model hydrographs - usgs · model hydrographs by w. d. mitchell abstract model hydrographs are...

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

Stock Number 2401-2050

CONTENTS

Abstract __ _____________________________________________________ 1Introduction. _____________________________________________________ 1Elements of the model hydrograph_____--___--_---____-____,______ 3

Translation hydrograph___-___-___-__--____-___________________ 3Storage____________________________________________________ 4

Routing consideratians___-_-__---_______---___-__________ 6Linear routing__________________________________________ 7Nonlinear routing _________________________________________ 8

Duration.____________________________________________________ 10Linear models___________________________________________ 10Nonlinear models________________________________________ 11

Model hydrographs---_____-__---_-____-___---___-_-___-_____-_____ 15Linear models_______________________________________________ 15Nonlinear models____________________________________________ 15Application to specific areas________-______-__-_________________ 16

Example 1______________________________ 16Example 2__________________________________ 18Example 3____._________._______________ 18Example 4______________________________ 18Example 5____________________________ 21Example 6______________________________ 22

Determination of hydrograph parameters.-___________________________ ?2Determination from observed hydrographs_________-____--____-. 23

Characteristic time, T______________________________________ ?3Storage constants, k and £________________-_-___-__---_-____ T3

Determination from basin characteristics_____________--__-_--____ 27Unit hydrograph-_________________________________________________ ?**Summary and conclusions___________________--____________________- f7References_________________________________ f

ILLUSTRATIONS

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

2. Translation hydrographs, finite values of D/T____________ 143-6. Hydrographs for:

3. Tributary to Second Creek at Keptown, I1L__ _ 174. Tributary to Kankakee River near Bourbonnais,

Ill_________________________-_-_-___-_ _ 195. Mazon River near Coal City, 111 ______________ 2T6. Tributary to Vermilion River at Lowell, 111., and for

tributary to Mud Creek near Tower Hill, Ill____ 21m

IV CONTENTS

FIGURES 7-10. Graphs of: Page7. Analyses for storage constants of model hydro-

graphs _____________________________________ 258. Analyses for storage constants of observed hydro-

graphs. ____________________________________ 269. Observed versus computed values of T. __________ 29

10. Observed versus computed values of k __________ 3011. Proportional graphs, resulting from routing through linear

storage, S=0.20 0_________________________ 3112. Nonproportional graphs, resulting from routing through

nonlinear storage, S=10 0°-5 _________________________ 3213. Nonproportional graphs, resulting from routing through

nonlinear storage, 5=0.01 02 ______________________ 3314. Semilogarithmic plotting, recession limbs of graphs from

figures 11, 12, and 13___________________.__ 3415. Typical recessions, previously published unit hydrographs_ 3516. Recession hydrographs, all for Money Creek above Lake

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

TABLES

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

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

3-28. Linear model hydrographs (S=W); k/T= :3. 0.20________________________--______-__.______ 414. 0.25_________-__-_---_____---_--__---____-___- 425. 0.30__________-_-___-_____-_-_---_---___--_._- 436. 0.35-_- _ _ -__-__ 447. 0.40_______________--____-__---_-_----_____-__ 458. 0.45 ___ --_ 469. 0.50______________________-_--______-_________ 47

10. 0.55________________.__-____-_---_----____--__ 4811. 0.60________________________________________ 4912. 0.70________________________________._________ 5013. 0.80.__________________________--__--_________ 5114. 0.90. ________________________-__---___-__---_ 5215. 1.00._____________--_________--__--_--_-_-____ 5316. 1.10________________________________________ 5417. 1.20________________________________-_____--_- 5518. 1.30______________________________--______--_- 5619. 1.40___________________________ 5720. 1.50__________________________________________ 5821. 1.60_______________________________-__--_-.__- 5922. 1.80____________________________ 6023. 2.00_______________________________-______--._ 6124. 2.20__________________________________________ 6325. 2.40_____________________.-______ 6426. 2.60____________________________ 6527. 2.80________________________--.___ 6628. 3.00.________._______________.___--__-._------ 68

CONTENTS

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

29. 2.0._.___-_-_. _.___._..._..._..__._..____.._ 7030. 5.0._.___ _... .. _ ___ __. 7231. 7.0.____.____-.__ ____________________ _ __._ 7432. 8.0.-. __ _ _ ___ _-__ ___ 7633. 9.0 _ _ __ -__ _ ___ __ 7834. 10.0.____-_____-_____________________________ 8035. 11.0__________ _____________________________ 8236. 12.0__-____ __________________________________ 84

SYMBOLS

(The following symbols are listed in alphabetical order. Each symbol indicatesthe basic term usually represented, with no attempt to show the many and un avoidable 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 dimension-

less) .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 con verted 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 facili tated 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 pro portionality 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 appro priated 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, in stantaneous 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's immediately 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 dis tance 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=AP e (5,280) 2/12, or V= 2,323,200 AP e . Since the entire flow would pass the outlet in the period of Thours, the average rate of flow would be Qa= 2,323,200 AP e/3,600 T= 645.333 APe T cubic feet per second.

The preceding considerations define, in a general way, the transla tion hydrograph for instantaneous rainfall excess. The hydrograph is for a drainage area of A square miles and represents instantaneous rainfall excess of P e 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 signifi cant, but these will be dealt with at a later time, perhaps in a sub sequent 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/AP e 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 dis cussed 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 subse quently, 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 com putations at a time for which the outflow is known, as at the begin ning 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 de velopments 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 in stantaneous translation hydrograph.

The third item needed for computation of 02 is a definitive expres sion for storage. In reservoir routing, storage is assumed to be a func tion 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-dis charge 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 ex hibit the characteristics of linear storage. The number of exceptions, however, is so great that nonlinear storage (x other than unity) can not 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 dimen sion 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 spe cific 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 computa tions. As pointed out above, A< should be small enough that the aver age 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 adjust ments 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.

Tab

le 1. S

ecti

on

of

typ

ical

model

h

yd

rog

rap

h

(lin

ear)

com

puta

tions

H T (1)

0.5

0.5

2.5

4.5

6.5

8

.60

.62

.64

.66

.68

.70

.72

.74

.76

.78

.80

.82

.84

.86

.88

.90

.92

.94

.96

.98

1.0

01.0

21

.04

1.0

61.0

81

.10

£T APe (2)

1,2

90.6

67

1,2

39

.04

01,1

87.4

13

1,1

35

.78

71

,08

4.1

60

1,0

32.5

33

98

0.9

07

929.2

80

87

7.6

53

82

6.0

27

77

4.4

00

72

2.7

73

67

1.1

47

61

9.5

20

567.8

93

516.2

67

46

4.6

40

41

3.0

13

36

1.3

87

30

9.7

60

25

8.1

33

20

6.5

07

154.8

80

10

3.2

53

51

.62

7

0 0 0 0 0 0

I21

l +

01.2

AP

e A

Pe(3

)

2,5

29.7

07

2,5

29.7

07

2,4

26

.45

32

,32

3.2

00

2,2

19.9

47

2,1

16

.69

32,0

13.4

40

1,9

10.1

87

1,8

06.9

33

1,7

03

.68

0

1,6

00.4

27

1,4

97

.17

31

,39

3.9

20

1,2

90

.66

71

,18

7.4

13

1,0

84

.16

09

80

.90

7877.6

53

77

4.4

00

67

1.1

47

567.8

93

464.6

40

361.3

87

25

8.1

33

154.8

80

51.6

27

0 0 0 0 0

Inst

hgh

(4)

816.6

89

859.3

71

893.0

72

918.6

46

93

6.8

68

94

8.4

37

953.9

88

95

4.0

93

94

9.2

71

93

9.9

92

926.6

80

909.7

19

889.4

56

866.2

06

840.2

54

811.8

56

781.2

46

74

8.6

35

714.2

13

678.1

52

640.6

09

601.7

24

561.6

26

520.4

30

478.2

40

435.1

52

393.7

09

356.2

13

32

2.2

88

291.5

94

263.8

23

0.0

2T

hgh

(5)

793.1

02

838.0

30

87

6.2

22

90

5.8

59

927.7

57

942.6

52

951.2

12

954.0

40

951.6

82

944.6

32

933.3

36

91

8.2

00

89

9.5

88

87

7.8

31

85

3.2

30

826.0

55

796.5

51

76

4.9

40

73

1.4

24

696.1

82

65

9.3

80

621.1

66

58

1.6

75

54

1.0

28

49

9.3

35

45

6.6

96

414.4

30

374.9

61

33

9.2

50

306.0

41

27

7.7

08

Sum

mat

ion

0.0

2T

hg

h(6

)

7,9

66

.42

48,8

04.4

54

9,6

80

.67

610,5

86.5

35

11,5

14.2

92

12,4

56.9

44

13

,40

8.1

56

14,3

62.1

96

15,3

13.8

78

16,2

58.5

10

17

,10

1.8

46

18

,11

0.0

46

19

,00

9.6

34

19,8

87.4

65

20,7

40.6

95

21,5

66.7

50

22,3

63.3

01

23,1

28.2

41

23,8

59.6

65

24

,55

5.8

47

25,2

15.2

27

25,8

36.3

93

26

,41

8.0

68

26,9

59.0

96

27,4

58.4

31

27,9

15.1

27

28

,32

9.5

57

28,7

04.5

18

29

,04

3.7

68

20,3

50.7

09

29,6

28.4

17

Su

mm

atio

nla

g

O.I

T(7

)

4,4

65.1

30

5,0

73.6

40

5,7

27.4

50

6,4

27.1

62

7,1

73.3

22

7,9

66

.42

48

,80

4.4

54

9,6

80.6

76

10,5

86.5

35

11,5

14.2

92

12

,45

6.0

44

13

,40

8.1

56

14,3

62.1

06

15

,31

3.8

78

16

,25

8.5

10

17,1

91.8

46

18

,11

0.0

46

19

,00

9.6

34

19

,88

7.4

65

20,7

40.6

95

21

,56

6.7

50

22,3

63.3

01

23,1

28.2

41

23,8

59.6

65

24

,55

5.8

47

25

,21

5.2

27

25

,83

6.3

93

26

,41

8.0

68

26

,95

9.0

96

27,4

58.4

31

27

,91

5.1

27

O.I

T

Sum

mat

ion

hgh

lag

0.2

T(8

) (9

)

70

0.2

59

2,0

76.1

54

74

6.1

63

2,4

69.6

72

790.6

45

2,9

04.3

82

83

1.8

75

3

,38

1.2

76

868.1

94

3,9

01.2

54

898.1

04

4,4

65

.13

09

20

.74

0

5,0

73

.64

09

36

.30

4

5,7

27.4

50

945.4

69

6,4

27

.16

29

48

.84

4

7,1

73

.32

2

94

6.9

80

7

,96

6.4

24

940.3

78

8,8

04.4

54

92

0.4

88

9

,68

0.6

76

91

4.7

17

10,5

86.5

35

89

6.4

37

11,5

14.2

02

874.9

81

12

,45

6.9

44

85

0.6

51

13,4

08.1

56

823.7

21

14

,36

2.1

96

704.4

40 1

5,3

13

.87

87

63

.03

0

16

,25

8.5

10

729.6

95

17

,19

1.8

46

69

4.6

18

1

8,1

10

.04

6657.9

65

19,0

09.6

34

61

0.8

86

19,8

87.4

65

580.5

17

20

,74

0.6

95

539.9

80

21,5

66.7

50

498.6

33

22,3

63.3

01

457.2

00

23

,12

8.2

41

416.9

34

23

,85

9.6

65

378.4

56

24,5

55.3

47

34

2.6

58

25,2

15.2

27

0.2

Thg

h(1

0)

589.0

27

63

3.4

78

677.6

29

720.5

26

76

1.3

04

799.1

81

833.4

52

863.4

75

888.6

72

908.5

19

922.5

42

930.5

50

932.8

96

93

0.0

93

922.6

40

910.9

81

895.5

14

876.6

04

854.5

70

829.7

34

802.3

38

77

2.6

35

74

0.8

43

70

7.1

63

671.7

74

63

4.8

38

596.6

26

557.6

28

518.4

10

479.4

36

441.3

19

Sum

mat

ion

lag

0.5

T(I

D 0 1.2

29

7.2

57

22

.54

55

1.1

27

96

.65

5162.4

31

25

1.4

43

36

6.3

95

50

9.7

35

68

3.6

75

890.2

17

1,1

31.1

73

1,4

08.1

83

1,7

22.7

29

2,0

76.1

54

2,4

69.6

72

2,9

04.3

82

3,3

81.2

76

3,9

01.2

54

4,4

65

.13

05

,073.6

40

5,7

27.4

50

6,4

27.1

62

7,1

73.3

22

7,9

66.4

24

8,8

04

.45

49

,680.6

76

10

,58

6.5

35

11,5

14.2

02

12,4

56.9

44

0.5

Thg

h(1

2)

31

8.6

57

35

2.1

29

38

6.9

37

422.5

60

458.5

27

494.4

12

529.8

29

564.4

30

597.8

99

62

9.9

51

66

0.3

27

68

8.7

93

71

5.1

38

73

9.1

71

76

0.7

19

77

9.6

24

795.7

45

80

8.9

54

819.1

36

82

6.1

84

830.0

04

830.5

10

82

7.6

25

821.2

77

81

1.4

04

79

7.9

48

781.0

04

76

0.9

54

73

8.2

89

71

3.4

57

68

6.8

59

H t"1

g H jig CO O *=j H

W H f<J O o f 5 o 0 o Jjfc 3 CC

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 unrealis tic, 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. Neg ligible 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 in stantaneous 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 com putations. 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 relation ship 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 transi tion hydrograph should be used, rather than the instantaneous translation hydrograph.

446-3715 O 72 3

Tab

le

2.

Tra

nsf

orm

ati

on

of

tran

slati

on

hydro

gra

ph

from

in

stan

tan

eo

us

to fi

nit

e v

alu

es

of

D/T

H

-4 to1 1 T

0.0

0.0

2.0

4.0

6.0

8

.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

51.6

27

10

3.2

53

15

4.8

80

20

6.5

07

258.1

33

30

9.7

60

36

1.3

87

413.0

13

46

4.6

40

51

6.2

67

567.8

93

61

9.5

20

67

1.1

47

72

2.7

73

774.4

00

826.0

27

877.6

53

929.2

80

98

0.9

07

1,0

32

.53

31

,08

4.1

60

1,1

35.7

87

1,1

87

.41

31,2

39.0

40

1,2

90.6

67

1,2

39.0

40

1,1

87.4

13

1,1

35.7

87

1,0

84.1

60

1,0

32

.53

39

80

.90

7929.2

80

877.6

53

826.0

27

hgh 0.0

00

25.8

14

77

.44

0129.0

66

18

0.6

94

23

2.3

20

283.

946

335.

574

387.

200

438.8

26

490.4

54

542.0

80

593.7

06

645.

334

696.

960

748.

586

800.

214

85

1.8

40

903.

466

955.

094

1,0

06

.72

01,0

58.3

46

1,1

09

.97

41,1

61.6

00

1,2

13.2

26

1,2

64.8

54

1,2

64.8

54

1,2

13.2

26

1,1

61.6

00

1,1

09.9

74

1,0

58.3

46

1,0

06.7

20

955.

094

903.

466

85

1.8

40

tion

0.0

00

25.8

14

103.2

54

232.3

20

41

3.0

14

64

5.3

34

929.2

80

1,2

64

.85

41

,652

.05

42

,090

.88

0

2,5

81.3

34

3,1

23.4

14

3,7

17

.12

04

,362

.45

45

,059

.41

4

5,8

08.0

00

6,6

08.2

14

7,4

60.0

54

8,3

63

.52

09

,318

.61

4

10,3

25.3

34

11,3

83.6

80

12,4

93.6

54

13,6

55.2

54

14

,86

8.4

80

16,1

33.3

34

17,3

98.1

88

18,5

11.4

14

19,7

73.0

14

20,8

82.9

88

21,9

41.3

34

22

,94

8.0

54

23

,90

3.1

48

24

,80

6.6

14

25

,65

8.4

54

D/T

=

0.1

0.0

00

5.1

63

20.6

51

46

.46

48

2.6

03

129.0

67

180.

693

232.3

20

283.

947

335.

573

387.

200

438.

827

490.4

53

542.0

80

593.7

07

645.

333

696.

960

748.

587

800.

213

851.8

40

903.

467

955.

093

1,0

06.7

20

1,0

58.3

47

1,1

09.9

73

1,1

61.6

00

1,2

02

.90

21

,22

3.5

52

1,2

23.5

52

1,2

02

.90

2

1,1

61.6

00

1,1

09.9

73

1,0

58.3

47

1,0

06.7

20

055.

093

D/T

=

0.2

0.0

00

2.5

81

10.3

2523

.232

41.3

01

64.5

3392

.928

126.

485

165.

205

209.

088

258.

133

309.

760

361.

387

413.

013

464.6

40

516.

267

567.

893

619.

520

671.

147

722.

773

774.

400

826.0

27

877.

653

929.

280

980.

907

1,0

32.5

33

1,0

78.9

97

1,1

15.1

36

1,1

40.9

49

1,1

56.4

37

1,1

61.6

00

1,1

56

.43

71,1

40.9

49

1,1

15.1

36

1,0

78.9

97

D/T

=

0.5

0.0

00

1.0

33

4.1

30

9.2

93

16.5

21

25.8

13

37.1

71

50.5

94

66.0

82

83.6

35

103.2

53

12

4.9

37

148.6

85

174.4

98

202.3

77

232.3

20

26

4.3

29

298.4

02

33

4.5

41

372.7

45

413.0

13

455.3

47

499.7

46

54

6.2

10

594.7

39

645.3

33

694.

895

740.3

26

781.

628

818.7

99

85

1.8

40

880.7

51

905.5

32

926.1

82

942.7

03

D/T

=

0.7

0.0

00

.738

2.9

50

6.63

811.8

00

18

.43

826.5

51

36

.13

94

7.2

02

59.7

39

73.7

528

9.2

40

106.2

03

124.6

42

144.

555

165.9

43

188.

806

213.1

44

238.

958

266.2

46

295.

010

325.

248

356.

962

390.

150

424.8

13

460.9

52

497.0

91

531.

755

564.

943

596.

657

626.

895

655.

659

682.

947

708.

760

733.

099

D/T

=

1.0

0.0

00

.516

2.0

65

4.6

46

8.2

60

12.9

07

18.5

86

25

.29

733.0

41

41.8

18

51

.62

762

.468

74.3

4287.2

49

101.

188

116.1

60

132.1

64

149.2

01

167.2

70

186.3

72

206.5

07

227.6

74

249.8

73

273.

105

297.3

70

322.

667

347.

964

372.

228

395.

460

417.6

60

438.8

27

458.9

61

478.0

63

496.1

32

513.1

69

D/T

=

1.5

0.0

00

.344

1.3

77

3.0

98

5.5

07

8.6

04

12.3

90

16.8

65

22.0

27

27.8

78

34.4

18

41.6

46

49.5

62

58.1

6b

67.4

59

77.4

40

88.1

10

99.4

67

111.5

14

124.2

48

137.6

71

151.7

82

166.5

82

182.0

70

198.2

46

215.1

11

231.9

76

948.1

52

263.6

40

278.4

40

292.5

51

30

5.9

74

31

8.7

09

330.7

55

342.1

13

D/T

=

2.0

0.0

00

.258

1.0

33

2.3

23

4.1

30

6.4

53

9.29

312.6

49

16.5

21

20.9

09

25.8

133

1.2

34

37.1

71

43.6

2550.5

94

58

.08

066

.082

74

.60

183

.635

93

.18

6

10

3.2

53

11

3.8

37

12

4.9

37

13

6.5

53

148.

685

16

1.3

33

17

3.9

82

186.1

14

197.7

30

20

8.8

30

21

9.4

13

22

9.4

80

23

9.0

31

24

8.0

66

256.

585

g O O H ^ tti «! 0 0 O s TJ §j

Tab

le

2. T

ransf

orm

ati

on of

tran

slati

on

hydro

gra

ph

from

in

stanta

neous

to fi

nit

e v

alu

es

of

D/T

Conti

nued

11 T

0.7

0.7

2.7

4.7

6.7

8

.80

.82

.84

.86

.88

.90

.92

.94

.96

.98

1.0

01.0

21.0

41.0

61.0

8

1.1

01

.20

1.3

01

.40

1.5

0

1.6

01

.70

1.8

01

.90

2.0

0

2.1

02.2

02.3

02.4

02.5

0

^li.

APe

774.

400

722.

773

671.

147

619.

520

567.

893

51

6.2

67

46

4.6

40

413

. 013

361.

387

30

9.7

60

258.

133

206.

507

154.8

80

10

3.2

53

51

.62

7

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

54

2.0

80

490.

454

438.8

26

387.

200

33

5.5

74

28

3.9

46

23

2.3

20

18

0.6

94

129.0

66

77.4

40

25

.81

40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ouii

ima

tio

n

26,4

58.6

68

27,2

07.2

54

27

,90

4.2

14

28,5

49.5

48

29,1

43.2

54

29

,68

5.3

34

30,1

75.7

88

30

,61

4.6

14

31

,00

1.8

14

31,3

37.3

88

31,6

21.3

34

31,8

53.6

54

32,0

34.3

48

32,1

63.4

14

32,2

40.8

54

32

,26

6.6

68

32,2

66.6

68

32,2

66.6

68

32

,26

6.6

68

32

,26

6.6

68

32

,26

6.6

68

32

,26

6.6

68

32,2

66.6

68

32,2

66.6

68

32

,26

6.6

68

32,2

66.6

68

32

,26

6.6

68

32

,26

6.6

68

32,2

66.6

68

32

,26

6.6

68

32,2

66.6

68

32,2

66.6

68

32

,26

6.6

68

32,2

66.6

68

32,2

66.6

68

D/T

=

0.1

903.

467

851.8

40

800.

213

748.

587

696.

960

645.

333

593.7

07

542.0

80

490.4

53

438.8

27

387.

200

335.

573

283.

947

232.

320

180. 6

^3

129.0

67

82

.60

346.4

64

20.6

51

5.1

63

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D/T

=

0.2

1,0

32.5

33

980.

907

929.

280

877.6

53

826.0

27

774.4

00

722.

773

671.

147

619.5

20

567.8

93

516.2

67

464.6

40

413

. 013

361.

387

309.7

60

258.

133

209.

088

165.2

05

126.

485

92.9

28

64.5

330 0 0 0 0 0 0 0 0 0 0 0 0 0

D/T

=

0.5

955.0

93

963.

354

967.

484

967.4

84

963.

354

955.0

93

942.7

03

926.

182

905.5

32

880.7

51

851.8

40

818.7

99

781.

628

740.3

26

694.

895

645.

333

59

4.7

39

54

6.2

10

499.7

46

455.3

47

413.0

13

232.3

20

103.2

53

25.8

13

0 0 0 0 0 0 0 0 0 0 0

D/T

=

0.7

755.

962

776.

613

794.

313

809.0

64

820.

864

829.7

14

835.6

14

838.

565

838.

565

835.6

14

829.7

14

820.

864

809.

064

794.

313

776.

613

755.

962

733.

099

708.

760

682.

947

655.6

59

626.

895

460.9

52

295.0

10

165.9

43

73.7

52

18.4

38

0 0 0 0 0 0 0 0 0

D/T

=

1.0

529.1

73

544.1

45

558.0

84

57

0.9

91

582.

865

59

3.7

07

603.5

16

612.

2Q

2620.0

36

626.7

48

632.4

27

637.

073

640.

687

643.2

68

644.

817

645.

333

644.

817

643.

268

640.6

87

637.

073

632.4

27

59

3.7

07

529.1

73

43

8.8

27

322.6

67

206.5

07

116.1

60

51.6

27

12.9

07

0 0 0 0 0 0

D/T

=

1.5

352.

78

236

2.7

63

372.0

56

380.6

61

388.

57

7

395.8

04

402.3

44

408.

195

413.3

58

41

7.8

32

421.

61

842

4.7

15

427.

12

5428.8

46

429.8

78

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

430.2

22

421.

61

839

5.8

04

352.

78

2292.5

51

215.1

11

137.6

71

77.4

40

34 .

418

8.6

04

0

D/T

=

2.0

26

4.5

87

27

2.0

73

27

9.0

42

285.

495

29

1.4

33

29

6.8

53

301.

758

30

6.1

46

310

. 018

31

3.3

74

31

6.2

13

31

8.5

37

320.

343

32

1.6

34

32

2.4

09

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

32

2.6

67

31

6.2

13

296.

853

264.

587

219.

413

16

1.3

33

H F g H !^ CO O H S g 0 0 e 9 G O 8 i Wi H-i Cc

1400

1200

1000

-

80

0

~

600

40

0 -

200

G

W

O o w fe H QQ

0.2

0.4

0.6

0.8

1.

0H

/T

FIG

UR

E 2

. T

ran

slat

ion

hyd

rogr

aphs

, fi

nite

val

ues

of D

/T.

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 tech niques 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 com paratively 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 "Applica tion 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 deter mine the appropriate table, then compute D/T to determine the app^o- priate 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 dem onstrate 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 byits 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


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 ex pressed 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 subse quently 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 com pare 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 4002 O OLU

O5 300D 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.


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 multi plying 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 com pare 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 sub sequently described, the storage is nonlinear (z=0.5), the value of k is

APPLICATION TO SPECIFIC AREAS 19240

2000 2100

TIME OF DAY. IN HOURS

2200

FIGURE 4. Hydrographs for tributary to Kankakee River near Bourbonnais, 111.

446-375 O 7&


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 sub sequent1 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/ VAP e/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/APefT=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 con verted 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 in crease 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 topo graphic maps. However, information for the other physiographic factors which influence the hydrograph is available in a total, in tegrated 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 Hydro- graph"), 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 down ward 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 anal ysis 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-


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 flood- routing 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 run off, 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.


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


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."


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 under standing 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, S t , F, 124,2, I'd)

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

446-317® O 72 5


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

wherekc=CkL*S10/&5*Stf,

Tc computed lag time,k c= 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:

Ct0.837 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. 39217. 6 . 339

1 (Significant at 6-percent level.

e -1.20-.873-.860

f

0. 258

Coefficient of correlation0.885.929. 939

Coefficient of correlation

0. 921.959. 970

Standard error (percent)

56. 244.441.9

Standard error (percent)48.935.430. 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

OI

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 propor tion to the amounts of the rainfall excesses. This principle requires that the storage effect be a linear one. A rigorous mathematical de velopment of this statement is not presently available, but a demon stration 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


,,_.,,« ,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 specifi cations for true unit hydrographs.

UNIT HYDROGRAPH 312000

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 re cession 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 illus trated in figure 14, which shows the semilogarithmic plot for the re cession limbs of the curves of figures 11, 12, and 13.


2000 -

1500

1000

500

H/T

FIGURE 12. Nonproportional graphs, resulting from routing through non linear 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

4.0

FIG

UR

E 13

. Non

prop

orti

onal

gr

aphs

, re

sult

ing

from

ro

utin

g th

roug

h no

n

line

ar s

tora

ge,

S=

0.01

O2.


300 -

2.6 3.0H/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


1000

800

600

400

200

100

EXPLANATIONo

Mitchell (1962, synthetic)

Mitchell (1948, actual)

DU.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^ Blooming- ton, 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 condi tions 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 hydro-

graph is available, take T as the time from ending of rainfall excessto the point of inflection on the recession limb of the hydrograph.If such Jiydrograph is not available, use the formula

°-602T=5.33 L

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 .


(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/AP e). 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 dis tributed 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 Water-

Supply 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

Tabl

e 3. Linear M

odel Hy

drog

raph

s (S = kO

); k/T =0.20

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01

.40

1.5

01.6

01

.70

1.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

54

.86

7189.7

65

373.1

83

586.0

18

816.6

89

948.4

37

926.6

80

811.8

56

640.6

09

435.1

52*

263.8

23

15

9.9

50

96

.97

45

8.7

93

35 .

645

21

.61

11

3.1

03

7.9

44

4.8

17

2.9

20

1.7

70

1.0

73

.650

.394

954.0

93

0.6

4

D/T

=0.

1

0.0

00

19

.33

1117.4

04

278.4

96

47

7.7

95

700.2

59

898.1

04

946.9

80

874.9

81

72

9.6

95

53

9.9

80

34

2.6

58

*207.7

46

125.9

52

76.3

62

46

.29

62

8.0

69

17

.01

810.3

18

6.2

56

3.7

93

2.2

99

1.3

94

.845

.511

948.8

44

0.6

8

D/T

=0.

2

0.0

00

9.6

66

68

.36

81

97

.95

0378.1

46

589.0

27

79

9.1

81

92

2.5

42

910.9

81

80

2.3

38

634.8

38

441.3

19

275.2

02*

166.8

4ci

10

1.1

57

61.3

29

37.1

82

22

.54

31

3.6

68

8,2

87

5.0

24

3.0

46

1.8

46

1.1

19

.678

932.8

96

0.7

4

D/T

=0

. 3

0.0

00

6.4

44

45.5

78

13

8.4

10

291.2

32

485.5

17

692.0

53

848.4

48

90

6.6

88

850.5

52

71

4.8

85

53

7.4

44

363.4

61

22

5.4

52

*1

36.6

87

82

.87

05

0.2

42

30.4

61

18.4

68

11.1

97

6.7

89

4.1

16

2.4

95

1.5

13

.917

90

6.6

88

0.8

0

D/T

=0.

4

0.0

00

4.8

33

34.1

84

103.8

08

223.2

56

39

3.4

88

588.6

63

75

5.7

85

855.0

81

862.4

40

772.9

09

621.8

29

455.0

20

304.0

84

188.1

79*

114.0

89

69.1

70

41

.93

625.4

25

15.4

15

9.3

46

5.6

66

3.4

35

2.0

83

1.2

62

87

1.6

25

0.8

6

D/T

=0.

5

0.0

00

3.8

66

27.3

47

83.0

46

17

8.6

05

318.6

57

494.4

12

660.3

27

779.6

24

830.0

04

79

7.9

48

686.8

59

539.0

12

389.2

06

258.5

40

15

9.8

03

*96.8

85

58.7

39

35 .

612

21.5

91

13.0

90

7.9

37

4.8

12

2.9

17

1.7

68

830.5

10

0.9

2

D/T

=0

.6

0.0

00

3.2

22

22

.78

969.2

05

148.8

38

265.5

47

415.2

31

569.8

40

696.1

02

771.3

02

781.6

66

722.0

66

607.0

07

470.1

69

337.0

65

223.1

66

137.8

47*

83.5

74

50.6

69

30.7

20

18.6

25

11.2

92

6.8

46

4.1

51

2.5

16

785.9

27

0.9

6

D/T

=0.

7

0.0

00

2.7

62

19.5

34

59.3

19

127.5

75

227.6

12

355.9

12

491.1

95

613.4

31

700.9

01

738.2

56

718.9

50

648.5

91

538.2

84

41

3.9

10

295.5

27

195.2

94

120.5

86*

73.1

08

44.3

24

26.8

73

16.2

93

9.8

78

5.9

89

3.6

31

738.8

53

1.0

2

D/T

=0.

8

0.0

00

2.4

16

17.0

92

51

.90

4111.6

28

199.1

61

311.4

24

429.7

96

539.1

69

627.9

64

680.7

86

688.8

07

655.0

50

583.2

62

480.5

44

367.9

59

26

2.0

95

173.0

10

106.8

02*

64.7

52

39.2

58

23.8

01

14.4

30

8.7

49

5.3

04

690.8

90

1.0

6

D/T

=0

.9

0.0

00

2.1

48

15.1

93

46.1

37

99.2

25

177.0

32

276.8

21

382.0

41

479.2

61

56

0.3

38

61

8.1

88

643.2

16

63

5.3

55

596.2

62

526.9

40

432.2

94

330.1

93

234.8

64

154.9

33

95.6

30*

57.9

79

35.1

51

21.3

11

12.9

21

7.8

34

644.2

10

1.1

2

D/T

=1

.0

0.0

00

1.9

33

13.6

74

41.5

23

89

.30

3

159.3

28

249.1

39

343.8

37

431.3

35

504.3

04

558.3

03

590.6

35

599.6

69

584.4

15

544.2

72

478.8

75

391.8

72

298.8

76

212.4

09

140.0

65

86.4

47*

52.4

11

31

.77

619.2

65

11.6

80

599.7

81

1.1

8

D/T

=1.

5

0.0

00

1.2

89

9.1

16

27

.68

259.5

35

106

.21

916

6.0

93

22

9.2

25

287.5

57

336.2

03

372.2

02

39

5.0

45

408.8

95

417.2

92

422

.38

3

425

.46

9426.0

52

419

.35

9401

.48

13

70

.04

5

323.6

14

263.8

93

200.8

54

142

.57

993.9

66

426

.40

11.5

6

D/T

=2.

0

0.0

00

.967

6.8

37

20.7

62

44

.65

1

79.6

64

124.5

69

171.9

18

21

5.6

68

25

2.1

52

279.1

51

296.2

84

306.6

71

312.9

69

316.7

87

31

9.1

02

32

0.5

05

321.3

56

32

1.8

72

32

2.1

85

32

2.3

75

32

1.5

23

31

5.7

22

301.8

40

277.9

76

322.3

90

2/0

2

Summarized from computations at

in

terv

als

H/T

= 0.

02.

*Rec

essi

on co

effi

cien

t 0.

6062

7759

ap

plic

able

be

yond

this

po

int.

Table

4. Linear M

odel

Hy

drog

raph

s (S =

kO); k/

T =0.25

to

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

45

.28

81

60

.77

7323.3

13

51

7.3

79

732.5

76

87

1.3

59

87

9.2

30

79

9.3

66

660.7

06

48

2.6

41

*323.4

55

216.7

72

14

5.2

76

97.3

61

65

.25

043.7

29

29

.30

61

9.6

40

13

.16

2

8.8

21

5.9

11

3.9

61

2.6

54

1.7

79

879.2

30

0.7

0

D/T

=0.

1

0.0

00

15.8

48

98

.47

8238.9

92

41

8.3

01

623.6

07

814.6

41

883.7

87

844.9

90

733.8

51

574.2

30

39

7.9

66

*266.7

07

17

8.7

41

11

9.7

89

80.2

80

53

.80

236.0

57

24.1

65

16

.19

4

10

.85

37

.27

34

.87

43

.26

62.1

89

883.7

87

0.7

0

D/T

=0.

