HYDROGRAPH STUDY AND PEAK DISCHARGE DETERMINATION · a flood hydrograph is presented in Figure 2. Since the shape of the flood hydrograph is a steep triangle, two hydrograph parameters,

HYDROGRAPH STUDY AND PEAK DISCHARGE DETERMINATION

OF HAWAIIAN SMALL WATERSHEDS: ISLAND OF OAHU

by

I-Pai Wu

Technical Report No. 30

HAES Journal Series No. 1107

March 1969

This is a report of cooperative research published with theapproval of the Director of the Water Resources Research Centerand the Director of the Hawaii Agricultural Experiment Station.

Project Completion Reportfor

PILOT STUDY OF SMALL WATERSHED FLOOD HYDROLOGY, PHASE IIOWRR Pro~ect No. B-003-HI, Grant Agreement No. 14-01-0001-1493

Principal Investigator: I-pai WuProject Period: September 1, 1967 to December 31, 1968

The programs an~ activities described herein were supported in part byfunds provided by the United States Department of the Interior as authorized under the Water Resources Act of 1964, Public Law 88-379. It wasalso supported by funds provided by the Hawaii Agricultural ExperimentStation, College of Tropical Agriculture, University of Hawaii, City andCounty of Honolulu.

ABSTRACT

Hawaiian small watersheds are unique in watershed hydrology

because of the high infiltration rate3 small size3 and mountainous

topography. The flood hydrograph which has a short time to peak and

small recession constant can be expressed as a steep triangular shape.

A peak discharge equation is derived from the concept of a triangular

hydrograph and a linear storage of recession flow. The peak discharge

equation can be shown as a very simple form 3 Q = CAR3 where C is apcoefficient and can be determined by the hydrograph time parameters;

time to peak and recession constant3 A is the watershed area3 and R

is surface runoff in inches. A Zineari ty test between peak discharge

and runoff has been made for Hawaiian small watersheds and a good

linear relationship was found between peak discharge and surface run

off which is less than six inches not only for an individual small

watershed but for watersheds of similar size.

CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi

INTRODUCTI ON .

CHARACTERISTICS OF FLOOD HYDROGRAPHS : 2

DEVELOPMENT OF PEAK DISCHARGE EQUATIONS FROM A TRIANGULAR HYDROGRAPHSTUDY. . . . . . . . . . . . . . . . . . . . . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5

LINEARITY TEST OF THE HYDROGRAPHS 9

DETERMINATION OF PEAK DISCHARGE 10

DISCUSSION OF THE RESULTS 19

CONCLUSIONS 23

ACKNOWLEDGEMENTS 23

BIBLIOGRAPHy 24

APPENDICES 25

APPENDIX A: FLOOD HYDROGRAPHS OF HAWAIIAN SMALL WATERSHEDS 27

APPENDIX B: COMPOSITE DIMENSIONLESS RECESSION LINE OF HAWAIIANSMALL WATERSHEDS 65

APPENDIX C: TABULATED BASIC INFORMATION OF FLOOD HYDROGRAPHS:INCLUDES WATERSHED AREA, DATE, PEAK DISCHARGE, VOLUME OF RUNOFF,AND RECESSION CONSTANT OF HAWAIIAN SMALL WATERSHEDS 75

LIST OF TABLES

Table

1 Watershed Characteristics and Average Time Parameters ofSmall Hawaiian Watersheds (Oahu) 6

2 Linearity Test of Hawaiian Small Watersheds (Oahu) 15

v

LIST OF FIGURES

Figure

1 Map of Oahu Showing Locations of Gaging Stations during Fiscal

Year 1967 ················· 3

2 Hydrograph Showing Discharge in Waihee Stream at Station 2838,and in Waiahole Stream, at Station 2910, on Oahu during Febru-

ary 3-5, 1965 ·············· 4

3 A Typical Triangular Hydrograph ········· 7

4a Linearity Test of Hawaiian Small Watersheds: Group 1 11

4b Linearity Test of Hawaiian Small Watersheds: Group 2 12

4c Linearity Test of Hawaiian Small Watersheds: Group 3 13

4d Linearity Test of Hawaiian Small Watersheds: Group 4 14

5 Relationship Between Time to Peak and Recession Constant ofHawaiian Small Watersheds ············· 17

6 Relationship Between Recession Constant and Area ofHawaiian Small Watersheds 18

7 Comparison of Measured Peaks of Flood Discharge with ThoseCalculated by Using Equation (9) 20

8 Calculated Peaks of 6 Inches and 4 Inches of Runoff UsingEquation (9) Are Superposed on the Recorded Peak Flood Dis-charged Plotted against the Drainage Area · 21

9 Comparison of the Depth-Duration Relation of 100-Year Frequency Rainfall, Probable Maximum Rainfall, and Standard ProjectStorm of Oahu, Hawaii with the World's Greatest Rainfalls(11) 22

vi

INTRODUCTION

Increased utilization of land in potential flood areas has

created flood problems in Hawaii. Inadequate bases for planning and

design of flood protection stem largely from lack of basic rainfall

and stream runoff data. Watersheds in Hawaii differ from watersheds in

continental areas in she, topography, precipitation received, infil

tration capacity, vegetation cover, interflow, and channel storage,

Peak discharge equations and drainage design criteria which are avail

able are empirically derived under temperate and continental conditions,

and hence result in unsatisfactory fit to tropical oceanic-island

conditions.

Hawaiian watersheds are small in size, mostly less than five

square miles. This is the only region in the United States with fairly

long rainfall and stream flow records for watersheds of this size. The

variations of precipitation in Hawaii in both space and time are so

extreme that in spite of the extraordinary density of rain gages, a

clear understanding of the distribution of precipitation during a storm

is lacking for any watershed of consequence. Since the true rainfall

pattern or the average amount of rainfall falling in any watershed is

practically unknown, the steep rainfall gradients, which sometimes

exceed twenty-five inches per mile, present a great difficulty in the

study of rainfall-runoff relations.

Therefore, the study of peak flow of Hawaiian small watersheds

deals primarily with the channel phase of runoff, which, as defined by

Larson (1), to a large extent determines the time distribution of run

off. This study i? based on the evaluation of about 200 hydrographs

from twenty-nine small watersheds on the island of Oahu.

The existing drainage design criteria for the Hawaiian Islands

are arbitrarily set into two groups: the rational formula is used

for areas less than 100 acres with the coefficient "e" revised from

mainland standards and frequency analysis or envelope curves based on

maximum experience are used for watersheds larger than 100 acres (2).

A frequency analysis for annual peak discharge was made for twenty

three watersheds (island of Oahu) The peak discharge of 100-year return

periods was correlated with watershed characteristics and 100-year

twenty-four-hour precipitation for the determination of peak discharge

2

for ungaged areas (3).

CHARACTERISTICS OF FLOOD HYDROGRAPHS

The typical characteristics of Hawaiian small watersheds are:

small size, steep slope, and high infiltration. Due to the small size

and steep slope, the time of concentration is short and in turn the

time to peak of the hydrograph is also short. The highly permeable

soil absorbsa large amount of rainfall. A less intense and small rain

fall which will not produce a large amount of runoff or significantly

increase stream flow will produce a flat small hydrograph. For a

heavy intense storm whose intensity is much greater than infiltration

capacity, a sharp rise will be produced in the hydrograph. The flood

hydrograph for a single storm which has a sharp rise and a steep slope

of recession can be expressed as a steep triangular shape.

Flood hydrographs were collected from twenty-nine small watersheds

on the island of Oahu. The base flow was small when compared with peak

discharge, hence, an arbitrary line was drawn to separate base flow

from the hydrograph. Peak discharge and amount of runoff for each

hydrograph were measured and determined. A map showing the location

of gaging stations on Oahu is shown in Figure I and a typical shape of

a flood hydrograph is presented in Figure 2.

Since the shape of the flood hydrograph is a steep triangle, two

hydrograph parameters, the time to peak and the recession constant,

which express the slope of the rising and recession part of the hydro

graph, respectively, can be used to determine the size of the hydrograph.

