COMPUTER METHODS IN WATER RESOURCES · 2011. 9. 13. · 6.11. Hardy-Cross Method 6.12. Hardy-Cross...

COMPUTER METHODS IN

WATER RESOURCES

COMPUTER METHODS IN WATER RESOURCES

THEODORE V. HROMADKA 11, PH.D., R. C.E. Depw-tment uf Civil Engineering University of California, Irvine

TIMOTHY J. DURBIN, M.S., R.C.E. United States Geological Survey, Sacramento, CA

JOHANNESJ. DEVRIES, PH.D., R.C.E. University of California, Davis

Mission Viejo, CA

To Laura, Valerie and Donna

ACKNOWLEDGEMENTS

Recognition is aranted to the San Bernardino County Flood Control District. California. for usc of figures and software contained in their hydrology manual. Gratitude is also extended to Burchard Gt.phios of Garden Grove, California for preparation of diagrams and figures, a,nd to Advanced Engineering Software of Irvine, California.

TABLE OF CONTENTS

ClIAPTER PAGE

1. Introduction 1

1.1; Discuss ion 1.2. Presentation

2. A Synthetic Unit Hydrograph Model

1 1

3

2.1, Introduction 3 2.1.1. Background 3 2.1.2. Terminology S 2.2. Determination of Synthetic Distribution

Graphs 6 2.3. Development of a Synthetic Unit Hydrograph 9 2.4. Intensity-Duration Curves for Design Storm

Point Precipitation 18 2.5. Area-Averaged Point Rainfall 20 2.6. Synthetic Critical Storm Patterns 20 2.6.1. Design Storm Pattern Approach 20 2.6.2. Depth-Area Relationships 26 2.6.3, Modified Composite Storm Pattern 26 2.6.4. Design Storm Point Precipitation 31 2.7. Effective Rainfall Estimation 31 2.7.1. S.C,S. Hydrologic Soil Groups 31 2.7.2. Antecedent Moisture Condition 33 2.7.3. Impervious Areas 37 2.7.4. Watershed Development Conditions 38 2.7.5. Estimation of Infiltration Rates 38 2.8. Synthetio Runoff Hydrograph Development 44 2.9. Instructions for a Synthetic Runoff

Hydrojraph Development 46 2.10. A Synthetic Runoff Bydrograph Program 50 2.11. PROGRAM 2.1. Data Study 50

3, Open Channel Flow HydrauliCS 81

3.1. Introduction 81 3.2. Conservation of Mass~ Momentum. and Energy 81 3.2.1. Conservation of Mass 81 3.2.2. Conservation of Momentum 82

3.2.3. Conservation of Energy 3.3. Fundamentals of Hydraulics 3.3.1. Hydraulic Grade Line and

Energy Grade Line 3.3.2. Specific Energy 3.3.3. The Specific Force 3.3.4. The Hydraulic Jump in a

Rectangular Channel 3.4. Gradually Varied Flow 3.4.1. S Profiles 3.4.2. M Profiles 3.4.3. C Profiles 3.4.4. The Standard Step Method 3.S. PROGRAM 3.1. Irregular Channel

Backwater Curve Analysis 3.5.1. PROGRAM 3.1. Data entry 3.6. Unsteady Flow Analysis 3.7. Derivation of the St. Venant Equations 3.7.1. Continuity Equation 3.7.2. Equation of Motion 3.7.3. Assumptions Used in the DerivatioD of

St. Venant Equations 3.7.4. Meaning of the Various Ter.s in the

St. Venant Equations 3.8. Unsteady Flow Profiles by the Implicit

Method with Double Sweep 3.8.1. Contin~ity Equation 3.8.2. Equation of Motion 3.9. Finite Differences 3.9.1. Continuity Equation 3.9.2. Equation of Motion 3.9.3. Double-Sweep Method 3.9.4. Upstream Boundary Conditions 3.9.5. Forward Sweep Computations 3.9.6. Downstream Boundary Conditions 3.9.7. Backward Sweep 3.10. PROGRAM 3.2. Unsteady Flow AnalySiS 3.10.1. Program Structure 3.10.2. PROGRAM 3.2. ~pplication

4. Modeling Groundwater Flow

4.1. Introduction 4.2. Equation of Groundwater Flow 4.2.1. Continuity Equation 4.2.2. Mathematical Definition of the

Groundwater Problem 4.3. Finite-Element Method 4.3.1. Introduction

xu

83 84

84 84 85

88 89 89 ., 91 ., 9' 95 96

110 112 114

the 118

119

119 120 120 120 122 123 124 126 127 128 128 129 129 130

144

144 145 145

148 150 150

4.3,2. Galerkin Method of Weighted Residuals 151 4.3.3. Trial Functions in One Dimension 153 4.3,4. Application to One-Dimensional Problem 155 4.3.5. Trial Functions in Two Dimensions 158 4.4. Program for Finite-Element Analysis 179 4.4.1. Program Structure 179 4.5. Regional Groundwater Problem 201 4.5.1. Geohydrologic Silting 208 4.5.2. Groundwater Model 211 4.5.3. Modeling Approaches 213

5. Modeling Groupdwater Transport 219

5.1. Introd'llct ion 219 5.2. Equation of Solute Transport 220 5.2.1. Continuity Equation 220 5.2,2. Mathematical Definition of tho

Transport Problem 228 5.3. Finite-Element Method 231 5.3.1. Galerkin Method 231 5.3.2. Assembly of Solution 236 5.3.3. Solution of the System of Equations 241 5.4. Program for Finite-Element Analysis 242 5.4.1. Program Structllre 242 5.4.2. Application to a Simple P~blem 261 5.5, Regional Solute-Transport Problem 261 5.5.1. Hydrologic Silting 261 5.5.2. Transport: Model 261 5.5.3. Modeling Approach 270

6~ Water Systems

6.1. Flow in Pipes and Pipe Networks 6.1.1. Introduction 6.1.2. Basic Equations for Pipe

276

276 276

Flow Analysis 276 6.2. Water Prop~rties 277 6.3. Flow Classification-Reynolds Numb~r 278 6.4. Pipe Friction Losses 278 6.4.1. The Darcy-Weisbach Equation 218 6.4.2. Empirical Form~las 281 6.5. Minor Lossn 284 6.5.1. Bend Losses 285 6.5.2. Entrance and Exit Loss Coefficients 287 6.S.3. Bxpansion and Contractions 287 6.6. Pipe flow Calculations-Single Pipe 287 6.7. Flow in Noncircular Conduits 291 6.8. Mll-ltiple Pipes 292

XIII

6.9. Three Reservoir Analysis 6.10. Pipe Networks 6.11. Hardy-Cross Method 6.12. Hardy-Cross Pipe Network Program

7. Storm Drain System Analysis

7.1. Introduction 7.2. Pressure Flow CADI Model

Appendix A- Lag Relationships

xiv

294 296 297 298

306

306 306

344

1.1. Discussion

CHAPTER 1 INTRODUCTION

Recently there has been a significant increase in the number of practicing civil engineers using computer programs for the preparation of water resource related studies. With the advent of inexpensive microcomputer systems, detailed hydrology and hydraulics studies can be prepared at a fraction of the CDst of analysis prepared by hand calculations. Additionally, lI'ith the availability of software prepared especially for microcomputers. new advanoes in water resources are readily distributed for use in pract leal design.

The main objective of this book is to provide both a summary of the basic principles used in water resources related engineering projects. and a collection of FORTRAN computer programs to apply these principles to a microcomputer system. The book focuses upon the following six major fields:

1. Watershed hydrology for urbanized watersheds,

2. Channel hydraulics for storm drain pipeline systems.

3. Water distribution systems.

4. Unsteady and steady flow in open channels.

5. Groundwater flow modeling,

6. Groundwater contamination modeling.

1.2. Presentation

This book has several features that should appeal to both the student or practicing civil engineer who wishes to advance his skills and prepare a comprehensive software library for use on a microcomputer system which supports FORTRAN. These features include:

1

COMPUTER METHODS IN WATER RESOURCES 2

1. Review of fundamental principles employed in the subject analysis procedures,

2. FORTRAN compnter programs tailor~d for use on a microcomputer system.

3. Detailed example problems,

4. Comprehensive proaram documentation including. when appropriate. user-f~iendly inpll.t form sheets for display on tne computer terminal.

It is stessed that the included software is currently in extensive use by small and large civil engineering fir.lIS. colleges, and publ:lc agencies. Sever.l of the programs are utilized for county~wide water resourceS planning purposes and flood control engineering.

CHAPTER 2 A SYNTHETIC UNIT HYDROGRAPH MODEL

2.1. Introduction

In this chapter~ a synthetic unit bydrograph methodology is developed and the associated computer code presented for use on microcomputers. Such a synthetic runoff hydro graph approach may be used for generating estimates of the peak flow rates needed for the design of flood control channels. and estimates for a time distribution of runoff volume for the design of detention basins.

2.1.1. Background

The unit h,dr08r8ph method is a synthetic bydrograph approach initially advanced by L. K. Sherman (1932). The keystone of the method is the assumption that watershed discharge is related to the total volume of runoff, aDd that the time factors which affect the unit hydrograph shape are invariant. The basic unit hydcosraph theocy was extended by F. F. Snyder (1938) to transpose storm rainfall-runoff relationsbips from gaged watersheds to hydrologically and geographically similar watersheds which lack rainfall-runoff stream g&.ge data. The basic assumptions used in this later work are that the watershed rainfall-ruDoff relationships are functions of watershed areB~ slope and certain shape factors. The method is uBed to estimate a ti~e distribution of runoff accumulating at the watershed downstream point of concentration when stream gage data is either unavailable or inadequate to provide a sound statistical analysiS.

To determine the rainfall-runoff relationships to be transposed to ungaged .atersheds~ stream gage records are studied for various types and sizes of gaged watersheds. For example~ the U.S. Army Corps of Engineers (Los Angeles Office) has determined :several runoff time-distribution patterns for watersheds in the State of California. These relationships provide a basis for transposing to ungaged watersheds a characteristic time distribution of runoff which is the average distribution for several si~ilar watershed ba:sins. This approaQh i:s considered applicable when watersheds are physiographicalty and hydrologically similar. In Southern California, the counties of Orange, Riverside, and San Bernardino (which together represent a vast spectrum of flood control conditions) have succc:ssfully utilized this approach in the development of county-wide flood

3


control facilities. Because the methodology used in tho California watersheds would apply elsewhere (with appropriate modificatioDs for local watershed rainfall-ruDoff relationships). the text and supplemental computer programs are based aD the California rainfall-runoff relationships with the intent that the programs can be easily modified by the user to accomodate other regional watershed runoff tendencies.