2

0.0

00

7.9

24

57

.16

3168.7

35

32

8.6

47

520.9

54

719.1

24

849.2

14

864.3

88

789.4

20

654.0

40

486.0

98

33

2.3

36

*222.7

24

14

9.2

65

100.0

34

67.0

41

44

.93

03

0.1

11

20

.17

9

13.5

23

9.0

63

6.0

74

4.0

70

2.7

27

87

1.2

28

0.7

6

D/T

=0.

3

0.0

00

5.2

83

38

.109

11

7.7

73

251.9

24

42

6.9

67

618.8

49

774.0

12

84

7.8

06

820.8

76

717.6

90

568.6

82

412.9

68

281.1

38*

18

8.4

12

12

6.2

70

84

.62

45

6.7

13

38.0

08

25.4

72

17

.07

011.4

40

7.6

67

5.1

38

3.4

43

85

0.1

02

0.8

2

D/T

=0.

4

0.0

00

3.9

62

28.5

82

88

.33

0192.9

05

344.8

44

52

3.8

85

685.0

84

791.7

56

819.3

17

759.2

14

637.7

59

493.1

88

354.4

11

240.8

01*

161.3

79

108.1

53

72.4

82

48

.57

632.5

54

21.8

17

14.6

21

9.7

98

6.5

66

4.4

00

821.0

17

0.8

8

D/T

=0.

5

0.0

00

3.1

70

22.8

65

70.6

64

154.3

24

27

9.0

45

438.8

04

595.8

66

71

7.0

65

780.

175

770.3

00

68

6.9

65

563.5

49

430.2

99

307.4

86

20

8.6

96

*139.8

64

93.7

34

62.8

18

42.1

00

28.2

14

18.9

08

12.6

72

8.4

92

5.6

91

78

5.6

32

0.9

4

D/T

=0 .

6

0.0

00

2.6

41

19.0

54

58

.88

6128.6

03

23

2.5

38

368.3

11

512.9

68

63

7.3

86

71

9.8

63

745.8

51

708.2

44

61

6. Q

22499.4

14

378.5

47

269.6

19

182.8

81*

122.5

63

82.1

39

55.0

48

36.8

92

24.7

24

16.5

69

11

.10

47

.44

1

745.8

51

1.0

0

D/T

=0

.7

0.0

00

2.2

64

16.3

32

50.4

74

110.2

31

199.3

18

315.6

95

441.9

51

56

0.3

99

651.1

67

699.0

58

696.1

53

645.1

67

554.3

24

445.1

82

335.9

38

238.7

88

161.9

06*

108.5

06

72.7

18

48.7

34

32

.66

121.8

88

14.6

69

9.8

30

703.9

69

1.0

4

D/T

=0.

8

0.0

00

1.9

81

14.2

91

44.1

65

96.4

52

174.4

03

276.2

33

386.7

07

492.3

30

582.0

81

641.5

50

661.4

21

642.4

72

586.8

64

500.0

08

399.5

69

300.6

71

213.4

46

14

4.6

88

*96.9

67

64.9

85

43.5

52

29.1

87

19.5

60

13.1

09

661.4

21

1.1

0

D/T

=0.

9

0.0

00

1.7

61

12.7

03

39.2

58

85.7

35

155.0

25

245.5

41

343.7

39

437.6

27

519.1

66

581.2

08

61

4.4

85

617.5

64

5 90

. 94

7534.9

67

453.3

71

361.1

51

271.2

69

19

2.4

15

130.4

11*

87.3

99

58.5

73

39.2

54

26.3

07

17.6

30

61

9.9

20

1.1

6

D/T

=1

.0

0.0

00

1.5

85

11.4

33

35

.33

277.1

62

139.5

23

220.9

87

30

9.3

65

393.8

64

46

7.2

49

524.6

72

562.8

84

579.7

07

573.6

82

543.8

31

489.4

98

413.4

14

328.6

41

246.5

59

174.7

93

118.4

55*

79.3

86

53

.20

335.6

55

23.8

95

580.3

67

1.2

2

D/T

=1.

5

0.0

00

1.0

57

7.6

22

23.5

55

51

.44

1

93.0

15

147

.32

4206.2

44

262.5

76

311.5

00

349.7

82

376.3

13

394.0

93

40

6.0

09

413.9

95

419

.34

7421

.87

7417

.71

6403

.39

4376.5

87

335.7

37

281.9

12

223.3

18

167.2

03

118

.42

6

42

1.8

77

1.6

0

D/T

=2.

0

0.0

00

.79

25

.71

61

7.6

66

38.5

81

69

.76

1110.4

93

154.6

83

19

6.9

32

23

3.6

25

262.3

36

282.2

34

295.5

70

304.5

07

310.4

96

314.5

10

31

7.2

00

31

9.0

03

320.2

12

321.0

21

321.5

64

32

1.1

35

31

6.4

55

30

4.6

68

283.8

63

32

1.6

68

2.0

4

Summarized from co

mput

atio

ns at

in

terval

s H/T

= 0.

02.

*Rec

essi

on co

effi

cien

t 0.

6701

7692

ap

plic

able

be

yond

this point.

Tabl

e 5. Linear M

odel

Hydrographs

(S = kO

); k/T

= 0.30

li T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

38.5

47

139.3

59

284.7

80

462.1

62

662.4

42

802.0

33

828.8

47

774.8

61

66

2.9

88

50

9.6

42

*365.1

30

261.5

95

187.4

18

134.2

75

96.2

00

68

.92

34

9.3

80

35

.37

82

5.3

47

18

.16

01

3.0

11

9.3

22

6.6

79

4.7

85

830.8

22

0.6

8

D/T

=0.

1

0.0

00

13

.42

784.7

64

20

9.0

68

371.3

21

560.7

62

74

2.8

27

823.0

27

807.2

90

72

2.8

18

589.1

05

43

3.5

38

*310.6

06 '

222.5

31

15

9.4

32

114.2

24

81.8

35

58

.63

142.0

06

30.0

96

21.5

62

15.4

48

11.0

69

7.9

31

5.6

82

826.5

51

0.7

2

D/T

=0

. 2

0.0

00

6.7

13

49.0

95

14

6.9

20

29

0.1

95

46

6.0

41

651.7

94

78

2.9

27

815.1

58

765.0

54

655.9

62

511.3

22

37

2.0

72

*266.5

68

19

0.9

82

136.8

28

98

.03

070.2

33

50

.31

83

6.0

51

25

.82

91

8.5

05

13.2

59

9.5

00

6.8

06

816.1

89

0.7

8

D/T

=0.

3

0.0

00

4.4

76

32.7

30

102.4

19

221.7

18

380.3

84

558.3

03

708.8

72

791.0

48

784.3

78

706.4

05

581.8

21

444.4

16

32

2.2

25

*230.8

56

165.3

96

118.4

97

84.8

97

60.8

24

43

.57

7

31

.22

12

2.3

69

16.0

26

11

.48

38

.22

7

798.5

31

0.8

4

D/T

=0.

4

0.0

00

3.3

57

24.5

48

76.8

15

169.6

45

306.4

79

470.9

94

624.4

84

733.4

76

773.9

90

735.5

60

63

8.1

88

514.0

17

38

8.9

45

281.5

27*

20

1.6

98

144.5

06

103.5

30

74.1

74

53.1

42

38.0

74

27.2

78

19.5

44

14.0

02

10.0

32

773.9

90

OT"9

0

D/T

^0.5

0.0

00

2.6

85

19.6

28

61.4

52

135.7

16

247.8

68

39

3.7

48

541.4

01

661.

045

731.

345

73

7.0

13

675.1

56

572.6

71

455.7

20

343.0

42

24

8.0

66

*177.7

26

127.3

31

91.2

26

65.3

58

46.8

26

33.5

49

24.0

36

17.2

21

12.3

38

74

3.2

83

0.9

6

D/T

=0.6

0.0

00

2.2

38

16.3

65

51.2

10

113.0

97

206.5

57

330.3

61

465.2

95

585.7

16

671.3

41

707.6

38

686.4

34

614.3

97

514.3

15

406.3

38

304.9

06

220.3

61*

157.8

76

113.1

10

81.0

37

58.0

59

41.5

96

29.8

02

21

.35

21

5.2

98

708.0

32

1.0

2

D/T

=0.

7

0.0

00

1.9

18

14.0

27

43.8

94

96.9

40

177.0

49

283.1

67

400.7

42

514.1

51

605.3

02

659.5

93

668.4

81

632.7

44

558.4

16

463.6

17

36

4.6

08

273.0

39

197.2

57*

141.3

24

101.2

51

72.5

41

51.9

72

37.2

35

26.6

77

19

.11

3

670.4

30

1.0

6

D/T

=0.

8

0.0

00

1.6

78

12.2

74

38.4

07

84.8

23

154.9

18

247.7

71

350.6

49

451.5

61

54

0.2

35

60

3.2

77

631.3

36

62

3.7

47

581.4

68

508.5

43

419.9

43

329.2

61

24

6.2

38

177.8

50*

127.4

20

91.2

90

65.4

04

46.8

59

33.5

72

24.0

53

632.

635

1.1

2

D/T

=0

.9

0.0

00

1.4

92

10

.91

034.1

40

75.3

98

13

7.7

05

220.2

41

311.6

88

401.3

87

481.7

00

545.6

65

584.4

17

595.6

99

579.1

67

534.5

75

464.7

30

382.3

76

299.1

91

223.5

45

161.4

33*

115.6

58

82.8

63

59.3

67

42.5

34

30.4

73

595.6

99

1.2

0

D/T

=1

.0

0.0

00

1.3

43

9.8

19

30.7

26

67.8

58

123.9

34

198.2

17

280.5

20

361.2

48

433.5

30

492.4

41

534.4

52

557.0

36

558.3

82

537.1

94

492.5

40

426.4

41

350.0

01

273.4

73

204.2

00

147.4

46*

105.6

37

75,6

83

54.2

23

38.8

48

560.4

85

1.2

6

D/T

=1.

5

0.0

00

.895

6.5

46

20.4

84

45

.23

9

82.6

23

132.1

45

187.0

13

240.8

32

289.0

20

328.2

94

357.1

96

377.9

03

392.7

39

403.3

68

410.9

83

415.5

43

41

3.8

01

40

2.6

64

37

9.9

15

343.9

68

295.4

77

241.3

46

188.0

55

14

0.2

46

415.8

13

1.6

2

D/T

=2.

0

0.0

00

.671

4.9

10

15.3

63

33.9

29

61

.96

79

9.1

08

140.2

60

180.6

24

21

6.7

65

246.2

20

26

7.8

97

28

3.4

28

294.5

54

302.5

26

308.2

37

312.3

29

315.2

60

317.3

61

31

8.8

65

31

9.9

43

32

0.0

45

316.3

60

30

6.3

03

288.0

21

32

0.2

83

2.0

6

£_,

M « > S H 2 o c b_ c W GO

Summ

ariz

ed from computations at in

terv

als

H/T

= 0.02.

*Recession co

effi

cien

t 0.71644279 applicable be

yond

this po

int.

Tabl

e 6. Linear Mo

del

Hydrographs

(S = kO

); k/

T =

0.35

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

33.5

48

122.9

23

25

4.2

50

417.0

98

603.6

31

740.8

67

779.8

22

744.9

26

65

4.5

38

522.4

50*

392.5

78

294.9

91

221.6

62

16

6.5

61

125.1

58

94.0

46

70.6

68

53

.10

13

9.9

02

29.9

83

22

.53

01

6.9

30

12

.72

29

.56

0

779.8

22

0.7

0

D/T

=0.

1

0.0

00

11.6

47

74

.38

3185.6

92

33

3.4

98

508.7

30

681.2

76

76

7.1

28

767.4

71

70

3.5

62

591.3

72

454.5

49*

341.5

56

256.6

53

192.8

53

144.9

14

108.8

92

81.8

23

61

.48

34

6.2

00

34.7

16

26.0

86

19

.60

21

4.7

30

11

.06

8

776.1

99

0.7

4

D/T

=0.

2

0.0

00

5.8

23

43

.01

5130.0

37

259.

595

421.1

14

595.0

03

72

4.2

02

767.2

99

73

5.5

17

64

7.4

67

52

2.9

60

398.0

53*

299.1

04

22

4.7

53

168.8

84

126.9

03

95.3

58

71

.65

353.8

42

40.4

58

30

.40

12

2.8

44

17

.16

61

2.8

99

767.2

99

0.8

0

D/T

=0.

3

0.0

00

3.8

82

28

.67

79

0.5

74

197.8

58

342.6

40

507.8

35

652.3

78

738.6

25

746.0

54

687.4

68

58

3.1

61

462.4

92

35

0.9

19

*263.6

87

19

8.1

40

14

8.8

86

11

1.8

76

84.0

66

63.1

69

47.4

67

35.6

67

26.8

01

20.1

39

15.1

33

752.0

88

0.8

6

D/T

=0.

4

0.0

00

2.9

12

21.5

07

67

.93

0151.3

05

275.5

76

427.2

99

572.6

58

681.1

51

729.8

59

707.3

83

62

9.2

38

522.7

60

411.0

32

311.4

03*

233.9

94

175.8

28

132.1

21

99.2

78

74.6

00

56

.05

642.1

21

31.6

51

23.7

83

17

.87

2

730.9

00

0.9

2

D/T

=0.

5

0.0

00

2.3

29

17.2

06

54

.34

4121.0

44

222.7

90

356.7

16

49

5.2

65

611.6

21

68

5.6

34

70

2.1

62

656.8

16

57

1.7

02

4-69

.538

36

7.3

97

278.1

05*

208.9

74

157.0

27

117.9

93

88.6

63

66.6

23

50.0

62

37.6

17

28.2

67

21.2

40

704.0

47

0.9

8

Vi/

«re

-

D/T

=0.

6

0.0

00

1.9

41

14.3

38

45.2

87

100.8

70

185.6

58

299.2

04

425.1

18

540.6

33

626.9

44

66

9.9

23

66

0.8

93

60

4.2

73

519.1

94

423.4

24

330.3

16

24

9.9

03

*187.7

82

141.1

03

106.0

28

79.6

72

59.8

67

44.9

85

33.8

03

25.4

00

672.6

49

1.0

4

D/T

=0

.7

0.0

00

1.6

64

12.2

90

38.8

17

86

.46

0

15

9.1

36

256.4

61

366.0

51

474.0

26

563.9

08

621.8

62

639.1

55

615.2

73

554.6

13

472.5

74

383.6

37

298.6

84

225.8

92*

169.7

39

12

7.5

46

95.8

40

72.0

16

54.1

15

40.6

63

30.5

55

639.1

55

1.1

0

D/T

=0.

8

0.0

00

1.4

56

10

.75

433.9

65

75.6

52

139.2

44

224.4

03

320.2

94

416.2

28

502.7

18

567.3

41

60

0.9

48

601.9

56

570.4

46

509.3

93

431.6

16

349.2

94

271.5

76

205.3

41*

154.2

97

115

. 942

87.1

21

65.4

65

49.1

92

'36.9

64

605.4

59

1.1

6

D/T

=0.

9

0.0

00

1.2

94

9.5

59

30.1

91

67.2

47

123.7

72

199.4

70

284.7

06

369.9

81

448.1

54

51

2.5

68

554.8

09

572.1

27

563.5

87

528.4

91

468.8

95

39

5.7

58

31

9.5

75

24

8.2

33

18

7.6

58

*

141.0

10

105.9

58

79.6

19

59

.82

7"

44

.95

6

572.1

27

1.2

0

D/T

=1

.0

0.0

00

1.1

65

8.6

03

27

.17

260.5

22

111.3

95

179.5

23

256.2

35

332.9

82

403.3

39

462.4

76

50

6.7

66

533.4

84

540.5

80

526.5

15

490.1

33

432.8

95

364.3

65

293.7

66

228.0

30

172.3

64*

129.5

18

97.3

22

73.1

30

54.9

52

540.8

10

1.2

8

D/T

=1.

5

0.0

00

.77

65

.73

518.1

15

40.3

48

74.2

63

119.6

82

17

0.8

34

22

1.9

88

268.8

92

308.3

17

338.6

20

361.3

91

378.5

01

391.3

58

40

1.0

19

407.5

02

407.9

98

399.7

17

380.5

64

348.9

63

305.2

84

255.4

49

205.2

66

15

9.1

00

40

8.7

14

1.6

6

D/T

=2

. 0

0.0

00

.58

24.3

01

13

.58

63

0.2

61

55

.69

88

9.7

61

128.1

18

16

6.4

91

201.6

69

23

1.2

38

25

3.9

65

27

1.0

43

283.8

76

293.5

19

300.7

64

306.2

09

310.3

00

313.3

74

315.6

84

317.4

20

318.1

42

31

5.4

03

30

6.8

55

290.7

33

31

8.1

87

2.0

8

W

Sum

mar

ized

fr

om

com

puta

tions

at

inte

rvals

H

/T

= 0.0

2.

*R

eces

sion co

eff

icie

nt

0.7

5141884 ap

pli

cab

le

bey

ond th

is p

oin

t.

Tabl

e 7. Linear Mo

del

Hydr

ogra

phs

(S = kO

); k/T =0.40

l± T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

29.6

95

10

9.9

31

229.5

25

379.7

69

55

3.8

82

687.1

93

733.9

01

713.1

64

639.9

07

525.7

47*

409.4

32'

31

8.8

50

'248.3

07

19

3.3

71

15

0.5

89

11

7.2

73

91.3

27

71.1

22

55

.38

8

43

.13

43

3.5

91

26

.15

92

0.3

71

15

.86

4

734.6

17

0.7

2

D/T

=0.

1

0.0

00

10

.28

36

6.2

58

166.9

59

302.4

91

465.1

47

628.3

59

716.

638

72

8.2

76

68

0.2

30

585.7

04

46

5.2

65

*362.3

31

282.1

69

219.7

41

171.1

25

13

3.2

65

103.7

81

80

.82

16

2.9

41

49.0

16

38

.17

229.7

26

23.1

50

18

.02

7

73

1.6

38

0.7

6

D/T

=0.

2

0.0

00

5.1

42

38

.27

1116.6

09

23

4.7

25

383.8

19

546.7

53

672.4

99

722.4

57

70

4.2

53

63

2.9

67

525.4

85

41

3.7

98

*322.2

50

25

0.9

55

195.4

33

152.1

95

118.5

23

92

.30

171.8

81

55.9

78

43.5

94

33

.94

926.4

38

20

.58

8

72

3.7

32

0.8

2

D/T

=0.

3

0.0

00

3.4

28

25.5

14

81

.16

71

78

.57

0

311.5

32

46

5.3

32

603.3

81

691.0

91

708.3

81

664.7

37

57

7.0

66

47

1.1

00

36

9.9

22

*2

88

.080

224.3

45

17

4.7

10

13

6.0

57

10

5.9

56

82

.51

4

64 .

25 9

50

.043

38.9

71

30

.34

92

3.6

34

710.2

91

0.8

8

D/T

=0.

4

0.0

00

2.5

71

19.1

35

60.8

75136.4

98

250.2

14

390.7

39

528.1

59

63

4.6

05

688.3

76

677.7

12

614.8

69

523.3

83

423.8

67

33

2.3

76

*

258.8

41

20

1.5

75

156.9

78

122.2

48

95.2

02

74.1

40

57.7

37

44.9

64

35 .

016

27.2

69

691.5

88

0.9

4

D/T

=0.

5

0.0

00

2.0

57

15.3

08

48.7

00

109.1

98

202.2

28

325.8

43

455.9

19

568.1

82

643.7

30

66

7.8

42

635.2

23

564.3

61

475.1

40

383.0

42

30

0.1

26

*233.7

26

182.0

16

141.7

46

110.3

86

85.9

65

66.9

46

52.1

35

40.6

01

31.6

18

667.8

42

1.0

0

D/T

=0.

6

0.0

00

1.7

14

12.7

57

40

.58

390.9

99

168.5

23

273.2

50

390.9

76

501.3

12

586.8

57

634.0

59

634.0

79

589.7

41

517.3

29

432.5

73

347.7

22

27

2.3

16

*212.0

69

165.1

50

128.6

12

100.1

58

77.9

99

60.7

43

47.3

04

36.8

39

639.8

80

1.0

4

D/T

=0

.7

0.0

00

1.4

69

10.9

34

34

.78

677.9

99

144.4

48

234.2

14

336.5

91

439.1

61

526.8

71

586.6

92

609.9

46

595.2

58

545.8

02

474.8

17

395.2

23

317.0

86

248.2

40-

19

3.3

19

15

0.5

49

11

7.2

41

91.3

03

71.1

03

55.3

72

43.1

22

610.0

35

1.1

2

D/T

=0.

8

0.0

00

1.2

85

9.5

68

30.4

38

68.2

49

126.3

92

204.9

37

294.5

17

385.5

52

46

9.2

95

534.2

26

571.5

14

578.9

94

556.1

22

505.0

44

436.8

55

362.4

79

290.4

23

227.3

12*

17

7.0

22

13

7.8

58

107.3

58

83.6

06

65.1

09

50

.70

4

579.9

10

1.1

8

D/T

=0.

9

0.0

00

1.1

43

8.5

05

27.0

56

60.6

66

112.3

49

182.1

66

261.7

93

342.7

12

418.2

94

482.2

29

526.5

63

548.2

71

546.0

13

518.7

46

467.9

42

403.1

23

333.7

34

267.1

34

20

9.0

49

*

162.7

99

126.7

81

98.7

32

76.8

88

59.8

78

550.3

08

1.2

4

D/T

=1

.0

0.0

00

1.0

28

7.6

54

24

.35

054.5

99

101.1

14

163.9

50

235.6

14

308.4

41

376.4

64

435.0

35

480.5

33

510.1

40

521.6

61

513.3

86

483.9

84

434.4

74

373.1

89

308.4

43

246.7

14

193.0

45*

150.3

36

117.0

76

91.1

74

71.0

02

521.6

61

1.3

0

D/T

=1.

5

0.0

00

.686

5.1

03

16.2

33

36

.39

9

67.4

09

109

.30

0157.0

76

205.6

27

250.9

76

290.0

23

32

1.0

41

345.1

96

364.0

07

378.6

57

39

0.0

65

398.2

64

400.7

65

395.0

23

379.0

53

351.3

11

31

1.9

65

266.1

71

219.1

62

175.0

16

400.8

52

1.6

8

D/T

=2.

0

0.0

00

.51

43

.82

71

2.1

75

27

.30

0

50.5

57

81

.97

5117.8

07

15

4.2

21

188.2

32

217.5

17

240.7

81

25

8.8

97

273.0

06

28

3.9

93

292.5

49

299.2

12

304.4

01

308.4

42

311.5

89

314.0

40

315.4

34

31

3.6

08

306.4

17

292.1

94

315.4

34

2.1

0

Summ

ariz

ed from computations at

in

terv

als

H/T

= 0.

02.

*Rec

essi

on coefficient

0.778760205

appl

icab

le be

yond

th

is po

int.

Table

8. Linear Mo

del

Hydr

ogra

phs

(S = ko

); k/T

= 0.45

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

26

.63

699.4

07

209.1

19

348.4

11

511.3

87

640.0

54

69

1.6

35

681.4

94

621.9

29

52

2.7

91

*41

8 . 6

04335.1

80

268.3

82

214.8

96

17

2.0

69

137.7

77

11

0.3

19

88

.33

47

0.7

29

56

.63

44

5.3

48

36

.31

12

9.0

74

23

.28

0

59

4.2

35

0.7

4

D/T

=0.

1

0.0

00

9.2

05

59.7

28

151.6

26

276.6

54

42

8.2

09

582.5

92

67

1.3

47

690.9

70

655.2

39

575.1

84

46

8.8

46

*375.4

10

30

0.5

95

240.6

89

192.7

22

154.3

14

12

3.5

60

98

.93

67

9.2

18

63.4

31

50

.79

04

0.6

69

32.5

64

26

.07

4

691.8

71

0.7

8

D/T

=0.

2

0.0

00

4.6

03

34

.46

7105.6

77

214.1

40

352.4

31

505.4

00

626.9

70

68

1.1

58

67

3.1

05

61

5.2

12

52

2.0

15

42

2.1

28

*3

38

.00

2270.6

42

21

6.7

05

173.5

18

138.9

37

111.2

48

89.0

77

71.3

25

57

.11

14

5.7

29

36

.61

62

9.3

19

684.6

50

0.8

4

D/T

=0.

3

0.0

00

3.0

68

22.9

78

73.5

20

16

2.6

69

285.4

96

42

9.1

51

560.7

16

648.3

03

672.5

19

640.4

64

566.4

23

473.1

47

38

1.6

17

*305.5

64

24

4.6

.195.9

08

156.8

65

125.6

03

100.5

72

80

.52

964.4

80

51.6

30

41.3

41

33.1

02

672.5

81

0.8

8

D/T

=0.

4

0.0

00

2.3

01

17.2

33

55.1

40

12

4.3

03

299.0

54

359.7

70

48

9.7

00

59

3.2

79

650.0

37

648.1

85

59

7.5

60

51

8.6

70

430.0

09

346.3

85*

277.3

54

222.0

80

177.8

21

142.3

83

11

4.0

07

91.2

87

73.0

94

58.5

27

46.8

64

37

.52

4

656.1

75

0.9

4

D/T

=0.

5

0.0

00

1.8

41

13.7

87

44. 1

1299.4

43

185.0

84

299.7

62

422.0

86

529.9

54

605.6

71

635.0

67

612.3

17

553.1

30

475.0

55

39

2.1

45

315.6

52*

252.7

46

202.3

76

162.0

44

129.7

50

103.8

92

83.1

87

66.6

09

53.3

35

42

.70

6

335.

057

1.0

0

Vi/

nre

-

D/T

=0.

6

0.0

00

1.5

34

11.4

89

36.7

60

82

.86

9

154.2

37

251.3

36

361.6

93

466.9

00

55

0.8

35

600.5

90

60

7.3

63

572.8

33

511.0

41

435.9

94

35

8.9

08

28

8.7

63

*2

31

.21

5185.1

36

148.2

40

118.6

97

95.0

42

76.1

01

60.9

35

48.7

91

609.9

96

1.0

6

D/T

=0

.7

0.0

00

1.3

15

9.8

48

31

.50

97

1.0

31

132.2

03

215.4

31

311.3

37

408.7

32

493.8

05

554.3

14

581.7

70

574.2

27

533.9

42

472.4

19

401.2

41

329.6

80

26

5.1

62

*212.3

18

170.0

05

136.1

24

108.9

96

87.2

74

69

.88

155.9

55

583.0

74

1.1

2

D/T

=0.

8

0.0

00

1.1

51

8.6

17

27.5

70

62.1

52

115.6

78

188.5

02

272.4

20

358.7

91

439.5

46

503.9

78

543.6

30

555.9

75

540.0

23

497.2

85

437.4

57

37

0.3

75

303.9

15

24

4.3

84

*195.6

80

156.6

83

125.4

58

100.4

55

80.4

35

64.4

05

555.9

75

1.2

0

D/T

=0.

9

0.0

00

1.0

23

7.6

59

24.5

07

55.2

46

102.8

25

167.5

57

242.1

51

318.9

26

391.7

30

454.6

17

500.0

74

524.9

39

527.5

99

506.7

64

463.4

45

405.9

97

342.9

51

281.1

40

226.0

32*

180.9

86

144.9

17

116.0

37

92.9

12

74.3

95

529.2

89

1.2

6

D/T

=1.

0

0.0

00

.921

6.8

93

22.0

56

49.7

21

92.5

42

150.8

01

217.9

36

287.0

33

352.5

57

410.0

76

456.0

40

487.6

08

50

2.5

05

498.9

08

475.3

59

432.5

32

377.7

53

318.5

50

260.9

47

209.7

72*

167.9

67

134.4

92

107.6

89

86.2

28

503.3

74

1.3

4

D/T

=1.

5

0.0

00

.614

4.5

96

14

.70

433.1

48

61.6

95

10

0.5

34

14

5.2

91

19

1.3

55

235.0

38

273.3

84

304.6

40

329.6

67

349.7

07

365.7

53

378.6

01

388.2

75

39

2.5

30

389.0

18

375.8

55

351.5

37

316.0

83

274.0

38

230.1

45

18

8.2

00

392.5

30

1.7

0

D/T

=2.

0

0.0

00

.460

3.4

47

11

.02

824.8

61

46

.27

17

5.4

01

108.9

68

14

3.5

17

176.2

79

20

5.0

38

228.4

80

247.2

51

262.2

80

27

4.3

15

283.9

51

29

1.6

67

29

7.8

45

302.7

91

306.7

52

30

9.9

24

31

2.0

03

311.0

50

30

5.0

97

29

2.5

68

312.1

24

2.1

2

to* &

O O H f

.*1 e » o o S3 > TJ w 02

Summ

ariz

ed from computations a

t in

tervals

H/T

= 0.02.

*Rec

essi

on co

effi

cien

t 0.

8007

0806

ap

plic

able

be

yond

th

is po

int.

Tabl

e 9. Linear M

odel

Hydrographs

(S = ko); k/T

= 0.50

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

24

.14

79

0.7

14

19

2.0

09

32

1.7

37

47

4.7

44

59

8.5

17

653.0

54

65

0.9

06

602.3

51

51

5.8

00

*4

22

.29

1345.7

33

283.0

55

23

1.7

39

189.7

27

15

5.3

31

12

7.1

70

104.1

15

85

.24

0

69

.78

65

7.1

35

46.7

77

38

.29

83

1.3

55

658.3

75

0.7

4

D/T

=0.

1

0.0

00

8.3

31

54.3

67

138.8

54

254.8

20

396.5

60

542.7

37

630.

785

656.0

74

62

9.9

80

561.8

19

46

7.5

50

*38

2.78

-8313.3

92

25

6.5

76

210.0

61

17

1.9

79

140.7

81

115.2

74

94

.37

6

77.2

65

63.2

58

51

.79

04

2.4

02

34.7

15

65

6.0

74

0.8

0

D/T

=0.

2

0.0

00

4.1

66

31.3

49

96

.61

01

96

.83

7

325.6

90

469.6

49

586.7

61

643.4

29

64

3.0

27

595.9

00

51

4.6

85

42

5.1

69

*348.0

90

284.9

84

233.3

19

19

1.0

20

15

6.3

80

128.0

27

104.8

25

85

.82

07

0.2

62

57

.52

44

7.0

96

38

.55

9

64

9.4

91

0.8

4

D/T

=0.

3

0.0

00

2.7

77

20

.89

967.1

84

149.3

47

263.4

11

398.0

39

523.3

61

609.8

65

638.9

46

615.9

58

553.1

16

470.7

19

387.9

10*

317.5

85

260.0

10

212.8

72

174.2

74

142.6

78

116.8

10

95.6

38

78

.30

064.1

05

52.4

83

42.9

69

638.9

46

0.9

0

D/T

=0.

4

0.0

00

2.0

83

15.6

75

50.3

88

114.0

93

211.1

50

333.2

43

456.2

26

556.5

39

614.8

94

619.6

64

578.8

56

510.5

34

431.3

87

35

5.0

77

*

290.7

04

238.0

02

194.8

49

159.5

24

130.6

02

106.9

24

87.5

43

71.6

72

58.6

79

48

.04

1

624.0

20

0.9

6

D/T

=0.

5

0.0

00

1.6

66

12

.54

04

0.3

10

91.2

74

170.5

86

27

7.4

68

392.7

51

496.1

95

571.2

27

604.2

79

589.2

42

539.6

42

470.1

06

39

6.4

25

32

6.0

74

*266.9

59

21

3.5

58

178.9

34

146.4

94

119.9

35

98.1

91

80.3

93

65.8

18

53.8

86

60

4.8

97

1.0

2

D/T

=0.

6

0.0

00

1.3

89

10

.45

033.5

92

76.0

62

142.1

55

232.6

12

336.3

54

436.6

38

518.4

93

569.6

59

581.4

91

554.8

33

501.9

34

435.3

51

365.3

64

300.3

91*

245.9

30

201.3

44

164.8

41

134.9

56

11

0.4

89

90.4

57

74.0

61

60.6

34

582.4

14

1.0

8

D/T

=0

.7

0.0

00

1.1

90

8.9

57

28.7

93

65.1

96

121.8

47

19

9.3

81

289.4

93

382.0

28

464.2

58

524.6

82

555.0

72

553,1

05

520.3

41

466.8

83

403.1

67

337.7

38

277.5

90*

227.2

64

186.0

63

15

2.3

30

124.7

13

102.1

03

83

.59

268.4

40

558.2

18

1.1

4

D/T

=0.

8

0.0

00

1.0

41

7.8

37

25.1

94

57

.04

6

106.6

16

174.4

59

25

3.3

07

335.3

16

413.0

22

476.4

54

517.5

41

533.5

37

523.1

41

487.3

71

434.7

80

37

4.2

68

31

3.1

18

25

7.3

00

*2

10

.65

3

172.4

63

141.1

96

115.5

98

94.6

41

77.4

83

533.6

06

1.2

2

D/T

=0.

9

0.0

00

.925

6.9

66

22.3

95

50.7

08

94.7

70

155.0

74

225.1

62

298.0

59

368.0

56

42

9.5

55

475.4

64

50

2.5

68

509.0

76

493.5

22

456.5

58

405.5

80

34

8.3

25

291.1

36

23

9.1

97

*

195.8

32

160.3

29

131.2

62

107.4

65

'87.9

82

509.4

97

1.2

8

D/T

=1

.0

0.0

00

.83

36

.27

020.1

55

45

.63

7

85.2

93

139.5

67

202.6

45

268.2

53

331.2

51

387.4

33

433.3

55

466.1

97

483.6

50

483.8

26

465.1

76

428.1

00

379.1

00

325.0

20

271.4

60

223.0

04*

182.5

75

149.4

75

122.3

76

10

0.1

90

485.9

35

1.3

6

D/T

=1.

5

0.0

00

.555

4.1

80

13

.43

730.4

25

56

.86

293

. 04

5135.0

97

178.8

35

220.8

34

25

8.2

88

289.4

58

31

4.9

78

335.8

70

352.9

76

366.9

80

377.8

89

383.6

50

382.0

78

371.3

82

350.0

96

318.1

31

279.5

31

238.6

19

19

8.9

35

384.0

10

1.7

4

D/T

=2.

