Model Hydrographs

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2005

Prepared in cooperation with State of 

Illinois Department of Public ff^orks 

and Buildings, Division of Highways
Model Hydrographs

By W. D. MITCHELL

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2005

Prepared in cooperation with State of 

Illinois Department of Public tf^orks 

and Buildings, Division of Highways

A discussion of the use of time and 

areal characteristics of a drainage 

basin to describe its flood hydrograph

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1972
UNITED STATES DEPARTMENT OF THE INTEPIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress catalog-card No. 79-186800

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 - Price 45 cents (paper cover)

Stock Number 2401-2050
CONTENTS

Abstract __ _____________________________________________________ 1

Introduction. _____________________________________________________ 1

Elements of the model hydrograph_____--___--_---____-____,______ 3

Translation hydrograph___-___-___-__--____-___________________ 3

Storage____________________________________________________ 4

Routing consideratians___-_-__---_______---___-__________ 6

Linear routing__________________________________________ 7

Nonlinear routing _________________________________________ 8

Duration.____________________________________________________ 10

Linear models___________________________________________ 10

Nonlinear models________________________________________ 11

Model hydrographs---_____-__---_-____-___---___-_-___-_____-_____ 15

Linear models_______________________________________________ 15

Nonlinear models____________________________________________ 15

Application to specific areas________-______-__-_________________ 16

Example 1______________________________ 16

Example 2__________________________________ 18

Example 3____._________._______________ 18

Example 4______________________________ 18

Example 5____________________________ 21

Example 6______________________________ 22

Determination of hydrograph parameters.-___________________________ ?2

Determination from observed hydrographs_________-____--____-. 23

Characteristic time, T______________________________________ ?3

Storage constants, k and £________________-_-___-__---_-____ T3

Determination from basin characteristics_____________--__-_--____ 27

Unit hydrograph-_________________________________________________ ?**

Summary and conclusions___________________--____________________- f7

References_________________________________ f

ILLUSTRATIONS

Page 

FIQTJEE 1. Translation hydrograph, instantaneous._____---___-_-_-- 5

2. Translation hydrographs, finite values of D/T____________ 14

3-6. Hydrographs for:

3. Tributary to Second Creek at Keptown, I1L__ _ 17

4. Tributary to Kankakee River near Bourbonnais,

Ill_________________________-_-_-___-_ _ 19

5. Mazon River near Coal City, 111 ______________ 2T

6. Tributary to Vermilion River at Lowell, 111., and for

tributary to Mud Creek near Tower Hill, Ill____ 21

m
IV CONTENTS

FIGURES 7-10. Graphs of: Page

7. Analyses for storage constants of model hydrographs _____________________________________ 25

8. Analyses for storage constants of observed hydrographs. ____________________________________ 26

9. Observed versus computed values of T. __________ 29

10. Observed versus computed values of k __________ 30

11. Proportional graphs, resulting from routing through linear

storage, S=0.20 0_________________________ 31

12. Nonproportional graphs, resulting from routing through

nonlinear storage, S=10 0°-5 _________________________ 32

13. Nonproportional graphs, resulting from routing through

nonlinear storage, 5=0.01 02 ______________________ 33

14. Semilogarithmic plotting, recession limbs of graphs from

figures 11, 12, and 13___________________.__ 34

15. Typical recessions, previously published unit hydrographs_ 35

16. Recession hydrographs, all for Money Creek above Lake

Bloomington, 111., computed by various methods___-__- 36

TABLES

Page

TABLE 1. Section of typical model hydrograph (linear) computations-. 9 

2. Transformation of translation hydrograph from instantaneous to finite values of D/T_________________________..__ 12

3-28. Linear model hydrographs (S=W); k/T= :

3. 0.20________________________--______-__.______ 41

4. 0.25_________-__-_---_____---_--__---____-___- 42

5. 0.30__________-_-___-_____-_-_---_---___--_._- 43

6. 0.35-_- _ _ -__-__ 44

7. 0.40_______________--____-__---_-_----_____-__ 45

8. 0.45 ___ --_ 46

9. 0.50______________________-_--______-_________ 47

10. 0.55________________.__-____-_---_----____--__ 48

11. 0.60________________________________________ 49

12. 0.70________________________________._________ 50

13. 0.80.__________________________--__--_________ 51

14. 0.90. ________________________-__---___-__---_ 52

15. 1.00._____________--_________--__--_--_-_-____ 53

16. 1.10________________________________________ 54

17. 1.20________________________________-_____--_- 55

18. 1.30______________________________--______--_- 56

19. 1.40___________________________ 57

20. 1.50__________________________________________ 58

21. 1.60_______________________________-__--_-.__- 59

22. 1.80____________________________ 60

23. 2.00_______________________________-______--._ 61

24. 2.20__________________________________________ 63

25. 2.40_____________________.-______ 64

26. 2.60____________________________ 65

27. 2.80________________________--.___ 66

28. 3.00.________._______________.___--__-._------ 68
CONTENTS 

TABLES 29-36. Nonlinear model hydrographs (S=kOx ); x=0.5;

29. 2.0._.___-_-_. _.___._..._..._..__._..____.._ 70

30. 5.0._.___ _... .. _ ___ __. 72

31. 7.0.____.____-.__ ____________________ _ __._ 74

32. 8.0.-. __ _ _ ___ _-__ ___ 76

33. 9.0 _ _ __ -__ _ ___ __ 78

34. 10.0.____-_____-_____________________________ 80

35. 11.0__________ _____________________________ 82

36. 12.0__-____ __________________________________ 84

SYMBOLS

(The following symbols are listed in alphabetical order. Each symbol indicates

the basic term usually represented, with no attempt to show the many and unavoidable duplicate uses.)

A Drainage area (square miles).

D Duration of rainfall excess (hours).

H Time from beginning of rainfall excess (hours); also change in elevation 

between highest point on the drainage divide and channel bed at gage 

(feet).

/ Inflow (sometimes expressed in units of cubic feet per second, but mo~e 

often in terms of the dimensionless ratio QT/APe).

k A coefficient in the relation between storage and outflow (hours).

L Length of a drainage basin (miles).

0 Outflow (sometimes expressed in units of cubic feet per second, but mo~e 

often in terms of the dimensionless ratio QT/APJ.

Pe The amount of rainfall excess (inches).

Q Rate of discharge (cubic feet per second).

S Basin storage (cubic feet).

T Base length of instantaneous translation hydrograph (hours).

t Increment between successive abscissa of hydrographs (usually dimensionless) .

x Exponent in the relation between storage and outflow (dimensionless).
MODEL HYDROGRAPHS

BY W. D. MITCHELL

ABSTRACT

Model hydrographs are composed of pairs of dimensionless ratios, arrayed in 

tabular form, which, when modified by the appropriate values of rainfall excels 

and by the time and areal characteristics of the drainage basin, satisfactorily 

represent the flood hydrograph for the basin.

Model hydrographs are developed from a dimensionless translation hydrograph, having a time base of T hours and appropriately modified for stor^n 

duration by routing through reservoir storage, S=kOx. Models fall into tvo 

distinct classes: (1) those for which the value of x is unity and which have all tl 3 

characteristics of true unit hydrographs and (2) those for which the value of x is 

other than unity and to which the unit-hydrograph principles of proportionality 

and superposition do not apply.

Twenty-six families of linear models and eight families of nonlinear models in 

tabular form form the principal subject of this report. Supplemental discussions 

describe the development of the models and illustrate their application. Other 

sections of the report, supplemental to the tables, describe methods of determinir <r 

the hydrograph characteristics, T, k, and x, both from observed hydrograpl * 

and from the physical characteristics of the drainage basin.

Five illustrative examples of use show that the models, when properly converted to incorporate actual rainfall excess and the time and areal characteristics 

of the drainage basins, do indeed satisfactorily represent the observed flood 

hydrographs for the basins.

INTRODUCTION

This report presents an array of model hydrographs and explairs 

their development, their use, and their relation to unit hydrographs.

A model hydrograph is a generalized expression for the distribution, 

with respect to time, of the surface runoff from a drainage arer,. 

Although expressed in terms that make it applicable to many areas, 

it may be readily converted to explicit terms for a particular arer,. 

Like the unit hydrograph, it is not concerned with the amount of 

rainfall excess that may result from a given pattern of rainfall, but 

only with the time distribution of the excess.

A model hydrograph is distinctive from a unit hydrograph. The 

latter normally is prepared for a particular drainage area and for a 

unit amount of rainfall excess in a particular time. These restrictions

1
2 MODEL HYDROGRAPHS

limit the use of the unit hydrograph to the area from which it is 

derived. The model hydrograph, on the other hand, ir designed to 

apply to a wide range of sizes and types of drainage areas that have 

a wide range of conditions of rainfall excess. This application is facilitated by expression of the coordinates of the models in terms of 

dimensionless ratios.

Another important distinction between the two concepts, as will 

be shown subsequently, is that the unit-hydrograph principle of proportionality of ordinates limits use of the unit hydrograph to those 

areas for which the storage effect is linear. Many drainage areas do, 

indeed, appear to have linear storage or storage so rear to linear 

that the differences may be disregarded. The widespread success of 

the customary unit-hydrograph procedures is adequate testimony to 

this fact. But occasionally an area is found for which storage effects are 

so far from linear that unit-hydrograph techniques are not applicable. 

For areas with marked nonlinear storage, ordinates of hydrographs are 

not in linear proportion to rainfall excess, and the unit-hydrograph 

techniques of proportionality and superposition cannot te applied. To 

include these types of areas, the general principles for analysis and 

synthesis of hydrographs must be expanded. The term "model hydrograph" has been adopted to designate this new and broader concept, 

under which the unit hydrograph becomes a special, simplified case 

of the model hydrograph.

The full implications of this more generalized approach to the 

analysis and synthesis of the hydrograph are not, as yet, completely 

realized. Some of the techniques which eventually may be of general 

use, as well as some of those which must be restricted to the special 

case of the unit hydrograph, have not yet been recognized. Much 

work remains to be done, especially with regard to the effects of 

nonuniform distribution of rainfall excess and the effects, for nonlinear 

models, of high initial inflow from antecedent rainfall. Nevertheless, 

significant progress has been made, and a record of that progress is 

the theme of this report.

The basic concepts of this report were developed over a period of 

several years. Materials and conclusions from other projects within 

the Illinois District of the Water Resources Division have been appropriated as needed. For example, the adoption of the dimensionless 

form for the hydrographs resulted from earlier studies (Mitchell, 1948 

and, particularly, Mitchell, 1962). Needed impetus for the completion 

of the project did not develop, however, until intensive analyses were 

undertaken in connection with a district project intended to determine 

floodflows from small drainage areas and prosecuted in cooperation 

with the Illinois Department of Public Works and Buildings, Division 

of Highways. As it became more apparent that the techinques described
INTRODUCTION 3

in this report were well adapted to analysis of the small-basin flood 

data and that these projects would clearly benefit from each other, 

the two projects were closely coordinated. Many of the tables and 

most of the illustrations which appear in this report have been taken 

from the work done in connection with the Division of Highways 

cooperative project.

In the preparation of this report, three other members of the district 

staff have rendered invaluable assistance. George W. Curtis supervised 

the long and tedious manual computations for the linear models, a 

chore which has extended intermittently over a period of about 8 

years, Terence E. Harbaugh contributed many valuable suggestiors, 

reviewed the manuscript with great care, made numerous tests of 

validity, and provided the computations for the nonlinear models. 

Oscar G. Lara supervised the statistical analyses and contributed 

suggestions which led to the systematization of the nonlinear models.

ELEMENTS OF THE MODEL HYDROGRAPH

Three principal elements enter into the concept and the use of model 

hydrographs. These are (1) the concept of the dimensionless, instantaneous translation hydrograph, (2) the effects of storage, ard 

(3) the effects of storm duration.

TRANSLATION HYDROGRAPH

To understand the translation hydrograph, consider a strange, 

wonderland basin in which there is no such thing as storage. Runoff 

from such a basin would differ greatly from that to which we are 

accustomed. As soon as a rainfall excess appeared on any part of a 

drainage basin, it would flow immediately to the drainage outlet. 

("Immediately" is an ambiguous term, but let it suffice for the 

present.) The result at the outlet would be first, a quick, sharp rise 

to a peak greatly in excess of present natural occurrence and second, 

a very rapid recession to a state of no flow.

How quick, how sharp, and to what peak? These questions may be 

answered by a more deliberate consideration of translation flov^, 

a purely hypothetical type of flow uninfluenced by storage. Let 

a drainage area, A, be divided into equal, minute parts, dA. Assume a 

magic carpet whereby rainfall excess accumulating on any dA may b°. 

transported to the outlet in an interval of time proportional to tire 

distance it must travel. Now assume that rainfall excess of any depth, 

Pe , appears instantaneously, simultaneously, and uniformly over 

the entire basin, A. Then flow at the outlet would occur as follows: 

During the first instant, flow from the area immediately adjacert 

to the outlet;during the next instant, flow from those dA'simmediately 

beyond the first; at any time, H, after appearance of rainfall excess,

41416-375 O 72 2
4 MODEL HYDROGRAPH&

flow would be from those areas removed from the outlet by the distance corresponding to the value of H, and the rate of flow would be 

proportional to the number of dA's at that particular distance. Flow 

would increase to a maximum for that particular value of H at which 

the corresponding distance taps the maximum numbe1* of dA's: it 

would then begin to decrease and would fall to zero after that time, T, 

when the flow arrives from the most distant dA.

The total volume of flow, V, would equal the product of A and Pe ; 

if V were expressed in cubic feet, with A in square mitas and Pe in 

inches, V=APe (5,280) 2/12, or V= 2,323,200 APe . Since the entire 

flow would pass the outlet in the period of Thours, the average rate 

of flow would be Qa= 2,323,200 APe /3,600 T= 645.333 APe T cubic 

feet per second.

The preceding considerations define, in a general way, the translation hydrograph for instantaneous rainfall excess. The hydrograph 

is for a drainage area of A square miles and represents instantaneous 

rainfall excess of Pe inches; it has a time base of Thours and an average 

ordinate of 645.333 APe/T cubic feet per second. The precise shape 

of the graph is dependent upon the shape of the drainage area and upon 

how distances (between the dA's and the outlet) are measured. Should 

distances be measured by air line? Should they be measured along 

principal stream channels? Should they be weighted to allow for 

differences in slope and roughness? Experience with many hydrographs 

indicates that, in general, these questions are not important. In rare 

instances, one or another of these considerations may become significant, but these will be dealt with at a later time, perhaps in a subsequent report. For the present, and for the large majority of drainage 

areas, a sufficiently accurate assumption is that the maximum ordinate 

of the instantaneous translation hydrograph is twice the average 

ordinate and occurs at time H = T/2 and that the graph is two straight 

lines connecting this maximum ordinate to the zero ordinate at 

H= 0 and at H= T. Subsequent manipulations of this graph are so 

extensive that even appreciable variations from this ideal shape 

become almost completely obliterated.

One further observation concerning this hydrograph is that its 

usefulness is greatly enhanced by reducing it to dimensionless terms, 

QT/APe for the ordinate and H/T for the abscissa. Figure 1 presents 

in dimensionless form the instantaneous translation hydrograph.

STORAGE

The instantaneous translation hydrograph, as shown in figure 1, is 

only a starting point for further developments toward a model hydro-
ELEMENTS OF THE MODEL HYDROGRAPH

1290 2/

FIGURE 1. Translation hydrograph, instantaneous.

graph. For natural drainage areas, the runoff hydrograph never appears 

in this simple form, but is modified by at least two important factor?. 

One of these factors is storage. (The other, duration, will be discussed later.)

The extremely diverse and complicated nature of the actual storage 

facilities within a drainage basin would appear, at first glance, to 

preclude any successful effort toward basin-wide evaluation. But 

experience with many hydrographs indicates that, in general, and for 

the large majority of drainage areas, the effect of basin storage may 

be represented as a modification of the translation hydrograph by the 

techniques of reservoir routing, and that, as will be shown subsequently, to determine the storage relationships needed to make the 

modification for a particular drainage area is usually feasible.
MODEL HYDROGRAPHS 

ROUTING CONSIDERATIONS

The basic relation between inflow, outflow, and storage is expressed 

by the equation of continuity, which for an incompressible fluid such 

as water mav be written

(1)

that is, the inflow, /, is equal to the outflow, 0, plus the change of 

storage, AS/Ai. If the time increment, AZ=^ ti, is sufficiently small, 

the values of / and 0 may be considered to be the average of their 

respective values at time t\ and U, or (/!+/2)/2 and (Oi + 02)/2. Further, 

A$ may be expressed as the difference in storage volume at times t\ 

and £2, or &S=S2 Si. Equation 1 may then be expressed as

02= (2&/AO - 0i - (2&/AO + (/i + /,) . (2)

Three items of information are required by equation 2. One of these 

is a starting value, or the value of #1 at the beginning of the first 

increment of time, A£. (For succeeding increments of time, #1 is the 02 

of the preceding step.) To obtain the initial Oi, simply start the computations at a time for which the outflow is known, as at the beginning of a flood period, when the outflow generally is equal to the inflow. 

In many cases the initial outflow will be zero, or at leapt, so small as 

to be of no practical consequence. In fact, for simplicity in the developments immediately following, initial outflow is assumed to be 

zero.

The second item of information is an inflow hydrograph from which 

to determine values of /i and /2 for successive times at intervals of 

At. This information is provided by graphs such as figure 1, the instantaneous translation hydrograph.

The third item needed for computation of 02 is a definitive expression for storage. In reservoir routing, storage is assumed to be a function of outflow and is represented by the generalized expression

S=kO*, (3)

in which k is a coefficient of proportionality, 0 is the outflow, and x 

is an exponent dependent upon the relative slopes of the stage-discharge and the stage-storage relations.

A special case arises when the value of x is unity. Tl en, and only 

then, the storage is said to be linear. Many runoff hydrographs exhibit the characteristics of linear storage. The number of exceptions, 

however, is so great that nonlinear storage (x other than unity) cannot be ignored. But let us first consider the simple, special case 

linear storage, or

8=kO. (4)
ELEMENTS OF THE MODEL HYDROGRAPH 7 

LINEAR ROUTING

In equation 4, S has the dimension of cubic feet, and 0 has the 

dimension of cubic feet per second. Therefore, k must have the dimension of time. Routing computations may be greatly simplified by 

expressing k in dimensionless form, or as a ratio to T. Let k/T=r; 

then S=rTO.

In the generalized routing expression, equation 2, A£ also has the 

dimension of time. Here, again routing computations will be facilitated 

by expressing A£ as a ratio to T. Let M/T=p. Then

= (2r/p)0. 

Equation 2 then becomes

02= (2r/i>)01 -0,- (2r/p)02 + (/!

or

0,(2r/i>+l) = 01 (2r/p-l) + (/1 +/a). (5)

For any specific problem with linear storage, r will have a fixed specific value, such as r=k/T=0.20, and p will have a fixed specific value, 

such as p=M/T 0.02; hence 2r/p will have a specific value, such as 

2X0.20/0.02=20, and equation 5 will assume the form

02 =(19<91 +/1 +/2)/21. (5a)

Note that this simple form of the routing equation is appropriate 

onty when storage is a linear function of outflow and that the constants 

in the equation will vary with the values of k and A£. For example, 

if k becomes 0.5T(r=0.5) while M remains 0.02T(p=0.02), then

Q»=(4901 +/1 +/,)/51. (5b)

Values of k used in this report cover a considerable range, but the 

value of A< has been kept the same for most linear routing computations. As pointed out above, A< should be small enough that the average values of / and 0 during the interval will be virtually the same as 

the average of their respective values at the beginning and end of the 

interval. For this purpose alone a time increment of O.lT7 might be 

sufficiently small ; however, in order that there may be no doubt as to 

the accuracy of the computations and also to provide more accurate 

data concerning both time and magnitude of peak discharge, the value 

of M has been taker} as 0.02jT for most linear routing computations. 

(For exceptions, see footnotes to tables at end of report.)
8 MODEL HYDROGRAPHS

Table 1 presents a section of a typical linear routing computation. 

In this instance, the storage equation is $=0.20 0, or k/T=Q3Q; the 

routing equation assumes the specific form of equation 5p,. Columns 1 

and 2 are a listing of the coordinates of figure 1, the instantaneous 

translation hydrograph, at intervals of A£=0.02T. Any given line in 

column 3 is the sum of column 2 on that line and column 2 on the 

preceding line; this process provides the /i+/2 terms of the routing 

equation. Column 4 is the modified, or outflow, instantaneous hydrograph and is obtained by taking a value from column 4, multiplying 

it by 19, then adding the value of column 3 of the following line, 

and dividing the sum by 21. (See equation 5a.) The quotient is entered 

as the value for the second line of column 4. The remaining columns 

of table 1 will be discussed subsequently.

NONLINEAR ROUTING

Nonlinear routing must take account of problems that are numerous, 

varied, and of considerable importance. One of these is the adjustments for duration, but this problem must be reserved until the 

whole subject of duration is considered. Other problems concern the 

magnitude of flow at the beginning of rainfall excess and tl °, magnitude 

of rainfall excess. These, too, will be reserved for later discussion. 

The problem which deserves immediate attention is the solution of 

the nonlinear routing equation.

When, in equation 3, x assumes any value other than unity, equation 

2 cannot be reduced to a simple form such as equation 5a. Except for 

a few special cases, the routing equation remains so cumbersome that 

solutions are prohibitively tedious or are rough and unsatisfactory 

approximations. (This situation is improved by use of an electronic 

computer, but such equipment became available only near the end 

of this study.)

Fortunately, there are at least two special cases in which the routing 

equation may be solved with satisfactory accuracy and reasonable 

speed on desk calculators which are able to abstract square root. 

These cases are

x=2.0 

and

a;=0.5.

The first case now appears to have limited practical value in that 

x for natural drainage basins appears rarely to exceed unity. On the 

other hand, the second case is quite practical; several small drainage 

basins have been found to have a value of x near 0.5.

