »(IJ; '0.5D0»(TIJBF»»I3PF) IP(n J3 (*(»)) .«.1.0D-1*)»(IJ)»C.O FILT1630 TILT1640 ISN 0136 c» T(Io,"0.SD0»(TIJBP»TI3PF)

I»(I.GE.1.»ND.I.LE.S.»NC.3.CE.1.IBB.J.TE.5.ANB.IT.LE.3) FILT1650 FILT1660 c» 1P8INT 20,I,J.IJ,»IICD(I3),B(IJ),>)I»J ,HTW .HIJRF .BI3PF FILT1670 c« 2OTHD(IJ),YTBC(IJ),0<I3),*(I3).0IIJ ,»INJ ,0IPJ ,YIPJ , FILT160O c« 10IJBP.«IJN7.0IJEP,YIJPf FILT1690 ISN 0137 c c 90 CONTINOE FILT1700

FILT1710 FILT1720

377

T<L* 0134 UN 1)114 IS* 01UO IS* 0141 TSN 0102 IS* 0143 ISX 0144 IN* 0145 ISN 0146 ISN 014"* TSN 0144 IS* 0141 ISN 0150 TSN N152 ISN 0153

ISN 0154 ISN 0155 ISN 015* ISN 0157 IS* 0158 IS* 0154 IS* 0161 IS* 0162 IS* 0163 IS* 0164 IS* 0165 ISH 0166 IS* 0167 ISR 0168 IS* 0164 IS* 0170 IS* 0171 IS* 0172 IS* 0173 IS* 0174 IS* 0175 TS* 0176 IS* 0177 IS* 0178 ISN 0179 ISN 0180 IS* 0181 ISN 0182 IS* 0183 ISN 0184 ISN 0185 ISN 0186 ISN 01B, ISN 0188 ISN 0189 ISN 0190 IS* 0191 IS* 0192

IJ-IJP1 FILT1730 42 CONTINTL' FILT17B0 94 CON71HOP TILT17S0

IJ«0 FILT1760 00 17FL J«1,KT FILT1770 HTRJ«DTR(J) TILT17B0 DTU1>0TL(J»1) FTLT1790 NO 176 T»1,RX FIL71800 7J«IJ*1 TILT 1810 DX»T«NXR(I) TILT1820 NNXI*ONI(J*V r ILTI830 CALL IITFIOS|«BXH.NPIO(IJ)) TILT1840 T* (NR*AI*.IQ.O) 00 TO 174 TLL'»'IE50 TD1J»I,J») FILT1860 I.1P1«IJ»KX MLT1870

C* I*(T.OT.1. AND. 1.LB. 5.AND,J.OB.'..AND.J.I*.5.AND.IT.LB.3) FTLT1880 C« 1P«I*T 20,1,J,IJF»THD{IJ) ,H(IJ) ,HIM ,H1PJ .HIJNP ,HIJPF , FILT1890 C" 20THP (I J) ,TTHD (IJ) ,0 (I J) ,V(IJ) ,UIPJ ,*IHJ ,UIPJ ,»IPJ , HLT140" C« 1U7J1P,T1JN»,0IJRF,»IJFP FILT1410

HIJ-H(IJ) FILT1920 •JIJ«TL(I.1) 'TLT193C »IJ"T(:J) FILT1940 TIJ-T(IJ) FILT195C

C IF NDXH«NFXP»NBTH»*DTP»0, THIN OC TO 450 (AS INTISICR XODI) FILT1960 I*SIDP.JA*t(RA!l(,HFlO(IJ)) FILT1970 I» (INSTOE.FO.O) 00 TO 17C FILT19B0 1» (NBXH) 56,96,98 HLT1990

46 HIHJP.HIFJYC FILT2000 NIUF»DTPJFC FILT2010 »IHJ»«»IPJFC PILT2020 T1HJF-TIPJFC FILT2030 00 TO 132 7ILT20 40

98 *H"NHBBTP(NBXH) FILT2050 00 TO (104,102,180,100),NH FILT2060 00 TO 180 TILT2070

100 HIHJF«HIJ«RXII1*(FLU-H(IP1J)) FILT2080 00 TO 106 FILT2090

102 HIH.JF.HIJ FILT2100 00 TO 10F FILT2110

104 HIHJP-HBO(NBXH) FILT2120 106 *0»*08DTP(NBXH) FILT2130

00 TO (112,110,180,108),*0 FILTZ140 GO TO 180 FILT2150

108 DIHJF»0IJ*DXII1*(0IJ-0(IF1J)) FILT2160 GO TO 114 PILT2170

110 OIHJF-OIJ FILT2180 GO TO 114 FILT2190

112 DIHJP-OBD(NBXH) FILT2200 114 *»"NTBDTP(*BXH) FILT2210

GOTO (120,118,180,116),HV FILT2220 00 TO 180 FILT2230

116 »IHJF-»IJ*DXLI1»(»IJ-»(IP1J)) FILT2240 GO TO 122 FILT2250

118 TIBJF-TIJ FILT2260 GO TO 122 FILT2270

120 FIHJP-VBD(NBXH) FILT2280 122 *T»*TBDTP(*BXH) FILT2290

GO TO (130,128,180,124),NT FILT2300

378

ISN 0193 tsn 014a ISN 0191 ISN 0196 TSM 0197 ISM 01O" UN 019° ISN "200 ISN 0201 ISN 0?f>2 'RN 0201 ISN 0204 TSN 020* TSf 0206 TSN 0207 ISN 0708 ISN 02l)*> UN 0210 ISN 0211 ITO 0212 ISH 0211 »SN 0214 ISH 0215 ISN 0216 TSH 0217 ISH 0218 TSN 0219 TSN 0220 TSH 0221 TS* 0222 ISN 1221 TSH 0274 TSH 0225 »SH 0226 ISN 0227 'SN 05?« TSN 0224 TSN 0230 ISN 0211 TSN 0732 TSN 0231 TSH 0234 ISH 0235 ISH 0236 ISH 0237 ISH 023" TSH 0239 TIN 0240 ISH 0241 ISN 0242 TSN 0243 ISN 0244

TSN 0245 ISN 0246 TSN 0247 TSN 024R ISN 024°

124 126

128 1 30 132 134

116

11P 1 iiQ 142 144

106 1UP 150 152

154 156 158 16C

162 164 166

168

C »•• 170

10 "0 1*9 IT (011,17) 126 ,126 r 130 TI17»"TT.1*rXI11* (ITJ"T (IP1J) ) AO TO 13? TIN.1F-TTJ no '0 112 ",I!M»-*B'MNPJH) CONTINUE I» (NFXP) 1311,134,136 HTP,)TC«FIJ»MI1MH (IRIJ)-HIJ) HTPJF-HIPJFC 0I1>,)FC«DIJ*CIII.I1*(0 (IF1J) -UIJ) 0TP.1F-0TPJTC »TpjfC»»M*tXl.11*(V (IP1J) -VTJ) »TPJ»«»:PJFC T7PJFC"TIJ*C«.I1«(',(IP1J)-TTJ) TT»,1F«TIMFC no TO 172 NH"NHBOTP(NEXP) CO TO (142,1110.180,138) ,KH IO TO M HIP,7F-HIi1*CXSI»(HM-HIN1J) HO TO 144 HIPJF-1IJ no TO 14* HIPJF"HBD(HBXP) HT1»HUBDTP(HP*P) 00 TO (150,148,180, 146) ,BO 60 TO IBS ffTP.7F«UTJ+BXflT* (OIJ-OIH1 J) (JO TO 152 0IPI3F«OIJ no TO 152 l)IPJF»0BD(N8XP) NV»H»BDTP(HEXP) no TO (158,156,160,154) ,NV 60 "0 180 VIP3F»»I.I*tXRI»(1W-7IH1J) 00 TO 160 VIP.1F-NI3 no TO 160 9TPJp«VBD(liBXP) NT-BTBHTP(HBXP) no TO (163,166,180,162) ,BT no •'o iso IF (OIPJF) 168,1(4,164 TIPJF«TIJ*CXfI« (TIJ-TIR1J) CO TO 172 TIPJF«TTJ SO TO 172 TTPJP=TED(N8xr) no TO 172 BFGIH CUCOtyriCIN FOR IBTIBICP HCOH. CONTINUE HIHJF«HTPJTC MIPJFC»H»J • PX1I1»(H(IF1J)-BT3) HIPJP«HIPJFC OlfMF-UIPJFC

F:L-2310 FIL72120 FTLT2330 FTTT?3L(C FILT235C FUT2369 Flf'ZITO FHT23R0 FILT239C 7UT340P FTLT2H0 TILM2420 FILT2430 "ILT2440 FIT'2450 FILT246C 'ILT2470 FIF2480 FIL"2490 ?IL",2500 FILT2510 FILT2520 FILT2510 FII,R2540 RIV2550 FILT2560 FILT2570 FILT2580 FILT2590 FILT2600 FILT2«10 FILT2620 »ILT2630 »ILT2640 FILT265C FILT2660 FILT2670 FILT2680 FILT2690 FILT2700 FILT2710 FIIT2720 FILT2730 PILT2700 "IL'R2750 FILT 27 60 FILT2770 FILT2780 FTLT2790 FILT2800 FILT2810 FILT2820 FTLT2830 FILT2840 FILT2850 FILT2860 FILT2870 FILT2B80

379

TSN 0250 ISH 0251 TSN 0252 ISH 0253 TSN 0254 ISN 0255 ISH 0256 ISH 0257

ISN 0258 ISH 0259 ISN 0260 ISH 0261 ISH 0262 ISN 0263 ISH 026U

ISH 0265

ISN 0266

ISH 0267

ISN 026B TSN 0269 ISN 0270 ISH 0271 ISN 0272 ISN 0273 ISN 02711 ISM 0275

ISH 0276

DIPJPC=OIJ * DILI1*(0 (IP 1J) -01 J) BIPJP=OIP3PC VIHap«VIPJFC YIPJFC-VIJ • 0*tI1*(V(IPlJ)-«IJ) VIPJP«VIP,TFC i'IH3P«TIPJFC TIP.JPOTIJ • DXLI1* (T(IFIJ)-TIJ) TTP3P-TIPJFC

C •»• P.N0 CALCULATION EOR INTERIM HOtl. 172 COHTIHOE

HIH1J=HIJ UIH1J«0IJ VIH1J»VIJ TIH1J»TT0 H (IJJ "0.5D0* (HIHJP+HIPJF) O(IJJ»O.5PO« (OiMap^niPj")

C* IF(1ABS(B(IJ)| .iT.1.0P-1«)0(IJ)=C.0 V (I J) »0.5DC» (VIH0F+VIP3F)

C« IF (DABS (V (10) ) .LT.1.0D-14)V(IJ)«0.0 T(IJ)»0.5DC»(TIHJF*TIPJP)

C* IT(I.GE.1.A*D.I.LE.5.XHD.J,(;E. 1. IND.J. IE.5. AND.IT.LC.3) C* 1PBINT 20,I.J,IJ,BT(tn(IJ) ,ifIJ| ,HIKJF,HIPJF,BIJHP,HIJFP, C» 2BTHD (I J) ,»THD (IJ) ,0 (I J) ,» (IJ) .UIFOF .YIHJT .OIPJ F .YIPJF , C* 3tJIJHP,VIOHF,0IJPF,VIJPP

174 COHTIHDE C C

176 COHTINOE 178 COHTIHOP

SO TO 182 180 PBIHT 1010

STOP 2 182 RETURN 1000 »ORHAT(///' 0' • (I,J) ,I«« ,73,3X, •13,3X, ,IJB <,13/(4*26.18)) 1010 FOBHAT (//• o**************'**************************'/ »

> «0 OROGRAH IS HOT SET TO HANDLE THIS TYPE OP BOUNDARY1 , > * CONDITION'//,'0**********************,*******l,*****"**VI END

•OPTIONS IN EFFECT* NAHE* HATB,OPT«02,lIliJ,.CNT=6C,Sm=0i)IJDK. •OPTIONS IH EFFECT* SODBCE,EBCDIC,NOLIST,NOCECK,LCAD.NCHA{,NOEDIT.NOID.NOXRFP •STATISTICS* SODPCE STATEHEHTS • 275 .PROGRAH SIZE = 4726 •STATISTICS* HO DIAGNOSTICS GENERATED

PILT2890 PIIT2900 PILT2910 PIIT2920 PILT2930 PUT 29 40 FIIT2950 PILT2960 FILT2970 PILT2980 FILT2990 PUT 30 00 FILT3010 FILT3020 FILT30 30 PILT3040 FILT3050 FILT306O FILT30. w FILT3080 FILT3090 FILT3100 PILT3110 P U T 3120 EILT3130 PIL*31H0 PILT3150 PItT3160 PILT317G ?~LT3180 FILT3190 FILT3200 "TLT3210 FT.LT3220 TILT3230 FILT321* 0 FILT3250 FILT3260

«**••• gun OF COMPILATION ****** 771! BTTFS OP CORE UOT 0SF.1

380

CS/360 FORTFAN H COMPILER OPTIONS - NASI- HAIR ,OPT=02.LIHECNT=60. SI Z t*0000K.

SOCBCE,EBCDIC, ROUST,NOBICR .LOAD.NCIAP.NOEDIT.NOID .NOXREF ISN 0002 SUBROUTINE GENCNI.'HK) GENC ISN 0003 IMPLICIT 3EA1»B (A-H.O-Z) GENC ISN 0004 DIHENSION IQ.1VF (25) .IGKDVF (4,25) ,GRDV (»,;=) GENC ISN 0005 COS BOM/BEG ION/DEPTH (25) , SR (25) , IIREG (25) , IHREG (25) ,JLREG (25) , GENC

> JHREG (25) ,INT? (25) ,IGENF(25),ITCPF(25).IE0TF(25) GENC ISN 0006 INTSGER«2 1LBEG,IHRFG,3LBEG,3HREG GENC ISN 0007 INTEGER«2 INTF.IGENF.ITOPP.IBOTF GENC ISN 0008 CO MB ON/CONE IN/ ANL, ATHP.CFIJ .CKIO (4) ,CKIFJ (4) , CKIH J (4) ,CKI JP (4) . GENC

ISN 0009

ISN ISN ISN

ISN ISN ISN ISN

ISN ISN ISN

0011 0012 0013

0019 0015 0016 0017

0018 0019 0020

ISN 0021

ISN ISN ISH ISN ISN

ISH ISN ISN ISN ISN ISN

0022 0023 0025 0026 0027

0028 0029 0030 0031 0032 0033

CKIJH(9) , CXB.DXF,DYH,DYP,DXIP1,ITJP1,DXII,DXRI,DXLI1,DXR11,DTLJ ,GENC DYRJ,DYIJ1,DYRJ1,GBIJ.GICBIJ(4| .CBIJ.QKBIJ(4),SBXIJ.SBYIJ,GXIBJ , GENC GXIPJ,GIIJH,GTIJP,GTIJ,GKTIJ(4),QTIJ,QKTIJ(4).STXIJ.STIIJ.QDVIJ .GENC QXIBJ,QXIP3,QYIdN,QYIJP ,GKXIH3 (9) ,GKXIP J (9) ,GKXIJH(4) ,GKTIJP(9) , GENC HTKIJ (9) ,HTRIJH(4) .HTEIFJ (4) .HTFIHJ (4) , BTRIJP (4) ,HIJ . HIJB ,HIPJ RIH J, HI*1P ,U1J,UIJH,UIPJ,UIHJ,01JP,VIJ,VIJR,VIPJ,VINJ,VIJP ,TIJ , TIJN,TIPJ,TIHJ.TIJP,RCKTFD(4),RCIJ,ROIJH,ROIPJ,ROIBJ,ROIJP , SRKTPD (4) ,SHTCKE (4) ,SHTTPD,SXXIHJ »SXX1PJ,STTI JM ,SYYIJP, SXYUM , SXIIPJ,SXYISJ,SXIIJP,ROIBJD,BCIEJD,RCIJHr,ROIJPD,EQTME,tDIJ , HCIHJ ,BC1PJ ,RCIJN,HCIJP ,GP,ROCKC (4) ,SPHIK(4) ,DENSK(4) .BOPKIJ (4) GKDVIJ (4) .EXI.DYJ ,QDV (25),HED(25) ,DBD(25) ,7BD(25) ,TBD(25) , CNBD(4,25),TBIJ,HCBIJ ,DCKBIJ(4),HTXEIJ (4),BNIJ,UBI3,VBIJ,NBIJ,

> ROBIJ ,HTBIJ ,CKB1<1 (4) ,TTIJ,HCTI J , ECKTIJ (4) , HTKTIJ (4) .DTIJ.VTIJ, > NTU,R0TIJ,BTTIJ,C1CTIJ(4) ,QBD(25) ,GBD (25) ,GKBD (4,25) ,SBDN(25) , > SBDSH (25) , BIND, BIND X, BIND Y , 13 ,IH 1 J,IF1 J.IJH1 ,I.1P1 ,INTBT,K0IJ, > ROIB1J,KOIP1J,ROUB1V N0IJF1 ,NSXN,NBXF, NEYN,NBYP,NBEGIN,NBNDF , > IXQV (25) ,JYQV (25) ,NHBDTP (25) ,N0EDTF(25) ,NVB0TP(25) , NTBDTP (25) , > NXGRL,NYGFL,NREG,NINTLF,NTOPF.HEOTFvNTElfC,NTHAX,NGENF IF (NGEHF.EQ.O) GO TO 14

ANY INPOT VARIABLE CAN BE SET HEBE PRINT 1000 DO 10 I=1,NGENF READ(50,1010) IGENFC,CD* (IGENFC).ICDVF(IGENFC) ,(GKDV(K,IGENFC),

> IGKD»F(X,IGINEC) ,K=1,«!C) 10 CONTINOE

PRINT 1020 DO 12 K=1,NGENF PRINT 1030,K.IGEBFC.QDV(K) ,IQD»* (N) ,GKCV(1.K),IGKDVP(1 , K) , GKDV (2,

> R>,IGKDVP(2,K) 12 CONTINOE 14 CONTINOE

RETORN C » * * * « * * »

c *

cc cc

BNTBY GENCCN • •••••to********** IQVA=IGENF(NREGIN) I" (IQ7A.LE.0) GO TO 22

16 DO 18 K»1,NK 18 GKDVXJ (K) *GKDV (K ,IQVA) »GNRLFC (IGKOVF (X ,"CVA) ,X)

QDVIJ*QOV(IQVA)»GNRLFC(IQDVP(IQVA) ,X) IF GXDVIJ(K) HEBE DIFFERENT THAN AEOVE. SONE EVALUATION COOLC HAVE COHE HERE. 20 RETURN 22 QDVIJ-O.DO

DO 24 K»1,NK 24 GKOVIJ(K)=O.DO

RETORN

GENC GENC GENC GENC GENC

.GENC GEHC GENC GENC GEHC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GENC GEHC GENC GENC GEHC GENC GENC GENC GENC GENC GKNC GENC GENC GENC GENC GENC

1000 FORHAT (////'1',1X,* INPOT INFORHA7ICN FBOH SOBROOTINE GENCON:V1X, GEHC

10 20 30 40 50 60 70 80 90

100 110 120 130 140 150 160 170 180 190 2 0 0 2 1 0 2 2 0 230 240 250 2 6 0 270 2 8 0 290 300 310 320 330 340 350 360 370 380 390 UOO 910 420 430 440 450 460 470 480 49C 500 510 520 530 540 550 560

381

ISM 003O ISM 0035 ISM 0036 ISH 0037

>. V/2X.'IGENFC - INTERNALGENC 570 > GENERATION FUNCTION (AN INDEX)•/2X,>QEV - VALOE O® HEAT GENEHATIOGEHC 560 >N PER UNIT VOLOHE IN INTERNAL GENERATION FONCTIONV2X, • iqOVF - GENGENC 590 >1?RAL PURPOSE FUNCTION TO EE USEE OH ODV'/SX, 'GKDV(K) - VALUE OF H7- GENC 600 >SS GENERATION PER UNIT VOLUME FOF SPECIE N I* INTERNAL GENERATION GENC 610 >FUNCTION'/2X.,IGRDVF(N) - GENEFAI PDPPOSI FUNCTION TO BE USED ON GGENC 620 >KDV(*)•/> GENC 530

1010 FORHAT(I5,5X,3(E10.2,I5,5X),10X/(10X,3IF10.2,I5,5X) ,10X)) GENC 6«0 1020 FORHAT(//5J,'1C',6X,'IGENFC',5X,,CDV>,10X,'IODVF,,SX,'GKDV(1)',5X. GENC 650

> 'IGKDVF(I) ',5X,'GKDV(2) 1 . 5X, ' IGKDVF (2) •) GENC 660 1030 PORNlT(ax.I2,5X,I5,5X,El0.2,3X,IS,2(8X,E10.2,1X.I5)) GENC 670

END GENC 6B0 •OPTIONS IN EFFECT* NAME* HAIN,OPT=02,LIHECHT»60,STZE*C0CCIC, •OPTIONS IH EFFECT* S0DRCE, EBCDIC,HOLIST. NOEECIC.TCAC.NOEA F.NOEDIT, VOID. NOXREF •STATISTICS* SOOBCB STATEHERTS » 36 .PROGRAM SIZE = 1020 •STATISTICS* NO DIAGNOSTICS GENERATED

END OF COHPILATION «*•*•• 117K BXTES OF CORE NOT USED

382

ISN 0002 ISN 0003 IS* 0004

ISN 0005 ISN 0006

ISN 0007 ISN OOOR

ISH OOOO ISN 0010 ISN 0011 ISN 0012 ISH 0013 ISN 0014 ISN 0015 ISN 0016

ISN 0017 ISN ooie ISN 0019 ISN 0020

ISN 0021 ISN 0023 ISN 0024 ISH C025

BHDC 10 BHDC 20 BNDC 30 BNOC 40 BNDC 50 BHDC 60 BNDC 70 BNDC 80 BNDC 90 BNDC 100 BNDC 110 BNDC 120 EH DC 130

CS/360 FORTRAN H

COHPILER OPTIONS - BAHE» RAIN,0FT»02,LIHECST«6C>, SIZE»ODOOlt, SODRCE,EBCDIC,NOLIST.HODECK,LOAD,N0HAP,N0EDIT,N0ID,H0XR3P

SUBROUTINE ENOCHI (NR.2,DX,Y,OT,KX.KY.HCHICK) IHPLICIT REAL*8 (A-H.O-Z) DIHEHSION PHBD(25),F0Bt(25) ,FVBD(25) ,PTBt <25) , FCKBD (4,25) , > PQBD(25) ,TGBB (25) .FSBDN (25) .FSBESH (25) ,FGKBD(4, 25) ,RO(25) DIHPNSION IHEDF(25) ,I0BDF(25) ,IVBDF(25),ITB0i'(25) ,IGBDP(25) . > IQBDP(25) ,ISNBDP(25) ,ISHBDP(25) .ICKBDF (4.25) , IGKBDF (4,25) DI8ENSION IINT (25), JINT (25)

C •** Z IS REALLY CDR X ABB AT. BOT THE NAHE X IS USED AFTER THE ENTRY C ••* TOR AHCTHBF EUFPOSB.