Although there are several theoretical shortcomings associated with the unit hydrograph approach (such as the assumption of a linear system where runoff hydrographs resulting from a unit period of effective rainfall can be directly snmmed)~ the general approach continnes to be widely used throughout the United States as a runoff synthesis method for ungaged watersheds. This chapter will examine the general unit hydrograph approach and several currently used variations of the method. A FORTRAN computer program is provided for a severe deSign storm condition (Rl'l)lIadka et al.. 1983a) w-hich is readily adaptable to currently available microcomputers.

The unit hydrograph approach involves several assumptions which are imprecise approximations of the corresponding hydrologic prOcesses. These basic assumptions are that (1) the critical storm rainfall pattern is uniformly distributed throughout the watershed. (2) there exists a direct proportionality betweeD watershed runoff and the effective rainfall volume. (3) for any volume of effective rainfall occurlng within a specified duration. the resulting runoff hydrograph is of a constant duration. and (4) the basin unit hydrograph is invariant throughout the critical design storm. The requirement that the watershed runoff is proportional to the effective rainfall has a direct analogy to a linear systems approach. Consequently. the unit hydrograph method can be conSidered a black-box modeling approach where the major characteristics of the model are determined by correlating the model output (runoff hydro graph) to the input data {rainfall records}. Al though the lumped-system model produces only approximations of the complex hydrologiC characteristics of tbe watershed# its use continues to be widespread due to the ease of application. However. all of the several individual processes involved in the total watershed hydrologic system have an associated probabilistic relationship which represents the changing of the variable with respect to time and with respect to the fluctuation of the other variables. Thus. to incorporate the diverse probability effects into a lumped-system or a more sophisticated distributed parameter model. the general model has to be structured towards statistical interpretation of model results and an associated interval of confidence. For studies involving a severe critical design storm over a highly urbanized watershed~ however. several of the variables may be eliminated from the hydrologic system model and the corresponding uncertainty is significantly reduced. For this type of condition. the unit

A SYNTHETIC UNIT HYDROGRAPH MODEL

hydrograph approach provides a runoff hydrograph which can be successfully used for flood control design purposes in watersheds which are hydrologically similar to gaged watersheds which have had unit hydrographs determined. A detailed analysis of the sensitivity of the unit hydrograph approach to the uncertainty associated to the precise definition of each model input parameter is given in Garen and Burges (1981). In that study~ it was shown that the model output of the runoff hydrograph is very sensitive to variations in the input parameter set. The level of discretization of the watershed into smaller subareas to be linked together in a link-node model of the watershed is addressed in Zaghloul (1981) and includes the sensitivity effects of including the various routing processes in a complex model. The basic linearity assumption introduces theoretical difficulties which are discussed in Helweg et ale (1982). That study proposes methods for incorporating model memory and nonlinearity effects into a complex watershed model. Although the statistical COmponent and the nonlinearity element~ should be included into the general runoff hydrograph generator. the difficulties associated with applying such sophistications in the general flood control study environment usually preclude their inclusion into a local agency's hydrology design criteria.

2.1.2. Terminology

In order to discuss the development of unit hydrographs for both gaged and ungaged watersheds. the following definitions are presented for the several terms:

BffectiTe a.inf.ll: the total rainfall less infiltration losses. evaporation. transpiration. absorption. and detention. This part of the rainfall runs off the watershed surface in a relatively brief time period.

Uait Hydroaraph: the unit hydrograph for a point of concentration on a watershed is a hydrograph showing the time distribution of runoff which results from a unit one inch of effective rainfall over the entire tributary watershed. The unit effective rainfall is assumed to occur as a constant rainfall with respect to both space and time throughout the unit duration. Figure 2.1 illustrates the general formulation of the unit hydrograph.

Distribution Graph: the distribution graph is a unit hydrograph whose ordinates are expressed in terms of percent of ultimate discharge. A distribution graph is generally developed as a block graph with each block representing its associated percent of unit runoff which occurs during the specified unit time period. The unit time used in the distribution graph is identical to the unit time specified for the unit hydrograph.

S .... tion Uydrolr.ph: the summation hydrograph for a point of concentration is a hydro graph showing the time distribution of the rates of runoff that would result from a continuous series of unit

5


effective rainfalls over the tributary watershed. Tho ordinates are o%pressod as rate of runoff in percent of tho ultimate rate of runoff.

La,: tho watershed lag is the time (hours) from the bog inning of a continuous series of unit effective rainfalls over tho watershed to tho instant when tho rate of reanl tins t1Uloff at tho point of concentration reaches SO percent of the ultimate rate of rUDoff. Another definition for lag is the time from the center of mass of tho effoctive rainfall to the peak of the corresponding runoff hydro graph. Some hydrologists define lag as the time from tho effective rainfall center of mass to the runoff hydrograph center of mass. In this chapter. however. the first definition of lag will be used for both the theoretical and computer program development.

VIti.ate _iacharse: the ultimate discharge (or the ultimate rate of runoff) is the maximum rate of watershed runoff which can result from a specified effective rainfall intensity. Ultimate discharge occurs when the rate of runoff on the summation hydrograph is equivalent to the rate of effective rainfall. For a unit effective rainfall intensity of one inch oc~urring in a unit interval of one hour. the ultimate discharge is 645 cis for every square mile of watershed.

S-Graph: the S-graph is a summation hydrosraph developed by plotting watershed discharge in percent of ultimate discharge as a function of time expressed in percent of watershed lag. Figure 2.1 illustrates each of the above unit hydrograph concepts and definitions.

2.2. Determination of Synthetic Distribution Graphs

In order to develop synthetic distribution graphs. adequate storm rainfall and watershed runoff information is required for several streams in the vicinity of the watershed under study. The distribution graphs for each of the gaged streams can be determined by trial and error attempts to duplicate the runoff hydrographs resulting from severe storm events. The derived distribution graphs are then verified by using them to reproduce runoff hydro graphs for other major storm events. In this procedure, the watershed is assumed to be a linear system which ignores the variation of the unit hydrograph during the storm eveDt. Models to approximately include memory and other nonlinearity effects have been studied by Helweg et al. (1982), among others~

It is assumed that the drainage areas within a given region are physiographical1y and hydrologically similar. Because no two drainage areas have identical hydrologic characteristics, the corresponding rainfall-runoff patterns are dissimilar and the distribution graphs will differ. Therefore, a direct transposition of distribution graphs between watersheds is usually


3 u

= • • ~ ;;

• 0 • • w u " w .--. w· ow ". •• •• u-!!!:i 0'

~ • ~

o

'00

.0

00

I

UNIT STOR.-E'~CTIVE ItAINfALL AT I-INCH/UNIT PER'OO

I rUIUT TUII

I UNIT GR ... ," (UNIT GIIAPH 0III01"AT!' EQUAL UNtT DISTRIBUTION GRAPH ORDINATIS IlUt..T'PLIEO IT ut.T'III"TE DISCH .... 'E.IC I I

I I I

.00 400 800 800 1000 ltoo TIME (PERCENT OF LA' TIMEI

SYNTHETIC UNIT HYOROGRAPH UNIT STOIUI-EP'nCTIVE RAIN'AlL AT I-INCH/UNIT PERIOG (UNIT G .... PH)

L..-UNIT TlMEly"It'''IU)

I (' .• """'0*""''' IIO$ITIOI'\ I --1""- S-GRAI"H O,FIIT ONI UNIT TIlliE PIIUOD

1£ .. V'-..1 UIIIT 015TllllUTI01II GRAPH!h PRIf'leIPLES Of SUPlEfllPOIITION)

.00 400 100 800 1000 1200

nME (P!RCINT OF LAS TIllE) UNIT PISTRIBUTION GRAPH

,..-COMTIMUOUS "ncTIVE RAWA'-", OF 1-1~CH/\fttIT ""100

UlTIMATE OISCHAftGf-OCCURS WHEN THE I'I:ATE M RUNO ........ TeHl!8 THI! un OF EFFECTIVE RAINFALL {HNCH/ HOUR. 64& e.f.S./SQUAltE MILEl

SUMMATION HYDROGRAPH

;--CONTINUOUS EFFEcnVE RAlI'ff'ALL AT I-INCH/UNIT PERIOO

b':bf-;; _ r-- LAG TIlliE-OCCURS WHEN DISCHA"GE EQUALS "; I 50% OF ULTI .... T£ DISCHARGE. ~" 0' O~~~~--""~-------Cc.oC--------:~--------~~--------7.0,---------.,.-----

100 % OF ULTIMATE DISCHARGE

o 100 200 400 600 800 1000 1200 TIME (PERCENT OF LAG TIME) S-GRAPH

Fig. 2.1. Derivation of a Synthetic Unit Hydrograph.

7


not feasable. However. most distribution graphs exhibit certain characteristics which appear to be related to the empirical factor of watershed 1ag. Details for determining watershed lag for watersheds where the time distributioD of runoff is known and for the use in developing synthetic distribution graphs are discussed in the following steps:

(U. Summation Hydrograph. The first step in determining watershed lag is the development of a characteristic summation hydro graph. which is the rUDoff hydrograph that results from a continuous and uniform sequence of unit effective rainfalls. The ordinates of the summation hydro graph are expressed as discharle in percent of ultimate discharge. The summation hydrograph for a point of concentration is also determined by adding a continuous series of identical distribution graphs each offset by one unit period. By examination, the time required to reach the ulti.lllate discharge is equal to the length of the distribution graph base less one unit period.

(2). Lag. Watershed lag can be defined as the time from the beginning of unit effective rainfall to the instant that the summation hydrograph reaches SO percent of ultimate discharge. When the lags determined from summation hydrographs tor several gaged watersheds are correlated to the hydrologic characteristics of the watersheds, an empirioal relationship is usually apparent. This relationship can then be used to estimate lag for nngaged watersheds. AnalysiS of watershed lags estimated for several types of watersheds indicate that a lag factor is expressed by

C2.1)

where watershed lag in hours

"" a constant = length of longest watercourse (miles)

s

"" length along longest watercourse. measured from the point of concentration to a point opposite the watershed area centroid

"" mean watershed slope along watercourse (feet~ile) m "" a constant

For Southern California watersheds. it is assumed that

• n m Ct

;

;

;

a basin factor (see Fig. 2.2' O.3~ 24.

