X-551-68-1167 PREPRI NT

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

B ROSENBAUM N SNOW shy

$GPO PRICE

CFSTI PRICE(S) $

Hard copy (HC)

_ q MAY 1968 Microfiche (MF)

ff653 July 65

GODDARD SPACE FLIGHT CENTER GREENBELT MARYLAND

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X-551-68-367

Preprint

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

13 Rosenbaum N Snow

May 1968

GODDARD SPACE FLIGHT CENTER Mission amp Trajectory Analysis Division

Greenbelt Maryland

Bendix Employee under contract to GSFC Contract Number NAS 5-10750

PRECEDING PA3E BLANK NOT FIL-M

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

B Rosenbaum N Snow

ABSTRACT

The ray path of an RF signal undergoes bending in the interval of atmosshypheric propagation between a satellite and an earth-based tracking station Resultant refraction is a perturbation on observed elevation angles and Doppler shifted signals As a practical tool for the computation of corrections a matheshymatical model simulating the tracing of the refracted ray path has been proshygrammed for use by the Goddard Space Flight Center computer facilities

ii

PRECEDING PAGE BLANK NOT FILAED

CONTENTS

Page

ABSTRACT

I INTRODUCTION 1

II REFRACTIVITY MODEL 1

1 Relation of Refractivity to the Index of Refraction 1 2 Tropospheric Refractivity Profile 2 3 Ionospheric Refractivity Profile - Chapman Model 2

III METHOD OF COMPUTATION 2

IV USERS GUIDE 5

1 Introduction 5 2 Programming System 5

3 Required InputOutput Units 5 4 Restrictions 5 5 Input 5 6 Output 7

7 Program Listing 14

V REFERENCES 17

ILLUSTRATIONS

Figure Page

1 The Geometry of the Ray-Tracing 3

V

LIST OF SYMBOLS

c reciprocal scale height of troposphere (km

f signal frequency (MHz)

h altitude (km)

h altitude of Nm

-2H scale height of the ionosphere

n index of refraction

N refractivity

Ne electron density (m 3)

Nm maximum of the N profile

r radial distance (kin)

r o earth radius (km)

3 true elevation angle at earth surface

8 refraction angle at satellite

6 refraction angle at earth surface

0 elevation angle at satellite

Stotal bending angle

vi

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

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00

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1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

X-551-68-367

Preprint

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

13 Rosenbaum N Snow

May 1968

GODDARD SPACE FLIGHT CENTER Mission amp Trajectory Analysis Division

Greenbelt Maryland

Bendix Employee under contract to GSFC Contract Number NAS 5-10750

PRECEDING PA3E BLANK NOT FIL-M

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

B Rosenbaum N Snow

ABSTRACT

The ray path of an RF signal undergoes bending in the interval of atmosshypheric propagation between a satellite and an earth-based tracking station Resultant refraction is a perturbation on observed elevation angles and Doppler shifted signals As a practical tool for the computation of corrections a matheshymatical model simulating the tracing of the refracted ray path has been proshygrammed for use by the Goddard Space Flight Center computer facilities

ii

PRECEDING PAGE BLANK NOT FILAED

CONTENTS

Page

ABSTRACT

I INTRODUCTION 1

II REFRACTIVITY MODEL 1

1 Relation of Refractivity to the Index of Refraction 1 2 Tropospheric Refractivity Profile 2 3 Ionospheric Refractivity Profile - Chapman Model 2

III METHOD OF COMPUTATION 2

IV USERS GUIDE 5

1 Introduction 5 2 Programming System 5

3 Required InputOutput Units 5 4 Restrictions 5 5 Input 5 6 Output 7

7 Program Listing 14

V REFERENCES 17

ILLUSTRATIONS

Figure Page

1 The Geometry of the Ray-Tracing 3

V

LIST OF SYMBOLS

c reciprocal scale height of troposphere (km

f signal frequency (MHz)

h altitude (km)

h altitude of Nm

-2H scale height of the ionosphere

n index of refraction

N refractivity

Ne electron density (m 3)

Nm maximum of the N profile

r radial distance (kin)

r o earth radius (km)

3 true elevation angle at earth surface

8 refraction angle at satellite

6 refraction angle at earth surface

0 elevation angle at satellite

Stotal bending angle

vi

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

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03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

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c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