DIHENSION Z(1),DX(1),Y(1),DY(1) COHHON/COHEIH/ ANL, ATHP ,CPIJ ,CKI 0 (4) ,CKIE J (4) . CKIfl J (4) .CKIOP'4) , > CKIJH (4).EXH.DXP.DYH.EYP,DXIP1,DYJP1, DXLI.DXRI.DXLI1.DXR11,uYLJ , > DTP J. OY1J1.DYRJ 1,GBIJ,GKEIJ (4) ,CBIJ,QIIB IJ (4) , SBX1.1.SBYI J, GXIHJ , > GXIPJ,GYIJH,GYIJP,GTIJ,GRTIJ(4) ,CTIJ. CKTTJ (4) .STXIJ.STYIO.QDVIJ .BHDC 140 > QXIH«J,QXIPJ,QYIJH,QYIJP,GFXIHJ (4) ,GKXIPJ (4) ,GKYIJH (4) ,GKYIJP(4) , BNDC 150 > HTKIJ (4) , HTRIOH (4) ,HTKIPJ (4) , HTKIHil (4) . HTKIJP (4) , RIJ. H U H ; HIPJ , BHDC 160 > HIHJ,HIJ?,UIJ.aiJH.UIPa,UIHJ.aiJP,VIJ,»IOH.»IPa.VIHJ,YiaP,TIJ , BHDC 170 > TIJH.TIPJ.TIHJ,TIJP,ROKTPC(4),BCIJ,ROIJE,BOIPJ,ROIRJ,ROIJP , BNDC 180 > SHFTPD(4) ,SHTCKD(4) ,SBSTPD,SXXIHJ,SXXIPa,SYYlaH,SYYIJP,SXYIJH , BHDC 190 > SXYIPJ«SXYinJ,SXYIJP,ROinJD,RCIEJC,ROTJHE,ROIJPD,EQTnP,TDIJ , BNDC 200 > HCIHJ,HCIE«7, HCIJH, HCIJP.GR, R0C3E (4) ,SPRTX(4),DENSK (4) ,RODKI J (4) , BNDC 210 > GKDVIJ<4) .DXI.DYJ ,QDV(25) ,HBD(25) ,0BE(S5) ,VBD(25) ,TBD(25) , BNDC 220 > CKBD(4,25),TBIJ,HCBIO .DCKBIJ (4),BTKBIJ(4),BNIJ,OBIJ,VBIJ,BBIJ. BNDC 230 > ROBIJ,RTBIJ.CKBIJ(4),TTIJ,HCTIJ,DCKTIJ(4).HTXTIJ(4),DTIJ,VTIJ, BNDC 240 > BTIJ,»0TIJ,HTTIJ,CKTIJ(4) ,QBD (25) ,GBt (25) ,GKBD (4,25) , SBDH(25) , BHDC 250 > SBDSH (25) ,HIND, KIHDX,HINDI ,IJ,IR1TJ,IE10,IJH1,IJP1,INTRT,K0XJ, BNDC 260 > K0IH1J,K0IF1J .K0IJH1 .KOIOP1 -,NB XII.NBXE, NEYd.NBYP, HREGIN.HBNDP , BNDC 270 > IXO»(25),3TO»(25),HHBDTP(25),NUEOTP(25) ,BVBDTP(25) ,HTBDTP(25) , BNOC 280 > HXGRL,NYGFL,N8EG,NIN71P,NTOPP,NEOIF,NIBIFC,NTHAX,NGENP BNDC 290 COHHON/SCRATH/XINT(25).TINT(25) BNOC 300 PRINT 1000 BNDC 310 PRINT 1010 BNDC 320 PRINT 1020 BNOC 330 HP0¥»0 BNOC 340 HPRI=0 BNDC 350 DO 10 1= 1, HBRDP BHDC 360 READ(50,1030) NBN,NHBDTP (HBN) ,NBBETE (N3N) ,BVBDTP(NBB) .NTBDTE (NBN) BNDC 370

C NBTYP»1, CONSTANT FLUX GOING OOT (OPEN CHANNEL FLOWING OOT EOB TEHPBNDC 380 C NBTIP-2, ADIABATIC (NO HEAT DIFFUSION FOR TEHPEBATURE, BNDC 390 C OPEN CHANNEL FLOWING OUT FOB ViLOCITY) BNDC 400 C NBTYP=3, ISCTHERHAL (OPEN CHANNEL FLCNIBG IN POB TEHF AND VELOCITY)BNDC 410 C NBTYP=4, CONSTANT FLUX COHIHG IH (CONSTANT EXTERNAL BEAT FLUX BHDC 420 C WITH KHOSN HEAT TRAHSFER COEFFICIENT POR TEHPEBATORE BNDC 430 C AND EXTERNAL KNONH STRESS, LIKE FRICTION, POR VELOCITY) BNDC 440

READ(50,1040) FHBD(HBN) .FOBD(HBN) ,PVBD IN3H) ,PTBD (NBH) ,XINT (HBH) , BNDC 450 > YIHT(NBN) BNDC 460 READ(50, 1010) FGED(NBN) ,FQBD (NBN) .FSBDK(HSN) ,PSBDSH(NBN) BNDC 470 BEAD (50,1040) (FCR3D (F.RBN) ,FGKEC (F,HBN) , R**1I NK) BNDC 480 READ(50, 1030)IHBDP(NBN) ,IDBDF (NBN) ,IVBDF (RUN) .IT3DP (NBN) , BNDC 490

> IGBDP (NBN) ,IQBDE(NBN) .ISNBDF(RBB) ,ISHEDE (KBN) , (ICKBDF (K, HBH) , BNDC 500 > IGKBDF (K, NBN) ,K=1,HK) BNDC 510 IP (FTED (NBN) .GE.O.) GO TO 10 BNDC 520 NPBT«1 BHDC 530

C •»• CALCOLATE NODE CONTAINING THE POINT (XIHT.YINT). BNDC 540 CALL BSERCH (IIHT (HBN) ,XINT (HBN) , Z,RX,DX, ' X • ,NBN,HPON, 1) BNDC 550 CALL BSERCH (JIHT (HBH) .TINT (NBN) .Y.RY.DY,' Y NBH,HPON, 1) BNDC 560

383

ISN 0026 ISN 0027 ISN 0029

ISN 0029 ISN 0030 ISM 0031 ISN 0033 ISN 0034 ISN 0035 ISN 0037 ISH 0038 ISN 0039 ISH 0040 ISH 0041 ISH 0042 XSH 0043

ISH 0044 ISH 0045 ISH 0046 TSH 0047 ISH 0048 ISN 0049 ISN 0050 ISN 0051 ISN 0052 ISN 0053 ISN 0055 ISN 0056 ISH 0057 ISN 0058 ISH 0059 ISR 0060 ISH 0061 ISH 0062 ISH 0063 ISH 0064 ISH 0065 ISH 0066 ISN 0067 ISH 0068 ISH 0069 ISH 0070 ISH 0071 ISN 0072 ISH 0073

ISH 0074

10 CONTIHOE BNDC 570 NCHECK"HCHECK+100000*HPON BHDC 580 PBIBT 1050,(NBH,NHBDTP(HBN),NOBDTE(HBH),HVBDTP(NBH| .NTBDTP(NBN) , BNDC 590

> PRBDfKBN) .FOBD(NBH) , FVBD(NBH) , FTED (NBB) ,BBN»1,NBNDF) BHDC 600 C BE R U T DESIGNED FOR NK«2 BNDC 610

PRINT 1060,(HBHfFGBD(HBH),F0BD(NE»),F5SDH(NBN) ,FSBDSH(NBN) , BHOC 620 > FGBBD(1,HBN),PGKBD(2,BBH) ,FCKEC (1 ,HBN) , FCKBD (2, HBH) ,HBN» 1 ,HBHDF) BHDC 630 PRIHT 1070, (I1BH,1HBDF(HBH) .I0BDF (RBB) ,IVEEF(HBH) ,ITBDF(1IBN) , BHDC 640 > XGBDF(NBN),IQBD?(HDN) ,ISNBDF (NBB),ISHGDF (NBN) ,NBB»1,HBHDF) BNDC 650 IF (BPBI.EC.C) GO TO 14 BNDC 660 PRIHT 1080 BHDC 670 DO 12 NBB>1,NBBDF BNDC 680 IF <FTBD(NBB).GE.O.) GO TO 12 BNDC 690 DTPP»-FTED (HBH) BHDC 700 PRINT 1090, NBH,DTPP,XINT(NBN) ,TINT (HBH) ,IIHT(NBN) ,JIHT(HBN) BHDC 710

12 COHTIHOE BHDC 72b 14 COHTIHOE BHDC 730

DEHS«62.2D0 BHDC 740 SPHTfl1« DO BHDC 750 RBTORH BHDC 760

BHDC 770 EBTRT BKDCON(KX,HK,T,CK) BHDC 780

C * * * o « * * * * » * * * * * v » * * 4 BNDC 790 DIHF.BSIOH T (BX, 1) ,CK (NK,KX,1) BHDC 600 DO 26 HBN-1,BBHDF BHDC 810 HBD(NBN)*FRBD(HBN)*GNRtFC(IflBDF(NBV),X) BNDC 820 OBD(NBN)«FOED(BBB)»GBRLFC(7DBDF(NEN) ,X) BNDC 830 VBD(NBN)»FVBD(HBH)*GBRIFC(IVBDF(NBN) ,X) BNDC 840 DO 16 R=1,BK BHDC 850

16 CNBD (K,HBH)• FCKBD (K,NBH) *GHRLFC (ICBBDF (K,HBH) , X) BHDC 860 GBD(NBN)«FCBD(NBB)*GNBI?C(IGBOf (BBB) ,X) BHDC 870 IF <FTED(NBN).LT.O.) GO TO 20 BHDC 880

19 TBD(NBN)•FTBD(HBN)*GBHIFC(ITBDf(NBB),X) BBDC 890 CALL HATPRP (CKBD (1,BBN) ,TBD(HBN) ,DEHS,SPHT,ROTPD) BBOC 900 RO(NBB)»tEHS BHDC 910 GO TO 22 BNDC 920

20 FLPP-GBD(BBB) BNDC 930 I«IINT(NBHJ BBDC 940 J*JI»T(N8H) BHDC 950 CALL HATPRP(CK(1,I,J),T(I,0) , DEHS.SPHI ,RCTPD) BHDC 960

C «•* -FTBD(NBB) •QEP(HEH) BHDC 970 TBD(NBH)»T(I,J) + (-FTED(HEN)) BHDC 980 RO(HBH)"DEHS BNDC 990

22 COHTIHOE BHDCIOOO QBD (HBH) •FCED(NBN)*GBRLFC(IQBDF (BBN) ,X( BNDC 1010 DO 24 K=1,BK BHDC1020

24 GKBD(K ,HBH)=FGKBD (K,BBB) *GBBLFC (IGKBDF (K ,HEB) , X) BBDC1030 SBDH (NEB) =TSBDH (HBH) »GBS1FC(ISBBDF (BBH) , X) BHDC 1040 SBDSH (HBH) *FSBDSH (HBN) *GNRLFC (IS EBDF (RGB) ,X) BBDC1050

26 COHTIHOE BBDC1060 RETCRN BHDC1070

1000 FOBBAT(////'1•,1X,1INPOT IBFORBATIOB FROH SBBBODTIBE BHDC0H:'/1X, BBDC1080 > . ... ... ') BHDC 1090

1010 FOBHAT ('0',1X,'HBH - BOUNDARY CCBDITICH BOBBER'/ BBDC1100 >• • ,1X,1NHBDTP - TTPE OF BCOHEAB1 COHDITICB FOR WATER ELEVATION B BN0C1110 >(HHBDTP)'/* f,IX,'NO - TXPE OF BCOBDARJ CONDITION »OR VELOCITY U (BNDC1120 >NDBDTP)•/* '»1X,'HV - TXPE OF BCONCART CONDITION FOR VILOCITY V < BNDC1130 >HVBDTP)•/' ',1X,1BT - TYPE OF BOONDARY CCBDITION FOR TFHP. OR SPECBHDC1140

384

ISH 0075

TSN 0076 ISN 0077 ISN 0078

• ISN 0079

ISN 0080

ISN 0081

ISN 0082 ISN 0083

CONCENTRATION (NBTDTP) •/' ',1X,'FH - VALUE OP BOOHDARY CONOITDNDC1150 OR HATIR ELEVATION (FHBD) '/ flNr>C116C *,'»U - VALUF OF BOONCART CCHBITICN FOG VELOCITY U (FUBD)'/ BNDC1170 X.'FV - VALUE OF BOUNtARY CCNCTTICN fOK VELOCITY V (FVBOJ'/ BNOCII8O X.'FT - VALU» 0» BOUNEARY CCBOITICN FOR TEMP. (FTBD) •/ BNDC1V90 X.'FO • VALUE OF BOOHtANT CCNEITICN FOR 1ASS FLUX (FOED)V BNSC1200 X.'FO - VALOE CF BOtlNtARY CCNEITICN (OR HIAT FLUX (FOBO) •/ BNDC1210 X.'FSEBN - VALUE OF BOUBDARY CONDITIO FOB NOR1AL STBESSES'/ BNDC1220 IX.'FOR (1) - VALUF OF IOONDAFY COHtXTICB FOR BASS FLUX OF SPICBNOC1210

>TE K (POKBD) •/ ' '.IX.'FCK - VAIIF CF EOUNIARY CONDITION FOP SPRCIBNDC1240 >ES CONCENTRATION (FCKBD)') BNDC1250

1020 FORNATC '.lll.'IHBDF - MULTIPLIER FONCTICN FOB fHBO'/ ' '<1*> BNDC1260 > 'II - MULTIPLIER »OBCTION FOB PUBD'/ • '.1X, BNDC1270 > 'IV - BOITIPLItR FONCTION FOF PVBOV ' '.IX. BN0C1280 > 'IT - HUITIPIIER FUNCTION FOR 1TB0V • '.IX. BNDC1290 > 'IG - HUITIPIIER FUNCTION FOF FGBD'/ • '.IX, BNDC1300 > '10 - BUITlPIIER FUNCICN FOB IQBDV • '.IX. BNDC1310 > 'ISN - FUITIPIIEB FONCTION FOB ISBDM/ ' '.IX, BN9C1320 > •ISH - H0ITIP1IER FUBCTIOB tOf PSBDSM') BNDC1330

1030 FORBAT<1915*10X| BHDC1199 1040 FOBBAT(7E10.3.10X» BNOC1350 1050 FONHAT(//' BOUNDARY CONCITiONS AT STARTING TIN*'/' NBN'.2X. ENDC1360

> 1NHBDTP'.3X.*NU,fl3X.'HVv.3X.'NT'.23X.'FRt,13X. BNDC1370 > 1FO'13X'FV'13X*FT'/(13.18.16.215.15X.1P4E15.6)) BNDC1380

1060 FOBBAT(//'C BBN'7X'FO'12X'TQ'12X 'FSBDN'IOX'FSBDSH'9X'FOK(1J'9X, BNOC1390 > ' FGK(2) '6X'FCK |1) 1 3X'FCK|2) '/ (I3.1X,1P6I14.6.0P2F9.3)) BNDC1400

1070 FOBBAT(//< BULTIPLIER FONCTIONS FOR BCORCARY CONDITIONS'/' NBN'.BNOC1410 > 4X,'IHBDP',2X,'I0',3X,»IV',3X,'IT«,3X,'I0',3X,'IQ',JX,«ISH',2X, BN0C14 20 > 'ISB'/(13.18,16.615)) BNDC1430

1080 FOPJ1AT (///' PONEB PLAN! ON BOUNBABY.'// • BBB',4X.'DTPP(NBN)' ,6X. BNDC1490 > 'XINT',10X,'YXNT',9X,'I',5X,'J'/) BN0C1450

1090 FOBBAT(14.1PE13>3.2E14«5.216) BN0C1460 END BN0C1470

•OPTIONS IN EFFECT* NABE* BAIN,OPT*02,LIHPCNT«60.SIZE-0000K,

•OPTIONS IN EFFECT* SOURCE,EBCDIC.NOLIST,NODECK.tCAC.NOBAr.NOEOIT.NOID,NOEBEF •STATISTICS* SOURCE STATIHEHTS « 82 .PBCGBfB SIEE « 10102

•STATISTICS* BO DIAGBOSTICS GEHIRATEE • ••••• £ R D 01. COMPILATION «•**»« 93N BYTES OF CORE NOT USED

385

OS/360 "OHTFAN H COHPILEF OPTIONS

ISM 0002 ISN 0003 ISN 0004

ISN 0005 ISN 0006 ISN 0007 ISH OOON

ISN OOOO IS* 0010 IS* 0011 ISH 0012 ISN 0013 ISM 001(1 ISN 0015

ISN 0016 ISN 0017 ISN 001B ISH 0019 ISN 0020 ISN 0021 IS* 0022 ISN 0023

ISN 0021 ISN 0025 ISN 0026 ISN 0027 TSN 0028 ISN 0029 ISN 0030

NAME" H»IH,OFT=02,IINEC>T«60,EIZI=OOOON, SOORCE,EBCDIC,HOLIST.HOOECK.LOJD.HOHAP.NOBDIT.NOID.NOXREF

SOBBODTINE BCTCNI(NK) IHPLICIT REAL*8 (A-H.O-Z) DIMENSION OB (25) ,VB(25) .HE (25) ,TE(25) ,CB (25) ,HCB (25) . BMANSC(25) ,

> CKB(4.25) ,DCKB (4,25),ICKB¥(4,25),ICCKtF (4,25) . I0BF(25) ,IVBF(25) > TNBF(25),ITEF(25) ,IQBF (25) , IHCBF (25) COHMON/REGICN/DEFTH (25) ,SH (25) .TIBEB(25) .IHREG (25) ,JLREG(25) , > JHREG (25) , INTF (25) ,IGENF(25) .ITCPF (25), IEOTF (25) INTEGEF*2 IIBEG,IHREG,JLREG,JHREG INTEGER*2 INIF,IGENF,ITCPF,IBOTf COHHON/COHBIK/ ANL,ATHP,CPU,CKIJ(4) ,CKTf J (4) ,CKH1J (4) ,CKIJP(4) , > CKIJH(4),CXH,DXP,DYn,CYP,DXIP1,CYJF1,EX1I,0XRI,DXLI1,DXRI1,DYLJ > DYRJ,DYIJ1,DYRJ1,GBIJ,GKBIJ (4) ,CBI J.QtBTJ (4) , SBXIJ , SBYIJ,GXIH J , > GXIPJ,GYIJH,GYIJP,GTI3,GKTIJ(4),QT13,CKTIJ(4),STXIJ,STYIJ,QDTIJ > OXIHJ,QXIPJ.QYIJH.QYTJP.GKXIBJ(4) ,GKX1PJ(4) ,GKYTJH (4) ,GKYIJP(4) > HTKIJ (4) , HTKIJH (4) ,HIKIPJ(4) ,HT*IH.1 (4) ,HTKT JP (4) , HIJ, H U H ,HIPJ , > HIMJ,HUP,OIJ,OIJH,»JIPJ,OIHJ,OIJP,»IJ,VIJE,»IPJ,TIHJ,TIJP,TIJ , > TUN.TIPJ.TIHJ,TUP,RCKTPD(4) .ECU.ROIJB.ROIPJ.ROIMJ.ROUP , > SHFTPD(4),SHTCKD(4),SHTTPD,SXXinj,SXXIPJ,SYYIJH,SYIIJP,SXYIJH , > SXYTPJ,SXYIBJ,SXYIJP,R01HJD,RCItJE,POIJEC,ftOUPD, EfiTHP.TDIJ , > HC1M3, HC1PJ ,HCIJH.HC7JP,GR, ROCKC (4) ,SFHTK(4) ,0ENSK(4) .RODKIJ (4) > OKD7IJ(4) ,BXI,DTJ ,QDV (25) ,HBD (25) ,0BE (25) ,VBD(25) ,TBD (25) , > CKBD (4,25) ,TBIJ,HCBU ,0CKBIJ(4) .RTKB1J (4) ,BHIJ,QBIJ,VBIJ ,VBIJ, > ROEIJ,HTBIJ,CKBIJ(4),TTI J,HCTIJ ,ECKT IJ (4) ,HTKTU (4),0TIJ,»TIJ, > NTIJ,ROTIJ,HTTIJ,CKTIJ(4) ,QBD(25) ,GBD(25) ,GKED(4,25) ,SBDN(25) , > SBDSH (25) ,NIND,«INDX,HINEY ,U,IH1J,IF10,IJ11 ,IJP1, IN TRT, KOI J, > KOIN1J,KOIP1J,KOIJM1,KOIJF1 ,N8XH,NBXF,NEYIIrNBYP, NBEGlNtNBNDF , > 1X07(25) ,aY07 (25) ,NHBDTP(25) ,N0EDTP(25) ,HVBDTI>(25) ,NTBDTP(25) , > NXGBL,NYGFL,NREG,NIRTLF,NTOPF,N£OTF,N1BIFC,NTHAX,!IGENF PRINT 1000 PRINT 1910 PRINT 1020 DO 10 L«1.NBCTF READ(50, 1030) I,DB(I) ,VB (I) . HB (I) ,TB (I) , CE (I) , HCB (I) , BHANGC (I) READ (50, 1050) (CKE(K,I) ,DCKB(K,I) ,(»1,NX) READ (50,1040) IOBF(I) ,I7BF(I) ,IHEF (I) , ITBF (I) , IQBF (I), IHCEF(I) ,

> (ICKBf(K,l), IDCKBF (K,I) ,K=1,NK) 10 CONTINOE

PRINT 1060 00 12 I»1,HBCTP PRINT 1070 ,1 ,QB (1) . HCB (I) ,0B(I) ,VB(I) ,«B(I).TB(I) , BHANGC (I),

> (DCKB(K,I),CKB(K,I) ,K*1,BK) 12 CONTINOE

PRINT 1080 DO 14 I-1.NBOTF PRINT 1090,1 *XCBF(I) .IHCBT (X) .IDE* (I) , 1YET (I) , 1NBF (I) ,ITBF (I) ,

> (IDCKBY (K,1) , ICKBF (K,I) ,K>1,NK) 14 CONTINDE

DENS-62.2DC SPHT-1.D0 RF.TOBN » • • » » # • » » » • » • * « • » » • » , « • • » FNTRY BOTCON NBT'IBOTF(NREGIN) TBIJ'TE (NBT) »GNRIFC (ITEF (NET) , X) DO 201 K-1.HK

10 20 30 40 50 60 70 80 90

BOTC BOTC BOTC .BOTC BOTC BOTC BOTC BOTC BOTC EOTC 100 .BOTC 110 BOTC 120 ,BOTC 130 .BOTC 140 BOTC 150 BOTC 160 BOTC 170 BOTC ISO BOTC 190 .BOTC 200 BOTC 210 BOTC 220 BOTC 230 BOTC 240 BOTC 250 BOTC 260 BOTC 270 BOTC 280 EOTC 290 BOTC 300 BOTC 310 BOTC 320 BOTC 330 BOTC 340 BOTC 350 ECTC 36 ti EOTC 370 BOTC 380 BOTC 390 BOTC 400 BOTC 410 EOTC U20 BOTC 430 BOTC 440 BOTC 450 BOTC 460 BOTC 470 BOTC 480 BOTC 490 BOTC 500 BOTC 510 EOTC 520 BOTC 530 BOTC 540 BOTC 550 EOTC 560

386

TSH 0031 TSH 003? ISR 0033 ISN 003U ISH 0035 ISH 0036 ISN 0037 ISN 003R ISN 003° TSN OOOP TSH 0 0 0 1 ISN 0002 ISN 00U3 ISN OOOO ISN 0005

ISN oons

ISH 00O7

ISN oo«a ISN 0009 IS* 0050 ISN 0051

ISN 0052 ISH 0053

ISH 0050 ISH 0055

C 201 CKBX J(H) *CRB (K,NBT) *GHRLPC (ICKBF (K,NBT) , 1) EOTC 570 C » U HATPRF (CKE«TBI*1*0ENS,SPHT,RCTPH) BOTC 580 BOBIJXCEBS BOTC 590 HTBIJ«SPHT*TEIO BOTC 600 DO 16 B=1,NB BOTC 610

C •»• NOTE BEABBANCERENT. BOTC 620 CKBTJ(B)»CKB(K,NBT)*GmFC(TCKEE«.HBT).X) BOTC 630 DCKBTJ(K)*CCKB (K,N9T)*CNRIFC(IECFEF(K,»BT),X) BOTC 6«0

16 HTKBIJ(K)«SFHTK(M*tBIJ BOTC 650 BNIJ>BHABGC(NBT) BOTC 660 QBIJbQB(NBT)•GBPLFC(IQBF(NET),X) BOTC 670 HCBIJsBCB(BBT)*GHRLFC(IHCEE(NBT),X) BOTC 680 UBIJ'UB (NBT)'GNPLFC(IOBF (NET),X) BOTC 690 WIJ"TB (NBT) *GBBIFC (IVBP (BBT) , X) BOTC 700 BBIJ*NB(NBT)•GBBIFC(IHBP(NBT)* X) BOTC 710 RFTffPN BOTC 720

1000 PORMAT(////,0,.1X,,IBPOT IBFORHAIIOH FROM SOBROOTIHE BOTCOB:'/U. BOTC 730 > . •) BOTC 700

1010 F0RRAT ('O'.IX.'CB - BEAT COMING FRCtl THE BOTTOV/ BOTC 750 >• '.IX.'HCB - HEAT TBANSFFR COIFHCIENT ECR THE BOTTOHV BOTC 760 >' 't1X,»OB - VFtCCtTT GF HASS COBING FROH THE BOTTOM IB X-DIBECTIOBOTC 770 >«'/' '.IX.'»B - TEtOCITt OP MASS CCMIHO FBCM THE BOTTOM I* T-DIBICBOTC 7B0 >TION*/' • ,1X,'BB - VILOCIT1 OF RASS SOBIBG ?B0H THE BOTTOM III Z-EIBOTC 790 >B?CTIOH»/' »,1X,>TB - TEMFEBA10BE OF RASS COMING FROH THE EOTTOH'/EOTC BOO >• '.IX.'BHABbC - HABBIBG CCEF. FCR mCTIOB HITH THE BOTTOHV BOTC 810 >• '.IX.'OCKB - MASS BIFPBSION COEFFICIENT FOB SPECIE K FBOH BOTTOMBOTC 820 >•/• '.lE.'CRB - MASS CONCENTRATION OT SPECIES CONING PROH EOTTOH')EOTC 830

1020 FORHAT(• '.IX.'XQB - RBITIIIIEB EOBCTICN EOB QB'/ > •IHCB - MOITIPLI'P FDBCTIOH FOB HCB'/ • '.IX, •IBB - BOITIPLIER PONCHOS FOB OBV • •, IX, •ITB - HOITIPIIER PONCTIOB FOB »B'/ • ',1X, •IBB - HOtTIPlIEB FOHCTIOH FOB SB'/ • • ,1X, •IT3 - nOLTIPlIEB TBNCTIOB FOB TEV ' * .1*.