Results of the nonlinear routings will be described as the need 

arises.
Table 1. Section of typical model hydrograph (linea

H

T

(1)

0.50

.52

.54

.56

.58

.60

.62

.64

.66

.68

.70

.72

.74

.76

.78

.80

.82

.84

.86

.88

.90

.92

.94

.96

.98

1.00

1.02

1.04

1.06

1.08

1.10

£T

APe

(2)

1,290.667

1,239.040

1,187.413

1,135.787

1,084.160

1,032.533

980.907

929.280

877.653

826.027

774.400

722.773

671.147

619.520

567.893

516.267

464.640

413.013

361.387

309.760

258.133

206.507

154.880

103.253

51.627

0

0

0

0

0

0

I21l + 01.2

APe APe

(3)

2,529.707

2,529.707

2,426.453

2,323.200

2,219.947

2,116.693

2,013.440

1,910.187

1,806.933

1,703.680

1,600.427

1,497.173

1,393.920

1,290.667

1,187.413

1,084.160

980.907

877.653

774.400

671.147

567.893

464.640

361.387

258.133

154.880

51.627

0

0

0

0

0

Inst

hgh

(4)

816.689

859.371

893.072

918.646

936.868

948.437

953.988

954.093

949.271

939.992

926.680

909.719

889.456

866.206

840.254

811.856

781.246

748.635

714.213

678.152

640.609

601.724

561.626

520.430

478.240

435.152

393.709

356.213

322.288

291.594

263.823

0.02T

hgh

(5)

793.102

838.030

876.222

905.859

927.757

942.652

951.212

954.040

951.682

944.632

933.336

918.200

899.588

877.831

853.230

826.055

796.551

764.940

731.424

696.182

659.380

621.166

581.675

541.028

499.335

456.696

414.430

374.961

339.250

306.041

277.708

Summation

0.02T hgh

(6)

7,966.424

8,804.454

9,680.676

10,586.535

11,514.292

12,456.944

13,408.156

14,362.196

15,313.878

16,258.510

17,101.846

18,110.046

19,009.634

19,887.465

20,740.695

21,566.750

22,363.301

23,128.241

23,859.665

24,555.847

25,215.227

25,836.393

26,418.068

26,959.096

27,458.431

27,915.127

28,329.557

28,704.518

29,043.768

20,350.709

29,628.417

Summation

lag O.IT

(7)

4,465.130

5,073.640

5,727.450

6,427.162

7,173.322

7,966.424

8,804.454

9,680.676

10,586.535

11,514.292

12,456.044

13,408.156

14,362.106

15,313.878

16,258.510

17,191.846

18,110.046

19,009.634

19,887.465

20,740.695

21,566.750

22,363.301

23,128.241

23,859.665

24,555.847

25,215.227

25,836.393

26,418.068

26,959.096

27,458.431

27,915.127

O.IT 

hgh 

(8) 

700.259 

746.163 

790.645 

831.875 

868.194 

898.104 

920.740 

936.304 

945.469 

948.844 

946.980 

940.378 

920.488 

914.717 

896.437 

874.981 

850.651 

823.721 

704.440 

763.030 

729.695 

694.618 

657.965 

610.886 

580.517 

539.980 

498.633 

457.200 

416.934 

378.456 

342.658 
10 MODEL HYDROGRAPHS

DURATION

The preceding section has shown how the instantaneous translation 

hydrograph may be modified by reservoir routing to produce hydrographs such as that shown as column 4 of table 1. Some of these 

begin to resemble actual, natural, hydrographs. But then still is one 

important difference: duration, or the interval of time during which 

rainfall excess is generated.

In the development of the initial hydrograph (fig. 1), it was specified 

that "rainfall excess of any depth, Pe , appears instantaneously, 

simultaneously, and uniformly over the entire basin, A." Routing 

a hydrograph does not change its rainfall-excess characteristics. 

We must recognize, therefore, that the resulting graphs are for 

rainfall excess that "appears instantaneously, simultareously, and 

uniformly over the basin." Because these characteristics are unrealistic, our models must be adjusted to accommodate rainfall excess as 

it actually occurs. Adjustments for lack of simultaneous and uniform 

excess must await later consideration, but the adjustment for duration 

(finite, rather than instantaneous) may be made now.

The duration, D, or time interval during which rainfall excess is 

generated, obviously has the dimension of time and normally is 

expressed in hours. In keeping with the dimensionless character of 

the hydrographs so far developed, however, let duration be expressed 

by the dimensionless ratio, D/T.

LINEAR MODELS

For linear models, transformations for duration normally are 

effected, after routing for storage, by means of the summation curve, 

as follows: Prepare a summation curve for any available hydrograph 

whose D/T value is 2; list a second summation curve identical to 

first but lagged by a time interval equal to the desir?,d duration, 

D/T=y; subtract the ordinates of the second curve from those of the 

first and divide the remainders by the value of the ratio yjz. Table \, 

beginning with column 6, illustrates the procedure. It is not possible 

to start the transformations from column 4, since these are the values 

for instantaneous duration and the ratio y/z would be infinity. Negligible error will result, however, in computing the hydrograph for 

a finite time of very short duration, such as At=0.02TI, merely by 

averaging the successive ordinates, at intervals of Ai, of the instantaneous hydrograph. This has been done to obtaii column 5, 

the 0.02 T hydrograph. Column 6 is the summation cf column 5. 

Column 7 is identical to column 6, but has been lagged by an interval
ELEMENTS OF THE MODEL HYDROGRAPH 11

of 0.1 T. Column 8 is the differences between columns 6 and 7 divided 

by y/z=Q. 10/0.02=5 and is the hydrograph for a duration D/T= 0.10, 

or the 0.10 T hydrograph. The remaining columns in table 1 illustrate 

the computation of other hydrographs, all with k/T values of 0.20 

but with succeedingly longer values for D/T.

The question may be raised as to whether the transformations 

for D/T should be made before, rather than after, the instantaneous 

translation hydrograph is routed through storage. The answer is that 

for linear models the choice is only a matter of convenience, for the 

final results will be the same regardless of the sequence of the computations. Routing computations are more laborious than D/T 

transformatioms, and fewer routings are required if they are made 

before, rather than after, the transformations for D/T.

NONLINEAR MODELS

In nonlinear models, an instantaneous translation graph routed 

through nonlinear storage and then transformed to a particular D/T 

unfortunately results in a graph different from that obtained from the 

same instantaneous translation graph transformed to the particular 

D/T and then routed through the same nonlinear storage. In the 

sequence of their natural effects, duration is prior to storage; thus it 

is necessary in nonlinear models to make D/T transformations to 

the translation graph before routing.

Transformations for the translation hydrograph may be made in 

a manner identical to the transformation described for linear models. 

Computations for the transformations to D/T values of 0.1, 0.2, 0.5, 

0.7, 1.0, 1.5, and 2.0 are given in table 2. In this table the summation 

curve is given but once; the reader may obtain the appropriate value 

of the lagged summation curve by deducting D/T from H/T, and tl^n 

by reading the value from the indicated line of column 4.

Translation hydrographs for these finite values of D/T are plotted 

in figure 2. As D/T approaches unity the shape of the graph approaches 

that of the normal probability curve, and for values greater than 

unity, the graph approaches a trapezoid. The base of the graph, in all 

cases, is (D/T) + 1, and the upper base of the trapezoid is (D/T) 1. 

The maximum ordinate is closely approximated by a simple relationship that changes at the point D/T=l. For smaller values of D/T the 

relations is Qm= 645.333(2.0 D/T); for higher values, Qm=645.333/ 

(D/T).

For nonlinear storage developments, the appropriate finite transition hydrograph should be used, rather than the instantaneous 

translation hydrograph.

446-3715 O 72 3
Table 2. Transformation of translation hydrograph from instanta

1 1

T

0.00

.02

.04

.06

.08

.10

.12

.14

.16

.18

.20

.22

.24

.26

.28

.30

.32

.34

.36

.38

.40

.42

.44

.46

.48

.50

.52

.54

.56

.58

.60

.62

.64

.66

.68

Ui

APe

0.000

51.627

103.253

154.880

206.507

258.133

309.760

361.387

413.013

464.640

516.267

567.893

619.520

671.147

722.773

774.400

826.027

877.653

929.280

980.907

1,032.533

1,084.160

1,135.787

1,187.413

1,239.040

1,290.667

1,239.040

1,187.413

1,135.787

1,084.160

1,032.533

980.907

929.280

877.653

826.027

hgh

0.000

25.814

77.440

129.066

180.694

232.320

283.946

335.574

387.200

438.826

490.454

542.080

593.706

645.334

696.960

748.586

800.214

851.840

903.466

955.094

1,006.720

1,058.346

1,109.974

1,161.600

1,213.226

1,264.854

1,264.854

1,213.226

1,161.600

1,109.974

1,058.346

1,006.720

955.094

903.466

851.840

tion

0.000

25.814

103.254

232.320

413.014

645.334

929.280

1,264.854

1,652.054

2,090.880

2,581.334

3,123.414

3,717.120

4,362.454

5,059.414

5,808.000

6,608.214

7,460.054

8,363.520

9,318.614

10,325.334

11,383.680

12,493.654

13,655.254

14,868.480

16,133.334

17,398.188

18,511.414

19,773.014

20,882.988

21,941.334

22,948.054

23,903.148

24,806.614

25,658.454

D/T = 0.1

0.000

5.163

20.651

46.464

82.603

129.067

180.693

232.320

283.947

335.573

387.200

438.827

490.453

542.080

593.707

645.333

696.960

748.587

800.213

851.840

903.467

955.093

1,006.720

1,058.347

1,109.973

1,161.600

1,202.902

1,223.552

1,223.552

1,202.902

1,161.600

1,109.973

1,058.347

1,006.720

055.093

D/T =0.2

0.000

2.581

10.325

23.232

41.301

64.533

92.928

126.485

165.205

209.088

258.133

309.760

361.387

413.013

464.640

516.267

567.893

619.520

671.147

722.773

774.400

826.027

877.653

929.280

980.907

1,032.533

1,078.997

1,115.136

1,140.949

1,156.437

1,161.600

1,156.437

1,140.949

1,115.136

1,078.997

D/T = 0.5

0.000

1.033

4.130

9.293

16.521

25.813

37.171

50.594

66.082

83.635

103.253

124.937

148.685

174.498

202.377

232.320

264.329

298.402

334.541

372.745

413.013

455.347

499.746

546.210

594.739

645.333

694.895

740.326

781.628

818.799

851.840

880.751

905.532

926.182

942.703

D
Table 2. Transformation of translation hydrograph from instantaneous 

11

T

0.70

.72

.74

.76

.78

.80

.82

.84

.86

.88

.90

.92

.94

.96

.98

1.00

1.02

1.04

1.06

1.08

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

^li.

APe

774.400

722.773

671.147

619.520

567.893

516.267

464.640

413 . 013

361.387

309.760

258.133

206.507

154.880

103.253

51.627

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

hgh

800.214

748.586

696.960

645.334

593.706

542.080

490.454

438.826

387.200

335.574

283.946

232.320

180.694

129.066

77.440

25.814

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

ouiiima

tion

26,458.668

27,207.254

27,904.214

28,549.548

29,143.254

29,685.334

30,175.788

30,614.614

31,001.814

31,337.388

31,621.334

31,853.654

32,034.348

32,163.414

32,240.854

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

32,266.668

D/T = 0.1

903.467

851.840

800.213

748.587

696.960

645.333

593.707

542.080

490.453

438.827

387.200

335.573

283.947

232.320

180. 6^3

129.067

82.603

46.464

20.651

5.163

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

D/T = 0.2

1,032.533

980.907

929.280

877.653

826.027

774.400

722.773

671.147

619.520

567.893

516.267

464.640

413 . 013

361.387

309.760

258.133

209.088

165.205

126.485

92.928

64.533

0

0

0

0

0

0

0

0

0

0

0

0

0

0

D/T = 0.5

955.093

963.354

967.484

967.484

963.354

955.093

942.703

926.182

905.532

880.751

851.840

818.799

781.628

740.326

694.895

645.333

594.739

546.210

499.746

455.347

413.013

232.320

103.253

25.813

0

0

0

0

0

0

0

0

0

0

0

D/T 
1400

1200

1000 -

800 ~

600

400 -

200

0.2 0.4 0.6 0.8 1.0

H/T

FIGURE 2. Translation hydrographs, finite values o
LINEAR MODELS 15 

MODEL HYDROGRAPHS

The foregoing sections have presented the concept of the translation 

hydrograph, both instantaneous and finite, and have shown how tle-se 

translation hydrographs may be modified by reservoir routing techniques to represent actual runoff hydrographs. It should again be 

pointed out, and emphasized, that by expressing these hydrographs 

in terms of dimensionless ratios, rather than absolute values, a comparatively few computations will provide a systematized set of tables, 

of modest extent, from which an almost limitless number of flood 

hydrographs readily may be computed. To compute a flood hydrograph, select the appropriate hydrograph from the tables and multiply 

all the values by appropriate simple constants which are functions 

of the time and areal characteristics of the specific drainage area. 

(This conversion process is described in detail in the section "Application to Specific Areas.") The systematized tables from which this 

final computation is made are presented in tables 3-36 and constitute 

the model hydrographs.

LINEAR MODELS

Tables 3-28 constitute the linear models. Each table is distinguished 

from all the others by its unique value of the ratio k/T, which ranges 

from 0.2 to 3.0. Values of this ratio have been chosen such that by 

using the table whose value is nearest to the actual k/T ratio for a 

specific area, the tabular values will be within 5 percent of true values. 

Each table is similar to all the others in that it provides model hydrographs for various values of the ratio D/T ranging from instantaneous 

to 2.0. To select the proper linear model, first compute k/T to determine the appropriate table, then compute D/T to determine the app^opriate column within the table.

NONLINEAR MODELS

Tables 29-36 are by no means an exhaustive array of all possible 

nonlinear models, but they do appear to be a representative one. For 

all these models, the storage equation for the reservoir routing1 is 

S=k01/2 , which approximates the degree of nonlinearity most common 

in analyses of actual flood hydrographs. Further experience may demonstrate the need for a more extensive array of nonlinear models, but 

the present array is sufficient to illustrate the techniques for nonlinear 

computations and also sufficient to cover most of the problems so far 

encountered.

Each of the nonlinear models is distinguished from all the others by

its unique value of the ratio k/^APe/T, which ranges from 2.0 to 12.0. 

Values of this ratio have been chosen such that by using the table 

whose value is nearest to the actual ratio for a specific area, the tabular
16 MODEL HYDROGRAPHS

values will be within 5 percent of the true values. Each tatle is similar 

to all the others in that it provides model hydrographs for various 

values of the ratio D/T, ranging from instantaneous to 2.0. To select 

the proper nonlinear model, first compute k/^'APe /T, to determine the 

appropriate table; then compute D/T to determine the appropriate 

column within the table.

APPLICATION TO SPECIFIC AREAS

All the model hydrographs, both linear and nonlinear, are expressed 

in terms of dimensionless ratios. To prepare a flood hydrc <*raph for a 

specific area, only the proper time and areal dimensions must be 

incorporated into the appropriate model.

For all models, the abscissa of the hydrograph is expresred in terms 

of H/77 , in which H is hours from beginning of rainfall excess. To 

obtain the proper time expressions for any flood hydrograph, multiply 

the values of H/T, as given in column 1 of all the tables, by the value 

of T for the specific area.

Likewise, for all models, the ordinates of the hydrograph are expressed in terms of QT/APe . To obtain the proper discharge, in cubic 

feet per second, for any flood hydrograph, multiply the values of 

QT/APe by the value of APe/T for the specific area.

The following examples, involving both linear and nonlirear models, 

will illustrate the procedures and indicate the accuracy of results.

EXAMPLE 1

A tributary to Second Creek, at Keptown (Effingham County), 111., 

has a drainage area of 1.62 sq mi. As determined by methods subsequently described, the storage is linear, the value of k is 1.03 hr, and 

the value of T is 1.52 hr. For the storm of July 15, If 57, rainfall 

excess of 0.87 in. occurred in 0.67 hr, beginning at 1045 hr. Compute 

the surface-runoff hydrograph from the appropriate model, and compare with the surface runoff from the observed hydrograph.

By using the values just given, Jfc/T=1.03 hr/1.52 hr=0.68; D/T= 

0.67 hr/1.52 hr=0.44. The appropriate model is taken from table 12 

(fc/7^0.7), columns 1 and 6. The value of APe /Tis (1.62 sq miX0.87 

in.)/1.52 hr=0.927 cfs. The model is converted by multiplying the 

values from column 1 by 1.52 hr and the values from column 6 by 

0.927 cfs.

Four graphs are shown in figure 3. The two light lines show the total 

observed runoff and the estimate for base flow. The dashed line is 

the difference between the first two graphs, or the actual surface 

runoff. This line should be compared with the heavy continuous line 

which is the converted model hydrograph.
APPLICATION TO SPECIFIC AREAS 17

600

500

Q 400

2 

O 

O

LU

O

5 300

D 

O

D 200

100

1010

T Pe =0.87 inch

1200 1400 

TIME OF DAY, IN HOURS

1600

FIGURE 3. Hydrographs for tributary to Second Creek at 

Keptown, III.
18 MODEL HYDROGRAPHS

EXAMPLE 2

A tributary to Kankakee River, near Bourbonnais (Kankakee 

County), 111., has a drainage area of 0.192 sq mi. As determined by 

methods subsequently described, the storage is linear, the value of k is 

0.405 hr, and the value of Tis 0.88 hr. For the storm of July 12, 1957, 

rainfall excess of 1.90 in. occurred in 0.75 hr, beginning at 1945 hr. 

Compute the surface-runoff hydrograph from the appropriate model, 

and compare with the surface runoff from the observed hydrograph.

By using the values just given, &/T=0.405 hr/0.88 hr=0.46; 

D/T=0.75 hr/0.88 hr=0.85. The appropriate model is taken from 

table 8 (fc/T=0.45), columns 1 and 10. The value of APe/T is 0.192 

sq miX 1.90 in./0.88 hr=0.415 cfs. The model is converted by multiplying the values from column 1 by 0.88 hr and the values from column 

10 by 0.415 cfs.

Four graphs are shown in figure 4. The two light lines show the total 

observed runoff and the estimate for base flow. The dashed line is 

the difference between the first two graphs, or the actual surface 

runoff. This line should be compared with the heavy cont;nuous line, 

which is the converted model hydrograph.

EXAMPLE 3

Mazon River near Coal City (Grundy County), 111., has a drainage 

area of 470 sq mi. As determined by methods subsequently described, 

the storage is linear, the value of k is 20 hr, and the value of T is 30 hr. 

For the storm whose peak occurred on May 12, 1943, rainfall excess 

of 1.79 in. occurred in 20 hr, beginning at 1600 hr on May 10. Compute 

the surface-runoff hydrograph from the appropriate model, and compare with the surface runoff from the observed hydrograph.

By using the values just given, k/T=20 hr/30 hr=0.67; D/T=20 

hr/30 hr=0.67. The appropriate model is taken from table 12 (k/T= 

0.7), columns 1 and 9. The value of APe/T is 470 sq miX1.79 in./30 

hr=28.0 cfs.

Four graphs are shown in figure 5. The two light lines show the total 

observed runoff and the est;mate for base flow. These two graphs are 

the same as those shown in the report by Mitchell (1948, p. 115). The 

dashed line is the difference between the first two graphs, or the actual 

surface runoff. This line should be compared with the heavy continuous 

line, which is the converted model hydrograph.

EXAMPLE 4

A tributary to Vermilion River, at Lowell (La Salle County), 111. 

has a drainage area of 0.126 sq mi. As determined by methods subsequently described, the storage is nonlinear (z=0.5), the value of k is
APPLICATION TO SPECIFIC AREAS 19

240

2000 2100 

TIME OF DAY. IN HOURS

2200

FIGURE 4. Hydrographs for tributary to Kankakee River near 

Bourbonnais, 111.

446-375 O 7&
20 MODEL HYDROGRAPHS

15.0

MAY 10 11 12 13 

TIME, IN DAYS

14

FIGURE 5. Hydrographs for Mazon River near Coal City, 111.

1.34 hr, and the value of T is 0.32 hr. For the storm of June 12, 1957, 

rainfall excess of 0.045 in. occurred in 0.067 hr, beginning at 0625 hr. 

Compute the surface-runoff hydrograph from the appropriate model, 

and compare with the surface runoff from the observed hydrograph.

By using the values just given, kj T/APe/T=lM/ V(0.126X 0.045) / 

0.32=10.1; D/T=QM7 hr/0.32 hr=0.2. The appropriate model is 

taken from table 34 (k/ ^APejT= 10.0), columns 1 and 4. The value of 

APe/T is 0.126 sq miX 0.045 in./0.32 hr=0.018 cfs. The model is 

converted by multiplying the values from column 1 by 0.32 hr and the 

values from column 4 by 0.018 cfs.

Four graphs are shown in figure 6. The two light lines show the total 

observed runoff and the estimate for base flow. The dashed line is the 

difference between the first two graphs, or the actual surface runoff.
APPLICATION TO SPECIFIC AREAS 

160

140

120 -

100

21

0640 0700 1700 1800 19CO

TIME OF DAY, IN HOURS

FIGURE 6. Hydrographs for tributary to Vermilion River at Lowell, 111. (left) 

and for tributary to Mud Creek near Tower Hill, 111., (right).

This line should be compared with the heavy continuous line, which is 

the converted model hydrograph.

EXAMPLE 5

A tributary to Mud Creek, near Tower Hill (Shelby County), 111., 

has a drainage area of 0.204 sq mi. As determined by methods subsequent1 y described, the storage is nonlinear (a?=0.5), the value of k is 

4.40 hr, and the value of T is 0.58 hr. For the storm of June 19, 1£ 56,
22 MODEL HYDROGRAPBS

rainfall excess of 0.47 in. occurred in 0.25 hr, beginning at 1700 hr. 