Time to peak, L , which is affected by a combination of storm and water-p

shed characteristics, varies both within a single watershed and in

comparison to others. The time to peak is determined arbitrarily by

following the general slope of the rising part of the hydrograph. Be

cause the variation within a single watershed is small compared with

variations among watersheds, an average time to peak can be determined

for each watershed. The recession constant, K, theoretically influenced

by watershed characteristics, only varies among watersheds and may be

considered a constant within a watershed since the variation within any

single watershed is small.

~:'A: I 120

-'\::>

,,' 0 " 1'!l'·OC' " 00' .,' 1!l1".0'

"I L I I I~

t0 , . ,

"'LES

OAHU

1--1",EXPLANATION

0Ga9in9 Station

•-_.- .. Creat .taq. Station<

-,-;'

'".,-- , .. '-/-........... . .•••-.f~- ---=--,- I I I I..>0"

"<0

I D, I I I I I I I I-

,,' 0" IH'OO' IS' ocr .S' ISf"4O'

FIGURE 1. MAP OF OAHU SHOWING LOCATIONS OF GAGING STATIONS DURING FISCAL YEAR 1967.[FROM USGS PROGRESS REPORT NO. 10 (4)]

IoN

4

WA. \,A.. HOLE.100

500

2.50

~o.(

(/)

zo..J..J«~

zo..J..J_ oL__..J::=--- ~_i__.:.__=~_========3

~ IOOOr----~---:-=---------...----------...,Z 1'-1100W..U>a=.( 750Iu(()

o

DAYS

FIGURE 2. HYDROGRAPH SHOWING DISCHARGE IN WAIHEE STREAM AT STATION 2838, AND INWAIAHOLE STREAM, AT STATION 2910, ON OAHU DURING FEBRUARY 3-5, 1965.[FROM USGS REPORT R26 (5)]

The recession constant, K, is a constant or coefficient of an

assumed linear storage model of recession flow, S = KQ, where S is

the surface-water storage and Q is the outflow. Theoretically, the

K-value can be determined by plotting the recession curve on semi-log

paper or plotting in its dimensionless form Q/Qp against time on semi

log paper. However, there is not only one straight line for the reces

sion curve but two or three where the last two are caused by interflow

and ground water. The recession flow of Hawaiian small watersheds is

largely surface runoff, therefore the first part of the recession is

used to determine the recession constant which is designated as Kl .

Plotting the recession in the dimensionless form, Qp/Q, has the advan

tage of eliminating the effect of the size of the hydrograph and a

single line can be drawn to represent the recession characteristics

for each watershed.

The flood hydrographs for each watershed (up to 1966) were plotted

and are shown in Appendix A. The dimensionless plotting of recession

curves and the Kl-values of each watershed are shown in Appendix B. A

list of flood hydrographs including watershed area~ dates of the flood

hydrograph, time to peak, recession constants, inches of runof~

average figures of time to peak, and recession constant are given in

Appendix C.

The two hydrograph time parameters for Hawaiian small watersheds

are short and range from about fifteen minutes to two hours. The aver

age figure of time to peak and recession constant and several commonly

used watershed characteristics are listed in Table 1.

DEVELOPMENT OF PEAK DISCHARGE EQUATIONSFROM A TRIANGULAR HYDROGRAPH STUDY

The typical shape of flood hydrographs of small watersheds, as

shown in Figure 2, and in Appendix A, indicates the possibility of

using a triangular hydrograph to design the size of Hawaiian hydro

graphs and determine the peak rate of flow of a small watershed.

The general form for the peak discharge is shown in Figure 3.

. The triangular hydrograph has been applied by Mockus (7), and Holtan

and Overton (8) as an approach for the determination of peak discharge

and may be expressed as,

5

6

Table 1. Watershed Characteristics and Average Time Parametersof Small Hawaiian Watersheds (Oahu).

Average Estimated....Time ParametersLength Slope Time of

Watershed Watershed Area of of Height* Concen- Time to RecessionMain Main of tration peak ConstantNo.

sq. mi. 1 acresStream Stream Watershed t c t p Kl***

ft % ft hr hr hr

2000 1.38 883 16,840 3.63 1.510 0.59 1.11 0.76

2080 4.04 2,586 49,100 0.73 1,600 1.90 1.92 1.61

2116 2.13 1,363 15,720 12.40 3,121 0.41 0.38 0.72

2118 3.27 2,093 12,000 13.30 3,566 0.29 1.34 1.44

2128 4.29 2,7 46 47,640 2.64 2,096 1.70 0.95 0.74

2130 45.70 29,248 2.58 2.40

2160 26.40 16,896 0.90 1.61

2230 6.07 3,885 50,940 1. 58 2,568 2.29 1.30 1.03

2245 2.59 1,658 38,840 3.75 2,792 1.21 0.25 0.75

2270 8.78 5,619 1.25 2.80

2280 2.73 1,747 22,840 3.50 2,480 0.68 1.27 1.01

2290 2.61 1,670 14,660 4.63 2,276 0.42 0.71 0.66

2390 1.06 678 7 ,283 12.60 1,920 0.20 0.76 0.72

2400 1.14 730 9,100 14.90 2,814 0.23 0.66 0.83

2440 1.18 755 11,700 8.65 2,141 0.34 0.75 0.70

2460 1.04 666 12,240 9.40 2,165 0.35 0.83 0.73

2470 3.63 2,323 22,480 4.92 2,435 0.68 0.58 1.27

2540 2.04 1,306 14,360 4.43 2,540 0.40 0.94 0.54

2739 4.38 2,803 25,480 1.15 2,782 0.75 0.80 1. 32

2750 0.97 621 5,594 11.80 2,128 0.14 0.70 0.48

2830 0.28 179 1,438 23.00 2,222 0.03 0.58 0.43

2838 0.31 198 2,250 19.70 2,069 0.05 0.55 0.59

2840 0.93 595 4,875 11.40 2,377 0.19 0.80 0.42

2910 0.99 634 3,750 6.92 2,500 0.09 0.79 0.45

2960 3.74 2,394 0.75 0.94

2965 3.'74 2,394 21,700 2.73 2,630 0.63 0.66 1. 34

3030 2.78 1,779 0.74 0.75

3300 9.79 6,266 69,040 2.60 2,260 2.53 0.90 2.43

3450 2.98 1,907 68,300 1.81 1,740 2.75 0.57 1.64

*Difference in the elevation between the gaging station and the highest point of the watershed[see WRRC, Technical Report No. 15, p. 25 (3»).

**Estimated from Kirpich formula (6).***Estimated from the composite dimensionless recession line (see Appendix B).

•..u.....

o....(!)II:C%o!!!o

;',,

_______ ACTUAL HYDRI)GRAPH

_____ TRIANGULAR tllYDROGRAPH

l.trI

1I

I,t,I

\\

" ' ......... _----- ----

I:--+;--i TI ME. (t)t p r

FIGURE 3. A TYPICAL TRIANGULAR HYDROGRAPH.

"'-.J

8

2+ t )

r(1)

where Qp is peak discharge, A is the area of the drainage basin, R is

runoff or effective rainfall expressed as depth of water over the basin,

t p is time to peak, and t r is the time from the peak rate to the end of

the triangle. Since the typical hydrograph shape is a steep triangle,

t r can be expressed by the recession constant, Kl' The section of

the recession curve, from the peak to approximately 50 percent of

the curve, can be plotted as nearly a straight line on semi-log paper.

Hence, the recession constant, Kl , can be calculated as,

(2)

2.3 log 0.5 Qp

Since !It can be replaced as 0.5 t r accordin2; to the triangular shape

then,

2.3 log 2

or,

Kl = 0.724 t r ,

t r = 1. 38 Kl'

The peak discharge equation can be expressed as a function of

the two hydrograph parameters, time to peak and recession constant,

2Q = A~ (Kl )P t p 1 + 1.38

t p

(3)

This relation can also be derived by using Holtan and Overton's

(8) result that the recession constant, K, can be considered as the

time lapse between a given flow rate and the occurrence of 1/3 times

that rate. If the hydrograph shape is close to a triangle, the fol

lowing relations may exist:

K = 0.67 t r ,

t r = 1. 5 K.