0

0.0

00

.41

73

.13

51

0.0

78

22

.81

9

42.6

47

69

.78

3101.3

23

134.1

26

165.6

25

193.7

16

217.0

94

23

6.2

33

251.9

03

264.7

32

27

5.2

35

283.8

34

290.8

73

296.6

36

30

1.3

55

30

5.2

18

307.9

64

307.8

36

30

3.0

13

29

2.0

08

30

8.3

68

2.1

4

Summarized fr

om computations at

intervals

II/T

=

0.02

. ^R

eces

sion

co

effi

cien

t 0.31370390 ap

plic

able

be

yond

this po

int.

Table 10. Linear Mo

del

Hydr

ogra

phs

(S = kO); k/

T =

0.55

GO

ri T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

22

.08

48

3.4

14

177.4

65

298.7

96

442.8

74

561.7

48

617.9

39

621.8

70

582.2

29

506.2

61*

422.0

88

351.9

10

293.4

00

244.6

18

20

3.9

47

170.0

37

141.7

65

118.1

94

98

.54

3

82

.15

86

8.4

99

57

.11

04

7.6

14

39

.69

7

62

5.9

78

0.7

6

D/T

=0.

1

0.0

00

7.6

10

49

.88

7128.0

54

236.1

42

369.1

77

507.7

92

594.4

14

623.7

15

605.2

26

546.8

93

46

2.9

50

*385.9

78

32

1.8

05

268.3

00

223.6

92

18

6.4

99

15

5.4

90

12

9.6

37

108.0

83

90. 1

137

5.1

30

62

.63

95

2.2

24

43

.54

0

62

3.7

15

0.8

0

D/T

=0.

2

0.0

00

3.8

05

28.7

49

88

.97

1182.0

98

302.6

59

438.4

84

551.1

03

60

9.0

64

614.4

70

576.0

60

504.9

22

42

4.4

64

*353.8

92

29

5.0

52

245.9

96

20

5.0

95

170.9

94

142.5

63

118.8

60

99.0

98

82.6

22

68

.88

557.4

31

47

.88

2

618.0

20

0.8

6

D/T

=0.

3

0.0

00

2.5

37

19.1

66

61.8

50

138.0

28

244.4

57

371.0

37

490.4

61

575.3

07

60

7.7

85

59

1.9

45

538.3

56

465.2

74

39

0.2

44

*3

25

.36

1

271.2

65

226.1

63

188.5

60

157.2

09

131.0

70

109.2

78

91.1

09

75.9

61

63.3

31

52.8

01

608.2

04

0.9

2

D/T

=0.

4

0.0

00

1.9

02

14.3

74

46

.38

8105.4

23

195.8

15

310.2

91

42

6.8

81

523.7

74

582.7

87

592.5

62

559.6

96

500.2

62

429.4

07

359.7

58*

299.9

44

250.0

74

208.4

95

17

3.8

29

144.9

27

12

0.8

31

10

0.7

41

83.9

91

70.0

26

58.3

83

594.4

58

0.9

6

D/T

=0.

5

0.0

00

1.5

22

11.4

99

37.1

10

84.3

39

158.1

74

258.2

10

367.1

16

466.2

48

54

0.0

65

57

5.6

08

566.6

40

524.9

53

464.5

71

397.

185

33

2.5

45

*27

7.25

5231.1

57

192.7

23

160.6

80

133.9

64

111.6

91

93.1

21

77.6

38

64.7

29

57

7.1

95

1.0

2

D/T

=0.

6

0.0

00

1.2

68

9.5

83

30.9

25

70.2

82

131.8

12

216.4

44

314.2

44

409.8

82

489.4

11

541.2

03

556.8

32

536.5

29

491.0

95

431.8

59

368.2

70

30

8.2

04

*256.9

60

214.2

37

178.6

17

148.9

19

124.1

59

103.5

15

86.3

04

71.9

55

556.8

32

1.1

0

D/T

=0.

7

0.0

00

1.0

87

8.2

14

26.5

07

60.2

42

112.9

81

185.5

23

270.4

39

358.4

54

437.7

88

497.6

23

530.0

24

532.4

24

505.8

55

459.2

67

402.1

21

342.3

02

28

6.3

88

*238.7

71

199.0

72

165.9

73

138.3

78

115.3

70

96.1

88

80.1

95

535,1

42

1.1

6

D/T

=0.

8

0.0

00

.951

7.1

87

23.1

94

52

.71

2

98.8

59

162.3

33

236.6

34

314.5

99

389.3

01

451.4

27

493.2

89

512.0

18

506.0

97

476.1

60

429.8

20

37

5.1

68

318.9

51

26

6.7

94

*2

22

.43

5

185.4

52

154.6

18

128.9

10

107.4

77

89.6

07

512.8

50

1.2

2

D/T

=0

.9

0.0

00

.846

6.3

89

20.6

17

46.8

55

87.8

74

144.2

96

210.3

42

279.6

43

346.8

91

406.8

11

452.7

07

481.3

65

490.8

83

479.6

75

448.1

08

402.7

84

350.7

59

297.9

16

24

9.1

59

*

207.7

33

173.1

94

144.3

98

120.3

90

100.3

73

490.8

83

1.3

0

D/T

=1

.0

0.0

00

.761

5.7

50

18.5

55

42

.16

9

79.0

87

129.8

66

189.3

08

251.6

79

312

. 2 0

2

366.8

91

412.4

25

446.0

34

465.4

09

468.6

25

454.0

76

421.9

47

37

8.0

55

328.6

47

278.9

33

23

3.2

55

*194.4

73

162.1

39

135.1

81

112.7

05

469.3

87

1.3

6

D/T

=1.

5

0.0

00

.50

73

.83

31

2.3

70

28

.11

3

52

.72

58

6.5

77

126.2

05

167.7

85

208.1

34

244.5

94

275.4

57

301.1

89

322.6

43

340.5

29

355.4

42

367.3

68

374.4

08

374.5

14

365.9

77

347.3

72

318.5

28

283.0

77

244.9

77

20

7.5

31

375.4

20

1.7

6

D/T

=2.

0

0.0

00

.380

2.8

75

9.2

78

21.0

85

39.5

43

64.9

33

94

.65

4125.8

40

156.1

01

183.4

45

20

6.5

93

22

5.8

92

241.9

82

255.3

97

266.5

82

275.9

07

283.6

81

290.1

63

295.5

67

30

0.0

73

303.4

49

304.0

86

30

0.2

95

293.5

21

30

4.2

75

2.1

6

Sum

mar

ized

fr

om

com

puta

tions

at

inte

rvals

H

/T

= 0.0

2.

*R

eces

sion coeff

icie

nt

0.8

3373620

ap

pli

cab

le

beyo

nd th

is p

oin

t.

Tab

le 11. L

inear

Mod

el

Hydro

gra

phs

(S

= kO

);

k/T

=

0.6

0

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

20

.34

47

7.1

97

164.9

52

278.

865

414.9

21

529.0

31

585.9

91

594.5

74

562.2

07

49

5.1

78

*419.1

53

354.8

00

300.3

27

254.2

16

215.1

86

182.1

48

154.1

82

130.5

11

110.4

73

93

.51

37

9.1

57

67.0

055

6.7

17

48

.00

8

596.4

43

0.7

6

D/T

=0

.1

0.0

00

7.0

02

46

.08

81

18

.80

42

19

.98

6

345.2

66

47

6.9

38

56

1.7

11

59

3.8

37

58

1.4

00

53

1.2

40

456.1

53*

386.1

19

326.8

38

276.6

57

23

4.1

80

19

8.2

27

16

7.7

93

14

2.0

31

120.2

25

10

1.7

67

86

.14

37

2.9

19

61 .

724

52.2

46

59

4.6

79

0.8

2

D/T

=0.

2

0.0

00

3.5

01

26.5

45

82

.44

6169.3

95

282.6

26

411.1

02

51

9.3

24

577.7

74

587.6

18

55

6.3

20

49

3.6

96

42

1.1

36

*356.4

78

301.7

48

255.4

19

216.2

04

18

3.0

10

15

4.9

12

131.1

28

110.9

96

93.9

55

79.5

31

67.3

22

56.9

85

589.1

62

0.8

8

D/T

=0.

3

0.0

00

2.3

34

17.6

97

57.2

98

128.2

92

228.0

19

347.3

96

46

1.3

05

544.1

61

578.9

82

568.8

26

522.9

30

457.8

37

389.7

03*

329.8

71

27

9.2

25

236.

355

200.0

66

169.3

50

143.3

49

121.3

41

102.7

12

86.9

43

73.5

95

62.2

96

580.3

12

0.9

2

D/T

=0.

4

0.0

00

1.7

51

13.2

72

42.9

73

97.9

70

182.5

36

29

0.2

48

40

0.9

75

494.4

38

553.4

71

567.0

47

540.6

57

488.7

28

425.0

87

361.4

42*

305.9

49

258.9

76

219.2

14

185.5

58

157.0

69

132.9

54

112.5

42

95.2

64

80.6

38

68.2

58

567.8

93

0.9

8

D/T

=0.

5

0.0

00

1.4

00

10.6

18

34.3

79

78.3

76

147.4

29

241.4

16

344.5

41

439.5

48

511.8

30

549.0

25

544.8

68

509.7

50

456.3

50

395.4

01

335.9

89*

284.4

04

240.7

39

203.7

78

172.4

91

146.0

09

123.5

92

104.6

17

88

.55

67

4.9

60

551.9

80

1.0

4

D/T

=0.

6

0.0

00

1.1

67

8.8

48

28

.64

965.3

13

122.8

58

202.3

47

294.7

98

386.0

90

463.1

89

515.0

65

533.5

46

518.4

09

479.2

64

426.4

01

368.5

31

31

3.0

29

*264.9

69

224.2

87

189.8

52

160.7

04

136.0

31

115

.146

97.4

68

82.5

04

533.5

46

1.1

0

D/T

=0.

7

0.0

00

1.0

00

7.5

84

24.5

56

55.9

83

105.3

06

173.4

40

25

3.6

85

337.5

18

413.9

91

472.9

11

506.6

49

51

2.4

85

491.0

42

450.3

20

398.9

41

344.2

02

292.2

81*

247.4

06

209.4

21

177.2

68

150.0

52

127.0

15

107.5

15

91.0

08

513.6

20

1.1

8

D/T

=0.

8

0.0

00

.875

6.6

36

21.4

87

48.9

85

92.1

43

151.7

60

221.9

74

296.2

04

368.0

04

428.6

48

47

0.8

16

491,5

83

489.2

79

464.2

44

423.3

03

373.8

52

322.1

51

273.5

00*

231.5

09

195.9

65

165.8

78

140.4

11

118.8

54

10

0.6

06

493.5

14

1.2

4

D/T

=0.

9

0.0

00

.77

85

.89

81

9.0

99

43.5

42

81.9

05

134.8

98

197.3

10

263.2

92

327.8

92

386.1

41

431.7

03

461.4

05

473.2

77

465.6

54

438.6

81

398.2

94

350.9

56

302.1

37

256.4

69*

217.0

93

183.7

62

155.5

49

131.6

68

111.4

53

47

3.3

61

1.3

2

D/T

=1.

0

0.0

00

.700

5.3

09

17.1

89

39.1

88

73.7

15

121.4

08

177.5

79

23

6.9

63

29

5.1

03

348.2

27

393.1

42

42

7.1

45

447.9

49

453.6

16

442.5

07

414.6

36

375.2

44

330.0

64

283.9

46

24

0.9

99

*2

03

.99

8172.6

78

146.1

67

123.7

26

453.7

76

1.3

8

D/T

=1.

5

0.0

00

.467

3.5

39

11

.46

02

6.1

25

49

.14

380.9

39

118.3

86

157.9

75

196.7

35

232.1

51

26

2.5

61

288.3

02

310.0

92

32

8.5

35

344.1

47

35

6.8

95

365.0

09

366.5

57

359.9

04

343.6

73

317.6

21

28

5.0

35

249.5

60

214.2

84

366.8

55

1.7

8

D/T

=2

.0

0.0

00

.350

2.6

54

8.5

95

19

.59

4

36

.85

76

0.7

04

88

.79

01

18

.48

21

47

.55

2

17

4.1

14

19

6.9

21

21

6.2

27

23

2.5

69

246.4

02

258. I

ll268.0

22

276.4

12

283.5

13

289.5

25

294.6

13

29

8.5

70

299.9

12

297.0

58

28

8.6

71

29

9.9

32

2.1

8

Sum

mar

ized

fr

om

com

puta

tions

at

inte

rvals

H

/T

= 0

.02

. *R

eces

sion coeff

icie

nt

0.8

4646864

ap

pli

cab

le

beyo

nd th

is

po

int.

4^

C

O

Tabl

e 12. Linear Mo

del

Hydr

ogra

phs

(S =

kO); k/

T =

0.70

Cn O

_n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

17

.57

567.1

75

144.5

39

24

5.9

69

36

8.2

60

47

3.4

85

530.3

37

545.2

54

523.8

19

47

0.8

73

*408.1

87

353.

845

30

6.7

37

265.9

00

230.5

01

199.8

14

173.2

12

150.1

53

130.1

62

112.8

33

97.8

12

84

.79

07

3.5

02

63

.71

8

545.3

46

0.7

8

D/T

=0.

1

0.0

00

6.0

39

39.9

92

10

3.7

91

193.4

64

305.5

63

425.0

24

50

5.5

10

540.9

15

53

7.2

41

499.6

90

43

8.8

14

*3

80

.39

53

29

.75

3285.8

52

247.7

96

214.8

07

186.2

09

16

1.4

19

13

9.9

29

12

1.2

99

105.1

51

91

.15

279.0

18

68.4

98

543.8

27

0.8

4

D/T

=0.

2

0.0

00

3.0

20

23.0

16

71.8

92

148.6

28

249.5

13

365.2

93

46

5.2

67

523.2

12

539.0

78

518.4

66

469.2

52

409.6

04*

355.0

74

307.8

02

266.8

24

231.3

02

200.5

08

17

3.8

14

15

0.6

74

13

0.6

14

113.2

25

98.1

52

85

.08

573.7

58

539.0

78

0.9

0

D/T

=0.

3

0.0

00

2.0

13

15 .

344

49.9

41

112.4

16

200.9

39

308.0

17

412.0

32

490.4

83

527.8

89

525.9

49

491.9

15

439.6

33

38

2.9

87

*332.0

00

287.8

00

24

9.4

85

216.2

71

187.4

78

16

2.5

19

140.8

82

122.1

26

105.8

67

91.7

74

79.5

56

531.5

24

0.9

4

D/T

=0.

4

0.0

00

1.5

10

11.5

08

37.4

56

85.8

22

160.7

02

256.9

60

357.3

90

444.2

53

502.1

72

520.8

39

504.1

65

46

4.0

35

412.1

63

358.7

03*

310.9

49

269.5

52

233.6

66

202.5

58

175.5

90

152.2

34

131.9

49

114.3

83

99.1

55

85.9

55

520.8

39

1.0

0

D/T

=0

. 5

0.0

00

1.2

08

9.2

06

29.9

64

68.6

57

129.7

70

213.5

67

306.6

70

394.0

95

462.8

50

501.6

76

504.4

34

479.4

11

437.1

79

386.9

01

33

6.5

22

*291.7

21

252.8

83

219.2

17

190.0

32

164.7

33

142.8

01

123.7

90

107.3

10

93.0

24

507.3

08

1.0

6

Vi/

ore

-

D/T

=0

.6

0.0

00

1.0

06

7.6

72

24.9

70

57

.21

4

108.1

41

178.9

79

262.2

24

345. 7

11417.9

53

468.9

90

491.1

99

483.7

61

454.4

68

411.9

57

363.7

17

31

6.2

36

*274.1

35

237.6

39

206.0

02

178.5

76

154.8

02

134.1

93

116.3

28

100.8

41

491.9

17

1.1

2

D/T

=0.

7

0.0

00

.863

6.5

76

21.4

03

49.0

41

92.6

93

153.4

10

225.6

26

302.0

37

373.0

72

429.6

29

464.6

79

475.3

70

461.7

60

430.3

80

388.5

06

342.4

44

297.6

61*

258.0

33

223.6

81

193.9

02

168.0

87

145.7

09

126.3

11

109.4

95

475.3

70

1.2

0

D/T

=0.

8

0.0

00

.755

5.7

54

18.7

28

42.9

11

81.1

06

134.2

34

197.4

23

265.0

37

331.4

37

388.9

00

430.7

77

454.1

44

457.1

68

439.7

71

407.5

57

366.7

93

322.9

14

28

0.6

31

*243.2

70

210.8

83

182.8

08

158.4

70

137.3

73

119.0

84

458.5

06

1.2

6

D/T

=0.9

0.0

00

.671

5.1

15

16.6

47

38.1

43

72.0

94

119.3

19

175.4

87

235.5

89

295.2

82

350.1

32

394.4

46

425.1

79

440.3

23

438.1

32

41

8.4

41

386.1

40

346.7

28

304.9

71

264.9

97*

229.7

18

199.1

35

172.6

24

149.6

42

129.7

20

441.6

16

1.3

4

D/T

=1

.0

0.0

00

.60

44

.60

31

4.9

82

34.3

29

64.8

85

107.3

87

157.9

38

212.0

30

265.7

54

315

. 723

359.0

00

393.0

41

415.6

37

424.8

76

419.0

99

398.0

77

366.1

47

328.1

98

288.4

66

25

0.6

27

*217.2

61

188.3

37

163.2

63

141.5

28

424.9

70

1.4

2

D/T

=1.

5

0.0

00

.403

3.0

69

9.9

88

22.8

86

43

.25

77

1.5

91

105.2

92

141.3

53

177.1

69

210.4

82

239.7

36

265.0

96

287.0

79

306.1

36

322.6

56

336.5

74

346.3

22

35

0.1

63

346.5

94

334.3

10

31

2.9

85

285.3

61

25

4.5

68

223.3

19

350.1

63

1.8

0

D/T

=2

.0

0.0

00

.302

2.3

02

7.4

91

17

.16

4

32

.44

253.6

94

78

.96

9106.0

15

13

2.8

77

15

7.8

61

17

9.8

02

19

8.8

22

215.3

10

229.6

02

241.9

92

252.7

32

262.0

43

270.1

14

27

7.1

10

283.1

75

288.1

31

29

0.6

89

289.4

50

283.2

02

29

0.7

85

2.2

2

Summ

ariz

ed from co

mput

atio

ns at

intervals

H/T

= 0.

02.

*Recession co

effi

cien

t 0.

8668

6944

ap

plic

able

be

yond

this po

int.

Tabl

e 13. Linear Model

Hydrographs

(S = kO); k/T

= O.

J

_n_

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

15

.46

959.4

54

128.6

03

219.9

59

330.9

14

428.2

23

483.7

64

502.4

47

488.6

01

446.0

50*

393.

635

347.3

81

306.5

60

270.5

37

238.7

47

21

0.6

93

185.9

35

164.0

86

144.8

04

127.7

89

112.7

74

99

.52

187.8

27

77

.50

6

502.4

47

0.8

0

D/T

=0

.1

0.0

00

5.3

08

35

.32

09

2.1

39

17

2.6

14

273.9

65

383.1

22

45

9.1

30

49

5.8

73

49

7.9

66

46

9.4

81

41

9.3

18

*370.0

46

326.5

62

28

8.1

89

254.3

24

224.4

40

19

8.0

66

174.7

92

15

4.2

52

13

6.1

26

12

0.1

32

106.0

15

93

.55

78

2.5

63

501.0

15

0.8

6

D/T

=0.

2

0.0

00

2.6

54

20.3

14

63.7

30

13

2.3

76

223.2

89

328.5

44

421.1

26

477.5

02

49

6.9

20

483.7

24

44

4.4

00

39

4.6

82

*348.3

04

30

7.3

75

271.2

56

239.3

82

211.2

53

18

6.4

29

164.5

22

14

5.1

89

128.1

29

113.0

73

99

.78

68

8.0

60

49

6.9

20

0.9

0

D/T

=0.

3

0.0

00

1.7

69

13.5

43

44.2

56

100.0

24

179.5

73

276.5

67

372.0

72

446.0

42

484.3

23

487.7

74

462.2

55

419.6

15

37

1.9

75

*32

8.26

5

289.6

92

255.6

51

225.6

10

199.0

99

175.7

03

155.0

57

136.8

37

12

0.7

58

106.5

68

94.0

45

490.3

00

0.9

6

D/T

=0

.4

0.0

00

1.3

27

10.1

57

33.1

92

76.3

45

143.5

10

230.4

60

32

2.2

08

403.0

23

459.0

23

480.6

12

470.6

60

439.2

03

396.3

52

351.0

29*

309.7

80

273.3

79

241.2

55

212.9

06

187

.888

165.8

09

146.3

26

129.1

31

113.9

57

100.5

66

480.8

71

1.0

2

D/T

=0.

5

0.0

00

1.0

62

8.1

26

26

.55

36

1.0

76

11

5.8

69

19

1.4

32

276.1

94

356.9

41

422.0

11

46

1.1

14

46

8.3

54

45

0.5

37

416.6

75

374.7

19

331.6

88*

292.7

12

258.3

16

227.9

62

201.1

75

177.5

35

156.6

74

138.2

63

122.0

16

107.6

78

46

9.2

19

1.0

8

D/T

=0.

6

0.0

00

.885

6.7

71

22.1

28

50.8

97

96.5

58

160.4

11

236.0

48

312.8

07

38

0.4

45

429.9

23

45

4.1

48

451.9

69

429.8

74

395.2

60

354.6

53

31

3.8

13

*276.9

38

244.3

96

215.6

77

190.3

34

167.9

68

148.2

30

130.8

12

115.4

41

456.1

79

1.1

4

D/T

=0.

7

0.0

00

.758

5.8

04

18

.96

743.6

26

82.7

64

137.4

96

203

.08

5273.1

66

33

9.2

58

393.1

64

428.4

08

442.1

34

434.0

54

409.6

34

375.1

26

336.0

51

29

7.2

78

*262.3

46

23

1.5

18

204.3

13

180.3

05

159.1

18

140.4

20

123.9

20

442.1

52

1.2

2

D/T

=0

.8

0.0

00

.664

5.0

78

16.5

96

38

.17

3

72.4

18

120.3

08

17

7.7

00

239.6

84

301.2

66

355.5

36

396.4

34

421.1

13

427.6

87

415.8

21

390.2

20

356.2

91

318.8

03

281.9

67*

248.8

34

219.5

94

193.7

90

171.0

18

150.9

22

133.1

88

427.9

04

1.2

8

D/T

=0

.9

0.0

00

.590

4.5

14

14.7

52

33

.93

1

64.3

72

106.9

41

157.9

55

213.0

52

268.3

82

319.9

57

362.6

23

393.5

02

410.6

07

412.1

87

397.8

76

371.8

00

338.7

10

30

2.8

02

26

7.7

76

*

23

6.3

11

208.5

43

184.0

37

162.4

12

143.3

27

413.5

22

1.3

6

D/T

=1

.0

0.0

00

.53

14

.06

313.2

77

30.5

38

57.9

35

96.2

47

142.1

60

191.7

47

241.5

44

288.4

92

32

9.8

93

363.

365

386.8

08

39

8.3

65

396.4

01

38

0.5

33

354.4

26

32

2.3

18

287.9

47

254.6

12*

224.6

93

198.2

90

174.9

89

154.4

27

399.2

87

1.4

4

D/T

=1.

5

0.0

00

.354

2.7

08

8.8

51

20.3

59

38

.62

36

4.1

64

94.7

73

12

7.8

31

161.0

29

192.3

28

220.2

82

244.9

52

266.7

23

285.9

36

302.8

90

317.4

99

328.3

49

333.8

59

332.6

35

323.4

46

305.9

13

282.3

72

255.5

51

227.8

58

334.2

50

1.8

4

D/T

=2

.0

0.0

00

.265

2.0

31

6.6

38

15

.26

9

28

.96

748.1

23

71

.08

095.8

74

12

0.7

72

14

4.2

46

16

5.2

12

18

3.7

14

200.0

42

214.4

52

227.1

68

23

8.3

90

248.2

93

257.0

33

264.7

45

271.5

52

277.2

93

280.8

28

280.8

98

276.3

96

28

1.3

60

2.2

6

from co

mput

atio

ns at

intervals

H/T

= 0.02.

*Recession co

effi

cien

t 0.

8824

9115

ap

plic

able

be

yond

this point.

CFT to

Table

14. Linear Model

Hydrographs

(S = kd); k/T =0.90

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

13.8

14

53.3

22

115.8

21

19

8.8

95

300.3

79

390.7

07

444.3

91

46

5.2

83

456.8

30

42

2.1

20

*377.7

29

338.

005

30

2.4

58

27

0.6

51

24

2.1

88

21

6.7

18

193.9

27

173.5

33

155.2

83

138.9

52

124.3

39

111.2

63

99

.56

28

9.0

92

465.8

36

0.8

2

D/T

=0.

1

0.0

00

4.7

36

31

.62

582.8

33

155.8

03

248

. 245

348.6

40

420.3

20

457.3

17

463.2

75

441.4

61

39

9.5

30

*357.5

14

319.9

16

286.2

72

256.1

66

229.2

27

205.1

20

183.5

49

16

4.2

46

146.9

73

131.5

15

11

7.6

84

105.3

08

94.2

34

464.4

05

0.8

8

D/T

=0.

2

0.0

00

2.3

68

18

.18

05

7.2

29

11

9.3

18

202.0

24

298.4

42

384.4

80

438.8

18

460.2

96

452.3

68

42

0.4

96

37

8.5

22

*3

38

.71

5303.0

94

27

1.2

19

242.6

96

217.1

73

19

4.3

34

17

3.8

97

15

5.6

09

13

9.2

44

12

4.6

00

11

1.4

96

99

.77

1

46

0.9

59

0.9

2

D/T

=0.

3

0.0

00

1.5

79

12.1

20

39.7

31

90.0

87

162.2

93

250.8

96

33

9.0

68

408.7

59

44

6.9

71

454.0

18

434.7

55

399.5

02

358.9

87*

32

1.2

34

287.4

51

257.2

22

230.1

71

20

5.9

65

184.3

05

164.9

22

147.5

78

132.0

57

118.1

69

105

. 742

454.9

39

0.9

8

D/T

=0.

4

0.0

00

1.1

84

9.0

90

29.7

98

68.7

49

129.6

26

208.8

80

293.2

52

368.6

30

422.3

88

445.5

93

440.3

96

41

5.4

45

37

9.6

05

34

0.8

08

*

304.9

67

27

2.8

95

244.1

96

218.5

15

195.5

35

174.9

72

156.5

71

140.1

05

125.3

70

112.1

86

446.5

94

1.0

2

D/T

=0.

5

0.0

00

.947

7.2

72

23.8

39

54.9

99

104.6

48

173.4

29

251.1

68

326.0

65

387.5

59

426.2

03

43

6.3

81

423.8

19

396.3

39

360.9

39

323.8

80*

289.8

19

259.3

40

232.0

67

207.6

62

185.8

23

16

6.2

81

148.7

93

133.1

45

119.1

43

436.4

30

1.0

8

D/T

=0.

6

0.0

00

.789

6.0

60

19.8

66

45.8

33

87

.20

714

5 . 3

14214.5

78

285.2

56

348.9

33

396.5

43

421.7

57

423.2

36

406.5

02

37

7.9

95

343.4

76

30

8.1

04

*275.7

02

246.7

08

220.7

63

197.5

47

176.7

72

158.1

81

14

1.5

46

126.6

60

425.2

15

1.1

6

D/T

=0.

7

0.0

00

.67

75.1

94

17.0

28

39.2

85

74.7

49

124.5

54

184.6

00

24

9.2

55

310.9

19

362.1

52

396.9

70

412.5

80

408.4

76

389.3

26

36

0.5

91

32

7.1

55

293.3

92*

26

2.5

38

23

4.9

28

210.2

22

188.1

14

168.3

31

150.6

28

134.7

87

413.2

46

1.2

2

D/T

=0.

8

0.0

00

.59

24

.54

51

4.8

99

34.3

75

65.4

05

10

8.9

85

161.5

25

218.6

90

276.0

07

327.2

37

366.8

24

39

2.0

38

400.9

97

393.2

01

372.6

81

344.1

70

311.9

01

27

9.6

62

*250.2

51

223.9

33

200.3

83

179.3

10

160.4

53

143.5

79

400.9

97

1.3

0

D/T

=0.9

0.0

00

.526

4.0

40

13.2

44

30.5

55

58

.13

89

6.8

76

143.5

78

194.3

91

245.8

66

294.3

91

335.2

69

365.7

89

384.0

24

388.2

49

377.9

74

356.7

42

328.7

20

297.6

39

266.8

38*

238.7

76

213.6

65

191.1

95

17

1.0

88

153.0

95

388.6

02

1.3

8

D/T

=1.

0

0.0

00

.47

43.6

36

11.9

19

27.5

00

52

.32

487.1

88

129.2

20

174.9

52

221.2

79

26

5.4

25

30

4.9

05

337.4

94

36

1.2

02

374.2

49

375.0

41

363.1

00

341.5

80

314.2

03

284.3

00

25

4.8

51

*228.0

50

204.0

67

182.6

06

163.4

02

376.2

90

1.4

6

D/T

=1.

5

0.0

00

.316

2.4

24

7.9

46

18.3

33

34

.88

358.1

25

86.1

47

11

6.6

35

147.5

20

176.9

50

203.5

86

227.4

20

24

8.7

48

26

7.8

32

284.9

10

299.8

76

31

1.4

43

31

8.1

57

318.7

20

31

1.9

68

29

7.4

93

27

7.3

18

253.8

50

22

9.2

48

319.3

10

1.8

6

D/T

=2

.0

0.0

00

.237

1.8

18

5.9

60

13.7

50

26

.16

24

3.5

94

64

.61

08

7.4

76

11

0.6

40

132.7

13

152.6

89

170.5

65

18

6.5

61

200.8

74

213.6

83

225.1

44

235.4

00

244.5

77

252.7

90

260.1

38

266.4

77

270.7

80

271.9

04

268.8

26

271.9

84

2.2

8

Summ

ariz

ed from co

mput

atio

ns at intervals

H/T

= 0.

02.

*Rec

essi

on co

effi

cien

t 0.89483523 is ap

plic

able

beyond this po

int.

Tabl

e 15. Linear Mo

del

Hydr

ogra

phs

(S =

ko); k/T

= 1.

00

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

12.4

78

48.3

35

10

5.3

45

181.4

96

27

4.9

65

359.1

46

410.7

50

432.8

78

428.3

34

39

9.6

58

*361.6

24

327.2

10

296.0

72

267.8

96

242.4

01

219.3

33

198.4

61

179.5

74

16

2.4

85

147.0

22

133.0

31

120.3

71

108

. 916

98

.55

1

434.1

13

0.8

4

D/T

=0.

1

0.0

00

4.2

74

28

.62

97

5.2

31

141.9

65

226.9

13

319.7

94

38

7.4

25

42

4.0

56

43

2.6

34

415.8

32

38

0.3

37

*344.1

42

311.3

91

281.7

57

254.9

44

230.6

83

208.7

30

188.8

66

170.8

92

154.6

29

139.9

14

126.5

99

11

4.5

51

10

3.6

50

433.0

31

0.8

8

D/T

=0.2

0.0

00

2.1

37

16.4

51

51.9

30

108.5

98

18

4.4

39

27

3.3

53

35

3.6

10

40

5.7

41

42

8.3

45

42

4.2

33

39

8.0

84

362.3

95*

327.7

66

296.5

74

26

8.3

50

242.8

14

21

9.7

07

198.7

98

17

9.8

79

16

2.7

61

14

7.2

72

13

3.2

57

12

0.5

76

10

9.1

01

42

9.7

58

0.9

4

D/T

=0.

3

0.0

00

1.4

25

10.9

68

36.0

45

81 .

942

148.0

36

229.5

57

311.3

77

377.0

92

414.7

05

424.1

74

409.6

01

380.1

04

34

5.2

90

*312.4

30

282.6

97

25

5.7

95

231.4

52

209.4

26

189.4

96

171.4

63

155.1

44

140.3

82

127.0

22

114.9

34

424.3

99

0.9

8

D/T

=0.

4

0.0

00

1.0

69

8.2

26

27.0

34

62.5

25

11

8.1

85

190.9

76

269.0

24

33

9.5

47

390.9

77

414.9

87

413.2

15

393.2

36

36

2.9

25

32

9.4

07

*

298.0

58

269.6

94

24

4.0

28

220.8

06

199.7

93

180.7

79

16

3.5

75

148.0

08

133.9

22

121.1

77

417.0

00

1.0

4

D/T

=0.

5

0.0

00

.855

6.5

80

21

.62

750.0

20

95

.40

2158.5

06

230.2

66

300.0

31

358.1

64

395.9

48

40

8.0

57

399.4

00

376.8

67

346.6

92

314.5

14*

284.5

83

257.5

01

232.9

96

210.8

23

19

0.7

60

172.6

06

15

6.1

80

14

1.3

16

"127. 8

68"

408.0

57

1.1

0

D/T

=0.

6

0.0

00

.712

5.4

84

18

.02

241.6

83

79.5

02

132.8

01

196.6

60

262.5

64

322.1

31

367.7

76

393.3

46

397.4

04

384.7

32

361.

015

331.4

00

30

0.5

42

*271.9

41

246.0

62

22

2.6

45

201.4

57

182.2

85

164.9

38

149.2

41

135.0

38

398.1

27

1.1

6

D/T

=0.

7

0.0

00

.61

14

.70

015.4

48

35.7

28

68.1

45

113.8

29

169.1

76

22

9.1

45

286.8

60

335.5

17

369.5

70

386.3

17

385.1

17

370.0

21

345.8

62

317.0

12

287.4

26*

260.0

73

235.3

23

212.9

29

19

2.6

65

174.3

30

157.7

40

142.7

28

387.8

34

1.2

4

D/T

=0.