PRECEDING PA3E BLANK NOT FIL-M

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

B Rosenbaum N Snow

ABSTRACT

The ray path of an RF signal undergoes bending in the interval of atmosshypheric propagation between a satellite and an earth-based tracking station Resultant refraction is a perturbation on observed elevation angles and Doppler shifted signals As a practical tool for the computation of corrections a matheshymatical model simulating the tracing of the refracted ray path has been proshygrammed for use by the Goddard Space Flight Center computer facilities

ii

PRECEDING PAGE BLANK NOT FILAED

CONTENTS

Page

ABSTRACT

I INTRODUCTION 1

II REFRACTIVITY MODEL 1

1 Relation of Refractivity to the Index of Refraction 1 2 Tropospheric Refractivity Profile 2 3 Ionospheric Refractivity Profile - Chapman Model 2

III METHOD OF COMPUTATION 2

IV USERS GUIDE 5

1 Introduction 5 2 Programming System 5

3 Required InputOutput Units 5 4 Restrictions 5 5 Input 5 6 Output 7

7 Program Listing 14

V REFERENCES 17

ILLUSTRATIONS

Figure Page

1 The Geometry of the Ray-Tracing 3

V

LIST OF SYMBOLS

c reciprocal scale height of troposphere (km

f signal frequency (MHz)

h altitude (km)

h altitude of Nm

-2H scale height of the ionosphere

n index of refraction

N refractivity

Ne electron density (m 3)

Nm maximum of the N profile

r radial distance (kin)

r o earth radius (km)

3 true elevation angle at earth surface

8 refraction angle at satellite

6 refraction angle at earth surface

0 elevation angle at satellite

Stotal bending angle

vi

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

PRECEDING PAGE BLANK NOT FILAED

CONTENTS

Page

ABSTRACT

I INTRODUCTION 1

II REFRACTIVITY MODEL 1

1 Relation of Refractivity to the Index of Refraction 1 2 Tropospheric Refractivity Profile 2 3 Ionospheric Refractivity Profile - Chapman Model 2

III METHOD OF COMPUTATION 2

IV USERS GUIDE 5

1 Introduction 5 2 Programming System 5

3 Required InputOutput Units 5 4 Restrictions 5 5 Input 5 6 Output 7

7 Program Listing 14

V REFERENCES 17

ILLUSTRATIONS

Figure Page

1 The Geometry of the Ray-Tracing 3

V

LIST OF SYMBOLS

c reciprocal scale height of troposphere (km

f signal frequency (MHz)

h altitude (km)

h altitude of Nm

-2H scale height of the ionosphere

n index of refraction

N refractivity

Ne electron density (m 3)

Nm maximum of the N profile

r radial distance (kin)

r o earth radius (km)

3 true elevation angle at earth surface

8 refraction angle at satellite

6 refraction angle at earth surface

0 elevation angle at satellite

Stotal bending angle

vi

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

LIST OF SYMBOLS

c reciprocal scale height of troposphere (km

f signal frequency (MHz)

h altitude (km)

h altitude of Nm

-2H scale height of the ionosphere

n index of refraction

N refractivity

Ne electron density (m 3)

Nm maximum of the N profile

r radial distance (kin)

r o earth radius (km)

3 true elevation angle at earth surface

8 refraction angle at satellite

6 refraction angle at earth surface

0 elevation angle at satellite

Stotal bending angle

vi

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

A PROGRAMMED MATHEMATICAL MODEL

TO SIMULATE THE BENDING OF RADIO

WAVES IN ATMOSPHERIC PROPAGATION

I INTRODUCTION

The ray path of an RF signal undergoes bending in the interval of atmos shy

pheric propagation from a satellite to an earth-based tracking station The

refraction introduces a perturbation on tracking measurement of elevation angle

and measurement of Doppler shift and its conversion to range rate Correction of the effect can be performed through a calculation of the finite refraction

angles between the line-of-sight and the ray parli at both the emitter and receiver

This document presents the mathematical model and its associated computer program to simulate the ray tracing of a signal path in a spherically stratified atmosphere While many such routines performing similar traces exist (Refershy

ence 1) they are not adapted to the newly installed IBM 360 computers at Goddard Space Flight Center (GSFC) This program has been checked out and run at GSFC on computer models IBM 36091 and IBM 36095 An exponential model is used for the tropospheric refractivity profile and the Chapman function is used for the ionospheric profile The refraction effect on elevation angle attributable to the troposphere and ionosphere can thus be calculated from a single routine The computation procedure is essentially that of the National Bureauof Standards tropospheric ray tracing program (Reference 2) A sample calculation is inshycluded in Chapter IV Users Guide