Therefore,

~= AR ( 2 )

t Kp 1 + 1.5 t

P

(4)

9

As Kl is the measured figure from the first part of the recession and

covers a great par~ of the recession flow and K cannot be determined

directly, equation (3) is easier to apply for the peak discharge esti

mation.

'LINEARITY TEST Of THE HYDROGRAPHS

The modified peak discharge equation, equation (3), expresses

a linear function for peak discharge and runoff if the two hydrograph

time parameters of a watershed are constant. The assumption of line

arity has been used since 1932 when Sherman (9) introduced the unit

hydrograph concept that peak discharge is directly proportional to the

volume of runoff for a given duration of unit hydrograph. The most

important property of such a linear re~ationship is that of superposi

tion which allows a flood hydrograph to be constructed if the duration

of effective rainfall and its corresponding unit hydrograph are known.

In fact, the peak discharge-runoff relation produced by a water

shed system is so complex that it is rarely linear. If a linear system

does not exist, the use of a linear model to determine the hydrograph

and its peak will 'yield a poor estimate. A test of linearity must

therefore be made before the linear model, equation (3) can be used.

Such a linearity test was made by using about 200 hydrographs

for twenty-nine small watersheds on the island of Oahu. The test was

made by plotting the peak discharge per unit area of all the storms

that were recorde~ for every watershed in this study, ~fA, against

runoff, R, expressed in inches. If a linear relation can be obtained,

the peak discharge, ~, should be directly proportional to the amount

of runoff since the area of a given watershed is constant. Results

have shown that a good linear relation exists between Q fA and Randp

further that this relation is unique and uninfluenced by time to peak.

The time to peak of Hawaiian hydrographs, affected mainly by a short

intense storm, is short enough that its variation would not signifi-

10

cantly affect the general shape of a storm hydrograph. Furthermore,

small Hawaiian watersheds of Oahu can be presented as four groups and

each group can be expressed by a single linear relationship between

Qp/A and R as shown in Figures 4a, 4b, 4c, and 4d. By studying the

watersheds in each group, it seems that the linear relation holds true

for small watersheds of similar size, and the watershed area is sig

nificantly correlated with the recession constant, Kl , as shown in

Table 2.

Four empirical relations have been found and may be used for

determining peak discharge and for verifying the derived equations.

They are:

a.

b.

c.

d.

For a watershed area of less than 1 square mile:

~ = 1.4 AR ~)

For a watershed area from 1 to 3 square miles:

Qp= 0.9 AR (6)

For a watershed area from 3 to 6 square miles:

Qp = 0.6 AR (7)

For a watershed area larger than 6 square miles:

Qp = 0.32 AR. (8)

The linearity test proves that Hawaiian small watersheds can be

treated as a linear system and the linear equation, equation (3), can

be used. However, there are a few points where eight or nine inches

of runoff do not follow the linear pattern and may fall away from the

linear line (see Figures 4a and 4b). Six inches can be considered as

the limit of this linear relation of the small watersheds studied when

the duration of the storms is short and insignificant. The linear rela

tion may still be applied to flood hydrographs when the amount of runoff,

R, is larger than six inches. In this case, the hydrograph is a result

of linear superposition which is possibly superposed with certain time

lqgs according to the storm duration.

DETERMINATION OF PEAK DISCHARGE

The peak discharge equation, equation (3), can be further simpli

fied if the time parameters, time to peak, t , and recession constant,p

Kl

, are known. There is no good correlation between time to peak and

recession constant. If they can be expressed by the linear line,

ben

fa 6,6.1)

O(8.e ,9.9 )

/

•/

VJ

I Waterah -d Hum

tI I/' 2390

oj 2MO27502~0

I 2838

If:o IAR2830

a Qp. 1.4

0007 a

IIo a

a 0

3

2

c(

~

6

7

5

•...ua...........:! 4u

o 2 3 4

R (In.)5 6 7 8

FIGURE 4a. LINEARITY TEST OF HAWAIIAN SMALL WATERSHEDS: GROUP 1.

I-'I-'

2I-'N

7 i I I I I iii iii

61 I I I I I I I I I I

y o

Water1hed Numbers

20002 1162245246022902440247029103030

o

o

A

o

Qp • 0.9 I AR

%o

2

n

--ell.. 5u0

"co-u4

<l"'-

Q.

a 3

I I0

60

o

2 3 4R (In.)

5 6 7 8

FIGURE 4b. LINEARITY TEST OF HAWAIIAN SMALL WATERSHEDS: GROUP 2.

3

27392960296534502128211822302280

Numbers

8764 ~

R (In.)

32

I

)

,V Watershec

/)

V,.".

/'Qp =0.6 AR

! /'0

V6'0 ./ o 0I

~oo

~o

7

~

"Q.

a

;-I~-UUo--

FIGURE 4c. LINEARITY TEST OF HAWAIIAN SMALL WATERSHEDS: GROUP 3.

....~

4I-'~

Numbers

21303300216020802270

shed

87654R (In.)

32

j

,Qp.0.32 AR

~

Waterl

0 .------

~~

------0

00 ~-~~

00 0

0~

-o

3

<"00.

4

7

2

6

......If..g ~

"14U......

FIGURE 4d. LINEARITY TEST OF HAWAIIAN SMALL WATERSHEDS: GROUP 4.

Table 2. Linearity Test of Hawaiian Small Watersheds (Oahu).

15

Watershed Watershed RecessionGroup No. Area Constant

(sq. mi.)

I 2390 1.06 0.72

2540 2.04 0.54

2750 0.97 0.48

2830 0.28 0.43

2838 0.31 0.59

2840 0.93 0.42

Area Range(approx. )

Less than

1 sq. mi.

LinearRelation

~=1.4 AR

(Fig. 4a)

II 2000 1.38 0.76

2116 2.13 0.72

2245 2.59 0.75

2290 2.61 0.66

2400 1.14 0.83 From 1 to ~=0.9 AR2440 1.18 0.70 3 sq. mi. (Fig. 4b)

2460 1.04 0.73

2470 3.63 1.27

2910 0.99 0.45

3030 2.78 0.75

III 2118 3.27 1.44

2128 4.29 0.74

2230 6.07 1.03

2280 2.73 1.01 From 3 to Q =0.6 AR

2739 4.38 1.32 6 sq. mi. (Fig. 4c)

2960 3.74 0.94

2965 3.74 1.34

3450 2.98 1.35

IV 2080 4.04 1.61

2130 45.70 2.40Larger than Q =0.32 AR

2160 26.40 1.61 6 sq. mi. (Fig. 4d)2270 8.78 2.80

3300 9.79 2.43

16

t p = Kl , as shown in Figure 5, a simple relation can be derived, from

equation (3),

or,

ARQp = O. 84 Ki""

Qp = CAR

(9)

(10)

where C is a coefficient and a function of the hydrograph time para

meters, time to peak and recession constant.

The simple form, shown as equation (10), can be applied to the

four groups of basins of varying areas. The results are shown in Table 2.

The derived equation, equation (9), is simple enough to use.

The peak discharge can be estimated for a given design runoff, R, from

any watershed (including ungaged watersheds) if the area, A, and reces

sion constant, Kl , are given. Since the recession constant, Kl , is

mainly affected by watershed characteristics, multiple correlation are

made between Kl-values and watershed characteristics. Results indicate

that watershed area alone is the most significant factor for its corre

lation to the recession constant. A regression equation is obtained

and may be expressed as,

Kl = 0.43 + 0.0003A (11)

where the recession constant, Kl , is in hours and watershed area, A,

is in acres. The linear regression between Kl and A is shown in

Figure 6.

So far, the only factor which remains unsolved is the amount of

runoff, R. To determine the amount of runoff from a given storm is

in itself a complicated research problem. A reasonable solution is

yet to be found.

If the amount of runoff, R, can be reasonably estimated, the

peak discharge can be calculated by using equation (9).

3

~2s:

Q.--.xC.,

Q.