'.IX,

• IDCKB - ROLTIPLIER FONCTIOB EOF DCKBV •ICKB > HB1TIFLIEB FOHCTION FOB CBB>)

1030 POSBAT(t5.SX.6E10.5.10X/C7E10.5.10X)) 1010 FORMAT (10IS,10X) 1050 FORHAT(7E10.5,10X) 1060 FOBBAT(//• EOTTCR CONDITIONS AT STARTING TIME'/' TCT. NO.'.SX,

> •0B,,7X,«BCB,,6X,,O8',6X,'»B',6X, •HB',6*.,TB' ,7X, • BHANGC ,5X, > • BCBB (1) • ,6X,*CKB(1) MX,'BC<b(2) • ,6*.'cue (2) •)

1070 FOBHAT(1X,IS,OX,3F9.2,1POE9.2,1X.OP11.2) 10B0 FOBHAT(//• ROITICLIER FOBCTIOH ECB BOTTCB CONDITIONS'/

> • FCT.NO.',ai,>IOB',2X,iinCB<,1X,,IUE,,2X,'IVB,t2X,lIBB'.2X. > 'ITB',2X, •IDCKB(1),.1X,«ICKB(1)'.1X,,IBCRB(2),,1X,»ICKB12)M 1090 FORMAT(2X,13,IX,18,515,IX,0(15,OX))

END

BOTC 800 BOTC 850 BOTC 860 BOTC 870 BOTC HBO BOTC 690 BOTC 900 BOTC 910 BOTC 920 BOTC 930 BOTC 900 BOTC 950 BOFC 960 BOTC 970 BOTC 9SO BOTC 990 BOTCIOOO BOTC 1010 BOTC 1020 B0TC1Q30

•OPTIONS IN E»FFCT« HAME- MAIH,OFT»02,IINECNT*60,JIZE«09CCN, •OPTION'S IN EFFECT* SOURCE, EBCDIC, NOLI ST, NO £ECK,LCAC, NO EAE,HOEDXT,NOXD, HO XR£P •STATISTICS* SOURCE STATEMENTS • 50 ,FFCGRAR SJZE • 7600 •STATISTICS* HO OIAGHOSTICS GENEBATEB •••••• ENB OF COMPIIATXON •*•*•• 105K BXSES OF COBE NOT OSEB

387

CS/360 FORTRAN II CONPIIFR CPTIOHS - RAH!" HAIH,OPT»02,LXNEC»T«60,STEE.OOOOK,

SOOFCE,EECDIC,N01TST,BODECl:,I.CAD,IIO!IAP,NOEDIT,NOIO,NOXREE TSH 0002 SUBROOTINE TCPCHI(HK) TOPC 10 IStl 0001 IHPIICIT REA1«8 (A-H.O-Z) TOPC 20 ISH 0004 DIREBSION 0T(25) ,VT(25) ,«T(25) ,TT(25) ,CT«i5) ,HCT(25). TD(25) . TOPC 30

> 0SOl(25),CNT(4,25) ,DCKT(4,25) ,ICBTF(0,2EI ,IDCKTM4,25), I0TF(25| .XOPC 10 > IVTP(25) ,INTF(25),ITTF (25) .ICTF (25). IHCTF (25) . XTDF(25), TOPC 50 > XQSOLP(25),BNDX(25).HBDY(25) TOPC 60

ISH 0005 COHHOH/RSGIOH/DEFTH(25) ,SB(25) ,II8EG(2C) .IHREG (25) , JLREG(25) , TOPC 70 > JHPEG(25) ,I«TV<251 .IGEHF(25),TTCFT(25),IEOTF(25) TOPC BO

ISH 0006 IPTEGFB*2 ILPEG,IHREG,JIPEG,JHREC TOPC 90 ISH 0007 IHTEGER*2 IHTF.IGEHF.ITOPF.IBOTF TOPC 100 ISH 0008 CONNOR/COHEIR/ ABl.ATBP,CPIJ,CRIJ(U) ,CHIfJ(U) ,C<lnj(4) ,CKIJP(4) , TOPC 110

> CKUN(4),EXH, CXP.DYN, DTP, DXIPl.tYJPl.nXlI.IXRI, 0X1.1. .DXRH.DYIJ ,T0PC 120 > DTR.1,DYlJ1,DTR01,^3IJ,GFEIJ(tl) ,(B1J.QtBIJ(4) . SBXI J, SBYIJ , GXIHJ , TOPC 130 > nXIPJ ,GEIJH,GYTi3P,GTXJ,GRTIJ (4) ,C?U,CKTZJ (4) ,STXIJ, ST/U,QDVXJ ,TOPC 140 > QXIRJ,QIIPJ,QYIOH,QYIJP,GKXIRJ(ll) ,GEXIPJ(4) ,GKYIJN(4) ,GKYIJP(4) ,TOPC 150 > HTKIJ (4),HTKI3H (4) ,HTKIPJ(4) .HTHBJ (4) , RTRTJP (4) , HIJ. HI JR ,HIPJ , TOPC 160 > HIRJ,HIJP,OIJ,OIJH,OIPJ,CinJ,OIJF.VIO,«JOF.VIPJ.VIUJ.VTJP.TIJ , TOPC 170 > TIJN,TIPJ,TIHJ, TIJP, RCKTPC(4) , RCI J.PCIJ B .BOIPJ, ROHJ , ROUP , TOPC 180 > SRIfTPD(«) ,SRTCKD(4) ,SRTTPP, SXXIBJ.STXIP J.SYYIJN.SmJP, SX YIJB , TOPC 190 > SXYIPJ,SXYIRJ,SXYTJP,ROIHJD,RCIFJD,RCUFG,ROIJPD,EQTnP,TDIJ , TOPC 200 > HCXRJ,HCIPJ,HCIJH.HCIJF,GF.R0CKE(4),SFHTK(4) ,DENSK(4) ,R0DKIJ(4) .TOPC 210 > GKD»IJ(4) ,0X1,OYJ ,QD»(25),HBD(;5) ,0BD(25).VBD(25) ,TBD<25) , TOPC 220 > CKBb(4,25) ,TBTJ,HCBIO ,CCKBIJ (4) .HTBBU (4) ,BHU,UBIJ,VBIJ,«BIJ, TOPC 230 > ROBTJ,RTBU,CKBTJ(4) ,TTXJ.HCTIJ,ECKTIJ(II) ,HTKTIJ(4) ,OTIJ,VTIJ, TOPC 240 > «TIJ,R0TIJ,HTTU,CKTU(4) ,QBD (25) ,GBD (25) ,G«IBT> (4 , 25) ,SBDN (25) , TOPC 250 > SBDSH(25).HIND.BINDX.NINtY ,IJ,IRIJ.XF1J.IJH1,I3P1.INTRT.KOIJ , TOPC 260 > NOIH13,KOIF13,KOUH,KOI3P1 ,HB1R,HBXF,*EYH,HBYP.HREGTR,HBH0? , TOPC 270 > IX0»(25),JYQ7(25),NHBBTP(25),BCS0TP(2E) ,RVBDTP(25) ,HTBDTP(25) , TOPC 280 > HXGRL,NEGFX,HREG,NIHTIF,BTOPF,HECTF,NTBIEC,HTHAX,NGENF TOPC 290

ISH 0009 PBIBT 1000 TOPC 300 ISH 0010 PRIBT 1010 TOPC 310 ISB 0011 PRTBT 1020 TOPC 320 ISH 0012 DO 10 LB1,HTCPF TOPC 330 ISB 0013 READ(50« 1030) I.OT(I) ,VT II) ,HT (I) ,TT(I) . CT (I) . HCT (I) ,TD(I) ,QS0L(I) TOPC 340

> .NHDX(I) .NBDYO) TOPC 350 ISB 0014 READ(50,1050) (CBT{K.D .DCBT(K.I) ,K»1,H«| TOPC 160 ISB 0015 REAfy(50. 104C) IDTF (X) .TVTF (I) ,IUTE (I) , ITTF (X) .IQTF(I) , IHCTF (I) . TOPC 370

> ITDF(I) .ICSCIF(I) . (ICKTF(K.I) ,ItCBTF(K, 1),K=1,BK) TOPC 380 ISH 0016 10 COHTIHD" TOPC 390 ISB 0017 PPIHT 1060 TOPC 400 ISH 0018 DO 12 I»1, NTOP / TOPC 410 ISH 0019 PBIBT 107O,I,QT(I),flCT(I).OT(I> ,VT(I) ,BT(I),TT (I).TD(I) ,gS0X(I) , TOPC 420

> (DCKT (K,I) ,CKT (B,I) ,ICX1, 2) TOPC 430 ISB 0020 12 CCHTIHDE TOPC 440 ISB 0021 PBIBT 10B0, (I,IQ1F(I) ,IHCTF(I) ,IBTF(I) ,IVTF(I) ,IWTF(I) ,XTT?(I) , TOPC 450

> XTDF(I)aXQSCLF(I),(IDCKTE(K,1). 1CBTF (K. I) .K=1 ,BK) .1-1,BTOPE) TOPC 460 ISH 0022 DEHS<162.2D0 TOPC 470 ISN 0023 SPHT'I.DO TOPC 480 ISH 0024 BETOBH TOPC 490

C » » » » » » » » » » » » » » » » * » « « TOPC 500 ISB 0025 ENTRY TOPC CD TOPC 510

C » * « » » » » « » » » * * * * » « » » » TOPC 520 ISH 0026 HTP"ITOPF(BBEGIH) TOPC 530 ISB 0027 TTIJ«TT(MTE)»CNRIPC(ITTF(HTP) ,X) TOPC 540

C DO 201 R»1,BN TOPC 550 C 201 CBTIJ (K) aCKT (K,NTP) •GHHLFC (ICKTF (B ,HTP) , X) TOPC 560

388

ISN 0C2A ISN 002'' TSN 00 30 ISN 0<M1 RSN 003? ISN orm ISN 0030 TSN 0015 TSN 00 36 TSN ONN TSN 0038 TSN 00 3° TSN OOAO ISN 0001 IS,* 0002 TSN 0001 TS>I OOOU

TSN onufi

TSN 10 07 TSN OQOFL TSN <JCU9 ISN ONS" ISN 0051 TSN 0052 ISN 0051 TSN 0050

ISN 0055 ISN 0057 ISN 0059 ISN 0051

CALL MATPRF(CFT.ITTJ,HENS,SPHT.BCTFE) R0TTJ»CFNS HTTTJ»SPHT«TTIJ PO 1U Itsl.NH

C ••* MOT* PF»?P»NGEMENT. CKTIJ(K) =CKT IK.NIP) DCKTIJ (K) = tCKT (K,NT P) •GNFLFC (TfC l*TF (< , NTF) , X)

1U HTK'IJ(K)*SFH?K(K)*TTTJ QTTJ=0T(NTE)•GNFIFC(TOTp (NTP),X) •*r>T.1»TD('.lTE) •GNFIFC(T?DF (NTP) ,V) QSOLIJ=QSOL (NTP) »r;NFLFC (TCSOL* (NTP) .X) U?TJ=UT (NTP)*GNRI"C (TUTF (NTP) ,X( VTI.TsVT (HTE) •GNFI»C (IVT" (NTP) ,T) MTTJnHT (NTT) »nNRI"C (IWT» (NTP) ,X) »TNnX = M!ltlX (NTP) VTNDY=HNDY (NTP) «IND=D3Q9T («INtX«*?*1ITNCY»»2) IF (HCT(NTP) .GE.O.) GOTO 16

TO' .. 570 TOI'C 580 TOPC 590 TOPC 600 TOPC 610 TOPC 620 TOPC 610 TOPC 600 TflPC 650 TOPC 660 TOPC 670 TOPC 680 TOPC 690 TOPC 700 TOPC 710 TOPC 720 TOPC 730 TOPC 700

C •«• CALCULATE HE AT EXCHANGE CCEFF. AkD EQUILIBRIUM TEMP. BASED ON THE TOPC 750 C «** EDINGFS ANE 1EYIB HFTHCD. TOPC 760

BETA3 (TIJ4TD1J) *(5.1D»5*(1IJ*TI0)-O.0Ctt5CO)»O.255DO TOPC 770 C ••« 1/5280 = .18939390-3 TOPC 780 C *•• 1/20 = .U166667D-1 TOPC 790

HCTIJ=.01666670-1*(15.7D0» (BETA*C.26D0)« (70.D0*0.700 •(0. 1893939D-ir/v 800 > 3«VIND) "SCO)) TOPC 810 *Q?MP=TDIJ«0SOLIJ/HCTIJ TOPC 820 r,0 TO 18 TOPC 830

16 HCTIJsHCT(NTP) »GNPLFC (IHCTF (NTP) ,X) TOPC 800 EQTHP=TDTJ TOPC 850

1R RFTURH TOPC 860 1000 "ORMAT(////'0*,1X,'INPUT INF0RHR1ICN FROM SUBROUTINE TOPCON!'/1X, TOPC 870

> I — 1) TOPC 880 1010 "OR"AT ('0',1X,'0T - HFKT COHING "RCH TH? TOP'/ TOPC 890

>• '.IX.'HCI - HEAT TRANSFFP COHEITCIENT FCB TOP'/ TOPC 900 >' 1 , 1X . ' PT - VEICCITY OF HASS CCNING FRCP THE TOP IN X-DIRECTION'TOPC 910 >/' ',1X.'VT - VFLOCITY OF HASS CCHING FECM THE TOP IN S-DIRECTICNTOPC 920 >'/' *.IX,'NT - VFLOCITY CF HASS COHING FFCM THE TOP IN Z-CIRECTIOTOPC 930 >N</' '.IX, 'TT - T?HP*BATUHE Of HASS CCKIHG PROH THE TCP'/ TOPC 900 >* '.IX,'ID - DEW-POINT TEMPEBATUFE'/ TOPC 950 >' ',1X,'QSCL - SOLAR HEAT FLOX'/ TOPC 960 >' ',1X,1DCKT - HASS DIFFUSION COEFFICIENT FO^ SPECIE K FROM TOP"/ TOPC 970 >* '.IX.'CKT - HftSS CONCENTRATION OF SPICIIS COMING FROM THE TOP') TOPC 980

1020 "ORMUT (' '.IX.'IQT - MULTIPLIER FUNCTION POR OT'/ ' ',1X, TOPC 990 > 'IHCT - MULTIPLIER FUNCTICN FOR HCT'/ • ',1X, > 'IDT - HUITIPLIFP FUNCTICN FOB UTV ' ' , 1X, > 'IVT - MULTIPLIER PUNCTION FOP VT'/ ' ',1X, > 'IWT - MUITIPITEP FONCTION FOB NT'/ * *,1X, > 'ITT - MULTIPLIER "UNCTION FOR IT •/ • • ,1X, > 'ITD - MULTIPLIER FONCTION FOB TO'/ ' ',1X, > 'IQSOL - MULTIPLIER FUNCTION FOF QSOL'/ ' ',1X, > 'TDCKT - MUITIPLTER FUNCTION FOB DCKT'/ ' ',1X, > 'ICKT - MULTIPLIER FUNCTICN FCB CKT,1

10 30 "ORHAT (I5,5X,6E10.5, 10X/(7F10.5, 10X) ) 1000 FORMAT (1015,10X) 1050 FORMST(7E10.5.10X) 1060 "OP1*AT (//' TOP CONDITIONS AT STfFTIHG TIME'/

TOPC1000 TO PC 1010 TOPC1020 TOPC1030 TOPC1QOO TOPCIOSO TOPC1060 TOPC1070 TOPC1080 TOPC 1090 T0PC1100 TOPC1110

FCT. NO,',6X,'QT'tTOPC1120 > eX.'HCT'.SX.'OT'.fiX.'VT'.eX.'NT'.eX.'TT'.SX.'TD'.eX.'QSOL'.SX, > * DCKT (1) ' ,3X.'CKT(1) ' . 3X » 'DCKT { 2) '.3X.'CKT(2) *)

TOPC11 30 TOPC1100

389

TSH 0060 1070 »ORHAT (1X,IS,6X,fiFe.2ti|p10.2) TOPC1150 ISM 0061 10AC FORI'Ti//' WHTIPLIES FOHCTICd fCF TCP CCNDITIPNS </' FCT. HO.', 10PC1160

> "i. 'IQT', 2X,* IHCT'.U.'IOT ,2X, 'TV- • , 2* , ITDT • , 2X, < ITT« , 2X , • ITU • , TOPC 5170 > 2X,'IQS0l',U,'TnCKT<1| > ,1X. ' ICIIT{1) < ,1t. •triCKT (2) ,,1X,,:CKT{2) '/topciieo > (3X.I7.6X,7(13,2X>,2X,I3 ,3X,« (I« ,BXM) 70PC119G END TOPC1200 ISH 0062

•OPTIONS IH EFFECT' •OPTIONS IN E"F"CT» •STATISTICS* •STATISTICS*

SAMR= HAIN,OFT=02,lINFCtIT=60 ,ST-5F»00 C CK. SOURCE, EECDTC.NOLIST.NOt^CK.lCAE.NOMt.NOEOTT NOIP,XOXPEF

SOURCE STATEMENTS = 61 .fFCGSAl SIZE = S920 NO DIAGNOSTICS riFNESATEC

»**•«* E|JD O® COMPILATION ••••«* 105K EYTSS OF CORE NOT USFD

390

* * * * * *

CS/360 FORTRAN H COF?TieP. OPTIO»S - NAME- MAIN,OPT=02,LIHECFT=60 ,ST?E=000OK,

SOURCE,EBCDIC,HOIIST.HCCECK,LOAD,NOSAP.NOEDIT,NOID.NOXRSF ISN 000? SUBROUTINE INTCON(HK,KX,KY,H,U,V,T,CK,C,FE5T) INTC 10

Q= (ERPHSB,EftfiOPL.ERPVFL,EPFTNP,EFBCSK) INTC 20 REST*(H,0, V,T,CK,EBHHSF,ERRUFL,EFRVFL,FRRTf1P,ERRCSK) INTC 30

ISN 0003 IMPLICIT REAL**) (A-H,0-2) INTC 90 ISN OOOtt DIMENSION H <KX ,KT) , U (KX,KT) ,V (KX ,KY) ,T (KX , KY) , CK (HK,KX,KY) , INTC 50

> RPST(NttOVE),0(1) INTC 60 ISN 0005 COHHON/BSGICN/DEFTH (25) ,SM(25) ,TIRFG(25) .IHREG (25) . JLREG(25) , INTC 70

> JH9EG (25) ,INTF (25) »IGENP(25),TTCPF(25),IECTF(25) INTC 80 ISN OOOS TNn*EGER*2 ILREG, IHRPG,JLPFG, JHBEG IHTC 90 ISN 0007 INTEGER*2 INTF.IGENF.ITOPF.IBOTF INTC 100 ISN 0008 COHHON/CON EI N/ ANL, ATHP ,CPIJ ,CKI J (4) ,CFI F J (4) . CKIN J (4) „CKIJP (4) , INTC 110

> CKIJH(4) ,£XN,DXF,DYH,DYP,CXIP1,CYJP1,DXII,1XRI,DXLI1,DXBI1,DYLJ ,INTC 120 > DYPJ.DYLJ1 .DYRJ1,GBIJ,GKEIJ (9) ,CPU,OKBTJ(») ,SRXIJ,SBYIJ,GXIKJ , IHTC 130 > GXTPJ1'iYIJM,GYIJP,GTIJ,GNTIJ(ll) ,CTIJ,CK'TIJ(U) ,STXIJ,STYIJ,Qa»IJ .INTC 140 > OXIHJ,QXIFJ,QYIJM,QYIJP,GKXI(IJ(«( ,GKXTPJ(U) ,GKYIJM(I|) ,GKIIJP(«) ,INTC 150 > HTKIJ (9) .HTKIJH (4) .HTKIPJ (4) ,HTKIHJ(4) .FTKIJP (4) .HIJ.HUH.HIPJ . INTC 160 > H1MJ, HIJP ,U1J. UIJH ,UIP J , UIMJ, OIJF.VIJ.VIJP.tfl P>1, VINJ, VI JP ,TIJ , IN'C 170 > TI JH.TIPJ ,TIt1 J , TIJP.POKTPC (4) .BCU.FCIJ P., FOIPJ, P0I3J. ROUP , TNTC 180 > SHKTPD(U) .SHTCKD(U) .SHTTFC.SXXTBJ.SXXTPJ,SYYIJN,SYYIJP.SXYIJH . INTC 190 > SXYIP J. SX YINJ.SXYIJP,B0TMJD,RCI IJD,FCIJPE,ROIJPD, EQIMP.TDU , INTC 200 > HCIHJ .HCIFJ«HCI JH.HCIJP.GF»ROCKt (9) , SFHTK (4) . DENSK (4) .RODKIJ (4) .INTC 210 > GKDYIJ(ll) ,DXI,DYJ , QDY (25) , HSD (25) ,UBE (25) ,VBI5 (25) ,TBD (25) , IHTC 220 > CKBD(4,25).1BIJ,HCBIJ ,DCKBTJ (ft),HTKE13(4),BNIJ.UBTJ,VBIJ,HBIJ, IHTC 230 > FOBIJ.HTBIJ«CKBIJ(4) ,TTIJ,HCTIJ,CCKTIJ(4),HTKTIJ(9) .U1IJ.VTIJ, INTC 290 > HTIJ,80TI.7,HTTIJ,CKTIJ(U) ,QBD(25) .GB*:(<-),GKBD(U,25) .SBDH (25) , IHTC 250 •> SBDSH(25) ,«IND,VINDX,NINCY ,TJ , IN 1 J, IF1J ,1JM1 .IJP1 .INTBT, KOIJ , INTC 260 > K0IN1J.K0IP1J , K0IJM1 , KOI JP1 ,NB*H,NBXF,NBY1,NBYP.NREGIIi,NBHDP , INTC 270 > TXQV(25),JYQV(25),NHBDTP(25),HUEDTP(25) ,N»BDTP (25) .HTBDTP (25) , IHTC 280 > NXGRL.NYGFL.NRFG.HINTLF« NTQFF .NECTF.NTBLFC,NTHAX.NGENF INTC 290

ISH 0009 COHNON/DROU/TIH.DTH.TM,PERIOD,IT,NHCVE.LHCVP.H INTC 300 ISH 0010 COMHON/IHDFIT/DTKiiT, STM,SriH,PRB'I!1,CPRTTH,CP7SEC,TIDAt,FDTM, INTC 310

> TNDTH.NBTMC,IFINIS.IDTHCF,ISTART.TFIOT.NCPD INTC 320 TSN 0011 COMMON/SCR ATfl/STH (25) , STU (25) , STV (25) , STT (25) , STCK (9,25) , INTC 330

> ISTHF (25) ,ISTUF(25) .ISTVF (25) ,ISTTF(25) ,ISTCK?(4, 25) ,KINT (25) INTC 340 ISN 0012 IF (ISTART. NF. 0) GO TO 32 INTC 350 TSN 0014 PRINT 1000 THTC 160 ISH 0015 IF (HINTLF.LE.25.AND.1.LE.NIHTIFJ GC TC 12 INTC 370 ISN 0017 PRINT 1010,NTNTLF TNTC 380 ISN 0018 10 CALL EXIT INTC 390 ISN 0019 12 DO 14 N=1,NINTLF INTC 400 ISN 0020 14 KINT(H)=-1 INTC 910 ISN 0021 DO 20 1=1,NINTLF TNTC U20 ISN 0022 BEAD(50,1050) TNTFC,STH(TNTPC) ,STU (TNTFC),STV(TNTFC),STT(INTFC) INTC 430 ISN 0023 TF (1.LF.INTFC.AND.TNTFC.LE.NINTtF) GO TC 16 INTC 440 ISN 0025 PRINT 1020,INTFC,NTNTIF INTC U50 ISN 0026 GO TO 10 INTC 460 ISN 0027 16 IF (KINT(INTFC) .EQ.-1) GC TO 18 INTC 970 ISN 0029 FPINT 1030.INTFC INTC 980 ISN 0030 GO TO 10 INTC 990 TSN 0031 IR BEAD (50,1060) (STCK (K,INTFC) ,K=1 ,HP) INTC 500 ISN 0032 READ(50,1040) TSTHF(INTFC),ISTUF (INTFC),ISTVF(INTPC),ISTTF(IHTFC) ,INTC 510

> (ISTCKF(K,INTFC),K=1,NK) INTC 520 ISN 0033 20 KINT(INTFC)=INTFC INTC 530 ISN 0034 DO 26 1=1,NBEG TNTC 540 ISN 0035 NINL=INTP(I) INTC 550 ISN 0036 TL=IIRRG(L) INTC S60

391

ISH 0017 IH=THFEG(L) INTC 570 ISH 0034 JL=.USF1(L) TNTC 580 ISH 003' JM»Jli?EG(L) IHTC 590 ISH 0040 DO 24 1=11,II! INTC 600 ISH 0041 DO 20 J=JL,JH INTC 610 TSN 0042 H(I.J) =STH (HTML) •GNP.LFC(ISIHF(MIKL) .X) INTC 620 ISN 0043 U(I,J)»STU(NINL) •GNPLFC (IS1UF (UTSL) ,7) INTC 630 ISN 0044 V(T,J)=STV(»IMLJ»GNRLFC(ISTVF(NIM),X) INTC S40 ISN 0045 T(T,J)=STT(NTNI) •GHPLFC(ISTTF(NIFl), X) INTC 650 ISN 0006 DO 22 K=1,NK INTC 660 IRN 0047 CK(K,I,J)=STCK(K,HINL)»G»RlFC(TSTCKt tK,NTNL) ,X| INTC 670 ISN 0048 22 CONTINUE INIC 680 TSN 0049 24 CONTINUE ISTC 690 TSN 0050 26 CONTINO? INTC 700 ISN 0051 DO 29 T»1,LHCVE INTC 710 ISN 0052 2A 0(1) »0. INTC 720

C» READ HERE ANT SPFCTAL INITIAL VARIABLES THAT ABE NOT AS INTC 730 C« SPECIFIED AECVE TNTC 740

PPINT 1070 INTC 750 DO 30 I*1.NINTLF IHTC 760

30 PEIHT 1080,1,STH (T) ,STU(I) ,STV(I) .STT (I) , (STCK (K.I) ,K=1,NK) INTC 770 PRINT 1090, (I, ISTHF (I) ,TST0F (I) .ISTVF (I) ,ISTTF (I) , (ISTCKF (K,I) , K=INTC 780

> I.Hfl) .I=1,NI»TLF) IHTC 790 RETURN INTC 90C

C FEAD INITTAL CONDITIONS FRO* RESTAFT Fill INTC 810 32 READ (11) STS,SDTL,KXI.,KT1,SK1 INTC 820

IF (EX.EQ.KXL.AKD.KY.FQ.KYI.AHC.KK.EQ.tiKl) <30 TO 34 INTC 830 "PINT 1100,KX1,KYI.NKt.STK.KX.KY.NK INTC 840 CALL EXIT INTC 350