C2.2)


The basin factOI:5 of Fi&. 2.2 were determined by the U.S. Army Corps of Engineers by duplicating major storm runoff hydrographs from several Sou~horn California watersheds. The relationship between watershed lag and Eq. (2.1) is illust:u.ted in the plot of Appendix A. From (2.1)~ the synthetic unit hydrograph approach is a strong fenction of the watershed lag. and a wide range of results are generated by a variation of the basin factor. (3). S-Graph. After lag factors are determined for several gaged watersheds. the next step in determining synthetic distribution graphs is the development of S-graphs~ which are sutlt.mation bydrographs modified so that the percent of ultimate discharge is plotted against tillle expressed in percent of watershed lag. The derivation of a S-graph is identical to the development of a summation hydro graph except that the relationships are now expressed with respect to watershed lag. Four S-graphs assumed applieable in Southern California watersheds are shown in Figs. 2.3a .. b.c.d. These S-graphs are for use in watersheds classified as valley. foothill. mountain. or desert. According to the definitions. each S-graph reaches SO percent of ultimate discharge at 100 percent of watershed las.

(4). Application of Lag and S-Graphs. To use the S-graphs. a watershed lag is estimated from Figs. 2.1 and 2.2. A unit period is selected (usually at 15 to 2S percent of the watershed lag time) and amassed unit periods are expressed as accumulated percentages of the watershed lag. These percentages of lag are used for superimposing a block graph on the selected S-graph and the resulting block graph pattern is used in determining the accumulated mean percentage of ultimate discharge for each accumulated unit period. Finally. the incremental mean percentage of Ultimate discharae for each unit petiod is estimated by a series of successive subtractions. The following section describes in detail the discussed procedure as applied in developing a watershed unit hydrograph.

2.3. Development of a Synthetic Unit Dydroaraph

For watersheds where stream gage 6ata is inadequate for statistical analysis .. a synthetic I1nit hydrograph may be used to approximately describe the time distribution of runoff gathering at the point of concentration. A method for developing a synthetic unit hydrograph is described in the following steps:

(1). Estimate the watershed la8 1uin8 tQPographic information~ Eq. 2.1. and the appropriate basin factors (such as Fig. 2.2 tor Southern California watersheds).

(2), Select a unit period duration. This unit period will be the time base for describing unit rainfalls and the corresponding runoff hydrographs. Usually. 15 to 2S percent of the watershed lag is adequate for computational purposes,

9


• n = O.OU 1. Drainage area has fairly uniform, gentle slopes 2. Most watercQurses either improved or along paved streets 3. Groundcover consists of some grasses - large 96 of area impervious 4. Main water course improved channel or conduit

• n= 0.020 1. Drainage area has some graded and non-uniform, gentle slopes 2. Over half of the area watercourses are improved or paved streets 3. Groundcover consists of equal amount of grasses and impervious area 4. Main watercourse is partly improved channel or conduit and partly greenbelt (see

n*: 0.025)

n* = 0.02' 1. Drainage area is generaUy rolling with gentle side slopes 2. Some drainage improvements in the area - streets and canals 3. Groundcover consists mostly of scattered brush and grass and~smal1 % impervious 4. Main watercourse is straight channels which are turfed or with stony beds and

weeds on earth bank (greenbelt type)

n' = 0.030 (Foothill Area) 1. Drainage area is generally rolling with rounded ridges and moderate side slopes 2. No drainage improvements exist in the area 3. Groundcover includes scattered brush and grasses 4. Watercourses meander in fairly straight, unimproved channels with some

boulders and lodged debris

n* :: 0.040 (Foothill Area) 1. Drainage area is composed of steep upper canyons with moderate slopes in lower

canyons 2. No drainage improvements exist in the area 3. Groundcover is mixed brush and trees with grasses in lower canyons 4. Watercourses have moderate bends and are moderately impeded by boulders and

debris with meandering courses

n*:: 0.050 (Mountain Areas) 1. Drainage area is quite rugged with sharp ndges and steep canyons 2. No drainage improvements exist in the area 3. Groundcover, excluding small areas of rock outcrops, includes many trees :lnd

considerable underbrush 4. Watercourses meander around sharp bends, over large boulders and conSider dole

debr is obstruction

• n = 0.200 1. Drainage area has comparatively Wliform slopes 2. No drainage improvements exist in the area 3. Groundcover consists of cultivated crops or substantial growths of grass and

fairly dense small shrubs, cacti, or similar vegetation 4. Surface characteristics are such that channelization does not occur

Fig. 2.2. Basin n * Parameter Descriptions.

A SYNTHETIC UNIT ]IYDROGRAPII MODEL

~m

*~ I~I h.~ l,':

