APPLICATION OF SCS INFILTRATION MODEL

VOL, 18, NO. 3

WATER RESOURCES BULLETIN AMERICAN WATER RESOURCES ASSOCIATION JUNE 1982

APPLICATION OF SCS INFILTRATION MODEL'

Sree Kumar and Subhash C Jab2

ABSTRAfl: The SCS infiitration model ws applied to the Ralston Cnek watershed in eastern Iowa. The criteria to determine the various model parameters were revised to obtain a better agreement between the observed and computed total runoffs. A procedure to calibrate the infiltration model is presented. The infiitration model was used in con- junction with an overland flow model to develop flood hydrographs. The results indicate that SCS intlltration model adequately describe the distribution of losses. (KEY TERMS: hydrology; infiltration; overland flow; rainfall-runoff relationships; rainfall excess.)

INTRODUCTION Watershed models, flexible in their capacity for encom-

passing a wide range of physical and economical variability, are'increasingly being used to analyze and evaluate changes on watershed basins. The Iowa Institute of Hydraulic Research recently developed a distributed parameter watershed model (Jain, et al, 1981) to analyze the effects of land-use patterns on both flooding and sedimentation. Such models require the distribution of rainfall excess, both spatial and temporal, as one of the input data, in addition to topographic, land-use, and soil characteristics of soil cover complexes. Most of the exist- ing infdtration models (Kostiakov, 1932; Horton, 1940; Hol- tan, 1961; Philip, 1957) are not suitable for a distributed watershed model, primarily due to lack of experimental data required in estimating the model parameters for various soil and land-use characteristics.

An infiltration model developed by the Soil Conservation Service (SCS) was incorporated into the distributed watershed model. The SCS model parameters are related to soil type, land-use, and land treatment, and are well classified and tabu- lated in USDA (1971). The parameters can reflect watershed modifications in the computation of rainfall excess. This paper describes the application of the SCS infdtration model to the watershed of the north branch of the Ralston Creek, which lies northeast of Iowa City, Iowa (Figure 1). The 3.01 square mile watershed is largely rural, where agricultural prac- t ices predominate. It has a channel length of four miles and a drop in elevation of about 140 feet. The valley has fairly steep slopes in its southern and eastern sections with a gently rolling

configuration over the western and northwestern parts. Con- tinuous records of rainfall, runoff, and ground water elevations have been recorded since 1924, making the north branch of Ralston Creek unique in view of watershed size and length of record.

\

Figure 1. Ralston Creek Watershed.

THE SCS INFILTRATION MODEL The original SCS infiltration model was developed for pre-

dicting total unoff volumes from watersheds where only total precipitation data were available; the time distribution of rainfall was not considered. However, the original model was later extended for determining of flood hydrographs. A plot of accumulated runoff versus accumulated rainfall shows that runoff starts after an initial abstraction, I,, and that the relationship is nonlinear during the initial stages, and quickly a p proaches linearity. For the simplest case where rainfall and runoff begin simultaneously (i.e., I, = 0)

'Paper No. 81147 of the Woter Resources Bullerin. Discussions are open until February 1,1983. zRespectively, 2403 E. Seneca, No. 8, Pasadena, California 91107; and Aasociatc Professor, Iowa Institute of Hydraulic Re=&, The University of

Iowa, Iowa City, Iowa 52242.

603 WATER RESOURCES BULLETIN

Kumar and Jain

+ = Q (linear region) S P

where:

F = actual retention/infdtration = P - Q - I,, S‘ = potential maximum retention,

Q = actual cumulative runoff, and P = potential maximum runoff (cumulative precipitation).

This equation is derived conceptually for the limiting case where P-Q-rconstant as P--. If initial abstraction occurs, Equation (1) is written as

F=Q s P-I,

where S = S‘ t I,. On substituting F = P - Q - I, in Equa- tion (2),

(P-IaI2 Q =

(P-Ia)+S (3)

L = P - Q (4)

where L = accumulated loss which includes I,. An empirical relationship (USDA, 1971) for I, derived from records of natural rainfall and runoff from experimental watersheds is

I, = 0.2 s ( 5 )

The parameter S (inches) which represents the maximum available storage is transformed into another parameter called curve number

1000 CN = - s+10

This transformation makes interpolation, averaging, and weighting operations more nearly linear. The maximum potential retention S is implicitly detennined from a number of watersheds in single complex, i.e., uniform soil and vegetative cover. The hydrologic soil cover complex curve number CN is a parameter whose quantification is based on extensive field studies and soil classifications mapped over most of the U.S. The SCS provides tables of curve numbers (0 defined with respect to (1) soil group, (2) land use, (3) land treatment, and (4) antecedent moisture conditions (AMC).