H REFRACTIVITY MODEL

The following equations were used in the construction of the refractivity model

1 Relation of Refractivity to the Index of Refraction

The relationship of refractivity N to the index of refraction n is expressed by the equation

N (n- 1) x 106

1

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

2 Tropospheric Refractivity Profile

The exponential tropospheric refractivity profile is expressed as

N(r) = N(r 0 + h) = N e-ch

where

0 lt h lt 50 km

3 Ionospheric Refractivity Profile - Chapman Model

The refractivity in the ionosphere is a function of free electron density Ne and signal frequency f as expressed in the following equation

-4038 x 106 N(r 0 + h) N(r) = 2

where

hgt 50 km

The altitude profile for electron density is given by the Chapman function

- z)Ne = N exp 12(1- z - e

where

(h - h) z

H

II METHOD OF COMPUTATION

The ray tracing procedure divides the atmosphere into a series of thin laminations (Figure 1) The refraction between consecutive layers is then folshylowed SnellTs law which for a spherically stratified medium is given by

ni r cos 0 = cos 00 n o r o

2

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

Figure 1 The Geometry of-the Ray-Tracing

3

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

is the basis for the calculation This is rewritten for computation purpose

as

r - re (No- N) sin 2 (6i2) - 2 sin 2 (802) + r n x 10-6 cos 60

The incremental bending angle AT is determined by the general formula

An AT = - cos 0

n

Between the 1 th and (i + i)th lamination the bending A-i is calculated by

the expression

(Ni - Ni+) c ( 2) AT (ni + ni+)2cot i +

The total bending is given by

I

LEAT j=1

The error in the computation of r1 is made small by making the laminations

sufficiently thin

The refraction angle is calculated from the formula

Cos Ti - sin Ti tan 6i - nin0 tane i = (nn 0 ) tan 60 - sin T i - Cos T tan Oi

and the refraction angle 8i can be calculated by the formula

4

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

non i - cos T - sin 7- tan 00

sin r - cos T tan 00 + (noni) tan 0

The relation - = + S can be used as a check on the computation

IV USERS GUIDE

1 Introduction

This program computes the bending angle of radio waves in atmospheric propagation

2 Programming System

The program is written in double precision FORTRAN IV compiler language It is operational on the IBM 360Model 91 and Model 95 computers

3 Required InputOutput Units

No special equipment configurations are required Input is a source card deck and data cards Output is a standard printout

4 Restrictions

There are no restrictions on this program

5 nput

The following values are read into the computer in a D102 format

(1) The reciprocal scale height of the troposphere (c)

(2) The maximum electron density (N)

(3) The initial value of the refractivity (NO)

(4) The signal frequency in megahertz (f)

(5) The scale height of the ionosphere in kilometers (2H)

(6) The height of N (hm) and

5

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

_____

(7) The initial value of the angle between the ray path and the-radius vector in radians (60)

A sample input data card is shown below

156Sl-2 P00O 34451D+G1 1SEP+C 7SID+ 00 73 O0 404

jIt)(2) (3) (4) (5) ()(7) 000000 0i 0 00000 000 00000000 0000000 O O00000 0000 0 000000000 1 2 3 4 5 6 7 a 112 M1415 TO 7181 22 22232425227282953031323334353$373839404142434445464748495 51525354555657585960 I66364966667b86970 n 7374n76 V7879801 11111111~111111111 111111111 11 11111111111 11111111111111 1111111111111111 111

The following Job Control Language cards are required to successfully execute the program

C C

DSNAS033bJOBb(G700H310TDA002300005) 608MSGLEVEL=1 bEXECbFORTRAN SOURCESYSINbDDb

SOURCE LANGUAGE PROGRAM

C C

bEXECbLINKGO GODATA5bDDb

DATA CARDS

C C 1

CC = Card Column

b = blank column

6

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

6 Output

The values of the following parameters are printed as the input value of H is incremented by the program to its predetermined maximum (3000 kin) Forshymat is indicated following the parameter