~ "= , I=-

~~~

- . .:. -, , - - oc- .. ',:=" ,'c ,. II

-::Vee."',, i .. .-c("', c'\ ,~. ,"

...[

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.• .::, : _, .,. tee ' ... 1-, ,. -, . " I c

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.. . ••.. ,." . '",ec . .. (, I,':, .'. ,.,::. - ,:..:. ",,,I

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11


Fig. 2.3b.

I

I -!.

I

I

Fig.2,3c.

, I

I I

A SYNTHETIC UKIT HYDROGRAPH MODEL

13

NO

COMPUTER lIIETHODS IN WATER RESOURCES

14

,

-

~"

I I I

Fig. 2.3d.

r

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.

,

Ic' •.

c~'I'" •

,

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(3). Select _ "a.t.e1~$hed S-araph "hicb is determined from a set of gaged watersheds which are physiographica11y and hydrologically similar to the study watershed.

(4). The S-graph can be approximated by a block graph where the base of each blook is the selected unit period (expressed in percentage of watershed lag time) and the ordinate of each block is the time-averaged percentage of ultimate discharge (from the S-graph) for the corresponding unit period. The area of each block equals the area under the S-graph for each respective unit period.

(5). The unit distribution graph is approximated by calculating the difference between the ordinates of the block graph used to appro~imate the watershed S-grap~. This procedure is analogous to calculating the difference between the ordinates of two S-graphs which have been offset by one unit period.

(6). The final step in developing the synthetic unit hydrograph is to multiply the ordinates of the distribution block graph by the ultimate discharge defined by

where

K = 64S.vr

r = the watershed ultimate discharge (efs) A : drainage area (square miles) T = unit time period (hours)

(2.3)

A widely used unit hydrograph is the S.C.S. dimensionless unit hydrograph of Fig. 2.4. From the figure. the ooncept of time to peak (Tp' is used and is s.hown to be gecmetrically related to the watershed lag time. The County of San Diego. California (1975) uses the empirical watershed lag formulas of (2.1) and (2.2) plus the relationship

Tp "" (0.862)1ag (2.4)

Equation (2.4) is based on the geometric relationships for the bydrographs shown in Fig. 2.4 which includes the triangular version of the S.C.S. curvilinear unit hydrograph. From Fig. 2.4. it is assumed that

(2.S)

A tabulation of the S.C.S. dimensionless unit hydrograph ratios is given iu Table 2.1. FTom the tabl~~ it is seen that whatever the condition or classification of the watershed, the ratio of the time to peak to total unit hydrograpb duration is a constant. Additionally. it is seen that the volume of runoff nnder the riSing limb of the unit hydrograph is a constant 37.5

15

COMPUTER METHODS IN WATER RESOUll,~C""E"S ___________ _ 16

AT

. : : tIT.

Fig 2.4. S. C. S. dimensionless unit hydrograph andequu.,-@enttriangularhydrograph.

" ) 'j 1

I

Fig. 2.5. Definition QfEspey l()...minute unit hydrograph parameters.

A SYm'HETIC UNIT HYDROGRAPH MODEL

percent of the total runoff volume, and that the peak rate faotor associated to the unit rainfall is a constant 'Value of 484. The variability of the S.C,S, '«uit hydrograph with respect to otber peak rate factors is investigated by McCuen and Bondelid (1983). In their 5tudy~ methods to estimate a poak rate factor for ungaged watersheds is proposed using a gamma function distribution for the unit hydrograph aod the estimation of appro~imate watershed storage effects in the determination of the volume of runoff defined under the rising limb. As with many other unit hydrograph schemes. the assumption of linearity is once again utilized to develop a runoff hydragraph. Watershed peat rate factors aro determined by time-area analysis and attempts to duplicate runoff hydrographs. The study concluded that the peak rate factor of 484 may be inappropriate for many watersheds ..

Possibly, more insight into the mechanics of the unit hydrograph is gained by working with the Espey and Altman (1978) approach. This version of the unit hydrograph ;involves a set of fiv~ parameters which are defined according to Fig. 2.5. The variable relationships are of the form

where

= (3.')LO.23S-0.25r-0.18K,·57

= (12S890) AQ-o·9S

(31620)AO.96T -1.07 Q = p

L = H = S = I = A =

i!: l =

WSO ·W7S =

= (16220)AO. 93Q-o.92

(3240)AO. 79Q-O.78

main channel length (feet) drop in elevation along channel channel slope impervious area fraction watershed area (square miles) time to peak (minutes) base time (minutes) a dimensionless channel conveyance width at 50 percent and 75 percent

factor Q

(2.6)

The Espey unit hyd:rograph is sensitive to the channel conveyance factor (Ie) in a fashion analogous to .the sensitivity of the general u.nit hydrograph to the basin n factor. Both of these methods require some sort of tuning in order to evaluate their respective parameters ..

17


~~-- --

T.ABLE 2.1 ~ RATIOS FOR T1IB 8, C. S. UNIT Hf.l)ROORAPD

Time Ratio 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 l,BO 2,00 2.20 2.40 2,60 2.80 3,00 3,20 3,40 3.60 3,80 4,00 4.50 5,00

Discharge Ratio 0,000 0.030 0.100 0.190 0.310 0,470 0,660 0.820 0,930 0.990 1.000 0.990 0.930 0,860 0.180 0.680 O,S60 0.460 0.390 0.280 0.207 0.147 0.107 0.077 0.055 0.040 0,029 0.02l. 0.015 0.011 O,OOS 0.000

Mass Curve Ratio 0.000 0.001 0.006 0.012 0.03S 0.065 0.107 0.163 0.228 0.300 0.37S 0.450 0.522 o .SB9 0.650 0.700 0.751 0.790 0.822 0.871 0.908 0.934 0.953 0.967 o .9'l'l 0.984 0.989 '3.~Sg.

0.99S 0.997 0.999 1.000

2.4. Int~nsity-Duration CGrves for Design Storm Point Precipitation

Rainfall intensity verSUs storm duration data is roquired for usc In de.eloping a synthetic 4esign storm. Intensity-duration curves caSl be developed for a watershed by e&timating the area-avt;raged one h!)ur POil1t preCipitation values iroB synthesized 10ed rain gage data, or from reliable po;i.nt precipitation maps. Usin. Fig. 2.6~ U.e one hou.r pOint. precipitation value is plotted~ and a straight line is drawn with the appropri.ate slopc~ Genu'ally, slopes vary froll about 0.30 to 0.80.

A SYNTHETIC UNIT HYDROCRAPH MODEL

,. STORM DURA.TlON {MINUTES}

DESIGN STORM FREQUENCY'_ YEARS ONE HOUR POINT RAINFALL '_/NCHES LOG-LOG SLOPE= _____ PROJECT LOCAT/ON·' ______ _

Fig. 2.6. Intensity-duration curves calculations sheet.

19


2.5. Area-Averaged Point Rainfall

Due to the potential variation of precipitation depth (for a given duration) throughout a watershed. approximate methods arc required in order to estimate an area-averaged polDt rainfall for the enUre watershed. The three most often used Ilethods are the arithmetic method~ the Thiessen poly,on method~ and the isohyetal method. The application of these methods is shown in Fig. 2.7.

The arithmetic method is a Simple average of point rainfall values. It is the least accurate of the three approaches for a:t'oa-averaging.

The Thiessen polygon method utilizes an area-averaged value based on polygons associate'd to each rain gage in the vicinity of the watershed. The polygons are determined by constrnctins perpendicular bisectors to li~es connecting the several rain gages.

Final1y~ the isohyetal method is a more preCise approach in which a map of the interpolated point rainfall isohyetals are plotted on the watershed and the area-averased point rainfall is directly estimated by contou% integration.

2.6. Synthetic Critical Storm Patterns

2.6.1. Design Storm Pattern Approach

The ~se of computer .atershed simulatiou techniques for hydrologic analysiS has become widespread with the advent of inexpensive digital computer availability. Generally speaking. the oasis of the hydrologic model in! approach is to study tho effects of a severe storm event (or design storm) upon the watershed. Consequently~ the docision as to what critical storm to use for stDdy purposes has a significant impaQt upon the ultimate design objective in providing flood ~ontrol.

The critical storm approach falls into two categories: (1) a severe storm pattern of record, and (2) a synthetic critical storm pattern. Tho critical storm patterJl of record is a historical rainfall event which is assumed to be associated with tho severe flooding event. The storti! may have occurred within tho vicinity of the .. atershed~ or may have occurred elsewhere but is assumed to be transposable to the study watershed without violating the assumptions of uniformity of hydrologic or geographic characteristics. For examp1e~ the U.S. Army Corps of Engineers (Los Anseles~ Calif.> utilize for study purposes a critical storm pattern based on a 1943 thunderstorm (Fig. 2.8). From Fig. 2.8. the 3-hour duration storm is composed of twelve IS-minute unit durations of precipitation depths. These unit rainfall values are estimated from peak 15-, 30-, 60-~ and 180- minute duration precipitation-depth values as a function of watershed area. The storm pattern is based upon a 3.3-inch total storm rainfall. In transposing the storm to another watershed~ the local 3- hour

A SY:-ITHETIC UNIT HYDROGRAPH MODEL

(j . io')

( I. 72')

( LiO')

(1.84")

(I.io')

( 1.72')

Fig. 2. 7. Point rainfall area_averaging method.'!.

(3.76")

( 1.80")

ARITHMETIC MEAN

(3.76")

( I .80")

THIESSEN METHOD

0-{Yo

la.O}

~SOHYETAL METHOD

21

(I) UJ J:: U z z .8

-' -'

" "-Z " •• a:

.2

.1 1


22

• 6 20 DRAINAGE AREA IN SQUARE MILES

UNIT PERIOD

2 3

• • • 7 8 9

10

" "

HYETOGRAPH COMPUTATION

AMOUNT

.07 (R(lBO)- R(60))

.05 (R(l80)- R(60»

.11 IR0801- RISOil

.05 (R(IBO)- R(60)}

.20 (ROBO)-ReSO»

.22 (R(l80)- R(60»

.14 (R{lUO)- R(60»

.16 (RUaOJ-R(6.J»

.18 (R(SOJ-R(30»

.52 (tH60}-~(30)) IUO (RCHS)) 1.00 CResol-RCIS))

"lNI. PERIOD ", hi ~lINUTf:S

Fig. 2.8. Critical storm depth-area-duration curves.

100


duratiun procipitation-depth i~ estimated (for the dc~ircd return £requen~y) and the adjusted storm pattern is obtained by a simple ratio. For Il depth of 3.3 inchc$~ the J:tlsulting storm pattern is SbOWR in Fig. 2.9. A difficulty with this stOrm pattern is tAat the precipitation-depth ratio of interior durations to the total 3-hour duration may not be appropriate for the local region of ill.tere$t~ and an unacceptably high (or low) precipit.ation depth may be assigned to the interior unit rainfalls. For e~.mple~ the design objective may be to provide flood protection fOr a 100-year return frequency rainfall for the critical duration of every hydraulic structure within a watershed. Then using a 100- year 3-hour depth _lth the given storm pattern may pOSSibly result in a 150- year (or 50- year) return frequency rainfall depth to be assigned for some oritical dUration. Designing the structure for snch a runoff rate would result in an overdesisn (or underliesign).