.2•EF

0 //

7V 0

0

~0

0

0 0c

0 oC6

V 0

0

o I

Recession2

Constant K. (hr.)3

FIGURE 5. RELATIONSHIP BETWEEN TIME TO PEAK AND RECESSIONCONSTANT OF HAWAIIAN SMALL WATERSHEDS. 1-1

'-J

K, • 0.43 + 0.0003A I-'00

A VV

//

)

/./'

4/6v/

~A

6

67 6

6

4

vt: f

:w:

3

IIIcr:l 2o:I:

zo-f1)

f1)

lUUlUII:

...z~f1)

zou

1000 2000 3000 4000 5000 6000 7000 8000

WATERSHED AREA A. (ACRES)

FIGURE 6. RELATIONSHIP BETWEEN RECESSION CONSTANT AND AREA OF HAWAIIANSMALL WATERSHEDS.

19

DISCUSSION OF THE RESULTS

The reliability of the derived simple peak discharge equation,

equation (9), has been tested and found to be good when the measured

peaks of discharge are compared with those calculated from equation (9).

A good agreement of measured discharge and calculated discharge is shown

in Figure 7. All the data points were distributed close to the 45° line.

Equation (9) has shown that the peak discharge, ~, is a function

of the watershed area, A, recession constant, Kl , and inches of runoff,

R. Since Kl can be expressed as a function of A, the peak discharge

will be a single function of watershed area, A, for a given amount of R.

~ = f(A) (12)

for R = 1,

where f(A) may be read as a function of A. Peak discharges from runoff

other than one inch can be simply expressed as,

~ = R f(A) (13)

because of the linearity characteristic of the peak discharge and

runoff of Hawaiian small watersheds. However, the limitation of

R within six inches should be emphasized. Since the duration of ef

fective rainfall is small, 0.5 to one hour may be a good estimate of

the duration of rainfall. More than six inches of rainfall in an hour

will not occur frequently and, as a matter of fact, it is larger than

the lOa-year maxi~um rainfall for the island of Oahu (10). Using

equation (9), the peak discharge, Qp, was plotted against the water

shed area for six inches and four inches of runoff. Results are super

posed on a graph where all the extreme peak floods from each station

are plotted against the drainage area and shown in Figure 8. It is

very interesting to find that the curve of six inches of runoff is about

an envelope curve for all the extremes and the four-inch runoff curve

passes through the upper part of all the extremes. A comparison of

the depth-duration relation of lOa-year frequency rainfall, probable

maximum rainfall, and standard project storm of Oahu, Hawaii with the

world's greatest rainfall is shown in Figure 9. In addition to the

lOa-year maximum rainfall on Oahu, a four-inch rainfall with a duration

Q.o

~....::J•CCIIE......o

IIIC)a::ct:ro(/)

o

:w::4l&.IQ.

/0

IAI 0./0 IeILn" n'

jy7;00

o 0 BOOo 0 0

~oo ~"o°oo 0

f(0 00h. '1B 0<0' 0 0' 0f" 0 cP 00

I""" I~ 0 oo~ cfl: 0 0

Cl:>

01/o 1/

10 I~ I~I 0 0 0 1:9...., alT _ 0

o 0, I .;...; 00 0

1/ '0 0

o I V~0° 0 Va

Vc[,'O~o 0

o 0

100 0

V1/

VV

VV

No

10 100 1000

PEAK DISCHARGE? Qp? (Calculated)

FIGURE 7. COMPARISON OF MEASURED PEAKS OF FLOOD DISCHARGE WITH THOSE CALCULATEDBY USING EQUATION (9).

21

4001005010

R- S- I-I--~---I....- I...- 10- C

A ....- R-.-~ --- -- ..~ V L-,.-

.".... ~

./----_0 ~

..... \; 4p... :/ ./ cP

V I( 1,;100'" A 0 --u

1/ "'"/ .., 1....-

4 4 I...

V 0 l/ Q

./ 0 D ..

~V D j/

A lC lC

P 0 lr

It,

"1.1""0

P3

I

10

300

100

ofu

050o

Drainage Area in 100 Acres

Legend

o Windward Side

4 Honolulu District

o Between Mountain Ranges

x Leeward Side in Waianae District

FIGURE 8. CALCULATED PEAKS OF 6 INCHES AND 4 INCHES OF RUNOFF USING EQUATION (9)ARE SUPERPOSED ON THE RECORDED PEAK FLOOD DISCHARGE PLOTTED AGAINST THEDRAINAGE AREA.

NN

II I 1'1 I I II I r 11 T II III I I I I III I I I I II/~• Wot'.LD'S q"'.""Te~T R"I"'lI'AL.L. .....

••'>~ -- .,,.~ -~ -'\'~

~ -..~""'. -

Q •

1-' ./-

I- lc'~~ pll.oeA&L.E MAXIMU.... POINT ~

I- ........~ r ~ l,.)i RAIN~ALL. j O"WU HAWAII. -~ bY'

-to-

~ ~t; -

e,..->'" • ..........: ~ STANDARD PROJac.T SToAM,

~ • ~~ l,..-:I,.oo'HO"O~U'-U ....~o W'''DWAR.l) -

~ l0 V l>- $\Dl! of O!",HU.

• .A ~

I- ./ ..,........-./ / @--e--e 100 - Y.AR. MAll. R,A.... PA...... -='I-- /

-.-/. ::::;..--- - 0 ............

==V • l-#"/ VI- ~ • -V b~~

........ 100- "(EAR. Q.A'Nf'A"L., --:::- Ho .....ol.-uL-lo.> ""NO W1NO~ACl.O -

........-:: .M'"0 ........ f-1 roalof'1 OA;U'I, ,I 11-,,-~ I I I I 1 I II I.. I I I I " I I I

4·

2

1086

2.0

2.00

1000eooE>OO

4-00

2000

..J....<LL%

«a:

~

l':r 100~ 80

..:. ~O

+0

2 ..,." 8 10 1.0 "f<) 101O -' "9 12. /8 2.+ 5 10 .2.0 ~ :3 ,,(} 12 24-\. A JL A ~

V V V V--MI,..UTES HOUR5 OAY~ MON"nfS

DURATlOW, D

FIGURE 9. COMPARISON OF THE DEPTH-DURATION RELATJON OF lOO-YEAR FREQUENCYRAINFALL, PROBABLE MAXIMUM RAINFALL, AND STANDARD PROJECT STORMOF OAHU, HAWAII WITH THE WORLD'S GREATEST RAINFALLS (11).

23

of about one hour is shown as the lOa-year rainfall in the Honolulu

and windward areas of Oahu.

CONCLUSIONS

In summary, the following conclusions may be made:

1. The relationship between peak discharge and surface runoff expressed

in inches appears to be linear for a given small watershed re

gardless of intensity, duration, and size of the storm. The time

to peak which varies slightly in different hydrographs will not

change the general shape of the hydrograph or the linearity of the

peak discharge and runoff relation. However, this linear relation

cannot be extended beyond six inches of runoff.

2. Two hydrograph time parameters, time to peak and recession constant,

are both small and of nearly the same magnitude owing to the typi

cal shape of the steep triangular hydrograph of Hawaiian small

watersheds.

3. Watershed area is the most significant factor in estimating the

recession constant and is the dominant factor in determining flood

peak discharge.

4. The derivation of the simple peak flow equation, equation (9), was

based on stream flow records of twenty-nine watersheds on Oahu with

areas ranging from 0.2 to ten square miles. The applicability of

equation (9) to watersheds smaller than 100 acres is not known.

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to the Hawaii Agri

cultural Experiment Station, College of Tropical Agriculture, University

of Hawaii, City and County of Honolulu, and the Office of Water Resources

Research, U. S. Dept. of the Interior, for their support of this project.

He is also grateful to the Water Resources Division, USGS, Honolulu,

Hawaii, for giving him access to the flow records used in this study

and to Dr. L. S. Lau, Associate Director, Water Resources Research Cen

ter, University of Hawaii, who provided helpful discussion and review

of the manuscript.

24

BIBLIOGRAPHY

1. Larson, C. L. and R. E. Machmeier. 1968. "Peak Flow and CriticalDuration for Small Watersheds." Trans. of ASAE, Vol. 11, No.2,pp. 208-213.

2. Chow, V. T. 1966. An' Investigation of the Drainage Problem ofthe City and County of Honolulu. Unpublished report, City andCounty of Honolulu, Hawaii.