Compute the surface-runoff hydrograph from the appropriate model, 

and compare with the surface runoff from the observed hydrograph.

By using the values just given, k/ VAPe/T=4.40/V(0.204X 0.47)/ 

0.58=10.8; D/T=0.25 hr/0.58 hr=0.43. The appropriate model is 

taken from table 35 (kf T/APe fT=ll.&), columns 1 and 6. The value of 

APefT is 0.204 sq miX0.47 in./0.58 hr=0.165 cfs. The model is converted by multiplying the values from column 1 by 0.58 hr and the 

values from column 6 by 0.165 cfs.

Four graphs are shown in figure 6. The two light lines show the 

total observed runoff and the estimate for base flow. The dashed line 

is the difference between the first two graphs, or the actual surface 

runoff. This line should be compared with the heavy continous line, 

which is the converted model hydrograph.

EXAMPLE 6

Assume that for example 5 the rainfall excess had be?n 1.00 in. 

and that all other factors were as previously given. After selecting the 

appropriate model, compute the peak discharge of surface runoff.

By using the values given, kj ^APe/T=4AQf V(0.204X 1.00)/0.58= 

7.4; D/T=QA3, as before. The appropriate model is taken from table 

31(fc/VAPe/T=7.0), columns 1 and 6. The value otAPJT is 0.204 sq 

miX 1.00 in./0.58 hr=0.352 cfs. The model indicates thet the peak 

discharge will occur at 0.8X 0.58 hr=0.46 hr after beginning of rainfall 

excess and will have a magnitude of 914.OX 0.352 cfs 322 cfs.

This last example has been included to illustrate the fret that for 

nonlinear storage peak discharges are not proportional to amount of 

rainfall excess. A comparison of examples 5 and 6 shows that an increase in rainfall excess of 113 percent (from 0.47 in. to 1.00 in.) 

produced an increase in peak discharge of 158 percent (from 125 cfs 

to 322 cfs.)

DETERMINATION OF HYDROGRAPH PARAMETERS

Two types of phenomena combine to produce the flood hydrograph. 

One of these is the meteorological event the amount, duration, and 

distribution of rainfall. The other is the physiographic character of 

the drainage basin. For the most part, past meteorological events are 

only a rough and uncertain guide to future intensities anc1 durations. 

Also, barring the advent of bulldozers (and neglecting the ephemeral 

effects of temperature and antecedent precipitation), the physiographic 

character of a drainage basin changes only imperceptibly, from day 

to day, and from decade to decade. ("Eternal as the hills" is a realistic 

expression.) Thus, although successive flood hydrographs for a given 

basin may vary greatly because of the variations in the meteorological
DETERMINATION OF HYDROGRAPH PARAMETERS 23

events, they will nevertheless have certain invariable characteristics, 

reflecting the relatively constant, unchanging physiography of the 

basin. These characteristics, once accurately determined for a basin, 

may be applied with confidence to a synthesis of other hydrographs 

for that basin.

The hydrograph does not, of course, provide direct information on 

discrete elements of the physiography, such as area, slope, or stream 

density. In fact, for area, the hydrograph provides no information 

whatsoever; this must be obtained from other sources, such as topographic maps. However, information for the other physiographic 

factors which influence the hydrograph is available in a total, integrated form as certain constant (or at least nearly constant) hydrograph parameters. These parameters are the characteristic time, T 

and the storage constants, k and x.

DETERMINATION FROM OBSERVED HYDROGRAPHS

The most direct, and most satisfactory, method of determination 

of hydrograph parameters is appropriate analysis of observed 

hydrographs. All three of the significant parameters, T, k, and x, 

may be determined by such analysis. The principal shortcoming of 

this method is the lack of observed hydrographs for ungaged areas.

CHARACTERISTIC TIME, T

In the discussion of translation flow (section "Translation Hydrograph"), T was considered to be the time required for flow to arrive 

at the outlet from the most distant point of the drainage basin. Many 

hydrologists have assumed, although none has rigorously proved, that 

this is the time from ending of rainfall excess to the point of inflection 

on the recession side of the hydrograph. Even in the absence of rigorous 

proof, experience has demonstrated repeatedly that this lapse of time 

is a constant for a given basin and adequately serves the purposes 

for which the concept of T was intended.

The characteristic time, T, for any given basin is determined by 

subtracting the time of ending of rainfall excess from the time of 

occurence of the inflection (change of curvature from concave downward to concave upward) on the recession limb of the hydrograpb.

STORAGE CONSTANTS, k AND x

In view of the assumption upon which the model hydrographs are 

developed that the hydrograph of surface runoff is a translation 

hydrograph modified by reservoir storage, S=kOx appropriate analysis of the hydrograph should disclose the values of k and x. For linear 

storage, the value of x is, of course, unity, and a procedure for deter-
24 MODEL HYDROGRAPHS

mining k already has been published (Mitchell, 1962, p. 23). Briefly, 

this procedure involves computation of a recession coefficient, r, for 

any convenient time, At, and substitution in the formula

&=.A*(l+r)/2(l r).

When storage is linear, r has the same value for all points equally 

spaced in time on a recession curve, but when storage if nonlinear, 

the value of r will vary with the discharge. Hence, to determine the 

value of k, as well as x, for nonlinear storage a new procedure is 

required.

The formula for k, just described, was developed frorr the floodrouting equation

02 = QSi/M) -0,- (2S2/A<) + (/! + 72)

(see section "Routing Considerations") and the assumption that if 

beyond the point of inflection on the recession limb of the hydrograph, 

inflow has been completed, both /i and 72 are zero. Starting with 

this same assumption, Shen (1962) found that both k and x could 

be evaluated by the following procedure : On logarithmic coordinates, 

plot AQ/A< as ordinate and average Q as abscissa, fit a straight line 

to these points, and determine the slope and the intercept (at Q=l) ; 

to obtain the value of x, subtract the slope of the line from 2.0, and 

to obtain k, multiply the intercept by x and take the reciprocal of 

this product.

Figure 7 shows examples of Shen's procedure. The points plotted 

there are derived from routed graphs which appear later as figures 1 1 , 

12, and 13. Some of the points are from the curves for 1 inch of runoff, others from the curves for 2 inches of runoff; alinement of the 

points is independent of this variation. One curve is horizontal (zero 

slope), with an intercept of 50. Hence, the value of x is 2 0=2, the 

value of k is 1/(2X50) = 0.01, and the storage equation is $=0.01 O2 . 

For the second line, the slope is 1.0 and the intercept is 5.0; so x=2 1 

= 1, fc=l/(lX5) = 0.20, and the storage equation is £ 0.2 0. For 

the steepest line, the slope is 1.5 and the intercept is 0.2; so z=2.0 

 1.5=0.5, fc=l/(0.5X0.2) = 10, and the storage equatior is £=10.0 

0°- 6 .

Shen's method is further illustrated by figure 8. The five sets of 

data plotted here are for the same five stations that were used to 

describe the application of model hydrographs to specific areas.

The open circles are for the tributary to Second Creek at Keptown, 

II]., and for the storm of July 15, 1957. The values of actual surface 

runoff (the dashed line of fig. 3) were used to compute tl ?,se points.
DETERMINATION OF HYDROGRAPH PARAMETERS 25

2000

1000 -

500

1.0 10 20 50 100 

Qavg , CUBIC FEET PER SECOND

200 500 10CO

FIGURE 7. Analyses for storage constants of model hydrographs.

Slope of the line is 1.0, and the intercept is 0.94; thus the constants 

are z=1.0, and fc=1.06. (Determinations for other storms, not shown 

here, give an average value for k of 1.03, as used in "Example 1.") 

The solid circles are for the tributary to Elankakee River near 

Bourbonnais, 111., and for the storm of July 12, 1957. The values of 

actual surface runoff (the dashed line of fig. 4) were used to compnte 

these points. Slope of the line is 1.0, and the intercept is 2.8; tl us 

the constants are z=1.0 and &=0.357. (Determinations for other
26 MODEL HYDROGRAPHS

1000

500

200

100

50

20

10

1 5

<

0.5

0.2

0.1

0.05

0.02

0.01

EXPLANATION 

SYMBOL STRFAM

10 20 50 100 200 500 1000 2000

FIGURE 8. Analyses for storage constants of observed hydro graphs.

storms, not shown here, give an average value for k of 0.405, as used 

in "Example 2.")

The open triangles are for Mazon River near Coal City, 111. The 

published unit hydrograph (Mitchell, 1948) was used to compute 

these points. Slope of the line is 1.0, and the intercept is 0.05; thus 

the constants are z=1.0 and Jt=20, as used in "Example 3."
DETERMINATION OF HYDROGRAPH PARAMETERS 27

The solid triangles are for the tributary to Vermilion River at 

Lowell, 111., and for the storm of June 12, 1957. The values of actual 

surface runoif (the dashed line of fig. 6) were used to compute these 

points. Slope of the line is 1.5, and the intercept is 1.5; thus the 

constants are z=0.5 and fc=1.34, as used in "Example 4."

The open squares are for the tributary to Mud Creek near Tower 

Hill, 111., and for the storm of June 19, 1956. The values of actual 

surface runoff (the dashed line of fig. 6) were used to compute these 

points. Slope of the line is 1.5, and the intercept is 0.45; thup the 

constants are a; =0.5, and fc=4.40, as used in "Example 5."

From these examples, which initially were chosen with other 

objectives in view, it should not be assumed that all observed hydrographs will result in plots for which slope of the lines will be precisely 

1.0 or 1.5. Present knowledge concerning nonlinear hydrographs 

is so meager that slopes cannot be predicted. Our present experience 

indicates that for most of these plots the slopes will be near to 1.0 

and that for the few others the slopes will tend to cluster about 1.5; 

but any slope appears to be possible. Thus, because a better understanding of nonlinearity is needed and models presently are available 

only for the two cases cited, the lines for all analyses should be drawn 

with slopes of either 1.0 (when possible) or 1.5 (when necessary).

DETERMINATION FROM BASIN CHARACTERISTICS

The storage effect results from physiographic influences. Therefore, 

the expression for a hydrograph may be correlated with the observable 

physical characteristics of its drainage basin.

Efforts have been made by means of multiple regression analyses 

to relate T and k for basins having linear storage characteristics to 

observed values of area (.4), length (L), slope between point? 10 

percent and 85 percent of the distance along the channel from the 

site to the divide (o\0/8s), soils infiltration index ($<), a surface-storage 

index giving percentage of the basin in lakes, ponds, and swamps 

($,), percentage of basin covered by forest (F), rainfall intensity 

(/24,2), and drainage density (D^. Many of the drainage basins 1 ave 

no forest cover or surface storage; so a constant of 0.5 was added to 

these two basin characteristics to prevent the computer from stopping 

when attempting to take logarithms of zero values. Data for 48 

stations were used in the regressions for T, and data for 43 stations 

were used in the regressions for k. The initial array of data followed 

the general arrangement described by

J- ==/(-^> L, OiQ/85, Si, St , F, 124,2, I'd)

and

k=f(A, L, $io/85, Si, St , F, /24,2, Dd). 

446-317® O 72 5
28 MODEL HYDROGRAPHS

Stepwise multiple regression performed on these data indicated that 

only three independent variables were significant at either the 1-percent 

or 5-percent level. The general equations are

and 

where

kc=CkL*S10/&5*Stf,

Tc computed lag time,

kc=computed storage time,

Ot, Ck=regression constants,

Z=length of stream, in miles,

$io/85=slope, in feet per mile,

St= surf ace-storage index+0.5, in percent,

a, 6, c, d, e, /=regression coefficients.

The following table gives the regression coefficients, significant at 

the 1-percent level, to be used in the above equations and also 

indicates the coefficient of correlation and standard errcr of each 

equation:

Ct

0.837 

5.02 

5.33

0.898

.650

.602

Regression factors for Tc

-0. 460

-.448 1 0. 231

Regression factors for kc

Ok d 

67.2 ._...._..._

16. 5 0. 392

17. 6 . 339

1 (Significant at 6-percent level.

e 

-1.20

-.873

-.860

f

0. 258

Coefficient of 

correlation

0.885

.929

. 939

Coefficient of 

correlation

0. 921

.959

. 970

Standard error 

(percent)

56. 2

44.4

41.9

Standard error 

(percent)

48.9

35.4

30. 6

The equations giving the best estimates of T and k were used to 

compute Tc and kc for those stations used in the regression analyses. 

Figures 9 and 10 show the extent of agreement between the computed 

and actual values.

Data for more stations are being continually added to those data 

for stations described in the previous section. It is hoped that continued 

study based on these additional data and minor refinements to those 

existing will eventually lead to more accurate correlations.

For nonlinear storage effects, the data are, as yet, too few to warrant 

any attempt at correlations.

UNIT HYDROGRAPH

Many hydrologists now regard the unit hydrograph as a translation 

hydrograph modified by some element of reservoir-type storage. Only
UNIT HYDROGRAPH 29

30.0 -

10.0 - /

5.0 -

= 3.0

O

I

0.5 

0.3

0.1

"1 

/

/

/ / 

0.1 0.3 0.5 1.0 3.0 5.0 10.0 30.0

Tc , IN HOURS

FtouBE 9. Observed, T0 , versus computed, Te, values of T.

recently, however, has there been a realization that to define a true 

unit hydrograph, the reservoir storage must be a particular type, 

namely linear storage.

A principle of the unit-hydrograph technique is that for rainfall 

excesses uniformly distributed over a given area and within a grfven 

time, the ordinates of the graph of surface runoff are in linear proportion to the amounts of the rainfall excesses. This principle requires 

that the storage effect be a linear one. A rigorous mathematical development of this statement is not presently available, but a demonstration is quite simple.

In figure 11, the lower curve results from routing the translation 

hydrograph of figure 1 through linear storage, £=0.20 0. (See table 3, 

cols. 1, 2.) Suppose now that for figure 1 Pe had been in units of 

"double inches," of sixths of a foot, rather than twelfths. In that case, 

the ordinates of figure 1 would all have been doubled. The higher
30 MODEL HYDROGRAPHS

,,_.,,« ,0.339 -0.860 ,5,0.258 K - 17.6 L, 10/85

30.0

10.0 -

5.0

3.0 -

30.0

FIGURE 10. Observed, k 0 , versus computed, kc , values of k.

curve in figure 1 1 results from routing these doubled ordinates through 

the same linear storage, $=0.20 0. Comparing the curves cf figure 11 

shows that all ordinates of the second curve are twice those of the 

first. This relation meets the requirement of the unit-hydrograph 

principle that ordinates of the unit hydrograph be in linear proportion 

to rainfall excess.

In figure 12, the same two translation hydrographs have been 

routed through nonlinear storage, $=10 0°- 5, to obtair the two 

graphs. Obviously there is no constant of proportionality between the 

ordinates of these graphs; hence they cannot be true unit hydrographs.

In figure 13, the same translation hydrographs have been routed 

through nonlinear storage, $=0.01 O2 . Again, the resulting graphs 

have no constant of proportionality, and thus fail to meet the specifications for true unit hydrographs.
UNIT HYDROGRAPH 31

2000

1500

1000

500

0.5 1.0 1.5

H/T

FIGURE 11. Proportional graphs, resulting from routing through linear storage,

5=0.200.

A quick method for testing linearity of storage effect in any hydrograph is to plot it semilogarithmically and note the shape of the recession limb. If the value of x is greater than unity, the recession will 

be concave downward; if less than unity, concave upward. Only when 

this recession is a straight line is the storage effect linear, and only 

then is the graph a true unit hydrograph. These statements are illustrated in figure 14, which shows the semilogarithmic plot for the recession limbs of the curves of figures 11, 12, and 13.
32 MODEL HYDROGRAPHS

2000 -

1500

1000

500

H/T

FIGURE 12. Nonproportional graphs, resulting from routing through nonlinear storage S= 10 O0 -5 .

It is interesting to note the extent to which some of the so-called 

unit hydrographs in the published literature conform to the criterion 

of straight-line recession. Figure 15 shows some typical examples 

(from Mitchell, 1948). Figure 16 shows the hydrograph derived from 

observed data for Money Creek above Lake BloomiEgton, 111.,
400

FIGURE 13. Nonproportional graphs, resulting from routing 

linear storage, S=0.01 O2 .
34 MODEL HYDROGRAPHS

300 -

2.6 3.0

H/T

FIGURE 14. Semilogarithmic plotting, recession limbs of graphs from figures 11,

12, and 13.
UNIT HYDROGEAPH 35

10,000

15 20 25 

TIME, IN HOURS

50 60 70 

TIME, IN HOURS

80

FIGURE 15. Typical recessions, previously published unit hydrography

(Mitchell, 1948) and also the graphs derived by the synthetic methods 

proposed by Commons (1942), the U.S. Department of Agriculture 

Soil Conservation Service (1957), and Mitchell (1948). The graph 

labeled "Mitchell (1962, synthetic)" is the graph derived by methods 

described earlier in the section "Application to specific areas."

Although some of these last examples have been called unit hydrographs, we should not be swayed by this fact, for the recession lines 

must be straight in semilogarithmic plots if the storage effect is to be
36 MODEL HYDROGRAPHS

1000

800

600

400

200

100

EXPLANATION

o 

Mitchell (1962, synthetic)

 

Mitchell (1948, actual)

D

U.S. Department of Agriculture 

Soil Conservation Service (1957)

 

Mitchell (1948, synthetic)

A

Commons (1942)

15 20 25 30 

TIME, IN HOURS

35 40

FIGURE 16. Recession hvdrographs, all for Money Creek above Lak^ Bloomington, 111., computed by various methods.

considered linear. And the storage effect must be linear if the graphs 

are to meet the requirement of linear proportionality of ordinates 

and thus be considered true unit hydrographs.

As mentioned in a foregoing section, areas occasionally are found 

for which the semilogarithmic plot for the recession limb of the actual 

hydrograph (even after eliminating base flow) departs significantly 

from a straight line. True unit hydrographs cannot be developed for
SUMMARY AND CONCLUSIONS 37

these areas. Instead, they must be approached with the broader 

concepts of the model hydrograph.

The special case of the unit hydrograph is applicable only to those 

areas for which linear storage effect may be assumed. The model 

hydrograph with its broader concepts is applicable to those areas for 

which the storage effect is nonlinear.

SUMMARY AND CONCLUSIONS

Model hydrographs are composed of pairs of dimensionless ratios 

(H/T, QT/APg) arranged in tabular form. Under appropriate conditions these dimensionless models may be converted to flood hydrographs for specific areas. The conversion is accomplished merely by 

multiplying the abscissas (HIT) by the value of T for the drainage 

basin and multiplying the ordinates (QT/APe) by the appropriate 

value of APe/T.

A dimensionless, isosceles translation hydrograph, for which the 

time base is T hours, is transformed by summation-curve techniques 

to a family of hydrographs with storm duration (D/T) ranging from 

0.1 to 2.0. Each of these hydrographs is then routed through varfous 

single elements of reservoir storage, S=kOx to provide families of 

model hydrographs. Twenty-six of the families are linear models 

(z=1.0), with values of k ranging from 0.2T to 3.0T. The remaining 

eight families are nonlinear models, for which x is 0.5 and for which 

the value of k/-jAPe/T ranges from 2.0 to 12.0. The linear models are 

sufficiently extensive to cover most computational needs; the ran&e of 

nonlinear models may eventually need to be extended, particularly 

to cover values of x other than 0.5 and conditions of initial inflow 

other than zero.

For a specific drainage area, the appropriate model is selectee1 by 

the following procedure: 

1. Determine T, in hours, for the basin. If a suitable runoff hydrograph is available, take T as the time from ending of rainfall excess

to the point of inflection on the recession limb of the hydrograph.

If such Jiydrograph is not available, use the formula

T=5.33 L°-602

2. Determine values for the storage factors, k and x. (k should be 

computed in hours; a; is a dimensionless number.) If a suitable 

runoff hydrograph is available, follow the method outlined in the 

section "Application to Specific Areas" and illustrated by examples 

1-5. If such hydrograph is not available, assume z=5.0, and 

compute k by formula

&=17.6L°-339 SWss- 0 ' 860 -SV-258 .
38 MODEL HYDROGRAPHS

(Techniques are not yet available for computing nonlinear storage 

factors from measured physiographic characteristics.)

3. Determine the storm characteristics, D, in hours, and Pe , in inches. 

These are obtained from meteorological data and from estimates of 

precipitation losses, except that when reproducing an observed 

hydrograph, Pe is the volume of surface runoff.

4. Determine the appropriate model family (tables 3-36). If the storage 

is linear (z=1.0), the family is identified by the value of the ratio 

k/T; if the storage is nonlinear (x=»0.5), the family is identified by 

the value of the ratio k/-\/APe/T

5. Determine the appropriate member of model family (the column 

of the table containing proper values of the ordinates QT/APe). 

This column is identified by the value of the ratio D/T. 

The conditions under which the models may be used are often the 

same as those usually described for unit hydrographs, but with one 

restriction. In general, the models may be used only to compute the 

flood hydrograph from storms for which rainfall excess is evenly distributed with respect to both time and area and unaffected by ice or 

melting snow. For linear models, the unit-hydrograph techniques of 

superposition may be used to develop complex hydrographs for 

storms for which rainfall excess is nonuniform with respect to time. 

But for nonlinear models superposition techniques are not appropriate. 

Further, nonlinear models presented here all are predicated on initial 

flow of zero; more work will be required to determine adjustments 

necessary when initial flow is substantially greater.

REFERENCES

Commons, G. G., 1942, Flood hydrographs: Civil Engineering, v. 12, p. 571-572.

Mitchell, W. D., 1948, Unit hydrographs in Illinois: Illinois Dept. Public Works 

and Bldgs. Div. of Waterways, 294 p.

 1962, Effect of reservoir storage on peak flow: U.S. Geol. Survey WaterSupply Paper 1580-C, 25 p.

Shen, John, 1962, A Method of determining the storage-outflow characteristics 

of nonlinear reservoirs: U.S. Geol. Survey Prof. Paper 450-E, p. 167-168.