The second category of critical storm patterns is the synthetic critical storm pattern. This approach is an attempt to accotllodate some of the concerns whioh are associated yith using critical storm patterns of record. Several synthetic storm patternS have been proposed~ such as Keifer and ehu (1957), Huff (1961), T-erstriep and Stall (1974). PilBT.1m and Cordery (975). among others. For example. Hershfield (1962) developed a normalized time distribution of total mass rainfall versus storm duration. This generalizod distribution is given in Table 2.2.

TABLE 2.2. HERSHFIELD MASS RAINFALL DISTRIDUTION

Storm Dotation

0.00 0.10 0.20 0.30 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.80 0.90 1.00

Mass Rainfall

0.00 0.06 0.12 0.20 0.29 0.34 0.45 0.63 0.73 0.31 0.36 0.94 0.99 1.00

A widely osed set of oritical storm patterns was developed by the tl.S. Department cf A&ricu.lt'l1re. Soil ConStlr'Vaticu Service (S.C.S •• 1913). The synthetic storm patterns are presented in normaliLed mass rainfall f~shiou for both a 6- hou! And 24- hour dnration critical stor~ event. The 24- hOur storm pattern is

23

COMPUTER METHODS Tl' WATER RESOURCES

24

further classified a$ a type r or type Ir~ in order to better represent different stOUI preoipitation intensity chuacteristic.s as avet_sed over broad rogiOns of the United States. Tho S.C.B. developed the dimen,ionless synthetic 8t~rlll pattert1-$ uaill8 the ~.S. leatber SerVlce rainfall frequency rep~:tts. The patte~s are based npon regionally averaled rainfall Rage data for watershed aroaa less than approl1mUe1y 400 square miles, .,.ith dllratic.ns to 24 hOllts. and retll:r:n.. frequ

A SY)1THETIC UNIT HYDROGRAPH MODEL

25

NOTE' 1.1 INCHES OF UNIT RAINFALL EQIMLS A 4.4 INCH/HOUR INTENSITY.

Flg. 2.9. Inch depth criticul storm patlern(JO $quare mile Qrea).


appropriate for dosign study purposes for both small and largo watersheds. The dimensionless S. C. S. 24- hour type I pattern is presented in Table 2.3.

An c%amination of both the Bershfield and the S.C.S. synthetic storm patterns indicate that neither pattern guarantees a critical precipitation depth for an arbitrary critical duration. That is, both patterns define each interior storm duration as " fixed percentage of total storm mass rainfall. The Composite Method for developing a synthet Ie storm pattern is analogous to the approach used by the S.C.S, except that the local rain gage data is used to determine the unit rainfalls. This method simply uses the local rainfall intensity-duration curves with the desired return frequency, and incremental unit rainfalls are determined by successive subtractions. The unit rainfalls are then arranged in sOlbe nested pattern with the peak intensities usually defined to OCcur at 0.50, 0.67, or some percentage of the total storm duration. Fig.res 2.10 a,b,c show a typical composite st~rm pattern which is used for design hydrology purposes in the County of San Bernardino, California (Hromadka and Gaymon, 1983b).

2.6.2. Depth-Area Relationships

A critical storm pattern can be directly applied towards estimating peak flow rates and runoff volumes associated to small watersheds where stream gage records are inadequate for statistical freqnency analysis. As the watershed area increases in size, however, studies indicate (Miller et al., 1973, Myers and Zehr, 1980) that the area-averaged point rainfall values used in the design storm pattern shonld be adjnsted. For example, the NOAA Atlas '2. includes point rainfall depth.-area reductio1\. relationships (Fig. 2.11) for 30- minute, 1-, 3-. 6-, and 24- hour point rainfall values as a function of watershed size.

2.6.3. Modified Composite Storm Pattern

The composite storm pattern approach can be modified to include the effects of depth-area adjustment. However, due to the adjnstment factors being available for only a few durations, an interpolation procedure is reqnired for the remaining durations within the storm pattun. One approach is to plot the adjusted point rainfall values on standard log-log paper and assume a straight line relationship (see Fig. 2.12). Other relationships can be used, but the log-log plot is convenient in that the resulting mass rainfall plot is simple to apprOXimate numerically. Unit :rainfalls axe determined for the modified composite stor'lrl pattern by successive subtractions of unit durations along the adjusted mass rainfall plot. The unit rainfalls are then arranged as is shown in Fig. 2.13.

· ! •

.~

\ a • • • ~ i • 0 • • • •

• • , • . ~

__ ~A=SYNTHETIC UNIT HYDROGRAPH MODEL

; , · •

1--

. • , ;

· , -

RIO " llOE TOT~L M .... Of' C.'T,,,..'- STOfIOO R"'H~"''''' DURING""" """" " ........ , ...

• , • • · • ,

.~

• • , • ,

• •

..•. • , , · ·

•••

••

• • • ,

STOUI TIME IMI


100 -~

"- ........ 24-HOUiIII-

90

\ "- a-HOUit

,

I-

1\ - "

" -

\ " \ "

I-HOUR

"

SO-MltlUT!I

0 , 0 ~ AREA (SQUARE MLES) S

Fig. 2.11. NOAA Atlas - 2 depth-area curves.


STORM ouRATION-MlNUTES

PROJECT LOCATION ?.!I4MPLE I'R081.£M

NOTES /00 VR." 5 MIJ/. • 0. 55 • ./10 MIJ/. .. /.l3! I 1I0l/R- /.52 #

!I HouR .. 2,90. 41110l/1l'" 4.t9 ! 24 !IOt.IR ... 9·8'

Fig. 2.12. Area-averaged mass rainfall plotting sheet.

29


30

MASS RAINFALL DISTRIIUTION (PERCENT OF TOTAL 2'~ HOUR STORM'

a o UNIT RAINf"'-L. {INCHES)

Fig. 2.13. Example synthetic 24-hour critical storm.


2.6.4. Design Storm Point Precipitation

In order to generate a rnnoff hydrograph. a 4e5ign storm rainfall pattern needs to be developed which incorporates the local rainfall intensity-duration tendenc ies. Generally, point precipitation isohyetal information is adequate (e.g. NOAA Atlas 2, 1913) for estimating local rainfall depths of a desired return frequency. Such isohyetal maps can be used to obtain peak point precipitation depths for storlb durations from 15 minutes to 24 hours and with return frequencies from 2 years to 100 years. Because additionAl rainfall dtttli may alter the 8tllti8ti081 patterns used to develop the isohyetal maps, such generalized data should always be verified with a ~eceDt frequency analysis for 811 rain gaZes within the vicinity of the study watershed.

The peak S-minote. 30-minute. I-hour. 3-hour. 6-honr i and 24-hour area-averaged point precipitation values should be determined to tvaloate the critical design storm pattern Dsed to develop the runoff hydrogrllph. Extrapolation procedure$. are of ton used to estimate intermediate dUration point precipitation values. For example. it may be assumed that the peak 3-hour point precipitation value is related to the peak I-hoor and 6-hour point precipitation values by straightline interpolation on log-log paper. Using the appropriate I-hour point precipitation valoe i the peak 5-minote and 30-minute point rainfalls can be estimated using Fig. 2.6.

To account for the areal effects on point precipitation values~ reduction factors can be used to adjust the area-averaged point rainfalls (e.g. NOAA Atlas 2. or locally determined depth-area curves). In the unit hydrograph approach. the volume of watershed runoff is related to the watershed average depth of preoipitation rather than the depth at specific points within the watershed. Depth-area curves approximately relate the average of all point preCipitation values for a specific duration and frequency to the average depth of precipitation within the watershed for the same duration and frequency. The NOAA Atlas depth-area curves of Fig. 2.11 provide adjustment factors for the SO-minute. 1-hour. 3-hour. ~-hour. and 24-hour point precipitation values. These curves are an average for the entire United States. however. and local depth-area tendencies may differ substantially.

2.7. Bffective Rainfall Estimation

2.7.1. S.C.S. Hydrologic Soil Groups

A major factor affecting infiltration is the condition of the soil. The soil surface characteristics. ability to transmit water through subsurface layers and the available soil stora&e capacity are all variables in defining the infiltration rate function. The S.C.S. classified more than 4000 soil types into four general categories whieh provide a elas!1ifieation of infiltration rates

31


32

and corresponding runoff rates. These soil groups are defined in Table 2.4. The S.C.S. also uses ourve numbers (eN) to describe the soil runoff potential. Further studies in California watersheds. however~ provide some adjustments to the eN valnes. Runoff index numbers (RI) aro used in this chapter to describe tbe use of these modified eN values.

Soil infiltration rates can be estimated for each of the soil groups by laboratory studios and measurements. Such measurements show that given a sllfficient water supply. an initially dry soil will have an associated infiltration rate which essentially decreases with time. Consequently, if the soil is subjected to a continuous rainfall rate which exceeds the infiltration capacity~ the infiltration loss rate will decrease with increaSing storm duration. Depending on the condition and cover of the soil. a relative minimum infi! tration rate for the S.C.S. soil groups are given in Table 2.S (e.g. U.S. Burea'U. of Reclam.ation. 1973).

TABLE 2.4. S.C.S. HYDROLOGIC SOIL GROUPS

(A): Low runoff potential. SoUs havins a high infiltration rate C"Ion .. nOD thoroughly 'Wetted. Consists chiefly of deep. well drained sravels and sands.

(B): Soil8 hevins moderate infIltration rates when thoroughly wetted. COD8ists mainly of moderately deep, well drained soils with moderately fine to moderately coarse testure.

(e). Soils havins low infiltration rates when thoroushly wetted and consisting chiefly of soils with a layer that illpedes the downward migration of water, or soils with moderately fine to fine texture.

(D): High runoff potential. Soils having a very low rate of infiltration when thoroughly wetted and consisting chiefly of clay soils with a high swelling potential, soils with a high water table (eliminating soil water storage capacity), soils with a claypan or clay layer at or near the soil surface~ or shallow soils over a nearly impervious layer.

TABLB 2.5. IIINIMUII INFILTRATION RATES

S.c.S. Soil Group InfU tration Rate (ilVhr)

A 0.30 0.45 B 0.15 0.30 C 0.05 0.15 D 0.00 0.10

Soil Cover

The type of vegetation or ground cover on a watershed~ and the quality or density of that cover. have a major impact on the


infiltration capacity of the soil. A widely used system for defining the effeets of soil cover was developed by the S.C.S. and is based on the three categories given in Table 2.6.

In most cases, cover type and quality can be readily determined by an inspection of the watershed. U.S. Forest Service and S.C.S. personnel may also be helpful in estimation of sBoh information. Cover types are listed in Fig. 2.14 which relate RI numbers for various cover qualities. General descriptions of cover types are given in Fig. 2.15.