H (altitude in kilometers) F 71

N (refractivity) E 155

Ni - Ni+ 1 (difference between successive values of N) E155

e (angle between ray path and radius vector in milliradians) E155

AT (discrete portion of the bending angle in milliradians) E155

7- (bending angle in milliradians) E155

(refraction angle at the earth surface in milliradians) E155

8 (refraction angle at the satellite in milliradians) E155

6 + S (the sum of epsilon and delta in milliradians) E155

In addition initial values and constants used in the equations are printed A sample output follows

7

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

12 14

028541E C3 027660E O

08PIt3F 01 05306E 01

4CC31 0400305

03 03

12148F-0 02015E-01

3lQ06E 00

01647 O0

071942-01 D30997

-01

l711 -l

0 7 7

13 F -I

o36600

C0306F o0

36 1

026806E C3 025978E 0

0e2750F 01 0802C4F 01

00041F C40047F

13 03

)20171c-oI 0309tS-01

3116 00 CPOIF 00

C4024E-01 010413F 00

DS6617-0I V-54 5-O

164F 00 n2001

o OD

20 025176E 03 077728F 01 0403525 03 01R930F-DI 0t913F 3D n1352F 00 0l05F CO 031111F 00

22 024399E 03 075128E 01 040055F 03 3S32F-O1 m13744F 00 C1540 90 3 3 1 9 CC r9 P 3 74q O0

24 024646E 03 073003E 03 040061W 03 17q3E-01 01 56F 00 013516F 00 307 on IOq26F 00

26 022915F 03 07074OF 03 CA0069F 03 017715-OI 11749F 00 145ampE 00 11701r 0 PT740E 00

28 022208E 03 06896E 01 0400755 03 D1669hF-01 flpPP0F 00 P155015 OC 333410F 0C 02po0F 00

30 021523F 03 066448E 0 C400lE 0 116178F-CI C30S3Tr CO 0164543 00 01051F o0 03537F 10

32 34

0208585 03 020214E 03

0643qb 062408F

01 01

C400865 03 040302F 0

015677F-01 ItI1IOF-O

03PI04F CO 213623E 00

017384F 00 Cl 2CW 00P

017211 1533

0

32104F 33403

00 00

36 019590E 03 0604F25 01 040008F 03 36710F-C3 n39009F O0 O10t490 0 O1 Ior C D904F CC

38 01898SE 03 058614F 03 040104F 03 DI42A2E-0I 016921E 00 OICSF 0 016465 02 06521E 00

40 49

018399E 03 01701e O

013874C O 0122PF O

040110- 03 040125F 03

)I3P20E-nl )3170F-01

03703S 00

D41174F O0

0200ISl 00

0221A4 00

D63SRF 0 31710C

P3$102r00 06174 PC

00

50

55 60 65

01572qE 03

014543E 03 013446E 03 012432E C3

011861C 02

010066F O 010IF 02 093747C 01

040141 03

040157F 03 C401725 0 04018e O

23023F-01

027-33E-01 025A19F-0I 3238585-Cl

0449 5f 0

4(9AQ4 CO n4057F 00 rt57C 00

4049F 00

2462p2 00 CA0

c 0

30345 00

0104 7F 0 I441-AEO

016F 00 044080F 00 O230643 0POdeg4W73 00 21640r D 051057F o6

70

75 80

011495F 03

0106268F 03

098268F 02

086o79E 01

080142r 01

07409F 01

040205F C3 040221C 03

040239F 03

O2OCOF-o0 3203743--03 A34433C-01

054162F 00 0561q9 00

C580slr 00

31920E o0 033479C 0

034050 =

00

02213PF 00 0P272A4 0

02l31p3 00

q51ApE 3561005 O0S33F

o 00

00

85 090856E 02 068S32F 03 043SF 03 31740E-01 C59823E 30 03639$F 00 023465F 0 00

90 0840065 02 063345F 01 040271E 01 0I60S5F-CI 061432F 00 C1770PF 0 0272o9 0 61412 00

95 077672E 02 05859c 03 0402SRF 03 314R65F-01 C52915F 00 D3Pqf6 00 030o O F 062O30

100 330

071815E 02 061393E 02

010422F 02 8a006r Cl

040305F 01 040330E 01

01373RE-01 0244C-C01

054O2F 00 066719E 00

34021F O0 04

V 504F 00

0240eF 9P2431F

C0 90

0e423 166F

00 OP

120 052483E 02 076165C 03 0403745 03 020=64-01 06ASII 00 0446I 03 OP12OF 03 068921F 00

130 0448675 0 065113E 01 04C409F 03 017819E-01 070603F 00 04652ampE 00 0247OE 01 0706015 00