3. Wu, I-pai. 1967. Hydrological Data and Peak Discharge Determination of Small Hawaiian Watersheds: Island of Oahu. TechnicalReport No. 15, WRRC and Technical Paper No. 939, HAES, Universityof Hawaii.

4. Hoffard, S. H. and K. H. Fowler. 1968.Floods in Hawaii through June 303 1967.Division, Honolulu, Hawaii.

An Investigation ofUSGS, Water Resources

5. Hoffard, S. H. 1965. Floods of December 1964 - February 1965 inHawaii. Report R26, USGS, Water Resources Division, Honolulu,Hawaii .

6. Kirpich, Z. P. 1940. "Time of' C.oncentration of Small AgriculturalWatersheds." Civil Engineering3 Vol. 10, No.6, p. 362.

7. Mockus, V. 1957. Use of Storm and Watershed Characteristics inSyntheUc Hydrograph Analysis and Application. Paper presentedat the annual meeting of the AGU, Pacific Southwest Region, Sacramento, California.

8. Holtan, H. N. and D. E. Overton. 1963. "Analyses and Applicationof Simple Hydrographs." Journal of HydrologY3 Vol. 1, No.3,pp. 250-264.

9. Sherman, L. K. 1932. "Streamflow from Rainfall by the Unit-GraphMethod." Engineering News Record3 Vol. 108, pp. 501-505.

10. U.S. Weather Bureau. 1962. Rainfall-Frequency Atlas of theHawaiian Islands -- for Areas to 200 Square Miles 3 Duration to24 Hours3 and Return Periods from 1 to 100 Years. TechnicalPaper No. 43.

11. Paulnus, J. L. H. 1965. Indian Ocean and Taiwan Rainfalls SetNew Records. Monthly Weather Review, Vol. 93, No.5, pp. 331-335.

APPENDICES

APPENDIX A: FLOOD HYDROGRAPHS

OF HAWAIIAN SMALL WATERSHEDS

29

Ill±thh+rtchj"P3 5 79/1

Jon. 14, 19237

WATER$HED NO.2 000

o24 1 3 5

OCt. 28, 1936

2000

1000

3000

QCcfs)

4000

5000

Time

2400

024Mar. 2) /939

Chrs.)

II

_J

/3o

800

QCcfst

1600

30

2000

22 24 I 14 16 18 20

Mar. 12, 19~1 Mar. 3, 1939Ti me (hn.)

10 12 14 16

Dec. 20, 1924

400

0 10 12 14 16

Mar. I, 19~2

NO. 2000

800

1200

1600

Q

(cf.)

2400

1600

Q(cf.)

800

o2~0~22~~24~Oct 6, 1961

( hn.)

31

1600

NO.2 0 80

,,I,,,,,,,, -,-'

I ! 'ri°t-l-+t"tt1"'o, ! I ! I1 3 5 7 9

Mar. 13, 1962( hra.)

800

1200

Q(cfs)

1200

I-I/,

, ! I ! I ! I ! I ! I ! ,! I ! ! ! I ! I

16 18 20 22 24

Feb. 21, 1959Oct. 23, 1958

Tim. (hra.)

II,I/, ,, ,/'

I ,/I ,/J' I ! 8/-(! IQ" ! Ik! I 'R! Io

800

400

Q( cfs)

32

, , ! I! ! ! ! I , ! ! I, ! , !

6 15 ~ 17 ~ 19Jan. 31, 1963

234 5JCI1. 10, 1965

( hre.)

14 15 16Sept. 9, 1965

Tim e (hn.)

NO. 2116

50

120

360

100

240

480

150

Q(cfa)

200

Q

(efe)

33

,/

II,,

. ,'. ,,

'/'.

/ './ -._._._._._.-.-,

I "I ! I ! I ! I , I ! I ! I ! I ! ! ! !24 I 2 3 4 5

Nov. /3, /~

NO. 2118

400

o

200

600

800

1000

Q

(ets)

Time (hrs.)

1600

1200

Q(ds)

800

400

o6000

4800

Q(cfs)

3600

24°0

1200

o

34

NO. 2128

24

14 16 16Dec.. 6, 1~57

357OV. 21. 195'1'

Time (hrs.)

I ._-.-.-.--------I I I 'J·'"C, I , ! , ,! ,! I, , ! ! I! !

21 23 1 3 5 'TApr. 16, 1960

Time. ( hrs·)

35

'1000

No. 2130

'I' i me (i'll's.)

_.-,I, _.-f' - __._._0

5000

1000

3000

13 1'\ 23

Novo 2 8. 1 9 54

3 5

Time (hl"s.)

36

NO. 2160

_~_._. _ _ 0-

16 18j 963

I , ! , I I I

IIII _._.-.-.

-t-._'I

! "' , I ! I ! I I ! ! I ,8 10 \2 14

Ap .... 14,4 (, 8Ma)' 12, j 9~0

Time (hrs.)

800

j 600

24°0

3200

0:3

180 0

1600

Q(~ts)

j 200

Q

(cfs)

800

400

o13

Tim e (h r.s. )

37

] 2 000

NO. 2160

10000

Q(cfs )

800 0

6000

4000

2000

o f Jm L"±'c1"t'Q', ! ! I ! I ! I3 23 24 I 3 5 'T 9

Apr. 16, 1.960

Time (hrs.)

38

5000

NO. 2230

4000

3000

'2000

\000

Ti me (hr5')

39

500

400

Q

( cfs)

300

200

NO. 2245

--' --'..-'

05 6 7 8

feb. 28, 195"8

Time ( hrs. )

100

3 00

Q( cfs)

200

\00

_.-.--_.-o

18 19 20 2\

.Dec. G, 19 5 '"('

TilTle (hrs.)

22.

402400

NO. 22'70

\ "3 5 7Oct. 23, j 9 5 e

, ! ! I, I , I , I , I ! I

, _.-'J................._._._.-.-.-.-.

II

! ,,! ! I21 22

( hrs.)'Time

400

800

j200

1600

2000

1200

Q(cts )

800

4°0

o7 e \0 12 '4 ,6

Jan. S2 I, i 9l;S

Time ( hr5·)

2000NO. 2280

41

3 5Dec. 7. 1942

Time (hr •. )

3 5Mar. 2.1939

T;me (hrs.)

Q

( cfs)

Q

( cfs)

1600

1200

800

400

0 '5 17 20Mar. 26, 1952

1600

1200

800

400

o

20 22 24 1 3Dec. 14. 1965

8 10 12Jon. 1,1937

I !

42

2400

2000

1600

Q(eft) 1200

800

400

1200

800

Q(cft)

400

o10

NO.2280

12 14 16

F.b. 28, 1932

12 14 16

Oct. 4, 1963

1200

800

400

o8

Tim. (h r •.)

18

10 12 I

Mar. 3, 1933

22241 3

Nov. 13, 1964

Time (hr •. )

43

1600NO. 2290

\200

4 20 22 2"'4Oc:t-. 6. 1961

1 '3 5 7 20 22 z+ 2S~pr. 2.8, 1937 Ap... :3, 1939

Time (hrs.)

II-'-'-'-'-'~--

III

1'3 ~1 2'3ApI"". 1, 192"3

o

600

400

Q( c.f5)

3200

2400

,600

Boo

o5 'T 9 11

:P~c.. 23, 193+lEt 16 20

Mar. 2Et, 195'2

T i lT1 e (hrs· )

e 10 \2/'Iov. 5, 1925

44

2000

1600

\200

800

NO. 2390

400

of~ 15 17 19

Apr: 11, 19303 5 'T '3

:PC!'c. 30, 1960

Time. (hrs.)

21 24' '3 5"Nov. 28, 19S4

600

Q( cfs)

400

200

o20 22 .2-4- I

:Dec.. 6, 195622 2+ I "3

Mar-. 1, 1939

'Ti me (hrs.)

22 .24 I "3J>~c.. 13, j92'(

45

2000

NO. 2400

\600

Q(cfs )

(200

800

400

III

o ..._~I.....""""-,l",,i,,""''''\8 20 22

Fet>. 2'7,1935

3000 'Time ( hI's.)

6l(cfS )

2000

o7 17

19E>0 "'ov. \ 7,

'Time (hrs.)