TABLE 2.6. SOIL COVER QUALITY DEFINITIONS

POOR: Heavily grazed or regularly burned areas. Less than SO percent of the ground surface is protected by plant cover or brush and tree canopy.

FAIR: Moderate cover with SO percent to 7S percent of the ground surface protected.

GOOD: Heavy or dense cover with more than 7S percent of tho ground surface protected.

2.7.2. Antecedent Moisture Condition

In order to accomodate the effects of prior precipitation events, the S.C.S. antecedent moisture condition (AMC) criteria are often used to adjust the infiltration loss rates. ABC curves were determined by analysis of rainfall-runoff data collected from a large number of watersheds where vegetative cover and soil condit ions were \no ... n. For each ... ateIshed, the 14-hour runoff volume was plotted against the 24-bour rainfall. To accomodate scatter in the data. three runoff index numbers (that is. S.C.S. eN values) were associated to each watershed. The RI number which resulted in an equal number of high and low rUDoff predictions was defined to be an AMC II condition. Lower and upper enveloping RI numbers were associated to ANC I and AMC III conditions, respectively. The ANC designations are defined as follows:

TABLE 2.7. ANfECIlDENT MOISTURE CONDITION (AMC) DEFINITIONS

AMC I: Lowest runoff potential. Tae watershed soils are dry enough to allow satisfactory grading or cultivation to take place.

A_C II: Moderate runoff potential. An intermediate condition which is generally assumed for annDal flood studies.

AXe III: Highest runoff potential. The watershed is practically saturated from prior precipitation events. Heavy rainfall (or light rainfall with low temperatures) has occurred within the last five days.

33


Runoff IndelC Numbers of H~rolo!iic SoU..cover ComeJexes For Perviou$ Areas-AMC II

Quality of SoH Group Cover Type (I) Cover (2) 1\ -" 0

NATURAL CoveRS-

Barren 78 8. '1 '3 (Rockland, ert>ded and Sn.ded land)

Chaparrel, Sroadleaf '00' 53 70 80 8> (ManzlJIlita, ceanothus and scrub oak) Pair 40 63 n 81

Goad 31 51 " 78 Chaparrel, Narrowleaf >00, 71 &2 8. '1 (Chamist' and redshank) Fair " 72 81 8. Grass, Annual or Perennial P~ '7 78 86 8.

Fair ,0 6. 7. 8. Goad 38 6\ 7, 80

Meadow," or Cienegas Poor 63 77 " 88 (Areas with seasonally high water table, Fair '1 70 80 .. principal "egetati.on is $Od forming grass) Good 30 '8 71 78

open Brusn ..... 62 76 .. .. (Soft wood shrubs - buckwheat, sage, etc.) Fair

_. •• 77 8,

Good " 63 ]j 81 Woodland Poo, ., 66 77 83

(Coniferous or broadleaf trees predominate. Fair 36 60 73 7, Canopy density is at least .50 percent.) Good 2$ " 70 77

Woodland, Gra$S Poo, " " 82 8. (Coniferous O!" broadleaf trees with canopy Fair --., 77 82

den}lty from 20 to 50 percent) Good 3) ,. 72 7. URBI\N COVERS -

Residential or Commercial. Landscaping (Lawn, shruln, etc.)

Good 32 56 .. 7> Turf Poo< >8 7_ 8' 87

(Irrisated Ilfld mowed grass) Pa.ir .- " 77 82 Good 33 58 72 79 AGRICUt TURAL COVERS ~

Fallow 77 S6 '1 9_ (Lllfld plowed but not tilled or seeded)

Fig. 2.14 (1 of2). Runoffin.dex numberR {or pervwus areas.


35

Runoff lndex Numbers of H~drolo8ic Soil-Cover Come:lexes For Pervious Areas-AMC U

Quality of SOU Groue Cover Type (I) Cover (2) " 0 C; ID

AGRICULTURAL COVERS (Continued)

legumes, Close Seeded Poor 66 77 85 (Alfalfa, sweetclover. timothy, etc.) Good >8 72 81

Orchards, Evergreen Poo, >7 73 82 (Cjtrus, avocados, etc.) Fair -- 65 77 Good )J 58 72

Pasture, DryJand Poo, 68 7' 86 (Annual grasses) Fair ., 6' 7'

Good " 61 7_ Pasture, Irrigated Poo, 58 7_ n

(Legumes and pereMia! grass) Fair .- 65 77 Good 33 58 72 Row Crops Poo' 72 81 88

(Field crops - tomatoes, sugar beets, etc.) Good 67 78 S>

Small grain Poo' 65 76 8_ (Wheat, oats, barley, etc.) Good 6J 75 83

Notesl

1. All runoff index (RI) numbers are for Antecedent Moisture Condition CAMe) D.

2. Quality of cover definitions:

Poor-Heavily grazed or regularly burned areas. Less than '0 percent of the ground surface is protected by plant cover or brush and tree canopy.

Fair-Moderate cover with '0 percent to 75 percent of the ground surface protected.

Good-Heavy or dense cover with more than 7.5 percent of the ground surface protected.

Fig. 2.14 (2 of2). Runoffindex numbers for pervious arcas.

8' 8>

86 !2 7,

8' 8_ 80

87 82 7'

91 8'

88 87

COMPUTER 'METHODS IN WATER RESOURCES 36

peryioul .~~ 01 =:"::;:·~'ndwJlje .. m"..·y ..... !reeL poria

- 1.ettuee. tomatoes, beets, tulIps or any field crop planted in rows apart th&t mast of the soU surface is exposed to rainfall Impact

t~;:.~;~ the growing season. At plow!nl, planting and harvest dmes it is e to fallow.

- Whe&t, OIlta, barley, flu., e'tc.. planted In lOWS c;kqe enough u..t is not exposed except dlM'i", plant1n& and Ihortly thereafter.

Legume, - A1faUa, sweetclover, timothy, etc. and combinations are either planted In close fO'" or bto&dc:ut~

~ - Fallow land Is land plowed but not yet seeded or tUled.

- Areas with an open cover of brOlldleaf at coniferous trftS pines, with the interveninll lI'Ouncf space occupied by BMual

grasses or . The trees may occur singly or in small clumps. Canopy density, the amount of Bround surface shaded at hish noon, is from 20 to 50 percent.

WoodJand _ Areas on which eonif@f'ous or broadl$af U.s predominate. The canopy density is at least -'0 percent. Open areas may have. cover of annual « peJ"eMial grasses or of brush. Herbaceous plant cover under the trees is usually sparse because of leaf or needle litter accumulation.

- Land on which the pdnclpe.l vegetation consists of evergreen shrubs hard, stiff leaves such as manzonlta, c:eanothus and scrub oak. The is usually dense or moderab!Jy denS!!. DIffusely branehed evergreen fine needle~like leaves, such as chamise and redchank, with dense

high growth are also included in this soil cover •

... Land on which the principal vesetation consists of annual such .. annual bromes, wild tNariey, soft chess, ryesrus and

... lrrl&ated land planted to perennial grasses and legumes for and which is cultivated only to establish or renew the stand

pa5t\ll'e 11 c:onsi.dered as annual grass.

Meadow • LaneS weu with .euonally hish water table, k:tcaUy called cienegas. Principal vegetatioo consists of sod-forming gruses interspersed with other plants.

... Land planted to such deciduOus trees a$ apples, aprl.COU,

_ l.and planted to evergreen trees which include citrus and plantmas•

Turf .. Coif courses, parks and similar lands where the predominant cover is irrigated mowed close_grown turf grass. Parks in which trees are dense may be clusiUecl as woodland.

Fig. 2.15. S. C. S. cover type descriptions.


As a guide in selecting the watershed AMC condition for the hydrologic analysis~ the following agricultural season precipitation limits may be considered:

TABLE 2.8. ANTECEDENT MOISTURE CONDITION CRITERIA

!Me Total S-Day Antecedent Rainfall (inch) (dormant season) (growing season)

I II III

less than 0.5 0.5 - 1.1 over 1.1

less than 1.4 1.4 - 2.1

over 2.1

Should the RI number be modified for AMC I or III, the following table can be used to determine an adjusted RI number:

TABLE 2.9. AIde RllNOFF INDEX NUMBER RELATIONSHIPS

RI For Corresponding RI for AMe Condition AMC II I III

100 100 100 95 87 99 90 78 98 85 70 97 80 63 94 75 57 91 70 51 87 65 45 83 60 40 79 55 35 75 50 31 70 45 27 65 40 23 60 35 19 55 30 15 50 15 12 45 20 9 39 15 7 33 10 4 26

5 2 17 0 0 0

2.7.3. Impervious Areas

In analysis of urban watersheds, the effects of the impervious surfaces on the assumed area-averaged infiltration rate

37

COMPUTER METHODS IN WATER RESOCRCES 38

for the entire watershed must be included. Estimated ranges of impervious percentages for various types of land use development aro given in Fig. 2.16. Values liveD are for the actual percentage of area covered by an impervioQs surface. However. the actual impervious area needs to be reduced due to the local drainago practices. For example. an impervious surfaco may drain acrOss a perviOlls surface where infiltration may take place. To acconnt for this infi! tratioD, the actual impervious area may be reduced by a factor such as 10 percent. This type of adjustment is included in the estimation of watershed loss rates for use in the synthetic unit hydrograph method.

2.7.4. Watershed Development Conditions

Should tho flood oontrol faoilities be expeoted to provide for the public protection for an extended period, then the maximum urbanization should be assumed in determining the watershed loss rates. All available long range urbani~ation master plans should be examined to insure that reasonable land use assumptions are included in the analysis. Pa~ticular attention should be directed to local landscape practices. For example, it is common to nsc ornamental gravels underlain by impervious plastic materials as a substit"te for lawns and shrubs, resulting in an increase in the effective impervious percentage.

2.7.5. Estimation of Infiltration Rates

The S.C.S. approach assumes that daily stor. rainfall is related to the subsequent runoff by

where R '" total runoff (in.) P = total precipitation (in.)

Ia = initial abstraction S = 1000~I - 10

(2.71

Figure 2.11 pJ:ovides a. plot of Eq. 2.1 as a faBction of ttl numbers. In the figure, it is assumed that the initial abstrac-tion can be estimated by

Is = 0.28 (2.8)

Other studies su-ggest that the above S.C.S. value of (2.8) is too high and a value of O.OSS to 0.10S is Ilore appropriate (Aron et a1.. 1977). As discussed previollsly. severe design storm conditions may reduce the Ia value even further and may even be


ACTUAL IMPERVIOUS COVER

Recommended Value

Land Use (I) Range-Percent For Average

Conditions.Percent (2)

Ne.tural or Agriculture a - La a Single Family ResidentW: (3)

100,000 SF (2.' acre) Lots , - L' LO IJO,OOO Sf (1 acre) Lots 10 - 2, 20 20,000 SF (1/2 acre) Lots 30 - ., 40 7,200. 10,000 SF Lots ., - $5 lO

Multi~le Family Ruidentiab

Condominiums ., - 70 U Apartments .. - .. 80

Mobile Home Park 60 - ., 75 Commercial, Downtown Business

or lndustr1a1 80 - 100 .0

Notes;

1. Land use should be baaed an ultimate development of the watershed. Long range master plans for the County and incorporated cities should be reviewed to insure reasonable land use assumptions.

2. Recommended values are based on average conditions which may not apply to a particular study area. The: percentage impervious may vary greatly even on comparable sized lots due to differences in dwelling size, improvements, etc. Landscape practices Shoulo al$o be considered as it is common in some areas to use ornamental gravels W\derlain by impervious plastic mateTials in pl&ee of lawns and shrubs. A field investigation of • study area should always be made, and a review of aerial photos, where available, may assist in estimating the percentage of impervious coyer in developed areas.