30 CONTINUE INTC 860 C ••« ALLOWS AS INPUT DTH TO EE CSEC HITH A RESTA1T FILE INTC B70

TF (SRTH.1T.0.) GO TO 36 INTC 880 S9TB»SDTL IHTC 890 GO TO 38 INTC 900

?« SDTH=-SDT5 INTC 910 3R CONTINUE INTC 921

READ (11) REST TNTC 930 PFPIND 11 IHTC «40

C«»» THIS FPEFS THE BUFFERS ASSCCIA7EE VITH 11 AT THIS INTC 950 C««« POINT.( 11 REFERS TO DISK) INTC 960

RETURN IHTC 970 1000 FORF AT(////'01,IX,*INPUT INFOFSAUCN FSOH SUBROUTINE TNTCON:'/1X, INTC 990

>. •// INTC 990 >2X,•STH - INITIAL VALUE EOF NATEF SURFACE ELEVATION. H. MEASURED 'INTC1000 >1.111 THE B01TCHV2X,*STU - INITTAI VALUE FCR HATT9 VELOCITY,, U, IN TNTC1010 >\-DI1>ECTI01l'/2X,»STV - INITIAL VHUS FCR NATEP VELOCITY, V, IN Y-DINTC1020 >IRECTIONV2X,* S1HS - INITIAL VALUE FOR SATE OF CHANGE OF 3ATEP. ELEIN-"C1030 >VATION <JITH RESPECT TO TIHF'/ INTC1040 >2X, 1 STT - INITIAL VALUE FCF HATEf TEHEESHTURE, 7.'/2X, INTC1050 VSTCK(I) - INITTAL VALUE FOR BASS CCNCEN1FRTION OF SPECIES(I)/2XINTC1060 >,'ISTHF - HOITIELIER FONCION FOE STHV IN7C1070 >2X,1ISTUF - NULTIPLIEF PUNCTION FCR STC'/JX.'ISTVF - tiOLTIPLTER FUINTC1080 >HCTICN "OP STV V2X, 'I5THSF - IWflTtllEls FENCTICN FOR STSSV INTC1090 >2T,'ISTTF - HULTIPLIEP FUNCTION TCP STT'/2X, 'ISTCKF (I) - KULTIPLIETNTC1100 >R FUNCTION *C?. STCK (!)»/) ISTC111C

ISN 0074 1010 FOFSATP N1N7LF='I2,1X'IS NOT IN THE FANCE 1 TO 25.') ISTC 1120 ISN 0075 1020 FOR HAT (' INTFC = * 12. 1 X'IS NOT IS THE FAXG? 1 TO NI»TtE='I2) INTC1130 ISN 0076 1030 FOR>1AT(' TEE INITIAL CONDITION 'CNCTION VALOF IHTFC='I2, INTC1140

TSH 0053 ISN 0054 ISN 0055 ISN 0056 ISH 0057 ISN 005B ISH 0059 ISH 0061 ISK 0062 ISH 0063

TSN 0064 ISN 0065 ISH 0067 ISN 0068 ISN 0069 ISN 0070 ISN 0071

ISN 0072 ISN 0073

392

ISH 0017 ISB 0078 ISH 0079 ISH 0080

ISR 0081 ISM 0082

ISH 0083

> IX'HAS AJREAEY BPFH 0SE!>. *) IHTC11S0 10»0 FORHAT |19I5,10X) INTC1160 1050 FOPHAT(l5.5>,6E10.5,10X/(7E10.5,10X)) IHTC1170 106P »ORHAT|7E10.5,10X) IHTC1180 1070 PORHA T ( / / ' INITIAL COHPITIOHSV FOXCTICH HO. '5X« STH'6X* STO* ,SX. IHTC1190

> •STT*6X,SlT,3X'STCKn) •2X,STCK(2| •) IHTC1200 1080 FORHAT (IX,I7,6X,9F9•2) 1HTC1210 1090 FORHAT (//' HOLTIDLIEH FOHCTIOH EOB INITIAL CONDITIONS*/ INTC1220

> • PCT.HO.,.«X,ISTH,,2X,'ISTB',2X.*ISI»',2X,'ISTT',2Xt«ISTCH(1) '.IHT«:1230 > «TSTC<(2) V(«X,I3,5X,«(I3,3X) ,2115,5X))) INTC12H0

1100 FORHAT (• 1PAHAHETER DISAGREEHENT 1* RESTAF1V/ ISTC1250 > • FROH RESTART FILE, KX»'I»,2X*KY=•IK.2X'HK«'I1,2X,ST8='1PE10.9/INTC1260 > • PROH IRFOT FILE, KX=* ia,2I'RY«'M ,2X'HK='II) IHTC1270 EHO tHTC12R0 ISN 0080

•OPTIONS IN EFFECT* NAHE= HAIH,OFT«n2,LIHECNT»60,SIZE*C&C0K.

•OPTIONS IN EFFECT* SOORCE,EECDIC,NOLVST,NOCECK,LCAD,NCPAc,BOEDIT«NOID,NOXBEF

•STATISTICS* SODF.CE STA". EHEHTS = 83 .PRCGRAH SIZE » 005* •STATISTICS* NO DIAGNOSTICS GENERATED ••*•** END OF C0HPILATI0N ••*••• 101X BYTES OF CORE NOT UFEn

393

CS/3SC F'i-'IN =( COIPIfj OPTIONS - NAMF = HA 'H ,OPT=02 .LT'IEC M«f . EI 2 c" >01 OK .

ISN 0002 SDBPOOTTNF FIXCH(NK) FLXC 10 TSN 0303 THPLICIT FEAL-8 (A-H.0-7) FLXC 20 ISM 0C04 COMB ON/CO flPTN/ SN'.A'tlF.CFIJ.CKT J(U| ,0 'Tf J (!) ,CKTHJ {*•»> .CKTJIIU) , rLtC 30

> CKIJS (4) ,YXN, CXF.0Y9,Btr,rXT'>1, EYJP1 .txtl.ox?: .D*1T1.BX»T1, BFIJ .FLXC 10 > nYR.l,DYlJ1,DY331,<*.BTJ,GPF'M (U) .CSTJ.IIH'TJ (4) ,S'3XI.I,SaYIJ,GXIKJ , rLXC 50 •> GXIPJ,1YIJS,GYIJP.C,»IJ,'!K",IJ (U> ,CT:J, C*!TI.I (4) .3TXTJ.5TYIJ.ODYIJ ,FLXC 6C » QXTNJ,QX:PJ,QTIJ!I,QYTJP,G<'X:IJ<.I) . W U V <uf .it* u s (4) ,R*YIJP(4) ,FL*C 70 > HTKIJ (9) ,HTFT J.1(9) , HTNtPJ (9) . NT * t"M (1 ) , H !K* JP (S) , HT3, PT jr ,HI PJ , FLXC PC > HISJ.HIJF ,0:J,0TJ.1,0rFJ.')t»J.'J: JFf»T; .VIJP.VISJ.VTJIJ.VIJP.I'TJ , FLXC 90 > TTJH,TIPJ,TI(1JrTT..lrI!,0KTFt(<H ,FCI J.FCIJ P ,V>IP-1. POIHJ , ROIJF , FLXC 100 > SNKTPD(9) ,SHTCKD(3) , SHTTF r , SXJt ti 3 ,SX J TP 3 ,STYTJ1,ST TIJF, SX Y: Jt> , FJ.XC 110 > STYIPJ,SXYISJ,SX*TJPT30IWD,!'CIFJC,Pf.TJI!C,H0r.JrC, S3TPt?,TD:j . FLXC 120 > HCTU.HCTFJ.HCIJN, HC7 JP ,GF,EOCKC (U) . £F"T F (9).OESSK (U) ,B0DKIJ(9) , FLXC 130 > GKDTIJ(U).CXI,D7J . 9EV (25) . HBC (25) ,-tlpt (I5) , VBO (25) ,TBC (25) , FLXC 110 > CKBD(4,25) .TBI.1.HCBIJ .DCrBTJ (») ,H*WglJ .SSIJ.Bai J.VEIJ ,VBI J. FLXC 150 > P0BIJ.HI3IJ,CKBIJ{»> .TT7J,HCTIJ ,rcrTU(J) ,9Tl''TJ f «) ,07M,VTIJ, FLXC 160 > »7IJ,FCTI3.HTTJ.J.CKTIJ(<») .031 Jib) ( 25) .r.KBD (4, 25) ,SBDN{25) . FLXC 170 > S9DSH(25) ,NTND,9INDX.HINRY .1 \„IM V?,, IT1; ,I.1K 1 ,T JP1 .1HTBT, *0X J , FLXC 180 > KCIFLL J.X0IF1J ,H9IJI11 .K0IJF1 •,NET1."BYP,NSEGIN,NEVDF . FLXC 190 > TX5V(25) . JYPV (25) .NHSDTF (2V .10'. '.TP<2'F .NV30T?(25) .NTE2TP (25) , FLXC 200 > NXGRL,NYGFL.NEEG,NINTLF.NTOFT.STOTF.NTBIFC,1?HAX,NGENF FLXC 210

ISN 0005 DATA 06TH/2492IIAAAAAAAAAAAP/ FLXC 220 TSN ooof. DINFNSION EFXC (0) ,DKYC (4) ,DKXINJ «U) ,DKXI 5 J (1) . BUYTJI (1) .DKYTJP (4) FLXC 230 TSN 0007 DIHENSTUN SFXH(S) FLXC 240 TSN OOOFL EOHTVAIEHCE (HF XP ,HBX"I (2) ) , (.1BYH. KBXKFS)) . (H3TP .NBXR(TT) ) FLXC 250 TSU 0009 ABS (X)COABS(I) FLXC 260 TSRR 0010 SOBT (X'l =DSCBT( X) FLXC 270 IS* 0011 RLAD(50,1000) XKFC.YXPC.XTVSC.YTVSC FLXC 280 ISM 0012 PRINT 10N,XKPC,YKPC,*L»SC,'ITVSC FLXC 290 ISN oni3 PRINT 102', FLXC 300 ISN 0019 READ (50,1000) ( DKXC (K) ,DFYC (K) ,K«1,NN) FLXC 310 7SN cois DO 10 K=1,NK FLXC 320 TSN 0016 1D PRINT 1039,F,DRXC(K) ,DKYC(K) FLXC 3 30 TSN 0017 RETURN FLXC 340

c « i * * * * * * * * * * * * * * * * * * FLXC 350 ISN 0018 ENTRY FLXCCNTCK.U.V.T.NFTG) FLXC 360

c « v * * * * * * * * * * * * * * * * * * * FLXC 370 ISN 0011 DIHENSION CK (1) .0(1) . V (1) ,T(1) , NFIG(1) FLXC 300

cc TH* 7RANSP0F? COEFFICIENTS SPOUID EF OICBLITED BAS'T ON FLXC 390 cc VELOCITIES AND TELOCITY GRADTEJfTS. FOB THP TINE BEING THEY SILL B? FLXC 900 cc SET EQOAL TO THF TNFBT CCEFFICITH7S THES5FLVE3. FLXC 910 c CALCULATION OF ALL THE TNTFPFAL FTOXFS FLXC tl 20

TSN 0020 TFH=O.OOH»3DC»HIM*ROTHJ»SCRT (UIP0*0TH.HV7!!J-»VIMJ) FLXC 930 TSN 0P21 XKPI!1J=XKPC«TFN»CPTJ FLXC 94C TSN 0022 XTVIHJ"XTVSC*TFM FLXC 450 ISN 0023 YTVIHJAYTVSC*TEN FLXC 960 TSK 0079 DO 12 K=1,NK FLXC 970 ISN 0026 12 D?XTNJ(K)=DKXC(K) FLXC 480 ISN 0026 I" (NBXN) 11.1U.30 FLXC 990 ISN 0021 14 QXIHJ » 2.»XKPIHJ»(T(IH1J)-TIJ)/tRK FLXC 500 TSN 0021 GXIHJ=POIHJC«OIHJ FLXC 510 ISN 0020 DO 16 N=1, NK FLXC 520 ISN 0030 16 GKXI1J(M = I.*PCINJ«9KXINJ(F) «(CK (K0IH1 J*F)-CFI J(K) )/DXH FLXC 530 ISN 0031 SXXTHJ=9.»«VINJ»(DIJ-0 |IH1J))/CXF FLXC 540 ISN 0032 I" (NBYN) 18,18,20 FLXC 550 ISN 0033 18 D?HJH1=0XLI»0(IJH1) •DXFI«0(IJH 1-1) FLXC 560

394

ISN 0034 ISN 0035 ISN 0036

ISN 0037 ISN 0038 ISN 0039 ISH 0040 ISN oom ISH 0042 ISH 0043 ISS 0044 TSV 0045 ISN 0046 IS'FL 0047 ISB 0048 ISN 0049 ISN 0050 TSN 0051 ISN 0052 ISH 0051 ISN 0054 ISM 0055 ISN 0056 ISN 0057 IS» 0058 ISK 0059 IS.N 0060 IPS 0061 ISN 0062 ISH 0063 ISH 0064 ISB 0065 ISN 0066 ISN 0067 ISN 0068 ISN 0069 ISN 0070 TSH 0071 ISN 0072 ISN 0073 ISN 0074 ISN 0075 ISN 0076 ISH 0077

ISN 0078 ISN 0079 ISN 0080 ISN 0081 ISH 0082 ISN 00R3 ISN 0084 ISN 0085 ISN 0086 ISN 0 087 ISH OOBP

UIB1JH=DYLJ«B(IH1J) + DYRa«0 (IJN1-1) FLTC 570 DIHJN=OIJ-rXHI» (0IJR-0IB1JR1 -DYRJ» (0IH0-0IBJH1) FLXC 500 GO TO 22 FLXC 590

CC TT WILL BE ASSOtlFC HEBE THAT OIHB (NBYH) =DIE (NBYH| =VB (NBril) FLXC 600 CC THE S A M FOB CTHER SOCH BAIE POINT BODNtABT VELOCITIES. FLXC 610

20 OIMJ11=OIJH FLXC 620 22 IF (NBYP) 24,24,26 "LXC 630 24 C1IBJP1=DXL1»0(IJF1) •DXHI'O (IJP1-1) FLXC 640

UINiaP=DYLJ1»0(IJP1-1)»0YRJ1»a(IBta) FLXC 650 OIHJP=OIJ-EJ»I»(DIJP-DIM1JP)tDYBJ1»(OIBJE1-1IMJ) FLXC 660 GO TO 28 FLXC 670

26 OIBJP—OIJP FLXC 680 28 SXYI9J=YIVIH0* (OIBJP-UIMJHJ/DYJ *2 . «XTVIB J« ( VI J-V [1(11J) ) /DXB FLXC 690

GO TO 62 FLIC 700 30 QXIB3=QB0(NBXH)*4.»XKPIHJ»(TIBJ-TIO)/EXM FLXC 710

GXIBJ-GED (NBXH) •HOIBJD*HTMJ FLXC 720 DO 32 K=1,NK FLXC 730

32 GKXIBJ (K)=GKEB (K,NBXBJ •4.»E0IBJ«EFXIBJ MCKIBJ (K) -CKIJ(K))/DXR FLXC 740 SKXIBO=SBDB(NBX«) •8.»XTVISJ« IDIJ-DIMJ/OXH -'LXC 750 IF (NBYB) 34,34,44 FLXC 760

34 CALL GTFIGS(BBXB,BFLG(IJH1)) FLXC 770 NDJB=NOBDTP (BBXH(I) ) FLXC 780 GO TO (40,38,216,36) ,NOJN FLXC 790 GO TC 216 FLXC 800

36 OIHJN1=0(IJB1)»DXLI1»(0(IJH1)-n{IJH1 + 1)) FLXC 810 GO TO 42 FLTC 820

38 DmiH1=B(IJH1) FLXC 830 GO TO 42 FLXC 840

40 0IHJH1=0BD (BBXHP)) FLXC 850 42 0IHjn=DYL3»DIHJ*CYpJ«0IHJH1 FLXC 860

GO TO 46 FLXC 870 44 OIHJE=OIM FLXC 880 46 IP (BBYP) 48,48,58 FLXC 890 48 CALL GTFIGS (BBXB.NFLG (IOP1)) FLXC 900

NOJP=NOBDTP(BBXB(1)) FLXC 910 GO TO 554,52,216,50),HBJP FLXC 920 GO TO 216 FLXC 930

50 OINJP1=D(IJP1) •PXL11*(0 (IJF1) -0(I0P1 + 1)) FLXC 940 GO TO 56 FLXC 950

52 0IH0P1=B(T3P1) F5-XC 960 GO TO 56 FLXC 970

54 0INJP1»DBD (HBXH (1) ) TLXC 9R0 56 0IHJP=0YlJ1»alHJPUDTHJ1»0IHJ FLXC 990

GO TO 60 FLXC1000 58 orsjp=oiHj FLXC1010 60 SXYIMJ=SBDSH(NBXB) •YTVIBJ»(0IBJP-0IHJM)/ESJ*4."XTVIHJ*(VIJ-VMJ) /FLXC1020

> DXH FLXC1030 62 TEN=0.00443E0*HIFJ *RCIPJ •5QRT(CIPJ »0IFO *VIFJ «VIFJ ) ELXC1040

XKPIPJ =XKFC*TEH*CPIJ FLXC1050 XTVTPJ =XTVSC+TEH FLXC1060 YTVIPJ =YTVSC+TEB FLXC1070 DO 64 K=1,SK FLXC1080

64 PKTIPJ(K)=EKXC (K) FLXC1090 IF (HBXP) 66,66,82 FLXC1100

66 QXIPJ=2.«XKIIPJ*(TIJ-T(IP1J ))/DXF FLXC1110 GXIPJ=ROIPJE«DIPJ FLXC 11 <i0 DO 68 B=1,S* FLXC 1130

68 GKXTPJ(K) = 2.«ROIPJ»DKXIPJ(K) »(CKIJ(K) -CK (K0IF1J+K) ) /DXP FLXC 11 40

395

TSH 0089 STTIP.1 = 4.«*TMP<J'(HIP10 ) -IJIJ)/EXP FLXC1150 ISH 00°0 I" (NPYFL) 70,70,, 72 FLXC1160 ISH 0091 70 DIPJH1=EXLI1«I) 5IJH1+1) • DXFI1*0 (TJB1) FLXC1170 ISN 00«2 0TP1JN=DTLJ»D(IP1J) • DYBJ«U (IJFLLH) FLXC11B0 ISN 0C91 UIPJH=DI0*TJ5T1» (BTPUN-BTJ?) -TYE3» (0IE3-DIPJ«1) YLXC1190 ISN 0C94 GO TO 14 FL XC 12 0 0 ISN 0095 72 I7I PJN=O?JN FLXC12T0 TSN 0096 74 IF (NPYP) 76,76,78 FLXC1220 ISN 009T 76 nipjpi=nxLii«U (IOPI+1) • DXFII*O (ijpi) FLXC1230 ISN 009H 0TP1JP=DYL01*D(I0P1*1) + DYBJ1»D (IE1J) FLXC1240 ISN 0099 UIPJP=OIA»EXPN*{OIFIAP-OUF) •EYFJI*CDIRJII-DIPJ( FLXC1250 ISN 0100 GO TO BO FLXC1260 TSN 0101 7B 1IPJP=DT.1P FLXC1270 ISH 0102 80 SXYTPJ=YTVIFJ»(OIPJP-DIPJHJ/DYJ «2.»XTYIPJ«(V(IP1J) -VIJ) /DXP FL XC 12 8 0 ISN 0103 GO TO 114 FLXC1290 ISN 0104 02 QXTPJ=QDD(NEXP) •4.*XKFI?J» (TIJ-T1E J)/TXP FLXC1300 ISN 0105 GTIPJ=GSD(NEXF)•E0IPJD«1IFJ FLXC1310 ISN 0106 no 84 K=1,NK FLXC1320 ISN 0 10*7 84 GKXIPJ (K) = GKED(K,NBXP) •4„»F0IPJ*tKXIPJ (K) * (CKIJ(K) -CKIPJ(K) )/DXP FLXC1330 TSN 0108 STXIPJ=SBDN(NBXP)«8.«XTVIFJ*(0IPJ-AIJ)/DXF FLXC1340 ISN 0109 I" (NBYM) 66,86,56 FLXC1350 ISN 0110 86 CALL GT^LGS (FBXH ,N^LG (XJP.1)) FLXC136 0 ISN 0111 NUJN=N08DT~ (NEXP) FLXC1370 ISN 0112 GO -0 (92,90,216,18),NOJB FLXC1380 ISN 0113 GO TO 216 FLXC1390 ISN 0114 8R TJIP.1H1=0(TJH1)*DXHT*(0(IJH1)-0 (I0B1-1) ) FLXC1400 ISN 0115 GO TO 94 FLXC1410 ISN 0116 90 nipj"ii=a(uri) FLXC1420 ISN 0117 GO TO 94 FLXC1430 ISN 01 IB 92 I1TPJB1=0BD(BEXP) FLXC1440 ISN 9119 94 DTPJN=SYIJ»DIPJ*DYBJ»0IP3H1 TLXC1450 ISN 0120 GO TO 98 FLXC 14 6 0 TSH 0121 96 OIPJH=DIFJ FLXC1470 TSN 0122 98 I" (NBYP) 1C0,100,11C FLXC1480 ISN 0121 100 CALL GTPLGS(BBXB,NFLG(IJP1)) FLXC1490 ISN 0121 NOJP=NOBDTE(BEXP) FLXC1500 ISN 0125 GO TO (106,104,216,102) .NOJP FLXC1510 ISN 0126 GO TO 216 FLXC1520 ISN 0127 102 NIPJP1=0 (IJF1) +DXBI* (0 (IJP1) -0 (I0E1-1) ) FLXC15 3 0 I^N 0128 GO TO 108 FLYC1540 ISN 012Q 104 DIPJP1=D(IJP1) FLXC1550 ISN 0130 GO TO 108 FLXC15 6 0 ISN 01 :1 106 UIPJP1=0BD (BBXP) FLXC1570 ISN 0132 10P DTPJP=DYLJ1»0IPJE1«-1)YBJ1*0IPJ FLXC1580 ISN 0133 GO TO 112 FLTC1590 TSN 0138 110 UTPJF=DrPJ FLXC1600 ISN 0135 112 SXYIPJ=SBDSH(NBXP)«-YTVIPJ* (0IPJP-DIPJH)/TYJ»4. »XTVTPJ» (VIPJ-VIJ) /FLXC1610

> DTP FLXC162 0 ISH 0136 114 T':N=0.00443DO*HIJH»HOIJH»SQBT(UIOB«UIJE*VIJB«VIJH) FLXC1630 TSN 0117 YKPIJH=YKFC*TEB»CPIJ FLXC16 4 0 ISN 0 13FT XTTIJH=XTVSC+TEB FLXC1650 ISN 0139 YTVIJH=YIVSC+TEB FLXC1660 ISN 0110 no 116 K=1,HK FLXC1670 TSN 0141 116 TLKYIJH (K) = EKYC (K) FLXC 1680 ISN 0142 IF (NBTB) 118,118,134 FLXC1690 TSN 0143 11R QYIJH=2. «YKFIJH« (T(IJH1 ) -TIJ) /DYH FLTCHOO ISN 0144 GYIJB-FOIJEO*VIJH FLXC1710 ISH 0145 DO 120 K«1,NK FLXC1720

396

ISH 0116 120 GKYTJ!" (») =2. »BOT.JM*DKYI JH (K) * (CK (KOIJH 14 K) -CKIJ (K) ) /DYN FLXC1730 ISH 0117 SYYIJMs8.*YTVIJH* (VI3-V (I JH1 ) )/t?tl FLXC17U0 ISB 0118 IP (HBXB) 122,122,128 FLXC17 50 ISH 0109 122 VIHJB1=PXLI»V{IJH1) •DXBI*V (IJH1-1) FLXC1760 ISH 0150 VIH1JB=DYLJ*V(IH1J) •DYEJ*V(IJM1-1) FLXC1770 ISH 0151 VJHJfl=VIJ-BXBI* (VIJH-VIH 1JM) -EYBJ* (VIHJ-VIBJB1) FLXC1780 ISH 0152 GO TO 126 FLXC1790 ISH 0153 128 VISJB=VTMJ FLXC1800 ISH 0158 126 IF INCSPJ 128,128,130 PL XC 1810 ISB 0155 128 • IPJM1=nXLI1»V(IJN1 + 1) • DXBI1*V(IJH1) FLXC1B20 ISB 0156 VIP1JH=DYLO*V(IP1;j) • DIBO»V(IJB1*1) FLXC1830 ISH 0157 VIPJN=VIJ*rXFI1* (VIPUK-VIJN) -DYFJ*<VIEJ-VIPJB 1) FLXC1880 ISH 0158 GO TO 132 ELXC1850 ISB 0159 130 VIPJH=VIPJ FLXC1860 ISH 0160 132 SXYIJN=2.*YT»IJB* (UIJ-0 (IJB1) > /DJB + XTVIJI1* (VIPOM-VIMJB) /DXI FLXC1870 ISH 0161 GO TO 162 FLXC1880 ISH 0162 138 QYTJH=QED(HBYM)*0.*YKPIJB« (TI J B-TIJ)/DYN FLXC1890 ISH 0163 GYIJH=GED(HBYB)+801JMD*VIJB FLXC1900 ISH 0168 00 136 K=1.HK FLXC19 10 ISH 0165 136 GKYIJH (K) =GKET) (K.BBYB) *8 . «BOI JBMKYIJB (K) » (CKIJM(K)--CKIJ (K))/DYM FLXC1920 ISB 0166 STYIJH=SBDN (BBYN) *8.«YTVIJB* (VIJ-7IJH) /DTE FLXC1930 ISH 0167 IF (BBXN.GT.O) GC TO 106 FLXC1980 ISH 0169 CALL GTFLGS(BBXH,NFLG(IM 1 J)) FLXC1950 ISH 0170 NYIM=HVBDTP(BBYMJ FLXC1960 ISH 0171 GO TO (182,180,216,138),NVIH FLXC1970 ISH 0172 GO TO 216 FLXC1990 ISH 0173 138 VIHUH=V(IH1J) •DYLJ1* (V (IB 1J) -V(IJPI-I)) FLXC1990 ISH 0178 GO TO 188 FLXC2000 ISH 0175 180 VIH1JR»7IBia FLXC2010 ISH 0176 GO TO 188 FLXC20 20 ISH 0177 182 VIM1JH=VBD(BEYM) FLXC20 30 ISH 0178 188 VIBJB«=DXII*VIJB • DXBI*VIH1JH FLXC2080 ISN 0179 GO TO 18e FLXC2050 ISN 0180 186 VIHJI1=VIJN FLXC2060 ISN 0181 188 IF (HBXP.GT.O) GO TO 158 FLXC2070 ISN 0183 CALL GTFLGS (MBXB ,NFLG (IP1 J) J FLXC2080 ISN 0188 NVTP=NVEDTF(MBYM) FLXC20 90 ISN 0185 G O T O (150.152.216,150) ,HVIP FLXC2100 ISN 0186 GO TO 216 fLXC2110 ISN 0187 150 VTP1JH=V(IP1J) • DYLJ1* (V(IP1J) -V(IJF1*1)) FLXC2120 ISN 0189 GO TO 156 FLXC2130 ISN 0189 152 VIP1JPI»VIP1J FLXC2180 ISN 0190 GO TO 156 FLXC2ISO ISN 0191 158 VTP1JM=VED (BEYM) FLXC2160 ISN 0192 156 VTPJM=DXLI 1*VIP 1JN • PXRII'VIJM FLXC2170 ISN 0193 GO TO 160 FLXC21B 0 ISN 0198 158 VTP.1M=VIJM FLTC2190 ISN 01°5 160 SXYIJB=S8DSH(HBYB) +8.*YTVIJK« (0TJ-0IJI1)/Cli!»XTVia>1« (VIPJM-VIMJM) ELXC2200