\000

46

\600

NO. 2440

\ 200

Q(cfs)

800

400

0 ..._ ......101;5;;__.......................

4- 6 8:Dec.. '30, 1960

_._.": , I ! ! , ! I ! I ! " , ! , ,

15 17 19 2\ 23

MQY 16, 192 7

Time (hrs.)

14 16 18 20Nov. \ 7,1948

47

1600NO. 2460

\ 200

_.- .._.-"12 1"5

Fe b. 2 a, 193211

1'7 18 19Nov. \ 7, 1949

16

_.-8

.Mar.

'Time (hrs.)

16

16 1'7 18Oc"t-. t 5, 193 B

Time (hrs.)

14 15Mar. 23. 1927

13o

800

o

400

100

200

300

400

48

2000

1600

1200

800

400

NO. 2-+ 'TO

IIIIIIIII

IIIk._._._.-·-·I

IIIII _

IIT'tO' I I I, II I , I'T 9 11 n

Mar. 11, 1951

Time (hrs.)

2000

\000

1200

800

No. 2540

49

15' 17 19 21Apr. 1-4, 196'3

Time (hrs.)

50

2000

e 10 12 14MAr. 12, 1962

61~ .21 2'3

M~7 13, 196010 12 14 16 1'7

1'1(1)' 1'3, 196Q

NO. 2'739

\600

800

\200

Q(cfs )

T irne (hr-s·)

51

2000

NO. 2750

.2+123+Nov. 20, 19S7

Time (hrs.)

o\0 12

t\rr-. '0, 19~1

o '-..._--"..;;~19 2021 222~ I'T IS 192021:Dt'c.. ~. 19~6 :Pee. G, '9S7

400

80Q

800

1200

\600

1200

Q( cfs)

Q( cfS)

Ti me (hrs.)

52

500

400

Q( C.f5)

300

200

100

o

~oo

Q

(cfs )

20

NO. 2830

21 22

Sep"t.26, 19"37

,I ...............

I L-· T -·/(· ! ! I r-j-·-.-I·-·-·-,·-·-·T-·-+ 5 Eo 9 \0 \ 1

A pc-. 8, 1939 Sept". 27. 1937

Time (hc-s.)

,12

200

100

o12 13

June 11, 1937

2

2, 19"398

Apr. 7,14 15feb. 28, 1938

Time (hrs.)

53

NO. 2830

22

Apr. 16, 196023 12110

Dec. 26, 19569

o~-""""....__.......- ....._.....

\00

300

200

QCCf5)

TimQ (hr~.)

S4

200

23 2+Mar. 23, 1964-

Q(C.ts )

100

No. 2838

,I -'-',-'-'T" I1014 15 16

Ma)' 1 (, 196"3

Time (hrs.)

1

1800

1.+ ISMay 14, 1963

Time ( hrs·)

'3 4-feb. 4, 1965

2.o

600

300

\500

Q

(c.fs)

1200 400

Q(cfsl

~oo '300

55

1000

NO. 2840

800

Q

(Cfs )

600

I ;-1--+-',-'1'-',- I16 '7 18 19

/'1cH. \4, 1943

II

: ...-' .---,--+--, I I1'3 20 2 I 14 I 5 16

May 9, 1940 Mo.)' 8, 1943

Time (hrs.)

I18

o ..............L_...__....L~~...19 .20 2 I 22

Nov. \4, 19+'1

200

400

6000

-i 0oo

2000

o23 2+ 1

Fe b. :3, 1'3"'5

Time (hr5.)

56

i 600

\200

Q( cfs)

800

400

o

NO. 2910

.-.-

2 '3 -4-Feb. 3, \965

400

300

200

100

o

2.0 21 22. 23

Arr. 16. t960'T i me (hrs.)

10 ItJan. 26, 1956

Time (h.-s.)

57

1600NO. 2~60

1200

Q(CiS )'

eoo

! , E';j·,-r'""',-j' ! ! ! !

i7 1~ 21 :2'3 1 2.

1"1"1 18, 1917

Time (hr:!>.)

400

58

2000

1600NO· 2965

_.-"I _.-

'

I ~._._

- I ... -f 15.1-:"! ! ! ! I ! ! , ! ! I w.~.u..L..l..I..I."u........I..I..r;IO.I."""""'I;,;l;,;,,(;,,l,,..I..I."""",j,,,j,""

f 0 12 14 1& 10 (2 14 t & t 5 17 19 21

Mar. 6. 196'3 Har. 26, 19~'3 :Dec. 4, 1960

-'-'-'-" ---+--

2-+ i

400

°

aDO

1200

'Time (hrs.)

4000

"3000

Q(cfs )

2000

1000

1~ 15 1'7NOV. 1, 1961

Time (hr.s.)

1600

~200

Q: cfs )

600

400

8

NO. 2.965

10 12 14 16 t aAllj' 26, 19 G5

18

fe b. 18, 19 G0

59

Time (hr~.)

60

1600

1200

Q(cfs)

600

400

o

1600

t 200

aoo

400

o

NO. 3030

Time

1-._._'-'-'-'-'I ! ! ! I ! I ! ! ! I ! I

'7 19 21 2~

May 4, 1~&5

Time (nrs.)

I _I , 1[+,1 iTiTjT, I ! !6 10 {2 14 16

Jan. 26, {95-6

o( c.fs )

5000

4000

'3000

2000

100 0

o

NO.303o

12 14 16Nov. 1, 1961

Time ( hrs.)

61

62

i 2.00

400

2000

1600

QCCfs)

12.00

600

400

o

NO. 3300

Time (hrs.)

Time (hl"s.)

(0 12 14 16 18

Sept-. 5, 1962.

63

1600

400

NO. 3450

800

I _.-.

o ..........__......~.......I..I."""-...........~IIIIo;;;I~~..............~ ..~~;..I",l~u.~...u~~~! ,'-iTt; t,ri"r; I ! I ! !1~ 11 13 is 9 11 13 15 17 1910 12 t..... 16 18

Nov. i, 1959 MQr. 30, 1960 Mat". 2&, 19"'3

lZ00

Q

(<:fs)

Time ( hr-s.)

2000

1600

Q(cfS )

1200

600

400

o I ! !

9

I _.-.-.-.I 1.11"'1·1'"' I ! I! I!11 t~ 15 17

Jan. 6, 19!>+

'T i me (hr5· )

............

APPENDIX B: COMPOSITE DIMENSIONLESS RECESSION LINE

OF HAWAIIAN SMALL WATERSHEDS

10 120 110TIM! ("'I.)

oI "'-.....~~_..I......o 120

(.Ia.)

I 0 10 120TIME (.'a. )

NO. 2111 NO. 2111 0

7 70

6 • 0

00

a I

00

40 4

0

8> 000

0

Qp Q, 00- I 0

1C1=0.711 - I K1

8 1.44Q Q

00

& 0

0

2 2 0

0

0

a

0

67

WATERSHED NO. 2000 NO. 2010

I

7 0

10

0

e00

0 0

4 4

00 •

50

0 5Q, Qp- 0 -Q

8K,· 0.71 Q o K1= "II

0

2 0 2 0

0

80

0

o 80 120 180TINI (min.)

• 0 1O 120 110 0 10 110 110 140TIME (1II1n.) TINE ( IIIln.)

NO. 1180 ho. 22107

0

8o 0

0 a0

00

40

0

0

00 5

0 0

Op Op- 0 0-0 0 0

0

2 0 'k: 1.11 2 Itl Loa0

1 1

0

68

WATIRIHID NO. 2111 MO. 211O0

O'

T ~ q,

10

o 00

o 0,00

0

4 0 4

00

I I0

Qp Op o 0

- K1: 0.77 - 0

K;: 2.400 0

0

2 2

69

oo

,0 120 180TIME (min.)

o

I0 .0 110 lao 0 .0 110 .ao 140

TIMe: (mil. ) TIIiI ( .In.)

NO. 2210 NO. 22.01

••

0

4 4co 0

o 0• 0 I0

Qp 0 Qp- - 00

Q Q000 0

0 "18 1.01 K: 0."0 1

o 0

70

o 80 120TIME ( •• ft.)