8

0.0

00

.53

44

.11

31

3.5

17

31.2

62

59.6

27

99.6

01

148.0

29

201.0

36

254.5

81

30

2.9

81

341.1

20

366.3

92

376.9

51

372.1

97

355.6

37

33

1.4

65

303.4

77

27

5.1

06

*248.9

26

225.2

36

203.8

02

184.4

07

166.8

57

150.9

78

377.1

61

1.3

2

D/T

=0

.9

0.0

00

.475

3.6

56

12.0

15

27

.78

9

53.0

01

88

.53

4131.5

81

17

8.6

99

226.7

69

272.4

98

311.5

76

341.4

55

360.2

80

366.3

74

359.1

69

341.7

53

317.8

28

290.7

42

263.5

27*

238.4

48

215.7

56

195.2

23

176.6

45

159.8

34

366.3

74

1.4

0

D/T

=1.

0

0.0

00

.42

73.2

90

10.8

13

25 .

010

47.7

01

79.6

81

118.4

23

160.8

29

204.0

92

245.6

75

283.2

82

314.8

33

338.4

49

35

2.4

28

355.2

31

346.3

20

328.4

51

304.9

32

278.7

57

252.6

37*

22

8.5

95

206.8

40

187.1

56

169.3

45

355.6

34

1.4

8

D/T

=1.

5

0.0

00

.285

2.1

94

7.2

09

16

.67

3

31

.80

15

3.1

20

78.9

49

107.2

19

13

6.0

61

163.7

84

18

9.1

39

212.0

82

232.8

42

25

1.6

25

268.6

22

283.7

16

295.7

22

30

3.2

98

305.2

26

300.4

07

28

8.4

15

271.0

27

250.3

93

228.4

61

305.3

47

1.8

8

D/T

=2

.0

0.0

00

.214

1.6

45

5.4

07

12

.50

5

23

.85

13

9.8

40

59

.21

28

0.4

14

10

2.0

46

122.8

38

141.8

55

15

9.0

62

17

4.6

31

18

8.7

19

201.4

66

213.0

00

223.4

37

232.8

80

241.4

25

249.1

56

255.9

38

260.8

37

262.8

02

260.8

87

262.8

02

2.3

0

Summarized from co

mput

atio

ns at

intervals

H/T

= 0.

02.

*Recession coefficient

0.90

4834

36 applicable be

yond

this point.

O*

00

Table

16.-

-Lin

ear Mo

del Hy

drog

raph

s (S

= kO); k/

T =

1.10

". T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

11

.37

94

4.2

01

96

.60

31

66

.88

4

253.4

88

332.2

41

381.7

19

404.4

65

402.8

00

37

8.8

48

*345.9

26

315.8

64

28

8.4

15

263.3

51

24

0.4

65

219.5

67

200.4

86

183.0

64

167.1

56

15

2.6

29

139.3

65

127.2

54

116.1

95

10

6.0

96

406.6

05

0.8

4

D/T

=0.

1

0.0

00

3.8

95

26.1

51

68.9

06

130.3

57

208.9

59

295.3

14

359.2

17

395.1

34

405.4

98

39

2.5

27

36

2.1

48

*330.6

76

301.9

40

275.7

01

251.7

41

229.8

64

20

9.8

88

191.6

49

174

. 994

159.7

87

145

. 900

133.2

22

121.6

44

11

1.0

72

405.4

98

0.9

0

D/T

=0.

2

0.0

00

1.9

47

15

.02

347.5

29

99.6

32

169.6

58

252.1

37

327.2

66

377.1

76

40

0.3

16

399.0

12

377.3

37

34

6.4

12

*316.3

08

28

8.8

20

263.7

21

240.8

03

21

9.8

76

200.7

68

183.3

22

16

7.3

91

152.8

44

13

9.5

61

127.4

33

116.3

58

402.6

04

0.9

4

D/T

=0.

3

0.0

00

1.2

98

10.0

15

32.9

84

75.1

38

136.0

74

211.5

44

287.8

30

349.8

89

386.6

16

397.7

20

386.7

24

361.7

84

331.5

88*

302.7

72

276.4

61

25

2.4

35

230.4

98

210.4

67

192.1

77

175.4

77

160.2

27

146.3

03

133.5

89

121.9

79

397.7

20

1.0

0

D/T

=0.

4

0.0

00

.97

47

.51

224.7

38

57.3

27

108.5

93

175.8

84

248.4

62

314.6

56

363.7

91

388.0

94

388.8

27

372.7

12

346.8

23

317.6

16*

29

0.0

15

264.8

11

241.7

98

220.7

86

201.5

99

184.0

79

'168.0

83

153.4

76

140.1

38

127.9

60

39

0.9

73

1.0

6

D/T

=0.

5

0.0

00

.779

6.0

09

19

.79

04

5.8

62

87.6

54

145.9

38

212.5

51

277.7

96

332.8

24

369.5

38

38

2.9

05

377.1

97

35

8.5

58

332.5

98

30

4.4

41

*277.9

84

253.8

27

231.7

69

211.6

27

193.2

36

176.4

44

161.1

10

147.1

09

134.3

25

383.0

84

1.1

2

D/T

=0

. 6

0.0

00

.649

5.0

08

16

.49

238.2

18

73.0

45

122.2

64

181.4

84

242.9

81

299.0

80

342.7

75

368.3

06

374.2

00

364.6

54

344.7

48

319.1

22

292.0

12*

266.6

35

243.4

64

222.3

06

202.9

87

185.3

47

169.2

40

154.5

33

141.1

03

374.4

27

1.1

8

D/T

=0.

7

0.0

00

.55

64.2

92

14.1

36

32.7

59

62.6

10

104.7

98

156.1

14

212.0

06

266.1

98

312.4

29

345.5

42

362.9

31

36

3.8

77

351.9

46

331.4

61

306.3

71

280.2

80*

255.9

23

233.6

82

213.3

75

194.8

32

177.9

01

162.4

41

148.3

24

365.2

99

1.2

6

D/T

=0.

8

0.0

00

.487

3.7

56

12

.36

928.6

64

54.7

84

91.6

98136.6

00

185.9

92

236.1

92

281.9

89

318

. 644

343.6

84

355.3

07

35

2.8

55

339.4

20

318.7

62

29

4. 3

112

69

.20

1*

245.8

07

22

4.4

45

204.9

40

187.1

31

170.8

68

156.0

20

355.8

99

1.3

4

D/T

=0

.9

0.0

00

.43

33

.33

810.9

95

25.4

79

48.6

96

81

.50

9121.4

22

165.3

26

210.3

81

253.5

63

290.8

96

319.9

81

339.0

46

346.4

62

341.6

20

327.2

48

306.6

65

282.9

04

25

8.7

33

*

236.2

49

21

5.7

18

196.9

72

179.8

54

164.2

24

346.4

62

1.4

0

D/T

=1 .

0

0.0

00

.389

3.0

05

9.8

95

22

.93

1

43

.82

773.3

58

109.2

80

148.7

93

189.3

43

228.5

96

264.4

21

294.8

74

318.1

77

332.7

11

336.9

90

33

0.4

45

315.5

12

295.1

63

272.1

13

248.8

39*

227.2

14

207.4

69

189.4

39

172.9

76

337.0

20

1.4

8

D/T

=1.

5

0.0

00

.260

2.0

03

6.5

97

15

.28

7

29.2

18

48

.90

67

2.8

53

99.1

96

126.2

29

152.3

97

176.5

40

19

8.5

86

218

. 715

23

7.0

95

253.8

78

268.9

42

281.1

91

289.3

74

292.3

50

289.0

72

279.1

11

26

4.0

45

245.8

12

226.1

84

292.3

50

1.9

0

D/T

=2.

0

0.0

00

.195

1.5

02

4.9

48

11

.46

5

21

.91

33

6.6

79

54

.64

07

4.3

97

94

.67

2

114.2

98

132.4

05

148.9

39

164.0

36

177.8

21

190.4

08

201.9

01

212.3

96

22

1.9

78

23

0.7

28

238.7

17

24

5.8

18

251.1

71

25

3.8

08

252.8

44

253.9

30

2.3

2

Summ

ariz


in

tervals

H/T

= 0.

02,

*Rec

essi

on co

effi

cien

t 0.

9130

9842

applicable be

yond

this po

int.

Tabl

e 17

. Linear Mo

del

Hydr

ogra

phs

(S = kO

); k/T

= 1.20

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D^In

st.

0.0

00

10.4

58

40

.71

98

9.2

00

154.4

44

235.1

12

309.0

54

356.4

44

379.4

06

379.8

91

359.6

98*

33

0.9

38

304.4

77

280.1

31

257.7

33

237.1

26

218.1

66

200.7

22

18

4.6

72

169.9

06

156.3

22

143.8

23

13

2.3

24

121.7

44

112

. 010

382.2

76

0.8

6

D/T

=0.

1

0.0

00

3.5

78

24.0

69

63.5

62

120.5

36

19

3.5

95

274.2

97

334.7

86

369.7

99

381.3

73

371.3

81

34

5.1

27

*317.5

31

292.1

41

268.7

83

247.2

92

227.5

20

20

9.3

28

192.5

90

177.1

91

163.0

23

14

9.9

89

137.9

97

126.9

63

116.8

12

381.3

73

0.9

0

D/T

=0.

2

0.0

00

1.7

89

13

.82

44

3.8

16

92

.04

9

157.0

66

23

3.9

46

30

4.5

41

352.2

92

375.5

86

376.3

77

358.2

54

33

1.3

29

*304.8

36

280.4

62

258.0

37

237.4

06

2,18

.424

20

0.9

59

18

4.8

90

17

0.1

07

15

6.5

06

143.9

93

13

2.4

80

12

1.8

88

378.6

42

0.9

6

D/T

=0.

3

0.0

00

1.1

93

9.2

16

30.4

03

69.3

89

125.8

98

196.1

43

267.5

59

326.2

94

361.9

86

374.1

84

365.9

60

344.6

80

318.2

66*

292.8

18

26

9.4

05

247.8

65

228.0

47

209.8

13

193.0

36

177.6

01

163.4

01

150.3

36

138.3

16

127.2

57

374.1

84

1.0

0

D/T

=0.

4

0.0

00

.895

6.9

12

22.8

02

52.9

36

100.4

41

16

2.9

98

23

0.8

03

293.1

19

340.0

64

36

4.3

35

366.9

20

35

3.8

53

331.

545

305.8

95*

28

1.4

37

258.9

34

238.2

31

219.1

82

201.6

57

185.5

33

170.6

98

157.0

50

144.4

93

132.9

40

368.1

41

1.0

6

D/T

=0.

5

0.0

00

.716

5.5

30

18

.24

24

2.3

49

81.0

68

135.2

12

19

7.3

55

258.6

03

310.7

70

346.3

27

36

0.4

93

357.0

42

341.5

10

318.9

93

29

4.1

75

*2

70

.65

3249.0

13

229.1

02

210.7

84

193.9

30

178.4

24

164.1

58

151.0

33

138.9

57

361.0

28

1.1

2

D/T

=0.

6

0.0

00

.596

4.6

08

15.2

02

35.2

91

67.5

57

113.2

73

168.4

74

226.0

96

279.0

64

320.8

72

346.1

27

353.3

33

34

6.2

25

329.3

89

307.0

42

283.0

66*

260.4

32

239.6

09

220.4

51

202.8

24

186.6

07

17

1.6

86

157.9

59

145.3

29

353.3

33

1.2

0

D/T

=0.

7

0.0

00

.511

3.9

50

13.0

30

30.2

49

57

.90

697.0

91

144.9

18

197.2

35

248.2

78

292.2

52

324.3

37

342.0

42

344.5

91

335.1

62

317.6

61

295.6

82

272.5

32*

25 0

. 74

1230.6

92

212.2

47

195.2

76

179.6

63

165.2

97

152.0

81

345.2

39

1.2

6

D/T

=0.

8

0.0

00

.447

3.4

56

11.4

01

26.4

68

50.6

68

84.9

55

126.8

03

173.0

28

220.2

52

263.6

66

298.8

62

323.4

86

335.8

04

335.1

15

324.1

78

306.3

93

284.8

88

26

2.5

39

*241.5

47

222.2

33

204.4

64

188.1

16

17

3.0

75

159.2

37

33

6.9

88

1.3

4

D/T

=0

.9

0.0

00

.398

3.0

72

10.1

34

23.5

27

45.0

38

75.5

15

112.7

14

153.8

02

196.1

77

237.0

44

272.7

17

300.9

36

320.0

03

328.3

57

325.3

57

313.4

38

295.6

08

274.6

32

253.0

56*

232.8

22

214.2

06

197.0

79

181.3

21

166.8

24

328.6

24

1.4

2

D/T

-1.0

0.0

00

.358

2.7

65

9.1

21

21.1

75

40.5

34

67.9

64

101.4

42

138.4

22

176.5

59

21

3.6

98

247.8

52

277.1

99

300.0

56

314.8

81

320.2

51

315.5

73

303.0

27

285.3

06

264.8

88

24

4.0

53

*224.5

39

20

6.5

85

190.0

68

174.8

71

320.2

51

1.5

0

D/T

=1.

5

0.0

00

.239

1.8

43

6.0

81

14

.11

6

27

.02

34

5.3

09

67

.62

89

2.2

81

11

7.7

06

142.4

65

165.4

73

186.6

42

20

6.1

18

224.0

37

240.5

23

255.4

53

26

7.8

03

27

6.4

05

280.1

82

278.1

44

269.8

57

25

6.7

38

240.5

49

222.9

11

280.2

70

1.9

2

D/T

=2.

0

0.0

00

.179

1.3

82

4.5

60

10

.58

7

20.2

67

33.9

82

50

.72

16

9.2

11

88

.28

0

106.8

49

12

4.1

05

139.9

82

15

4.5

89

168.0

28

180.3

92

191.7

68

202.2

35

211.8

64

220.7

24

22

8.8

75

236.1

96

241.8

92

245.0

62

244.8

76

245.4

35

2.3

4

£ S H » j_j 3 i o g ^ M CO

Summ

aris


intervals

H/T

= 0.

02.

*Recession co

effi

cien

t 0.92004262 ap

plic

able

beyond this point.

Ol

Tab

le 18. L

inear

Mod

el

Hydro

gra

phs

CS

- kO

~);

k/T

=

1.3

0

Cm

OS

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

9.5

60

37

.53

482.5

56

143.3

64

218.7

89

288.6

27

334.1

71

357.2

20

359.4

40

342.3

76*

317.

015

293.5

32

271.7

89

251.6

56

23

3.0

15

21

5.7

55

199.7

73

18

4.9

75

171.2

73

158.5

86

146.8

39

135.9

62

125.8

91

11

6.5

66

360.9

0.8

6

D/T

=0.

1

0.0

00

4.7

80

23

.54

760

.045

112.9

60

18

1.0

77

253.

708

311.3

99

345.

695

358.3

30

35

0.9

08

329.

695*

30

5.2

73

282.6

60

26

1.7

22

24

2.3

36

224.

385

20

7.7

64

192.3

74

178.1

24

164.9

30

152.7

13

141.4

01

130.9

27

12

1.2

28

35

8.4

0.9

2

D/T

=0.

2

0.0

00

2.3

90

14.1

64

41.7

96

86

.50

2

147.0

18

217.3

92

282.5

53

328.5

47

35

2.0

13

354.6

19

340.3

02

31

7.4

84

*293.9

67

272.1

91

252.0

29

233.3

60

216.0

74

200.0

69

185.2

49

171.5

27

158.8

21

147.0

57

136.1

64

126.0

77

35

5.9

0.9

6

D/T

=0.

3

0.0

00

1.5

93

9.4

42

29.4

57

65.5

17

118.0

27

182.5

82

248.7

28

303.6

01

338.4

75

351.6

44

346.3

11

328.6

26

305.8

76*

283.2

19

262.2

40

242.8

14

224.8

28

208.1

74

192.7

54

178.4

76

165.2

55

15 3

. 01

41

41

.68

0131.1

85

35

1.8

1.0

2

D/T

=0.

4

0.0

00

1.1

95

7.0

82

22.0

93

50.3

33

94.4

07

151.9

47

214.7

86

272.9

70

31

7.2

83

341.5

83

346.1

57

336.0

52

317.1

34

29

4.8

38

*

27

2.9

98

252.7

76

234.0

52

21

6.7

15

200.6

62

185.7

98

17

2.0

35

159.2

92

147.4

92

136.5

67

34

6.2

1.0

8

D/T

=0.

5

0.0

00

.956

5.6

65

17

.67

440.2

66

76.4

82

126.2

67

183.8

38

24

0.9

68

290.0

42

32

4.0

08

33

9.2

05

337.9

80

325.3

73

306.0

52

28

4.3

37

*26

3 2

/52

43

.77

3225.7

16

208.9

96

19

3.5

15

179.1

81

165.9

08

153.6

19

142.2

39

34

0.2

1.1

4

D/T

=0.

6

0.0

00

.797

4.7

21

14.7

29

33.5

55

63.7

35

10

6.0

20

157.1

23

210.8

14

260.5

28

300.1

86

324.9

56

333.5

50

328.7

60

31

4.7

65

295.4

33

274.3

45*

254.0

23

235.2

07

217.7

84

201.6

52

186.7

15

172.8

84

160.0

78

148.2

20

33

3.6

1.2

0

D/T

=0.

7

0.0

00

.68

34

.04

712.6

25

28.7

62

54

.63

090.8

74

135.3

59

184.0

61

231.8

88

273.4

39

304.4

02

322.1

44

326.2

80

319.1

84

30

4.4

18

285.2

83

264.8

34*

245.2

16

227.0

52

210.2

34

194.6

61

180.2

41

166.8

90

154.5

28

326.5

1.2

8

D/T

=0.

8

0.0

00

.598

3.5

41

11.0

46

25.1

66

47.8

01

79.5

15

118.4

39

161.6

51

20

5.8

45

24

7.7

65

280.4

71

304.5

11

317.2

09

318.2

10

309.5

77

294.4

14

275.5

93

255.7

76*

236.8

30

219.2

87

20

3.0

43

188.0

03

174.0

77

161.1

82

31

9.0

1.3

6

D/T

=0.

9

0.0

00

.53

13.1

48

9.8

19

22.3

70

42.4

90

70.6

80

105.2

80

143.6

90

18

3.5

05

22

1.9

63

255.9

80

283.2

27

30

2.0

83

311.0

43

309.7

80

300.1

12

284.7

86

266.3

46

247.1

48*

228.8

41

211.8

90

196.1

94

181.6

61

16

8.2

05

31

1.6

1.4

4

D/T

=1

.0

0.0

00

.478

2.8

33

8.8

37

20.1

33

38

.24

163.6

12

94.7

52

129.3

21

165.1

54

200.2

45

232.7

36

260.9

09

283.1

71

298.0

47

304.1

73

301.2

41

290.8

77

27

5.5

45

257.5

24

23

8.9

27

*221.2

28

204.8

41

189.6

68

175.6

18

30

4.3

1.5

2

D/T

=1.

5

0.0

00

.31

91

.88

85

.89

11

3.4

22

25

.49

442.4

08

63.1

68

86

.21

4110.1

03

133.4

96

155.4

76

175.8

28

194.6

72

212.1

20

228.2

76

242.9

16

255.1

97

264.0

19

268.3

63

26

7.2

87

260.5

54

249.2

21

234.9

03

219.0

96

26

8.7

1.9

4

D/T

=2 .

0

0.0

00

.239

1.4

16

4.4

19

10.0

67

19

.12

03

1.8

06

47

.37

66

4.6

60

82

.57

7

100.1

22

116.6

07

131.8

71

146.0

04

159.0

90

171.2

07

182.4

26

192.8

14

20

2.4

33

211.3

39

219.5

86

22

6.9

82

23

2.8

75

236.4

19

23

6.8

33

23

7.1

2.3

6

Electronically computed at

intervals

H/T

= 0.

10,

and

expanded manually to

ob

tain

peak value.

*Rec

essi

on coefficient

0.92

5925

923

applicable be

yond

th

is point.

Tab

le 19. L

inear

Mod

el

Hydro

gra

phs

(S

= ko);

k

/T

= 1.4

0

Q T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

8.9

01

34.9

91

77

.08

3134.0

75

204.9

39

270.9

16

314.5

40

337.3

53

340.7

91

32

6.1

89

*303.6

93

282.7

49

263.2

49

245.0

94

228.1

91

212.4

54

197.8

02

184.1

60

171.4

60

159.6

35

148.6

25

13

8.3

75

128.8

32

119.9

47

111.6

75

103.9

73

96

.80

39

0.1

27

83.9

11

34

1.6

0.8

6

D/T

=0.

1

0.0

00

4.4

51

21.9

46

56

.03

7105.5

79

169.5

07

23

7.9

27

29

2.7

28

32

5.9

47

33

9.0

72

333.4

90

31

4.9

41

*293.2

21

272.9

99

25

4.1

72

236.6

43

220.3

22

20

5.1

28

190.9

81

177.8

10

165.5

47

154.1

30

143.5

00

133.6

04

124.3

90

115.8

11

107.8

24

10

0.3

88

93.4

658

7.0

19

33

9.4

0.9

2

D/T

=0.

2

0.0

00

2.2

25

13.1

98

38

.99

180.8

08

13

7.5

43

203.7

17

265.3

28

309.3

37

332.5

09

336.2

81

324.2

16

30

4.0

81

*2

83

.11

02

63

.58

5

245.4

07

22

8.4

82

212.7

25

19

8.0

54

184.3

95

171.6

78

15

9.8

39

148.8

15

13

8.5

52

128.9

97

12

0.1

00

111.8

18

10

4.1

06

96.9

26

90

.24

2

33

6.9

0.9

6

D/T

=0.

3

0.0

00

1.4

84

8.7

99

27.4

78

61.1

87

110.3

74

171.0

05

233.3

87

285.5

34

319.2

40

33

2.8

36

32

9.1

68

313.8

84

29

3.7

21

*273.4

64

254.6

04

237.0

46

220.6

98

205.4

77

191.3

06

178.1

13

16

5.8

29

154.3

92

14

3.7

45

13

3.8

31

124.6

02

116.0

08

108.0

08

100.5

59

93.6

24

33

3.3

1.0

2

D/T

=0.

4

0.0

00

1.1

13

6. 5

9Q20.6

08

47.0

03

88.2

67

142.2

63

20

1.4

35

256.5

27

29

8.9

18

322.8

09

32

8.3

63

320.1

81

30

3.6

63

28

3.8

33

*

264.2

59

246.0

34

229.0

66

21

3.2

68

198.5

60

184.8

66

172.1

17

160.2

47

14

9.1

95

138.9

06

129.3

26

120.4

07

11

2.1

03

104.3

72

97.1

74

32

8.6

1.0

8

D/T

=0.

5

0.0

00

.890

5.2

79

16

.48

737.6

03

71.5

04

118.1

99

172.3

56

226.3

38

273.0

36

305.8

33

321.

235

321.3

34

310.7

44

29

3.7

65

274.3

95*

255.4

71

237.8

53

221.4

40

206.1

77

191.9

57

178.7

19

166.3

94

154.9

18

144.2

34

134.2

87

125.0

26

116.4

03

108.3

76

100.9

01

32

2.7

1.1

4

'.u/r

tfe

-'

D/T

=0.

6

0.0

00

.74

24

.39

913.7

39

31.3

35

59.5

87

99.2

41

147.2

87

197.9

54

245.1

27

283.1

12

307.3

51

316.5

67

313.2

78

301.3

16

284.2

44

26

5.3

83

*247.0

81

230.0

41

214.1

76

199.4

05

185.6

53

172.8

49

16

0.9

29

149.8

30

139.4

97

129.8

77

120.9

20

11

2.5

80

104.8

16

31

6.8

1.2

2

D/T

=0.

7

0.0

00

.636

3.7

71

11

.77

626.8

59

51

.07

485.0

64

126.8

82

172.8

10

218.1

14

257.7

50

287.6

59

305.3

32

310.3

43

30

4.8

35

29

2.0

77

275.1

13

25

6.7

75

*239.0

66

222.5

79

207.2

29

192.9

37

17

9.6

31

167.2

43

155.7

09

144.9

70

134.9

72

125.6

64

116.9

97

108.9

29

31

0.3

1.3

0

D/T

=0.

8

0.0

00

.55

63

.30

010.3

04

23.5

02

44.6

90

74.4

31

111.0

22

15

1.7

65

193.5

93

232.5

36

264.8

99

288.3

54

301.2

91

303.3

21

296.3

10

28

3.1

07

266.3

64

248.5

51*

231.4

09

215.4

50

200.5

91

186.7

58

173

.878

161.8

86

150.7

22

140.3

27

130.6

49

121.6

39

113.2

50

30

3.6

1.3

6

D/T

=0

.9

0.0

00

.495

2.9

32

9.1

59

20.8

90

39.7

25

66.1

61

98.6

86

134.9

02

172.5

77

209.1

37

241.6

92

268.0

46

286.6

48

296.0

55

295.9

12

287.8

67

274.4

43

257.9

89

240.6

91*

224.0

91

208.6

37

194.2

48

180.8

52

168.3

79

156.7

67

145.9

55

135.8

89

126.5

18

117.7

92

297.0

1.4

4

D/T

=1.

0

0.0

00

.445

2.6

40

8.2

43

18.8

01

35.7

52

50.5

45

88.8

18

121.4

12

155.3

19

188.6

68

219.7

18

246.8

45

268.5

41

283.4

01

290.1

14

288.3

54

279.5

94

266.0

97

249.9

71

23

3.1

77

*2

17

.09

5202.1

23

188.1

84

175.2

06

163.1

22

151.8

73

141.3

99

131.6

47

122.5

68

29

0.4

1.5

2

D/T

=1.

5

0.0

00

.297

1.7

60

5.4

96

12

.53

4

23.8

35

39.6

96

59.2

12

80

.94

1103.5

46

125.7

79

146.7

75

166.3

23

184.5

23

20

1.4

68

217.2

44

23

1.6

35

24

3.8

47

252.8

44

257.6

59

25

7.3

95

251.8

09

241.8

60

229.0

37

21

4.7

25

200.2

13*

186.4

05

173.5

50

16

1.5

81

150.4

37

258

.21.9

4

D/T

=2.

0

0.0

00

.223

1.3

20

4.1

22

9.4

01

17.8

76

20.7

72

44

.40

960.7

06

77

.66

0

04.3

34

110.0

81

124.7

42

138.3

92

151.1

01

162.9

33

173.9

49

184.2

06

19

3.7

55

20

2.6

45

21

0.9

22

218.4

06

224.4

84

22

8.3

63

22

9.3

03

22

6.6

18

22C

.113

21

0.4

96

198.8

72

186.2

69

22

9.4

2.3

8

Ele

ctr

on

icall

y

com

pute

d at

inte

rvals

H

/T

= 0.1

0,

and

expa

nded

m

anual

ly

to

ob

tain

pe

ak valu

e.

*R

eces

sion coeff

icie

nt

0.9

31034483

ap

pli

cab

le

beyo

nd th

is p

oin

t.

Tabl

e 20

.--L

inea

r Mo

del

Hydrographs

(S =

ko); k/

T =1.50

Or

00

_n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

Pea

kT

ime

D=

Inst

.

0.0

00

8.4

12

32.9

30

72.5

16

126.1

96

193.0

62

255.4

38

297.1

43

319.5

11

323.7

87

31

1.1

41

*2

91

.07

5272.3

03

254.7

41

238.3

12

222.9

42

208.5

63

19

5.1

12

18

2.5

29

170.7

56

15

9.7

43

149.4

40

139.8

02

130.7

85

12

2.3

51

32

4.3

22

0.8

8

D/T

=0.

1

0.0

00

2.8

74

19

.42

551.5

57

98.2

65

158.6

09

225.9

60

277.8

89

309.8

22

32

3.0

48

31

8.7

73

301.0

01*

281.5

89

26

3.4

28

246.4

39

230.

545

215.6

76

201.7

66

188.7

53

176.5

80

165.1

91

154.5

36

144.5

70

135.2

45

126.5

23

323.5

55

0.9

2

D/T

=0.

2

0.0

00

1.4

37

11

.15

03

5.4

91

74

.91

1

128.4

37

192.2

84

25

1.9

24

29

3.8

56

31

6.4

35

320.9

11

30

9.8

87

291.2

95*

27

2.5

08

254.9

34

23

8.4

92

223.1

11

208.7

21

195.2

60

182.6

66

170.8

85

159.8

64

149.5

53

139.9

08

130.8

84

321.4

07

0.9

8

D/T

=0.

3

0.0

00

.958

7.4

33

24

.61

956.4

16

102.8

11

160.9

45

220.8

19

271.2

24

303.5

87

31

7.2

15

314.2

74

300.4

54

282.0

06*

263.8

19

246.8

04

230.8

87

215.9

96

20

2.0

65

189.0

33

176.8

41

165.4

36

154.7

66

144.7

84

135.4

46

317.3

11

1.0

2

D/T

-0.4

0.0

00

.719

5.5

75

18.4

64

43

.03

0

81

.96

4133.5

98

190.1

81

243.0

70

284.1

80

307.3

83

313.1

61

306.1

03

29

1.1

98

273.1

14*

255.5

00

239.0

22

223.6

07

20

9.1

85

195.6

94

183.0

72

171.2

65

160.2

19

149.8

86

140.2

19

3-1.3

j.9

81.0

8

D/T

=0.

5

0.0

00

.575

4.4

60

14.7

71

34.4

24

66.1

46

no.

763

162.4

56

214.1

09

259.0

66

291.0

99

30

6.1

07

30

6.8

47

297.

568

28

2.2

46

26

4.6

00

*2

47

.53

5231.5

71

216.6

36

202.6

64

189.5

93

17

7.3

65

165.9

26

155.2

24

145.2

13

30

7.9

35

1.1

6

D/T

=0.

6

0.0

00

.479

3.7

17

12.3

10

28.6

87

55

.12

292

. 78

2138.6

18

187.0

17

A.32

6

6

269.0

17

292.7

49

302.0

21

299.6

10

289.0

46

273.6

29

256.4

46*

239.9

07

224.4

35

209.9

60

196.4

18

183.7

50

171.8

99

160.8

12

150.4

41

302.3

57

1.2

2

D/T

=0.

7

0.0

00

.411

3.1

86

10.5

51

24.5

89

47.2

47

79.5

27

119.2

26

163.0

75

206.4

50

244.6

24

273.5

86

29

1.1

55

296.5

07

292.0

14

280.6

89

265.3

50

24

8.6

35

*232.6

00

21

7.5

98

203.5

64

190.4

35

178.1

53

166.6

63

155.9

14

295.5

07

1.3

0

D'T

=0.

8

0.0

00

.359

2.7

87

9.2

32

21.5

15

41

.34

169.5

86

104.3

22

143.0

50

183.0

72

220.4

91

251.6

71

274.5

86

287.6

89

290.2

49

284.3

31

272.5

62

257.4

02

24

1.1

50

*225.5

97

211.0

47

197.4

36

184.7

02

172.7

90

161.6

45

290.5

02

1.3

8

D/T

=0.

9

0.0

00

.319

2.4

78

8.2

07

19.1

25

36.7

48

61.8

54

92.7

31

127.1

56

163.0

50

198.1

50

229.4

36

25

4.9

95

27

3.3

47

283.1

06

28

3.6

15

276.7

02

264.6

96

24

9.7

75

23

3.9

75

*

21

8.8

85

20

4.7

68

191.5

62

179.2

07

167.6

49

28

4.4

38

1.4

6

D/T

=1.

0

0 2 717 33 55 83

114

146

178

208

234

255

270

277

276

269

257

242

227

212

198

185

173

278 1

.000

.28

7.2

30

.386

4 1

.07

3.6

69

.458

.440

.745

.622

.435

.651

.838

.656

.850

.821

.209

.102

.45

5

.09

7*

.450

.748

.930

.939

.36

8.5

4

D/T

=1.

5

0.0

00

.19

21

.48

74.9

24

11.4

75

22

.04

93

7.1

13

55

.63

976.2

93

97

.83

0

119.0

82

139.1

48

15

7.9

21

175.4

83

191.9

12

207.2

82

221.4

69

233.6

25

242.7

71

24

7.9

92

248.4

31

243.6

69

234.7

81

223.1

43

210.0

41

248.8

82

1.9

6

D/T

=2.

0

0.0

00

.14

41

.11

53

.69

38

.60

6

16

.53

727.8

35

41

.72

95

7.2

20

73

.37

3

89

.31

1104.3

61

118.4

41

131.6

12

143.9

34

155.4

61

16

6.2

45

176.3

33

185.7

71

194.6

00

20

2.8

60

21

0.4

43

21

6.7

00

22

0.8

84

22

2.2

97

22

2.2

97

2.4

0

Summarized from computations at

in

terv

als

H/T

= 0.

02.


0.93

5506

03 applicable beyond th

is point.

Tab

le 21. L

inear

Mod

el

Hydro

gra

phs

(S

= k

O);

k/T

=

1.6

0

r^

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

7.8

22

30.8

15

68.0

58

11

8.6

89

18

1.8

96

241.2

72

281.4

05

303.4

61

308.5

36

29

7.6

59

*279.6

19

262.6

72

246.7

53

231.7

98

21

7.7

50

204.5

53

19

2.1

56

18

0.5

10

16

9.5

70

159.2

93

14

9.6

39

140.5

70

13

2.0

51

124.0

48

116.5

29

10

9.4

67

102.8

33

96.6

00

90.7

46

30

8.8

0.8

8

D/T

=0.

1

0.0

00

3.9

11

19

.31

94

9.4

37

93.3

74

150.2

92

211.5

84

26

1.3

38

292.4

33

305.9

99

30

3.0

98

28

8.6

39

*271.1

46

254.7

13

239.2

76

224.7

74

211.1

52

198.3

54

186.3

33

175.0

40

164.4

32

154.4

66

145.1

04

13

6.3

10

128.0

49

120.2

88

112.9

98

106.1

50

99.7

17

93.6

73

30

6.7

0.9

4

D/T

=0.