> DXI FLXC2210 ISN 0196 162 T^M=0. C08B3BO*HIJP*BOTJP*SQRT(OIJF«niJF+YTJP*VTJP) FLXC2220 ISN 0197 YKPIJP«YKPC+TEB*CPIJ FLXC 2230 ISN 01OB XTVTJP«XTVFC«TEB FLXC228 0 ISN 0199 YTVIJP=TTVSC«TEN FLXC22 50 ISH 0200 DO 168 K=1,NB FLXC 2260 ISN 0201 168 DKYIJP(M=EKYC (K) FLXC 227 0 ISN 0202 I* (HBYP) 166, 166,182 FLXC22S0 ISN 0203 166 QYIJP=2.*YKFIJP* (TI J-T (TJP1 ))/DTP FLXC2290 ISN 0208 GYIJP=POIJFD*VIJF FLXC2300

397

TSF 0705 no 165 Pss1 ,NK FLXC'310 TSN 0206 16P OKYTJP («!| =2. • F0T0P*NKYI.LP (») • (CKM (F.) -CK (><0 :,1P1»<<) )/HYP FLXC2 320 RSW 0 20*7 SYYIJI> = 4.»1T»TJp» (V (T.1F1 ) -VT.1) /TYF "LXC2330 ISN 02 OP I" (NBXtn 17C, 11C,172 FLXC23K0 ISN 020° 170 VTWJP 1=0X1.3*11 (I JT 1> +07ST.«V(TJRI-1) F1.XC2350 ISN 0210 VIHIJP=PYIOI«V (TJP1-1) •nyojuv (iru) FLXC236G ISN 1211 VLF JP=VIJ-RXBI* (VIJP-VI* 1JP) •1JY3J1* (VT-.LF 1-VI1J) FLXC2370 ISN 0212 GO TO 174 FLXR2380 TSN 0211 172 VI1JP=VTMJ FLXC2 390 ISN 0214 1711 TF (HPXP) 176, 176,178 FLXC240C ISN 0215 176 VTPJPI=")XIII»V(!:O'I + I) »• n*"II«v(ijri) FLXC3310 TSN 0216 VTpUp=rYt..L1«V (TJP1»1) • DYC.11»V (TP1.1) FLXC2420 ISN 0217 VIPJP=VT.1*rXFT1* (VTF1.1P-VIJP) *DYFJ1» (VTE.U1 - V F T) FLXC2430 ISN 021" NO TO 180 FLXC2B40 ISN 021") 176 VIP.JF=VIP.1 FLXC24 50 ISN 022" 180 SXYIJP=?.*YTVIJP« (U (IiTF 1) -UTI!) /RYFTXTVTJE* (VI?JD-VT1.JP)/DXI FLXC2460 ISN 0221 GO TO 210 FLXC 2470 ISN 0222 182 QYT1P=QED (CBYP) , "YKPIJP* (TI.T-* TJF)/PYP FLXC24B0 ISN 0223 GYI.LP=G8N (NBYP) TTOT JPT1*YTJF FLXC249P ISN 022" NN 184 K=1,TLK FLXC 2500 ISN 0225 184 GKYIJP (K)=CKEN (K.NBYP) «4 . *FOI JP»TK YT.1P |K) • (CKI.T (K) -CKI3P (K) ) /DYP FLXC2510 TSN 0226 SYYIJr=SBD>'{HNYP)«-8. *YTVIJF* (VTJf-VTJ) /PYC FL XCJ520 ISN 0227 I" (NBXS.C.C) GO TO 194 FLXC2530 TSN 0221 C»LL GTFLGF(NTLX1,«IFI.G(I«1.1)) FIXC2540 ISN 023" NVTH=N\BDTFIHBYP) FLXC2550 ISN 0231 M TO (190,IFF,216,186), MVIM FLTC7560 ISN 0232 GO TO 216 FLXC2570 ISN 0233 186 VT1iaP=V(IMJ) OYRJ* (V (TH1J) -V (TJ11-1) ) FLXC2580 ISN 023TT GO TO 192 FLXC2590 ISH 0235 18S VIM1JP=VIH1J FLXC2600 ISN 0236 GO TO 19 2 FLXC26 10 ISN 0237 190 »TR1JP=V3B (HEYP) FLXC262C TSN 0238 192 TFTHJP=DXLT*VIJE • N*5I*VT11JP FLXC 2630 ISN 02 3") GO TO 196 FLXC2640 ISN 0240 194 VIf1JP=VTJP FLXC2650 ISN 02U1 196 I" (NBXP.Gi.O) GC TO 206 PLXC2660 TSN 0243 CALL GT'LGS (NFXH ,NPLG (IP 1.1) ) FLXC 2670 ISN 0240 HVIP=N\FOTF (HBYP) FLXC2S80 ISN 0245 G O T O (202,?CC,216,199) ,NVTP FLXC2690 TSN 0246 GO TO 216 FLXC2700 ISN 0247 198 VIP1 JP=V(I F1J) »D*RJ* (V (I®1 J) -V (IJ11» 1) ) FLXC2710 ISN 024R CO '0 204 FLXC272C ISN 024*3 200 VIP1JP=VTF1J FLXC 27 30 ISN 0 250 GO TO 204 FLXC2740 TSN 0251 202 7IP1.1P=Yei) (HFYP) FLXC2750 ISN 0252 204 VTP.1P=DXLI1*»IF1JP • PX'T1*VTJr FLXC2760 TSN 0253 GO TO 208 FL XC 27 7 C ISN 0254 206 VIPJP=VTJP FLXC 27 BC ISN 0255 208 SXYTJP=SBOSH (NBYP)*4.*Y-VTJP» (nlCr-yiJl/CYCtYTVTJO* (VIPJP-VIHOP) /FLXC 2790

> n x : FLXC 28 00 ISN 0256 210 COMTINOF FLXC2810 ISN 0 257 HXtlBI.1«(Hlr3-HI1«J)/11XI FLXC 2820 ISN 025(3

C HYrfil.ln (HI JF-HIJP) /BY."* FLXC 28 30

FLXC 2" 40 C CALCOtVTON Cf BCTVOH 'T-OX'S rLXC 28 50

TSH 025O CALL POTCON FLTC2460 TSN 0260 Gm.1*PCBIJ*50"T(»BIJ*PBTJ*t)5*'J*UfIJ»VET.1*VE M ) FLXC2R70 ISN 0761 00 712 K=1,NK M )

F1.IC2R9 0

398

TSH 0262 ISH 0 263 I3H 0261* ISH 0265 ISH 0266 ISH 0267 ISN 0268

ISN 0269 ISN 0270 ISN 0271 ISH 0272 ISN 0273 ISN 0270 ISH 0275 ISN 0276 ISH 0277 ISN 0278 ISN 027° ISN 0280

ISN 0281 ISN 0282 ISN 0283

GKBIJ (K) »-tCKBia (K) • (CKIJ (*) -CKBIJ (K) ) 212 Q*BIJ(K)» GKBI J (K) * HTKBIJ (K)

QBIJ—HCBIO* (TI J-TBIJ) BCIJ»1.«9D0*HIJ»»O6TH/BNIJ

C *•• CALCULATE STRESSES EBOH BOTTOB FFICTICN. COH» (RB«HOIJ»SQST(OIJ*OIJ»V1J*VIJ))/<BCIJ«BCIJ) SBXIJ»-CCH»OIJ SBYIJ«-CON*VIJ

C C CALCULATION CT TOP FLUXES

CALL TOPCON C ••• CALCULATE SIBD STRESSES

STXIJ"3.20-«»BIND*»IHDX STYIJ»3.2D-6*NIKE*WIHD* GTIJ«R0TIJ"SQRT(BTTJ*«TIJ»UTrJ*0TIJ'tVTI.T»7TTJ) DO 219 K>»1,HK GKTIJ(K)' -tCKTIJ IB) • (C*IJ IB) -CRTIJ (F) )

210 QKTIJ(K) • GKTIJ (M*HTFTIJ(K) C ••• HEAT EXCHANGE HITH THE ATHCSPHER!

OTIJ«-BCTIJ* (TTJ-EQT9P) BETttBN

216 STOP 7777 1000 FORMAT (7E10.3,10X)

FLXC2890 FLXC 29 00 FLXC 2910 FLXC2920 PIXC2930 FLXC290C FLXC2950 FLXC2960 FLXC2970 FLXC2980 FLXC2990 FLXC 3000 FLXC3010 FLXC 30 20 FLXC 30 30 FLXC3000 FLXC3050 FLXC3960 FLXC3070 FLXC3390 FLXC1090 FLXC1100 FLXC 31 ?0

1010 FOR«AT(////'0 ,,1X,,TNP0T IHFORBA1TCN FFOB SUBROUTINE FlXCON:'/1X, FLXC3120 >• ... ---'//. FLXC 3130 >2X,"COEFFICIENT FOR TOTAL EFFECTIVE TH'P'Al CONDUCTIVITY IN X-DIBEFLXC3100 >CTTON (XX»C) « ',1PE13.6/ FI.XC3150 >2X«1 COEFFICIENT FOP TOTAL EFFECTIVE THEBFAL CONDUCTIVITY IN Y-DIREFLXC3160 >CTIOB (YBPC) • ",E13.6/ PLXC3170 >2X.<C0EFFIC1EHT FOP TUBBDIENT VTSCCSI'I IB *-DTPFCTI0!l (XTVSC) « •,«LXC3180 >E13.6/ FLXC3190 >2X.'COEFFICIENT FOR TURBULENT VISCOSIT1 IN Y-DIPECTION (YTVSC) = •M.XC320C >,E13.6// "LXC32'0 >2X,'0KXC - COEFFICIEHT FOR TOTAL BTNAPY »FP»CTTVE DIF»<ISION COEPFTPIXC3220 >CI»NT CP SPECIE B TN X-tlRECTJCNV FLXC3130 >2*,' DKYC - CCEFFICIEBT FOP TOTAL 3THAPY EFFECTIVE nlFFUSION COF*FIFLXC3200 >CIEHT CF SPECIE K IN Y-BIPFCTTCN•)

1020 ?O9NAT('0 B«.6X,'DKXC |K) • ,8X, • C M C (K| V ) 1030 FOB>IAT(I5,2(2X,1PE13.6))

END

FI.XC32 50 "LXC3260 FLtC3270 *t.XC3290

•OPTIONS IN FFFFCT* BARF* RAIN.OFT«02,LIHFCHT«60 ,5IZS«G1SCK. •OPTIONS TN EFFECT* SOOBCE, EBCDIC, BnLTST.NOtFCX , It At .BCFAF ,NO».DTT ,MOT!),KOXI>'c

• STATISTICS* SOOBCE STATMENTS » 282 ,fBCG1IA!l SI7E • 7626 •STATISTICS* NO DIAGNOSTICS GENERATED

END OF COMPILATION •••••• 511 BYTIS OF CORF NOT HS'n

399

os/3eo POETS** n COMPILER OPTIONS - BAMI« MAIH,OPT»02,LIHECET»60,SIZB»000DK,

SODRCE,EBCDIC,ROUST, HODECK,LCAD,HOSAP,NOEDIT,NOID,NOXREF ISR 0002 SOBRODTINE SITE SETZ 10 ISH 0003 INPLXCIT BEA1*6 (A-H.O-Z) SETZ 20

C * • • THE VAIOE CP NZSP BOST BE SET HERE. THIS VALUE SROOLI SETZ 30 C »»» CORRESPOND TO THE BOBBER OF ELEMENTS TBAI ARE IH THE ARBAY SETZ 40 c * * » Z AS DEFINED HEBE. MOREOVER, EACH CASE EON REQUIRES EXACTLY SETZ 50 c (13«3NR) (KX) <KY) »»<KX*KY) SETZ 60 c ELEMENTS IN THE ARRAY Z. SETZ 70

ISN 0004 COMHON/Z/NZSP,ND0B,Z(8600) SETZ 80 ISH 0005 NZSP'8600 SETZ 90

c H.B., IN BAIB Z |6000) IS PASSED TO GEOH AS THE ADDRESS OF Y(1). SETZ 100 c * • * CONSEQUENTLY GIOH STORES INTO Z(6000) ,.. .,Z(6000+KY-1) . SETZ 110 c • * • THOS NEED NZSP.GE.6000+KY-1. PROGRAM TEREIHATES IH BAIN IF THIS SETZ 120 c * • • CONDITION IS NOT MET. SETZ 130

ISB 0006 SFTORH SETZ 140 ISN 0007 END SETZ 150

•OPTIONS IN EFFECT* NAME* MAIH,OPT=02,LINECNT«60,SIZE=00COK, •OPTIONS IH EFFECT* SOORCE,EBCDIC,NOLIST,HOtEr.K,lC»t,HORAI,NOEDIT,NOID,HOXREF •STATISTICS* SOOPCE SJATEMENTS = 6 .PROGRAM SIZE « 196 •STATISTICS* NO DIAGNOSTICS GENERATED •>«*** END 0 p CORPILATIOH •*•**• 129K BYTES OP CORE HOT USED

400

05/360 FORTS** B COMPILER OPTIONS - RAMI* MJIB,OPT»02,LISECKT»60.SIZI«0000K,

SOURCE.EBCDIC,NOIIST.IOCECK,LOAD,KORAP.NOFDIT.BOln.NOXREF ISN 0007 SUBROUTINE CHKDTB(DTH.*REG,KX,fl.U,lCTBCR) CHKD 10 ISN 0001 IMPLICIT pe*I*8 (A-H.O-Z) CHKD 20 ISN 0004 COHSOK/REGION/DEFTH (25) ,SB(25) .IIRE5(2£) ,IBRSG(25) , JLBEG (25) , CHKD 30

> JHPPGI25) .IN*r(25) ,IGENF{25),ITCPFC25),ISCTF(25) CHKD 40 ISN 0005 HTEGTR»2 IlBPG.IBSEG.JLBtG.aHiEG CBKD 50 ISN 0006 INTEGFM2 INTF.IGENF.ITOPF,JSCTF CHKD 60 ISN 0007 DIMENSION fl(KX,1),U(KX,1) CHKD 70

C • • • LOT ICR SELECTS TBE DISIBID CBITEHCN TO EETEBUSE THE SUITABILITY CBKD 80 c OF THE PROPCSED ETM. CHKD 90 c GB«12.2*36CC.«3600. CHKD 100

ISN 0009 GR*«.1731206 CHKO 110 TSN 0004 HTIM-1.D20 CHKD 120 ISN 0010 U?IM»l.D2t) CBKD 130 ISN 0 0 1 1 PRINT 1000 CBKD 140 ISN 0012 DO 18 M1,*BEG CBKD 150 ISB 0013 IL-II.PEG(R) CHKD 160 ISN 0010 IB'IRBEG(B) CHKD 170 ISN 0015 3L»JLRIG(B) CHKD 180 ISN 0016 JB*JHPEG(H) CHKD 190 ISB 0017 HTIHL-O.DO CHKO 200 TSN 0019 UTIHL-O.DO CHKD 210 ISN 0019 DO 12 I»It.IB CHKD 220 ISN 0020 DO 10 J'JL.JR CHKD 230

C A BES. R Bill CAUSE ABNORMAL EBD IR R**(1/6) IN TLXCON CHKD 240 TSN 0021 RTTML>DRAX1(BTlni,H (I,J)) CHKD 250 ISN 0022 10 0TIRL-DRAX1(tlTiRl,DABS(0(I,J))) CHKD 260 ISN 0023 12 CONTINUE CBKD 270 ISN Ov.24 HTIN«DHIB1 (BTIH,SH(H)/DS0B1((GR*GR)»8TIHI)) CHKD 280 ISR 0025 IF (OTIBl.BZ.O.) GO TO 14 CHKD 290 IS* 0027 Q-1.D20 CBKD 300 ISN 0028 GO TO 16 CHKD 310 ISN 00X9 111 Q'SM(R)/0TIfll CHKD 320 ISN 0030 16 UTIM«DMIN1 (OTin.tt CHKD 330 ISN 0031 18 CONTINUE CHKD 340 ISN 0032 PRINT 1010.BVI1.UTIM CHKD 350 TSN 0033 DTR-DMIB1 (tTH, BTIR.UTIM) CHKD 360 ISN 0034 BETUfiN CHKD 370 ISN 0035 1000 FORMAT f///2X,fTX HE IBCBBBMIT CBIIIFIA'/I*. CHKD 380

— ') CHKD 390 ISN 00 36 1 0 1 0 FORMAT(' CTH. tE.DTM (H)»• , 1PES. 2,5X, • DTB.IE.8TM(U) « ' ,E8.2) CHKD 400 ISN 0037 END CHKD 410

•OPTIONS IN EFFECT* NAHE» MAI*,OPT«02,II»FCBT-60,SIZE*COCCK, •OPTIONS IN EFFECT* SODRCE,EBCDIC,BOIIST,ROtICK.IC*C.BOtAI.BOEDIT.SOtD.NOXBEF •STATISTICS* SOURCE 3T»TEHE*TS « 36 .PBOGRArt SIZE - 110B •STATISTICS" NO DIAGNOSTICS GENERATED •••••• END OF COMPILATION •••••• 125* BTTES OP COSE NOT USED

401

CS/360 PCRTFAS H COHPILBR OPTIONS - NAHI" HAIH,OPT=02,LINECNT=60,SI2E»0000K,

SOURCE,EBCDIC,NCLIST.NODECK.LCAD,SONAP,NOEDIT,NOID,NOXREF ISH 0002 EOHCTIOR ARLFNC(H) ANLP 10 ISH 0003 IHPLICIT REAL'S (A-H.O-Z) ANLP 20 ISN 0009 COHHOH/COHEIR/ ANL,ATHP,CPIJ,CRIJ(9) ,CKIF0(9) ,CKIHJ(9) .CKIOP(O) .AHLF 30

> CKIJH(9),tXH,DXP,DTH,DYP,BXIP1,ETJrl,CXII,DXHI,DXLI1,DXRI1,DYlJ ,ANLF <10 > DYRJ,DYU1,DYRJ1,GBIJ,GKEIJ(9) ,CBIO,QKBIJ (9) .SBXIJ.SBYIJ.GXIHJ . AHLP 50 > GXIPJ,GIIJH,G*IOP,GTIJ,GKTIJ<«) ,QTia,CKTIJ(B) ,STXIJ,STIIJ,ODVIJ ,ANL»" 60 > QXIHJ.QXIPJ,QTIJH,OTIJF,GKXIHJ(l|) ,GKXI»J (1) .GKYIJH (9) .GKTUPd) ,ANLF 70 > HTKIJ (9),BTKIJH (9) .BTKIPJ (II) ,HTKIHJ(9) .H1KIJP (U) .HIJ.HIJH.HIPJ . ANLF 80 > HINJ,HUP,01J,UIJH,UIPJ,UIHJ,Ular,VIJ,VUE,VIFJ.VIH.J,VTJP,TIJ , ANLF 90 > TIJN,TIPJ,TIHJ,TIJP,HCKTFt(9) ,RCIJ,ROIOS,ROIPJ, ROIHJ,ROIJP , AHLF 100 > SHKtPD(H),SHTCKB(0),SHTTPC,SXXIHJ,SXXIPJ,S*II3H,SYYUPfSXIIJH . AHLF 110 > SXYIPJ,SXYIHJ,SXYI JP,ROI HOD, R CIF JD,R0IJFD, ROUP D, EQTHP.TDIJ , AHLF 120 > HCIHJ,HCIFJ,HCIJH.BCIJP,GF.P0CKn(9),SEHTR(9),DENSK(9),R0DKU(9) , ANLF 130 > GKDVU(9) ,DII,DYJ ,QDT(25) ,HBC (25) ,0BC(J«) ,VBD(25) ,TBD(25) , AHLF 100 > CKBD(U,25) ,TBIJ,HCBIJ .OCKBIJ (9) , BTKEIJ (9) , BN U , U B U ,VBI J.NBI J, AHLF 150 > ROBIJ,HTBU,CKBIJ(9) ,TTIJ »HCTT J ,ECKTU (9) ,HTKTIJ(9) ,0TIJ,1TIJ, AHLF 160 > •TU,R0TIJ,HTTIJ,CKTIJ(9) ,QBD ( 25) ,GBD (25) ,GKBD (9 , 25) , SBDH (25) , ANLF 170 > SBDSH (25) ,HIND.NIHDX.HINDI ,IJ. IH 1 J, 3 Fl J.UH1 .1JP1 .INTRT . KOI J, ANLF 180 > KOIH1J,KOIP1J,KOUH1,KOIJP1 ,NBXH.NBXF, 5BYH,N BYP, NREGIN ,NBNDF , ANLF 190 > IXQVt25),JY0V(25).NHBDTP(25),HOEDTP(25),*VBDTP(25),NTBDTP(2S) , ANLF 200 > HXGHL.NYGFL,NREG.NINTLF,»TOPF,NEOTF,»IEIIC,NTNAX,NGENF ANLF 210

ISN 0005 COHHON/nSOC/TIH,CTN,Tn,PEBTOC,NHCVE,LHCVE,N AHLP 220 ISN 0006 CONHON/INDFIT/DTHLT,STH,SCTH,PRBTH.EPRTTN,CPUSEC,TIOAL.FD?H, ANLP 230

> INDTH,NDTHC,IFINIS,LDTHCP,ISIART,IFLCT,SCPD ANLF 290 ISN 0007 IF (H.GT.10) GO TO 30 ANLF 250 ISN 0009 GO TO (10.12,11.16,10,20,22.2(1.26,28), H ANLF 260 ISN 0010 10 ASLPNC=1.0DC ANLF 270 ISN 0011 RFTOBH ANL" 280 ISN 0012 12 AHLFNC*90.0C0+2.25D0*nSIH(6.283185100*11 N/TIOAL) ANLF 290 ISN 0013 HETOBN ANLF 300 ISN 0019 IM IF (TIH.GT.5.") GO TO 28 ANLF 3jo ISN 0016 AHLFNC=(1.EO-DEXP(2.0*TIH**1.5)) ANLP 320 ISN 0017 RETBRH ANLF 330 ISH 0018 16 IF (TIH.GT.5.) GO TO 28 ANLF 390 ISH 0020 ANLFNC=(1.t0-DEXP(0.1*TIH**1.5)) ANLF.350 ISN 0021 RETURN ANLF 360 ISN 0022 18 AHl»HC»1.0EO AHLF 370 ISN 0023 RETURN ANLF 380 ISN 0029 20 ANLFNC«1.0CO ANLF 390 ISH 0025 RETURN ANLF 900 ISH 0026 22 ANl.FHC'l.ODO ANLF 910 ISN 0027 RETURN ANLF 920 ISN 0028 29 ANI.FNC-1.ODO ANLF 930 ISN 0029 RETURN ANLF 990 ISN 0030 26 ANLFHC'I.OrO ANLF 950 ISN 0031 RETORH ANLF 960 ISH 0032 28 AHLFHC*1.0T0 AHLF 970 ISH 0033 30 RETORN ANLF 980 ISN 0039 END ANLF U90

OPTIONS IH EFFECT* N A M * HAIH,OPT*02,LINFCNT*60,£IZE»OOOOK, OPTIONS IN EFFECT*.. SOURCE,EBCDIC,NOLIST,NOIECK.LCAC,N0EAE,N0EDIT.HOID.NOXREF STiTISTICS* SOURCE STATEHZNTS » 33 ,PPCGRAR SIZE • 750 STATISTICS* NO DIAGNOSTICS GENERATED

402

EHD OF COBPIiaTIOH ••**«• 121K BYTES OF COR" HOT OFEP

403

CS/360 FORTRAN H COBPILEB OPTIONS - NAHE» UAIN,OPI»D2,LINECIIT*60,iI ZE«0000K,

SOORCE,EBCDIC.BOLIST,HOBECK,LOAD ,R0H»P,N0EBIT,NOIB.NOXBEF ISB 0002 StJBROBTIHE DRIVE(KX,KY,NK,X,Y,BX,BY,BXI,EXR,BYl,BYR,H,U,V,T, CK, BRIV 10