U.S. Department of Agriculture Soil Conservation Service, 1957, Hydrographs: 

Natl. Eng. Handb., sec. 4, p. 3.16-1-3.16-14.
TABLES 3-36

446-375 O 72
Table 3. Linear Model Hydrographs (S = kO); k/T 

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

54.867

189.765

373.183

586.018

816.689

948.437

926.680

811.856

640.609

435.152*

263.823

159.950

96.974

58.793

35 . 645

21.611

13.103

7.944

4.817

2.920

1.770

1.073

.650

.394

954.093

0.64

D/T=0.1

0.000

19.331

117.404

278.496

477.795

700.259

898.104

946.980

874.981

729.695

539.980

342.658*

207.746

125.952

76.362

46.296

28.069

17.018

10.318

6.256

3.793

2.299

1.394

.845

.511

948.844

0.68

D/T=0.2

0.000

9.666

68.368

197.950

378.146

589.027

799.181

922.542

910.981

802.338

634.838

441.319

275.202*

166.84ci

101.157

61.329

37.182

22.543

13.668

8,287

5.024

3.046

1.846

1.119

.678

932.896

0.74

D/T=0 . 3

0.000

6.444

45.578

138.410

291.232

485.517

692.053

848.448

906.688

850.552

714.885

537.444

363.461

225.452*

136.687

82.870

50.242

30.461

18.468

11.197

6.789

4.116

2.495

1.513

.917

906.688

0.80

D/T=0.4

0.000

4.833

34.184

103.808

223.256

393.488

588.663

755.785

855.081

862.440

772.909

621.829

455.020

304.084

188.179*

114.089

69.170

41.936

25.425

15.415

9.346

5.666

3.435

2.083

1.262

871.625

0.86

D/T=0.5

0.000

3.866

27.347

83.046

178.605

318.657

494.412

660.327

779.624

830.004

797.948

686.859

539.012

389.206

258.540

159.803*

96.885

58.739

35 . 612

21.591

13.090

7.937

4.812

2.917

1.768

830.510

0.92

D/T=0.6

0.000

3.222

22.789

69.205

148.838

265.547

415.231

569.840

696.102

771.302

781.666

722.066

607.007

470.169

337.065

223.166

137.847*

83.574

50.669

30.720

18.625

11.292

6.846

4.151

2.516

785.927

0.96

D/T=0.7

0.000

2.762

19.534

59.319

127.575

227.612

355.912

491.195

613.431

700.901

738.256

718.950

648.591

538.284

413.910

295.527

195.294

120.586*

73.108

44.324

26.873

16.293

9.878

5.989

3.631

738.853

1.02

D/T

0

2

17

5

11

199

31

429

539

62

68

68

65

58

480

36

26

17

106

6

3

2

14

5

69

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.60
Table 4. Linear Model Hydrographs (S = kO); k/T 

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst .

0.000

45.288

160.777

323.313

517.379

732.576

871.359

879.230

799.366

660.706

482.641*

323.455

216.772

145.276

97.361

65.250

43.729

29.306

19.640

13.162

8.821

5.911

3.961

2.654

1.779

879.230

0.70

D/T=0.1

0.000

15.848

98.478

238.992

418.301

623.607

814.641

883.787

844.990

733.851

574.230

397.966*

266.707

178.741

119.789

80.280

53.802

36.057

24.165

16.194

10.853

7.273

4.874

3.266

2.189

883.787

0.70

D/T=0.2

0.000

7.924

57.163

168.735

328.647

520.954

719.124

849.214

864.388

789.420

654.040

486.098

332.336*

222.724

149.265

100.034

67.041

44.930

30.111

20.179

13.523

9.063

6.074

4.070

2.727

871.228

0.76

D/T=0.3

0.000

5.283

38.109

117.773

251.924

426.967

618.849

774.012

847.806

820.876

717.690

568.682

412.968

281.138*

188.412

126.270

84.624

56.713

38.008

25.472

17.070

11.440

7.667

5.138

3.443

850.102

0.82

D/T=0.4

0.000

3.962

28.582

88.330

192.905

344.844

523.885

685.084

791.756

819.317

759.214

637.759

493.188

354.411

240.801*

161.379

108.153

72.482

48.576

32.554

21.817

14.621

9.798

6.566

4.400

821.017

0.88

D/T=0.5

0.000

3.170

22.865

70.664

154.324

279.045

438.804

595.866

717.065

780.175

770.300

686.965

563.549

430.299

307.486

208.696*

139.864

93.734

62.818

42.100

28.214

18.908

12.672

8.492

5.691

785.632

0.94

D/T=0 . 6

0.000

2.641

19.054

58.886

128.603

232.538

368.311

512.968

637.386

719.863

745.851

708.244

616. Q22

499.414

378.547

269.619

182.881*

122.563

82.139

55.048

36.892

24.724

16.569

11.104

7.441

745.851

1.00

D/T=0.7

0.000

2.264

16.332

50.474

110.231

199.318

315.695

441.951

560.399

651.167

699.058

696.153

645.167

554.324

445.182

335.938

238.788

161.906*

108.506

72.718

48.734

32.661

21.888

14.669

9.830

703.969

1.04

D/

1

4

9

17

27

38

49

58

64

66

64

58

50

39

30

21

14

9

6

4

2

1

1

66

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.6
Table 5. Linear Model Hydrographs (S = kO); k

li 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst .

0.000

38.547

139.359

284.780

462.162

662.442

802.033

828.847

774.861

662.988

509.642*

365.130

261.595

187.418

134.275

96.200

68.923

49.380

35.378

25.347

18.160

13.011

9.322

6.679

4.785

830.822

0.68

D/T=0.1

0.000

13.427

84.764

209.068

371.321

560.762

742.827

823.027

807.290

722.818

589.105

433.538*

310.606 '

222.531

159.432

114.224

81.835

58.631

42.006

30.096

21.562

15.448

11.069

7.931

5.682

826.551

0.72

D/T=0 . 2

0.000

6.713

49.095

146.920

290.195

466.041

651.794

782.927

815.158

765.054

655.962

511.322

372.072*

266.568

190.982

136.828

98.030

70.233

50.318

36.051

25.829

18.505

13.259

9.500

6.806

816.189

0.78

D/T=0.3

0.000

4.476

32.730

102.419

221.718

380.384

558.303

708.872

791.048

784.378

706.405

581.821

444.416

322.225*

230.856

165.396

118.497

84.897

60.824

43.577

31.221

22.369

16.026

11.483

8.227

798.531

0.84

D/T=0.4

0.000

3.357

24.548

76.815

169.645

306.479

470.994

624.484

733.476

773.990

735.560

638.188

514.017

388.945

281.527*

201.698

144.506

103.530

74.174

53.142

38.074

27.278

19.544

14.002

10.032

773.990

OT"90

D/T^0.5

0.000

2.685

19.628

61.452

135.716

247.868

393.748

541.401

661.045

731.345

737.013

675.156

572.671

455.720

343.042

248.066*

177.726

127.331

91.226

65.358

46.826

33.549

24.036

17.221

12.338

743.283

0.96

D/T=0.6

0.000

2.238

16.365

51.210

113.097

206.557

330.361

465.295

585.716

671.341

707.638

686.434

614.397

514.315

406.338

304.906

220.361*

157.876

113.110

81.037

58.059

41.596

29.802

21.352

15.298

708.032

1.02

D/T=0.7

0.000

1.918

14.027

43.894

96.940

177.049

283.167

400.742

514.151

605.302

659.593

668.481

632.744

558.416

463.617

364.608

273.039

197.257*

141.324

101.251

72.541

51.972

37.235

26.677

19.113

670.430

1.06

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 
Table 6. Linear Model Hydrographs (S = kO); k

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

33.548

122.923

254.250

417.098

603.631

740.867

779.822

744.926

654.538

522.450*

392.578

294.991

221.662

166.561

125.158

94.046

70.668

53.101

39.902

29.983

22.530

16.930

12.722

9.560

779.822

0.70

D/T=0.1

0.000

11.647

74.383

185.692

333.498

508.730

681.276

767.128

767.471

703.562

591.372

454.549*

341.556

256.653

192.853

144.914

108.892

81.823

61.483

46.200

34.716

26.086

19.602

14.730

11.068

776.199

0.74

D/T=0.2

0.000

5.823

43.015

130.037

259.595

421.114

595.003

724.202

767.299

735.517

647.467

522.960

398.053*

299.104

224.753

168.884

126.903

95.358

71.653

53.842

40.458

30.401

22.844

17.166

12.899

767.299

0.80

D/T=0.3

0.000

3.882

28.677

90.574

197.858

342.640

507.835

652.378

738.625

746.054

687.468

583.161

462.492

350.919*

263.687

198.140

148.886

111.876

84.066

63.169

47.467

35.667

26.801

20.139

15.133

752.088

0.86

D/T=0.4

0.000

2.912

21.507

67.930

151.305

275.576

427.299

572.658

681.151

729.859

707.383

629.238

522.760

411.032

311.403*

233.994

175.828

132.121

99.278

74.600

56.056

42.121

31.651

23.783

17.872

730.900

0.92

D/T=0.5

0.000

2.329

17.206

54.344

121.044

222.790

356.716

495.265

611.621

685.634

702.162

656.816

571.702

4-69.538

367.397

278.105*

208.974

157.027

117.993

88.663

66.623

50.062

37.617

28.267

21.240

704.047

0.98

Vi/«re - 

D/T=0.6

0.000

1.941

14.338

45.287

100.870

185.658

299.204

425.118

540.633

626.944

669.923

660.893

604.273

519.194

423.424

330.316

249.903*

187.782

141.103

106.028

79.672

59.867

44.985

33.803

25.400

672.649

1.04

D/T=0.7

0.000

1.664

12.290

38.817

86.460

159.136

256.461

366.051

474.026

563.908

621.862

639.155

615.273

554.613

472.574

383.637

298.684

225.892*

169.739

127.546

95.840

72.016

54.115

40.663

30.555

639.155

1.10

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0
Table 7. Linear Model Hydrographs (S = kO); k/T 

l±

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

29.695

109.931

229.525

379.769

553.882

687.193

733.901

713.164

639.907

525.747*

409.432'

318.850 '

248.307

193.371

150.589

117.273

91.327

71.122

55.388

43.134

33.591

26.159

20.371

15.864

734.617

0.72

D/T=0.1

0.000

10.283

66.258

166.959

302.491

465.147

628.359

716.638

728.276

680.230

585.704

465.265*

362.331

282.169

219.741

171.125

133.265

103.781

80.821

62.941

49.016

38.172

29.726

23.150

18.027

731.638

0.76

D/T=0.2

0.000

5.142

38.271

116.609

234.725

383.819

546.753

672.499

722.457

704.253

632.967

525.485

413.798*

322.250

250.955

195.433

152.195

118.523

92.301

71.881

55.978

43.594

33.949

26.438

20.588

723.732

0.82

D/T=0.3

0.000

3.428

25.514

81.167

178.570

311.532

465.332

603.381

691.091

708.381

664.737

577.066

471.100

369.922*

288.080

224.345

174.710

136.057

105.956

82.514

64 . 25 9

50.043

38.971

30.349

23.634

710.291

0.88

D/T=0.4

0.000

2.571

19.135

60.875

136.498

250.214

390.739

528.159

634.605

688.376

677.712

614.869

523.383

423.867

332.376*

258.841

201.575

156.978

122.248

95.202

74.140

57.737

44.964

35 . 016

27.269

691.588

0.94

D/T=0.5

0.000

2.057

15.308

48.700

109.198

202.228

325.843

455.919

568.182

643.730

667.842

635.223

564.361

475.140

383.042

300.126*

233.726

182.016

141.746

110.386

85.965

66.946

52.135

40.601

31.618

667.842

1.00

D/T=0.6

0.000

1.714

12.757

40.583

90.999

168.523

273.250

390.976

501.312

586.857

634.059

634.079

589.741

517.329

432.573

347.722

272.316*

212.069

165.150

128.612

100.158

77.999

60.743

47.304

36.839

639.880

1.04

D/T=0.7

0.000

1.469

10.934

34.786

77.999

144.448

234.214

336.591

439.161

526.871

586.692

609.946

595.258

545.802

474.817

395.223

317.086

248.240-

193.319

150.549

117.241

91.303

71.103

55.372

43.122

610.035

1.12

D

3

6

12

20

29

38

46

53

57

57

55

50

43

36

29

22

17

13

10

8

6

5

57

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.7
Table 8. Linear Model Hydrographs (S = ko); k/

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

26.636

99.407

209.119

348.411

511.387

640.054

691.635

681.494

621.929

522.791*

418 . 604

335.180

268.382

214.896

172.069

137.777

110.319

88.334

70.729

56.634

45.348

36.311

29.074

23.280

594.235

0.74

D/T=0.1

0.000

9.205

59.728

151.626

276.654

428.209

582.592

671.347

690.970

655.239

575.184

468.846*

375.410

300.595

240.689

192.722

154.314

123.560

98.936

79.218

63.431

50.790

40.669

32.564

26.074

691.871

0.78

D/T=0.2

0.000

4.603

34.467

105.677

214.140

352.431

505.400

626.970

681.158

673.105

615.212

522.015

422.128*

338.002

270.642

216.705

173.518

138.937

111.248

89.077

71.325

57.111

45.729

36.616

29.319

684.650

0.84

D/T=0.3

0.000

3.068

22.978

73.520

162.669

285.496

429.151

560.716

648.303

672.519

640.464

566.423

473.147

381.617*

305.564

244.6.

195.908

156.865

125.603

100.572

80.529

64.480

51.630

41.341

33.102

672.581

0.88

D/T=0.4

0.000

2.301

17.233

55.140

124.303

299.054

359.770

489.700

593.279

650.037

648.185

597.560

518.670

430.009

346.385*

277.354

222.080

177.821

142.383

114.007

91.287

73.094

58.527

46.864

37.524

656.175

0.94

D/T=0.5

0.000

1.841

13.787

44. 112

99.443

185.084

299.762

422.086

529.954

605.671

635.067

612.317

553.130

475.055

392.145

315.652*

252.746

202.376

162.044

129.750

103.892

83.187

66.609

53.335

42.706

335.057

1.00

Vi/nre - 

D/T=0.6

0.000

1.534

11.489

36.760

82.869

154.237

251.336

361.693

466.900

550.835

600.590

607.363

572.833

511.041

435.994

358.908

288.763*

231.215

185.136

148.240

118.697

95.042

76.101

60.935

48.791

609.996

1.06

D/T=0.7

0.000

1.315

9.848

31.509

71.031

132.203

215.431

311.337

408.732

493.805

554.314

581.770

574.227

533.942

472.419

401.241

329.680

265.162*

212.318

170.005

136.124

108.996

87.274

69.881

55.955

583.074

1.12

D

1

1

2

3

4

5

5

5

5

4

4

3

3

2

1

1

1

1

5

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.
Table 9. Linear Model Hydrographs (S = ko); k/T 

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

24.147

90.714

192.009

321.737

474.744

598.517

653.054

650.906

602.351

515.800*

422.291

345.733

283.055

231.739

189.727

155.331

127.170

104.115

85.240

69.786

57.135

46.777

38.298

31.355

658.375

0.74

D/T=0.1

0.000

8.331

54.367

138.854

254.820

396.560

542.737

630.785

656.074

629.980

561.819

467.550*

382.78-8

313.392

256.576

210.061

171.979

140.781

115.274

94.376

77.265

63.258

51.790

42.402

34.715

656.074

0.80

D/T=0.2

0.000

4.166

31.349

96.610

196.837

325.690

469.649

586.761

643.429

643.027

595.900

514.685

425.169*

348.090

284.984

233.319

191.020

156.380

128.027

104.825

85.820

70.262

57.524

47.096

38.559

649.491

0.84

D/T=0.3

0.000

2.777

20.899

67.184

149.347

263.411

398.039

523.361

609.865

638.946

615.958

553.116

470.719

387.910*

317.585

260.010

212.872

174.274

142.678

116.810

95.638

78.300

64.105

52.483

42.969

638.946

0.90

D/T=0.4

0.000

2.083

15.675

50.388

114.093

211.150

333.243

456.226

556.539

614.894

619.664

578.856

510.534

431.387

355.077*

290.704

238.002

194.849

159.524

130.602

106.924

87.543

71.672

58.679

48.041

624.020

0.96

D/T=0.5

0.000

1.666

12.540

40.310

91.274

170.586

277.468

392.751

496.195

571.227

604.279

589.242

539.642

470.106

396.425

326.074*

266.959

213.558

178.934

146.494

119.935

98.191

80.393

65.818

53.886

604.897

1.02

D/T=0.6

0.000

1.389

10.450

33.592

76.062

142.155

232.612

336.354

436.638

518.493

569.659

581.491

554.833

501.934

435.351

365.364

300.391*

245.930

201.344

164.841

134.956

110.489

90.457

74.061

60.634

582.414

1.08

D/T=0.7

0.000

1.190

8.957

28.793

65.196

121.847

199.381

289.493

382.028

464.258

524.682

555.072

553,105

520.341

466.883

403.167

337.738

277.590*

227.264

186.063

152.330

124.713

102.103

83.592

68.440

558.218

1.14

D

2

5

10

17

25

3

4

47

5

5

5

4

43

3

3

2

2

17

14

1

5

Summarized from computations at intervals II/T = 0.02. ^Recession coefficient 0.3
Table 10. Linear Model Hydrographs (S = kO); k/

ri 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

22.084

83.414

177.465

298.796

442.874

561.748

617.939

621.870

582.229

506.261*

422.088

351.910

293.400

244.618

203.947

170.037

141.765

118.194

98.543

82.158

68.499

57.110

47.614

39.697

625.978

0.76

D/T=0.1

0.000

7.610

49.887

128.054

236.142

369.177

507.792

594.414

623.715

605.226

546.893

462.950*

385.978

321.805

268.300

223.692

186.499

155.490

129.637

108.083

90. 113

75.130

62.639

52.224

43.540

623.715

0.80

D/T=0.2

0.000

3.805

28.749

88.971

182.098

302.659

438.484

551.103

609.064

614.470

576.060

504.922

424.464*

353.892

295.052

245.996

205.095

170.994

142.563

118.860

99.098

82.622

68.885

57.431

47.882

618.020

0.86

D/T=0.3

0.000

2.537

19.166

61.850

138.028

244.457

371.037

490.461

575.307

607.785

591.945

538.356

465.274

390.244*

325.361

271.265

226.163

188.560

157.209

131.070

109.278

91.109

75.961

63.331

52.801

608.204

0.92

D/T=0.4

0.000

1.902

14.374

46.388

105.423

195.815

310.291

426.881

523.774

582.787

592.562

559.696

500.262

429.407

359.758*

299.944

250.074

208.495

173.829

144.927

120.831

100.741

83.991

70.026

58.383

594.458

0.96

D/T=0.5

0.000

1.522

11.499

37.110

84.339

158.174

258.210

367.116

466.248

540.065

575.608

566.640

524.953

464.571

397.185

332.545*

277.255

231.157

192.723

160.680

133.964

111.691

93.121

77.638

64.729

577.195

1.02

D/T=0.6

0.000

1.268

9.583

30.925

70.282

131.812

216.444

314.244

409.882

489.411

541.203

556.832

536.529

491.095

431.859

368.270

308.204*

256.960

214.237

178.617

148.919

124.159

103.515

86.304

71.955

556.832

1.10

D/T=0.7

0.000

1.087

8.214

26.507

60.242

112.981

185.523

270.439

358.454

437.788

497.623

530.024

532.424

505.855

459.267

402.121

342.302

286.388*

238.771

199.072

165.973

138.378

115.370

96.188

80.195

535,142

1.16

D

1

2

3

3

4

4

5

5

4

4

3

3

2

2

1

1

1

1

5

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.8
Table 11. Linear Model Hydrographs (S = kO); k/T 

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

20.344

77.197

164.952

278.865

414.921

529.031

585.991

594.574

562.207

495.178*

419.153

354.800

300.327

254.216

215.186

182.148

154.182

130.511

110.473

93.513

79.157

67.005

56.717

48.008

596.443

0.76

D/T=0.1

0.000

7.002

46.088

118.804

219.986

345.266

476.938

561.711

593.837

581.400

531.240

456.153*

386.119

326.838

276.657

234.180

198.227

167.793

142.031

120.225

101.767

86.143

72.919

61 . 724

52.246

594.679

0.82

D/T=0.2

0.000

3.501

26.545

82.446

169.395

282.626

411.102

519.324

577.774

587.618

556.320

493.696

421.136*

356.478

301.748

255.419

216.204

183.010

154.912

131.128

110.996

93.955

79.531

67.322

56.985

589.162

0.88

D/T=0.3

0.000

2.334

17.697

57.298

128.292

228.019

347.396

461.305

544.161

578.982

568.826

522.930

457.837

389.703*

329.871

279.225

236.355

200.066

169.350

143.349

121.341

102.712

86.943

73.595

62.296

580.312

0.92

D/T=0.4

0.000

1.751

13.272

42.973

97.970

182.536

290.248

400.975

494.438

553.471

567.047

540.657

488.728

425.087

361.442*

305.949

258.976

219.214

185.558

157.069

132.954

112.542

95.264

80.638

68.258

567.893

0.98

D/T=0.5

0.000

1.400

10.618

34.379

78.376

147.429

241.416

344.541

439.548

511.830

549.025

544.868

509.750

456.350

395.401

335.989*

284.404

240.739

203.778

172.491

146.009

123.592

104.617

88.556

74.960

551.980

1.04

D/T=0.6

0.000

1.167

8.848

28.649

65.313

122.858

202.347

294.798

386.090

463.189

515.065

533.546

518.409

479.264

426.401

368.531

313.029*

264.969

224.287

189.852

160.704

136.031

115 .146

97.468

82.504

533.546

1.10

D/T=0.7

0.000

1.000

7.584

24.556

55.983

105.306

173.440

253.685

337.518

413.991

472.911

506.649

512.485

491.042

450.320

398.941

344.202

292.281*

247.406

209.421

177.268

150.052

127.015

107.515

91.008

513.620

1.18

D

1

2

2

3

4

4

4

4

4

4

3

3

2

2

1

1

1

1

1

4

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.8
Table 12. Linear Model Hydrographs (S = kO); k/