2

0.0

00

1.9

56

11.6

15

34.3

78

71

.40

5

12

1.8

33

180.9

38

236.4

61

276.8

86

299.2

16

30

4.5

48

295.8

68

27

9.8

93

*262.9

29

246.9

94

23

2.0

25

217.9

63

204.7

53

192.3

44

180.6

86

16

9.7

36

159.4

49

149.7

85

140.7

07

13

2.1

80

124.1

69

11

6.6

43

109.5

74

102.9

33

96.6

95

30

4.7

0.9

8

D/T

=0

.3

0.0

00

1.3

04

7.7

43

24.2

22

54.0

43

97

.70

11

51

.75

02

07.7

38

255.1

18

28

6.5

90

300.5

10

299.2

45

28

7.6

28

271.4

99*

255.0

45

239.5

88

22

5.0

67

21

1.4

27

19

8.6

13

18

6.5

76

175.2

68

16

4.6

46

15

4.6

67

14

5.2

94

13

6.4

88

12

8.2

16

120.4

45

11

3.1

46

10

6.2

88

99.8

47

301.4

1.0

4

D/T

=0.

4

0.0

00

.978

5.8

07

18

.16

741.5

10

78.1

05

126.1

71

179.1

47

228.9

12

26

7.8

38

290.7

17

29

7.5

42

292.2

20

279.3

99

26

3.4

44

*

247.4

77

232.4

79

218.3

89

205.1

53

192.7

20

181.0

40

170.0

68

159.7

61

150.0

78

140.9

82

132.4

38

124.4

12

116.8

71

109.7

88

10

3.1

35

29

7.5

1.1

0

D/T

=0.

5

0.0

00

.78

24.6

46

14.5

33

33.2

08

63.2

66

104.8

01

153.2

05

201.8

04

244.3

29

274.8

90

290.3

01

292.2

63

284.7

19

271.3

74

255.7

10*

24

0.2

12

225.6

54

21

1.9

78

199.1

31

187.0

62

17

5.7

25

165.0

75

155.0

70

145.6

72

136.8

44

128.5

50

120.7

59

113.4

40

106.5

65

29

2.6

1.1

6

D/T

=0.

6

0.0

00

.65

23

.87

212.1

11

27.6

73

52.7

22

87.9

86

130.8

91

176.4

10

219.1

70

254.1

24

277.1

82

287.1

09

286.0

05

277.1

45

263.6

08

248.2

83*

233.2

36

219.1

00

205.8

22

193.3

48

18

1.6

29

170.6

22

160.2

81

150.5

67

141.4

42

132.8

69

124.8

17

117.2

52

110.1

46

28

8.0

1.2

6

D/T

=0.

7

0.0

00

.559

3.3

19

10.3

81

23.7

20

45.1

90

75.4

17

112.7

51

153.9

68

194.9

22

231.1

60

259.0

55

276.3

20

282.4

81

279.3

29

269.6

64

256.1

14

241.1

51*

226.5

35

212.8

06

19

9.9

09

187.7

93

176.4

12

165.7

20

155.6

76

146.2

41

137.3

78

129.0

52

121.2

31

113.8

84

28

2.5

1.3

0

D/T

=0.

8

0.0

00

.489

2.9

04

9.0

83

20.7

55

39.5

42

65.9

89

98.6

57

135.2

11

172.9

72

208.4

44

23

8.3

45

260.5

66

273.6

19

277.0

80

272.5

10

262.3

49

248.8

94

23

4.2

98

*2

20

.09

8

206.7

59

194.2

28

182.4

57

171.3

99

161.0

11

151.2

53

142.0

86

133.4

75

125.3

85

117.7

86

27

7.1

1.4

0

D/T

=0.

9

0.0

00

.435

2.5

81

8.0

74

18.4

49

35.1

48

58.6

57

87.6

95

120.1

88

154.1

87

187.4

30

21

7.3

55

241.9

89

259.9

16

269.8

03

271.2

68

165.6

92

255.2

39

241.9

43

22

7.7

14

*

213.9

13

200.9

49

188.7

70

177.3

30

166.5

82

156.4

86

147.0

02

138.0

93

129.7

24

121.8

62

27

1.5

1.4

6

D/T

=1

. 0

0.0

00

.391

2.3

23

7.2

67

16.6

04

31.6

33

52.7

92

78.9

26

10

8.1

69

138.7

69

16

9.0

79

19

7.5

51

222.7

34

243.2

62

257.8

52

265.3

00

265.2

57

258.9

59

248.3

49

235.2

53

221.3

86*

20

7.9

69

195.3

65

183.5

24

17

2.4

02

161.9

53

152.1

38

14

2.9

17

13

4.2

56

126.1

19

266.1

1.5

4

D/T

=1.

5

0.0

00

.261

1.5

49

4.8

44

11

.06

9

21.0

89

35

.19

45

2.6

17

72.1

12

92.5

12

112.7

19

131.9

62

150.0

38

167.0

19

182.0

70

197.9

55

211.7

71

223.7

07

232.8

34

23

8.2

78

239.2

21

235.4

13

227.6

64

217.2

56

205.3

92

19

3.2

05

*181.4

96

170.4

96

160.1

63

150.4

56

23

9.5

1.9

8

D/T

=2.

0

0.0

00

.19

61.1

61

3.6

33

8.3

02

15

.81

726.3

96

39.4

63

54

.08

46

9.3

84

84

.53

99

8.9

71

112.5

28

125.2

64

137.2

28

148.4

67

159.0

24

168.9

42

17

8.2

59

187.0

11

195.2

32

202.7

60

209.0

49

213.3

93

215.1

27

213.6

27

208.6

97

20

0.9

38

191.3

02

180.6

86

21

5.1

2.4

0

SI o § 5

Lectr

on

icall

y

com

pute

d at

inte

rvals

H

/T

= 0.1

0,

and

expa

nd'e

d m

anual

ly

to

ob

tain

pe

ak v

alu

e.

0.9

39

39

39

39

appli

cable

be

yond

th

is p

oin

t.^R

eces

sion co

eff

icie

nt

Crt CO

Tabl

e 22. Linear Mo

del

Hydrographs

fS = kO

); k/T

= 1.

n_ T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

6.9

77

27.5

29

60

.92

41

06

.46

7

16

3.5

01

217.4

52

25

4.5

34

275.6

58

281.6

88

273.4

38*

258.6

58

244.6

76

23

1.4

50

21

8.9

40

207.1

05

19

5.9

10

18

5.3

20

175.3

03

16

5.8

27

15

6.8

64

14

8.3

84

140.3

64

13

2.7

76

12

5.5

99

11

8.8

10

112.3

88

106.3

13

10

0.5

66

95

.13

0

28

1.7

0.9

0

D/T

=0.

1

0.0

00

3.4

88

17.2

53

44.2

27

83.6

95

134.9

84

190.4

77

235.9

93

265.0

96

278.6

73

277.5

63

26

6.0

48

*251.6

67

238.0

63

22

5.1

95

213.0

22

201.5

08

190.6

15

180.3

12

170.5

65

161.3

45

15

2.6

24

144.3

74

13

6.5

70

129.1

88

122.2

05

11

5.5

90

109.3

51

103.4

40

97

.84

8

27

9.9

0.9

4

D/T

=0.

2

0.0

00

1.7

44

10.3

71

30.7

40

63

.96

1

109.3

40

162.7

30

21

3.2

35

25

0.5

45

27

1.8

85

27

8.1

18

271.

805

25

8.8

57

*2

44

.86

5231.6

29

219.1

09

207.

265

196.0

61

185.4

63

175.4

38

165.9

55

15

6.9

85

148.4

99

14

0.4

72

132.8

79

125.6

96

118.9

02

11

2.4

75

10

6.3

95

100.6

44

27

8.1

1.0

0

D/T

=0.

3

0.0

00

1.1

63

6.9

14

21

.65

64

8.3

92

87.6

35

13

6.3

85

187.1

51

230.5

22

259.9

21

273.7

77

274.0

95

265.0

93

251.9

26*

238.3

08

225.4

27

213.2

42

20

1.7

15

190.8

12

180.4

97

17

0.7

41

16

1.5

12

15

2.7

81

144.5

23

136.7

11

129.3

21

122.3

31

115

. 718

109.4

63

103.5

46

27

5.2

1.0

4

D/T

=0.

4

0.0

00

.872

5.1

85

16

.24

237.1

66

70.0

40

11

3.3

46

161.2

87

206.6

38

242.5

60

264.3

31

271.8

45

268.4

88

258.3

35

245.2

43*

231.9

87

219.4

47

207.5

85

196.3

64

185.7

50

175.7

09

166.2

12

157.2

27

148.7

28

14

0.6

89

133.0

84

125.8

90

119.0

86

112.6

49

10

6.5

59

27

1.8

1.1

0

D/T

=0.

5

0.0

00

.698

4.1

48

12.9

94

29.7

33

56

.72

994.1

27

137.8

75

182.0

49

221.0

45

249.5

60

26

4.6

75

267.8

09

262.4

03

251.7

07

23

8.7

99

*225.8

91

213.6

80

202.1

30

191.2

04

180.8

69

171.0

92

161.8

44

153.0

96

144.8

20

136.9

92

129.5

87

122.5

82

115

. 95

6109.6

88

26

7.8

1.2

0

D/T

=0.

6

0.0

00

.581

3.4

57

10.8

28

24.7

77

47.2

75

79.0

21

117.7

71

159.0

79

198.1

53

230.4

64

252.3

08

262.5

07

262.8

52

256.2

01

245.2

60

232.5

84*

220.0

12

208.1

19

196.8

69

186.2

28

176.1

61

166.6

39

157.6

32

149.1

11

141.0

51

133.4

27

126.2

14

119.3

92

112.9

38

26

3.8

1.2

8

D/T

=0

.7

0.0

00

.498

2.9

63

9.2

81

21.2

38

40.5

21

67

.73

2101.4

45

138.8

18

176.1

64

209.4

97

235.5

48

252.2

17

259.0

15

257.4

72

250.0

33

239.0

09

226.5

88*

214.3

40

202.7

54

191.7

95

181.4

27

17

1.6

20

162.3

44

153.5

68

14

5.2

67

137.4

15

129.9

87

12

2.9

61

116

. 314

25

9.3

1.3

2

D/T

=0.

8

0.0

00

.436

2.5

93

8.1

21

18.5

83

35.4

56

59.2

65

88.7

65

121.9

02

156.3

00

188.8

38

216.5

66

237.5

63

250.4

47

254.7

87

251.9

16

243.9

67

232.9

60

220.8

04*

20

8.8

68

197.5

78

186.8

98

176.7

96

167.2

39

158.1

99

149.6

48

141.5

59

133.9

06

126.6

69

119.8

22

25

4.8

1.4

0

D/T

=0

.9

0.0

00

.388

2.3

05

7.2

19

16.5

18

31.5

16

52.6

80

78.9

02

108.3

57

139.3

21

169.7

73

197.4

17

220.4

66

23

7.6

18

247.6

42

250.1

47

24

6.3

15

238.0

39

227.1

10

21

5.2

22

*

203.5

88

192.5

83

182.1

73

172.3

26

163.0

11

154.2

00

145.8

65

137.9

80

130.5

22

123.4

67

250.1

1.5

0

D/T

=1.

0

0.0

00

.349

2.0

74

6.4

97

14

.86

6

28.3

65

47

.41

271.0

12

97.5

21

125.3

89

153.1

45

179.4

01

202.8

42

222.2

26

236.3

76

244.1

80

245.2

83

240.7

45

232

. 267

221.4

56

209.8

34*

198.4

92

187.7

62

177.6

13

168.0

12

158.9

31

150.3

40

142.2

13

134.5

26

127.2

54

245.5

1.5

6

D/T

=1.

5

0.0

00

.23

31

.38

34

.33

19

.91

1

18

.91

03

1.6

08

47.3

41

65 .

014

83

.59

2

10

2.0

97

11

9.8

33

13

6.6

11

15

2.4

82

167.4

95

18

1.6

96

19

4.8

98

206.4

55

215.5

27

22

1.3

19

22

3.0

76

220.5

53

214.4

45

205.8

76

19

5.9

10

185.5

53*

17

5.5

23

166.0

35

15

7.0

61

14

8.5

71

22

3.1

2.0

0

D/T

=2.

0

0.0

00

.174

1.0

37

3.2

48

7.4

33

14

.18

223.7

06

35

.50

64

8.7

61

62

.69

4

76.5

72

89

.87

5102.4

58

114.3

61

12

5.6

21

136.2

72

146.3

48

155.8

78

164.8

94

173.4

22

181.4

90

188.9

46

195.3

02

199.9

20

202.1

94

20

1.5

55

197.8

11

19

1.4

79

183.3

96

174.3

55

20

2.3

2.4

4

Elec

tron

ical

ly co

mput

ed at intervals

H/T

- 0.

10,

and

expanded ma

nual

ly to ob

tain

peak value.


0.94

5945

945

applicable beyond this point.

Tab

le

23

. L

inear

Mod

el

Hydro

gra

phs

(S

= k

O);

k/T

=

2.0

0

n_ T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

6.3

45

24

.96

95

5.2

75

96.6

92

14

8.6

80

19

8.0

30

23

2.3

85

25

2.4

75

258.9

96

25

2.6

11

*240.2

90

228.5

71

217.4

24

206.8

20

196.7

34

187.1

38

178.0

11

169.3

29

161.0

70

153.2

14

14

5.7

42

138.6

35

131.8

74

125.4

43

11

9.3

26

113.5

06

107.9

71

102.7

05

97.6

95

D/T

=0.

1

0.0

00

2.1

65

14

.69

93

9.2

11

75. 1

16

121.8

61

174.5

85

21

6.3

78

243.5

43

25

6.7

94

25

6.8

11

246.4

01*

234.3

84

222.9

53

212.0

80

201.7

37

19

1.8

97

182.5

38

173.6

35

165.1

66

157.1

10

149.4

48

142.1

60

135.2

27

128.6

33

12

2.3

60

116.3

93

110.7

17

105.3

17

100.1

80

D/T

=0.

2

0.0

00

1.0

83

8.4

32

26

.95

55

7.1

64

98.4

89

148.2

23

195.4

81

229.9

60

250.1

68

256.8

02

251.6

06

24

0.3

92

*2

28

.66

8217.5

16

20

6.9

08

196.8

17

187.2

18

178.0

87

169.4

01

161.1

38

15

3.2

79

145.8

04

13

8.6

94

13

1.9

30

125.4

96

119.3

76

113.5

55

108.0

17

102.7

48

D/T

=0.

3

0.0

00

.722

5.6

21

18.6

92

43.0

09

78.7

29

123.8

54

17

0.9

41

211.5

02

238.9

05

252.3

82

253.3

35

245.8

65

234.5

79*

223.1

39

212.2

56

201.9

05

19

2.0

57

18

2.6

90

173.7

80

16

5.3

04

15

7.2

42

149.5

73

14

2.2

78

13

5.3

40

12

8.7

40

122.4

62

11

6.4

90

11

0.8

09

105.4

05

D/T

=0.

4

0.0

00

.54

14

.21

614.0

19

32.7

98

62.7

22

102.6

93

146.9

85

189.0

92

222.

825

243.3

81

25

0.8

87

248.5

97

24

0.1

37

228.

954*

21

7.7

88

207.1

67

197.0

63

187.4

52

178.3

09

169.6

13

161.3

40

153.4

71

145.9

86

138.8

67

13

2.0

95

125.6

53

11

9.5

25

113.6

96

108.1

51

D/T

=0.

5

0.0

00

.433

3.3

73

11.2

15

26.2

38

50.6

11

85.0

94

125.4

30

166.2

97

20

2.6

32

22

9.6

22

24

3.9

85

247.5

86

24

3.4

68

234.

525

223.5

11*

212.6

10

202.2

41

192.3

77

182.9

95

174.0

70

165.5

80

157.5

04

149.8

22

142.5

16

135.5

66

128.9

55

122.6

66

116.6

84

110.9

93

D/T

=0.

6

0.0

00

.361

2.8

11

9.3

46

21.8

65

42.1

75

71.2

73

106.9

75

145.1

16

181.3

79

211.6

62

23

2.4

18

24

2.3

85

243.4

81

238.2

37

229.0

60

21

8.2

42

*2

07

.59

8197.4

73

187.8

42

178.6

81

169.9

66

161.6

76

153.7

91

146.2

91

139.1

56

132.3

70

125.9

15

119.7

74

113.9

33

D/T

=0.

7

0.0

00

.309

2.4

09

8.0

11

18

.74

2

36.1

50

61.0

91

92.0

02

126.4

85

16

1.0

70

192.1

55

216.6

25

232.6

99

239.6

09

238.9

95

233.0

23

223.7

52

213.1

41*

202.7

46

192.8

58

183.4

52

174.5

05

165

. 994

157.8

98

150.1

97

142.8

72

135.9

04

129.2

77

122.9

72

116.9

75

D/T

=0.

8

0.0

00

.27

12.1

08

7.0

09

16.3

99

31.6

32

53.4

55

80.5

02

11

0.9

45

142.7

73

173.0

37

198.9

36

218.8

44

231.4

81

23

6.1

68

23

4.3

38

227.8

82

218.6

00

208.2

03*

198.0

49

188.3

90

179.2

02

170.4

62

162.1

48

154.2

40

146.7

18

139.5

62

132.7

56

126.2

82

120.1

23

D/T

=0.

9

0.0

00

.241

1.8

74

6.2

31

14.5

77

28.1

17

47.5

15

71.5

57

98.6

18

127.1

50

155.4

44

181.1

89

20

2.8

75

219.3

01

22

9.3

25

232.3

42

229.6

22

222.8

44

213.6

04

20

3.4

21

*

193.5

00

184.0

63

175.0

86

166.5

47

158.4

24

150.6

98

143.3

48

136.3

57

129.7

07

123.3

81

D/T

=1.0

0.0

00

.217

1.6

86

5.6

08

13.1

19

25.3

05

42.7

64

64.4

02

88.7

56

114.4

35

140.1

16

16

4.5

40

186.5

08

204.8

82

218.5

79

226.5

66

228.2

98

224.9

14

217.9

23

208.7

60

198.7

90*

189.0

95

179.8

72

17

1.1

00

162.7

55

154.8

18

147.2

67

140.0

85

133.2

53

126.7

54

D/T

=1.

5

0.0

00

.14

41

.12

43

.73

88

.74

6

16

.87

02

8.5

09

42

.93

459.1

71

76.2

90

93

.41

1109.8

38

125.4

63

140.3

27

154.4

65

167.9

14

180.5

63

191.7

52

200.7

14

20

6.7

17

209.0

67

207.3

92

202.4

44

195.2

23

186.6

79

177.7

15*

169.0

48

160.8

04

152.9

61

145.5

01

D/T

=2.

0

0.0

00

.108

.84

32

.80

46

.56

0

12.6

53

21.3

82

32.2

01

44

.37

857.2

18

70.0

58

82.3

78

94

.09

7105.2

45

115.8

49

125.9

36

135.5

31

14

4.6

58

153.3

39

16

1.5

98

169.4

53

176.8

17

183.1

90

187.9

91

190.6

67

190.6

92

187.7

82

182.4

99

175.5

88

167.7

57

a

Table

23. Linear Model

Hydrographs

(S = kO); k/T

= 2.00 Continued

n T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03,9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

Pea

kT

ime

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

.29

490.6

47

86.2

26

82.0

21

78

.02

1

74

.21

670.5

96

67.1

53

63.8

77

60

.76

1

57.7

98

54

.97

95

2.2

99

49.7

48

47.3

21

45 .

014

42.8

18

40

.73

03

8.7

44

36

.85

43

5.0

56

258.3

52

0.9

4

D/T

=0.

2

97

.73

792.9

70

88

.43

784.1

24

80.0

21

76.1

1872.4

06

68

.87

465.5

15

62

.31

9

59

.28

05

6.3

89

53

.63

95

1.0

24

48

.53

5

46.1

67

43

.91

641.7

74

39.7

37

37

.79

935

.955

25

6.8

02

1.0

0

D/T

=0.

3

100.2

64

95.3

74

90.7

22

86.2

98

82

.08

9

78.0

86

74.2

77

70.6

55

67.2

08

63.9

30

60.8

12

57

.84

655.0

25

52

.34

249.7

89

47.3

61

45.0

51

42.8

54

40.7

64

38.7

76

36.8

85

254.2

31

1.0

6

D/T

=0.

4

102.8

77

97

.85

993.0

86

88.5

46

84.2

28

80.1

21

76.2

12

72.4

96

68.9

60

65.5

97

62.3

97

59

.35

456.4

59

53.7

05

51.0

86

48.5

95

46.2

25

43

.97

041.8

26

39.7

86

37.8

46

251.0

94

1.1

2

D/T

=0.

5

105.5

80

100.4

31

95.5

33

90.8

74

86.4

42

82.2

26

78.2

16

74.4

01

70.7

72

67.3

20

64.0

37

60.9

14

57.9

43

55.1

17

52.4

29

49.8

72

47

.44

04

5.1

26

42.9

25

40.8

32

38.8

40

247.5

86

1.2

0

D/T

=0.

6

108.3

77

103.0

91

98.0

63

93.2

81

88.7

31

84.4

04

80.2

88

76.3

72

72.6

47

69.1

04

65.7

33

62.5

27

59.4

78

56.5

77

53.8

18

51.1

93

48

.69

646.3

22

44.0

63

41.9

14

39.8

69

243.9

42

1.2

6

D/T

=0.

7

111.2

70

10

5.8

44

100.6

82

95.7

72

91.1

01

86.6

58

82

.43

178

. 41

174.5

87

70.9

49

67.4

89

64.1

97

61

.06

658.0

88

55.2

55

52.5

60

49.9

97

47.5

59

45.2

39

43.0

33

40.9

34

240.1

42

1.3

4

D/T

=0.

8

11

4.2

65

108.6

92

103.3

92

98.3

49

93.5

53

88.9

90

84.6

50

80.5

22

76.5

94

72.8

59

69.3

05

65.9

25

62.7

10

59.6

51

56.7

42

53.9

75

51.3

43

48

.83

94

6.4

57

44.1

91

42

.03

6

236.2

61

1.4

2

D/T

=0.

9

117.3

64

111.6

41

106.1

96

101.0

17

96.0

90

91.4

04

86.9

46

82.7

06

78.6

72

74.8

35

71.1

8567.7

13

64.4

11

61.2

70

58.2

81

55

.43

952.7

35

50.1

63

47.7

17

45.3

90

43

.17

6

232.3

42

1.5

0

D/T

=1.

0

120.5

73

114.6

93

109.0

99

103.7

79

98.7

18

93.9

03

89.3

23

84.9

67

80.8

23

76.8

81

73.1

32

69.5

65

66

.17

262.9

45

59.8

75

56.9

55

54.1

77

51.5

35

49

.02

14

6.6

31

44.3

56

228.4

10

1.5

8

D/T

=1.

5

138.4

05

131.6

55

12

5.2

34

11

9.1

27

113.3

17

10

7.7

91

10

2.5

34

97.5

33

91.1

118

8.2

52

83.9

48

79

.85

375.9

59

72.2

54

68

.73

0

65.3

78

62

.19

05

9.1

57

56

.27

25

3.5

27

50.9

17

20

9.0

67

2.0

0

D/T

=2.

0

159.6

81-

151.8

94

144.4

86

137.4

39

130.7

36

124.3

60

11

8.2

95

112.5

26

107.0

38

101.8

18

96

.85

292.1

29

87

.63

68

3.3

62

79

.29

6

75

.42

971.7

50

68.2

51

64 .

922

61

.75

658.7

44

191.0

33

2.4

6

Summ

ariz


in

terv

als

H/T

= 0.

02.

*Rec

essi

on co

effi

cien

t 0.

9512

2903

ap

plic

able

be

yond

th

is po

int.

Tabl

e 24. Linear Model

Hydr

ogra

phs

(S = kcO

; k/T

= 2.20

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

5.7

36

22

.69

05

0.3

63

88

.27

9

135.9

82

181.5

65

21

3.6

50

232.8

36

239.6

96

23

4.7

79

*2

24

.34

5214.3

74

204.8

46

19

5.7

42

18

7.0

42

17

8.7

29

17

0.7

86

163.1

95

15

5.9

42

14

9.0

11

14

2.3

89

13

6.0

60

130.0

13

124.2

35

118.7

13

113.4

37

108.3

95

103.5

78

98.9

74

23

9.7

0.9

0

D/T

=0.

1

0.0

00

2.8

68

14

.21

33

6.5

27

69.3

21

112.1

31

158.7

74

197.6

07

223.2

43

236.2

66

237.2

38

22

9.5

62

*219.3

59

209.6

10

200.2

94

191.3

92

182.8

86

174.7

58

166.9

91

15

9.5

69

152.4

77

145.7

00

139.2

24

133.0

37

127.1

24

12

1.4

74

11

6.0

75

110.9

16

105.9

87

101.2

76

23

8.2

0.9

6

D/T

=0.

2

0.0

00

1.4

34

8.5

41

25.3

70

52.9

24

90.7

28

135.4

52

178.1

90

21

0.4

25

229.7

54

23

6.7

52

233.3

99

22

4.4

61

*21

4.48

5204.9

52

195.8

43

187.1

39

178.8

22

170.8

74

163.2

80

156.0

23

149.0

88

142.4

62

136.1

31

130.0

80

124.2

99

11

8.7

75

113.4

96

108.4

51

103.6

31

23

6.8

1.0

2

D/T

=0.

3

0.0

00

.956

5. 6

^41

7.8

69

40

.02

0

72.6

59

113.4

08

156.1

71

193.2

08

219.0

39

232.2

49

23

4.3

55

228.7

20

21

9.5

10

*209.7

54

200.4

32

191.5

24

183.0

12

174.8

78

167.1

06

159.6

79

152.5

82

145.8

00

139.3

20

133.1

28

127.2

12

121.5

58

11

6.1

55

110.9

93

106.0

60

234.5

1.0

6

D/T

=0.

4

0.0

00

.71

74.2

70

13

.40

230.7

32

58.0

48

94.1

88

134.4

58

172.9

39

203.9

72

223.5

88

231.5

77

230.6

06

223.9

42

21

4.7

06

*

205.1

64

196.0

46

18

7.3

32

179.0

07

171.0

51

163.4

48

156.1

84

149.2

43

142.6

10

136.2

71

130.2

15

124.4

28

118.8

97

113.6

13

108.5

64

23

2.0

1.1

4

D/T

=0.

5

0.0

00

.574

3.4

16

10.7

22

24.5

86

47.0

12

78.1

93

114.8

72

152.2

15

185.6

04

210.6

25

224.7

83

229.1

33

226.4

07

219.2

13

21

0.0

43

*200.7

08

191.7

88

183.2

64

175. 1

18

167.3

36

159.8

99

152.7

92

146.0

01

139.5

12

133.3

12

127.3

87

12

1.7

25

116.3

15

111.1

46

229.1

1.2

0

yi/

nre

- -

D/T

=0.

6

0.0

00

.478

2.8

47

8.9

35

20.4

88

39.1

77

65.6

39

98.0

95132.9

34

166.2

24

194.2

10

213.7

82

223.8

79

225.8

80

22

2.0

55

214.5

76

20

5.5

17

*196.3

83

187.6

55

17

9.3

15

171.3

45

163.7

30

156.4

53

149.4

99

142.8

55

136.5

06

130.4

39

124.6

42

119.1

02

113.8

09

22

6.0

1.2

8

D/T

=0.

7

0.0

00

.410

2.4

40

7.6

58

17.5

61

33

.58

056.2

62

84.4

92

115.9

74

147.6

95

176.3

68

199.2

60

214.5

78

221.8

41

222.2

24

217.6

74

210.0

49

20

1.1

23

*192.1

84

183.6

43

175.4

81

167.6

82

160.2

29

153.1

08

146.3

03

139.8

01

133.5

87

127.6

50

121.9

77

116.0

56

22

2.7

1.3

6

D/T

=0.

8

0.0

00

.35

92.1

35

6.7

01

15.3

66

29.3

82

49

.22

973.9

30

10

1.8

35

131.0

10

158.8

88

183.0

18

201.7

72

213.9

57

219.1

47

218.3

70

213.3

26

205.6

37

19

6.8

56

*188.1

07

179.7

47

171.7

58

164.1

24

156.8

30

149.8

60

143.1

99

13

6.8

35

130.7

53

124.9

42

119.3

89

21

9.4

1.4

4

D/T

=0.

9

0.0

00

.319

1.8

98

5.9

56

13.6

59

26.1

18

43

.75

965.7

16

90.5

20

116.7

72

142.8

13

166.7

41

187.0

56

202.6

43

212.4

39

216.0

63

214.4

28

209.0

40

201.3

43

19

2.7

13

*

18

4.1

48

175.9

64

168.1

43

160.6

70

153.5

29

146.7

06

140.1

86

13

3.9

55

128.0

02

122.3

13

21

6.1

1.5

2

D/T

=1.

0

0.0

00

.287

1.7

08

5.3

61

12.2

93

23.5

06

39.3

83

59

.14

481.4

68

105.0

95

128.8

19

151.4

88

172.0

03

189.3

11

202.4

08

210.3

35

212.7

46

210.4

61

204.8

36

197.1

66

188.6

90*

180.3

04

172.2

90

164.6

33

157.3

16

150.3

24

143.6

43

137.2

59

131.1

58

125.3

29

21

2.7

1.6

0

D/T

=1.

5

0.0

00

.191

1.1

39

3.5

74

8.1

95

15

.67

12

6.2

56

39

.42

95

4.3

12

70

.06

3

85

.87

5101.1

83

11

5.8

07

12

9.7

81

14

3.1

34

15

5.8

94

167.8

95

178.5

98

187.2

95

193.3

12

19

6.0

02

19

5.1

30

191.2

38

18

5.2

24

177.9

48

170.2

30*

16

2.6

64

155.4

35

148.5

27

14

1.9

26

196.1

2.0

2

D/T

=2.

0

0.0

00

.143

.85

42

.68

06

.14

6

11

.75

319.6

92

2Q.5

724

0.7

34

52.5

47

64

.40

97

5.8

87

86

.85

5Q

7.33

6107.3

51

116.9

20

12

6.0

65

134.8

02

143.1

52

151.1

30

158.7

54

165.8

96

172.1

46

176.9

72

179.8

62

180.3

29

178.1

94

173.8

60

167.9

97

161.2

47

18

0.5

2.4

6

Elec

tron

ical

ly computed at

intervals

H/T

=0.10, and

expanded ma

nual

ly to

ob

tain

peak value.


0.955555556

applicable beyond this po

int.

Tabl

e 25. Linear Mo

del

Hydr

ogra

phs

(S = ko); k/

T =2.40

O5

n. T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

5.2

68

20

.85

74

6.3

46

81

.33

0

125.4

23

167.7

16

19

7.7

47

216

. 015

223.0

03

21

9.1

68

*210.2

23

201.6

42

193.4

12

185.5

18

177.9

46

17

0.6

82

16

3.7

16

15

7.0

34

15

0.6

24

14

4.4

76

13

8.5

79

132.9

23

127.4

97

122.2

93

117.3

02

11

2.5

14

107.9

22

103.5

17

99.2

91

223.1

0.9

2

D/T

=0.

1

0.0

00

2.6

34

13.0

63

33.6

02

63

.83

8

103.3

77

14

6.5

70

182.7

31

20

6.8

81

219.5

09

221.0

86

21

4.6

96

*205.9

33

197.5

27

189.4

65

181.7

32

174.3

14

16

7.1

99

160.3

75

153.8

29

14

7.5

50

141.5

28

135.7

51

13

0.2

10

12

4.8

95

119.7

98

114.9

08

110.2

18

10

5.7

19

10

1.4

04

22

1.7

0.9

6

D/T

=0.

2

0.0

00

1.3

17

7.8

48

23

.33

24

8.7

20

83

.60

7124.9

73

16

4.6

50

194.8

06

21

3.1

95

22

0.2

97

217.8

91

21

0.3

14

*201.7

30

193.4

96

185.5

98

178.0

23

170.7

56

163.7

87

157.1

02

15

0.6

89

144.5

39

138.6

39

132.9

80

127.5

53

122.3

46

117.3

53

112.5

63

107.9

68

103.5

62

22

0.4

1.0

2

D/T

=0.

3

0.0

00

.878

5.2

32

16.4

33

36.8

34

66.9

39

104.5

95

144.2

26

178.7

27

203.0

41

21

5.8

25

218.4

30

213

. 905

20

6.0

52

*197.6

42

18

9.5

75

181.8

37

174.4

15

167.2

96

160.4

66

153.9

18

147.6

35

141.6

10

135.8

30

130.2

86

124.9

68

119.8

67

114.9

74

110.2

82

105.7

80

21

8.5

1.0

8

D/T

=0.

4

0.0

00

.659

3.9

24

12.3

25

28.2

84

53.4

70

86

.84

7124.1

29

159.8

90

188.9

23

207.5

52

215.5

43

215.3

06

209.8

10

20

1.9

05

*

193.6

64

185.7

59

178.1

77

170.9

05

163.9

29

157.2

38

150.8

20

144.6

64

138.7

60

133.0

96

127.6

64

122.4

53

117.4

55

112.6

61

108.0

62

21

6.2

1.1

4

D/T

-0.5

0.0

00

.52

73

.13

99

.86

022.6

27

43.3

03

72.0

90

106.0

23

140.6

79

171.8

13

195.3

55

208.9

80

213.6

21

211.7

50

205.7

41

19

7.8

70

*189.7

94

182.0

47

174.6

17

167.4

90

160.6

53

154.0

96

147.8

06

141.7

73

135.9

87

130.4

36

125.1

12

120.0

06

115.1

08

110.4

09

21

3.7

1.2

2

D/T

=0.

6

0.0

00

.439

2.6

16

8.2

16

18.8

56

36.0

85

60.5

14

90.5

30

122.8

33

153.8

18

180.0

26

198.5

79

208.4

73

210.9

39

208.0

36

201.7

40

19

3.9

44

*186.0

28

178.4

35

171.1

52

164.1

66

157.4

66

151.0

39

144.8

74

138.9

60

133.2

89

127.8

48

122.6

30

117.6

25

112.8

24

21

1.0

1.2

8

D/T

=0.

7

0.0

00

.376

2.2

42

7.0

43

16

.16

2

30.9

30

51.8

69

77.9

73

107.1

52

136.6

44

163.4

27

184.9

78

199.6

29

206.9

09

207.8

71

204.2

78

197.8

22

19

0.1

24

*182.3

63

174.9

20

167.7

80

160.9

32

154.3

64

148.0

63

142.0

20

136.2

23

130.6

63

125.3

30

120.2

14

115.3

07

20

8.0

1.3

6

D/T

=0.