> BBBHSR,HTKB,DTND,VTHB,TTHt,CKTBt,NFIG,IJT,JYT,NCRECK,HH) BRIV 20 ISH 0003 IMPLICIT R m » 8 (A-H.O-Z) BRIV 30 ISN 0004 COHHOH/REGIOH/BEPTH (25) ,SH(25) ,IIREG(25) ,IBREG(25| ,JLREG(25) , BRIV 40

> JHREG(25) ,IBT*(25) ,IGENF (25) ,ITCPF (25) . IE0TF(25) DRIV 50 IS» 0005 INTEGEB»2 ILPEG, IBR EG, JLREG, JBBEG BRIV 60 ISH 0006 IHTEGEB»2 1HTE.IGEHP.ITOPP,1 BOTE DRIV 70 ISH 0007 COnnOH/CONEIH/ ABL,ATHF,CPIJ,CKI;)(4) ,C»IPJ(U) , CKIBJ (4) ,CKIJP(4) , DRIV BO

> CKXJI1 (4) , EXH, BKP,BTB,BYP,BXIP 1, CYJP1,CXIX,0XRI,DXL11 ,DX?.I1 ,DYLJ ,DRIV 90 > DTRJ,DTIJ1,BTBi]1,GBXJ,0KBIJ(«) ,CEIJ.OKBIJ(4),SBXIJ,SBYIJ.GXIHJ . BRIV 100 > GXIPJ.GTIJH,GIiaP,GTI0,GK7I,1(4) ,0TIJ,CKXM(4) ,STXIJ,STtXJ,OBVIJ ,BRIV 110 > OXIHJ,OXIPJ,OTiJB,OHJP,GKXIHJ(4| ,GKXIPJ(«) ,GKIIJH(4) ,GKTIJE(4) .BRIV 120 > HTKIO(4),BIKIJB(4),HTKIPJ(4),HTKIMO(4),BIKIJP(4),Hia,BIJB,HIPJ , BRIV 130 > HIH J,BIJP,0IJ,OIJH,BIPJ,OIB3,OX3P,VI3,VI3F,VIPJ,VIBJ,VXJP,TIJ , BRIV 140 > TIJH,TIPJ,TIHJ,TT.JP,RCKTPB(4) .RCIJ.R0IJH,ROIPJ,ROTBJ,RPTJP , BRIV 150 > SHKTPD(4) ,SHTCKB(4) ,SHTTPt,SXXIRJ.SXXIPJ .SYYIJB.SYYIJPjSXTIJH , BRIV 1G0 > SXYIPJ,SXTIBJ,SXriJP,SOIBJD,RCHJB,PCI3Bt,ROIJPD,EQUIP,TD1J . DRIV 170 > HCIHJ,HCIPJ,HCIJH,HCIJP,GE.P0CKI(4) .SFHTK (4) , BENSK (4) . RODKIJ (4) ,DBIV 180 > GKDVIJ(4) ,EXI,BYJ ,ODV (25) ,HBD(25) ,OBB(25) ,VBB(25) ,TBB(25) , BRIV 190 > CKBD(4,25),TBIJ,HCBIJ ,BCKBIJ(4),HTKBIJ(4)rBHIJ,UBXJ,VBIJ#WBXJ, DPIV 200 > ROBIJ,FTBIJ,CKBIJ(U),TTIO.HCTIJ,ECKTIJ(4),HTKTIJ(t) ,0TX3,VIIJ, BFIV 210 > »TIJ,B0TIJ,HTTIJ,CKTI3(4) ,QBB (25) ,GBI (25) ,GKBB (4,25) ,SBBH(25) , DRIV 220 > SBBSH(25) ,BIHB,«INBX,BIHBY ,1J , 1111 J, IF1 0 ,IJ(I1 , IJP1, IHTRT , KOI J , DRIV 230 > K0IH1O.K0IF1J,K0MR1,K0IJF1 .HBIH,HB>F, HETH,NBrP,N3EGIH,NBNDF , BRXV240 > IXQF(25),«JYQV<25).NHBDTP(25) ,H0IDTP(25) »BVBBTP(25) .NTBDTP (25) , BRIV 250 > HXGRl,N«GSl,HREG,NINTI,E.NTOPF,HECTF.NTBIEC.NTHAX,NGEHF BRIV 260

ISH 0008 DIMENSION BPIG |KX,KT) ,T (KX ,KX) ,H (HBOVF) , 0 (KX.KY) ,HH (KX,KY) BRIV 270 ISH 0009 COHHOH/lNBFIT/BTHI.T,STH.SBTH,PRB1B,DPBTTR,CPOSECfTIDAltFBTB, DRIV 280

> IHDTH.NBTBC.IFINIS.lDTRCB.ISTABl.IFLCT.HCPO BRIV 290 ISh 0010 CO(I>ION/DROC/lIll,BTH,Tn>PERIOB,IT,NBOVE,LflCV<:,N BRIV 300 ISB 0011 BIHERSIOH X(1) ,1(1) ,BX(1) ,EY(1) .V(1) .CK( 1) ,EBRHSR(1) ,HTHB (1) , BRIV 310

> OTBB(1) ,VIHB (1) ,TTHB (1) ,CRTBB (1) BRIV 320 ISH 0012 DIHEKSIOR CXl(1) ,BXR (1) ,BYl(1) ,BYR (1) BRIV 330 ISH 0013 DIHEBSION TBAX (1 0) .THIN (10),SHTDTR(10) BRIV 340 ISH 0014 DIHEHSION IXT (1) , JTT (1) BRIV 350 ISH 0015 IPITP»8 BRIV 360

C GR-32.2*36CC.*3600. BRIV 370 ISH 0016 GB«4.17312B8 BRIV 180 ISH 0017 HCPBb1OO,*CP0SEC BRIV 390

C •»» ICLOCK(O) FETORNS TIBE IB .01 SEC.. BRIV 400 ISH 0018 ITIBEÎCIOCK (0) DRIV 410 ISH 0019 ISTOP'O BRIV 420 ISN 0020 CALL GEBCNT(NK) DRIV 430 ISN 0021 CAll B&TPRI (NK) DRIV 440 ISN 0022 CALL BHBCNI(HK.X,DX,Y,DY,KX,KY,BCBECK) DRTV 450 ISH 0023 CAll BCTCNI(BK) BRIV 460 ISH 0024 CAll TOPCNI (BK) DRIV 470 ISN 0025 CAIL SOIFNI(BK,KX,KY) BRIV 480

C •»» SOLPNI CALLS FLXCNI. INITIALIZATION RCOTINES. DRIV 490 TSH 0026 CALL FIITEB (BK .KX.KY) BRIV 500 ISN 0027 CAll INTCOR(NK,KX,KY><i,D,V,T,CK,ERRHSB,H) BRIV 510 ISN 0028 IF (KCMCK.2Q.0) GO TO 10 DRIV 520 ISH 0030 PRIBT 1000,BCHECK DRIV S30 ISR 0031 CAIL EXIT BRIV 540 ISN 0032 10 COHTINOE DRIV 550 ISH 0033 DTH»SBTH BRIV 560

404

ISH 0031 ISN 0035 ISN 0036 TSN 0037 ISN 0038 ISN ooun ISN 0012 ISN 0043 ISN 0044 ISN 0045 ISN 0047 ISN 004") ISH 0"50 ISN 0051 ISN 1052 ISN 0053 ISN 0054 ISH 0OS5

ISH 0056 ISH 0057 ISH 0058 ISH 0059 ISH 0061 ISN 0062 ISN 0063 ISN 0064 ISN 0065 ISN 0066 TSN 0067 ISN 0068 ISN 00S9 ISN 0071 ISH 0073 ISN 0074 ISN 0076 ISN 0077 ISN 007B ISN 0079 ISN 0030 ISN 0081 ISN 0083 ISN 0084 ISN 0085 ISH 0086 TSH 0088 ISH 0089 ISH 0090

TM=ST« DRIV 570 PERTOn=TR/TICAL OHTV 580 FTM=STM*PPETH 0917 590 PRTTN=TB*DPETTN DRIV 600 IP (IPLOT.EQ.O) GO TO 12 DRIV 610 IF (ISTART.EQ.O) CALL PICTl(O) DRIV 620

C IT IS BS*B TC KEEP THE DELTA TIME FSCM CHANGim INITIALLY. ERIV 630 12 TT=9 D9IV 640

C ISS TS SWITCH OSED TO ZE90 TAVG CAICULATTCK 3?."W»!FN TIDAL PERIODS DSIV 650 ISS=0 DRIV 660 HDTH=0 DRIV 670

C STARTS MAJOR EO LCOP OF iHF PROGRAM DRIV 680 14 IF (LDTKCR.GT.O) CALL CHFETB (DTB ,t»REG, Kt, B.I.LOTBCR) DRIV 690

IP (THTRT.EQ.3) GO TO 20 DRIV 70P DT"1=DHIN1 (ITH,FDTN) DBIV 710 GO TO (16.ie.20) ,IHTRT DRIV 720

16 CALI, SOLBKG (KI. KY.NK.H.EBRBSR. HTED.K.U.V,T,CK, HTRD, OTND, VT1D, DRIV 730 > TTMO.CKTBB.DX DY.DXl.EXP.EYL.CYE.NFLG) DRIV 740 GO TO 22 DRIV 750

IP CALL SOLEUI(KX.KY.HK.H.BREHSR.HTFD.H.O.V.T.CK.HTHI.OTBD, VTMD. DRIV 760 > TTMD.CKTBD.BK.DX.DXI.tXB.CYL.CYI.HFLG) DRIV 770 GO TO 22 DSIV 780

20 CALL SOLAB <KX,KY,NK,H,EBEHSB,HTPE,H,U,Y,T,CK,HTBD,tJTKD, VTMD, DBIV 790 > TTMB.CBTBB.CX.DY.DXL.EXB.CY1•EY F.BFLG) DBIV 800

C •*• WRFN SOLAB SELECTED, DON'T VAST ETB MODIFIED EXTERNAL TO DRIV 010 C ••• SUBROUTINE SOLAB. DBIV 820 C ••» SOBROOTINE CBKDTH. IN THE FUTURE (AFTER 9/27/73), HAY ALTER DTB. DRIV 830

22 CALL FILTEN(HTHD.UTBD,VTBD.TTNO.CKTND.H.D.V.T.CK, DX,DY,EXI,DXR, DBIV 840 > DYL.DYP.BFIG) DRIV 850 PERI0D=TH/T1EAL DSIV 860 IT=IT+1 DBIV 870 IF (TSS.NE.O) GO TO 26 DPIV 880

C INITIALIZE THF REQUIRED ARRAYS. ORIV 890 DO 24 LS1,BTHAX DRIV 900 SRTDTH(l) =0. DBIV 910 TMAX(L)n0. ORIV 920

24 TBIN(L)=10000. DRIV 930 SBDTH«0. DRIV 940 rS3=1 DRIV 950

26 DO 28 L*1,KTMAX DHIV 960 SRTOTfl(I)«SHTDTB(L)+DTR*T(IXT(L) ,JIT(1)) ORIV 970 IF (TBAX(L) .IT.T (IXT(L) ,JYT(L))) TBAX (I) -T (IXT (L), JXT (L) ) DRIV 980

28 IF (THIN (L) .GT.T (IXT(L) ,JYI(L) ) ) THIN (I) =T (IXT (I) , JYT (I) ) DRIV 990 SBDTB«SBDTE*DTB DRIV1000 IF (SBDTN.LT.TIDAL) GO TO 32 DBIV1010 PRINT 1010 DBIV1020 DO 30 L-1.NTHAX DBIV1030 TAVG»SRTDTE (L) /SBOTR ORIV 1040

30 PRINT 1020,IXT (L).JYT(I) .TRIB(I) .TBAX(I) .TAVG D*IV1050 ISS'O DRIV1060

32 IF ((ICLOCK(O)-ITTNE) .LT.BCPU) GC TC 3* DRIV1070 34 PRIBT 1030 DBIV108C • IST0P-1 DRIV1090 GO TO 40 DRIV1100

36 TF (FTH.GT.TR) GC TO 38 DRIV1110 TSTOP-1 DBIV 1120 GO TO 40 - DBIV1130

38 IF (PBTTR.GT.TH) GO TO 46 BBIV1140

405

ISH OOQ2 ISH 0094 ISH 0095 ISH 0096 ISH 0097 ISH 0099 ISN 0100 ISH 0102 ISH 0104 ISH 0105 ISH 0107 ISH 0108 ISH 0110 ISH 0111 ISH 0112 ISN 0111 ISH 0115 ISH 0116 ISH 0117

ISH 01IR ISN 0120 ISH 0121 ISN 0122 ISH 0123 ISN 0124 ISN 0125 ISN 0126 ISN 0127

HO I» (IPLOT.EC.O) 00 TO 42 CULL PLOTX(I)

02 CALL QOTPBT 40 ORTTH»PRTTH«DPRTTH

IP (ISTOP.EB.1) CO TO 40 46 COHTIHO*

IP (IT.LT.IROTH) GO TO 14 IP (ETH.GE.FDTH) GO TO 14 NDTH«HDTH*1 IP (RDTH.IT.BDTHC) GO TO 14 NDTH'O IP (IHTPT.EC.3) GO TO 14 OTK-DTHIT»DTR GO TO 14

48 IP (IPIHIS.EQ.O) GO TO 50 CREATE A RESTART P H E

RRITE(IO) TH,OTH.KX,KY.HK SUITE (10) B

50 HRITEIS2.1C40) IH,DTH.IT.R1.KY,HF

DRIT1150 DRIV1160 DRIV1170 BR IV1180 BRIV1190 DRIV1200 DBIV1210 DRIV1220 DRIV1230 DRIV1240 DRIV1250 BRIT1260 IRIX1270 DRTV1280 0RIV1290 DRIV1300 OPIV1310 0RIV1320 DRIV1330

• RITE (52,1050) HB(1,1) ,HH(5,1) ,HE (9,1) ,HH (11,1), HI (21,1) ,RH(37,1) , DHIV1340 > HB(56,1) ,BH(57,1) ,0(1.1) ,0 (5,1) ,0 (9, 1) ,0(11,1) ,0(21,1) ,1(37,1) , DRIV1350 > 0(56,1) ,0(57,1) 0RIT1360 I» (IPtOT.HE.O) EHD PIIE IPLTP DRIV1370

52 RETDRH DRIV1380 1000 PORHATCI'///' IT HAS BEEN DECIDED THAT THIS CASE CANNOT BE DRIV1390

> RON.•//' CHICK PRINTED OOIPOT.'//' RCHEC* » ' I6> DRTV140S 1010 POFHATCI HODE ID. •/2X,IXT«4X'JtI,7X*TBIN,BX*THAX'M,TAVGV) 0RIV1410 1020 PORHIT(I5,T7.F13.«,2ri2.«) DRIV1420 1030 P0RHATC1 HAVE EXCEECEC TBF HAX.EEQOESTEt CPO TIHE.') DRIV1430 1040 FORHATC TH«' 1PE10. 3,IX,"BTH-' 1EE10.3. IX. 'IT*1 ,15, IX, • RX«' ,IS.IX, DF.IV1U40

> • KY«' ,15, IX^HK"', 15) DRIV1450 lOSO POR HAT I///1H .'THE HH AHE 0 VA10ES APE (1,1) , (5. 1) , (9, 1) , (11.1) , (2DRIV1460

>1,1) .(37,1), (56,1), (57,1) V'P6E11.«/6E 11.»/»H11.4) BRIV1470 END ORIV1480

•OPTIONS IH EFFECT* HARE* HAI*.OFT*02,IIRECNT»60.SI2E-000CK, •OPTIONS IR EFFECT* SOORCE,EECDIC,NOlX5T,NOD£CK,LCAt,NOHAt,HOEDIT,HOIO,NOXREP •STATISTICS* SOORCE STATEHEHTS * 126 ,ERCGFAH SIZE - 11R2 •STATISTICS* HO DIAGHOSTICS GEHEFA1EC •••••• BHD OF CQNPILATIOR •••••• 93R BYTES 0» CORE NOT OSED

406

cs/?eo FOSTPAN « COBPIttB OPTIONS - BABE- IAIN ,CPT»5? .LINECBT-6!! .SIEE-9009K.

SODRCE,FtCDIC.NCLIST.NCOICIt.LOAO.NC'IAP.SO?DIT.NOID.3(OXREP ISB 0002 SOBBODTINE SOl.AB (*X,RY.N!i ,Y ,1,P .H.C. V.T.CK.HTNO.OTND, tTND.TTND, SOW

SOU SOLA SOLA so a SOLA SOLA SOLA SOLA

tSB 0003 TSN 0000

ISB 0005 ISN 000$

ISN 0007

TSN 300» ISN 0010 ISN 0012

TSN 0013 ISN 0015 ISN 0016 ISN 0077 ISN 0018 ISF 001"» ISN 0020

10 > CATRD.DX.rY.EXL.tXR.CU.CTP.NFlG) SOLA 20

C ••• SOLA 30 C ••• SOLA 40 C ••» NONTNTCAL INTEGRATION 0» TN? SYSTEM CF DIFFERENTIAL »QOATIONS. SOiA SO C ••• TIA ADA1S-EASHPCFTH BETHCr. SOLA 60 C *•• SOLA 70 C ••• X (TNtDTM) » Y(TH) • (DTB/2) • (l*Y MTS)-V IH-DTB) J SOLA 80 C ••• SOU 90 c •*•

IMPLICIT SFAL*9 (A-R.O-Z) CONNON/CONEIv ABL.ATBP.CPIJ.CKIJ(WJ.CM13(»),CKIBO(4).CKIOP(4) > CNTJH(B) ,C«B,0ttr9tB.CtP,tXIP1.ETJFl.tXlI,'lXBI.0XlI1.DXRI1,DElJ .SOU 130 > DTRJ.DYtJI.DYRJI.GBIJ.GXEHtO) .IBIJ.QBBIO(») .S9XTj.SBYIJ.GXIBJ , SOLA ISO > GXIPJ,STI0B.GTIJP.GTIJ.<;RT;J(II} .CTIJ.CBTIJ(«) .StXIJ.STfZJ.QOTIJ .SOLA 150 > QXIU.OXIFJ.QtlaM.QTTOP.GKXIBilB) .GBXT«3(S) .GKTIJN(S) .GBYIJP(4) .SOU 160 > RT*IJ (0),PTKTJN(B),RTMPJ(4),BTBIBJ(4).BTBIJP(4).BIJ.BIJH.RIPJ . SOLA 170 > HIH3.H:3P.01J,BI3H.0IP3.O:fla,OIOF,TIJ,»TJB,»TPJ.1riHJ,TIJP,TIJ . > TIJH.TTPJ.TIBJ.TIJP.F0BTPBC9).BCIJ.SOIJB.EOIPJ.BOIBJ.BOIJP . > SHKTPDf?) ,StrrCSB(»> ,5ilT?Ft,SXXI!l.>.SXXTP,2,SYYl'JN,SYYIJP.5XYIJR . > SXTIPJ.SXTIFJ.SXTIJF.BCIBJD.RCIFJE.BCIJRC.ROIJPD,EQTBP.TDIJ . > HCIRJ.RCJPJ.RCTJK. RCIJP.GR.POCKr (4) .SFHTR (4) , D£NS1C(4) ,ROORIJ(«) > GKD»IJ(«) .DXI.DYJ .QD?(25).HBE (25) .NEC(25) ••BB(2S) ,TBD(25) . > CNBD(4,25) .TBIJ.HCBIJ .DCKBIJ(4) .BTKETJ (1) .BNIJ.OBIJ.FBIJ.BBIJ. > BOBI.I.BtBIJ.CKBIJ(B) ,TTIJ,HCTIJ,tCI<TT.l(4) ,RTKTIJ(4) .OTIO.rriJ, > BTIJ.B0TIJ.BTTTJ.CKTIJ(4) .QBE(25),GBE(25).GK8D(4.25),SBBB(25), > SBOSt*(25) .NIHD.NINDX.BINOY .IJ.IB1 J.IE10 .tJBI .1 JP1.ISTRT.B0IJ. > B0IR1J.BOIPIJ.BOIJM1.BOIOP1 .NBXB.BBXP,AETN.NBTP.NBEGIN.NBBBP . > I EOF (25) .ITTCF (25) .NHSOTf (25) .NntCTt (25) ,B*B0TP(25) ,NT8BTP(25) . > NXGRL.NEG! t .NBEG.NXNTLP. HT6PF.HECTF.NTEI FC. BTBAX.BGEBF COMMON/DBOt/TTg.ctH.TE.PEBIOC.IT.BRCBF.LBCFE.N DINEBSION T|1) ,B|1) ,0|1) ,»|1) .T|1».CB(1) ,«r10(1) .0TB0C1) .»TND(1).SUU 37 j

> TTND(1) .CRT HO (1) ,OX(1) ,BT(1) .DX1(1) .BIBI1) .BTL (1) . B»R (1) . BFLG (1) .SOLA 330

SOLA 100 SOLA 110 SOU 120

SOLA 1BC SOU 190 SOLA 200 SOLA 210

.SOLA 220 SOU 230 SOLA 240 SOLA 250 SOU 260 SOLA 270 50LA 280 SOLA 290 SOLA 390 SOLA 3TO

> Q(LNOBE) .F (LHOT!) OATA NQISTF/IO/.NSVOER/GI/

C »•• BILL PERFORM N01STP ONE-STIP INTEGRATIONS PRION TO APPLYING THE C ••• ATlAtlS-BASBFCSTH IROCEDOBE. TNITTAl STEPSIZE » DTB. C •«• THE A-B P20CED0RF SILL CONB'NCE *ITH A STEPSIZE » L • DTM C ••• SBEBE THE TBTEG8P L SAT7SFHS C L c N01STP - (NSYEEP • 1) C •»• CORRENTLT. »BEB TBS A-B fPCCEDDRE CCRHERCIS. THE STEPSIZE C ••• BOT EF ALTERED.

TP (TT.GT. HC15TP) GO TO 12 IF (IT.EQ.NC1STP) GO TO 10 CALL SOLRFG(KX.KY.HK.Y.Q.F.H.O.Y.T.CB-HTBE.OTND.VTBD.T7Ru.CKT!!!).