_n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

17.575

67.175

144.539

245.969

368.260

473.485

530.337

545.254

523.819

470.873*

408.187

353.845

306.737

265.900

230.501

199.814

173.212

150.153

130.162

112.833

97.812

84.790

73.502

63.718

545.346

0.78

D/T=0.1

0.000

6.039

39.992

103.791

193.464

305.563

425.024

505.510

540.915

537.241

499.690

438.814*

380.395

329.753

285.852

247.796

214.807

186.209

161.419

139.929

121.299

105.151

91.152

79.018

68.498

543.827

0.84

D/T=0.2

0.000

3.020

23.016

71.892

148.628

249.513

365.293

465.267

523.212

539.078

518.466

469.252

409.604*

355.074

307.802

266.824

231.302

200.508

173.814

150.674

130.614

113.225

98.152

85.085

73.758

539.078

0.90

D/T=0.3

0.000

2.013

15 . 344

49.941

112.416

200.939

308.017

412.032

490.483

527.889

525.949

491.915

439.633

382.987*

332.000

287.800

249.485

216.271

187.478

162.519

140.882

122.126

105.867

91.774

79.556

531.524

0.94

D/T=0.4

0.000

1.510

11.508

37.456

85.822

160.702

256.960

357.390

444.253

502.172

520.839

504.165

464.035

412.163

358.703*

310.949

269.552

233.666

202.558

175.590

152.234

131.949

114.383

99.155

85.955

520.839

1.00

D/T=0 . 5

0.000

1.208

9.206

29.964

68.657

129.770

213.567

306.670

394.095

462.850

501.676

504.434

479.411

437.179

386.901

336.522*

291.721

252.883

219.217

190.032

164.733

142.801

123.790

107.310

93.024

507.308

1.06

Vi/ore - 

D/T=0.6

0.000

1.006

7.672

24.970

57.214

108.141

178.979

262.224

345. 711

417.953

468.990

491.199

483.761

454.468

411.957

363.717

316.236*

274.135

237.639

206.002

178.576

154.802

134.193

116.328

100.841

491.917

1.12

D/T=0.7

0.000

.863

6.576

21.403

49.041

92.693

153.410

225.626

302.037

373.072

429.629

464.679

475.370

461.760

430.380

388.506

342.444

297.661*

258.033

223.681

193.902

168.087

145.709

126.311

109.495

475.370

1.20

D

1

1

2

3

3

4

4

4

4

4

3

3

2

2

2

1

1

1

1

4

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.
Table 13. Linear Model Hydrographs (S = kO); k/T 

_n_ 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

15.469

59.454

128.603

219.959

330.914

428.223

483.764

502.447

488.601

446.050*

393.635

347.381

306.560

270.537

238.747

210.693

185.935

164.086

144.804

127.789

112.774

99.521

87.827

77.506

502.447

0.80

D/T=0.1

0.000

5.308

35.320

92.139

172.614

273.965

383.122

459.130

495.873

497.966

469.481

419.318*

370.046

326.562

288.189

254.324

224.440

198.066

174.792

154.252

136.126

120.132

106.015

93.557

82.563

501.015

0.86

D/T=0.2

0.000

2.654

20.314

63.730

132.376

223.289

328.544

421.126

477.502

496.920

483.724

444.400

394.682*

348.304

307.375

271.256

239.382

211.253

186.429

164.522

145.189

128.129

113.073

99.786

88.060

496.920

0.90

D/T=0.3

0.000

1.769

13.543

44.256

100.024

179.573

276.567

372.072

446.042

484.323

487.774

462.255

419.615

371.975*

328.265

289.692

255.651

225.610

199.099

175.703

155.057

136.837

120.758

106.568

94.045

490.300

0.96

D/T=0.4

0.000

1.327

10.157

33.192

76.345

143.510

230.460

322.208

403.023

459.023

480.612

470.660

439.203

396.352

351.029*

309.780

273.379

241.255

212.906

187 .888

165.809

146.326

129.131

113.957

100.566

480.871

1.02

D/T=0.5

0.000

1.062

8.126

26.553

61.076

115.869

191.432

276.194

356.941

422.011

461.114

468.354

450.537

416.675

374.719

331.688*

292.712

258.316

227.962

201.175

177.535

156.674

138.263

122.016

107.678

469.219

1.08

D/T=0.6

0.000

.885

6.771

22.128

50.897

96.558

160.411

236.048

312.807

380.445

429.923

454.148

451.969

429.874

395.260

354.653

313.813*

276.938

244.396

215.677

190.334

167.968

148.230

130.812

115.441

456.179

1.14

D/T=0.7

0.000

.758

5.804

18.967

43.626

82.764

137.496

203.085

273.166

339.258

393.164

428.408

442.134

434.054

409.634

375.126

336.051

297.278*

262.346

231.518

204.313

180.305

159.118

140.420

123.920

442.152

1.22

D/

1

3

7

12

17

23

30

35

39

42

42

41

39

35

31

28

24

21

19

17

15

13

42

from computations at intervals H/T = 0.02. *Recession coefficient 0.8
Table 14. Linear Model Hydrographs (S = kd); k/

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

13.814

53.322

115.821

198.895

300.379

390.707

444.391

465.283

456.830

422.120*

377.729

338.005

302.458

270.651

242.188

216.718

193.927

173.533

155.283

138.952

124.339

111.263

99.562

89.092

465.836

0.82

D/T=0.1

0.000

4.736

31.625

82.833

155.803

248 . 245

348.640

420.320

457.317

463.275

441.461

399.530*

357.514

319.916

286.272

256.166

229.227

205.120

183.549

164.246

146.973

131.515

117.684

105.308

94.234

464.405

0.88

D/T=0.2

0.000

2.368

18.180

57.229

119.318

202.024

298.442

384.480

438.818

460.296

452.368

420.496

378.522*

338.715

303.094

271.219

242.696

217.173

194.334

173.897

155.609

139.244

124.600

111.496

99.771

460.959

0.92

D/T=0.3

0.000

1.579

12.120

39.731

90.087

162.293

250.896

339.068

408.759

446.971

454.018

434.755

399.502

358.987*

321.234

287.451

257.222

230.171

205.965

184.305

164.922

147.578

132.057

118.169

105 . 742

454.939

0.98

D/T=0.4

0.000

1.184

9.090

29.798

68.749

129.626

208.880

293.252

368.630

422.388

445.593

440.396

415.445

379.605

340.808*

304.967

272.895

244.196

218.515

195.535

174.972

156.571

140.105

125.370

112.186

446.594

1.02

D/T=0.5

0.000

.947

7.272

23.839

54.999

104.648

173.429

251.168

326.065

387.559

426.203

436.381

423.819

396.339

360.939

323.880*

289.819

259.340

232.067

207.662

185.823

166.281

148.793

133.145

119.143

436.430

1.08

D/T=0.6

0.000

.789

6.060

19.866

45.833

87.207

145 . 314

214.578

285.256

348.933

396.543

421.757

423.236

406.502

377.995

343.476

308.104*

275.702

246.708

220.763

197.547

176.772

158.181

141.546

126.660

425.215

1.16

D/T=0.7

0.000

.677

5.194

17.028

39.285

74.749

124.554

184.600

249.255

310.919

362.152

396.970

412.580

408.476

389.326

360.591

327.155

293.392*

262.538

234.928

210.222

188.114

168.331

150.628

134.787

413.246

1.22

D

1

1

2

2

3

3

3

4

3

3

3

3

2

2

2

2

1

1

1

4

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0.
Table 15. Linear Model Hydrographs (S = ko); k

n 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

12.478

48.335

105.345

181.496

274.965

359.146

410.750

432.878

428.334

399.658*

361.624

327.210

296.072

267.896

242.401

219.333

198.461

179.574

162.485

147.022

133.031

120.371

108 . 916

98.551

434.113

0.84

D/T=0.1

0.000

4.274

28.629

75.231

141.965

226.913

319.794

387.425

424.056

432.634

415.832

380.337*

344.142

311.391

281.757

254.944

230.683

208.730

188.866

170.892

154.629

139.914

126.599

114.551

103.650

433.031

0.88

D/T=0.2

0.000

2.137

16.451

51.930

108.598

184.439

273.353

353.610

405.741

428.345

424.233

398.084

362.395*

327.766

296.574

268.350

242.814

219.707

198.798

179.879

162.761

147.272

133.257

120.576

109.101

429.758

0.94

D/T=0.3

0.000

1.425

10.968

36.045

81 . 942

148.036

229.557

311.377

377.092

414.705

424.174

409.601

380.104

345.290*

312.430

282.697

255.795

231.452

209.426

189.496

171.463

155.144

140.382

127.022

114.934

424.399

0.98

D/T=0.4

0.000

1.069

8.226

27.034

62.525

118.185

190.976

269.024

339.547

390.977

414.987

413.215

393.236

362.925

329.407*

298.058

269.694

244.028

220.806

199.793

180.779

163.575

148.008

133.922

121.177

417.000

1.04

D/T=0.5

0.000

.855

6.580

21.627

50.020

95.402

158.506

230.266

300.031

358.164

395.948

408.057

399.400

376.867

346.692

314.514*

284.583

257.501

232.996

210.823

190.760

172.606

156.180

141.316"

127. 868"

408.057

1.10

D/T=0.6

0.000

.712

5.484

18.022

41.683

79.502

132.801

196.660

262.564

322.131

367.776

393.346

397.404

384.732

361.015

331.400

300.542*

271.941

246.062

222.645

201.457

182.285

164.938

149.241

135.038

398.127

1.16

D/T=0.7

0.000

.611

4.700

15.448

35.728

68.145

113.829

169.176

229.145

286.860

335.517

369.570

386.317

385.117

370.021

345.862

317.012

287.426*

260.073

235.323

212.929

192.665

174.330

157.740

142.728

387.834

1.24

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0
Table 16.--Linear Model Hydrographs (S = kO); k

". 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

11.379

44.201

96.603

166.884

253.488

332.241

381.719

404.465

402.800

378.848*

345.926

315.864

288.415

263.351

240.465

219.567

200.486

183.064

167.156

152.629

139.365

127.254

116.195

106.096

406.605

0.84

D/T=0.1

0.000

3.895

26.151

68.906

130.357

208.959

295.314

359.217

395.134

405.498

392.527

362.148*

330.676

301.940

275.701

251.741

229.864

209.888

191.649

174 . 994

159.787

145 . 900

133.222

121.644

111.072

405.498

0.90

D/T=0.2

0.000

1.947

15.023

47.529

99.632

169.658

252.137

327.266

377.176

400.316

399.012

377.337

346.412*

316.308

288.820

263.721

240.803

219.876

200.768

183.322

167.391

152.844

139.561

127.433

116.358

402.604

0.94

D/T=0.3

0.000

1.298

10.015

32.984

75.138

136.074

211.544

287.830

349.889

386.616

397.720

386.724

361.784

331.588*

302.772

276.461

252.435

230.498

210.467

192.177

175.477

160.227

146.303

133.589

121.979

397.720

1.00

D/T=0.4

0.000

.974

7.512

24.738

57.327

108.593

175.884

248.462

314.656

363.791

388.094

388.827

372.712

346.823

317.616*

290.015

264.811

241.798

220.786

201.599

184.079 '

168.083

153.476

140.138

127.960

390.973

1.06

D/T=0.5

0.000

.779

6.009

19.790

45.862

87.654

145.938

212.551

277.796

332.824

369.538

382.905

377.197

358.558

332.598

304.441*

277.984

253.827

231.769

211.627

193.236

176.444

161.110

147.109

134.325

383.084

1.12

D/T=0 . 6

0.000

.649

5.008

16.492

38.218

73.045

122.264

181.484

242.981

299.080

342.775

368.306

374.200

364.654

344.748

319.122

292.012*

266.635

243.464

222.306

202.987

185.347

169.240

154.533

141.103

374.427

1.18

D/T=0.7

0.000

.556

4.292

14.136

32.759

62.610

104.798

156.114

212.006

266.198

312.429

345.542

362.931

363.877

351.946

331.461

306.371

280.280*

255.923

233.682

213.375

194.832

177.901

162.441

148.324

365.299

1.26

Summarized from computations at intervals H/T = 0.02, *Recession coefficient 
Table 17. Linear Model Hydrographs (S = kO ); k/

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D^Inst.

0.000

10.458

40.719

89.200

154.444

235.112

309.054

356.444

379.406

379.891

359.698*

330.938

304.477

280.131

257.733

237.126

218.166

200.722

184.672

169.906

156.322

143.823

132.324

121.744

112 . 010

382.276

0.86

D/T=0.1

0.000

3.578

24.069

63.562

120.536

193.595

274.297

334.786

369.799

381.373

371.381

345.127*

317.531

292.141

268.783

247.292

227.520

209.328

192.590

177.191

163.023

149.989

137.997

126.963

116.812

381.373

0.90

D/T=0.2

0.000

1.789

13.824

43.816

92.049

157.066

233.946

304.541

352.292

375.586

376.377

358.254

331.329*

304.836

280.462

258.037

237.406

2,18.424

200.959

184.890

170.107

156.506

143.993

132.480

121.888

378.642

0.96

D/T=0.3

0.000

1.193

9.216

30.403

69.389

125.898

196.143

267.559

326.294

361.986

374.184

365.960

344.680

318.266*

292.818

269.405

247.865

228.047

209.813

193.036

177.601

163.401

150.336

138.316

127.257

374.184

1.00

D/T=0.4

0.000

.895

6.912

22.802

52.936

100.441

162.998

230.803

293.119

340.064

364.335

366.920

353.853

331.545

305.895*

281.437

258.934

238.231

219.182

201.657

185.533

170.698

157.050

144.493

132.940

368.141

1.06

D/T=0.5

0.000

.716

5.530

18.242

42.349

81.068

135.212

197.355

258.603

310.770

346.327

360.493

357.042

341.510

318.993

294.175*

270.653

249.013

229.102

210.784

193.930

178.424

164.158

151.033

138.957

361.028

1.12

D/T=0.6

0.000

.596

4.608

15.202

35.291

67.557

113.273

168.474

226.096

279.064

320.872

346.127

353.333

346.225

329.389

307.042

283.066*

260.432

239.609

220.451

202.824

186.607

171.686

157.959

145.329

353.333

1.20

D/T=0.7

0.000

.511

3.950

13.030

30.249

57.906

97.091

144.918

197.235

248.278

292.252

324.337

342.042

344.591

335.162

317.661

295.682

272.532*

25 0 . 741

230.692

212.247

195.276

179.663

165.297

152.081

345.239

1.26

D

1

1

2

2

2

3

3

3

3

3

2

2

2

2

2

1

3

Summarised from computations at intervals H/T = 0.02. *Recession coefficient 0
Table 18. Linear Model Hydrographs CS - kO~); k/

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

9.560

37.534

82.556

143.364

218.789

288.627

334.171

357.220

359.440

342.376*

317.015

293.532

271.789

251.656

233.015

215.755

199.773

184.975

171.273

158.586

146.839

135.962

125.891

116.566

360.9

0.86

D/T=0.1

0.000

4.780

23.547

60.045

112.960

181.077

253.708

311.399

345.695

358.330

350.908

329.695*

305.273

282.660

261.722

242.336

224.385

207.764

192.374

178.124

164.930

152.713

141.401

130.927

121.228

358.4

0.92

D/T=0.2

0.000

2.390

14.164

41.796

86.502

147.018

217.392

282.553

328.547

352.013

354.619

340.302

317.484*

293.967

272.191

252.029

233.360

216.074

200.069

185.249

171.527

158.821

147.057

136.164

126.077

355.9

0.96

D/T=0.3

0.000

1.593

9.442

29.457

65.517

118.027

182.582

248.728

303.601

338.475

351.644

346.311

328.626

305.876*

283.219

262.240

242.814

224.828

208.174

192.754

178.476

165.255

15 3 . 014

141.680

131.185

351.8

1.02

D/T=0.4

0.000

1.195

7.082

22.093

50.333

94.407

151.947

214.786

272.970

317.283

341.583

346.157

336.052

317.134

294.838*

272.998

252.776

234.052

216.715

200.662

185.798

172.035

159.292

147.492

136.567

346.2

1.08

D/T=0.5

0.000

.956

5.665

17.674

40.266

76.482

126.267

183.838

240.968

290.042

324.008

339.205

337.980

325.373

306.052

284.337*

263 2/5

243.773

225.716

208.996

193.515

179.181

165.908

153.619

142.239

340.2

1.14

D/T=0.6

0.000

.797

4.721

14.729

33.555

63.735

106.020

157.123

210.814

260.528

300.186

324.956

333.550

328.760

314.765

295.433

274.345*

254.023

235.207

217.784

201.652

186.715

172.884

160.078

148.220

333.6

1.20

D/T=0.7

0.000

.683

4.047

12.625

28.762

54.630

90.874

135.359

184.061

231.888

273.439

304.402

322.144

326.280

319.184

304.418

285.283

264.834*

245.216

227.052

210.234

194.661

180.241

166.890

154.528

326.5

1.28

D

Electronically computed at intervals H/T = 0.10, and expanded manually to obtain 

0.925925923 applicable beyond this point.
Table 19. Linear Model Hydrographs (S = ko); k/T 

Q

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

8.901

34.991

77.083

134.075

204.939

270.916

314.540

337.353

340.791

326.189*

303.693

282.749

263.249

245.094

228.191

212.454

197.802

184.160

171.460

159.635

148.625

138.375

128.832

119.947

111.675

103.973

96.803

90.127

83.911

341.6

0.86

D/T=0.1

0.000

4.451

21.946

56.037

105.579

169.507

237.927

292.728

325.947

339.072

333.490

314.941*

293.221

272.999

254.172

236.643

220.322

205.128

190.981

177.810

165.547

154.130

143.500

133.604

124.390

115.811

107.824

100.388

93.465

87.019

339.4

0.92

D/T=0.2

0.000

2.225

13.198

38.991

80.808

137.543

203.717

265.328

309.337

332.509

336.281

324.216

304.081*

283.110

263.585

245.407

228.482

212.725

198.054

184.395

171.678

159.839

148.815

138.552

128.997

120.100

111.818

104.106

96.926

90.242

336.9

0.96

D/T=0.3

0.000

1.484

8.799

27.478

61.187

110.374

171.005

233.387

285.534

319.240

332.836

329.168

313.884

293.721*

273.464

254.604

237.046

220.698

205.477

191.306

178.113

165.829

154.392

143.745

133.831

124.602

116.008

108.008

100.559

93.624

333.3

1.02

D/T=0.4

0.000

1.113

6. 59Q

20.608

47.003

88.267

142.263

201.435

256.527

298.918

322.809

328.363

320.181

303.663

283.833*

264.259

246.034

229.066

213.268

198.560

184.866

172.117

160.247

149.195

138.906

129.326

120.407

112.103

104.372

97.174

328.6

1.08

D/T=0.5

0.000

.890

5.279

16.487

37.603

71.504

118.199

172.356

226.338

273.036

305.833

321.235

321.334

310.744

293.765

274.395*

255.471

237.853

221.440

206.177

191.957

178.719

166.394

154.918

144.234

134.287

125.026

116.403

108.376

100.901

322.7

1.14

'.u/rtfe -' 

D/T=0.6

0.000

.742

4.399

13.739

31.335

59.587

99.241

147.287

197.954

245.127

283.112

307.351

316.567

313.278

301.316

284.244

265.383*

247.081

230.041

214.176

199.405

185.653

172.849

160.929

149.830

139.497

129.877

120.920

112.580

104.816

316.8

1.22

D/T=0.7

0.000

.636

3.771

11.776

26.859

51.074

85.064

126.882

172.810

218.114

257.750

287.659

305.332

310.343

304.835

292.077

275.113

256.775*

239.066

222.579

207.229

192.937

179.631

167.243

155.709

144.970

134.972

125.664

116.997

108.929

310.3

1.30

D

1

1

1

2

2

2

3

3

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

3

Electronically computed at intervals H/T = 0.10, and expanded manually to obtain 

0.931034483 applicable beyond this point.
Table 20.--Linear Model Hydrographs (S = ko); k

_n 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

Peak

Time

D=Inst.