140 0383555 02 055bt3c 01 040444F 03 015210F-0I 071129q 00 049E 00 C21 A 00 072125 PO

190 032780E 0 C17I3F O 040470Q3 03 012qqF-03 0342SF 00 349913E 00 923512F 07 973425r 00

200 014971E 0 03150 02 040657F 03 141495F-01 7753F 00 056271E 00 02102F 0 7075 O

300 03120P0 01 0472F 01 C430165 03 02734AP-01 O80312F 00 063767q 00 01695S 01 O012F On

400 ObO57F 00 051499F 00 041372r 03 096535F-02 090877 00 67q235 00 0325qF 00 0077F 00

500 01356E 00 026738F 00 P41725P03 1167-00F--O OOqq4F 00 070493 30 IIC51F 00 0C904F 00

600 -013176E 00 032622E 00 04075F 01 060035F--P3 091054F 00 072259 00 OS845F-Ot O381054F 00

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

-079882E 03 -030754F 02 0512510 03 -39070F--0 2334F 01 3600 -082800E 03

0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

-031003E 02 050O 03 -054624F-01 010076F 031 degI615 0 Co6OF 03 0007F 00 J444F 014300 -06075q6 01

-s3l4F10I 020444 02 016831 03 015051 01 0117194 0 31l 014400 -057649E 03 -030256F 02 053CS6E 03

4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

RENDING nF VA01n W4VFS IN ATMnSPHFOIC PRnfAGATIOI

Nm = 0424A50 12 HM 33073 H = 7811 NO = 14450

INITIAL THETA = 40000 C = 0IbA F = 016000 0 DO = 61701

ALL ANGULAP M A4OPFMFNTq ARF IN MILLIADIAN9

H N NIt) - N(I1) THETA 0ELTA TAU TAt) FSILON DELTA FPSILON+PLTA

00

01 03

034450F 03

O33q14F 03 032a675 03

0535q6F 01

010470E 0 010147F 02

040OOF 03 04002E 03 C400075 03

0 01267C-01 024753F-01

00 012672F-01 037429E-01

30 3603E0-CIStI-01

O 3RqC- 7 0

a15614F-Ol-

C0 3167P-O 037425E-O

05 07

031852E 030869C

03 03

0983gF 01

C141$4l 0

040012F 03

C40CBE 03

123P-6F-01

J2324PE-01

C61433E-01

0R4643-01

O310550I

0430455-0

003S4F-3

4C 03

61410F-shy

shy 46S3(-OI

10 029450E 03 0909235 01 040025F 03 03519E-01 011817F 00 0602E-oI Io7 6 32r-01 3131] 0

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0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

TAIl EPSTL0N FLi-TA rOOTLnNOFITA N N(1 - 113 THTA 0FLTA TAWH

07444 00 076A2l8-0I 0A82371 0O07596r-03 131127E 00700 -045795E 00 002C7F 00 0442)F 01

0427A C 03 030J44F-02 Jq132F 00 074309l 00 O6015 F-01 0tlt6 00

0l707C 0O 79162F10 0$43144-03 98I7071 00800 -013600E 01 021565F 01 0453280 03 043CnQ0 03 047101F-C

0A027-0 0 77F 0900 -035166E0 01 085026E 01 0434310 01 0I0846-02 nP77R 00 0 505C 00

1000 -080494F 01 03 0I325IF-01 C34603F 00 0765369 00 0CC096 -03 (114601 00

1100 -016952E 0 0144200 02 0437A3 100 8A7671F 00

n440lF 03 1306qlC-01 0S7A7PF O 0773041 09 O368F

10 83413531 00 1921931F 01200 -030972F 02 0223680 02

01 34731I-01 I023031 00 07824001300 -051340E 02 032054V 02 0444050 OC 0 971 00 o0004F 1003 067104r-02 PQ041F 00 070433

1400 -085394E 02 042509E 0 044721F F 01 18002 09 001341 01 030700 02

040321F 03 98540O9F-01 0107q01500 -012820E 01 053693F 00 092900 n0 3261F 0O 011006F 0104537 03 0I1065 00 C11106C 011600 -018190 03 0636600 0