2

IQp-Q

K: 1.271

o

WATERSHED NO. 2470 NO• 2540

•7 :E•

0

5 0

4 4

1 I0 .0 110 110 0

TIMa «•••.) •7 NO. 2700

810.

0

271e 0

0 0

5 50 0

0

40

00

I0

Q, Qp 0'

1(1: ••120 K: 0.4.- -Q Q 1

2 I

Q

Qp-

71

I O~""~'~O""'~'IOTI. (.'a.)(.aa.)

T'M.

t

• NO. 1100

15 15

0

4 4

Q, Q, 0

- I - IQ Q 0

0

0

a .112 K1• I ••'

0

0

WATERIHED NO. a••o NO. a•••

• •I

o 0

I 0

0

• ,4 4

0

00

o 0

Qp Gp 8 0- I - •Q Q 0

K= .•4 • KI I .••1 1

I a •

72

TIME (.,•• )

"

I '-'..L-~......llo....""'-~o 80 120

TIME (.'a.)

WATERSHED HO. 2400 NO.' 21eO7 7

• •0

5 5

4 0 4

~0

Qp QpI 0- I -Q Q

K: .8. 0.721·1

2 20

···.0 120

TIME (.,••)

NO. 2480

5

o

60 120 110

TIME (.'nJ

o

NO. 2440

5

4

3 •Qp 0

Qp

- -Q Q

2 2 Ie.-O.7.

K:O.701

73

I~""'''''''''''''''-~...Jo 80 120 110TIME (.1 •. )

•

I 0 0 0 10 ,!O( ••1.) TI"I (. a.)

NO. 2140 NO. .t,O

• •I ,

0

4 40

0 0

Qp I Qp I- -G G

2K

1:O.42 K

18 O. 4,8

WATERSHED NO. 2110 .... .1'1

•7 7

0

8 80

I 0 I0

0

0 0 0

Gp'4- 4

0 Gp- -Q Q

I K: 0.4'I K- 0.'.

I 1

74

WATIRIHID NO. '.10

•

•I

K: ... 41

I

o .0 110 110TIMI «.In.)

APPENDIX C: TABULATED BASIC INFORMATION OF FLOOD HYDROGRAPHS:

INCLUDES WATERSHED AREA, DATE, PEAK DISCHARGE,

VOLUME OF RUNOFF, AND RECESSION CONSTANT OF

HAWAIIAN SMALL WATERSHEDS

Watershed No. 2000 Area: 883.2 acres

77

Date t k1 Q R Qp/A(h~) (hr) (c¥s) (in)

1-19-17 0.75 0.77 2320 3.335 2.6263-25-20 2.00 0.75 4-060 8.226 4-.5961-14--23 1. 33 1.01 4-460 8.760 5.049

10-16-24 2.00 0.97 3620 7.604 4.09812-20-24 1.50 1.04 1935 2.556 2.19010-28-36 1.06 0.48 3430 3.557 3.8831-28-38 0.75 0.72 2480 2.667 2.8073- 2-39 1.67 0.29 3250 4.402 3.6793- 3-39 0.25 0.36 1740 1.111 1.9703-12-51 0.84 0.72 1620 2.178 1. 8343- 1-52 1. 33 1. 04 1339 2.245 1. 516

10- 6-61 0.75 0.72 2110 2.867 2.38911- 1-61 1.00 0.97 3100 4.184 3.509

5-14-63 1. 00 1.20 2920 5.069 3.3063-23-64 0.50 0.36 2630 2.779 2.977

Average t p = 1.11 hoursAverage kl = 0.76 hours


t kl Q RDate (h~) (hr) (c¥s) (in) Qp/A

7- 3-53 1.25 1. 95 1940 2.050 0.75010-23-58 2.75 1.68 1780 2.119 0.688

2-21-59 1. 84 1. 32 1960 1. 564 0.7588- 6-59 1. 92 1.77 1120 1.048 0.433

11- 1-61 1.50 1.68 1420 1.344 0.5493-13-62 2.33 1.20 1330 1. 519 0.5146-11-63 1. 82 1. 70 1320 1.412 0.510


Watershed No. 2116 Area: 1363 acres

Date t kl Qp R Qp/A(h~) (hr) (cfs) (in)

12-29-60 0.41 0.77 219 0.139 0.1601-31-63 0.50 0.77 563 0.397 0.4103-22-64 0.25 0.87 219 0.105 0.1603-24-64 0.50 0.48 356 0.200 O. :26J7-25-64 0.25 0.70 194 0.107 0.1421-10-65 0.50 0.70 414 0.306 0.3412-22-65 0.17 0.77 186 0.108 0.1369- 9-65 0.41 0.72 186 0.107 0.136

Average t pAverage k

l

= 0.37 hours= 0.721 hours

78


Datet p k1 Q R

Qp/A(hr) (hr) (c¥s) (in)

3-14-61 1. 25 1.60 644 0.550 0.30711-13-65 1.42 1.28 1060 0.826 0.506

Average t p = 1.34 hoursAverage k1 = 1.44 hours


Date t k1 Qp R(h~ ) (hr) (cfs) (in) Qp/A

11-21-57 0.41 0.87 1280 0.579 0.46612- 6-57 0.67 0.48 2350 0.872 0.855

4-16-60 0.75 0.80 1750 0.801 0.6373-13-62 1.41 0.87 1135 0.675 0.4135-14-63 1.50 0.82 5680 3.504 2.068


Watershed No. 2130 Area: 29248 acres

Date t .k1 Q RQp/A(h~) (hr) (c¥s) (in)

11-28-54 4.0 2.31 13600 2.279 0.4654-15-63 1. 83 2.48 6140 0.623 0.210

12-14-65 2.60 1.66 5610 0.724 0.19112-14-65 1. 91 3.09 11860 1.156 0.400


Watershed No. 2160 Area: 16~896 acres

Date t kl Qp RQp/A(h~) (hr) (cfs) (in)

11-19-52 0.50 1. 33 1795 0.160 0.1068- 6-59 0.50 1. 81 1805 0.181 0.1064-16-60 1.08 0.65 7967 0.757 0.4715-12-60 0.75 1. 21 3210 0.251 0.1895-14-60 1. 25 1. 40 11519 2.423 0.6812-13-61 1.67 2.22 3226 0.406 0.1904-14-63 0.58 2.17 3233 0.363 0.192


Watershed No. 2230

79

Area: 3884.8 acres

Date t kl Qp RQp/A(h~) (hr) (cfs) ( in)

10-23-58 1. 50 1.64 3810 2.017 0.9804-17-60 0.50 0.63 2880 0.768 0.7675-14-60 2.00 0.87 4320 2.299 1.112



Datet p k1 Qp R

Qp/A(hr) (hr) (cfs) (in)

12- 6-57 0.25 0.89 255 0.090 0.1532-28-58 0.25 0.60 535 0.252 0.322



Date t p kl Q RQp/A(hr) (hr) (c¥s) ( in)

1-21-55 1.42 2.48 1300 0.678 0.23110-23-58 1. 75 2.98 2300 0.968 0.409

5-13-60 0.58 2.60 1990 0.552 0.354


Watershed No. 2280 Area: 1747.2 Acres

Date t p k1 Q RQp/A(hr) (hr) (c¥s) ( in)

2-28-32 1.25 0.72 2240 1.845 1.2826- 3-32 0.75 0.65 1330 1.050 0.7613- 3-33 1.50 0.72 775 0.730 0.4431- 1-37 1.50 0.85 1409 1.231 0.8063- 2-39 1.00 1.08 1448 0.769 0.828

12- 7-42 1.00 0.46 1185 0.539 0.6783-26-52 1.50 1.45 1440 1.688 0.824

10- 4-63 2.00 1. 93 1030 1. 774 0.58911-13-64 0.50 0.77 1090 0.610 0.62312-14-65 1. 75 1.45 1810 2.711 1.035

Average t p = 1.28 hoursAverage k 1 = 1.01 hours

80


t p kl Qp RQp/ADate (hr) (hr) (cfs) ( in)

4- 1-23 0.75 0.85 1748 0.799 1.04511- 5-25 0.25 0.60 1500 0.646 0.89712-23-34 1. 00 0.87 2320 1. 873 1.400