8

0.0

00

.329

1.9

62

6.1

62

14

.14

2

27.0

64

45.3

85

68.2

27

94.0

87

121.1

96

147.1

99

169.8

36

187.5

98

199.3

66

204.7

28

204.6

03

200.5

32

193.9

94

186.4

05*

178.7

97

171.4

99

164.4

99

157.7

85

151.3

44

145.1

67

139.2

42

133.5

58

128.1

07

122.8

78

117.8

63

20

5.2

1.4

4

D/T

=0.

9

0.0

00

.29

31

.74

45

.47

812.5

71

24 .

05 7

40.3

43

60.6

46

83.6

33

108.0

23

132.2

95

154.6

99

173.8

47

188.7

01

198.2

66

202.1

73

201.2

38

196.8

29

190.2

58

182.7

85*

175.3

25

168.1

69

161.3

05

154.7

21

148.4

06

142.3

48

136.5

38

130.9

65

125.6

20

120.4

92

20

2.3

1.5

2

D/T

=1.

0

0.0

00

.26

31.5

70

4.9

30

11.3

14

21.6

51

36.3

08

54.5

81

75.2

70

97.2

20

119.3

29

140.5

35

159.8

22

176.2

15

188.7

77

196.6

13

199.3

87

197.8

34

193.1

84

186.6

15

179.2

62

*171.9

45

164.9

24

15

8.1

95

151.7

38

145.5

45

139.6

04

133.9

06

128.4

41

123.1

98

19

9.4

1.6

0

D/T

=1.

5

0.0

00

.176

1.0

46

3.2

87

7.5

42

14

.43

424.2

05

36

.38

85

0.1

80

64.8

14

79

.55

393.8

66

10

7.5

94

12

0.7

62

133.3

94

14

5.5

09

156.9

55

16

7.2

30

17

5.6

82

18

1.6

81

184.6

26

18

4.2

90

181.1

58

17

6.0

47

16

9.7

39

162.9

87*

15

6.3

34

14

9.9

53

143.8

33

13

7.9

62

184.9

2.0

4

D/T

=2.

0

0.0

00

.132

.785

2.4

65

5.6

57

10.8

26

18.1

54

27.2

91

37

.63

54

8.6

10

59.6

64

70

.39

98

0.6

96

90

.57

21

00

.04

5

109.1

32

11

7.8

48

126.2

08

134.2

27

141

. 918

149.2

95

156.2

40

162.3

75

167.2

05

170.2

58

171.0

79

169.4

96

165.8

70

160.8

12

154.9

07

17

1.1

2.4

8

g

O 0 t"1 W HN O o o W V W 50

Electronically computed at

intervals

H/T

= 0.10,

and

expa

nded

ma

nual

ly to ob

tain

pe

ak value.

'''R

eces

sion

coefficient

0.959183673

appl

icab

le be

yond

this point.

Tab

le 26. L

inear

Mod

el

Hydro

gra

phs

(S

= kO

);

k/T

=

2.6

0

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

Pea

kT

ime

D=

Inst

.

0.0

00

4.8

70

19

.29

84

2.9

22

75.3

95

11

6.3

84

15

5.8

26

18

4.0

39

201.4

46

208.4

56

20

5.4

60

*197.7

07

19

0.2

46

18

3.0

67

17

6.1

59

16

9.5

12

163.1

15

15

6.9

60

15

1.0

37

14

5.3

37

139.8

53

134.5

75

12

9.4

97

12

4.6

10

119.9

08

11

5.3

83

11

1.0

29

10

6.8

39

102.8

08

98.9

28

20

8.6

0.9

2

D/T

=0.

1

0.0

00

2.4

35

12

.08

431.1

10

59

.15

9

95.8

90

136.1

05

169.9

33

192.7

43

204.9

51

20

6.9

58

20

1.5

84

*193.9

77

186.6

57

179.6

13

172.8

35

166.3

13

160.0

37

153.9

98

148.1

87

14

2.5

95

137.2

14

132.0

36

127.0

54

122.2

59

117.6

46

113.2

06

108.9

34

104.8

23

100.8

68

20

7.3

0.9

6

D/T

=0.

2

0.0

00

1.2

18

7.2

60

21

.59

74

5.1

34

77.5

24

115.9

97

153.0

19

181.3

38

198.8

47

20

5.9

55

204.2

71

19

7.7

80

*190.3

17

18

3.1

35

176.2

24

169.5

74

163.1

75

157.0

18

151.0

92

145.3

91

139.9

04

13

4.6

25

12

9.5

45

124.6

56

119.9

52

115.4

26

111.0

70

106.

879"

10

2.8

46

20

6.2

1.0

2

D/T

=0.

3

0.0

00

.81

24

.84

015.2

10

34.1

18

62.0

53

97.0

51

133.9

76

166.2

60

189.2

09

201.5

51

204.4

98

200.8

40

194.0

72*

186.7

49

179.7

02

17

2.9

21

16

6.3

95

160.1

16

154.0

74

148.2

60

14

2.6

65

137.2

82

132.1

01

127.1

16

122.3

19

117.7

04

113.2

62

108.9

88

104.8

75

20

4.6

1.0

8

D/T

=0.

4

0.0

00

.609

3.6

30

11.4

07

26.1

97

49.5

61

80

.56

6115.2

72

148.6

68

175.9

33

193.6

46

201.5

59

201.8

67

197.2

94

190.4

58*

183.2

71

176.3

55

169.7

00

163.2

96

157.1

34

151.2

04

145.4

99

140.0

08

134.7

25

129.6

41

124.7

49

12

0.0

41

115.5

11

111.1

52

106.9

58

20

2.4

1.1

4

D/T

=0.

5

0.0

00

.48

72

.90

49

.12

620.9

58

40.1

36

66.8

70

98.4

39

130.7

66

159.9

24

182.1

38

195.2

34

200.0

42

198.8

25

193.7

58

186.9

33*

179.8

79

173.0

91

166.5

59

160.2

74

154.2

26

148.4

06

142.8

06

137.4

17

132.2

31

127.2

42

122.4

40

117.8

20

113.3

74

10

9.0

95

20

0.2

1.2

2

D/T

=0.

6

0.0

00

.40

62

.42

07.6

05

17.4

65

33.4

46

56.1

31

84.0

47

114.1

57

143.1

30

167.7

63

185.3

79

195.0

24

197.8

12

195.6

23

190.2

71

183.4

96*

176.5

72

169.9

09

163.4

97

157.3

28

151.3

91

145.6

78

140.1

81

134.8

91

129.8

01

124.9

02

120.1

89

115

. 654

111.2

89

19

7.8

1.3

0

D/T

=0.

7

0.0

00

.34

82

.07

46.5

18

14.9

70

28.6

68

48

.11

272.3

88

99.5

75

127.1

27

152.2

48

172.5

95

186.6

07

193.8

29

195.2

12

192.3

68

186.8

48

180.1

45*

173.3

47

166.8

06

160.5

11

154.4

54

14

8.6

26

143.0

17

137.6

20

132.4

27

127.4

30

122.6

21

117.9

94

11

3.5

41

19

5.3

1.3

8

D/T

=0.

8

0.0

00

.304

1.8

15

5.7

04

13.0

98

25.0

85

42.0

98

63.3

39

87.4

32

112.7

47

137.1

06

158.4

15

175.2

67

186.6

13

192.0

52

192.4

15

189.1

11

183.4

97

176.8

77*

170.2

02

163.7

79

157.5

99

151.6

52

145.9

29

140.4

22

135.1

23

130.0

24

125.1

18

120.3

96

115.8

53

192.7

1.4

6

D/T

=0.

9

0.0

00

.27

11.6

13

5.0

70

11.6

43

22.2

98

37

.42

056.3

02

77.7

18

100.4

90

12

3.2

15

144.2

70

162.3

67

176.5

33

185.8

36

189.9

17

189.5

15

185.8

81

180.2

19

173.6

89*

167.1

35

160.8

28

154.7

59

148.9

19

143.2

99

137.8

92

132.6

88

127.6

81

122.8

63

118.2

27

190.2

1.5

4

D/T

=1.

0

0.0

00

.244

1.4

52

4.5

63

10.4

79

20.0

68

33.6

78

50.6

72

69.9

46

90.4

41

111.1

37

131.0

52

149.2

41

164.7

96

176.8

41

184.5

36

187.5

56

186.5

67

182.6

92

177.0

16

17

0.5

80

*164.1

43

157.9

49

151.9

88

146.2

53

140.7

34

135.4

23

130.3

13

12

5.3

95

120.6

64

187.6

1.6

2

D/T

=1.

5

0.0

00

.162

.968

3.0

42

6.9

86

13.3

79

22

.45

23

3.7

81

46.6

31

60

.29

4

74

.09

18

7.5

30

10

0.4

62

11

2.9

06

12

4.8

80

13

6.4

02

147.3

27

15

7.1

91

165.3

83

17

1.3

19

17

4.4

32

17

4.5

06

17

1.9

80

16

7.6

01

162.0

88

15

6.1

34

*150.2

42

14

4.5

72

139.1

17

13

3.8

67

17

4.8

2.0

4

D/T

=2.

0

0.0

00

.12

2.7

26

2.2

81

5.2

39

10

.03

416.8

39

25.3

36

34.9

73

45

.22

0

55

.56

865.6

48

75.3

46

84

.67

993.6

60

102.3

02

110.6

17

118.6

19

126.3

20

133.7

28

140.8

58

147.5

97

153.5

95

158.3

92

161.5

47

162.6

35

161.4

90

158.4

40

154.0

44

14

8.8

40

162.6

2.5

0

Ele

ctr

onic

all

y

com

pute

d at

inte

rvals

H

/T

= 0

.10

, an

d ex

pan

ded

m

anual

ly to

o

bta

in

pea

k v

alu

e.

0.9

62264151

appli

cable

bey

ond th

is p

oin

t.*R

eces

sion co

eff

icie

nt

05

Tabl

e 27. Linear Mod

el Hydrographs

(S = kO

); k/T

= 2.

f

Oi

Oi

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

4.5

54

18.0

05

40

.03

970.3

56

108.6

67

145.5

82

17

2.1

46

188.7

21

195.6

60

19

3.2

98

*186.5

16

179.9

73

173.6

58

167.5

66

161.6

87

156.0

15

150.5

42

145.2

61

14

0.1

65

135.2

49

130.5

04

125.9

25

121.5

08

11

7.2

45

113.1

32

109.1

64

105.3

35

101.6

39

98.0

74

D/T

=0.

1

0.0

00

1.5

53

10

.58

028.3

48

54

.54

6

88.8

83

127.9

68

15

9.6

77

18

1.2

19

192.9

48

195.2

10

18

9.8

87

*1

83

.22

6176.7

97

170.5

94

164.6

10

15

8.8

34

15

3.2

63

147.8

86

14

2.6

99

137.6

93

132.8

63

12

8.2

01

123.7

04

119.3

64

11

5.1

77

111.1

37

107.2

39

103.4

77

99.8

47

D/T

=0.

2

0.0

00

.776

6.0

66

19

.46

44

1.4

47

71

.71

51

08

.42

6143.8

22

170.4

48

187.0

83

194.0

79

192.5

49

18

6.5

56

*1

80

.01

11

73

.69

6

167.6

02

16

1.7

22

156.0

49

15

0.5

75

145.2

93

140.1

96

135.2

78

130.5

32

125.9

53

121.5

34

117.2

71

113.1

57

109.1

88

10

5.3

58

101.6

62

D/T

=0.

3

0.0

00

.518

4.0

44

13.4

93

31.1

58

57.2

59

90.4

66

125.5

09

156.2

88

177.9

48

189.7

92

192.6

82

189.4

41

18

3.3

03

*176.8

72

170.6

67

16

4.6

79

158.9

02

153.3

28

147.9

49

142.7

59

137.7

51

132.9

19

128.2

56

123.7

56

119.4

15

115.2

26

111.1

84

107.2

84

103.5

21

D/T

=0.

4

0.0

00

.38

83

.03

310.1

20

23

.75

7

45.5

89

74

.93

6107.7

69

139.4

37

165.4

53

182.2

63

189.8

16

190.3

18

186.2

80

180.1

26*

173.8

07

16

7.7

09

161.8

25

156.1

48

15

0.6

71

145.3

85

140.2

85

135.3

64

130.6

15

126.0

33

121.6

12

117.3

46

113.2

29

109.2

57

105.4

25

D/T

=0.

5

0.0

00

.311

2.4

27

8.0

96

19.0

05

36.7

82

62.0

65

91.8

84

122.4

59

150.1

39

171.4

04

183

.788

188.4

98

187.6

14

183.1

43

177.0

23*

170.8

12

164.8

20

159.0

38

153.4

58

148.0

75

142.8

81

137.8

68

133.0

32

128.3

65

123.8

62

119.5

17

115.3

24

111.2

79

107.3

75

yi/

Hrg

-

D/T

=0.

6

0.0

00

.259

2.0

22

6.7

47

15.8

38

30.6

52

51

.98

078.3

34

106.7

73

134.2

07

157.6

51

17

4.4

75

183.6

94

186.5

48

184.7

77

180.0

54

173

. 991

*167.8

87

161.9

97

156.3

14

150.8

31

145.5

40

140.4

34

135.5

08

130.7

54

126.1

67

121.7

41

117.4

70

113.3

50

109.3

73

D/T

=0.

7

0.0

00

.222

1.7

33

5.7

83

13.5

75

26.2

73

44

.55

467.3

65

93.0

32

119.0

84

142.9

21

162.2

56

175.7

33

182.7

09

184.2

69

181.8

96

177.0

22

171.0

30*

165.0

30

159.2

40

153.6

54

148.2

64

143.0

63

138.0

44

133.2

01

128.5

29

124.0

20

119.6

69

115.4

71

111.4

21

D/T

=0.

8

0.0

00

.194

1.5

17

5.0

60

11.8

78

22

.98

938.9

85

58.9

44

81.5

97

10

5.5

21

12

8.6

00

148.7

92

164.8

77

17

5.8

66

181.1

95

181.8

11

179.0

13

174.0

53

168.1

37*

162.2

39

156.5

47

151.0

55

145.7

56

140.6

43

135.7

09

130.9

48

126.3

55

121.9

22

117.6

45

113.5

18

D/T

=0.

9

0.0

00

.17

31

.34

84

.49

810.5

59

20.4

34

34.6

53

52.3

95

72.5

30

93.9

69

115.4

86

135.4

09

152.6

18

166.2

02

175.2

80

179.3

52

179.2

58

176.1

52

171.1

45

165.3

11*

159.5

11

15 3

. 91

5148.5

16

143.3

06

138.2

79

133.4

28

128.7

47

124.2

31

119.8

73

115.6

68

D/T

=1.

0

0.0

00

.155

1.2

13

4.0

48

9.50

3

18.3

91

31.1

88

47.1

56

65.2

77

84.5

72

104.0

93

122.

927

140.1

91

155.0

36

166.6

41

174.2

14

177.3

00

176.6

59

173.3

26

168.3

01

16

2.5

49

*156.8

47

151.3

44

14

6.0

35

140.9

12

135.9

69

131.1

99

126.5

96

12

2.1

55

117.8

70

D/T

=1.

5

0.0

00

.104

.809

2.6

99

6.3

35

12.2

61

20.7

92

31

.43

74

3.5

18

56

.38

1

69

.39

582.0

54

94.2

69

106.0

56

117.4

29

128.4

03

138.8

88

148.4

00

156.3

70

16

2.2

46

165.5

00

165.8

27

163.7

28

159.8

94

154.9

88

149.6

53*

144.4

03

139.3

37

13

4.4

49

129.7

33

D/T

=2.

0

0.0

00

.078

.607

2.0

24

4.7

51

9.1

96

15

.59

423.5

78

32

.63

94

2.2

86

52.0

47

61.5

41

70.7

02

79

.54

28

8.0

72

96.3

02

10

4.2

44

111.9

07

11

9.3

01

12

6.4

36

13

3.3

21

139.8

87

145.7

68

150.5

35

15

3.7

76

15

5.0

91

15

4.2

50

151.6

28

14

7.7

40

143.0

85

Tabl

e 27. Linear Model

Hydrographs

(S = kO); k/T

= 2.80 Continued

11 T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

Pea

kT

ime

D=

Inst

.

94

.63

491.3

13

88.1

09

85 .

018

82.0

35

79.1

57

76.3

81

73

.70

171.1

15

68.6

20

66.2

13

63

.89

06

1.6

49

59

.48

65

7.4

01

55

.38

653.4

43

51.5

68

49

.75

94

8.0

13

46

.32

9

195.9

21

0.9

2

D/T

=0.

1

96 .

344'

92

.96

48

9.7

02

86.5

55

83

.51

8

80

.58

87

7.7

61

75.0

33

72

.40

16

9.8

61

67

.41

065

. 04

56

2.7

63

60

.56

158.4

36

56.3

86

54

.40

85

2.4

99

50

.65

748.8

80

47

.16

5

19

5.4

99

0.9

8

D/T

=0.

2

98.0

96

94

.65

49

1.3

33

88.1

28

85

.03

6

82

.05

379.1

74

76

.39

77

3.7

17

71

.13

0

68

.63

56

6.2

27

63.9

04

61.6

62

59

.49

9

57

.41

255.3

98

53.4

55

51

.58

049.7

70

48

.02

4

19

4.3

60

1.0

2

D/T

=0.

3

99.8

89

96.3

85

93.0

03

89.7

40

86.5

91

83.5

53

80.6

22

77.7

94

75.0

65

72.4

31

69.8

90

67.4

38

65.0

72

62.7

90

60.5

87

58.4

62

56. 4

1154.4

32

52.5

23

50

.68

048.9

02

192.7

00

1.0

8

D/T

=0.

4

101.7

27

98.1

58

94.7

14

91.3

91

88.1

85

85.0

90

82.1

05

79.2

25

76.4

46

73.7

64

71.1

76

68.6

79

66

.27

063.9

45

61.7

02

59

.53

75

7.4

49

55.4

33

53

.48

95

1.6

12

49.8

02

190.8

00

1.1

6

D/T

=0.

5

103.6

09

99.9

74

96.4

67

93.0

82

89.8

17

86.6

65

83.6

25

80.6

90

77.8

60

75

.12

9

72.4

93

69.9

50

67

.49

665.1

28

62.8

43

60.6

39

58.5

11

56.4

59

54.4

78

52.5

67

50

.72

3

188.7

03

1.2

2

^ji

/rtr

g -

D/T

=0.

6

105.5

37

101.8

35

98.2

62

94.8

15

91.4

88

88.2

78

85.1

81

82.1

93

79.3

09

76.5

27

73.8

42

71.2

52

68.7

52

66.3

40

64.0

13

61.7

67

59.6

00

57.5

10

55.4

92

53

.54

65

1.6

67

186.5

48

1.3

2

D/T

=0.

7

10

7.5

12

103.7

41

100.1

01

96.5

90

93.2

01

89.9

31

86.7

76

83.7

31

80.7

94

77.9

59

75.2

24

72.5

85

70.0

39

67.5

82

65 .

211

62.9

23

60.7

16

58.5

86

56.5

31

54.5

48

52.6

34

184.3

18

1.3

8

D/T

=0.

8

109.5

36

105.6

94

101.9

86

98.4

08

94.9

56

91

.62

48

8.4

10

85.3

08

82.3

15

79.4

27

76.6

41

73.9

52

71.3

58

68.8

54

66

.43

9

64.1

08

61.8

59

59.6

89

57.5

95

55.5

75

53.6

25

18

2.0

46

1.4

6

D/T

=0

.9

in.

610

107.6

95

103.9

17

100.2

71

96.7

54

93.3

59

90.0

84

86.9

23

83

.87

480.9

31

78.0

92

75.3

52

72.7

09

70.1

58

67.6

97

65.3

22

63.0

30

60.8

19

58

.68

656.6

27

54.6

40

179.7

49

1.5

4

D/T

XL

.O

11

3.7

35

109.7

46

105.8

96

102.1

81

98.5

96

95.1

3791.7

99

88.5

79

87.4

71

82.4

73

79.5

79

76.7

87

74.0

93

71.4

94

68.9

86

66.5

66

64.2

31

61.9

77

59.8

03

57.7

05

55

.68

1

177.4

37

1.6

2

D/T

-1.5

125.1

82

12

0.7

91

116.5

53

112.4

64

108.5

19

104.7

12

101.0

38

97

.49

494.0

74

90

.77

3

87

.58

98

4.5

16

81

.55

17

8.6

90

75.9

29

73

.26

670.6

95

68.2

15

65

.82

263.5

13

61.2

85

166.0

27

2.0

6

D/T

=2

.0

138.1

42-

13

3.2

96

12

8.6

20

124.1

08

11

9.7

54

11

5.5

53

11

1.4

99

107.5

88

10

3.8

13

100.1

71

96

.65

79

3.2

66

89

.99

486.8

38

83

.79

1

80

.85

178.0

15

75

.27

87

2.6

37

70

.08

96

7.6

30

15

5.0

91

2.5

0

Summarized fr

om co

mput

atio

ns at

intervals

H/T

- 0.02.

*Rec

essi

on coefficient

0.96491580 applicable beyond this point.

Tab

le 28. L

inea

r M

odel

H

ydro

gra

phs

(S

= kO

);

k/T

=

3.0

0

O5

00

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

4.2

54

16

.83

137.4

59

65

.87

2

101.8

18

136.5

40

16

1.6

60

177.4

94

184.3

46

182.5

12*

176.5

27

170.7

40

165.1

41

159.7

27

154.4

92

149.4

26

144.5

27

139.7

89

135.2

06

130.7

73

126.4

86

122.3

40

118.3

28

114.4

48

110.6

97

107.0

67

103.5

57

100.1

61

96.8

77

D/T

=0.

1

0.0

00

1.4

50

9.8

87

26.5

11

51

.05

3

83.2

53

119.9

60

149.8

55

170.3

08

181.6

27

184.1

13

179.5

04*

17

3.6

18

16

7.9

26

16

2.4

19

157.0

95

151.9

45

146.9

63

142.1

45

137.4

85

132.9

78

128.6

18

124.4

02

120.3

23

116.3

78

112.5

62

10

8.8

72

105.3

03

10

1.8

50

98

.51

0

D/T

=0.

2

0.0

00

.725

5.6

69

18

.19

93

8.7

82

67.1

53

10

1.6

06

134.9

08

16

0.0

81

17

5.9

67

18

2.8

70

181.

808

176.5

61*

17

0.7

72

16

5.1

73

15

9.7

57

15

4,5

20

14

9.4

54

14

4.5

54

139.8

15

13

5.2

31

130.7

98

12

6.5

10

122.3

63

11

8.3

51

11

4.4

70

11

0.7

17

107.0

88

10

3.5

76

10

0.1

80

D/T

=0.

3

0.0

00

.483

3.7

91

12

.61

62

9.1

51

53

.60

684.7

55

117.6

89

146.7

07

167.2

63

178.6

82

181.7

47

179.0

78

173.6

82*

167.9

87

162.4

80

157.1

53

152.0

01

147.0

18

142.1

98

137.5

36

133.0

27

128.6

66

124.4

48

120.3

68

116.4

21

112.6

04

108.9

12

105.3

42

101.8

87

D/T

=0.

4

0.0

00

.36

22

.83

49

.46

222.2

25

42

.67

670.1

92

101.0

30

130.8

44

155.4

37

171.4

76

178.8

88

179.7

15

176.2

90

170.8

67*

165.2

65

159.8

46

154.6

06

149.5

37

144.6

35

139.8

93

135.3

06

130.8

70

126.5

80

122.4

30

118.4

16

114.5

34

110.7

79

107.1

47

103.6

34

D/T

=0.

5

0.0

00

.290

2.2

67

7.5

70

17.7

80

34.4

31

58.1

33

86.1

26

11

4.8

86

14

1.0

00

161.1

72

17

3.0

81

177.8

34

177.3

57

173.5

16

168.1

12*

16

2.6

01

157.2

70

15

2.1

14

14

7.1

27

142.3

03

137.6

38

133.1

25

12

8.7

61

12

4.5

40

12

0.4

57

116.5

08

112.6

88

108.9

93

10

5.4

19

Vi/

nrg

-

D/T

=0

.6

0.0

00

.242

1.8

90

6.3

08

14

.81

7

28.6

92

48

.68

67

3.4

20

100.1

56

126.0

09

148.1

86

164.2

27

173.1

70

176.1

82

174.8

67

17

0.7

79

165.4

18*

159.9

94

154.7

49

149.6

75

144.7

68

140.0

22

135.4

32

130.9

92

126.6

97

122.5

43

118.5

26

114.6

40

110.8

81

107.2

46

D/T

=0.

7

0.0

00

.207

1.6

20

5.4

07

12

.70

0

24.5

93

41

.73

163.1

38

87.2

61

11

1.7

95

134.3

09

152.6

60

165.5

69

172.4

21

174.2

16

172.3

29

168.0

88

16

2.7

81

*157.4

44

152.2

83

147.2

90

142.4

61

137.7

91

133.2

73

128.9

04

124.6

78

120.5

90

116.6

37

112.8

13

109.1

14

D/T

=0.

8

0.0

00

.18

11

.41

74

.73

111.1

13

21.5

19

36.5

14

55.2

46

76.5

35

99.0

57

12

0.8

35

139.9

59

155.2

80

165.8

64

171.1

71

172.0

76

169.7

81

165.4

48

16

0.2

02

*154.9

50

149.8

70

144.9

56

140.2

04

135.6

07

131.1

62

126.8

61

122.7

02

118.6

80

114.7

89

11

1.0

25

D/T

=0.9

0.0

00

.161

1.2

60

4.2

05

9.8

78

19.1

28

32.4

57

49.1

08

68.0

31

88.

211

108.5

07

127.3

53

14

3.6

99

156.6

84

16

5.4

81

169.6

07

16

9.8

39

167.2

45

16

2.8

59

157.6

78*

152.5

08

147.5

08

142.6

72

137.9

95

13

3.4

71

129.0

95

12

4.8

62

12

0.7

69

11

6.8

09

112.9

80

D/T

=1.

0

0.0

00

.145

1.1

34

3.7

85

8.8

90

17.2

15

29

.21

144.1

97

61.2

28

79.3

90

97.8

02

115.6

07

131.9

80

146.1

21

157.2

58

164.6

42

16

7.8

41

167.5

52

164.7

35

160.3

21

15

5.2

08

*150.1

19

145.1

98

140.4

37

135.8

33

131.3

80

127.0

73

122.9

07

118.8

77

114.9

80

D/T

=1.

5

0.0

00

.097

.756

2.5

23

5.9

27

11.4

77

19

.47

42

9.4

65

40

.81

85

2.9

27

65

.20

17

7.1

68

88.7

42

99

.93

7110.7

65

12

1.2

38

131.2

71

14

0.4

10

14

8.1

18

153.8

81

157.1

96

157.7

73

156.0

76

152.7

44

148.3

94

14

3.6

24

*138.9

15

134.3

61

129.9

56

125.6

95

D/T

=2.

0

0.0

00

.072

.567

1.8

92

4.4

45

8.6

08

14.6

06

22

.09

83

0.6

14

39.6

95

48 .

901

57

.87

666.5

57

74.9

53

83

.07

4

90

.92

99

8.5

26

105.8

74

112.9

82

11

9.8

56

126.5

05

132.8

63

13

8.5

89

14

3.2

79

14

6.5

46

148

. Oil

14

7.4

57

14

5.2

29

14

1.8

06

13

7.6

50

Tabl

e 28. Linear Mo

del

Hydr

ogra

phs

(S = ko); k/T

= 3.00 Continued

IL

T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

Pea

kT

ime

D=

Inst

.

93

.70

190.6

29

87.6

59

84

.78

582.0

05

79.3

16

76.7

15

74.2

00

71.7

67

69

.41

4

67

.13

964.9

39

62

.80

960.7

50

58.7

58

56

.83

25

4.9

68

53.1

66

51.4

23

49

.73

74

8.1

06

18

4.6

65

0.9

2

D/T

=0.1

95

.28

19

2.1

56

89

.13

68

6 . 2

148

3.3

88

80

.65

478.0

08

75

.45

172.9

77

70

.58

4

68

.27

16

6.0

33

63

.86

86

1.7

74

59.7

49

57.7

90

55.8

95

54

.06

35

2.2

90

50.5

76

48.9

17

184.3

08

0.9

8

D/T

=0.

2

96.8

95

93.7

18

90

.64

68

7.6

75

84

.80

1

82

.02

179.3

31

76

.73

07

4.2

14

71.7

80

69.4

27

67

.15

264.9

50

62

.82

16

0.7

61

58

.76

95

6.8

42

54

.97

95

3.1

76

51.4

33

49

.74

7

183.2

33

1.0

4

D/T

=0.

3

98.5

47

95.3

16

92.1

91

89.1

69

86.2

46

83.4

19

80.6

83

78.0

38

75.4

79

73 .

004

70.6

11

68.2

96

66.0

57

63.8

92

61.7

97

59.7

71

57.8

11

55.9

16

54.0

83

52.3

10

50.5

94

181.7

47

1.1

0

D/T

=0.

4

100.2

36

96.9

49

93.7

71

90.6

97

87.7

24

84.8

48

82.0

66

79.3

75

Ik.

112

74.2

55

71.8

21

69.4

66

67.1

89

64.9

86

62.8

56

60.7

95

58.8

02

56.8

74

55

.00

953.2

06

51.4

62

180.0

23

1.1

6

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

.38

7.2

59

.235

.310

.480

.74

3.0

96

.535

.058

.66

3.3

47

.106

.939

.843

.815

.854

.95

7.1

23

.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

105.5

37

102.0

76

98.7

30

95.4

93

92.3

62

89.3

34

86.4

05

83.5

73

80.8

33

78.1

82

75.6

19

73.1

40

70.7

42

68.4

22

66.1

79

64.0

10

61.9

11

59.8

82

57.9

18

56.0

19

54.1

83

174.2

16

1.4

0

D/T

=0.

8

107.3

85

103.8

64

100.4

59

97.1

65

93.9

80

90.8

99

87.9

18

85

.03

68

2.2

48

79.5

52

76.9

43

74.4

21

71.9

81

69

.62

167.3

38

65

.13

162.9

95

60.9

30

58.9

33

57.0

00

55

.13

2

172.1

89

1.4

8

D/T

=0

.9

109.

105.

102.

98.

95.

92.

89.

86.

83.

80.

78.

75.

73.

70.

68.

66.

64.

62.

59.

58.

56.

170.

1.27

669

222

887

663

4

499

466

533

696

952

298

731

248

847

524

277

104

003

970

004

102

144

56

D/T

=1.

0

111.2

10

107.5

64

104.0

37

100.6

26

97.3

27

94.1

36

91.0

50

88.0

65

85.1

78

82.3

85

79.6

84

77.0

72

74.5

45

72.1

01

69.7

37

67.4

50

65.2

39

63.1

00

61.0

32

59

.03

157.0

95

168.0

89

1.6

4

D/T

=1.

5

121

117

113

110

106

102 99 96 93 90 87 84 81 78 76 73 71 68 66 64 62

157

.57

4.5

88.7

33

.005

.398

.910

.536

.272

.116

.06

3

.110

.254

.492

.820

.236

.73

7.3

19

.981

.720

.53

2.4

16

.86

0.0

8

D/T

=2

.0

133. 2

09*

12

8.8

42

12

4.6

17

12

0.5

32

11

6.5

80

112.7

58

10

9.0

61

10

5.4

86

10

2.0

27

98.6

82

95

.44

792.3

18

89

.29

18

6.3

64

83

.53

2

80

.79

37

8.1

45

75.5

83

73

.10

570.7

08

68

.39

0

148.0

58

2.5

2

Summ

ariz

ed from co

mput

atio

ns at

intervals

H/T

= 0.

02.

-Rec

essi

on coefficient

0.96

7215

98 ap

plic

able

be

yond

th

is point.

CO

Table

29. Nonlinear Mo

del

Hydr

ogra

phs

(S =

kOx);

x

= 0.

5; k/

/APe/T

=

2.0

n.

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

52.7

53

325.1

89

66

2.1

43

945.1

26

12

14

.25

81147.6

90

84

8.5

83

614.8

70

375.0

86

154.3

61

50

.61

12

6.6

16

16

.58

01

1.3

59

8.2

81

6.3

10

4.9

71

4.0

18

3.3

16

2.7

83

2.3

70

2.0

42

1.7

78

1.5

62

1.3

84

1.2

34

1.1

07

.999

.906

D/T

=0.

1

0.0

00

15

.99

2174.8

81

50

2.0

00

807.7

67

10

80

.04

51182.3

31

995.7

87

732.2

88

493.3

02

261.5

54

102.7

78

41.5

01

23

.13

21

4.8

55

10

.37

57

.66

55.8

99

4.6

82

3.8

07

3.1

57

2.6

61

2.2

74

1.9

65

1.7

15

1.5

11

1.3

40

1.1

97

1.0

76

.973

D/T

=0.

2

0.0

00

4.5

07

82

.15

2338.5

50

66

2.4

99

94

5.0

75

1132.6

59

10

88

.17

68

62

.96

3612.2

86

375.3

55

18

0.7

50

73

.66

43

4.1

07

20

.02

7

13

.24

29

.42

77

.06

05

.48

84

.39

0

3.5

93

2.9

95

2.5

35

2.1

74

1.8

85

1.6

50

1.4

56

1.2

95

1.1

59

1.0

44

D/T

=0.

3

0.0

00

2.0

96

42.3

02

213.8

09

508.5

07

807.2

73

1026.7

75

1087.1

79

966.9

03

738.3

99

492.4

18

281.4

17

135.6

34

60.0

96

29.9

07

18.1

35

12.2

22

8.8

11

6.6

60

5.2

13

4.1

93

3.4

46

2.8

83

2.4

48

2.1

05

1.8

29

1.6

04

1.4

18

1.2

63

1.1

32

D/T

=0.

4

0.0

00

1.2

07

25.9

07

141.2

07

374.6

91

66

2.8

99

905.

938

10

20

.66

29

95

.63

6845.6

49

615.3

91

391.1

71

221.7

99

111.1

23

52.0

20

27.1

25

16.8

25

11.4

96

8.3

67

6.3

67

5.0

10

4.0

46

3.3

37

2.8

00

2.3

82

2.0

52

1.7

86

1.5

69

1.3

89

1.2

39

D/T

=0.