> DX.DY.DXL.CXP.CYL.DYB.NFLGI C «•• CAN'T CHANGE SOLEOL TO SOLBKG OBIESS GIT HB ADDITIONAL SPACE C ••• ALLOCATION IH THE Z ABBAY. C ••• HEBE THE 0 OF BKG IS OSED TO HOLE Y'(TF-CTB)

IF (IT.HE.BSVDEB) GO TO 16 HRTT»(13)F RENIHD 13 GO TO 16

10 DTB«(NC1STF-(NSVCER + 1))•DTB DTBD2>.5D0*B*B R3AD(13)0

SOLA 340 SOLA 350 SOU 360 SOLA 370 SOLA 3B0 SOU 390 SOLA 400

DTE lAYSCLA 413 SOU 420 SOLA 4J0 SOLA 440 SOU 450 SOLA ft 60 SOLA 470 SOLA 4R0 SOU «90 SOLA 500 SOLA 510 SOU 520 SOLA 530 SOLA 540 SOU 550 SOLA 560

407

C ••* ROTE SELL. PSOGHARREt SO CTRD2 CIR'T El CHARGED XW IT'S VALBE SOU 570 C •»» HERE. SOU 580

ISH 0021 12 00 1» *»1,1RME SOU 590 ISR 0022 r<K»»T(*l«ETaP2»(3.D0«F(*»-O<K)J SOU 600 ISH 0023 »• Q(X)»F(*) SOU 610 ISH 002» TR*TH*DTH SOU 620 ISH 0025 TIR«T« SOU 830 ISH 0026 CALL eHOCOHfM.HE.T.CM SOLA 6U0 IS* 0027 CALL SCLPRC(RTI!B,BTHO,»T8B.T?HD,CrT«D,R,C.».T.CKtDX,DT,OI(L. DIR. SOLA 650

* ML,riT*,llPlG) SOLA 660 ISR 0028 If RETOM " SOLA 670 ISH 002* EHO SOLA 680

•OPTIOH5 IH EFFECT* HABI» MSH,OIT«02,ZIMC»T*60,SIIE»C0CCK, •OPTIOHS IH EFFECT* SOORCE, EBCDIC,HOLISI.HOtECIt .LCAE ,HCEAt .HOlBn.HOID.HOXaEP •STATISTICS* SOOFCF STATIREHTS « 28 ,PFCGRAR 5ITE « 1702 •STATISTICS* HO DIAGHOSTICS GENERATES •••**. {HO or CORPItATIOH **••*• 121K BITES OF CORE HOT OSEO

1721

CS/360 FORTRAN H COHFTIER CPTIORS - NAHE* HHH,OPI=O2,I.INECFT«60,SIZI=0000K,

SOBFCFrEICOIC.FOlIST.FODFCK.LCAn.IlOBAP.SOEOIT.BoID.SOXBEF ISH 0002 SUBROUTINE HHTPBI(NK) KATP 10 ISH 0003 IHPLICIT REAt*8 (A-H.O-Z) HATP 20 ISN 9004 COHHON/COHEIN/ ANL. ATHP .CPU ,CKI J (4) .CUE J (4) , CKIHJ (4) ,CKI0P(4) , HATP 30 > CKIJH(4) , CXR.OXF.DYH, CYP.rXIP1.tTJP1.CXII,1XRI.DXil1,DXRI1,DYLJ . HATP 40

> DTFJ,BTLJ1,ITPJ1,GBIJ,GFEI,1 (4) ,CBI J.QFBT 3 (4) , SBXIJ.SBYIJ.GXIHJ , HATP 50 > GXIPJ.GYIOH,GYTOP.GTIJ.GKH.J(4) .CTIJ.CMIJ (4) .STXIJ.STYIJ.ODVIJ .HATP 60 > QXIHJ,QXIPJ,QTIJH.QTIJP,GXXIHJ(4) .GKXIPJ (4) tGKTIJH (4) ,GRYIJE(4) .HATP 70 > HTKIJ(4) .HTKIJH (4) ,HTKIFJ(4) .HTFIHJ (4) .RIKTJP (4) .HIJ.HIJH.HIPJ , HATP 80 > HIHJ.HIJP.DIJ.OIJH.DIPJ.DIH3.01JP.YIJ.TIJE.VIPJ.VTNJ,VIJP.TIJ , HATP 90 > TIJR,TIPJ,TIHJ,TIJP,R0KTPD(4) ,ECM.ROIJH,ROIP.1,ROIHJ,ROUF , HATP 100 > SHKTPD (4) ,SRTCRC(4) .SHTTPD.SXXIEJ.SXXIPO.SYYIJH.SYYIJP.SXYUH , HATP 110 > SXYIP3.SXYIPJ.SXYT3P.R0IHJD.FCTEJE .RCIJFE.ROIJPD.EQTHP.TDIJ . HATP 120 > HCISJ,HCIFJ.HCIJH,HCIJP.GR,ROCKE(4),SPHTR(4),DENSE(4).RODKIJ(4) .HATP 130 > GXDVIJ(4? .DXI.DIJ .OPT (25) ,HBD(25) .tlBDCS) .VBD(25) ,TBD(25) . HATP 140 > CKBD(.,25) .TBIJ.HCBIJ ,DCFEIJ(4),HTKBU («) ,BNIJ,OBIJ,TBU,PBIJ, HATP 150 > ROBIJ.HTBIJ.CRBIJ(4) .TTIJ.HCTIO.CCKTIJ (4) .HTKT.1 (4) .UTIJ.TTU, HATP 160 > HTIJ.POTIJ.HTTU.CRTU (9) .QBD(25) ,GBE(25) ,GKBD(4,25) ,SBDN{25) , HATP 170 > SBDSH(25) . BIND, NINDX,BIND! ,la,IF1.1,IF10,IJH1,IJP1,INTRT,lt0IJ, HATP 180 > KOIH1J.ROIF1J.KOIJR1.K0IJP1 .NBXH.NBXF,KEYH,NEYP,NREGIN,NBNDF . HATP 190 > IXQV (25) .JYQV (25) . NRBDTP (25) .NDEDTF(2E) ,HVBDTP(25) ,NTBDTP(25) . HATP 200 > HXGRL.HYGFI.HREG.HINILP.RTOPF.NECTF,NIBIEC.RTHAX.NGENF HATP 210

ISN OOOS DIHESSIOB CKIR JD (4) ,CKIPJC(4) ,CKIJHC(4) ,CKIJPD(4) HATP 220 ISH OOOG DIHEHSIOH CONCH (1) HATP 230 ISN 0007 RETOBN HATP 240 1SN OOOR PSTRY HATPRF(C0NCK.T!NF,DENS,SPHT.R0TPE) HATP 250 ISN 0009 10 DEHS»O.DOO HATP 260 ISN 0010 SPHT'O.DOO HA TP 270 ISK 0011 ROTPD-C.EOO HATP 280 ISH 0012 SHT»P1;«0.DC0 HATP 290

CC EQUATIONS OF DENSITY AND SPECIFIC HEAT «S (UNCTIONS OF TEHPERATURE HATP 300 CC AHD CONCEHTEAIION HILL BE GIVEN BERE HATP 310 C HEANTIHE K*1 IS RATER AHD K=2 IS SALT. HATP 320

ISN 0013 DEHSK(1)*62.6651D0-0.000062338D0*IEHP**2 HATP 330 ISN oom DENSK (2) "46.C13D0 HA'P 340 ISS 0015 SPHTK (1)*1.000 HATP 350 ISN 0016 SPKTK (2) S1. OCO HATP 360 ISN 0017 R0KTPD(15—0.000124676DO*TEH£ HATP 370 ISN 0018 ROKTPD (2) «C.ODO HAT 380 ISN 001O SHKTPD (1)*O.ODO HATP 390 ISN 0020 SHKTPD (2) =C.ODO HATP 400 ISN 0021 DO 12 K*1.BK HATP 410 ISN 0022 ROC ED (K) -DERSIC (R) 1ATP 420 ISN 0023 SHTCKD (R) "SPATE (K) HATP 430 ISN 0024 ROTPD>BOIPD«CORCK(K)•ROKTPD(F) HATP 440 ISN 0025 SHTTPD«SHTTED*CONCH (R) *SBKTPD (X) HA TP 450 ISN 0026 DEHS*DENS*CCRCK (K) «PENSK (K) HATP 460 ISN 0027 12 SPHI»SPRT • COHCR (K) •SFHTK (K) HATP 470 ISN 0028 RETURN HATP 480 ISN 0029 END HATP 490

•OPTIONS IH EFFECT* RARE* HAIN,OET=02,tIHECNT=60,SIZE=COCCR, •OPTIOHS IR EFFECT* SOURCE. EECOIC,ROUST.HOCECK,lCAD,*OEAF,HOEBI"".NOID.HOIREF

•STATISTICS* SOURCE STATEHEHTS * 28 .PRCGRAH SIZE = 742 • STATISTICS* HO DIAGNOSTICS GENERATED

409

HD OF COMPILATION 121K ETT*S OF COSE 10T USTD

410

CS/360 TORTRAN n COMPILER OPTIONS - NAHE« HAIN,OPI>02,LINECII*60,STZE»OOOOK,

SOORCE,EBCDIC,NOIIST, HeDECK,LOAD,NOR&P.NOEDrr,NOID,NOXREF ISN 0002 SOBRCOTINE COTPRT OOTP 10 ISN 0003 IMPLICIT REAL'S (A-H.O-Z) OOTP 20 ISN ooon COHflON/ODT/NK,KX,KT,NKKX,IXO,ITO,IHO,I(lO,IVO,IRSO,IIO,rrlHDO,ICKO OOTP 30 ISN 0005 CONBON/DROO/TIN,DTB,TB,PERIOD,IT,NR0VE,LBC7E,N OOTP 40 ISN 0006 COHHON/COBBIK/ ANL, ATBE.CPIJ.CKI J (4) ,CFIFJ (4) . CKIHJ (4) .CKIJP(4) , OOIP 50

> CKIJH(4),CXB,DXP,DTR,DTP,DXIP1,CYJP1,CXII,DXRI,DXLI1,DXRI1,DYLJ ,OOTP 60 > DYBJ.DIIJ1,DYRJ1,GBIJ,GKBIJ(4),CEIJ.QKBIJ(0) ,SBXIJ.SBYIJ,GXIBJ , OOTP 70 > GXIPJ,GTIJH.GYIJP,GTTJ.GFTIJ(U) ,QTIJ,{KTIJ(4) ,STXIJ,STYIJ,QDVIJ ,OOTP 80 > QXIBJ,QXIPJ,QYIOB,QYIJP,GKXIHd(4) ,GKXIPJ «4) ,GKIIJB (4) ,GNTIJP(4) ,OOTP 90 > HTKIJ(4) , HTKIJH(4) .HTKIPJ (4) .HTKIHJ (4) , HTKIJP (4) . HIJ, HI JH ,HIPJ , ODTP 100 > nlBJ,HIJP,OTJ,OIJH,OIPJ,OIHJ,OIJP,VIJ,FIJB,FIFJ,VIBJ,VIJP,TIJ , OOTP 110 > TUB,TIPJ.TIBO,TIJP,ROKTPD(4) ,BCIJ,B03JE,BOIPJ.ROIBJ,ROUP , OOTP 120 > 5HKTPD(4),SHTCKD(4).SHTTFD,SXXIHJ.SXXIPJ,SYYIJN,SYYIJP,SXYIJH , ODTP 130 > SXYIPJ,SXYIBJ,SXTIJP,BOIfljn,BCIFJD,RCJJtD,ROIJPD,EgTHP.TDIJ , OOTP 140 > HCIHJ,HCIFJ,HCIJH,HCIJP,GR,ROCKt (4) ,SFHTK (4) ,DEHSK(4) ,RODKIJ (4) ,ODTP 150 > GKDTIJ(4) .EXI.DYJ ,QDV (25) ,HBC (25) ,DBt (25) ,VBD(25) ,TBD (25) , OOTP 160 > CKBD(4,25),TBIJ,HCBIJ .DCKBIJ(4).HTKBIJ(4),BNIJ,nBIJ,VBI3,KBIJ, ODTP n o > ROBIJ,HTBIJ,CXBIJ(4) ,TTIJ.HCTIJ,ICKTIJ(4),1TKTIJ(4),DTIJ,VTIJ, OOTP 180 > NTIJ,ROTIJ,HTTIJ.CKTIJ(4) ,QBD(25) ,GBt (25) ,GKBD (4, 25) ,SBDH(25) , ODTP 190 > SBOSH(25) ,HIHD,«IHDX,«INDT ,IJ,IH1J,IF1 J.IJH1 ,IJP1.INTRT.KOIJ, OOTP 200 > KOIH1J,KOIF1J,K0IJB1,K0IJE1 ,NBXH,HBXF,BEYR,N8YP,HREGIN,HBNOF . OOTP 210 > IXQV (25) , JYQV (25) , NHBDTP (25) , NOEDTP (25) ,NVBDTP (25) ,NTBDTP (25) . OOTP 220 > NXGBL,NYGRL,NREG,N1NTLF,NT0PF,NECTF,HTB1FC, NTHAX,HGEHF COTP 230

ISN 0007 DATA NOIINE/55/ OOTP 240 ISN 0008 DATA NC/03/ OOTP 250 ISN 0009 COHBOH/Z/HZSP,NDON,Z(1) OOTP 260 ISN 0010 NPOS'NOLINE OOTP 270 ISN 0011 KOIJS=ICKO ODTP 280 ISN 0012 DO 14 1=1,KX OOTP 290 ISN 0013 IJ=I ODTP 300 ISN 0014 KOIJsROIJS OOTP 310 ISN 0015 DO 12 J=1,KY CDTP 320 ISN 0016 HPOS=NPOS+1 OOTP 330 ISN 0017 IF (NPOS.LE.NOLINE) GO TO 10 OOTP 340 ISN 0019 HPOS=0 OOTP 350 ISN 0020 PBIHT 1000,IT,TH,PERIOD,DTH OOTP 360 ISN 0021 10 PBIHT 1010,1,J.Z (1X0*1) ,Z(IY0«J) ,2 (IH04TJ) ,Z(ID0*TJ) ,Z(I»0»IJ) , OOTP 370

> Z(IHS0 + IJ),Z(I?0»IJ) ,Z(ITTHDO*IJ) , (Z (FOTJ+K) , K-1, NK) OOT? 380 ISN 0022 X0XJSK0IJ+RRRX Ol'TP 390 ISH 0023 12 IJ=IJ»KX OOTP 400 ISN 0024 14 KOIJS=KOIJStHK. OOTP 410 ISH 0025 IP (INTRT.NE.1) GO TO 22 OOTP 420 ISH 0027 IF (HC.LE.O) GO TO 22 OOTP 430 ISN 0029 I0HO=IHO*LBCVF ODTP 440 ISN 0030 HC=HC-1 OOTP 450 ISH 0031 IOnO=IBO*LHCVE ODTP 460 ISN 0032 IQ70=IVO»LHCFE ODTP 470 ISN 0033 IQTO=ITO*LHOVE on TP 480 ISN 0034 IOCKO=ICKO*LHOVE ODTP 490 TSN 0035 HPOS^NOLINE OOTP 500 ISH 0036 KOIJS=IQCKO ODTP 510 ISN 0037 DO 20 1=1,KX OOTP 520 ISN 003B IJ=I OOTP 530 ISN 0039 K0IJ=K0IJS OOTP 540 ISN 0040 DO 18 J=1,KY OOTP 550 ISN 0041 HPOS=NPOS-»1 OOTP 560

411

tSK 0042 IS* 0044 ISB 0045 ISH 0046 ISK 0047 ISH 004R IS* 0049 ISR 0050 IS* 0051

ISH 0052 ISH 005.1 ISH 0054 ISH 0055

TP t»pos.LZ.«oi.in> oo RE 16 OOTP S70 HP0S«C CUTP 580 PRINT 1020,11 OtlTP 590

16 PRINT 10JO,I,J,2<IOHO«IJ),i(IQOO»IJ) ,Z(IStO*IJ) ,Z(XQTO«IJ) , OOTP 600 > (I(«IJ*K) ,F-1,»K) OOTP 610 KOIdMCXJtNKKX OOTP 620

1B TJ»IJ*ltX OOTP 630 20 KOr«IS"BOUS*HH OOTP 640 22 ROTORS OOTP 650

1000 TOMITI'1 ITHB."M4,1X,'TXHE«,,1F»12.£,3X,,PrBIOD»',B12.6,3X, OUTP 660 >'TIHE INCREMENT*' ,E12«6//, OOT» 670 >45X,'WELOCTTY',31,' VELOCITY',2X,'HATER EtF«.*,14X,'TESP.•,4X. OOTP 6B0 >'S0BSTA*CB PASS CONCEFTRATIONS VeX.'IBCI-'^X,'X-',9X,'Y-',7X, OOTP 690 >'BATEP>,8X,'XVt,9X,'XN',8X,tPATEt,16X,'BA7E,/«2X#'N0DF: CES',2X, OOTP 700 VL0CA1X0* LOCATION ELEVATION I-DIFECT. T-MBECT. OF CHARGE OOTP 710 > TEMP. 0» CRAHGF', BX.'CK(I)'. 6*. 'CKC2) •/> OOTP 720

1010 *0RRAT(2(1X.X3) ,1X,2P11.2.1P'13.J ,1F«E".3| OOTP 730 1020 wORHATf'131*'#X3,5X#'BOUNDING ERFCF ESTIMATES, Q.V 3X,* I•,5X,'J*,OUTP 740

> BX.'QH,,11X,«gO',11I,,0?'.11X.'CT,l OOTP 750 1030 T0RH»TaS,2X,I«, 1P6E11.3) OOTP 760

BHD OOTP 770 •OPTIOHS IH EFFECT* NAME* HAIH,OET«02,LIHEC*T*60.SIZE«OOOCK, •OPTIOHS IH EFFECT* SOORCE,EBCDIC,NOLISI,HOtFCK,LC*E,HOPAt,KOEBI~,NOID,*OXREF •STATISTICS* SOURCE STATEMENTS « 54 ,FRCCP*H SIZE • 15BB •STATISTICS* 10 DIAGNOSTICS GENERATED •*•••* shd OF COMPILATION *•*••• 113R BYTES or CORE NOT OSED

412

OS/TO PCF rFA N II COBPim OPTIONS - RARE- !1»IN.OPT'»02,LmcVI»60 ,ST2T=OOOON ,

SOORCE,EBCDIC,NOITST,NCDECK,IC»D,NC1AP,NORDIT,NOIP.NOXR2F ISH 0002 SUBROUTINE CHFK*t (UPX,XRFL,NXGBI,KSK,NAH!,1C,TR»G) CH2K 10 ISH 0003 IMPLICIT RFAl*8 (A-H.O-Z) CHEK 20 ISN 0004 DIMENSION XGRL(1) CHEK 30 ISH 0005 DATA CIL/Z3C10DOCOOOOOCOOO/ CHMK 40

C »»» DEL=16**-5 CHEK 50 ISN 0006 DO 20 H»1,NXGPl CHEK 60 ISN 0007 IF (OPX-XGRL (H)) 10,22,20 CIIEK 70 ISH 000ft 10 IF (H.GT.1) GO TO 12 CH^K 80 ISN 0010 «C=1 CHEK 90 TSH 0011 GO TO 16 CHEK 100 ISN 0012 12 IF (UPX .IE..5* (XGRL (N) +XGPI (H- 1) )) GO TO 14 CHEK 110 ISN 0014 MC=M CM»K 120 ISN 0015 GO TO 16 CHEK 130 ISH 0016 14 MC«H-1 CHEK 140

C IF OPX IS SUFFICIENTLY CLOSE TC JGFI(NC) IN A RELATIVE SENSE, CHEK 150 C * * * THEN DON'T PRINT REPLACEHFHT MESSAGE. HCHEVER , THE REPLACEMENT CH^K 160 c * * * DOES OCCUR. CHEK 170

ISN 0017 16 IF (DABS (UFX-XG4L (MC) ) .LE. EEL*XGF1 (HC) ) GCTO 18 CHEK 180 ISH 0019 PRINT 1000, IREG,NAME,OPX,XGPL(HC) CHEK 190 ISH 0020 »SK*1 CHEK 200 ISN 0021 18 OPXsXGRL (HC) CHEK 210 ISN 0022 GO TO 24 CHEK 220 ISN 0023 20 CONTINUE CHEK 230 ISH 0024 MC=NXGPL CHEK 240 ISH 0025 GO TO 16 CHEK 250 ISN 0026 22 BC*H CHEK 260 ISH 0027 24 RETURN CHEK 270 ISN 0028 1000 FORIATC IH REGION = * 12. 1 X'THE • 14 , 1X • EDGE 9AS CHANGED FROH» Fl 1. 5,CHEK 280

> IX'TO 'F11.51 CHEK 290 ISH 0029 BHD CHEK 300

•OPTIONS IN EFFECT* t'AHE= MAIN,OFT=02.1INECHT=60 ,SIZE=OOCCK, •OPTIONS IN EFFECt* SODRCE, EBCDIC, NOLIST, NOCECK,LCAC, NONA t, NOEDIT, VOID, NOXREF •STATISTICS* SOORCE STATEMENTS = 28 .FROGRAN SIZF = 714 •STATISTICS* NO DIAGNOSTICS GENERATED •»•«•• ehD OF COMPILATION »••••• 129K BYTES OF CORE NOT USED

413

CS/360 FCRTFAN H COMPILER CPTIONS - NAHE = HAIN,OPT«02,LINIC*I=60,SIZE=0000F,

SOURCE .EBCDIC,NOLIST,BCDECK,LC AD .ROMAP .HOEDIT ,ROID.HOXBEE ISR 0002 SOBRODTINE ESERCH(IXT,XTHAX,X,IASII, DX, pXSAHE ,H, NTEH ,HS) BSER 10 ISH 0003 IMPLICIT REAL*8 (A-H.C-Z)

,HS) BSEP 20

ISH 9004 REAL*4 XNAHE BSER 30 ISN 0005

c ••• DIHENSION X(1) ,DX (1) BINARY SEARCH THBO ORDERED ARRAY.

BSER BSER

40 50

ISN 0006 DATA DEL/Z3C10000000000000/ BSER 60 ISH 0007 IF (XTMAX.G7.X(1)) GO TC 10 BSER 70 ISH 0009 IXT=1 BSEB 80 ISH 0010 IF (XTHAX.GE.X (1) 500*DX (1) ) GO TC 26 ESEB 90 ISH 0012 IF ((X(1)-.5D0*DX(1) 1-XTHAX. IE.DII*DABS(XTHAX) ) GO TO 26 BSER 100 ISN 0014 GO TO 28 BSEF 110 ISH 0015 10 IF (XTHAX. IT. X(LASTI)) GO TO 12 BSEB 120 ISN 0017 IXT =LASSI BSER 130 ISN 0018 IF ;XTHAX.LE.X(LASTI)+.5D0*DX(;ASTI)) GO 10 26 BSEB 140 ISN 0020 IF (XTHAX- (X(LASII)*.5D0»DX(LASTI)), • LE •DEI*DABS(XTNAX)) GO 10 26 BSER 150 ISN 0022 GO TO 28 BSER 160 ISN 0023 12 HL=1 BSER 170 ISN 0024 HH-LASTI BSER 180 ISH 0025 14 IF (HH-HL.EC.1) GO TO 22 BSER 190 ISR 0027 H-(ML*RH)/2 BSER 200 XSN 0028 IF (XTHAX-X (N)) 16,20,18 BSER 210 ISN 0029 16 HH=N ESEB 220 ISK 0030 GO TO 14 BSBR 230 ISN 0031 18 HL=H BSER 240 ISH 0032 GO TO 14 ESER 250 ISN 0033 20 IXX=H BSER 260 ISH 0034 GO TO 26 BSEB 270 ISH 0035 22 IF (XTHAX.LE.. 5* (X (HI) *X (SI*1) ) ) GC TC 24 BSEB 280 ISH 0037 IXT=HH BSER 290 ISH 0038 GO TO 26 BSER 300 ISN 0039 24 IXT=HL BSER 310 ISN 0040 26 RETURH BSEB 320 ISN 0041 28 IF (HTEH.EC.O) PRINT 1UOO BSER 330 ISH 0043 NTBN»1 BSER 340 ISH 0044 IF (HS.NE.C) GO TO 30 BSER 350 ISH 0046 PRINT 1010,XNAHE,XHAHE,M BSER 360 TSH 0047 GO TO 26 BSER 370 ISN 0048 30 PRIST 1020,XNAHE,H ESER 380 ISN 0049 GO TO 26 BSER 390 ISN 0050 1000 FORHAT (• 1'//) BSER 400 ISN 0051 1010 FORHAT (• TBE'A 3,"CORDINATE OF THE H -TH TFHPERATURE MONITORING ESER 410

>POINT a s OOTSIEETHE'A3,'GBID. H='I2) BSER 420 ISN 0052 1020 FORHAT THE*,A3,'CORDIHATE IS NCT IH IHF GRID STRUCTURE. '/ BSER 430

> ' THE BOUNDARY FCN. NO = NBN = *,I2) ESER 490 ISN 0053 END BSER 450

•OPTIONS IN EFFECT* DANE* HAIH,OPT=02,LINECHT=60,SIZE=COCCK, •OPTIONS IN EFFECT* SOOBCE,EBCDIC,NOLIST,NOCECK,LCAD,NOEAE,NOEDIT.NOID,NOXREF •STATISTICS* SOBPCE STATEMENTS = 52 .PBCGRAH SIZE = 1108 •STATISTICS* NO DIAGNOSTICS GENEBAIET ****** BUD OF COMPILATION »***»* 121K BITES OF COBE NOT USED

414

CS/360 PCRTFAN 8 COHEIIEB OPTIONS - H»HE« HAIH,OPT»02,LIHICIT«60,SIIE*0000R,

SOURCE,EECDIC,NCLIST.HOCECX,IC»D,ROHAP.NCEDIT.NOID,NOXREF ISH 000? FOHCTICH GFFLFC(N.X) GHRL 10 ISH 0001 IHPLICIT REAL*8 (A-R.O-Z) GNRL 20 ISN 0000 COHHOH/COHEIS/ ANL, ATHP.CFIJ.CFIr'(»> ,C*IEJ (4) ,CKTHJ (4) ,CKTJP (4) , GNRL 30

> CKIJH |4),CXH,DXF.DYH,DYP,BXIP1,CY0P1,CXII.DXRT,DILT1,DXRI1,DILJ ,GNBf. 10 > DIRJ,CYL.)1,DYRJ1.GBIJ,GKEIJ(4) , CBIJ.QRBI J (4) ,SBXIJ,SBYIJ,GXIHJ , GNAC 50 > GXIPJ,SYIJH,GYIJ»,GTIJ,GKTTJ<4) ,CTIJ,CKTI<>(4) ,STXIJ,STYIJ,QBVIJ .GNRL 50 > QXlnj.QXIEJ,GYIJH,QYIJP.G!CXIHJ(0) .GFXIPJ (4) ,GKYZJH<4) ,GKYIJP(4) .GNRL 70 > HTKIJ(O) ,BTKIJH<4) .HTKIPJ(ft) ,BTFIHJ(4) .EIRIJP(4}.HIJ.HIJH.HIPJ . GNSL 80 > HIHJ,HIJP,tlJ,OIJN,BIPa,OIHJ,OIOE,VIJ,VTJS,VIPJ,YINO,»IJP,TIJ , GHBt 90 > T*JH.TIPJ,TIHJ,TIJP,FCKTEE(4) ,SCIJ,ROIJE.ROIPJ.ROIHJ .FOIJP , GHBt 100 > XTPD(4) ,SHTCFD(4),SHTTPC,SXXieJ,SXXlPJ,SYYTJH,SYYIJP,SXIIJH . GHBI» 110 > . XYIPJ,SXYIHJ,SXYIJP,ROIHJD,RCIEJO,ECIJPB,ROIJ?D,EQIi)P,TDIJ , GHRL 120 > HCIHJ.HCIFJ.HCIJH.HCIJP,GF,R0CKC(4) ,SEHTR(4) ,DENSK(4) ,RODKIJ(4) .GHBt 130 > GRDTIJ(4) ,DXI,DYJ ,QDV(2;).HEE(25),OBE(2J),VBD(25).TBD(25), GNBL 140 > CFBD(4,25).TBIJ.HCBIJ .OCKBIJ(4).HTKBIJI4).BNIJ.BBIJ.VBIJ.BBIJ, GHBt 150 > BOBIJ.HTEIJ.CKBIJ(4).TTIJ.HCTIJ,CCKTIJ (4).HTKTIJ(4),0TIJ,VTIJ. GNRL 160 > «TIJ,E0TIJ,BTTIJ,CKTIJ{4) ,QBD (25) ,GBE (25) ,GKBD (4, 25) ,SBDN (25) , GIRL 170 > SBDSB(25).BIHD.WIHDX.HINDI .IJ.IHIJ.IEIJ.IJHI.IJPI.INTRT.ROIJ. GNRL 180 > K0IH1J.X0IF1J.K0IJH1.FOIJP1 .HBXH.NBXE,FEYH.BBYP.HREGIN,NBRDF , GNRL 190 > IXQ»(25) ,OYC (25) ,RHBDTP(25) ,NDEtTP(25) ,*VBDTP(25) ,NTBDTP(25) , GNRt 200 > HXGRL.HYGEt.HREG.HINT1F.HIOPF.HEOTF.HIEIEC.HTHAX.HGEHF GNRt 210

ISN 0005 COHflON/TABLE/NTELP(10).TABARG(25«10).TABFVC(25,10) GNSt 220 C»»»««THIS YAtBE FOR X IS IHSERTED HERE TO TEST THE PBOORAH FOR GNRL 230 C NORKABILITY. GNRL 240