0.000

8.412

32.930

72.516

126.196

193.062

255.438

297.143

319.511

323.787

311.141*

291.075

272.303

254.741

238.312

222.942

208.563

195.112

182.529

170.756

159.743

149.440

139.802

130.785

122.351

324.322

0.88

D/T=0.1

0.000

2.874

19.425

51.557

98.265

158.609

225.960

277.889

309.822

323.048

318.773

301.001*

281.589

263.428

246.439

230.545

215.676

201.766

188.753

176.580

165.191

154.536

144.570

135.245

126.523

323.555

0.92

D/T=0.2

0.000

1.437

11.150

35.491

74.911

128.437

192.284

251.924

293.856

316.435

320.911

309.887

291.295*

272.508

254.934

238.492

223.111

208.721

195.260

182.666

170.885

159.864

149.553

139.908

130.884

321.407

0.98

D/T=0.3

0.000

.958

7.433

24.619

56.416

102.811

160.945

220.819

271.224

303.587

317.215

314.274

300.454

282.006*

263.819

246.804

230.887

215.996

202.065

189.033

176.841

165.436

154.766

144.784

135.446

317.311

1.02

D/T-0.4

0.000

.719

5.575

18.464

43.030

81.964

133.598

190.181

243.070

284.180

307.383

313.161

306.103

291.198

273.114*

255.500

239.022

223.607

209.185

195.694

183.072

171.265

160.219

149.886

140.219

3-1.3 j.98

1.08

D/T=0.5

0.000

.575

4.460

14.771

34.424

66.146

no. 763

162.456

214.109

259.066

291.099

306.107

306.847

297.568

282.246

264.600*

247.535

231.571

216.636

202.664

189.593

177.365

165.926

155.224

145.213

307.935

1.16

D/T=0.6

0.000

.479

3.717

12.310

28.687

55.122

92 . 78 2

138.618

187.017

A.32 66

269.017

292.749

302.021

299.610

289.046

273.629

256.446*

239.907

224.435

209.960

196.418

183.750

171.899

160.812

150.441

302.357

1.22

D/T=0.7

0.000

.411

3.186

10.551

24.589

47.247

79.527

119.226

163.075

206.450

244.624

273.586

291.155

296.507

292.014

280.689

265.350

248.635*

232.600

217.598

203.564

190.435

178.153

166.663

155.914

295.507

1.30

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0
Table 21. Linear Model Hydrographs (S = kO); k/

r^ 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

7.822

30.815

68.058

118.689

181.896

241.272

281.405

303.461

308.536

297.659*

279.619

262.672

246.753

231.798

217.750

204.553

192.156

180.510

169.570

159.293

149.639

140.570

132.051

124.048

116.529

109.467

102.833

96.600

90.746

308.8

0.88

D/T=0.1

0.000

3.911

19.319

49.437

93.374

150.292

211.584

261.338

292.433

305.999

303.098

288.639*

271.146

254.713

239.276

224.774

211.152

198.354

186.333

175.040

164.432

154.466

145.104

136.310

128.049

120.288

112.998

106.150

99.717

93.673

306.7

0.94

D/T=0.2

0.000

1.956

11.615

34.378

71.405

121.833

180.938

236.461

276.886

299.216

304.548

295.868

279.893*

262.929

246.994

232.025

217.963

204.753

192.344

180.686

169.736

159.449

149.785

140.707

132.180

124.169

116.643

109.574

102.933

96.695

304.7

0.98

D/T=0.3

0.000

1.304

7.743

24.222

54.043

97.701

151.750

207.738

255.118

286.590

300.510

299.245

287.628

271.499*

255.045

239.588

225.067

211.427

198.613

186.576

175.268

164.646

154.667

145.294

136.488

128.216

120.445

113.146

106.288

99.847

301.4

1.04

D/T=0.4

0.000

.978

5.807

18.167

41.510

78.105

126.171

179.147

228.912

267.838

290.717

297.542

292.220

279.399

263.444*

247.477

232.479

218.389

205.153

192.720

181.040

170.068

159.761

150.078

140.982

132.438

124.412

116.871

109.788

103.135

297.5

1.10

D/T=0.5

0.000

.782

4.646

14.533

33.208

63.266

104.801

153.205

201.804

244.329

274.890

290.301

292.263

284.719

271.374

255.710*

240.212

225.654

211.978

199.131

187.062

175.725

165.075

155.070

145.672

136.844

128.550

120.759

113.440

106.565

292.6

1.16

D/T=0.6

0.000

.652

3.872

12.111

27.673

52.722

87.986

130.891

176.410

219.170

254.124

277.182

287.109

286.005

277.145

263.608

248.283*

233.236

219.100

205.822

193.348

181.629

170.622

160.281

150.567

141.442

132.869

124.817

117.252

110.146

288.0

1.26

D/T=0.7

0.000

.559

3.319

10.381

23.720

45.190

75.417

112.751

153.968

194.922

231.160

259.055

276.320

282.481

279.329

269.664

256.114

241.151*

226.535

212.806

199.909

187.793

176.412

165.720

155.676

146.241

137.378

129.052

121.231

113.884

282.5

1.30

D

1

1

2

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1

2

Lectronically computed at intervals H/T = 0.10, and expand'ed manually to obtain 

0.939393939 applicable beyond this point.
Table 22. Linear Model Hydrographs fS = kO); k

n_ 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

6.977

27.529

60.924

106.467

163.501

217.452

254.534

275.658

281.688

273.438*

258.658

244.676

231.450

218.940

207.105

195.910

185.320

175.303

165.827

156.864

148.384

140.364

132.776

125.599

118.810

112.388

106.313

100.566

95.130

281.7

0.90

D/T=0.1

0.000

3.488

17.253

44.227

83.695

134.984

190.477

235.993

265.096

278.673

277.563

266.048*

251.667

238.063

225.195

213.022

201.508

190.615

180.312

170.565

161.345

152.624

144.374

136.570

129.188

122.205

115.590

109.351

103.440

97.848

279.9

0.94

D/T=0.2

0.000

1.744

10.371

30.740

63.961

109.340

162.730

213.235

250.545

271.885

278.118

271.805

258.857*

244.865

231.629

219.109

207.265

196.061

185.463

175.438

165.955

156.985

148.499

140.472

132.879

125.696

118.902

112.475

106.395

100.644

278.1

1.00

D/T=0.3

0.000

1.163

6.914

21.656

48.392

87.635

136.385

187.151

230.522

259.921

273.777

274.095

265.093

251.926*

238.308

225.427

213.242

201.715

190.812

180.497

170.741

161.512

152.781

144.523

136.711

129.321

122.331

115 . 718

109.463

103.546

275.2

1.04

D/T=0.4

0.000

.872

5.185

16.242

37.166

70.040

113.346

161.287

206.638

242.560

264.331

271.845

268.488

258.335

245.243*

231.987

219.447

207.585

196.364

185.750

175.709

166.212

157.227

148.728

140.689

133.084

125.890

119.086

112.649

106.559

271.8

1.10

D/T=0.5

0.000

.698

4.148

12.994

29.733

56.729

94.127

137.875

182.049

221.045

249.560

264.675

267.809

262.403

251.707

238.799*

225.891

213.680

202.130

191.204

180.869

171.092

161.844

153.096

144.820

136.992

129.587

122.582

115 . 95 6

109.688

267.8

1.20

D/T=0.6

0.000

.581

3.457

10.828

24.777

47.275

79.021

117.771

159.079

198.153

230.464

252.308

262.507

262.852

256.201

245.260

232.584*

220.012

208.119

196.869

186.228

176.161

166.639

157.632

149.111

141.051

133.427

126.214

119.392

112.938

263.8

1.28

D/T=0.7

0.000

.498

2.963

9.281

21.238

40.521

67.732

101.445

138.818

176.164

209.497

235.548

252.217

259.015

257.472

250.033

239.009

226.588*

214.340

202.754

191.795

181.427

171.620

162.344

153.568

145.267

137.415

129.987

122.961

116 . 314

259.3

1.32

Electronically computed at intervals H/T - 0.10, and expanded manually to obtain 

0.945945945 applicable beyond this point.
Table 23. Linear Model Hydrographs (S = kO); k

n_

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

6.345

24.969

55.275

96.692

148.680

198.030

232.385

252.475

258.996

252.611*

240.290

228.571

217.424

206.820

196.734

187.138

178.011

169.329

161.070

153.214

145.742

138.635

131.874

125.443

119.326

113.506

107.971

102.705

97.695

D/T=0.1

0.000

2.165

14.699

39.211

75. 116

121.861

174.585

216.378

243.543

256.794

256.811

246.401*

234.384

222.953

212.080

201.737

191.897

182.538

173.635

165.166

157.110

149.448

142.160

135.227

128.633

122.360

116.393

110.717

105.317

100.180

D/T=0.2

0.000

1.083

8.432

26.955

57.164

98.489

148.223

195.481

229.960

250.168

256.802

251.606

240.392*

228.668

217.516

206.908

196.817

187.218

178.087

169.401

161.138

153.279

145.804

138.694

131.930

125.496

119.376

113.555

108.017

102.748

D/T=0.3

0.000

.722

5.621

18.692

43.009

78.729

123.854

170.941

211.502

238.905

252.382

253.335

245.865

234.579*

223.139

212.256

201.905

192.057

182.690

173.780

165.304

157.242

149.573

142.278

135.340

128.740

122.462

116.490

110.809

105.405

D/T=0.4

0.000

.541

4.216

14.019

32.798

62.722

102.693

146.985

189.092

222.825

243.381

250.887

248.597

240.137

228.954*

217.788

207.167

197.063

187.452

178.309

169.613

161.340

153.471

145.986

138.867

132.095

125.653

119.525

113.696

108.151

D/T=0.5

0.000

.433

3.373

11.215

26.238

50.611

85.094

125.430

166.297

202.632

229.622

243.985

247.586

243.468

234.525

223.511*

212.610

202.241

192.377

182.995

174.070

165.580

157.504

149.822

142.516

135.566

128.955

122.666

116.684

110.993

D/T=0.6

0.000

.361

2.811

9.346

21.865

42.175

71.273

106.975

145.116

181.379

211.662

232.418

242.385

243.481

238.237

229.060

218.242*

207.598

197.473

187.842

178.681

169.966

161.676

153.791

146.291

139.156

132.370

125.915

119.774

113.933

D/T=0.7

0.000

.309

2.409

8.011

18.742

36.150

61.091

92.002

126.485

161.070

192.155

216.625

232.699

239.609

238.995

233.023

223.752

213.141*

202.746

192.858

183.452

174.505

165 . 994

157.898

150.197

142.872

135.904

129.277

122.972

116.975
Table 23. Linear Model Hydrographs (S = kO); k/T = 

n 

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3,90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

Peak

Time

D=Inst.

92

88

84

79

76

72

68

65

62

59

56

53

51

48

46

43

41

39

37

35

34

258

0

.931

.400

.088

.987

.086

.375

.845

.487

.293

.255

.365

.616

.001

.514

.148

.897

.756

.720

.783

.940

.187

.996

.90

D/T=0.1

95.294

90.647

86.226

82.021

78.021

74.216

70.596

67.153

63.877

60.761

57.798

54.979

52.299

49.748

47.321

45 . 014

42.818

40.730

38.744

36.854

35.056

258.352

0.94

D/T=0.2

97.737

92.970

88.437

84.124

80.021

76.118

72.406

68.874

65.515

62.319

59.280

56.389

53.639

51.024

48.535

46.167

43.916

41.774

39.737

37.799

35.955

256.802

1.00

D/T=0.3

100.264

95.374

90.722

86.298

82.089

78.086

74.277

70.655

67.208

63.930

60.812

57.846

55.025

52.342

49.789

47.361

45.051

42.854

40.764

38.776

36.885

254.231

1.06

D/T=0.4

102.877

97.859

93.086

88.546

84.228

80.121

76.212

72.496

68.960

65.597

62.397

59.354

56.459

53.705

51.086

48.595

46.225

43.970

41.826

39.786

37.846

251.094

1.12

D/T=0.5

105.580

100.431

95.533

90.874

86.442

82.226

78.216

74.401

70.772

67.320

64.037

60.914

57.943

55.117

52.429

49.872

47.440

45.126

42.925

40.832

38.840

247.586

1.20

D/T=0.6

108.377

103.091

98.063

93.281

88.731

84.404

80.288

76.372

72.647

69.104

65.733

62.527

59.478

56.577

53.818

51.193

48.696

46.322

44.063

41.914

39.869

243.942

1.26

D/T=0.7

111.270

105.844

100.682

95.772

91.101

86.658

82.431

78 . 411

74.587

70.949

67.489

64.197

61.066

58.088

55.255

52.560

49.997

47.559

45.239

43.033

40.934

240.142

1.34

Summarized from computations at intervals H/T = 0.02. *Recession coefficient 0
Table 24. Linear Model Hydrographs (S = kcO ; k/

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

5.736

22.690

50.363

88.279

135.982

181.565

213.650

232.836

239.696

234.779*

224.345

214.374

204.846

195.742

187.042

178.729

170.786

163.195

155.942

149.011

142.389

136.060

130.013

124.235

118.713

113.437

108.395

103.578

98.974

239.7

0.90

D/T=0.1

0.000

2.868

14.213

36.527

69.321

112.131

158.774

197.607

223.243

236.266

237.238

229.562*

219.359

209.610

200.294

191.392

182.886

174.758

166.991

159.569

152.477

145.700

139.224

133.037

127.124

121.474

116.075

110.916

105.987

101.276

238.2

0.96

D/T=0.2

0.000

1.434

8.541

25.370

52.924

90.728

135.452

178.190

210.425

229.754

236.752

233.399

224.461*

214.485

204.952

195.843

187.139

178.822

170.874

163.280

156.023

149.088

142.462

136.131

130.080

124.299

118.775

113.496

108.451

103.631

236.8

1.02

D/T=0.3

0.000

.956

5. 6^4

17.869

40.020

72.659

113.408

156.171

193.208

219.039

232.249

234.355

228.720

219.510*

209.754

200.432

191.524

183.012

174.878

167.106

159.679

152.582

145.800

139.320

133.128

127.212

121.558

116.155

110.993

106.060

234.5

1.06

D/T=0.4

0.000

.717

4.270

13.402

30.732

58.048

94.188

134.458

172.939

203.972

223.588

231.577

230.606

223.942

214.706*

205.164

196.046

187.332

179.007

171.051

163.448

156.184

149.243

142.610

136.271

130.215

124.428

118.897

113.613

108.564

232.0

1.14

D/T=0.5

0.000

.574

3.416

10.722

24.586

47.012

78.193

114.872

152.215

185.604

210.625

224.783

229.133

226.407

219.213

210.043*

200.708

191.788

183.264

175. 118

167.336

159.899

152.792

146.001

139.512

133.312

127.387

121.725

116.315

111.146

229.1

1.20

yi/nre - - 

D/T=0.6

0.000

.478

2.847

8.935

20.488

39.177

65.639

98.095

132.934

166.224

194.210

213.782

223.879

225.880

222.055

214.576

205.517*

196.383

187.655

179.315

171.345

163.730

156.453

149.499

142.855

136.506

130.439

124.642

119.102

113.809

226.0

1.28

D/T=0.7

0.000

.410

2.440

7.658

17.561

33.580

56.262

84.492

115.974

147.695

176.368

199.260

214.578

221.841

222.224

217.674

210.049

201.123*

192.184

183.643

175.481

167.682

160.229

153.108

146.303

139.801

133.587

127.650

121.977

116.056

222.7

1.36

D

1

1

1

1

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1

1

1

1

2

Electronically computed at intervals H/T =0.10, and expanded manually to obtain 

0.955555556 applicable beyond this point.
Table 25. Linear Model Hydrographs (S = ko); 

n.

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

5.268

20.857

46.346

81.330

125.423

167.716

197.747

216 . 015

223.003

219.168*

210.223

201.642

193.412

185.518

177.946

170.682

163.716

157.034

150.624

144.476

138.579

132.923

127.497

122.293

117.302

112.514

107.922

103.517

99.291

223.1

0.92

D/T=0.1

0.000

2.634

13.063

33.602

63.838

103.377

146.570

182.731

206.881

219.509

221.086

214.696*

205.933

197.527

189.465

181.732

174.314

167.199

160.375

153.829

147.550

141.528

135.751

130.210

124.895

119.798

114.908

110.218

105.719

101.404

221.7

0.96

D/T=0.2

0.000

1.317

7.848

23.332

48.720

83.607

124.973

164.650

194.806

213.195

220.297

217.891

210.314*

201.730

193.496

185.598

178.023

170.756

163.787

157.102

150.689

144.539

138.639

132.980

127.553

122.346

117.353

112.563

107.968

103.562

220.4

1.02

D/T=0.3

0.000

.878

5.232

16.433

36.834

66.939

104.595

144.226

178.727

203.041

215.825

218.430

213 . 905

206.052*

197.642

189.575

181.837

174.415

167.296

160.466

153.918

147.635

141.610

135.830

130.286

124.968

119.867

114.974

110.282

105.780

218.5

1.08

D/T=0.4

0.000

.659

3.924

12.325

28.284

53.470

86.847

124.129

159.890

188.923

207.552

215.543

215.306

209.810

201.905*

193.664

185.759

178.177

170.905

163.929

157.238

150.820

144.664

138.760

133.096

127.664

122.453

117.455

112.661

108.062

216.2

1.14

D/T-0.5

0.000

.527

3.139

9.860

22.627

43.303

72.090

106.023

140.679

171.813

195.355

208.980

213.621

211.750

205.741

197.870*

189.794

182.047

174.617

167.490

160.653

154.096

147.806

141.773

135.987

130.436

125.112

120.006

115.108

110.409

213.7

1.22

D/T=0.6

0.000

.439

2.616

8.216

18.856

36.085

60.514

90.530

122.833

153.818

180.026

198.579

208.473

210.939

208.036

201.740

193.944*

186.028

178.435

171.152

164.166

157.466

151.039

144.874

138.960

133.289

127.848

122.630

117.625

112.824

211.0

1.28

D/T=0.7

0.000

.376

2.242

7.043

16.162

30.930

51.869

77.973

107.152

136.644

163.427

184.978

199.629

206.909

207.871

204.278

197.822

190.124

182.363

174.920

167.780

160.932

154.364

148.063

142.020

136.223

130.663

125.330

120.214

115.307

208.0

1.36

Electronically computed at intervals H/T = 0.10, and expanded manually to obt

0.959183673 applicable beyond this point.
Table 26. Linear Model Hydrographs (S = kO); k/T 

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

Peak

Time

D=Inst.

0.000

4.870

19.298

42.922

75.395

116.384

155.826

184.039

201.446

208.456

205.460*

197.707

190.246

183.067

176.159

169.512

163.115

156.960

151.037

145.337

139.853

134.575

129.497

124.610

119.908

115.383

111.029

106.839

102.808

98.928

208.6

0.92

D/T=0.1

0.000

2.435

12.084

31.110

59.159

95.890

136.105

169.933

192.743

204.951

206.958

201.584*

193.977

186.657

179.613

172.835

166.313

160.037

153.998

148.187

142.595

137.214

132.036

127.054

122.259

117.646

113.206

108.934

104.823

100.868

207.3

0.96

D/T=0.2

0.000

1.218

7.260

21.597

45.134

77.524

115.997

153.019

181.338

198.847

205.955

204.271

197.780*

190.317

183.135

176.224

169.574

163.175

157.018

151.092

145.391

139.904

134.625

129.545

124.656

119.952

115.426

111.070

106.879"

102.846

206.2

1.02

D/T=0.3

0.000

.812

4.840

15.210

34.118

62.053

97.051

133.976

166.260

189.209

201.551

204.498

200.840

194.072*

186.749

179.702

172.921

166.395

160.116

154.074

148.260

142.665

137.282

132.101

127.116

122.319

117.704

113.262

108.988

104.875

204.6

1.08

D/T=0.4

0.000

.609

3.630

11.407

26.197

49.561

80.566

115.272

148.668

175.933

193.646

201.559

201.867

197.294

190.458*

183.271

176.355

169.700

163.296

157.134

151.204

145.499

140.008

134.725

129.641

124.749

120.041

115.511

111.152

106.958

202.4

1.14

D/T=0.5

0.000

.487

2.904

9.126

20.958

40.136

66.870

98.439

130.766

159.924

182.138

195.234

200.042

198.825

193.758

186.933*

179.879

173.091

166.559

160.274

154.226

148.406

142.806

137.417

132.231

127.242

122.440

117.820

113.374

109.095

200.2

1.22

D/T=0.6

0.000

.406

2.420

7.605

17.465

33.446

56.131

84.047

114.157

143.130

167.763

185.379

195.024

197.812

195.623

190.271

183.496*

176.572

169.909

163.497

157.328

151.391

145.678

140.181

134.891

129.801

124.902

120.189

115 . 654

111.289

197.8

1.30

D/T=0.7

0.000

.348

2.074

6.518

14.970

28.668

48.112

72.388

99.575

127.127

152.248

172.595

186.607

193.829

195.212

192.368

186.848

180.145*

173.347

166.806

160.511

154.454

148.626

143.017

137.620

132.427

127.430

122.621

117.994

113.541

195.3

1.38

D

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Electronically computed at intervals H/T = 0.10, and expanded manually to obtain 

0.962264151 applicable beyond this point.
Table 27. Linear Model Hydrographs (S = kO); k/

n 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

4.554

18.005

40.039

70.356

108.667

145.582

172.146

188.721

195.660

193.298*

186.516

179.973

173.658

167.566

161.687

156.015

150.542

145.261

140.165

135.249

130.504

125.925

121.508

117.245

113.132

109.164

105.335

101.639

98.074

D/T=0.1

0.000

1.553

10.580

28.348

54.546

88.883

127.968

159.677

181.219

192.948

195.210

189.887*

183.226

176.797

170.594

164.610

158.834

153.263

147.886

142.699

137.693

132.863

128.201

123.704

119.364

115.177

111.137

107.239

103.477

99.847

D/T=0.2

0.000

.776

6.066

19.464

41.447

71.715

108.426

143.822

170.448

187.083

194.079

192.549

186.556*

180.011

173.696

167.602

161.722

156.049

150.575

145.293

140.196

135.278

130.532

125.953

121.534

117.271

113.157

109.188

105.358

101.662

D/T=0.3

0.000

.518

4.044

13.493

31.158

57.259

90.466

125.509

156.288

177.948

189.792

192.682

189.441

183.303*

176.872

170.667

164.679

158.902

153.328

147.949

142.759

137.751

132.919

128.256

123.756

119.415

115.226

111.184

107.284

103.521

D/T=0.4

0.000

.388

3.033

10.120

23.757

45.589

74.936

107.769

139.437

165.453

182.263

189.816

190.318

186.280

180.126*

173.807

167.709

161.825

156.148

150.671

145.385

140.285

135.364

130.615

126.033

121.612

117.346

113.229

109.257

105.425

D/T=0.5

0.000

.311

2.427

8.096

19.005

36.782

62.065

91.884

122.459

150.139

171.404

183 .788

188.498

187.614

183.143

177.023*

170.812

164.820

159.038

153.458

148.075

142.881

137.868

133.032

128.365

123.862

119.517

115.324

111.279

107.375

yi/Hrg - 

D/T=0.6

0.000

.259

2.022

6.747

15.838

30.652

51.980

78.334

106.773

134.207

157.651

174.475

183.694

186.548

184.777

180.054

173 . 991*

167.887

161.997

156.314

150.831

145.540

140.434

135.508

130.754

126.167

121.741

117.470

113.350

109.373

D/T=0.7

0.000

.222

1.733

5.783

13.575

26.273

44.554

67.365

93.032

119.084

142.921

162.256

175.733

182.709

184.269

181.896

177.022

171.030*

165.030

159.240

153.654

148.264

143.063

138.044

133.201

128.529

124.020

119.669

115.471

111.421

D

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1
Table 27. Linear Model Hydrographs (S = kO); k/T = 2

11

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

Peak

Time

D=Inst.