5

0.0

00

.784

17.5

34

101.0

66

282.3

65

530.1

21

775.1

79

927.4

06

960.9

49

891.5

73

723.7

23

508.2

47

321.0

03

185.2

43

95.4

45

46.5

17

25.0

92

15.8

35

10

.93

88.0

20

6.1

36

4.8

49

3.9

29

3.2

49

2.7

32

2.3

29

2.0

10

1.7

52

1.5

41

1.3

66

D/T

=0.

6

0

12 7622

2

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

.89

8.9

94

.591

.80

4.3

76

.455

.050

.17

4

.415

.456

.515

.049

.487

.736

.946

.715

.832

.176

.675

.285

.974

.723

.517

D/T

=0.

7

0.0

00

.407

9.5

94

59

.73

6180.6

27

358.5

66

549.7

87

707.3

64

806.3

46

833.8

65

78

5.6

83

677.3

20

530.2

41

373.3

42

239.9

57

141.8

16

76.1

64

39.3

02

22.2

37

14.3

98

10.1

09

7.4

96

5.7

85

4.6

01

3.7

48

3.1

13

2.6

27

2.2

46

1.9

43

1.6

98

D/T

=0.

8

0.0

00

.31

37

.51

74

8.1

47

150.1

93

305.4

83

474.8

49

615.0

39

712.7

22

765.2

02

757.1

61

693.6

22

594.5

06

467.5

49

330.8

00

214.0

33

127.7

38

69.7

22

36.7

60

21.1

72

13.8

46

9.7

85

7.2

90

5.6

45

4.5

02

3.6

75

3.0

58

2.5

84

2.2

12

1.9

16

D/T

=0.9

0.0

00

.248

6.0

50

39.6

80

12

7.1

84

264.5

02

41

6.6

81

543.2

90

631.5

25

687.3

61

704.8

07

677.9

76

617.3

30

530.6

24

41

8.4

60

297.4

37

193.

611

116.5

64

64.5

27

34.6

58

20.2

68

13.3

70

9.5

03

7.1

09

5.5

22

4.4

14

3.6

10

3.0

08

2.5

46

2.1

82

D/T

=1.

0

0.0

00

.202

4.9

75

33.2

93

109.2

92

231.9

87

370.1

99

485.9

26

566.6

12

61

7.6

08

641.2

82

638.6

00

61

0.2

35

556.8

47

479.3

05

379.0

15

27

0.5

38

177.0

80

107.4

58

60.2

34

32.8

77

19.4

83

12.9

52

9.2

53

6.9

47

5.4

11

4.3

35

3.5

52

2.9

64

2.5

11

D/T

=1.

5

0.0

00

.091

2.3

19

16

.61

15

9.4

79

136.9

50

231.4

49

31

3.9

53

371.9

74

408.4

84

426.1

05

430.2

92

43

0.2

21

430.2

22

430.2

22

430.2

22

425.8

47

408.5

31

37

4.4

78

324.4

23

25

9.3

83

188.3

49

126.0

86

78

.93

14

6.3

72

26.8

33

16

.68

411.4

17

8.3

18

6.3

35

D/T

=2.

0

0.0

00

.051

1.3

37

9.9

63

37

.70

2

92.0

07

16

2.9

94

228.0

03

274.6

22

303.9

54

318.4

70

322.4

34

322.6

54

322.6

66

322.6

67

322.6

67

322.6

67

322.6

67

322.6

67

322.6

67

322.6

67

319.6

17

307.3

30

28

2.7

42

246.2

05

198.5

14

14

6.0

37

99.4

35

63.6

72

38

.63

0

Tabl

e 20. Nonlinear Mo

del

Hydr

ogra

phs

(S = kO

x);

= 2.0 Continued

n_ T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

0.8

26

.755

.694

.639

.591

.548

.510

.475

.444

.416

.390

.367

.346

.326

.308

.292

.277

.263

.250

.238

.226

D/T

=0.1

0.8

83

.806

.738

.678

.626

.579

.537

.500

.466

.436

.408

.384

.361

.340

.321

.304

.288

.273

.259

.246

.235

D/T

=0.

2

0.9

44

.859

.784

.719

.662

.611

.566

.526

.489

.457

.427

.401

.377

.354

.334

.316

.299

.283

.269

.255

.243

D/T

=0.

3

1.0

20

.92

4.8

41

.76

9.7

06

.650

.601

.557

.51

7.4

82

.450

.421

.395

.371

.350

.330

.31

2.2

95.2

80

.265

.25

2

D/T

=0.

4

1.1

11

1.0

03

.909

.82

8.7

58

.696

.641

.59

3.5

49

.511

.476

.445

.41

7.3

91

.368

.346

.32

7.3

09

.292

.277

.26

3

D/T

=0.

5

1.2

19

1.0

94

.98

8.8

97

.817

.748

.687

.634

.586

.54

3

.505

.471

.441

.413

.387

.36

4.3

43.3

24

.306

.290

.275

D/T

=0.

6

1.3

46

1.2

02

1.0

80

.976

.886

.808

.740

.680

.62

7.5

80

.53

8.5

01

.467

.437

.409

.384

.362

.341

.32

2.3

04

.288

D/T

=0.

7

1.4

96

1.3

28

1.1

87

1.0

67

.965

.87

7.8

00

.73

3.6

74

.62

2

.575

.534

.49

7.4

64

.434

.406

.382

.359

.339

.320

.302

D/T

=0.

8

1.6

75

1.4

77

1.3

13

1.1

74

1.0

56

.95

5.8

68

.793

.726

.668

.617

.571

.530

.493

.461

.431

.404

.379

.357

.33

7.3

18

D/T

=0.

9

1.8

91

1.6

55

1.4

61

1.2

99

1.1

62

1.0

46

.947

.861

.78

6.7

21

.663

.612

.567

.527

.490

.458

.428

.401

.377

.355

.335

D/T

=1.

0

2.1

55

1.8

69

1.6

37

1.4

46

1.2

86

1.1

52

1.0

37

.939

.854

.78

0

.715

.659

.608

.563

.523

.48

7.4

55.4

26

.399

.375

.353

D/T

=1.

5

4.9

87

4.0

30

3.3

25

2.7

90

2.3

75

2.0

46

1.7

82

1.5

65

1.3

86

1.2

36

1.1

09

1.0

01

.907

.82

7.7

56

.694

.64

0.5

92

.549

.510

.475

D/T

=2

.0

23

.22

61

4.9

03

10

.40

27

.68

35

.91

0

4.6

90

3.8

13

3.1

62

2.6

65

2.2

76

1.9

67

1.7

17

1.5

12

1.3

42

1.1

99

1.0

77

.973

.884

.806

.73

8.6

79

O f-1 % > w 3' s 0 O w > h0 w 02

Tabl

e 30. Nonlinear Mo

del

Hydrographs

(S = kO

x); x

= 0.

5; k/

/APe/T =

5.0

to

11 T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

12.1

16

115.3

85

366.4

50

706.4

20

1044.8

20

1137.7

41

953.

715

72

7.3

38

50

1.8

48

28

9.6

55

156.4

16

98.7

70

68.2

46

50

.05

0

38

.30

430.2

72

24.5

34

20.2

90

17

.06

1

14

.54

812.5

53

10

.94

29

.62

38

.53

0

7.6

13

6.8

36

6.1

72

5.6

01

5.1

06

D/T

=0.

1

0.0

00

3.1

72

51

.38

0229.4

64

53

5.9

45

88

0.9

65

10

97

.69

61

04

6.1

26

839.3

63

613.0

39

39

3.2

27

222.4

78

129.2

15

84

.90

760.1

90

44

.94

23

4.8

59

27 o

838

22

.74

91

8.9

42

16

.01

91

3.7

25

11

.89

11

0.4

03

9.1

78

8.1

57

7.2

98

6.5

68

5.9

42

5.4

02

D/T

=0.

2

0.0

00

.813

20.4

68

12

8.3

57

377.8

82

712.4

60

996.2

06

1075.2

02

94

1.7

85

724.7

63

501.1

78

306.3

40

17

6.4

06

108.4

28

73.6

76

53

.41

440.5

34

31

. 828

25

.66

321.1

35

17.7

11

15

.05

812.9

61

11

.27

39

.89

6

8.7

57

7.8

04

6.9

99

6.3

12

5.7

21

D/T

=0.

3

0.0

00

.36

49

.46

069.9

13

250.1

43

549.6

83

854.3

62

1022.4

26

99

6.8

48

'829.2

58

610.6

30

404.9

77

247.1

58

148.1

23

94.6

36

65.8

77

48.5

60

37.3

06

29.5

71

24.0

22

19.9

05

16.7

64

14

.31

412.3

65

10

.79

0

9.4

97

8.4

25

7.5

24

6.7

60

6.1

08

D/T

=0.

4

0.0

00

.20

65

.43

141.5

18

163.2

94

406.6

00

70

4.2

53

91Q

.135

981.0

19

897.5

51

71

4.8

43

508.6

28

334.6

06

208.7

01

129.2

39

84.9

19

60.1

97

44.9

47

34.8

63

27.8

40

22.7

51

18.9

43

16.0

20

13.7

25

11.8

92

10.4

03

9.1

78

8.1

57

7.2

98

6.5

68

D/T

=0.

5

0.0

00

.132

3.5

21

27.5

03

111.9

58

297.6

04

561.9

32

79

5.9

13

913.3

57

905.9

14

790. 1

15609.5

29

429.8

40

285.9

74

182.2

10

115.7

71

77.7

12

55

.87

642.1

49

32.9

45

26.4

68

21.7

35

18.1

70

15.4

17

13

.24

7

11.5

05

10

.08

78

.91

57

.93

77

.11

1

yi/

nre

-

D/T

=0.

6

0.0

00

.092

2.4

66

19.5

58

81

.66

6

22

4. 1

13443.8

03

669.5

70

81

9.5

35

865.3

90

814.4

01

68

7.0

85

524.6

99

372.4

46

251.0

34

162.8

89

105.6

45

72.1

26

52

.46

039.9

05

31.3

90

25.3

46

20.8

99

17

.53

014.9

16

12.8

47

11.1

81

9.8

20

8.6

94

7.7

51

D/T

=0.

7

0.0

00

.068

1.8

23

14.6

21

62.2

35

175.1

93

356.4

93

557.0

81

715.1

71

796.4

41

793.8

43

72

1.1

22

600.7

77

460.2

42

329.5

33

224.7

81

148.1

23

97.7

06

67.6

39

49.6

70

38.0

50

30.0

94

24.4

04

20.1

92

16.9

86

14.4

89

12.5

05

10.9

04

9.5

92

8.5

03

D/T

=0.

8

0.0

00

.052

1.4

02

11.3

44

49.0

23

140.9

19

293.4

41

468.3

75

61

6.7

32

713.0

44

74

4.7

59

71

4.6

27

639.5

81

532.8

01

410.4

19

29

6.3

28

204.2

89

136.4

13

91.2

71

63.9

29

47.3

29

36.4

78

28.9

86

23.5

94

19.5

82

16.5

15

14.1

17

12.2

07

10.6

61

9.3

91

D/T

=0.9

0.0

00

.041

1.1

12

9.0

58

39.6

26

115.8

86

246.1

35

400.3

98

535.3

20

630.3

11

679.3

23

680.6

00

642.0

32

573.1

84

478.7

66

370.8

88

26

9.8

46

187.7

97

126.8

54

85.9

21

60.7

90

45.3

28

35.1

22

28.0

25

22

.88

7

19.0

47

16.1

00

13.7

89

11.9

43

10

.44

5

D/T

=1.

0

0.0

00

.03

3.9

037

.39

932.7

00

97.0

35

209.6

64

346.9

19

470.4

30

559.4

84

611.2

66

629.6

32

618.5

94

581.0

10

519.0

64

434.9

64

338.7

60

248.1

96

174.1

97

118.8

71

81.3

80

58.0

87

43.5

86

33.9

33

27.1

76

22.2

60

18.5

71

15.7

30

13.4

95

11

.70

6

D/T

=1.

5

0.0

00

.015

.405

3.3

77

15

.40

7

47

.98

81

10

.13

9194.2

48

27

8.9

63

346.7

71

390.6

92

413.3

22

423.1

34

427.2

73

428.9

99

429.7

16

427.4

93

416.5

54

392.3

09

35

3.5

04

300.5

57

23

9.1

45

180.0

48

13

0.5

25

92.5

08

65

.85

648.5

47

37

.29

72

9.5

65

24

.01

8

D/T

=2 .

0

0.0

00

.00

8.2

29

1.9

25

8.9

36

28

.60

668.1

01

12

5.2

43

187.4

47

241.3

94

279.4

81

30

1.4

38

312.4

56

317.8

06

32

0.3

65

321.5

79

322.1

53

322

. 424

322.5

52

322.6

13

322.6

41

320.9

51

313.3

78

296.4

71

269.0

54

231.2

41

18

6.8

52

14

3.4

28

10

6.3

47

77.3

2^9

Table

30. Nonlinear

Mode

l Hydrographs

fS = kOx%

);AP

e/T

=

5.0 Continued

n.

T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

4.6

73

4.2

93

3.9

58

3.6

61

3.3

96

3.1

58

2.9

45

2.7

53

2.5

79

2.4

20

2.2

76

2.1

45

2.0

25

1.9

14

1.8

12

1.7

18

1.6

32

1.5

51

1.4

77

1.4

08

1.3

43

D/T

=0.1

4.9

32

4.5

21

4.15

Q3

.83

93

.55

5

3.3

01

3.0

73

2.8

68

2.6

83

2.5

16

2.3

63

2.2

24

2.0

97

1.9

81

1.8

74

1.7

75

1.6

84

1.6

00

1.5

22

1.4

49

1.3

82

D/T

=0.

2

5.2

10

4.7

65

4.3

74

4.0

29

3.7

24

3.4

52

3.2

09

2.9

91

2.7

94

2.6

16

2.4

54

2.3

07

2.1

73

2.0

50

1.9

38

1.8

34

1.7

39

1.6

50

1.5

69

1.4

93

1.4

23

D/T

=0.

3

5.5

45

5.0

57

4.6

30

4.2

56

3.9

25

3.6

31

3.3

69

3.1

34

2.9

24

2.7

33

2.5

61

2.4

04

2.2

62

2.1

32

2.0

12

1.9

03

1.8

02

1.7

09

1.6

23

1.5

43

1.4

69

D/T

=0.

4

5.9

42

5.4

02

4.9

32

4.5

21

4.1

59

3.8

39

3.5

55

3.3

01

3.0

73

2.8

68

2.6

83

2.5

16

2.3

63

2.2

24

2.0

97

1.9

81

1.8

74

1.7

75

1.6

84

1.6

00

1.5

22

D/T

=0.

5

6.4

08

5.8

05

5.2

83

4.8

28

4.4

30

4.0

79

3.7

68

3.4

91

3.2

44

3.0

22

2.8

22

2.6

42

2.4

78

2.3

29

2.1

93

2.0

68

1.9

54

1.8

49

1.7

53

1.6

63

1.5

81

^i/

nt

e -

D/T

=0.

6

6.9

53

6.2

73

5.6

88

5.1

81

4.7

39

4.3

52

4.0

10

3.7

07

3.4

37

3.1

95

2.9

78

2.7

82

2.6

06

2.4

45

2.2

99

2.1

65

2.0

43

1.9

31

1.8

28

1.7

33

1.6

45

D/T

=0.

7

7.5

90

6.8

17

6.1

56

5.5

87

5.0

93

4.6

62

4.2

84

3.9

50

3.6

53

3.3

89

3.1

52

2.9

40

2.7

48

2.5

74

2.4

16

2.2

73

2.1

42

2.0

21

1.9

11

1.8

10

1.7

16

D/T

=0.

8

8.3

36

7.4

49

6.6

97

6.0

53

5.4

98

5.0

15

4.5

94

4.2

24

3.8

97

3.6

06

3.3

47

3.1

14

2.9

05

2.7

17

2.5

46

2.3

91

2.2

50

2.1

20

2.0

02

1.8

93

1.7

93

D/T

=0

.9

9.2

13

8.1

86

7.3

23

6.5

89

5.9

60

5.4

17

4.9

46

4.5

33

4.1

70

3.8

49

3.5

63

3.3

08

3.0

80

2.8

75

2.6

89

2.5

21

2.3

68

2.2

28

2.1

01

1.9

84

1.8

77

D/T

=1

.0

10.2

51

9.0

52

8.0

52

7.2

09

6.4

92

5.8

76

5.3

45

4.8

82

4.4

77

4.1

21

3.8

05

3.5

24

3.2

74

3.0

49

2.8

46

2.6

63

2.4

98

2.3

47

2.2

09

2.0

83

1.9

68

D/T

=1.

5

19

.90

11

6.7

62

14 .

312

12

.36

41

0.7

88

9.4

96

8.4

24

7.5

23

6.7

60

6.1

07

5.5

45

5.0

56

4.6

30

4.2

55

3.9

24

3.6

31

3.3

69

3.1

34

2.9

23

2.7

33

2.5

61

D/T

=2

.0

56

.49

24

2.5

50

33.2

22

26

.66

72

1.8

83

18

.28

315.5

05

13

.31

71

1.5

62

10

.13

3

8.9

54

7.9

69

7.1

39

6.4

32

5.8

25

5.3

00

4.8

43

4.4

43

4.0

90

3.7

78

3.5

01

S3 00

Table

31. Nonlinear M

odel Hydrographs

(S = kO

x);

".

T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

6.4

67

67

.21

3241.4

53

53

1.7

89

878.1

63

1052.4

19

959.5

26

773.4

97

564.9

93

360.0

90

21

9.2

45

14

8.1

20

10

6.9

66

80

.94

2

63.4

19

51

.04

741.9

83

35

.14

129.8

48

25.6

70

22.3

12

19

.57

41

7.3

12

15

.42

0

13

.82

31

2.4

61

11

.29

21

0.2

80

9.3

98

D/T

=0.

1

0.0

00

1.6

58

28.6

93

142.5

13

379.4

32

705.4

89

972.4

42

10

09

.72

7866.4

68

667.8

87

460.2

79

288.8

53

184.7

46

12

8.6

93

94.9

10

72

.94

05

7.8

32

46

.99

138

. 94

33

2.8

04

28

.01

324.2

02

21.1

20

18

.59

21

6.4

93

14 .

731

13

.23

711

. 95

910.8

58

9.9

02

D/T

O.2

0.0

00

,420

11.0

69

75

.78

1251.8

37

540.3

28

844.5

32

997.2

71

939.5

34

766.3

10

56

2.2

43

373.0

08

23

6.9

45

15

7.7

41

11

2.7

93

84

.74

366.0

38

52.9

29

43

.38

13

6.2

08

30

.68

22

6.3

33

22

.84

920.0

15

17.6

77

15.7

27

14

.08

312.6

84

11.4

84

10.4

47

D/T

=0.

3

0.0

00

.18

75

.02

839.8

17

158.4

34

394.9

33

69

1.9

92

912.9

82

959.5

40

84

8.2

85

66

1.1

21

467.7

91

309.4

79

202.3

47

138.7

21

10

1.1

85

77.1

29

60.7

70

49

.13

140.5

51

34.0

43

28.9

88

24.9

83

21.7

55

19

.11

6

16.9

30

15.0

99

13.5

50

12.2

28

11.0

90

D/T

=0.

4

0.0

00

.106

2.8

60

23.1

07

99.6

37

27

8.8

38

545.0

80

79

0.5

41

91

3.9

88

888.3

06

747.3

59

563.1

08

394.7

80

265.3

34

177.9

29

124.7

39

92.4

09

71.2

56

56

.64

346.1

20

38.2

86

32

.29

627.6

12

23.8

79

20.8

57

18.3

75

16

.31

214.5

78

13

.10

611.8

47

D/T

=0.

5

0.0

00

.068

1.8

42

15.0

77

66.5

04

196.8

11

41

7.8

15

659.6

74

825.2

14

871.2

00

799.5

36

649.3

61

483.5

57

34

1.5

25

233.5

03

159.8

66

114.0

68

85.5

69

66.6

05

53.3

35

43.6

81

36.4

37

30.8

60

26.4

75

22.9

63

20.1

08

17.7

55

15.7

92

14.1

38

12

.73

2

m/r

t±-e

-

D/T

=0.

6

0.0

00

.047

1.2

85

10.6

13

47.5

56

144.0

77

319.2

74

53

6.7

21

718.6

94

811.1

58

802.3

56

707.7

73

566.3

59

422.8

98

301.8

55

209.5

90

145.9

65

105.6

49

80

.07

762.8

20

50.6

15

41.6

60

34.8

94

29.6

55

25

.51

6

22

.18

719.4

72

17.2

26

15.3

48

13.7

62

D/T

=0.

7

0.0

00

.035

.947

7.8

72

35.6

95

110.1

09

249.5

93

434.2

21

610.7

41

72

8.9

55

764.8

33

72

3.6

63

626.3

56

500.5

59

376.1

81

271.3

49

190.9

62

134.9

04

98.8

12

75.5

51

59.6

66

48.3

29

39.9

50

33.5

80

28.6

24

24.6

92

21.5

18

18 .

921

16.7

68

14

.96

2

D/T

=0.

8

0.0

00

.026

.72

76

.07

127.7

81

86.9

25

200.7

04

356.3

50

51

5.0

45

639.3

34

70

3.5

92

70

2.6

07

649.7

29

559.3

74

448.3

40

339.3

58

247.1

63

175.9

96

125.8

53

93.1

16

71.7

33

56.9

80

46.3

67

38.4

73

32.4

40

27

.72

623.9

71

20.9

32

18.4

37

16.3

64

D/T

=0

.9

0.0

00

.021

.576

4.8

24

22.2

37

70.3

85

16

5.0

20

298.1

26

438.2

67

555.6

09

631.5

50

657.9

77

639.7

54

58

6.4

59

504.6

92

406.2

29

309.6

38

227.5

13

163.6

82

118.2

87

88.2

89

68

.46

254.6

61

44.6

61

37.1

82

31.4

39

26

.93

42

3.3

34

20.4

12

18.0

07

D/T

=1.

0

0.0

00

.017

.46

73

.92

518.2

03

58.1

67

138.1

44

25

3.3

45

378.0

86

485.6

62

561.1

44

600.9

71

60

7.2

58

583.5

72

533.3

09

459.6

37

371.6

46

285.1

41

211.1

91

153.3

35

111.8

39

84.1

24

65 .

613

52.6

25

43.1

55

36.0

36

30.5

48

26.2

26

22.7

63

19.9

44

D/T

=1.

5

0.0

00

.008

.208

1.7

69

8.3

56

27

.52

768.2

33

131.8

50

207.9

62

28

1.2

75

339.4

41

37

8.1

05

401.0

33

414.1

02

421.3

88

425.4

02

425.6

38

41

7.9

59

39

8.3

98

365.3

42

318.7

42

262.9

68

207.1

21

158.1

83

118.8

36

89.6

72

69

.40

35

5.3

30

45

.15

437.5

55

D/T

=2.

0

0.0

00

.004

.118

1.0

02

4.7

79

16

.00

34

0.6

34

81

.00

2132.3

56

18

5.5

19

231.3

11

264.8

71

287.0

42

301.0

63

30

9.6

95

31

4.9

25

318.0

62

319.9

34

321.0

47

321.7

07

322.0

99

321.0

14

315.1

34

301.3

32

278.1

21

24

5.1

85

20

5.3

23

164.7

57

128.5

30

98.8

15

Tab

le

31. N

on

lin

ear

Mod

el

Hydro

gra

phs

(S

= kO

x);

x

= 0.5

; k

/=

7.0

C

onti

nued

n_ T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

8.6

25

7.9

44

7.3

40

6.8

03

6.3

22

5.8

91

5.5

03

5.1

51

4.8

33

4.5

42

4.2

78

4.0

36

3.8

13

3.6

09

3.4

21

3.2

47

3.0

86

2.9

37

2.7

98

2.6

69

2.5

48

D/T

=0.

1

9.0

68

8.3

34

7.6

86

7. in

6.5

99

6,1

39

5.7

26

5.3

54

5.0

16

4.7

10

4.4

31

4.1

76

3.9

42

3.7

27

3.5

30

3.3

48

3.1

79

3.0

23

2.8

78

2.7

44

2.6

18

D/T

=0.

2

9.5

44

8.7

53

8.0

57

7.4

40

6.8

92

6.4

03

5.9

63

5.5

68

5.2

10

4.8

86

4.5

91

4.3

22

4.0

76

3.8

51

3.6

44

3.4

53

3.2

76

3.1

13

2.9

62

2.8

21

2.6

91

D/T

=0.

3

10

.10

59

.24

58.4

90

7.8

25

7.2

34

6.7

08

6.2

38

5.8

15

5.4

34

5.0

89

4.7

76

4.4

91

4.2

31

3.9

92

3.7

74

3.5

73

3.3

87

3.2

16

3.0

57

2.9

10

2.7

73

D/T

=0.

4

10.7

61

9.8

18

8.9

94

8.2

69

7.6

29

7.0

60

6.5

53

6.0

98

5.6

89

5.3

20

4.9

86

4.6

82

4.4

05

4.1

52

3.9

21

3.7

08

3.5

12

3.3

31

3.1

64

3.0

09

2.8

65

D/T

=0.

5

11.5

25

10.4

82

9.5

74

8.7

80

8.0

81

7.4

62

6.9

11

6.4

19

5.9

78

5.5

81

5 2

234

.89

74.6

02

4.3

32

4.0

85

3.8

59

3.6

51

3.4

59

3.2

83

3.1

19

2.9

67

^i/

nre

- -

D

/T=

0.6

12.4

09

11.2

47

10.2

41

9.3

64

8.5

95

7.9

17

7.3

16

6.7

82

6.3

03

5.8

74

5.4

87

5.1

37

4.8

20

4.5

31

4.2

67

4.0

26

3.8

05

3.6

01

3.4

13

3.2

40

3.0

79

D/T

=0

.7

13

.43

412.1

28

11.0

04

10.0

30

9.1

79

8.4

33

7.7

73

7.1

89

6.6

68

6.2

01

5.7

82

5.4

04

5.0

62

4.7

51

4.4

69

4.2

10

3.9

74

3.7

57

3.5

57

3.3

72

3.2

02

D/T

=0.

8

14.6

21

13.1

44

11.8

79

10.7

89

9.8

42

9.01

58.2

88

7.6

45

7.0

75

6.5

66

6.1

10

5.7

00

5.3

30

4.9

95

4.6

90

4.4

13

4.1

59

3.9

27

3.7

13

3.5

17

3.3

36

D/T

=0.

9

16.0

03

14.3

17

12

.88

411

. 65

610.5

95

9.6

74

8.8

67

8.1

57

7.5

30

6.9

72

6.4

74

6.0

27

5.6

25

5.2

62

4.9

33

4.6

34

4.3

62

4.1

13

3.8

84

3.6

74

3.4

81

D/T

=1

.0

17.6

19

15 .

678

14 .

041

12.6

49

11.4

54

10.4

20

9.5

21

8.7

33

8.0

39

7.4

24

6.8

78

6.3

90

5.9

52

5.5

57

5.2

01

4.8

78

4.5

84

4.3

15

4.0

70

3.8

45

3.6

38

D/T

=1.

5

31

.73

027.1

64

23

.51

92

0.5

63

18.1

32

16.1

08

14

.40

61

2.9

59

11 .

721

10

.65

2

9.7

23

8.9

10

8.1

95

7.5

63

7.0

02

6.5

01

6.0

51

5.6

47

5.2

82

4.9

51

4.6

51

D.T

=2.

0

76.2

72

60

.17

14

8.6

96

40.2

25

33.7

92

28

.79

124.8

25

21.6

27

19

.01

116.8

42

15 .

025

13.4

87

12

.17

41

1.0

44

10.0

64

Q.2

098.4

59

7.7

97

7.2

10

6.6

86

6.2

18

Cn


1 0

1 IN

'<

11 "I

i VI <Q

1 0

1 H

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1 Q

1

1 .O1 IIl<, °

1 00

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i cT1 r- 1 o

l<, °

1 VO0)

a, o\ H H \

o

,o 1

i *1 0

,^1 O

1 1 "o

1^ ,°1 01 11 0"

1I ^, 0

,<o

1 .r tJi ti i&

3=1 H

O co O H CO

o o o r~ t-O CO

O vO O CO OO

0 H -0

O CO ON uo UO O H uo co LO O O CO O CM

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0 H r-| co

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rH

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o H OJ m oN d SirH CO

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co H co H r-

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oo H H r H*t co (N H H

CO rf O f O

csi co uo H r-

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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

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ON r~- i i 00 NO <N OO ^F O [^ NO CO ON ON uD

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co H ON uo OOO NO CO O rH

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^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 HH H H H H

o o o o oLO vO E-~- OO ON

Tab

le 32. N

onli

near

Mod

el

Hydro

gra

phs

(S

= kf

)x);

x

= 0

.5;

k/

/AP

e/T

=

8.0

C

on

tin

ued

LL T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

10

.94

11

0.0

89

9.3

32

8.6

58

8.0

54

7.5

11

7.0

21

6.5

78

6.1

75

5.8

08

5.4

73

5.1

67

4.8

85

4.6

26

4.3

86

4.1

65

3.9

61

3.7

71

3.5

94

3.4

29

3.2

76

D/T

=0.

1

11

.48

61

0.5

70

9.7

60

9.0

40

8.3

96

7.8

19

7.2

99

6.8

30

6.4

04

6.0

17

5.6

64

5.3

41

5.0

45

4.7

73

4.5

23

4.2

92

4.0

77

3.8

79

3.69

53

.52

33

.36

4

D/T

=0.

2

12

.07

01

1.0

85

10.2

16

9.4

46

8.7

59

8.1

45

7.5

93

7.0

95

6.6

45

6.2

36

5.8

64

5.5

24

5.2

13

4.9

28

4.6

65

4.4

23

4.1

99

3.9

92

3.8

00

3.6

21

3.4

55

D/T

=0.

3

12.7

54

11.6

86

10

.74

79

.91

69

.17

9

8.5

21

7.9

31

7.4

00

6.9

21

6.4

87

6.0

93

5.7

33

5.4

04

5.1

03

4.8

27

4.5

72

4.3

37

4.1

20

3.9

18

3.7

31

3.5

57

D/T

=0.

4

13

.54

912.3

82

11.3

59

10.4

59

9.6

61

8.9

51

8.3

17

7.7

47

7.23

56

.77

1

6.3

51

5.9

69

5.6

20

5.3

01

5.0

08

4.7

39

4.4

91

4.2

63

4.0

51

3.8

54

3.6

72

D/T

=0.

5

14

.46

913.1

84

12.0

62

11.0

78

10.2

10

9.4

40

8.7

54

8.1

40

7.5

89

7.0

91

6.6

42

6.2

33

5.8

61

5.5

22

5.2

11

4.9

26

4.6

63

4.4

21

4.1

97

3.9

90

3.7

98

'^i/

nre

~

D/T

=0.

6

15.5

30

14.1

04

12.8

66

11.7

84

10

.83

3

9.9

93

9.2

47

8.5

81

7.9

85

7.4

49

6.9

66

6.5

27

6.1

29

5.7

67

5.4

35

5.1

32

4.8

53

4.5

96

4.3

59

4.1

40

3.9

37

D/T

=0.

7

16.7

53

15.1

60

13.7

83

12

.58

61

1.5

39

10.6

17

9.8

01

9.0

76

8.4

29

7.8

48

7.3

26

6.8

54

6.4

26

6.0

37

5.6

82

5.3

58

5.0

61

4.7

88

4.5

36

4.3

04

4.0

89

D/T

=0.

8

18.1

65

16

.37

114.8

31

13.4

98

12.3

37

11

.32

010.4

24

9.6

30

8.9

23

8.2

92

7.7

25

7.2

15

6.7

53

6.33

55

.95

4

5.6

06

5 2

884

.99

74

.72

94

.48

24

.25

3

D/T

=0.

9

19.7

98

17.7

63

16.0

27

14.5

34

13.2

40

12

.11

21

1.1

22

10.2

48

9.4

74

8.7

84

8.1

67

7.6

13

7.1

14

6.6

62

6.2

51

5.8

78

5.5

37

5.2

25

4.9

39

4.6

75

4.4

32

D/T

=1.

0

21.6

98

19.3

71

17.4

00

15.7

16

14.2

65

13.0

06

11.9

07

10.9

41

10.0

89

9.3

32

8.6

58

8.0

54

7.5

11

7.0

21

6.5

78

6.1

75

5.8

09

5.4

74

5.1

67

4.8

85

4.6

26

D/T

=1.

5

37

.86

23

2.6

31

28

.41

52

4.9

68

22.1

13

19

.72

11

7.6

98

15

.97

11

4.4

86

13

.19

8

12

.07

51

1.0

89

10

.22

09

.44

98

.76

2

8.1

47

7.5

95

7.0

97

6.6

47

6.2

38

5.8

66

D/T

=2 .

0

85

.33

768.4

75

56.1

74

46

.92

13

9.7

85

34.1

64

29

.65

725.9

89

22.9

62

20

.43

5

18

.30

41

6.4

90

14

.93

31

3.5

87

12

.41

5

11.3

88

10

.48

49

.68

38

.97

18

.33

57

.76

4

78

I oI ^ i cT

MODEL HYDROGRAPHS

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> rH r- co r- > o m co r-> *tf c-l

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Tab

le 3

3.

No

nli

near

Mod

el

Hydro

gra

phs

(S

= kO

x);

/AP

e/T

=

9.0

C

on

tin

ued

n T

3.0

0

3.1

03.2

0

3.3

0

3.4

0

3.5

03.6

0

3.7

0

3.8

03.9

0

4.0

04.1

0

4.2

0

4.3

0

4.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

13

.44

8

12

.41

511.4

96

10

.67

6

9.9

40

9.2

78

8.6

80

8

.13

8

7.6

45

7.1

96

6.7

85

6.4

09

6

.06

35

.74

4

5.4

49

5.1

77

4.9

25

4.6

91

4.4

73

4.2

70

4.0

80

D/T

=0.