045637 03 013019C 00 013205F 03 085261 00 04631F CI 118C1F 02

03 314164F 00 14664F 01 0O06 1700 -0245566 03 01748F 02

09 n08547 00 n14A64F 01 1800 -0317300 03 C7722Ar 02 04=93PF 1

00317gr 00 01871 00 016221 1900 -034453E 00 0796880 02 046224F 01 0I5563E 00 0 62210 01

P 7 6 F 03

no 31t102 046 531 03 91543F 00 37 5F 03 0q5073C 00 0 30 00 n 01

2000 -047422S 03 07904RF 00470F 09 01031F P1

2100 -055327E 03 075521F 0 0467qRP A3 115704F 00 093cS 03 099123F 00

014898 00 20575F 11 010346- 01 0I92q1 01 JP71 01 2200 -062879E 03 069533F 02 047083C 03

F 01 33Q1700 01 01141n1 0 n2237 03 2300 -06g832E 03 061640F 01 04766F 03 01362F 00 02

023436 01 012AS 01 032173I 01 023476P 2l 2400 -075996F 03 052444E 02 0476486 03 0ollq3F 00

110134F 00 024450F 03 n337350 327151 0t 07445 01 2500 -081241E 03 042525F 02 047930F 0

01 033064r 1 05p61 03048P13E 03 o1611r-91 25241 0t 0122012600 -054g3E 02 032400F 02 0126q 0t 11226- 03 00541 03

2700 -057336 03 022495r 02 044E 0 061755C-01 0258q4F 01 F

013135F C 0487729 03 049qqF-0l 2610E I1 C01099 03 01321 96Cq 0l 2800 -090q83E 02

2000 -0-92296E 03 045169 01 n40051C 03 024702F-01 02655br0 01 033520 03 l03qr Cl 2658 01

027211 92664304331F 03 089021F-02 02f641F 01 P13O0201F 0t 01 03

01 C142040A3 I2QF cl 026584F 013000 -092751E C3 -031149F 01 04060q 0 -7797F-0U2 C265 43100 -092440F 0 -O7944F 03

l 0P6401F 0 3200 -091460 03 -015475E 02 C49P 60 03 -018CR3F-01 0064c3F 01 -14442F 02 9161C

3300 -089913E E

03 -020161F 02 050111F 91 -928336F-01 0263200 03 034062f 01 021 02 02A121F 0

01 753E 93 015215 3 031O4q1 l 5S 01050436F 03 -031721F-01

007084F 03 1 10 n3400 -057894E 03 -023987C 02 C5071R 03 -0473536-01 02-3I1F 01 152plr 91

3500 -065496E 03 -02656F 02 00 o24835 01

-029181F 02 350C1IF 03 -049407F-01 014835F 03 015760 01 60741

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0190750 03 0PI331F - 243t1F ^1 3700

051519 01 -354530E-Pt 037 Q0 03 (1661 02 70021 0r 123760F 01 3900 -076806E 03 -031763r 02 =

02 51785 03 -0550 8F-01 0232006 01 01631102 96R74A 00 13 0F 01

022644F 01 0164526 01 061140 00 171644r 03900 -073630E 03 -01295E

4000 -070401E 03 -012426E 02 052C4C 03 -05695 F-Cl 0546 r 0 122070 01-056416F-01 O207qE 01 0613C 03

4100 -067158E 03 -032220 02 052311F 03 n r 07159 01 016721 01 q4901C O 92I2P1F n3

35572 03 -05575F-01 00 02071 034200 -063935E 03 -031766F 02

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4500 -054624E 03 -020206P 02 053343C 03 -5 416F-01 (200390 0

4600 -051694E 03 -028247E 02 0535deg38 03 -049406F-01 degI495f 01 017011F 01 n2441 00 010435

-048869E 03 -027137F 0 053843F 03 -047450F-01 0I3961 03 0170591 n 03Ol01 00 03 061F 01

0170811 01 nl443 00 O38C07 014700 094091F 03 -04507-0l 085076 014800 -046156E 01 -025991C 0

03807F 031717080-030054139 03 -04316eF-01 0I3076E 01 037t05r

F1 01711A0 03 054761-01 017AFF 014000 -043557E 03 -024526F 02 l

02 0545P2 03 -04100F-C5000 -041074E 03 -0)365q0 9t2601 017p77F 01

5100 -03870P 03 -022501E 02 94S8250 03 -0356F-01 01727F 91 0171249 01 1F

0 -04367606-01 11690o 03 q17121 P3 144100 0l6t0 01 5200 -036458E 03 -021164F 02 055060