ISH 0006 X s 1.D0 GNRt 250 ISN 0007 IF (H) 14.10,12 GNRL 260 ISN 0008 10 GNRLFC'I.OEO GNRL 270 ISH 0009 RETORN GNRL 280 ISN 0010 12 CALL ATSH(X.TABARG(1,N).TAEFNC (1,H).NTELE(N) .1,ARG.VAL.5) GNRL 290 ISN 0011 CALL AII(X,ARG,YAL,T,5,0.C1,IER) GNRL 300 ISN 0012 GHRLFCSY GNRL 310 ISH 0013 RETORH GNRL 320 ISH 0014 14 H — » GNRL 330 ISN 0015 GNRLFC'ANLFNC(N) GNRL 340 ISN 0016 N=-N GNRL 350 ISN 0017 RETORN GNRL 360 ISH 0018 EHD GNRL 370

•OPTIONS IN EFFECT* •OPTIONS IN EPFECT* •STATISTICS* SOt:-iE STATEHENTS » •STATISTICS* HO DIAGNOSTICS GENERATED

HAHE= HAIN,OPT=02,IINECNT=6S,SIZE=C0CCK, I SOURCE.EBCDIC,NOLIST,HOEECK,LCAE,HOeAE,NOEDIT,MOID,NOXREF

17 ,PRCGBAH SIZE = 54 8

»»•»•• END OP COHPILATIOH *•»•*• 121K BITES OF CORE NOT DSHD

415

CS/360 FORTRAB H

COMPILER OPTIONS - BAHE" BAIN,OPT«02,LXHECIT>60,SIZE«0000K, SOURCE,EBCDIC,BOXIST,BODICE,LOAD,NOBAP.NOEDIT.HOID.HOXaEI

C 10 C 20 C 30 C SBBBOUTIBI AIT AO C 50 C PURPOSE 60 C TO INTERPOLATE FONCTION VAIUE T FOF A GIVEN AHGUBENT VALUE 70 C X USING A GIVEN TABLE (ABG,VAL) CF ARGUBEBT ABD FUNCTION 80 C VALUES. 90 C 100 C USAGE 110 C CALL All (X,ABS,VAl,Y,BDIB,ESS,XEB) 120 C 130 C DESCBIPIICN OF PARAHETEBS 190 C X TBE ABGURENT VALUE SPECIFIED BI IBPOT. 150 C AHG - TBE INPUT VFCTOB (EIBEBSION NDIK) OF ARGUBEHT 160 C VALUES OF IRE TABIE (NOT DESTROYED) . 170 C VAX - THE INPUT VICTOR (DIREBSICB NDIH) OP FOHCTIOH 180 C VILUES OF THE TABIE (DESTSCTED). 190 C I THE BESULT2BG IBTIBECLATED FONCTIOH VALOE. 200 C NDIH - AB IHPOT VALUE BB3CH SPIC1IIES THE HUHBER OI 210 C PCIHTS IH TABLE {»SG,9AI) . 220 C EPS - AN IHPOT COBSTABT BBICB IS USED AS UPPER BOUND 230 C FOB TBE ABSCLOTE IRROR. 200 C IEB - A RESULTING EBBOS PABABITIE. 250 C 260 C REMARKS 270 C (1) TABLE (ARG.VAL) SROULE BEPRESEBT A SIBGLE-VALUED 280 C FONCTION AND SHOULD EI STORED IB SOCH A NAY, THAT THE 290 C DISTANCES ABS(ARG(I)-X) INCREASE 8ITH INCREASING 300 C SUBSCBIPT I. TO GENERATE Tfl'iS CBDEB IN TABLE (ARG,VAL) , 310 C SUBBOUTIHES ATSG, ATSH OB ATSE COOID BE OSED IB A 320 C PREVIOUS STAGE. 330 C (2) NO ACTION EESICES EBROF MESSAGE IN CASE NDIH LESS 300 C THAN 1. 350 C (3) INTERPOLATION IS TERMINATED IITBER IF THE DIFFERENCE 360 C EITSEEN TOO SUCCESSIVE IHTERI01ATED VALUES IS 370 • C AESOIUIELY LESS THAH TCXEBABCE IPS, OB IF IRE ABSOLUTE 380 C VALUE CF THIS DIFFEKEBCE STOPS DIMINISHING, OR AFTEB 390 C (BEIB-1) STEPS, FURTHER IT IS TERMINATED IP THE 000 C PROCEDURE DISCOVERS TBC ARGUEEBI VALUES IH VECTOR ARG 010 C NHICB ABE IDENTICAL. DEPENDENT CN THESE FOUR CASES, <120 C rSBOB EARABETER IEB IS CODED IB THE FOLLORIBG FOBM 030 C IEH=0 - IT HAS P0SSIB1E TO PEACH THE REQUIRED 000 C ACCDBACY (NC IRROR). 050 C IER=1 - IT «AS XHPOSS3SXE TC IEACH THE REQUIRED 060 C ACCURACY BECAUSE OF RCDBDING ERRORS. . 070 C I2H«2 - IT HAS IMPOSSIBLE TC CBICK ACCURACY BECAUSE 080 C NDIH IS LESS TRAH 3, CB TBE REQUIRED ACCURACY 090 C COULD SOT EE BEACHEt tt MEANS OF THE GIVEB 500 C TABLB. NDIH SBCULD EE INCBEASED. 510 C IER»3 - THE PROCEDUBE tISCOVESED THO ARGUMENT VALUES 520 C IB VECTOR ARG NHICH ABI IDENTICAL. 530 C 500 C SDBBOUTINES ABD FUNCTION SUBPBCGBAHS FEQUIPED 550 C BONS 560

416

I«5N 0002 ISK 0003 ISK 0004 ISH OOOB ISH OOOfi ISN 0007

ISN OOOB ISH OOOO ISH 0010 ISH 0011 TSN 0012 ISN 0013 ISH 00 IK 'ISN 0015 ISH 0016 ISH 0017 isH.ooin ISN 0019 ISN 0020

ISN 0021 ISH 0022 ISN 0023

ISN 0024 ISN 00 25 '

ISN 0026 ISN 0027 ISN 0028

ISN 0029 ISN 0030 ISN 0031

•OPTIONS TN EFFECT*

•OPTIONS EFFECT*

METHOD INTERPOLATION I? DONE BY MEANS 0* SITK"')'! SCHiM" OP LAGRANGE INT^RPOIATTCK. ON PEfJFN Y COI-AIHS »?! T,IT'-F!PC!.»-'EI) FUNCTION VALUE AT PCTNT X. <4HICH IS IN T I P SENSE OF REMARK (3) CFTIMAI WITH PFSr»CT TC GTVEII T >BLP. "OR RPFFREKC*. SÊ V.B. HIIDEEFANtl, INTRCClUCTICS TO H'lMERTC.U ANAIYSIS, HCGRAW-HILI, HEW YOFr/TOFCKTC/lCKOCN, 1956, PP.49-50.

SUBROUTINE ALT (X ,ARG, VAI ,1 .NCTM .EFS.IEB)

IMPLICIT RIAL*8 (A-H.O-Z) DIMENSION ASG(1) ,VAL<1) IER»2 BBIT2-0.II0 IF (ND1H-1) 26,22,10

STA*>T OE AITRFN-IOOP 10 DO 21 ,3«2,NEII1

DELT1--;.'i:LT2 IEND=3-1 DO 12 1=1,IEHD H=ARG CI' AFG (J) IF (H) 12,34,12

12 VAUJ) = (VAI (I) • (X-AEG (3) ) -VAL (J) * (X-ARG (I))) /H DELT2 = DABS (VAL (J) -VAL (IEHDJ) V (3-2) 2C,20,14

14 IF (DFLT2-EPS) 26,28,16 16 IF (J-5) 2C, 18, 18 18 IF (DELT2-DELT1) 20,30,30 20 CONTINUE

END OF A IT KEN-LOOP

22 J=NDIM • 24 Y=VAl(J) 26 RETURN

THERE IS SOTFICIENT ACCURACY HITCIN NDIM-1 ITERATION STEPS 28 IER=0

GO TO 24 TEST VALUE DELT2 STARTS OSCILLATING

30 IER=1 32 J=IEHD

GO TO 24 THERE ARE 1BO IDENTICAL ARGUMENT VALUES IE VECTOR ARG

34 IER=3 GO TO 32 END

NAHE= HAIH,OM=02,LIHECHT=60,SIZE=G0fl0K,

SOURCE,EBCDIC,NOLIST.NCEECK.LCAC.NOKAE.NOEDTT.HOIC.NOXRFF

570 580 590 600 6 1 0 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 POO 8 1 0 S20 810 840 850 860 870 880 890 900 910 920 930 940 95(7 960 970 980 990

1000 1010 1020 1030 1040 1050 1060 1070 1080 1Q90

• STATISTICS* SOORCE STATEMENTS = 30 .PROGRAM SIZE = 738

417

•STATISTICS* WO DIAGNOSTICS GEREEATEC ••••*• BHD OP COMPILATION »••••* 129R BTTES OF CORE NOT OREl

418

CS/360 EOBTSAB H COI1PIIEB CPTTONS • BABE* MlIH ,OPT.02,LIHEC*T»60,S12I«0000K,

SOOPCE,EBCDIC, NOITST,NODICK.ICAD,MHAP,HOSDIT,NOID.HOXR;!F C 10 c 2 0 c 30 C SOBROUTIHE A1SB 40 C 50 C POBFOSE 60 C BOTH POINTS OP A GIVEN TABIE RITB BCBOTOBXC ARGOHERTS ARE 70 C SELECTED ABD ORDERED SOCB TRAT 80 C ABS(ARG(I)-X).GE.ABS(ABG(J)-X) IE I.CT.J. 90 C 100 C OSAGE 110 C CALL A1SH tI,Z.P,IB01l,ICCI,APG,VAL,RDIR) 120 C 130 C DESCRIPTICH OE PARAMETERS 100 C X - THE SEARCH IBGOHENT. 150 C Z TBE VECTOF CF ARGCNEHT VAXDES (DIMENSION IRON). 160 C TBE ARGOHENT VALUES MOST EE STORED IN INCREASING 170 C OR DECREASING SEQUENCE. 180 C F - IB CASE ICOL=1, I IS THE VECTOR OF FUNCTION VALUES 190 C (DIMENSION IRON). 200 C IH CASE ICOI*2, F IS AN IPCS BT 2 MATRIX. THE FI1ST 210 C CCLDRH SPECIFIES THE VECTCF OF FUNCTIOH VALUES ABE 220 C TBE SECOND THE VECTCB OE tERIVATIVES. 230 C IRON - THE DIMENSION OF VECTOF Z AND 0* EACH COLUMN 200 C IB MATRIX F. 250 C ICOL - THE NORBEF CF COtEMBS IB E (I.E. 1 OR 2) . 260 C ARG - THE RESULTING VEC1CB OF SEIECTED AND ORDERED 270 C ARGUMENT VALUES (CIMFRSION BOIM). 280 C VAL - THE RESOLTIRG VECTCB OF SELECTED FUNCTION VALUES 290 C (DIMENSION SDIH) IB CASE ICCL=1. IB CASE ICCL=2, 100 C VAL i s THE VECTOR OF FUBCTICN AND DERIVATIVE VALUES 310 C (DIMENSION 2»NDIB) VHICB ARE STORED IB FAIRS (I.E. 320 C EACH FtJNCTIOH VALUE IS "OXIOWED BY IIS DERIVATIVE 330 C VALUE). 340 C NDIR - THE NUMBER CF POINTS NHICB MOST BE SELECTED OOT OT 350 C THE GIVES TABLE (Z,F). 160 C 170 C REMARKS 380 C HO ACTION IH CASE IBCH LESS THAN 1. 390 C IF INPUT VALUE NDIH IS GREATER TflAF IRON, THE PPCGSA'J 400 C SELECTS OBLT A MAXIMUM TABIE CF IBCB POINTS. THIPEFPBS THE 410 C USER OUGHT TO CHECK CORRESPONDENCE EETWEKU TAELE (ARG.VAL) 420 C AND ITS DIMENSION ET CCHEAEISON CF NDIN ANO IH0«, IN OBDER 430 C TC GET CORBECT RESUITS IN FORTH"F «CBK WITH TABLE (ARG,VAL). 440 C THIS TEST BAT BI DOSE BFEOPE CR AFTEB CALLING 450 C SUBRCUTIHE ATSB. 460 C SUBROUTIHE ATSH ESPECIALLY CAB BE CSED FOR GENERATING THE 470 C TAELE (ARG.VAL) BEEEEn IH SUEBOUTIBES ALI, AHI. AND ACFI. 480 C 490 C SUBBOUTIHES ABD FUNCTION SUBPPCGFABS FEQUIRFD 500 C BOBF 510 C 520 C METHOD 530 C SELECTION IS DOBE BY SEARCHING THE SUBSCRIPT 3 OF THAT" 540 C ABGUBEHT, NHICH JS NEXT TO X (BIKARY SEAECH) . 550 C AFTEBBARDS NEIGHBOURING ARGDBFNT VAIDSS ARE TESTED ABD 560

419

<r SELECTED i * THF »ec»r S»NSE. *>?c c ">80 c 590 c IOC

ISH 0 0 0 2 snnRooim n s H ( * . z . r . i s c s , i c c i . » F G , v » T . u i i | 610 C 62C c 630

IS* 0003 THPIXC2T REAL*e (A-H.G-Z) 640 IS* 1004 CIHEISIO* 1(1) ,r»1t .A*S(1) 650

c 660 C CHS! IR0«»1 IS CHECKER COI 670

TS* 0001 ir (IRCN-1) 59.5C.10 680 ISN 0006 10 N'NPIN 690

C 700 C IF W IS GREATER THAN IRON. N IS SIT ECOSl TO IRON. 710

ISN 0007 I* (N-IROV) 10,19,12 720 ISH 010» 12 H*IROH 730

C 790 C CASE IR0H.CE.2 750 C SEARCHING FCR SOESCRIPI J SOCK IEAI Z<0) IS NEXT TO *. 760

ISH 0004 14 IF (2(IRON)-F (1) ) 18,16,16 770 TSN 0010 16 J=IRCB 780 TSN 0011 I»1 790 TSN 0012 GO TO 20 800 ISN 0013 18 I-IEOH 810 ISN 0014 J»1 820 ISN 3015 20 K»(J*I)/2 830 TSN 0C16 I* (X-Z(R)) 22.22,24 840 ISN 0017 22 850 ISH 0019 GO TO 26 860 ISN 0019 "24 I=K 870 ISN 0020 26 I® (lABS(J-I)-l) 28,28.20 880 ISN 0021 28 ir (DABS (Z (J)-X)-DABS (2(1)-;:)) 31,32,30 890 ISN no2? 30 J=I 900

C 910 C TABLE SELECTION 920

ISN 0023 32 K=J 930 ISN 9024 JL=9 940 ISN 0025 JP=0 950 ISH 0026 DO 98 1=1,N 960 ISN 0027 ARG(I)«Z(K) 970 ISN 0028 IF (ICOL-1) 36,36,34 98C ISN 0029 34 VAL(2«I-1)=F(K) 990 ISH 0030 KK=K+ISOH 1000 ISN 0031 VAL(2»I)«F(KK) 1010 ISN 0032 GO TO 38 1020 ISN 0033 36 VAL (I) =F (K) 1030 ISH 0034 38 JJR-J+JR 1040 ISN 0035 IF (03R-IRCH) 40,44,49 1050 ISN 0036 90 001=3-31 1060 ISN 0037 IF (JJL-1) 46,46,42 1070 ISN 003** 42 IF (DABS (Z(JJR«1«-X)-DABS (Z(3JL-1)-X)) 46,46,44 1080 ISH 0039 44 JL=JL*1 1090 ISN 0040 K=J-JL 1100 ISN 0041 GO TO 48 1110 ISN 0042 46 JR*JR«1 1120 ISN 0043 K=J»JR 1130 ISH 0099 98 CONTINOE 1140

420

ISN 3Q«S BROBB 1150 1160

C CASE I10l>1 1170 ISN 00S6 so » a c ( i ) » z ( i ) 1180 ISN 00<7 TAI(1)«T|1) 1190 ISR 00l(t IP (ICCt-2) SO,52,51 1200 ISN 0009 52 FAl(2)«F(2) 1210 IS* 0050 SI FETDN* 1220 IS* 0051 END 1230

•OPTIONS IN EFFECT* NAME- BAIB,OST»02,lINrC*T-60,SIZE«COCCK, •OPT 10IS I* EFFECT* SOOBCE,iecDIC,*OLISt,*OPECR,ICAt.NCF*I,»OEDXT,NOID,NO*SFF •STATISTICS* S908CE STATEMENTS « 50 .PBCGRAB SIZE " ">80 •STATISTICS* *0 DIAGNOSTICS GENERATED ••*»• END OP COHPXLATXON ••••»• 12IK BTIES OF COSE NOT DSE9

421

IS* 0502 IS* 0003 IS* 000* IS* 0005 IS* 0306 IS* 0007 ISK 0008 IS* 000® IS* 0010 IS* 0011 IS* 0012 IS* 0013 IS* 001B IS* 0015 IS* 0016 IS* 0017 is* ooia IS* 0019 IS* 0020 IS* 0021 IS* 0022 ISM 0023 ISR 0029

CS/360 FOSTFA* H COPFILSB CPTIOBS - ««!• R»I*.OPT»0;.lIRHCFT*6C,SIJt«OOOOR.

SOOFCE.EECDIC.BOlIST.NODICN.lCAB.BCEAP.NOEBIT.liOIB.NOXaFF

IE

1010

SOBKOOT1NE eOTZ(SK.BT,1CT) OOTZ 10 IMPLICIT BEAI*B (A-H.C-I) OOTZ 20 COBH9N/7./NZSF, NOBM. 2 ( 1) OOTZ 30 REAL*® ANAE OOTZ 90 DIBEBSION a*lil (8) OOTZ 50 PAT A ANA V • B'. • 01. • , >T« , «CX 1 * - » W W , •CB3*,'CB«'/ C0TZ 60 **KX*KT 0"TZ 70 B»BK** OOTZ 80 IR=9* (KX*BY)•* OOTZ 90 IH1«8*N*2*B*IB OOTZ 100 L*NK*tl OOTZ 110 BO 12 N«1,2 CBTZ 120 PFINT 1000,K OOTZ 130 no 1 0 J»1,l OOTZ m o Il«IH*1 OOTZ 150 IH«IH*N COTZ 160 PRINT 1010tA»AB<3). (I(T) ,I«IL,IB) COTZ 170 CONTINOF 00 TZ 18C IH«IH1 00 T2 190 arTOSN OOTZ 200 FORMAT('1VALOES SHE* B«1, EERIYATIYES SB«B K»2. K«'I2) OOTZ 210 FORMATJ//ir,A«/(1P10E13.5)) OOTZ 220 ENO OOTZ 230

•OPTIONS I* EFFECT* NAME* BAIB,0ET»02,LIBECBT»6C,SIZE=COCCB, •OPTIONS IN EFFECT* SOOHCE, f ECDTC,HOIIST, NOCECK, LCAE, NCEA f , NOEDIT,*OID, HOXRSF •STATISTICS* SOURCE STATEMENTS * 23 .PBOGBAH £171 = 650 •STATISTICS* BO B1AGNOSTICS GEBEBATEB *•**«• END OF COMPILATION «***•• 129K BYTES OF COBE NOT OSED

422

CS/360 FORTRAN H CQHEI1PR OPTIONS - NABE« NAIN,OPT=02,LINEC»T=60.STZE=0300K.

SOORCE,EECDIC,NOIIST,NCBICF.ICAD,NC1AP,NOFDIT,NOIB,KOXREF ISH 0002 SUBROUTINE EtOTX(IHPIT) PLOT 10 ISN 0003 ItlPLICIT RIAL'S (A-H.O-Z) PLOT 20 ISN 0004 COnHON/ODT /HR.KX.KT.BRM.IXO.ITO.IHO.m,m,I«SO.nO,ITTSOO.ICKO PLOT 30 ISH 0005 COEBON/BROB/TIH.OIB.Tfl.PEBIOC.IT.NBCVE.LECVE.N PLOT 40 ISN 0006 COHRON/COHBIF/ ANL,ATHP,CPIJ,CKIJ(4),CKIPJ(4),CKIBJ(4) ,CKIJP(4) , PLOT 50

> CKIJK(O) ,rXH.0XF,EYB.ETF,CXIP1.CYJP1,CXlI,DXRI,CXLI1,EXHI1.DYI.l .PLOT 60 > DTRJ,BYI31,:YR31,GBX3,GKEIJ(4).CBTJ,Q*BIJ(4).SBXIJ.SBYIJ.GXXBJ . PLOT 70 > eXTPJ,GYI3Rt6YI3P,GTI.J,GKTIJ(B) ,QTTJ,CKT1J(4) ,STXTJ,STTIJ,QDVI.J .PLOT 80 > QXIBJ,QXIF.).QYIJR,CYT3P,GKXI3J(«) ,GK5tI?J(4) .GKYIJH(4) ,GKYIJP(4) .PLOT 90 > HTFIJ (4) , BTKIJH (4) ,£IIKIPJ (4) ,BT*IRJ (4) , B1KT JP (4) . HIJ, HIJR.HIP3 , PLOT 100 > HIR3,HT3P,UIJ.UIJR,UIF3.UIH3.0IJP,?IJ,VTJt!,TIPJ,VIflJ,VIJP,TIJ . PLOT 110 > TUH,TIPJ,TIHJ,TUP.PCKTFr(4) ,RCIJ,R0XJ!!,R0IP3.R0IflJ,?0IJE . PLOT 120 > SHFTPD(4),SHTCKC(4),SBTTPD,SXXI»J,SXXIPO,STYIJR,SYYIJP.SXYIJH , PLOT 130 > SItIPJ,SXTieJ,SXTIJP.BCIHOB,RCIMC.FCIJet,aOI3PD,EQTRP,TBia , PLO- 140 > HCIHJ,BCXP.l,SCI3H,HCI3P,GB,R0CKt(4) ,SEHT» (4) , BENSK (4) .ROBKIJ (4) ,PLO? 150 > GFBVIJ(4) #tXI,DY3 ,Qnt(25),RBB(25),BBE(25).VBE(25) ,TBB(25). PLOT 160 > CKBB{4.25) .TBIJ.HCBIJ .CCRBIJ (4) .BTKETJ (4) .BNXJ.OBIJ.VBU ,"-<BX3. PLOT 170 > POBIJ,HTBIJ,CKBI3(4).TTI3.HCTI3.ECKTI3(4),HTKTI3(4).DTIJ.VTIJ, PLOT 180 > «TIJ,R0TIJ.BTTIJ,CKTI3(4) ,QBB<25) ,GBC(25) ,GKBB(4.2S) .SBDM25) . PLOT 190 > SBDSB(25).SINB.VINDX.NINDT ,13,IS1J,TEIJ,I3H1.IJP1.INTRT.KOIJ. PLOT 200 > KOI513,KOIE13,KOI3B1.K3IJP1 ,NBXH,BBXf,XEYB,NEYF,NBEGTS,*BSB? , PLOT 210 > IXQF (25) ,3YQV (25) ,NB£:BTP (25) ,RBEBTF (25) ,K»BBTP (25) .NTBBTP (25] . "LOT 220 > HXGBL,RYGBI,NBEG,NIH71F,HT0PF,BEC1F,*TEITC,RTRAI,HGEBF FLOT 23"

ISH 0007 COHROH/Z/NZSf,NC0B,Z(1) PLOT 240 C PLOT 250

ISH 0008 IPLTF"8 FLO7* 260 ISN 0009 IF (INPIT.BE.O) GO TO 14 PLOT 270 TSH 0011 DO 10 1=1,KX PLOT 2P0 ISN 0012 RB ITS (IPLTS) I, Z (1X0*1) FLOT 290 IS* 0013 10 CONT1BBE PLOT 300 ISH 0014 BO 12 J-1.NY PLOT 310 ISK 0015 »PITE(IPLIF):,Z(IY0»J) PLOT 320 ISR 0016 12 CONTINUE SLOT 330 ISN 0017 14 VfilTE(IP1TFJTH,PEBZOC,IT,DTB PLOT 340 ISN 0018 KOIJS»ICKO PLOT 350 ISS 0019 DO 20 X>1,RK FLOT 360 ISR 0020 IJ»I PLOT 370 ISR 0021 K O W K O M S PLOT 380 ISN 0022 DO 18 J*1,RT FLOT 390 ISH 0023 16 RRITZ(IPlTF)Z(IHO*IJi.Z(IUO*IJ) ,Z(I»0*I3), ZJINSOÎJ) ,Z(IT0*IJ) . PLOT 400

> Z (ITTBB0»I.7) , (Z (K0IJ*K) ,K«1 ,*K) PLOT 410 ISN 0024 K0Id«K0IJ»SK»X PLOT 420 ISN 0025 18 IJ«I3*KX PLOT 430 ISN 0026 20 K0IJ5*K0IJS+VK PLOT 440 ISR 0027 BETORB PLOT 450 ISH 0028 EBB PLOT 460

•OPTIONS IN EFFECT* HARE* BAX*.OFT«02,LIHECHT»60,SI2E«00C0K, •OPTIONS IN EFFECT* SOORCE.EECDIC.BOIIST.HOtECIS.ICAB.IICSAE.HOEDIT.HOID.ROXFEr •STATISTICS* SOOBCE STATEHEPIS » 27 .PBCGBAR SIZE « 716 •STATISTICS* BO DIAGNOSTICS GEB1BA1EE *•**•• END OF COBPILATIOR •*••*• 121K BITES OF COPE NOT OSEB •STATISTICS* HO BIASNOSTIC3 Ills STEP