1

14

.09

9

12

.99

11

2.0

09

1

1.1

34

1

0.3

51

9.6

49

9.0

15

8.4

42

7

.92

27

.44

8

7.0

16

6.6

20

6

.25

7

5.9

23

5

. 615

5.3

31

5.0

67

4.8

23

4.5

96

4.3

84

4.1

87

D/T

=0.2

14.7

96

13.6

07

12

.55

5

11.6

21

10

.78

8

10.0

41

9.3

69

8.7

62

8.2

13

7.7

13

7.2

58

6.8

42

6

.46

1

6.1

10

5.7

88

5.4

90

5.2

15

4.9

60

4.7

23

4.5

03

4.2

98

D/T

=0.

3

15.6

07

14

.32

013.1

87

12

.18

3

11.2

89

10.4

90

9.7

74

9

.12

88

.54

48.0

15

7.5

33

7.0

93

6

.69

1

6.3

22

5

.98

3

5.6

70

5.3

82

5.1

15

4.8

67

4.6

37

4.4

22

D/T

=0.

4

16.5

43

15

.14

213

. 91

1 12.8

25

11.8

61

11.0

02

10.2

33

9.5

42

8.9

19

8.3

55

7.8

43

7.3

76

6

.95

0

6.5

60

6

.20

1

5.8

72

5.5

68

5.2

87

5.0

27

4.7

85

4.5

61

D/T

=0.

5

17.6

21

16.0

84

14.7

39

13.5

56

12

.51

1

11.5

81

10.7

52

10.0

09

9.3

40

8.7

36

8.1

89

7.6

92

7

.23

8

6.8

24

6

.44

4

6.0

95

5.7

74

5.4

77

5.2

03

4.9

49

4.7

13

D/T

=0

.6

18.8

60

17.1

61

15.6

82

14.3

87

13

.24

5

12.2

35

11.3

35

10.5

32

9.8

11

9.1

62

8.5

75

8.0

42

7.5

58

7

.11

6

6.7

12

6.3

42

6.0

01

5.6

87

5.3

97

5.1

29

4.8

80

D/T

=0

.7

20

.28

0

18

.39

116.7

54

15

.32

6

14

.07

3

12.9

68

11

.98

9

11.1

16

10.3

35

9.6

34

9.0

02

8.4

30

7

.91

1

7.4

38

7

.00

7

6.6

12

6.2

50

5.9

16

5.6

09

5.3

25

5.0

62

D/T

=0.

8

21.9

13

19

.79

617.9

73

16

.39

0

15.0

08

13.7

93

12

.72

0

11.7

68

10

.91

910.1

59

9.47

58

.85

8

8.3

00

7

.79

2

7.3

30

6.9

08

6.5

21

6.1

66

5.8

39

5.5

38

5.2

59

D/T

=0

.9

23.7

94

21

.40

619.3

61

17

.59

6

16.0

61

14.7

20

13.5

39

12.4

95

11

.56

810.7

40

9.9

98

9.3

30

8

.72

7

8.1

81

7.6

84

7.2

32

6.8

18

6.4

39

6.0

90

5.7

69

5.4

73

D/T

=1

.0

25.9

68

23.2

55

20.9

47

18.9

65

17.2

53

15.7

62

14.4

57

13

.30

7

12.2

90

11.3

85

10.5

76

9.8

51

9

.19

7

8.6

07

8

.07

2

7.5

85

7.1

41

6.7

35

6.3

62

6.0

20

5.7

04

D/T

=1.

5

44

.03

6

38.1

79

33

.42

0

29

.49

9

26

.23

1

23

.47

721.1

36

19

.12

9

17

.39

415.8

86

14

.56

61

3.4

03

1

2.3

75

1

1.4

60

10.6

44

9.9

12

9.2

52

8.6

57

8.1

17

7.6

26

7.1

78

D/T

=2.

0

93.

76.

63.

53

. 45.

39

.34

. 30

. 26.

24

.

21.

19

. 1

7.

16.

14.

13.

12

.1

1.

10

.10. 9.

847

394

407

478

716

532

526

415

997

126

689

604

806

245

881

681

621

680

840

088

411

O _ H s5 3 2 o O RAPHS

CD

Table

34. Nonlinear Mo

del

Hydrographs

(S = kOx);

x

= 0.5; k/

/APe/T =

10.0

00 O

Jl T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

3.2

51

35.6

96

140.2

35

346.1

24

642.7

52

86

6.3

40

883.2

90

776.8

40

614.2

02

43

3.4

93

294.5

82

213.5

82

162.0

88

127.2

78

102.6

27

84.5

23

70.8

30

60

.22

25

1.8

34

45

.08

73

9.5

79

35.0

23

31

.21

22

7.9

91

25

.24

42

2.8

83

20

.83

91

9.0

57

17

.49

4

D/T

=0.

1

0.0

00

.823

14

.81

979.1

21

233.6

77

488.8

33

75

7.6

22

879.9

46

832.1

63

695.3

62

52

2.2

78

363.1

40

254.5

82

188.5

97

145.4

25

115.6

02

94.1

257

8.1

37

65

.91

25

6.3

52

48

.73

44

2.5

67

37.5

02

33

.29

029.7

51

26

.74

82

4.1

78

21

.96

22

0.0

37

18

.35

5

D/T

=0.

2

0.0

00

.207

5.6

09

40

.60

0147.4

91

35

4.1

76

62

3.1

18

824.0

24

859.7

59

76

4.6

44

607.9

29

44

1.4

65

308.6

86

222.

195

167.7

39

13

1.1

90

105.4

48

86.6

24

72.4

38

61.4

80

52

.83

74

5.8

99

40

.24

73

5.5

78

31.6

79

28.3

87

25

.58

323.1

76

21.0

93

19

.27

9

D/T

=0.

3

0.0

00

.092

2.5

20

20.8

29

89.2

54

24

6.4

02

48

4.9

76

717.5

65

836.1

13

80

8.6

10

683.1

79

52

3.9

90

378.0

95

26

9.3

48

197.9

25

15

1.6

94

120.0

21

97

.35

780.5

74

67.7

94

57.8

37

49.9

27

43.5

37

38

.30

333.9

60

30

.31

627.2

29

24

.59

122.3

19

20.3

48

D/T

=0.

4

0.0

00

.05

21.4

25

11

.91

154.5

78

167.1

05

36

4.4

85

592.7

13

760.9

80

809.2

31

737.8

99

600.3

77

454.4

46

33

0.8

17

23

9.8

68

179.1

97

139.0

47

111.0

74

90.7

92

75 .

613

63.9

54

54.8

03

47

.48

741.5

48

36.6

58

32.5

84

29.1

54

26.2

39

23.7

40

21.5

83

D/T

=0.

5

0.0

00

.033

.915

7.7

00

35 .

745

114.4

25

268.5

81

473.6

51

65

8.6

87

761.

698

75

6.0

34

66

0.6

74

528.1

58

400.3

76

294.8

09

217.0

39

164.3

62

128.8

55

103.7

66

85.3

72

71.4

81

60.7

31

52.2

40

45

.41

639.8

50

35.2

49

31.4

01

28.1

52

25.3

82

23.0

02

' V

J-/"

re ~

D

/T=

0.6

0.0

00

.023

.637

5.3

84

25 .

216

81

.91

1199.0

06

372.4

53

552.0

37

683.3

80

730.6

57

69

0.2

18

58

9.5

78

469.5

86

358.0

87

266.6

62

198.9

00

152.3

46

120.4

78

97.6

91

80

.82

467.9

88

57.9

89

50.0

49

43.6

37

38.3

85

34.0

28

30.3

74

27.2

78

24.6

34

D/T

=0

.7

0.0

00

.01

7.4

69

3.9

75

18.7

39

61.5

36

151.8

37

291.7

12

453.9

03

593.8

81

673.9

02

681.1

42

625.2

79

529.4

58

422.3

66

324.3

79

244.0

74

184.1

11

14

2.3

89

11

3.4

51

92.5

44

76.9

41

64.9

85

55.6

19

48

.14

5

42.0

86

37.1

04

32.9

57

29.4

70

26.5

08

D/T

=0.

8

0.0

00

.01

3.3

59

3.0

54

14.4

72

47

.92

4119.7

00

233.5

56

37

2.3

85

506.0

82

602.1

86

641.9

60

62

7.0

88

567.7

10

47

9.4

55

38

3.8

78

296.9

51

225.5

31

17

1.7

95

133.9

82

107.4

53

88.1

14

73.5

75

62.3

67

53.5

43

46.4

70

40.7

15

35.9

67

32.0

05

28.6

64

D/T

=0.

9

0.0

00

.01

0.2

84

2.4

20

11.5

12

38.3

80

96.8

11

191.3

17

309.4

86

429.3

03

527.4

27

586.1

34

60

0.9

01

576.2

53

51

8.1

57

437.7

24

35

2.0

28

274.1

99

21

0.0

07

161.3

52

126.7

67

10

2.2

58

84.2

47

70.6

19

60.0

56

51.7

02

44.9

79

39.4

91

34.9

50

31.1

50

D/T

=1

.0

0.0

00

.00

8.2

30

1.9

65

9.3

76

31

.42

97

9.9

24

159.6

43

261.4

61

367.3

71

459.1

03

524.3

49

557.8

36

559.2

14

530.7

44

475.7

78

402.5

96

325.2

89

255.0

16

19

6.8

00

152.3

65

12

0.4

92

97

.70

180.8

32

67.9

93

57

.99

450.0

52

43.6

39

38.3

87

34

.03

0

D/T

=1.

5

0.0

00

.00

4.1

03.8

79

4.2

37

14

.44

537.7

02

77.9

80

133.1

92

195.8

32

255.9

51

30

5.9

85

343.9

31

371.3

80

390.6

01

40

3.7

70

41

1.2

11

410.3

69

398.2

89

37

3.4

55

335.5

48

287.7

85

237.5

14

191.1

35

15

1.8

50

12

0.9

86

98 .

061

81

.10

368.2

02

58

.15

8

D/T

=2.

0

0.0

00

.00

2.0

58.4

962

.40

3

8.2

66

21

.87

64

6.1

30

80

.73

412

2 . 0

44

16

4.2

21

201.9

89

23

3.0

08

257.2

83

27

5.6

35

289.1

69

298.9

77

305.9

97

31

0.9

78

314.4

91

31

6.9

58

31

7.7

08

31

4.3

35

304.2

80

286.0

17

258.9

16

224.8

32

188.5

89

154.6

19

125.3

16

El W

Tab

le 3

4.

No

nli

near

Mod

el

Hydro

gra

phs

(S

= kO

x);

x

= 0.5

; k

/ /A

Pe/

T

= 10.0

Conti

nued

ii T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

05.0

0

D=

Inst

.

16

.11

61

4.8

95

13.8

07

12

.83

511.9

62

11.1

75

10

.46

39

.81

79

.22

98

.69

2

8.2

01

7.7

51

7.3

36

6.9

54

6.6

01

6.2

75

5.9

71

5.6

90

5.4

28

5.1

83

4.9

55

D/T

=0.

1

16

.87

61

5.5

69

14.4

08

13.3

73

12.4

45

11

.61

110.8

57

10.1

75

9.55

58

.99

1

8.4

74

8.0

01

7.5

67

7.1

67

6.7

98

6.4

57

6.1

40

5.8

47

5.5

74

5.3

20

5.0

82

D/T

=0.

2

17

.68

916.2

89

15 .

048

13 .

944

12 .

95 7

12

.07

21

1.2

74

10

.55

39

.89

99

.30

4

8.7

61

8.2

64

7.8

08

7.3

89

7.0

03

6.6

46

6.3

16

6.0

10

5.7

26

5.4

61

5.2

15

D/T

=0.

3

18.6

28

17

.11

61

5.7

82

14.5

98

13.5

42

12.5

97

11.7

48

10

.98

11

0.2

88

9.6

58

9.0

84

8.5

60

8.0

80

7.6

39

7.2

33

6.8

59

6.5

13

6.1

93

5.8

96

5.6

19

5.3

62

D/T

=0.

4

19

.70

718.0

65

16.6

20

15.3

42

14.2

06

13.1

92

12

.28

31

1.4

64

10.7

25

10.0

55

9.4

46

8.8

91

8.3

83

7.91

87

.49

0

7.0

96

6.7

32

6.3

96

6.0

84

5.7

95

5.5

25

D/T

=0.

5

20.9

42

19.1

47

17.5

73

16.1

86

14.9

57

13.8

63

12.8

85

12.0

06

11.2

15

10.4

99

9.8

50

9.2

59

8.7

20

8.2

27

7.7

74

7.3

58

6.9

74

6.6

20

6.2

92

5.9

87

5.7

05

i^i/

rtrp

-

D/T

=0.

6

22.3

56

20.3

80

18.6

55

17.1

41

15.8

04

14 .

617

13.5

59

12.6

12

11 .

761

10.9

94

10.2

99

9.6

68

9.0

93

8.5

68

8.0

88

7.6

46

7.2

40

6.8

65

6.5

19

6.1

98

5.9

01

D/T

=0.

7

23.9

72

21.7

83

19

.88

118.2

18

16

.75

6

15.4

62

14.3

13

13.2

88

12.3

69

11.5

42

10.7

95

10

.11

99

.50

48

.94

48.4

31

7.9

62

7.5

31

7.1

34

6.7

67

6.4

28

6.1

14

D/T

=0.

8

25.8

21

23

.38

02

1.2

70

19.4

34

17.8

25

16.4

09

15.1

55

14

.03

91

3.0

43

12.1

48

11.3

43

10.6

15

9.9

56

9.3

55

8.8

08

8.3

07

7.8

48

7.4

26

7.0

37

6.6

78

6.3

45

D/T

=0

.9

27.9

38

25

.19

922.8

44

20.8

05

19

.02

7

17.4

68

16

.09

314.8

75

13.7

89

12.8

19

11

.94

711.1

61

10.4

51

9.8

06

9.2

19

8.6

83

8.1

93

7.7

43

7.3

29

6.9

48

6.5

95

D/T

=1.

0

30.3

75

27.2

80

24.6

35

22.3

57

20.3

81

18.6

56

17.1

42

15

.80

414.6

18

13

.56

0

12 .

613

11.7

62

10.9

94

10

.29

99.6

68

9.0

93

8.5

69

8.0

88

7.6

46

7.2

40

6.8

65

D/T

=1.

5

50

.18

44

3.7

47

38.4

76

34.1

04

30

.43

8

27.3

33

24

.68

02

2.3

96

20

.41

51

8.6

86

17.1

68

15

.82

81

4.6

38

13

.57

81

2.6

29

11

.77

71

1.0

08

10

.31

19

.67

99

.10

48

.57

8

D/T

=2.

0

101.8

00

83

.90

57

0.3

57

59

.85

05

1.5

38

44

.84

63

9.3

81

34

.85

93

1.0

73

27

.87

3

25.1

44

22

.79

620.7

63

18.9

91

17

.43

6

16.0

65

14

.84

913.7

67

12

.79

81

1.9

29

11

.14

5

00 00

Table

35. Nonlinear Model

Hydrographs

(S = kO

x);

x

= 0.

5; k/ /APe/T = 11

.0

00

fcO

n T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

2.6

99

29

.92

51

19

.61

73

02

.46

0

577.5

81

802.7

11

844.4

08

762.8

24

617.9

69

44

8.3

29

313.2

34

231.4

91

17

8.1

82

14

1.4

46

11

5.0

39

95.4

13

80

.42

468.7

16

59.3

94

51.8

52

45

.66

34

0.5

20

36.2

00

32.5

37

29.4

03

26.7

02

24 .

35 6

22.3

07

20.5

06

D/T

=0.

1

0.0

00

.682

12

.35

96

6.8

90

201.7

49

43

3.3

80

691.6

96

828.2

97

806.0

64

690.6

30

53

1.8

78

379.9

41

272.7

52

205.5

07

160.4

92

128.8

52

105.7

51

88.3

65

74

.94

964.3

77

55.8

98

48

.99

343.2

95

38

.53

734.5

23

31.1

05

28

.17

125.6

34

23.4

25

21

.49

0

D/T

=0.

2

0.0

00

.171

4.6

62

34

.09

0126.0

15

309.9

87

560.9

53

76

4.2

48

820.9

92

749.6

61

610.7

21

45

4.8

15

326.1

23

239.6

23

18

3.6

39

145.2

87

117.8

47

97

.52

882.0

57

70.0

04

60

.42

852.6

94

4b

.35

84

1.1

00

36

.69

0

32

.95

42

9.7

61

27

.01

124.6

26

22.5

43

D/T

=0

.3

0.0

00

.076

2.0

91

17.4

11

75

.66

2

213.3

17

43

1.0

87

656.5

33

787.2

61

782.0

40

677.2

44

531.9

56

393.1

20

286.4

52

214.3

88

166.5

82

13

3.2

12

10

8.9

82

90

.82

67

6.8

66

65

.90

057.1

28

50.0

02

44.1

32

39.2

39

35.1

17

31.6

13

28.6

09

26.0

14

23.7

56

D/T

=0.

4

0.0

00

.04

31

.18

29

.93

046.0

16

143.4

34

320.4

21

535.6

47

707.3

12

772.2

93

721.7

57

60

1.0

74

465.2

71

346.1

99

256.2

24

194.6

68

152.9

94

123.4

46

10

1.7

25

85.2

85

72.5

39

62.4

57

54.3

42

47.7

16

42.2

32

37.6

44

33.7

65

30.4

56

27.6

12

25.1

48

D/T

=0.

5

0.0

00

.027

.758

6.4

09

30.0

29

97.6

06

234.0

18

423.4

38

60

5.1

83

71

8.2

48

730.

175

65

2.6

17

533.0

19

41

2.4

55

309.9

29

232.5

58

17

8.9

00

141.9

52

US

. 410

95.6

93

80.6

40

68.8

87

59.5

32

51.9

64

45.7

55

40.5

97

36.2

66

32.5

93

29.4

51

26.7

43

' ^J

-/"re

-

D/T

=0.

6

0.0

00

.019

.528

4.4

76

21.1

31

69.5

58

172.2

22

329.1

70

502.0

21

637.4

99

697.7

64

673.4

71

587.0

83

476.7

75

370.5

43

281.2

20

213.5

42

166.0

05

132.7

99

108.6

77

90.5

94

76.6

86

65.7

57

5 7

. 013

49.9

07

44 .

05 3

39.1

73

35

.06

131.5

66

28.5

68

D/T

=0.

7

0.0

00

.01

4.3

883

.30

215.6

74

52.0

79

130.7

15

256.6

55

409.2

17

548.7

54

637.2

34

657.5

97

61

5.1

85

530.4

10

430.7

25

336.7

32

257.9

51

197.9

08

155.2

43

125.0

72

10

2.9

39

86.2

15

73.2

68

63.0

38

54.8

14

48.1

03

42.5

55

37.9

15

33.9

95

30.6

54

D/T

=0.

8

0.0

00

.011

.297

2.5

36

12

.08

8

40.4

53

102.6

21

204.3

17

33

3.3

75

463.8

90

564. 5

116

14

.15

5610.7

92

562.1

24

482.5

14

39

2.7

58

308.9

71

238.7

08

18

4.8

09

146.1

09

118.4

46

97.9

79

82.4

05

70.2

77

60.6

47

52.8

72

46.5

05

41.2

23

36.7

94

33.0

42

D/T

=0.

9

0.0

00

.008

.235

2.0

08

9.6

05

32.3

28

82.7

17

166.5

72

275.4

37

39

0.9

28

490.8

68

556.4

04

58

0.4

25

565.1

86

515.5

90

442.0

52

361.0

58

285.7

81

222.5

03

173.6

47

138.2

38

112.6

86

93.6

35

79.0

47

67.6

28

58.5

20

51.1

40

45.0

74

40

.02

835.7

85

D/T

=1

.0

0 1 7

26 6813

823

133

2

424

494

535

544

523

475

407

334

266

208

164

131

107 89 76 65 56 49 43 38

.000

.007

.191

.630

.816

.42

8.1

11

.453

.533

.604

.667

.545

.081

.274

.350

.196

.646

.242

.107

.645

.001

.367

.617

.787

.05

8

.258

.610

.577

.780

.944

D/T

=1.

5

0.0

00

.003

.085

.729

3.5

22

12

.08

13

1.8

34

66.7

24

115.8

78

173.6

16

231.4

09

28

1.9

58

322.4

24

353.2

92

376.0

53

392.4

41

402.7

16

404.5

68

39

5.2

55

37

3.2

95

338.3

21

29

3.2

78

245.0

67

199.8

97

161.0

65

130.0

74

10

6.6

59

89

.05

77

5.4

89

64.8

06

D/T

=2.

0

0.0

00

.002

.048

.411

1.9

95

6.8

94

18

.38

139.1

75

69.5

08

10

6.7

85

14

6.2

29

18

3.0

90

21

4.8

16

240.8

40

261.4

49

27

7.3

48

28

9.3

78

298.

355

304.9

86

30

9.8

48

31

3.3

93

31

5.0

72

31

2.7

03

30

3.8

98

287.1

64

261.8

24

229.5

21

194.7

12

161.6

48

132.7

37

Tabl

e 35. Nonlinear Model

Hydrographs

(S = kO

*);

x =

0.5;

k/

/AP

e/T

= 11.0 Con

tinu

ed

u T

3.0

03.1

03.2

03.3

03.4

0

3.5

03.6

03.7

03.8

03.9

0

4.0

04.1

04.2

04.3

04.4

0

4.5

04.6

04.7

04.8

04.9

0

5.0

05.1

05.2

05.3

05.4

0

5.5

05.6

05.7

05.8

05.9

06.0

0

D=

Inst

.

18.9

15

17

.50

21

6.2

42

15 .

113

14

.09

8

13

.18

21

2.3

52

11.5

99

10

.91

210.2

85

9.7

10

9.1

82

8.6

96

8.2

47

7.8

33

7.4

49

7.0

92

6.7

61

6.4

52

6.1

64

5.8

95

5.6

43

5.4

07

5.1

85

4.9

77

4.7

81

4.5

96

4.4

22

4.2

58

4.1

02

3.9

55

D/T

=0.

1

19.7

85

18

.27

51

6.9

32

15

.73

21

4.6

55

13

.68

51

2.8

08

12

.01

31

1.2

90

10

.63

0

10

.02

79

.47

38

.96

48

.49

58

.06

2

7.6

61

7.2

89

6.9

44

6.6

23

6.3

23

6.0

44

5.7

82

5.5

37

5.3

08

5.0

92

4.8

89

4.6

98

4.5

19

4.3

49

4.1

88

4.0

37

D/T

=0.

2

20.7

14

19

.09

91

7.6

66

16

.38

81

5.2

44

14

.21

61

3.2

89

12.4

49

11

.68

71

0.9

93

10

.35

89

.77

79

.24

48

.75

38

.30

0

7.8

82

7.4

94

7.1

34

6.8

00

6.4

89

6.1

98

5.9

27

5.6

73

5.4

35

5.2

11

5.0

01

4.8

04

4.6

18

4.4

43

4.2

77

4.1

21

D/T

=0.

3

21

.78

120.0

42

18.5

03

17

.13

615

. 91

4

14.8

19

13

.83

31

2.9

42

12.1

35

11.4

01

10.7

31

10.1

19

9.5

58

9.0

42

8.5

67

8.1

28

7.7

23

7.3

47

6.9

97

6.6

72

6.3

70

6.0

87

5.8

23

5.5

75

5.3

43

5.1

25

4.9

21

4.7

28

4.5

46

4.3

75

4.2

13

D/T

=0.

4

23.0

00

21.1

16

19.4

55

17.9

82

16.6

71

15.4

98

14

.44

413.4

95

12.6

36

11.8

57

11.1

47

10.5

00

9.9

07

9.3

63

8.8

63

8.4

02

7.9

76

7.5

81

7.2

15

6.8

75

6.5

59

6.2

63

5.9

88

5.7

30

5.4

88

5.2

62

5.0

49

4.8

49

4.6

60

4.4

82

4.3

15

D/T

=0.

5

24.3

92

22.3

39

20.5

34

18.9

39

17

.52

4

16.2

61

15.1

31

14.1

14

13.1

96

12.3

65

11.6

10

10.9

23

10.2

94

9.7

19

9.1

90

8.7

04

8.2

55

7.8

39

7.4

55

7.0

98

6.7

66

6.4

57

6.1

68

5.8

99

5.6

47

5.4

10

5.1

88

4.9

80

4.7

84

4.5

99

4.4

25

D/T

=0.

6

25.9

78

23.7

25

21.7

54

20.0

18

18.4

82

17.1

17

15.8

97

14.8

03

13

.81

91

2.9

30

12.1

23

11.3

90

10

.72

21

0.1

10

9.5

50

9.0

35

8.5

60

8.1

22

7.7

17

7.3

41

6.9

92

6.6

68

6.3

65

6.0

83

5.8

19

5.5

72

5.3

40

5.1

22

4.9

18

4.7

25

4.5

44

D/T

=0.

7

27.7

82

25

.29

623.1

30

21.2

30

19

.55

6

18.0

72

16.7

51

15.5

69

14.5

09

13

.55

3

12.6

89

11.9

05

11

.19

110.5

40

9.9

44

9.3

97

8.8

94

8.4

30

8.0

02

7.6

06

7.2

38

6.8

96

6.5

78

6.2

82

6.0

05

5.7

46

5.5

03

5.2

76

5.0

62

4.8

61

4.6

72

D/T

=0.

8

29.8

37

27.0

77

24.6

83

22.5

93

20.7

58

19.]

38

17

.70

016.4

19

15.2

72

14.2

41

13

.31

112.4

70

11.7

06

11.0

10

10.3

74

9.7

92

9.2

57

8.7

65

8.3

11

7.8

92

7.5

04

7.1

43

6.8

08

6.4

96

6.2

05

5.9

33

5.6

79

5.4

41

5.2

17

5.0

07

4.8

09

D/T

=0.

9

32.1

82

29.0

98

26.4

38

24.1

26

22.1

05

20.3

28

18.7

57

17.3

62

16

.11

615.0

00

13

.99

61

3.0

90

12

.26

911.5

23

10

.84

3

10.2

21

9.6

52

9.1

28

8.6

47

8.2

02

7.7

91

7.4

10

7.0

56

6.7

27

6.4

21

6.1

35

5.8

67

5.6

17

5.3

82

5.1

62

4.9

55

D/T

=1.

0

34.8

67

31

.40

028.4

25

25.8

55

23.6

18

21

.65

919.9

34

18

.40

81

7.0

50

15.8

38

14.7

50

13

.77

112.8

86

12

.08

411.3

54

10.6

89

10.0

80

9.5

22

9.0

09

8.5

37

8.1

01

7.6

97

7.3

23

6.9

75

6.6

52

6.3

50

6.0

69

5.8

06

5.5

59

5.3

28

5.1

12

D/T

=1.

5

56.2

45

49

.27

84

3.5

31

38 .

735

34.6

91

31.2

49

28

.29

62

5.7

42

23

.51

921.5

73

19.8

58

18.3

40

16

.99

015.7

84

14.7

02

13.7

27

12.8

46

12 .

048

11.3

22

10

.65

9

10.0

53

9.4

97

8.9

86

8.5

16

8.0

81

7.6

79

7.3

06

6.9

59

6.6

37

6.3

37

6.0

56

D/T

=2.

0

109.1

92

90.9

86

76.9

90

65 .

999

57.2

08

50

.06

74

4.1

86

39

.28

435.1

55

31.6

46

28.6

37

26

.03

82

3.7

78

21.8

00

20

.05

8

18.5

18

17

.14

915.9

26

14

.82

91

3.8

42

12

.05

11

2.1

42

11.4

08

10

.73

810.1

25

9.5

63

9.0

47

8.5

72

8.1

33

7.7

27

7.3

50

00 go

Tabl

e 36. Nonlinear Mo

del

Hydr

ogra

pbs

(S =

kf)x

); x

- 0.5; k/

/APe/

T =

12.0

00

n^ T

0.0

0.1

0.2

0.3

0.4

0

.50

.60

.70

.80

.90

1.0

01.1

01.2

01.3

01.4

0

1.5

01.6

01.7

01.8

01.9

0

2.0

02.1

02.2

02.3

02.4

0

2.5

02.6

02.7

02.8

02.9

0

D=

Inst

.

0.0

00

2.2

74

25

.42

21

03

.02

8265.7

14

519.6

51

741.8

47

802.6

29

743.4

50

616.2

65

45

8.4

85

328.4

15

24

7.0

55

192.7

08

15

4.5

70

12

6.7

63

10

5.8

56

89.7

37

77.0

45

66

.87

1

58.5

92

51

.76

246.0

61

41

.25

43

7.1

63

33.6

51

30.6

15

27

.97

22

5.6

58

23

.61

9

D/T

=0.

1

0.0

00

.574

10

.45

95

7.2

27

17

5.5

17

385.4

07

63

0.8

85

776.2

97

775.5

82

680.3

89

53

6.3

90

392.6

99

288.0

42

220.4

63

17

4.2

50

141.2

30

11

6.8

04

98

.22

48

3.7

58

72

.27

3

63.0

02

55

.41

04

9.1

14

43

.83

43

9.3

62

35

.54

23

2.2

53

29

.40

02

6.9

10

24

.72

3

D/T

=0.

2

0.0

00

.144

3.9

34

28.9

98

108.6

88

272.6

90

505.3

80

706.7

79

779.6

00

72

9.5

78

60

8.1

63

463.6

28

340.

135

25

4.6

45

197.9

09

15

8.2

92

129.5

19

107.

955

91.3

72

78

.34

3

67

.92

059.4

51

52.4

75

46

.65

94

1.7

60

37.5

953

4.0

23

30.9

38

28

.25

425

. 90

5

D/T

=0.

3

0.0

00

.06

41

.76

21

4.7

59

64.8

50

185.9

65

384.1

79

599.8

90

738.0

58

751.

525

66

6.0

88

5 35

. O

il404.2

23

300,6

59

228.8

50

180.1

12

14

5.4

89

119.9

98

100.6

80

85.6

88

73.8

17

64.2

57

56.4

44

49

.97

64

4.5

60

39.9

80

36.0

72

32.7

10

29.7

98

27.2

58

D/T

-0.4

0.0

00

.036

.995

8.4

00

39

.27

1

124.1

72

282.9

01

484.1

71

655.3

97

733.0

96

701.0

72

596.7

96

47

1.7

59

358.2

31

270.1

61

208.4

54

16

5.7

89

135.0

41

112.1

41

94.6

21

80

.91

769.9

93

61

.14

653.8

78

47.8

34

42

.75

338.4

41

34

.75

131.5

69

28

.80

4

D/T

=0.

5

0.0

00

.02

3.6

385

.41

42

5.5

54

84.0

73

205.0

88

379.1

87

554.9

63

674.3

03

70

0.9

48

63

9.9

74

533.3

90

420.7

84

322.1

72

245.9

86

191.9

73

154.0

43

126.3

72

105.5

58

89.5

05

76.8

60

66.7

22

58.4

69

51

.66

0

45

.97

64

1.1

81

37

.10

033.5

97

30.5

68

Vi/

nre -

D/T

=0.

6

0.0

00

.016

.444

3.7

78

17.9

47

59.6

98

150.0

86

29

2.5

45

456.2

17

592.6

56

662.8

66

65

2.9

03

580.2

40

479.9

94

379.7

57

29

3.2

98

226.3

73

17

8.3

85

144.2

36

119.0

60

99.9

60

85.1

22

73.3

65

63.8

90

56

.14

2

49

.72

444.3

48

39.7

99

35 .

917

32.5

77

D/T

=0.

7

0.0

00

.012

.327

2.7

85

13

.29

3

44

.57

7113.4

27

226.7

39

369.0

97

505.8

02

599.8

53

63

1.2

35

601.3

02

527.5

01

435.6

58

346.3

00

26

9.6

88

210.1

29

166.9

74

135.9

11

112.7

98

95.1

30

81.3

19

70.3

16

61.4

09

54

.09

648.0

16

42

.90

738.5

73

34.8

65

D/T

=0.

8

0.0

00

.009

.250

2.1

38

10

.24

0

34.5

53

88.7

49

179.6

40

298.8

66

424.5

62

527.2

22

584.5

56

591.4

29

553.0

36

482.1

91

398.6

74

318.5

77

250.0

13

196.4

32

157.2

37

128.7

39

107.3

61

90.9

10

77.9

77

67.6

24

59.2

09

52.2

74

46.4

90

41.6

17

37.4

73

D/T

=0

.9

0.0

00

.007

.19

81

.69

38

.13

0

27.5

68

71.3

55

145.8

94

245.6

99

355.6

62

455.3

90

525.7

54

557.6

18

551.1

10

509.8

65

443.4

05

367.4

94

295.2

38

233.3

38

184.6

98

148.8

07

122.4

76

102.5

81

87.1

77

75.0

06

65.2

21

57.2

38

50.6

36

45.1

16

40.4

52

D/T

=1

.0

0.0

00

.006

.16

01

.37

36-

. 611

22.5

06

58.6

11

120.8

51

205.6

30

301.0

54

391.7

66

464.4

48

510.6

46

526.8

53

513.1

70

471.8

32

410.1

02

340.9

27

275.3

23

219.0

10

174.5

15

141.4

22

11

6.9

49

98.3

35

83.8

45

72.3

43

63.0

59

55

.45

749.1

53

43.8

67

D/T

=1.

5

0.0

00

.003

.071

.61

32

.97

3

10

.24

52

7.1

98

57

.61

11

01

.40

9154.3

35

209.1

84

25

9.1

80

30

1.0

51

334.4

62

306.2

09

379.5

53

392.6

02

397.1

79

390.6

84

371.6

47

339.6

45

29

7.3

80

251.3

33

207.5

31

16

9.3

40

13

8.4

14

11

4.6

86

96

.59

08

2.4

71

71

.24

1

D/T

=2.

0

0.0

00

.001

.040

.346

1.6

82

5.8

33

15

.64

33

3.6

21

60

.31

293

.885

130.4

71

165.8

68

197.5

37

224.5

56

246.8

16

264.6

57

278.6

69

28

9.5

08

29

7.7

95

30

4.0

78

308. 8

11311.5

32

310.2

51

302.7

32

287.5

20

263.9

02

233.3

37

199.9

76

167.8

83

13

9.4

65

NONLINEAR HYDROGRAPHS 85

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U.S. GOVERNMENT PRINTING OFFICE: 1971 O 446-375