0171170 01 -09511-03 36562F 03055301E 01 -034717h-0l 016562F 03 0 91621F nl

5300 -034322F 03 -0022F 02 174F 02 055542r 93 -032732F-01 030351S 01710 -0Q7npo-03

- Io6251 00 03 07F 01540C -032298E 03 -01 01 -030825F-1t 035q2E 1 0170Rq1 O

Ol0A60 -343240 00 256371 015500 -03037QE 03 -018332E 02 05777F

5600 - 028566E 03 -0171100 02 056011- 0 -020800 156371 03 911364 01 C1734 F 0l -03650nE0 0 11364F 01

- 3665 02 05243r 03 -02725IF-015700 -026853E 03 01 01 0170IRq 03 -Q100071 00 0t3051 03

5800 -025236E 03 -035249F OP 0504700 03 - 5 F-01 - 21200 n 1161F 0-0401F-03 01486F 03 016058E 03

5900 -023711E 03 -014173E 0 096702F 03

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

H N(TI - N( 11) THFTA nFLTA TAU TM) FPSTLON nCI TA rOSILnN+DELTA

6000 -072274F 03 -015a0F 0 C$6250 Q9 - ttF-0l 11461 0t rIA056c 01 -0pO 0 14643F n -

6100 -020q2 03 -0214f 02 C37154F 01 -)I11- 4amp3-2F 01 17IF 01 - r 0 14A1 01 1 deg

6400 -O2144E 0 -0IQo5r 02 o573T8r 03 -0lO77TF-0l0l 0143hfI 1= Cl -4S23F 09 O14P 4 01 0 0

300 -shy 011834AE 03 -C2P4r 02 076C 03 -0195-10F1 14 F 01 lAP4o0 01 -0ipl 90 tIflIF 1

600

6500 -0317E 03 -0I65F C3

-010611E 0 deg

-Q0CI 01 S7

0 0 -0t1l3F0-0I78 090C4In3 - 1Ah3F-C

125 01I3 O -0I0331 CS 175F oiIl111F o1 P1676OF SI -I W C0 01913F 01

6600 -015259E 03 -Cn34Qr 01 r-l Cl -11~C -I351r I CI67p SI -nl C6AF 01 lW6r n

6700 -01432W 03 -07oFAF 01 051476C 0l - I4l07r-0l 11g4109 01 1AI7l6 01 -n3)en0r 03 t r

6800 -0112amp4E 02 -C827ampIQ 01 C5qf0I 1i -1l1217F-01 3ol71 1 l6n442 01 -01O1 0 19177F Cl

6900 -012613F 02 -07721r c C3-04- 03 -0Id41r-0l lllf 01 0o OCl -S419W A5 91116F 0i 1

7000 -0118365 03 -072046F 01 01117E n3 - I116 0F-0 13046F 0 9 4550 01 -03Ol4 CC )114Ar nI

7100 -011I06F 03 -C132amp7E 02 0912FA 3 - 20 F-01 112914F 01 0I651cA 1 - 1770F CO 1 2 0 3 q A

7300 -0977CE 02 -0I7IC0E 02 C507465 9 -0l161NF-0I 12747F 0l 0163 91 -e6A0r 01t7418 0l

7500 -086361F 02 -010315C C C00l o -3171-48-0I C1251OF 01 014 3 n 1 - 1171F n 1115 01

F7700 -075747F 02 - Camp01 C604N7F n3 -0I40hlr-0l 0l24IF oI 0l62 -01 no0 1q7r 3 2421C 01

07000 -066663E 02 -079QF18 0 06Cq7l0 03 - 13b0n 9F0 26j75C 3 -3n44 0ol~08

8100 -C5666IE 02 -CC4ISC Cl S61134r 03 -11149E-01 l 112210-0 2C1 02 -0SI065 00 tl21765 02

8300 -051624E 02 -C61177F 01 C61763F 01 -30542E-02 012077 02 16011 01 - 13044 0 I0771 1

8500 -045426E 02 -C5454PF 01 07151F 11 - 9 0 1100n01Cl I22 1 03 4 2

A 108

8700 -03Q07l 02 -0420750 01 0621 C - 760545-C3 011F 01 15Al01 I - 0t04V 01 1 111 01 3 0 0