9-28-37 0.50 0.36 1432 0.423 0.8574- 3-39 0.50 0.82 1064 0.658 0.6363-26-52 1.50 0.60 1965 1.622 1.176

10- 6-61 0.50 0.53 1100 0.458 0.658



Datet p kl Qp R


12-13-27 0.50 0.72 314 0.521 0.4624-11-30 1. 50 0.67 2080 7.352 3.0663- 1-39 0.50 0.79 555 0.663 0.818

11-28-54 0.67 0.91 676 1.071 0.99612- 6-56 0.75 0.43 376 0.521 0.55412-30-60 0.67 0.53 1400 1.360 2.063



Date t p k1 Q RQp/A(hr) (hr) (c¥s) (in)

4-11-30 0.91 0.89 1500 2.826 2.1382-27-35 0.67 1.02 2180 3.956 2.9873- 2-39 0.67 0.53 1700 2.234 2.3304- 8-39 0.75 0.60 1140 1.156 1.562

11-17-48 0.75 1.08 1428 3.595 1. 95712-30-60 0.25 0.83 2867 3.741 8.929


Watershed No. 2440

81

Area: 755.2 acres

1 t p kl Q RDate

(hr) ·(hr) (c¥s) (in) Qp/A

5-16-27 1.00 0.96 1160 2.029 1.53511-17-48 1.00 0.72 950 1.430 1.25712-30-60 0.50 0.41 1100 1.117 1.456



Datet p kl Qp R


3-23-27 0.75 0.56 325 0.318 0.4874-11-30 0.75 0.86 1547 1.424 2.3242-28-32 0.67 .0.58 426 0.425 0.640

10-15-38 0.91 0.86 931 1.353 1.39811-17-49 0.75 1.02 781 1.060 1.173

3- 6-63 0.67 0.53 406 0.369 0.609



Datet p k1 Qp R


12- 3-50 0.92 1. 20 2090 1. 225 0.8993-11-51 0.50 1.39 1180 0.766 0.507

12-29-60 0.33 0.34 1460 0.448 0.628



t kl Qp RDate (h~) (hr) (cfs) (in) Qp/A

3- 6-63 0.67 0.37 2105 1.182 1. 6044-14-63 0.91 0.48 755 0.478 0.575

12-12-63 1. 25 0.77 665 0.568 0.506


82


Datet p kl Qp R


3- 5-60 1. 33 1. 57 1400 0.982 0.5005-13-60 0.33 0.65 1900 0.<+80 0.6765-13-60 0.75 1.25 865 0.459 0.3083-12-62 0.75 1.54 1470 0.636 0.523


Watershed No. 2750 Area: 620.8 acresji

Date t p kl Qp R(hr) (hr) (cfs) ( in) Qp/A

4-12-17 1.00 0.80 588 0.948 0.9474-19-17 0.67 0.48 542 0.600 0.8735- 8-43 0.50 0.48 1080 1. 328 1. 7392-29-48 0.75 0.55 712 1.106 1.1463-12-51 0.50 0.35 1030 1.138 1.6594-10-51 0.41 0.34 944 0.758 1.520

12- 6-56 1.00 0.35 1950 2.688 3.14111-20-57 1. 25 0.35 1010 1. 581 1.62612- 6-57 0.67 0.24 1720 1. 992 2.770

7- 3-58 0.75 0.48 970 1. 359 1.56212-30-60 0.25 0.72 1280 1. 201 2.061



Date t p k 1 Q RQp/A(hr) (hr) (c¥s) (in)

12-28-36 0.67 0.48 136 0.496 0.7586-11-37 0.33 0.55 169 0.412 0.9439-26-37 0.67 0.41 224 0.807 1. 2479-27-37 1.00 0.19 449 1.685 2.5052-28-38 0.41 0.19 223 0.407 1.2443- 2-39 0.50 0.31 177 0.407 0.9874- 7-39 0.50 0.42 180 0.535 1.0044- 8-39 0.50 0.48 203 0.636 1.132

11-15-42 0.50 0.36 169 0.412 0.9434-16-60 0.67 0.48 129 0.412 0.719



83

t p k 1 Q RQp/ADate

(hr) (hr) (c¥s) ( in)

4-15-63 0.25 0.81 148 0.378 0.7055-14-63 0.41 0.79 346 1.134 1. 7435-17-63 1.00 0.87 97 0.493 0.4883-23-64 0.33 0.62 146 0.463 0.7351-24-65 0.75 0.31 131 0.619 0.6602- 4-65 0.58 0.42 1700 6.134 8.568



t k 1 Qf) RDate (h~) (hr) (cfs) (in) Qp/A

5- 9-40 0.42 0.23 720 0.593 1. 2095- 8-43 0.59 0.36 506 0.510 0.850

11-14-47 1.00 0.65 937 1.386 1. 5743-14-63 0.75 0.38 512 0.522 0.8602- 3-65 1. 25 0.48 5100 9.897 8.568



t k 1 Qp RDate (h~) (hr) (cfs) (in) Qp/A

1-26-56 0.57 0.57 466 0.481 0.7354-16-60 1.00 0.34 813 1. 013 1.2832- 3-65 0.80 0.45 1800 2.821 2.840


84


Datet p k 1 Qp R


4-27-16 1.00 1. 26 680 0.333 0.2843-10-17 0.75 0.77 465 0.182 0.1945-18-17 0.50 1. 56 960 0.459 0.4012- 1-61 0.75 0.96 1240 0.713 0.518

Average tp = 0.75 hoursAverage k1 = 1.14 hours ,

I~


Datet p k 1 Qp R

Qp/A(hr) (hr) (cfs) ( in)

2-18-60 0.50 1. 97 1125 0.828 0.47012- 4-60 0.25 1.32 900 0.541 0.37611- 1-61 0.75 1.22 3510 2.174 1.466

3-13-62 1. 25 1.01 1885 1. 066 0.7873- 6-63 0.50 1. 51 1470 0.968 0.6143-26-63 0.50 1.59 1260 0.771 0.5267-25-64 0.33 1. 01 3070 1.870 1.2822- 4-65 1.17 1.27 4120 3.691 1. 7218-26-65 0.67 0.84 1585 0.877 0.622



t p k1 Qp RQp/ADate (hr) (hr) (cfs) (in)

1-26-56 0.75 0.84 1070 0.772 0.5141-21-57 0.91 0.84 1420 0.772 0.798

11-21-57 1.00 0.63 991 0.607 0.55612- 6-57 0.25 0.75 990 0.408 0.55610-31-61 1.00 0.63 1325 1.015 0.74411- 1-61 1.00 0.77 4130 2.343 2.321

3-26-63 0.50 0.72 1135 0.916 0.6377-25-64 0.67 0.65 1570 0.607 0.8825- 4-65 0.58 0.48 1635 0.853 0.918


Watershed No. 3300

85

Area: 6265.6 acres

Datet p k l Qp R


11- 2-59 1.0 2.53 580 0.244 0.0923-30-60 2.0 2.84 2242 1. 350 0.3578- 6-62 0.25 2.12 794 0.250 0.1269- 5-62 0.25 1. 93 744 0.178 0.1189- 6-62 0.50 2.05 1092 0.372 0.1663-26-63 1. 50 2.66 700 0.369 0.112



Date t p kl Q R(hr) (hr) (c¥s) ( in) Qp/A

11- 1-59 0.50 1. 63 635 0.517 0.3323-30-60 0.75 1. 89 1445 1.503 0.757

10-31-61 0.25 1.71 1580 1.493 0.82811- 1-61 0.25 1. 88 1185 1.132 0.621

3-26-63 1. 08 1. 60 1120 1.112 0.5875-14-63 0.91 1. 35 1840 1. 678 0.9431- 6-64 0.25 1. 45 1830 1. 297 0.959

Average t p = 0.57 hoursAverage k l = 1.64 hours

Documents

HYDROGRAPH STUDY AND PEAK DISCHARGE DETERMINATION · a flood hydrograph is presented in Figure 2. Since the shape of the flood hydrograph is a steep triangle, two hydrograph parameters,