94.634

91.313

88.109

85 . 018

82.035

79.157

76.381

73.701

71.115

68.620

66.213

63.890

61.649

59.486

57.401

55.386

53.443

51.568

49.759

48.013

46.329

195.921

0.92

D/T=0.1

96 . 344'

92.964

89.702

86.555

83.518

80.588

77.761

75.033

72.401

69.861

67.410

65 . 045

62.763

60.561

58.436

56.386

54.408

52.499

50.657

48.880

47.165

195.499

0.98

D/T=0.2

98.096

94.654

91.333

88.128

85.036

82.053

79.174

76.397

73.717

71.130

68.635

66.227

63.904

61.662

59.499

57.412

55.398

53.455

51.580

49.770

48.024

194.360

1.02

D/T=0.3

99.889

96.385

93.003

89.740

86.591

83.553

80.622

77.794

75.065

72.431

69.890

67.438

65.072

62.790

60.587

58.462

56. 411

54.432

52.523

50.680

48.902

192.700

1.08

D/T=0.4

101.727

98.158

94.714

91.391

88.185

85.090

82.105

79.225

76.446

73.764

71.176

68.679

66.270

63.945

61.702

59.537

57.449

55.433

53.489

51.612

49.802

190.800

1.16

D/T=0.5

103.609

99.974

96.467

93.082

89.817

86.665

83.625

80.690

77.860

75.129

72.493

69.950

67.496

65.128

62.843

60.639

58.511

56.459

54.478

52.567

50.723

188.703

1.22

 ^ji/rtrg -

D/T=0.6

105.537

101.835

98.262

94.815

91.488

88.278

85.181

82.193

79.309

76.527

73.842

71.252

68.752

66.340

64.013

61.767

59.600

57.510

55.492

53.546

51.667

186.548

1.32

D/T=0.7

107.512

103.741

100.101

96.590

93.201

89.931

86.776

83.731

80.794

77.959

75.224

72.585

70.039

67.582

65 . 211

62.923

60.716

58.586

56.531

54.548

52.634

184.318

1.38

D

1

1

1

1

Summarized from computations at intervals H/T - 0.02. *Recession coefficient 0.
Table 28. Linear Model Hydrographs (S = kO); k/

n

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

4.254

16.831

37.459

65.872

101.818

136.540

161.660

177.494

184.346

182.512*

176.527

170.740

165.141

159.727

154.492

149.426

144.527

139.789

135.206

130.773

126.486

122.340

118.328

114.448

110.697

107.067

103.557

100.161

96.877

D/T=0.1

0.000

1.450

9.887

26.511

51.053

83.253

119.960

149.855

170.308

181.627

184.113

179.504*

173.618

167.926

162.419

157.095

151.945

146.963

142.145

137.485

132.978

128.618

124.402

120.323

116.378

112.562

108.872

105.303

101.850

98.510

D/T=0.2

0.000

.725

5.669

18.199

38.782

67.153

101.606

134.908

160.081

175.967

182.870

181. 808

176.561*

170.772

165.173

159.757

154,520

149.454

144.554

139.815

135.231

130.798

126.510

122.363

118.351

114.470

110.717

107.088

103.576

100.180

D/T=0.3

0.000

.483

3.791

12.616

29.151

53.606

84.755

117.689

146.707

167.263

178.682

181.747

179.078

173.682*

167.987

162.480

157.153

152.001

147.018

142.198

137.536

133.027

128.666

124.448

120.368

116.421

112.604

108.912

105.342

101.887

D/T=0.4

0.000

.362

2.834

9.462

22.225

42.676

70.192

101.030

130.844

155.437

171.476

178.888

179.715

176.290

170.867*

165.265

159.846

154.606

149.537

144.635

139.893

135.306

130.870

126.580

122.430

118.416

114.534

110.779

107.147

103.634

D/T=0.5

0.000

.290

2.267

7.570

17.780

34.431

58.133

86.126

114.886

141.000

161.172

173.081

177.834

177.357

173.516

168.112*

162.601

157.270

152.114

147.127

142.303

137.638

133.125

128.761

124.540

120.457

116.508

112.688

108.993

105.419

Vi/nrg - 

D/T=0.6

0.000

.242

1.890

6.308

14.817

28.692

48.686

73.420

100.156

126.009

148.186

164.227

173.170

176.182

174.867

170.779

165.418*

159.994

154.749

149.675

144.768

140.022

135.432

130.992

126.697

122.543

118.526

114.640

110.881

107.246

D/T=0.7

0.000

.207

1.620

5.407

12.700

24.593

41.731

63.138

87.261

111.795

134.309

152.660

165.569

172.421

174.216

172.329

168.088

162.781*

157.444

152.283

147.290

142.461

137.791

133.273

128.904

124.678

120.590

116.637

112.813

109.114

D

1
Table 28. Linear Model Hydrographs (S = ko); k/T = 

IL 

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

Peak

Time

D=Inst.

93.701

90.629

87.659

84.785

82.005

79.316

76.715

74.200

71.767

69.414

67.139

64.939

62.809

60.750

58.758

56.832

54.968

53.166

51.423

49.737

48.106

184.665

0.92

D/T=0.1

95.281

92.156

89.136

8 6 . 214

83.388

80.654

78.008

75.451

72.977

70.584

68.271

66.033

63.868

61.774

59.749

57.790

55.895

54.063

52.290

50.576

48.917

184.308

0.98

D/T=0.2

96.895

93.718

90.646

87.675

84.801

82.021

79.331

76.730

74.214

71.780

69.427

67.152

64.950

62.821

60.761

58.769

56.842

54.979

53.176

51.433

49.747

183.233

1.04

D/T=0.3

98.547

95.316

92.191

89.169

86.246

83.419

80.683

78.038

75.479

73 . 004

70.611

68.296

66.057

63.892

61.797

59.771

57.811

55.916

54.083

52.310

50.594

181.747

1.10

D/T=0.4

100.236

96.949

93.771

90.697

87.724

84.848

82.066

79.375

Ik. 112

74.255

71.821

69.466

67.189

64.986

62.856

60.795

58.802

56.874

55.009

53.206

51.462

180.023

1.16

D/T=0.5

101

98

95

92

89

86

83

80

78

75

73

70

68

66

63

61

59

57

55

54

52

178

1

.963

.620

.387

.259

.235

.310

.480

.743

.096

.535

.058

.663

.347

.106

.939

.843

.815

.854

.957

.123

.348

.165

.24

D/T=0.6

103.

100.

97.

93.

90.

87.

84.

82.

79.

76.

74.

71.

69.

67.

65.

62.

60.

58.

56.

55.

53.

176.

1.

730

329

039

858

781

805

926

142

449

844

324

887

531

251

046

914

851

856

927

060

255

215

32

D/T=0.7

105.537

102.076

98.730

95.493

92.362

89.334

86.405

83.573

80.833

78.182

75.619

73.140

70.742

68.422

66.179

64.010

61.911

59.882

57.918

56.019

54.183

174.216

1.40

Summarized from computations at intervals H/T = 0.02. -Recession coefficient 0
Table 29. Nonlinear Model Hydrographs (S = kOx ); x = 0.

n. 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

52.753

325.189

662.143

945.126

1214.258

1147.690

848.583

614.870

375.086

154.361

50.611

26.616

16.580

11.359

8.281

6.310

4.971

4.018

3.316

2.783

2.370

2.042

1.778

1.562

1.384

1.234

1.107

.999

.906

D/T=0.1

0.000

15.992

174.881

502.000

807.767

1080.045

1182.331

995.787

732.288

493.302

261.554

102.778

41.501

23.132

14.855

10.375

7.665

5.899

4.682

3.807

3.157

2.661

2.274

1.965

1.715

1.511

1.340

1.197

1.076

.973

D/T=0.2

0.000

4.507

82.152

338.550

662.499

945.075

1132.659

1088.176

862.963

612.286

375.355

180.750

73.664

34.107

20.027

13.242

9.427

7.060

5.488

4.390

3.593

2.995

2.535

2.174

1.885

1.650

1.456

1.295

1.159

1.044

D/T=0.3

0.000

2.096

42.302

213.809

508.507

807.273

1026.775

1087.179

966.903

738.399

492.418

281.417

135.634

60.096

29.907

18.135

12.222

8.811

6.660

5.213

4.193

3.446

2.883

2.448

2.105

1.829

1.604

1.418

1.263

1.132

D/T=0.4

0.000

1.207

25.907

141.207

374.691

662.899

905.938

1020.662

995.636

845.649

615.391

391.171

221.799

111.123

52.020

27.125

16.825

11.496

8.367

6.367

5.010

4.046

3.337

2.800

2.382

2.052

1.786

1.569

1.389

1.239

D/T=0.5

0.000

.784

17.534

101.066

282.365

530.121

775.179

927.406

960.949

891.573

723.723

508.247

321.003

185.243

95.445

46.517

25.092

15.835

10.938

8.020

6.136

4.849

3.929

3.249

2.732

2.329

2.010

1.752

1.541

1.366

D/T=0.6

0

12

76

222

429

649

817

893

879

780

614

429

274

160

84

42

23

15

10

7

5

4

3

3

2

2

1

1

1

.000

.550

.675

.251

.353

.811

.878

.898

.994

.591

.804

.376

.455

.050

.174

.415

.456

.515

.049

.487

.736

.946

.715

.832

.176

.675

.285

.974

.723

.517

D/T=0.7

0.000

.407

9.594

59.736

180.627

358.566

549.787

707.364

806.346

833.865

785.683

677.320

530.241

373.342

239.957

141.816

76.164

39.302

22.237

14.398

10.109

7.496

5.785

4.601

3.748

3.113

2.627

2.246

1.943

1.698
Table 20. Nonlinear Model Hydrographs (S = kOx ); 

n_

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

0.826

.755

.694

.639

.591

.548

.510

.475

.444

.416

.390

.367

.346

.326

.308

.292

.277

.263

.250

.238

.226

D/T=0.1

0.883

.806

.738

.678

.626

.579

.537

.500

.466

.436

.408

.384

.361

.340

.321

.304

.288

.273

.259

.246

.235

D/T=0.2

0.944

.859

.784

.719

.662

.611

.566

.526

.489

.457

.427

.401

.377

.354

.334

.316

.299

.283

.269

.255

.243

D/T=0.3

1.020

.924

.841

.769

.706

.650

.601

.557

.517

.482

.450

.421

.395

.371

.350

.330

.312

.295

.280

.265

.252

D/T=0.4

1.111

1.003

.909

.828

.758

.696

.641

.593

.549

.511

.476

.445

.417

.391

.368

.346

.327

.309

.292

.277

.263

D/T=0.5

1.219

1.094

.988

.897

.817

.748

.687

.634

.586

.543

.505

.471

.441

.413

.387

.364

.343

.324

.306

.290

.275

D/T=0.6

1.346

1.202

1.080

.976

.886

.808

.740

.680

.627

.580

.538

.501

.467

.437

.409

.384

.362

.341

.322

.304

.288

D/T=0.7

1.496

1.328

1.187

1.067

.965

.877

.800

.733

.674

.622

.575

.534

.497

.464

.434

.406

.382

.359

.339

.320

.302
Table 30. Nonlinear Model Hydrographs (S = kOx ); x = 0.5

11

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

12.116

115.385

366.450

706.420

1044.820

1137.741

953.715

727.338

501.848

289.655

156.416

98.770

68.246

50.050

38.304

30.272

24.534

20.290

17.061

14.548

12.553

10.942

9.623

8.530

7.613

6.836

6.172

5.601

5.106

D/T=0.1

0.000

3.172

51.380

229.464

535.945

880.965

1097.696

1046.126

839.363

613.039

393.227

222.478

129.215

84.907

60.190

44.942

34.859

27 o 838

22.749

18.942

16.019

13.725

11.891

10.403

9.178

8.157

7.298

6.568

5.942

5.402

D/T=0.2

0.000

.813

20.468

128.357

377.882

712.460

996.206

1075.202

941.785

724.763

501.178

306.340

176.406

108.428

73.676

53.414

40.534

31. 828

25.663

21.135

17.711

15.058

12.961

11.273

9.896

8.757

7.804

6.999

6.312

5.721

D/T=0.3

0.000

.364

9.460

69.913

250.143

549.683

854.362

1022.426

996.848

'829.258

610.630

404.977

247.158

148.123

94.636

65.877

48.560

37.306

29.571

24.022

19.905

16.764

14.314

12.365

10.790

9.497

8.425

7.524

6.760

6.108

D/T=0.4

0.000

.206

5.431

41.518

163.294

406.600

704.253

91Q.135

981.019

897.551

714.843

508.628

334.606

208.701

129.239

84.919

60.197

44.947

34.863

27.840

22.751

18.943

16.020

13.725

11.892

10.403

9.178

8.157

7.298

6.568

D/T=0.5

0.000

.132

3.521

27.503

111.958

297.604

561.932

795.913

913.357

905.914

790. 115

609.529

429.840

285.974

182.210

115.771

77.712

55.876

42.149

32.945

26.468

21.735

18.170

15.417

13.247

11.505

10.087

8.915

7.937

7.111

yi/nre - 

D/T=0.6

0.000

.092

2.466

19.558

81.666

224. 113

443.803

669.570

819.535

865.390

814.401

687.085

524.699

372.446

251.034

162.889

105.645

72.126

52.460

39.905

31.390

25.346

20.899

17.530

14.916

12.847

11.181

9.820

8.694

7.751

D/T=0.7

0.000

.068

1.823

14.621

62.235

175.193

356.493

557.081

715.171

796.441

793.843

721.122

600.777

460.242

329.533

224.781

148.123

97.706

67.639

49.670

38.050

30.094

24.404

20.192

16.986

14.489

12.505

10.904

9.592

8.503

D

1

2

4

6

7

7

7

6

5

4

2

2

1
Table 30. Nonlinear Model Hydrographs fS = kOx%); 

n. 

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

4.673

4.293

3.958

3.661

3.396

3.158

2.945

2.753

2.579

2.420

2.276

2.145

2.025

1.914

1.812

1.718

1.632

1.551

1.477

1.408

1.343

D/T=0.1

4.932

4.521

4.15Q

3.839

3.555

3.301

3.073

2.868

2.683

2.516

2.363

2.224

2.097

1.981

1.874

1.775

1.684

1.600

1.522

1.449

1.382

D/T=0.2

5.210

4.765

4.374

4.029

3.724

3.452

3.209

2.991

2.794

2.616

2.454

2.307

2.173

2.050

1.938

1.834

1.739

1.650

1.569

1.493

1.423

D/T=0.3

5.545

5.057

4.630

4.256

3.925

3.631

3.369

3.134

2.924

2.733

2.561

2.404

2.262

2.132

2.012

1.903

1.802

1.709

1.623

1.543

1.469

D/T=0.4

5.942

5.402

4.932

4.521

4.159

3.839

3.555

3.301

3.073

2.868

2.683

2.516

2.363

2.224

2.097

1.981

1.874

1.775

1.684

1.600

1.522

D/T=0.5

6.408

5.805

5.283

4.828

4.430

4.079

3.768

3.491

3.244

3.022

2.822

2.642

2.478

2.329

2.193

2.068

1.954

1.849

1.753

1.663

1.581

^i/nte -

D/T=0.6

6.953

6.273

5.688

5.181

4.739

4.352

4.010

3.707

3.437

3.195

2.978

2.782

2.606

2.445

2.299

2.165

2.043

1.931

1.828

1.733

1.645

D/T=0.7

7.590

6.817

6.156

5.587

5.093

4.662

4.284

3.950

3.653

3.389

3.152

2.940

2.748

2.574

2.416

2.273

2.142

2.021

1.911

1.810

1.716

D
Table 31. Nonlinear Model Hydrographs (S = kOx );

". 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

6.467

67.213

241.453

531.789

878.163

1052.419

959.526

773.497

564.993

360.090

219.245

148.120

106.966

80.942

63.419

51.047

41.983

35.141

29.848

25.670

22.312

19.574

17.312

15.420

13.823

12.461

11.292

10.280

9.398

D/T=0.1

0.000

1.658

28.693

142.513

379.432

705.489

972.442

1009.727

866.468

667.887

460.279

288.853

184.746

128.693

94.910

72.940

57.832

46.991

38 . 943

32.804

28.013

24.202

21.120

18.592

16.493

14 . 731

13.237

11 . 95 9

10.858

9.902

D/TO.2

0.000

,420

11.069

75.781

251.837

540.328

844.532

997.271

939.534

766.310

562.243

373.008

236.945

157.741

112.793

84.743

66.038

52.929

43.381

36.208

30.682

26.333

22.849

20.015

17.677

15.727

14.083

12.684

11.484

10.447

D/T=0.3

0.000

.187

5.028

39.817

158.434

394.933

691.992

912.982

959.540

848.285

661.121

467.791

309.479

202.347

138.721

101.185

77.129

60.770

49.131

40.551

34.043

28.988

24.983

21.755

19.116

16.930

15.099

13.550

12.228

11.090

D/T=0.4

0.000

.106

2.860

23.107

99.637

278.838

545.080

790.541

913.988

888.306

747.359

563.108

394.780

265.334

177.929

124.739

92.409

71.256

56.643

46.120

38.286

32.296

27.612

23.879

20.857

18.375

16.312

14.578

13.106

11.847

D/T=0.5

0.000

.068

1.842

15.077

66.504

196.811

417.815

659.674

825.214

871.200

799.536

649.361

483.557

341.525

233.503

159.866

114.068

85.569

66.605

53.335

43.681

36.437

30.860

26.475

22.963

20.108

17.755

15.792

14.138

12.732

m/rt±-e - 

D/T=0.6

0.000

.047

1.285

10.613

47.556

144.077

319.274

536.721

718.694

811.158

802.356

707.773

566.359

422.898

301.855

209.590

145.965

105.649

80.077

62.820

50.615

41.660

34.894

29.655

25.516

22.187

19.472

17.226

15.348

13.762

D/T=0.7

0.000

.035

.947

7.872

35.695

110.109

249.593

434.221

610.741

728.955

764.833

723.663

626.356

500.559

376.181

271.349

190.962

134.904

98.812

75.551

59.666

48.329

39.950

33.580

28.624

24.692

21.518

18 . 921

16.768

14.962
Table 31. Nonlinear Model Hydrographs (S = kOx ); x = 0.5; k/ 

n_

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

8.625

7.944

7.340

6.803

6.322

5.891

5.503

5.151

4.833

4.542

4.278

4.036

3.813

3.609

3.421

3.247

3.086

2.937

2.798

2.669

2.548

D/T=0.1

9.068

8.334

7.686

7. in

6.599

6,139

5.726

5.354

5.016

4.710

4.431

4.176

3.942

3.727

3.530

3.348

3.179

3.023

2.878

2.744

2.618

D/T=0.2

9.544

8.753

8.057

7.440

6.892

6.403

5.963

5.568

5.210

4.886

4.591

4.322

4.076

3.851

3.644

3.453

3.276

3.113

2.962

2.821

2.691

D/T=0.3

10.105

9.245

8.490

7.825

7.234

6.708

6.238

5.815

5.434

5.089

4.776

4.491

4.231

3.992

3.774

3.573

3.387

3.216

3.057

2.910

2.773

D/T=0.4

10.761

9.818

8.994

8.269

7.629

7.060

6.553

6.098

5.689

5.320

4.986

4.682

4.405

4.152

3.921

3.708

3.512

3.331

3.164

3.009

2.865

D/T=0.5

11.525

10.482

9.574

8.780

8.081

7.462

6.911

6.419

5.978

5.581

5 223

4.897

4.602

4.332

4.085

3.859

3.651

3.459

3.283

3.119

2.967

^i/nre - - 

D/T=0.6

12.409

11.247

10.241

9.364

8.595

7.917

7.316

6.782

6.303

5.874

5.487

5.137

4.820

4.531

4.267

4.026

3.805

3.601

3.413

3.240

3.079

D/T=0.7

13.434

12.128

11.004

10.030

9.179

8.433

7.773

7.189

6.668

6.201

5.782

5.404

5.062

4.751

4.469

4.210

3.974

3.757

3.557

3.372

3.202

D
76 MODEL HYDROGRAPHS

1 0

1 IN

'<

1

1 "I

i VI <Q

1 0

1 H

'< 

1 Q

1

1 .