8900 -035171E 02 -C4271- 01 0oA0177 03 166220F--2 11040F 01 1S77- 01 orlr 00 t11 49 02

9100 -03D046F 02 -C37l79r Cl C6068 )I -)5P8C 1170 01 2SC I -0C161F 0ll-70 1 9 0 0

0300 C02722CE 02 -032712 cl C63AA08 03 -103474F-52 117308 CI01 206300 01l 01 S12l 01

1500 -023057F 02 -0PR7PC 0I 440308 I -)44072C02 111608 ii OSAOF 01 -0fl7A CA 0IC1P9 0

9700 -021079F 02 -32521C 01 C44 3F 11 -004038-02 C1407E SI 11S~ n2-04AC0 11 rC

9900 -018546E 02 -0114-A5 01 064754C 01 -)1305C-02 C12 3 t 111414F 01 0203 C l16098

10000 -0l7Z307E 02 -0I7ERF 0 06494 0 -)l5l72F-n 126C-F 01 A 4 01l - 780 1rCC

20000 -028672C-01 -028A45-Cl 00003C -1l742r-Cl 1141F 02 011710 C1 -ltf01 00 114210

30000 -047013F-04 -C474135-04 040977F 03 -025b46amp-04 01141WP 52 C13r7Rc01 1jAl~ f11OF

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

C

7 Program Listing A complete listing of the program follows

G LEVEL 1 MOD I MAIN DATE = 6812R 195912

DOUBLE PRECISION THETA(125)DELTAU(125)FPS(125)SN(125)AN(IS) IHAUX(6) TAU(125)GAMMA(I25)H(125) VOUBL PRECISION DARSINDEXPDSQRTDATANDTANDCOSTHETAO DOUBLE PRECISION COTHETATHE DOUBLE PRECISION DESUMCGAMIEPAA3DENIDENEDFN3ANUMI IANUM2ANUM3SNO DOUSCE PRECISION ANMHMHHANOFRo ANFZEXIEXPAPGDW F EQUIVALENCE (HAUX(I)H(1)) DATA HAUXODOI00300sC

7 0 0 oO00 100 FORMAT (80102)

DO 40 1=721 40 HCI)=H(I-1)+2DO

D 42 1=2233 42 H(I)=H(I-1)+5DO

DO 43 1=3438 43 HI)=H(I-1) + 10

H(39 =20ODO DO 44 1=40108

44 H(I)=H(I-1)+10000 DO 45 1=109122

45 HI)=H(1-1)+20ODO

H(123=1000000 H(124)=2000ODO H(125)=3000000

PROGRAM STOPS WHEN THFRE ARE NO MORE DATA CARDS TO BE PFAD IN 200 READ(S100END=122) CANMAN0FHHHMTHETA0

ANM=4248550+11 TATHE=DTAN(THETAO) COTHE=DCOS(THETAC) TO=THETAOI 0+3 RO=6373015DO SNO=1DOtANOID-6 EXI=2DO(DSIN(THETAO20))

2 00 62 1=1125 AH=HI)

IF(AHGT500) GO TO 58 AN(I)=ANODEXPC-CH(I)) SN(I)=IDOAN(I)ID-6

GO TO 60 58 Z=(HI)-HM)HH

ANE=ANMDEXP((1DO-Z-DEXP(-Z))200) AN(I)=(-403800ANEn D+6)F2 SN(I)=IDO + AN(I)ID-6

60 CONTINUE EX2=(ANO-AN(T)) SN(t) ID-6COTHE ARG=DSORT(RO(2(RO+H(I))) (EXI +H(I)PO -EX2)) THETAI)=2D0DARSIN(ARG)

62 CONTINUE WRITE(6105) ANMHMHHANOTOCFpO WRITE(6108) WRITE(BI10) ILCNT=14 THETA(1)=THETAO

EPS(I)=OOOO GAMMA(1)=OODO TAU(I)=OODO

11

V REFERENCES

1 Bjork C A and W M Layson Comparison of Refraction Correction Techshyniques PAA Technical Memo No 65 ETV-TM-67-2 (1967)

2 Bean B R and G D Thayer CRPL Exponential Reference Atmosphere U S Department of Commerce National Bureau of Standards (now ESSA) October 29 1959

13