l. For typIcal horse ranch subdivisions increase impervious area' percent over the values recommended in the table above.

Fig. 2.16. Actual impervious cover fOr developed areas.

39


40

entirely eliminated from the rainfall-ranoff budget. If it is assumed that Ia is negligible. then (2.7) is simplified to

R :: p2 ... (p + S) (2.9)

Letting P e = P-Ia. both (2,7) and (2.9) caD be written as

R = P 2~(p + S) (2.10) • • where P e is the precipitation CIcess in inches.

To estimate infUtration rates from (2.10). the method proposed by Chen (1975) is illustrated by the example calculations shown in Table 2.10.

TABLE 2.10. EXAMPLE COMPUTATION OF INFILTRATION LOSSES

Storm Time (hrl.)

6.0 6.25 6.50 6.75 7.00 7.25 7.50 1.15 8.00

notes:

Total Rainfall (In.)

2.5 2.60 2.70 2.85 3.00 3.20 3.55 4.05 4.80

Total Runoff ( in.)

0.46 0.50 0.55 0.63 0.71 0.83 1.04 1.36 1.89

Incremental Infiltration

Cin.)

0.06 0.05 0.07 0.07 0.08 0.12 0.18 0.22

loiil tration Rate ( in ...... hr)

0.24 0.20 0.28 0.28 0.32 0.48 0.72 0.88

(0 storm represents the peak 2 hours of a severe historical storm in Southern California

{ii} losses estimated assuming la=0.2S. and RI::70 for the pervious portions of the watershed

The incremental computation of tho infiltration losses in Table S.10 is by means of scanning the appropriate rainfall-runoff curve from Fig. 2.17 with respect to incremental precipitation. A difficulty with this procedure is that unacceptably high (and low) infiltration loss rates may be predicted. Given a maximum and minimum infiltration rate. however. the unacceptable incremental infiltration losses can be adjusted and the total infiltration losses distributed throughout the remaining design storm. Rallison (1980) gives a detailed account of the origin of the S.C.S. rainfall-runoff equation. The runoff curve numbers {and the analogous runoff index nU1I!obers} "ere developed by relating daily (24- hour periods) runoff to precipitation records. It is noted


" " z .. ~ ~

~ z .. '" " '"

~ ~

B tE: II ~m

0 ~

'" '" " 0 " , ..

~ N

III. II

24-HOUR STORM ~UNOFF, F'UINCH)

Fig. 2.17. S. C. S. 24-hour storm rainfall-runoff relationships.


42

that these curves were not designed to be a phYSical definition of the incremental runoff estimation approach.

In estimating soil infiltration rates, an index of runoff potential is determined for each soil cover complex within the watershed. The RI scale has a range of 0 to 100, where a low RI number indicates a low runoff potential and a high RI number indicates a high runoff potential


technique is to define a low loss rate percentage of rainfall to be attributed to infiltration losses during the lower intensity portion of the design storm event.

Assuming that the initial abstraction term (la) is ne&li&ible~ then (2.9) may be used to define

(2.15)

where Y• -- 1 (d ) low ass rate percentage ecima! fraction p "" 24 hour ,jreoipitation (in.) S : (100~RI ) - 10 • RI = area-averaged composite runoff index number

To calculate the area-averaged runoff index used in (2.1s). composite runoff index numbers must be computed for each RI number defined within the watershed by

where

RI.-J

• Rl j = compOSite runoff index number for area j Ai = fraction of area j that is impervious Ap = fraction of area j that is pervious

(2.16)

The above formula assumes an RI number of 100 (total runoff) for the impervious area fraction and uses an RI number selected from Fig. 2.14 for the pervious area fraction. The resulting composite runoff index number approximates the S.C.S. curve numbers for the subject development type. cover. perviousness. and soil group. The empirical relation of (2.16) is a simplification of a more complex relationship and, consequently. the RI associated to the impervious area fraction should not be reduced for the effects of effective imperviousness.

From the low loss rate percentage. the corresponding low loss rate. F'. is given by

F' = Y*I (2.17>

where I is the rainfall intensity. It should be noted that the adjusted loss rate of (2.14) is an upper bound to the low loss rate of F'.

In the determination of the low loss rate percentage. the area-averaged 24- hour point rainfall (P) is computed and an appropriate composite runoff index number estimated. and both values are substituted into (2.15).

43

COMPUTER METHODS INWATER RESOURCES

44

A third method in using a maxim.um (limiting) infiltration rate is incorporated into the ¢ index approach which holds the loss rate as constant th:r:oughout the entire severe design storm event. Table 2.11 compares the three diScussed methods in estimating the design storm watershed losses for the application problem presented in Table 2.10. In Table 2.11, it is assumed that the limiting F=O.44 in---hr and Y·=O.40.

Comparing Tables 2.10 and 2.11 it is noUd that limiting the incremental loss rate resulted in aD. additional ().19 inches of runoff duritlS the storm's peak 45 minutes of rainfall.

TABLE 2.11. COMPARISON OF INFILTRATION LOSS METRODS

Storm Incremental Incremental Low Loss IjJ index Time Rainfall Loss Approach Approach Loss

(hrs.) (in. ) C b.. ) (in. ) Un.)

6.0 0.00 6.25 0.10 0.06 0.04 0.10 6.50 0.10 0.05 0.0, 0.10 6.75 0.15 0.07 0.06 0.11 7.00 0.15 0.07 0.0' 0.11 7.25 0.20 0.08 0.08 0.11 7.50 0.35 0.11 O.l! 0.11 '1.15 0.50 0.11 0.11 0.11 8.00 0.75 0.11 0.11 0.11

SllJD : (2.30) (0.66) (0.61) (0.86)

2.8. Synthotic Runoff Bydrosraph Development

The several hydrologic elements of the critical storm patterD~ point rainfall determinatioll. watershed las estimation. and the unit hydro&raph appro~imat.ion a].-o I'vmbj.llll'd j:ll thO' cODvolution of effective rainfall with the unit hydrograph. FiSure 2.18 illustrates the procedure for developing a synthetic runoff hydrograph. Each unit interval (or unit period) of rainfall from the design storm patterll is split into the effective unit rainf.ll and the corresponding watershed unit loss. The reSlllting e:ffoctive rainfall storm pattern is 'then combined wHh the assumed watershed unit hydrosraph by a process called cOllvolution t(l produce tno synthetic runoff hydrogra.ph. Figure 2.18 shows a 12 unit period storm pattern and the corresponding unit period runoff hydrographs. Summins tosether the 12 unit period runoff hydrographs results in the deSign storm rUDoff hydrograph.

It should be noted that in the convolution approach. each unit period rusoff hydrograph has the same b.se period regardless of the magnitude of the associated unit rainfall. Also, each unit

" 0 " 0 • ~ • 4; .~ .1

h ~-~-~ •• i ,

" " : • « .1 • .~ .-0< •• ~o •• Z ~ .. •• -•

Fig. 2.18.


TIME (UNIT ,[ItIOG)

• 10

UNI'TIM!

TIII£ (UNIT PERIOD)

" LEGEND

o ItlIN''''L LOS. E3 EFFECTIVE "AlfiII

r-J!!!!.'-""""'- - THE UNIT GIt ...... REPRESENTS THt: 'LOCO HYDROGIIAPH RESULTING 'ROII A UNIT ,TOIUIII-IHCH EFfECTIVE RAINFALL 'N a UNIT ,1It10D).

OtslOM ,ro.ul m".;;, UNIT 1'1"100

THE DESIGN STORM. THI NU .. IU, SHOWN AeoVe: EACH UNIT PI!lUOD RUNO" HYDIlOO",,'H PUK CORltt:POfCt TO THt: ""'"OPlUAn UN,T [FnCTIVII! RAlN'ALL,

TIMI (UNIT ptRIODS)

Derivation of a runoff hydrograph.

45


period runoff hydrograph has a constant time to peak duration. Each of the unit period runoff hydrographs are se~n to be directly related to the volume of the associated effective rainfalls. Additionally, in the summation process it is assumed that there are negligible restrictions to the watershed runoff flow rates which are represented by tbe rnnoff hydro graph. These restrictions would occur due to channel capacity problems and watershed detention effects. Each of these concerns should be addressed after the waterslted runoff hydrograph is generated in order to ascertain whether the computed results are reasonable for the watershed conditions being studicQ. In many study situations. a single runoff hydrograph generation would be inappropriate due to the watershed conditions, and a more complex watershed mocel is required which includes submodels for channel and basin reuting effects. Such a watershed model suitable for Dlicrocomputers is given in Hromadka (1983).

Othe1" llnntrihutinns to the runoff 'hydrosraph such as baseflow and snowmelt can be summed to the synthet ie runoff hydro graph. Generally. such considerations are neglected in the study of urban watersheds. Ho~ever. detailed discussions of ancillary hydrologic processes are contained in texts such as Hje1mfe1t and Cassidy (1975).

2.9. Instructions for a Synthetic Runoff Hydrogrllph Development

In order to describe the salient features of the supplied FORTRAN compute~ p~ogram. a process step chart is provided which desc~ibcli ca.ll;ih OPC£&tiOll pcrfoJ:wod by tho p~o'I.-lI.m (ul,ILcd by &

superscript star>. and information which is to b~ provided by the program user. The computer program uses watershed S-cnrves developed for Southern California (U.S. Army Corps of Engineers) and also includes the dimensionless curvilinear S.C.S. unit hydrograph in S-g1:'aph fO:J:m. Additi01ally, the p1:ogram uses the NOAA Atlas .:z depth-area relationships of Fig. 2.11. This type of information can be easily replaced with local watershed S-curve information and other depth-area relationships in order to develop a runoff hydrograph generator program which represents local hydrologic characteristics. The basic elements of the program are as follows:

(1). The critical storm pattern is a composite 24 hour duration storm pattern composed of nested point rainfall peak intensities c~rresponding to each storm duration and assumed return frequency. The point rainfall values are adjusted by the depth-area relationships of the NOAA Atlas 2.

(2). Unit hydrographs are developed frem the Southern California S-graphs determined by the U.S. Army Corps of Engineers. Also included is the S.C.S. curvilinear unit hydrograph. The time base of the unit hydrograph is determined by the watershed lag relationship of (2.1) and (2.2).


PROJECT: DATE:

ENGINEER:

t. Enter the length of the longest wa.tercourse (feet)

2. Enter the length along the longest watershed watercourse measured from the point of concentration upstream to a point opposite the centroid of the watershed area {feed

3. Enter the difference in elevation between the most remote point in the watershed and the pOint of concentration (feet)

4. Enter the basin factor

5. Enter the watershed area (acres)

6. Enter bas-eflow (cfs/square mile)

7. Enter S-Graph proportions (decimal)

SCSI VaHey Foothill Mountain Desert

8. Enter adjusted loss rate (inch/hour)

9. Enter low loss rate percentage (decimal)

10. Enter watershed area_averaged 5-minute point rainfall (inches)"

Enter watershed area-averaged 30-minute point rainfall Unches}*