O

1 II l<, °

1 00 

1 0

1 E-^

i cT

1 r1 

o

l<

, °

1 VO

0) a, o

\ H 

H \

o

,^o 1

i *

1 0

,^

1 O

1 1 "

o

1^ ,°

1 0

1 11 0"

1I ^, 0

,<o

1 .

r tJ

i ti 

i&

3=1 H

O co O H CO

o o o r~ tO CO

O vO O CO OO

0 H -0

O CO ON uo UO 

O H uo co LO 

O O CO O CM

O CO ^f 

H

O 00 rH

O O ON ^f uo 

O O uo t~- CO

0 *f H 

(N

O CN CN H O 

0 0 t-- H H

O vO CO 

CN

O VO O ^f (N 

O CO OO uo C-J 

O O O O*l C 

O 00 tCO

O <N O ^p O 

O uo (N vO |-~

0 H r-| co

O H t- CO H 

O O CN O H

O C-l 00 O 

H CO

O ^f ON 00 O 

O H 00 CO O

O co H ON 

CO CN 

rH

O (N O CO CO 

O CO VD CO ^

O CO O CO

CM

o r*- \Q vo ON

o H OJ m o

N d rH SiCO

O O ^f O iO

O O co H LD

O O O O O 

O H C-J CO ^F

OO ID ON C^ [>-

01 c-] K£> H H

H CO vD i | vD

£§?; s *

i I ID ON OO ON ci ID o r*~- -^F

H H C-l

LQ r- H co CA

"* H ci co 5

Cl H CO LD O 

ID 0 Cl CN O

H ci co uo

CO <N CN O C-J

O F- CO CO LD

LD H O O ON 

CO ON H r~- OO

O *-p ^ rH ^f 

[^ rH CO O CO

C~- i 1 LD C-J C-l

LD OO O rH LD

H C-J ON (N -^F

(N ON (N O O

CO H CO UO ON

O 01 r- oo H

CO VD i | VO ON 

UO NO O f- Cl

LO UO CO rf CO

H 01 ^r co o

H ON 00 l> LD 

OO CN ^F O UO

^f O CO ^F ^ 

CM O t~- vD OO

CO uo O 00 CO

H c-J ^ co O

CN rH CO C-J ON

ON ON ^ CO OO

C~- ON ON r~~ UO

O O O O O

m o ON o &

O vD ON r | CO

ON CO H CN NO

O ID ^F CM CO 

H LD 00 O H

H uo NO r-- ^f 

oo oo r-- CN oo

-----

co H co H rON CO CO OO H

H <N Cl CO O 

"^ Ol CO vD O

CO H CO H ON

C-J VO vD OO I 1 

CO OO ON | \ \D 

LD i 1 ^F NO UO

 ^F oo CA c-i co 

co o r-- ^F 01

CO ON ID C- C-l

C-J ON CO ^f ND

oo r-- c-J ^F OJ

<*D \D i | i 1 "^F

H H ON O O 

ID 00 rH ON O

CS O CO ""f NO 

O CO ID ON NO 

r- ON O ON t~-

O ON CO C-J LO

CO CO CN CN ON 

ON ^ OO ON ON

CO O co O H

uo ^T CM H H

O CN ^f O ON

oo H H ^r H

*t co (N H H 

CO rf O ^f O

csi co uo H rOO ^f t~- C-J ON 

CO CN] H H

o o o o o 

O H CN co ^F

Cl CN ^f NO OO

CO LD OO ON CO

O H H H c-l

CN Cl CO CN CO 

H NO f- ID O

O C-l NO ON ON 

C-l (N H ON ^O

ON uD NO ^F O

^F CO CO Cl H

[^ CN ^f LD H

rf co C-J H i i

t~- ON i [ -^F i |

O 00 O H CO

UO NO ON -^F O 

co CM H H H

H oo H r- 0

LD CO ^F ON 1/3

H O 01 co oo

ON H LD H 00

01 CS H H

ON r~- i i 00 NO 

<N OO ^F O [^ 

NO CO ON ON uD

O ^F H co ^F

OO CM vD O r^ 

^f O CO NO | |

O H O ON <^

H H H

ON -^F r~~ O OO

^f O OO NO uo 

H H

00 O H H C-I 

oo H 01 co r--

CO H ^ ON ON 

r-j ON IT-- uo rf

CO ON H CM CO

O O ^ CN ^F

H

H co co r- oo

CO ON C-l E~~- ^f

C~- ON t-- r~- O 

OO NO UO ^f ^f

NO C-l CO OO CO

vD CN i 1 CO VO

I"- NO LD ^F CO

o o o o o

r- 01 ID ^F H

H O ID C-J H 

Cl (N H O 00

CN co ^F r- H

UO CM OO O O 

CO CS1 C] H H

Cl vD ON O CO 

H r-- uo H "^

Cl ON F- vD ID

H

CO ON Cl O 01

H

^f LO O CO LO r~- oo H r-- ON

o o oo o ^r

C~- CO CO NO ID

VD CO -^F (N CO

O O Cvl vO rH 

NO io ^f cO CO

ON sO Cl LD ON 

 ^F C~- ON t NO

(N ^ l> 01 CO

00 ON H CO ON

 ^F co co c-i c-i 

oo r-- NO oo co

vO CO Ol Ol C-l

H LD o r- co

co H ON uo O

OO NO CO O rH

l> CN CO ^F CM

ID O 00 CO H 

VO O CO (N VO

^f O NO CO O 

CO CO (N cN 01

r~- O ON r~- i I

OO CO rf NO CO

H l> ^ H ON 

CO 01 OJ (N H

o o o o o 

O H OJ co ^F

00 ON H ^F vD

& r- vo H co

O C-l CO CO OO

LO H r^- co O

O ON ^ CJ ^F

H

ID ^F 00 H 0 

oo co oo H rCM ON oo oo ^F

^. CO CO 0. CS

o r- ID o oi

co m o) ci c-J 

o o rf r~ H

CO O uo C*l O

CO CJ tN C-l C^l

ON H O O H 

CS LO CO [-- vD

O vD CO O OO 

CO CM 01 CN H

r- O ON H oo

co H co H H

<N OJ <N H H

H OJ uo vO CN 

CO OO O [-- LO 

O O VD vD O

^ c-i c> r^- m

OO CO C-l ^f OO

CN O OO VD ^ 

OJ c-J H H H

c-- m H 01 vo 

uo H H 00 tH &* O CO Ov

H 00 C-- uo co 

OJ H H H H

H c> vo co at~- \O ON ^ rH

ON r~ uo ^f CO

^f rH O LO vO 

O v£J CO H 01

H H H H H

O H vO O O 

^f |-- O-l O O

r-- uo ^F co H

H H H H H

o o o o o

LO vO E-~- OO ON
Table 32. Nonlinear Model Hydrographs (S = kf)x ); x = 0.5; k/ /A

LL

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

10.941

10.089

9.332

8.658

8.054

7.511

7.021

6.578

6.175

5.808

5.473

5.167

4.885

4.626

4.386

4.165

3.961

3.771

3.594

3.429

3.276

D/T=0.1

11.486

10.570

9.760

9.040

8.396

7.819

7.299

6.830

6.404

6.017

5.664

5.341

5.045

4.773

4.523

4.292

4.077

3.879

3.695

3.523

3.364

D/T=0.2

12.070

11.085

10.216

9.446

8.759

8.145

7.593

7.095

6.645

6.236

5.864

5.524

5.213

4.928

4.665

4.423

4.199

3.992

3.800

3.621

3.455

D/T=0.3

12.754

11.686

10.747

9.916

9.179

8.521

7.931

7.400

6.921

6.487

6.093

5.733

5.404

5.103

4.827

4.572

4.337

4.120

3.918

3.731

3.557

D/T=0.4

13.549

12.382

11.359

10.459

9.661

8.951

8.317

7.747

7.235

6.771

6.351

5.969

5.620

5.301

5.008

4.739

4.491

4.263

4.051

3.854

3.672

D/T=0.5

14.469

13.184

12.062

11.078

10.210

9.440

8.754

8.140

7.589

7.091

6.642

6.233

5.861

5.522

5.211

4.926

4.663

4.421

4.197

3.990

3.798

'^i/nre ~

D/T=0.6

15.530

14.104

12.866

11.784

10.833

9.993

9.247

8.581

7.985

7.449

6.966

6.527

6.129

5.767

5.435

5.132

4.853

4.596

4.359

4.140

3.937

D/T=0.7

16.753

15.160

13.783

12.586

11.539

10.617

9.801

9.076

8.429

7.848

7.326

6.854

6.426

6.037

5.682

5.358

5.061

4.788

4.536

4.304

4.089

D
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Table 33. Nonlinear Model Hydrographs (S = kOx ); 

n 

T

3.00 

3.10

3.20 

3.30 

3.40

3.50

3.60 

3.70 

3.80

3.90

4.00

4.10 

4.20 

4.30 

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

13.448 

12.415

11.496 

10.676 

9.940

9.278

8.680 

8.138 

7.645

7.196

6.785

6.409 

6.063

5.744 

5.449

5.177

4.925

4.691

4.473

4.270

4.080

D/T=0.1

14.099 

12.991

12.009 

11.134 

10.351

9.649

9.015 

8.442 

7.922

7.448

7.016

6.620 

6.257 

5.923 

5 . 615

5.331

5.067

4.823

4.596

4.384

4.187

D/T=0.2

14.796 

13.607

12.555 

11.621 

10.788

10.041

9.369 

8.762 

8.213

7.713

7.258

6.842 

6.461 

6.110

5.788

5.490

5.215

4.960

4.723

4.503

4.298

D/T=0.3

15.607 

14.320

13.187 

12.183 

11.289

10.490

9.774 

9.128

8.544

8.015

7.533

7.093 

6.691 

6.322 

5.983

5.670

5.382

5.115

4.867

4.637

4.422

D/T=0.4

16.543 

15.142

13 . 911 

12.825 

11.861

11.002

10.233 

9.542 

8.919

8.355

7.843

7.376 

6.950 

6.560 

6.201

5.872

5.568

5.287

5.027

4.785

4.561

D/T=0.5

17.621 

16.084

14.739 

13.556 

12.511

11.581

10.752 

10.009 

9.340

8.736

8.189

7.692 

7.238 

6.824 

6.444

6.095

5.774

5.477

5.203

4.949

4.713

D/T=0.6

18.860 

17.161

15.682 

14.387 

13.245

12.235

11.335 

10.532 

9.811

9.162

8.575

8.042 

7.558 

7.116 

6.712

6.342

6.001

5.687

5.397

5.129

4.880

D/T=0.7

20.280 

18.391

16.754 

15.326 

14.073

12.968

11.989 

11.116 

10.335

9.634

9.002

8.430 

7.911 

7.438 

7.007

6.612

6.250

5.916

5.609

5.325

5.062
Table 34. Nonlinear Model Hydrographs (S = kOx ); x = 0.5

Jl

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

3.251

35.696

140.235

346.124

642.752

866.340

883.290

776.840

614.202

433.493

294.582

213.582

162.088

127.278

102.627

84.523

70.830

60.222

51.834

45.087

39.579

35.023

31.212

27.991

25.244

22.883

20.839

19.057

17.494

D/T=0.1

0.000

.823

14.819

79.121

233.677

488.833

757.622

879.946

832.163

695.362

522.278

363.140

254.582

188.597

145.425

115.602

94.125

78.137

65.912

56.352

48.734

42.567

37.502

33.290

29.751

26.748

24.178

21.962

20.037

18.355

D/T=0.2

0.000

.207

5.609

40.600

147.491

354.176

623.118

824.024

859.759

764.644

607.929

441.465

308.686

222.195

167.739

131.190

105.448

86.624

72.438

61.480

52.837

45.899

40.247

35.578

31.679

28.387

25.583

23.176

21.093

19.279

D/T=0.3

0.000

.092

2.520

20.829

89.254

246.402

484.976

717.565

836.113

808.610

683.179

523.990

378.095

269.348

197.925

151.694

120.021

97.357

80.574

67.794

57.837

49.927

43.537

38.303

33.960

30.316

27.229

24.591

22.319

20.348

D/T=0.4

0.000

.052

1.425

11.911

54.578

167.105

364.485

592.713

760.980

809.231

737.899

600.377

454.446

330.817

239.868

179.197

139.047

111.074

90.792

75 . 613

63.954

54.803

47.487

41.548

36.658

32.584

29.154

26.239

23.740

21.583

D/T=0.5

0.000

.033

.915

7.700

35 . 745

114.425

268.581

473.651

658.687

761.698

756.034

660.674

528.158

400.376

294.809

217.039

164.362

128.855

103.766

85.372

71.481

60.731

52.240

45.416

39.850

35.249

31.401

28.152

25.382

23.002

' VJ-/" re ~ 

D/T=0.6

0.000

.023

.637

5.384

25 . 216

81.911

199.006

372.453

552.037

683.380

730.657

690.218

589.578

469.586

358.087

266.662

198.900

152.346

120.478

97.691

80.824

67.988

57.989

50.049

43.637

38.385

34.028

30.374

27.278

24.634

D/T=0.7

0.000

.017

.469

3.975

18.739

61.536

151.837

291.712

453.903

593.881

673.902

681.142

625.279

529.458

422.366

324.379

244.074

184.111

142.389

113.451

92.544

76.941

64.985

55.619

48.145

42.086

37.104

32.957

29.470

26.508

D

1

2

3

5

6

6

6

5

4

3

2

2

1

1

1
Table 34. Nonlinear Model Hydrographs (S = kOx ); x = 0.5; k/ /

ii

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

D=Inst.

16.116

14.895

13.807

12.835

11.962

11.175

10.463

9.817

9.229

8.692

8.201

7.751

7.336

6.954

6.601

6.275

5.971

5.690

5.428

5.183

4.955

D/T=0.1

16.876

15.569

14.408

13.373

12.445

11.611

10.857

10.175

9.555

8.991

8.474

8.001

7.567

7.167

6.798

6.457

6.140

5.847

5.574

5.320

5.082

D/T=0.2

17.689

16.289

15 . 048

13 . 944

12 . 95 7

12.072

11.274

10.553

9.899

9.304

8.761

8.264

7.808

7.389

7.003

6.646

6.316

6.010

5.726

5.461

5.215

D/T=0.3

18.628

17.116

15.782

14.598

13.542

12.597

11.748

10.981

10.288

9.658

9.084

8.560

8.080

7.639

7.233

6.859

6.513

6.193

5.896

5.619

5.362

D/T=0.4

19.707

18.065

16.620

15.342

14.206

13.192

12.283

11.464

10.725

10.055

9.446

8.891

8.383

7.918

7.490

7.096

6.732

6.396

6.084

5.795

5.525

D/T=0.5

20.942

19.147

17.573

16.186

14.957

13.863

12.885

12.006

11.215

10.499

9.850

9.259

8.720

8.227

7.774

7.358

6.974

6.620

6.292

5.987

5.705

i^i/rtrp - 

D/T=0.6

22.356

20.380

18.655

17.141

15.804

14 . 617

13.559

12.612

11 . 761

10.994

10.299

9.668

9.093

8.568

8.088

7.646

7.240

6.865

6.519

6.198

5.901

D/T=0.7

23.972

21.783

19.881

18.218

16.756

15.462

14.313

13.288

12.369

11.542

10.795

10.119

9.504

8.944

8.431

7.962

7.531

7.134

6.767

6.428

6.114

D
Table 35. Nonlinear Model Hydrographs (S = kOx ); x = 0.

n 

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

2.699

29.925

119.617

302.460

577.581

802.711

844.408

762.824

617.969

448.329

313.234

231.491

178.182

141.446

115.039

95.413

80.424

68.716

59.394

51.852

45.663

40.520

36.200

32.537

29.403

26.702

24 . 35 6

22.307

20.506

D/T=0.1

0.000

.682

12.359

66.890

201.749

433.380

691.696

828.297

806.064

690.630

531.878

379.941

272.752

205.507

160.492

128.852

105.751

88.365

74.949

64.377

55.898

48.993

43.295

38.537

34.523

31.105

28.171

25.634

23.425

21.490

D/T=0.2

0.000

.171

4.662

34.090

126.015

309.987

560.953

764.248

820.992

749.661

610.721

454.815

326.123

239.623

183.639

145.287

117.847

97.528

82.057

70.004

60.428

52.694

4b.358

41.100

36.690

32.954

29.761

27.011

24.626

22.543

D/T=0.3

0.000

.076

2.091

17.411

75.662

213.317

431.087

656.533

787.261

782.040

677.244

531.956

393.120

286.452

214.388

166.582

133.212

108.982

90.826

76.866

65.900

57.128

50.002

44.132

39.239

35.117

31.613

28.609

26.014

23.756

D/T=0.4

0.000

.043

1.182

9.930

46.016

143.434

320.421

535.647

707.312

772.293

721.757

601.074

465.271

346.199

256.224

194.668

152.994

123.446

101.725

85.285

72.539

62.457

54.342

47.716

42.232

37.644

33.765

30.456

27.612

25.148

D/T=0.5

0.000

.027

.758

6.409

30.029

97.606

234.018

423.438

605.183

718.248

730.175

652.617

533.019

412.455

309.929

232.558

178.900

141.952

US. 410

95.693

80.640

68.887

59.532

51.964

45.755

40.597

36.266

32.593

29.451

26.743

' ^J-/"re - 

D/T=0.6

0.000

.019

.528

4.476

21.131

69.558

172.222

329.170

502.021

637.499

697.764

673.471

587.083

476.775

370.543

281.220

213.542

166.005

132.799

108.677

90.594

76.686

65.757

5 7 . 013

49.907

44 . 05 3

39.173

35.061

31.566

28.568

D/T=0.7

0.000

.014

.388

3.302

15.674

52.079

130.715

256.655

409.217

548.754

637.234

657.597

615.185

530.410

430.725

336.732

257.951

197.908

155.243

125.072

102.939

86.215

73.268

63.038

54.814

48.103

42.555

37.915

33.995

30.654
Table 35. Nonlinear Model Hydrographs (S = kO*); x = 0.5; k/ /

u

T

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

5.10

5.20

5.30

5.40

5.50

5.60

5.70

5.80

5.90

6.00

D=Inst.

18.915

17.502

16.242

15 .113

14.098

13.182

12.352

11.599

10.912

10.285

9.710

9.182

8.696

8.247

7.833

7.449

7.092

6.761

6.452

6.164

5.895

5.643

5.407

5.185

4.977

4.781

4.596

4.422

4.258

4.102

3.955

D/T=0.1

19.785

18.275

16.932

15.732

14.655

13.685

12.808

12.013

11.290

10.630

10.027

9.473

8.964

8.495

8.062

7.661

7.289

6.944

6.623

6.323

6.044

5.782

5.537

5.308

5.092

4.889

4.698

4.519

4.349

4.188

4.037

D/T=0.2

20.714

19.099

17.666

16.388

15.244

14.216

13.289

12.449

11.687

10.993

10.358

9.777

9.244

8.753

8.300

7.882

7.494

7.134

6.800

6.489

6.198

5.927

5.673

5.435

5.211

5.001

4.804

4.618

4.443

4.277

4.121

D/T=0.3

21.781

20.042

18.503

17.136

15 . 914

14.819

13.833

12.942

12.135

11.401

10.731

10.119

9.558

9.042

8.567

8.128

7.723

7.347

6.997

6.672

6.370

6.087

5.823

5.575

5.343

5.125

4.921

4.728

4.546

4.375

4.213

D/T=0.4

23.000

21.116

19.455

17.982

16.671

15.498

14.444

13.495

12.636

11.857

11.147

10.500

9.907

9.363

8.863

8.402

7.976

7.581

7.215

6.875

6.559

6.263

5.988

5.730

5.488

5.262

5.049

4.849

4.660

4.482

4.315

D/T=0.5

24.392

22.339

20.534

18.939

17.524

16.261

15.131

14.114

13.196

12.365

11.610

10.923

10.294

9.719

9.190

8.704

8.255

7.839

7.455

7.098

6.766

6.457

6.168

5.899

5.647

5.410

5.188

4.980

4.784

4.599

4.425

D/T=0.6

25.978

23.725

21.754

20.018

18.482

17.117

15.897

14.803

13.819

12.930

12.123

11.390

10.722

10.110

9.550

9.035

8.560

8.122

7.717

7.341

6.992

6.668

6.365

6.083

5.819

5.572

5.340

5.122

4.918

4.725

4.544

D/T=0.7

27.782

25.296

23.130

21.230

19.556

18.072

16.751

15.569

14.509

13.553

12.689

11.905

11.191

10.540

9.944

9.397

8.894

8.430

8.002

7.606

7.238

6.896

6.578

6.282

6.005

5.746

5.503

5.276

5.062

4.861

4.672

D
Table 36. Nonlinear Model Hydrograpbs (S = kf)x ); x - 0.

n^

T

0.00

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

D=Inst.

0.000

2.274

25.422

103.028

265.714

519.651

741.847

802.629

743.450

616.265

458.485

328.415

247.055

192.708

154.570

126.763

105.856

89.737

77.045

66.871

58.592

51.762

46.061

41.254

37.163

33.651

30.615

27.972

25.658

23.619

D/T=0.1

0.000

.574

10.459

57.227

175.517

385.407

630.885

776.297

775.582

680.389

536.390

392.699

288.042

220.463

174.250

141.230

116.804

98.224

83.758

72.273

63.002

55.410

49.114

43.834

39.362

35.542

32.253

29.400

26.910

24.723

D/T=0.2

0.000

.144

3.934

28.998

108.688

272.690

505.380

706.779

779.600

729.578

608.163

463.628

340.135

254.645

197.909

158.292

129.519

107.955

91.372

78.343

67.920

59.451

52.475

46.659

41.760

37.595

34.023

30.938

28.254

25 . 905

D/T=0.3

0.000

.064

1.762

14.759

64.850

185.965

384.179

599.890

738.058

751.525

666.088

5 35 . Oil

404.223

300,659

228.850

180.112

145.489

119.998

100.680

85.688

73.817

64.257

56.444

49.976

44.560

39.980

36.072

32.710

29.798

27.258

D/T-0.4

0.000

.036

.995

8.400

39.271

124.172

282.901

484.171

655.397

733.096

701.072

596.796

471.759

358.231

270.161

208.454

165.789

135.041

112.141

94.621

80.917

69.993

61.146

53.878

47.834

42.753

38.441

34.751

31.569

28.804

D/T=0.5

0.000

.023

.638

5.414

25.554

84.073

205.088

379.187

554.963

674.303

700.948

639.974

533.390

420.784

322.172

245.986

191.973

154.043

126.372

105.558

89.505

76.860

66.722

58.469

51.660

45.976

41.181

37.100

33.597

30.568

Vi/nre -

D/T=0.6

0.000

.016

.444

3.778

17.947

59.698

150.086

292.545

456.217

592.656

662.866

652.903

580.240

479.994

379.757

293.298

226.373

178.385

144.236

119.060

99.960

85.122

73.365

63.890

56.142

49.724

44.348

39.799

35 . 917

32.577

D/T=0.7

0.000

.012

.327

2.785

13.293

44.577

113.427

226.739

369.097

505.802

599.853

631.235

601.302

527.501

435.658

346.300

269.688

210.129

166.974

135.911

112.798

95.130

81.319

70.316

61.409

54.096

48.016

42.907

38.573

34.865

5

4
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