Enter watershed area-averaged I-hour point rainfall (lnches)~

Enter watershed area.averaged 3-hour point rainfall (inches)*

Enter watershed area-averaged 6-hour point rainfall (inches)"

E.nter watershed area-a'leraged 24-hour point rainfall (inches)*

11. Enter 24-hour storm unit interval (minutes)

INote: use either SCS or Valley, Footr.ill, Mounta:n, De:.ert "Note: enter values unadjusted by depth-area factor ..

Fig 2.19. Program 2.1. Data entry form

47


(3). Watershed losses arc assumed equal to infiltration losses and are modeled by use of the adjusted loss rate of (2.14) and the low loss rate of (2.17).

Using the above three model assumptions. the synthetic r~noff hydrageaph is developed by the following steps:

I. Synthetio Valt aydrolraph De.el~nt A. On a suitable topographic map of the watershed. determine

the proposed drainage system boundaries. B. From the watershed map. determine the following watershed

physical iactors and onter them on the computer information form of Fig. 2.19:

A : drainage area (acres) L = length of the longest watercourse (feet) La = length along the longest watercourse. measured

upstream to a point opposite the oentroid of the watershed area (feet)

H = elevation difference along watercourse (feet) C·. Determine the watershed lag from (2.1) and (2.2) where

the basin factor is selected from Fig. 2.2. The basin factor is entered on the form of Fig. 2.19.

D. Select a unit time period to be used for the modeling purposes. Usually. a unit period of 15 to 25 percent of the watersfed lag time is adequate.

E. Select a S-graph appropriate for the watershed (see Figs. 2.3 a,b,c,d. or Fig. 2.4). Determine the average percentage of the ultimate discharge for each unit period. In reading the percentage of ultimate discharge from the S-grapb. the mean ordinate ovor the time period should be determined. The 8-grapbs may be averaged to apprOximate a combination of watershed runoff characteristics. Enter the desired S-graph proportions on the comput:r information form.

F. Compute the unit distribution graph by subtracting succestive unit percentages of ultimate discharge.

G • Compute the ordinates of the synthetic unit hydro graph by multiplying the ordinates of the unit distribution graph by the ultimate discharge defined by

K(cfs) = 64SA,.--T

where A is the drainage area in square miles, and T is the unit time period in hours.

II. Syat_tio Critioal Stora Pattern Deve1op ••• t A. Develop point precipitation isohyetal maps for the 1 hour.

6-hour. and 24-hour durations. and calculate an area-averaged value for each of these durations.

B. Unless point preoipitation data is available to determine area-averaged point prec ipitation values for the 5-minute. 30-

A S"YN1HEoT1CUNIT llYDROGRAPH MODBL

minute, and 3-hout' durations, use the area-averaged 1 hou.r value from step n.A to estimate the S-JDinnte and 30-minute values bv plotting on Fig. 2.6 using a slope of the intensity-duration plot which is characteristic of the watershed rainfall records. The 3~hour value can be esti.ated from the 1-hour Rod 6-hour v.lues by plotting on Fig. 2.20. Enter the area-averased point rainfall values on the computer information form.

e·, Adl~~~ Lll L~~~-LV~~~&.d ~in~ ~~infall v~l, •• f~~ dep~harea rtlatiooships such ~s given in the NOAA Atlas 2,

b • Develop a syntbetic critical storm IDass rainfall plot $noh as shoyn in FiB. 2,12 using PiS, 2.20.

Btl. Usins tlle unit time period specified for the unit llydrograph determination, calculate the synthetic storm pattern .:nit: ralnfalls by s1].eecssiv~ Gu,btraotions of the mass rainfall c~rve talues separated by a unit tilDe period.

F. Arrange the unit rainfalls into the critical storm p.tt~rn sho,..n in Figs.2.10a,b,o. It sllou,ld be n.gted that the computer stoted rainfall pattern sequence places the peak 5-minute o.11it rainfall at storm time of 16 hours. and essentially distributes tho remaining peak rainfall .... ymmotrioally about the peak 5-minute value.

IlZ. Floo' Ilydrolraph Dwelopuat A. Find the pervions area fraotion mean infiltration loss

rato. Adjust the lu~~ ~atc fur tho effoctivu impervio~s area fraction by

F = adJust.ed 1('1Ii~ rate (inch...-Jlollr) F = loss rate tor tho pervious area i~action A~: impervious area fraction

B. Comptl-to the low loss rate, F', from (2.17>' Use the low loss rate f


2. Repeat the above procedure for each anit effective rainfall. advancing the resulting unit period runoff hydrograph by one unit period.

3. Sum the unit period runoff hydrographs to produce the watershed runoff hydrograph.

E*o Add the baseflow to the flood hydrograph. Enter the base flow on the computer information form.

2.10. A Synthetic Runoff Hydrograph Computer Program

The detailed description of procedures for developing a 24-hour storm runoff hydrograph can be directly formulated into a FORTRAN computer program suitable for currently available microcomputer systems. The following table lists the several subroutines used in the computer proaram:

TABLE 2.12. RUNOFF HYDROGRAPH PROGRAM SUBROUTINES

Program Number

2.1

2.2 (no input)

2.3 (no input)

Program Description

Main program for developing the effective rainfall storm pattern distribution and the resulting runoff hydrograph.

Synthetic unit hydrograph genera-tor which develops a unit hydrograph from the S-curves of Figs. 2.3a~b .. c .. d or the S.C.S. uni t hydrograph of Flg. 2.4.

Output plotting program which plots the runoff hydragraph flow-rate and accumulated runoff volume as a function of storm time.

2.11. PROGRAM 2.1 Data Entry

The computer data entry variables are included in the following computer text pages. These example user-friendly screens show the variable range of values. and also include suggested program commands to provide a user-friendly environment.

'" "' iii i!: , .J

;i ... z .. 0: >-Z o Q.


51

STORM DURATION-MINUTES

PROJECT LOCATION _______________ _

NOTES ____________________________________ _

Fig. 2.20. Area-avera~ed mass rainfall pwttinR sheet.


Chapter Blbliolraphy

AroB." G •• MUhr, A. C •• and Lat.atos, D. Fo. -Infiltration Formula Based on S. C. S. Curve N •• ber." ASCE lournal of Irrigation and Drai.a.a •• 103 (IBRA), (1977).

Chen. C. L. ·Urban Stora Runoff Inlet Bydrosraph Study,- Rep. PRWG, 106-5, Utah Water Resources Lab •• Utah State University. Loaan, (1975).

Chen. C.L •• -Infiltratioa Formulas by Curve N •• ber Prooedure," ASCB 1. BYD. DIV .. (10S), (1982).

County of SaD Oieso, -HydrotolY Manual." San DieIO. Ca.. (981).

Balleson, P.S •• Dya •• io B,.droloa7. HoGraw-Bill, (1970).

Espey, W. Ho. and Altman, D. G., -Nomographs for Ten-Minute Unit Bydrographs for Small Urban Watersheds." Rep. EPA-600 ...... 9-78-03S Environmental Protection Asoney, Washington, D. C.. (1978).

Federal Aviation Ascney. -Dept. of Trans. Adv. Cireular on Airport Drainage-. Rep. A ..... C 050-5320-5B, Washinlton. D. C •• (1970) •

Freeze. R. A •• -The Mechanism of Natural Groundwater Recharle and Discharlo: 1. One-Dimonsional, Vertical. Unsteady. Unsaturated Flow Above a Recharging or Discharsins Groundwater Flow Syste •• -Wat. Res. Res •• (5). (1969).

Garen. D. C •• and Buries. S. I .• -Approximate Error Bounds for Simulated Bydrolrapha. - ASCE 1. HYD. DIV •• 107BYll. (1981).

Gray. D. D •• et al. -Antecedent Moisture Condition Probabilities.-

AseE 1. Irr. Drainale Div., (108), (1982).

Green. W. H., and Ampt, G. A •• -Studies on Soil Physics. I. the Floy of Air and Water Through Soils." J. Agr. Sci •• (9). (1911).

Guymon. G. L., Barr. M. E •• Berg, R. L .. and Bromadka II .. T. V •• -A Probabilistic-Deterministic Analyais of One-Dimensional Ice Segregation in a Freezing Soil Column. - Cold Rogions Soience and Technology, (5), (1981).

Helwig. O. 1.. Amorocho. I .. and Finch. R.H •• -Improvement of Noni inear Rainfall-Runoff Model." ASCE I. HYD. DIV.. I08HY7. (1982) •


Harshfield, D. JI •• -Extreme Rainfall Relationships, - ASCI J. HYD. DIV •• 88 (JlY6). (1962).

BjoI.tolt. A. T •• -CUrve-Number Procedure .s Infiltration Hothod,-ASCB J. HID. DIY., (106), (1980).

Bje1mfelt. Pl._or ••

i.. To; Iowa

foud Cassidy. 1. 1.. B.,.4%01017 foz E •• i ..... zs •• a State Univer.ity Press, (1975).

Holtan, H. N., -A Concept for InfU tration Estimates in Watershed Engineering. - U. S. Dept. of AS., ARS 41-;51. (1961).

Horton, R. Eo. -Tho Role of Infi! tratiOD in the Hydrologio eyele.-Trans. A. G. U •• (A), (1933).

Horton, It. Bo. -Determination of Infiltration Capacity for Large Drainago Basins, - Trans. A. 6. U., (18), 371, (1937).

Hromadka II, T. Vo. Coap.tor •• thods bl Urb ••• ,,'%01017 Lighthouse PublicatioDs. Mission Viejo, Ca •• 1983.

Hrolllladka II. T. V., Nestlingor. A. J •• and Schwarze. 1. W •• -A Modified S. C. S. RUDOff Hydrograph Method. - 10th Urban DrainagCl Symposium. Dniv. of Kentucky, Le%ington, Kentucky, (1983,).

Hromaelka II. T. V.. and GuymoD. G. L.. "San Bernardino County Hydrology Manual ... , County of San Bernardino, Ca., (1983b).

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and GuymoD, G. L., in Water Resources

Buff. F. A., "Time Distribution of Rainfall in Heavy Storms," Wat. Res. Res .• (4), (1967),

[eifer. C. J •• and Chn, B. H •• -Synthetic Storm Pattern for Drainage Duign," ASeE J. HYD. DIV., 83HY4, (1957),

Kibler. D. F •• "Urban Stormwater Hydrology," A. G. D •• Water Res. Mon n (7), (1982).

tirpic::h, Z. P., -Time of Concentration of Small Agricultural Watersheds,- Clv. Eng., 10(6), (1940).

La.ngbein, W. BH "Some Channel Storage and Unit Bydrograpb. Studies. - Trans. A. G. D •• (21). 620. (1940).

McCuen, R. B •• and Bonde lid. T. R.o -Estimating Unit lIydrograph Peak Rate Factors,- ASCE J. Ittig. and DraiD •• 109(2), (1983).

53

COMPUTER METHODS IN WATl!;R Rl!;SOURCES 54

lIala. R. G •• aad Bro .... S. II •• -SollsitiTity of Optiaized Para-oters itt Watershad Kodell,- 'At~ Res. Re •• ~ (14). (197a).

Miller, J. F •• Fredu:ic. R. B •• and Trac.,., I., J •• "Procipitation Frequency Atl •• of the Contermi:D.CKl.I Western United States." NOAA Atla. 2. Nat. We.ther Servo. Silver SpriDI" Md •• (1973).

Ifocl".. V. :t,. lfydrology, ~ U. s. (1972) •

"N.tio.a} EAsh,ceriA,. Handbook. Seotion 4. Dopt. of Agri .. S. C. So. Wa .. hiJl!ltoll~ D. C.~

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PhiliP. Profiles

I. R.. "The Thoo.ty of Infiltration: 3, Moi&tllro and lolation to Experiment.- Soil Sci. (84) .. (1957d).

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A SYNTHETIC UNIT HYDROGRAPHMODEL

Rubia. IH Steillltardt. :I.. and Beilll,cr. P.. -Soil W.ter Retations Durin. RdD Infiltration: II. Moisture" Content Profiles Durin, Rainl of Loy Intollsities, .. Soil Sci. Soc. Amer. Proe., (8). (1964) ,

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U. S. Army Corps of Engineers. Lo

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