The SCS method classifies various soils into four basic groups based on rainfall-runoff data, infiltration and trans- mission rates, and considerable subjective judgment. The hydrologic soil groups are A, B, C, and D in the order or decreas- ing permeability, i.e., from low runoff potential to high runoff potential. Three “antecedent moisture conditions” (AMC) are defined to account for the “wetness” of the watershed:

AMC I - dry state, least runoff potential; AMC I1 - average state, average runoff potential; and

AMC 111 - saturated state, maximum runoff potential.

The AMC is assumed to depend on the five-day antecedent precipitation and the state of vegetation, whether growing or dormant. During the study it was clear that runoff volumes and rainfall excess patterns are sensitive to AMC and hence proper evaluation of the ‘Lwetness” of the watershed is necessary. AMC is site dependent and requires rainfall-runoff studies to derive suitable criteria to distinguish different AMC’s.

Finally, the SCS model is dependent on the minimum infiltration rate (MIR) of the soil. If the rainfall rate is in excess of the upper bound of MIR, then the runoff volume and rainfall excess rate are not sensitive to MIR. However, a poper choice of MIR is needed if this condition does not exist. A number of rainfall-runoff studies with respect to seasonality are required to determine MIR for the different parts of watersheds. All required parameters and data are published in USDA (1971).

Aron, et al (1977), tested the SCS model against experimental data and found good agreement for uniform rainfall. They reported that I, = 0.2s performs adequately for large storms and underestimates runoff for small or medium storms. They suggest I, = 0.1s for the latter cases. However, they did not quantitatively defme the division between large, medium, and small storms. It should be noted that the curve numbers CN are based on the relationship, 1, = 0.2% It is expected that CN values would require redefinition for the case of I, = 0.1 S.

From Equation (4) the cumulative infiltration, F, can be written as

F = (P - Ia) - Q (6)

On substituting for Q from Equation (3)

(P - Ia) - s (P - I, + S)

F = ( 7 )

infiltration rate f(t) at time t, can be derived by differentiating Equation (7)

where P(t) = II(t) dt, and I(t) = rainfall intensity at time t. On examining Equation (8), one fmds that infiltration rate varies with rainfall intensity. Hence, maximum infiltration need not occur at the beginning of rainfall and the minimum infiltration rate may not be reached. These characteristics indicate that the infiltration rates predicted by Equation (8) need not be- have as the ideal case of infiltration capacity decay curves. For constant rainfall intensity I(t) = I,, Equation (8) becomes

s2 I, (Ict - I, + S ) 2 f(t) = (9)


Application of SCS Infiltration Model

At t = 0, Equation (9) becomes

and the iditration rate decays asymptotically as the inverse square of t and does not reach equilibrium. The latter beha- vior does not conform to the generally accepted nature of infiltration capacity curves.

SELECTION OF TIME INTERVAL The main issue in the application of the SCS model in finite

time increments is the. validity of rainfall dependent infiitration rates, because the basic SCS model was developed for predicting cumulative runoff from total precipitation without considering the time distribution of rainfall. The question arises as to what time interval one should adopt. The SCS (USDA, 1971) and USBR (1974) used one-hour intervals to develop rainfall excess hyetopaphs for design storms. Aron, e? a1 (1977), used 15-minute intervals to test the model with experimental data.

The normal practice for the prediction of design hydrographs from a watershed which is treated as a unit, is to use one-hour wewted rainfall. The Theissen polygon technique is generally adopted for the weighting operation. However, to develop overland flood hydrographs in each segment of the distributed model, it is necessary to use rainfall intensity in smaIl time increments (e.g., 5 minutes) because overland flow is sensitive to rainfall intensity. During the study it was observed that if the SCS model is used to compute infiltration in five-minute increments, the resulting infiitration tends to be erratic for complex storms. However, one would expect that the infiltration rates should not vary abruptly during five- minute periods.

The present model assumes that if time intervals of 1 hour are adopted then extreme changes in infiitration rate can be reduced to some extent. Though the rainfall excess pattern is sensitive to the time interval of computation, total runoff volumes vary insignificantly. Five-minute time increments were used to compute the rainfall excess, since rainfall distribution in five-minute increments was available for the Ral- ston Creek Watershed. It was assumed that the one-hour runoff computed by Equation (3) adequately represented the total rainfall excess during the time interval considered. How- ever, when one superimposes the five-minute precipitation data on one-hour inflltration rates, it was necessary to account for periods during which rainfall intensity is less than the loss rate. Hence the loss rate was corrected to maintain the balance between rainfall, runoff, and infiitration. l h i s scheme of computation is hereinafter referred to as the modified SCS model.

MODEL CALIBRATION The SCS infiltration model requires (1) allocation of suit-

able curve numbers, (2) defmition of minimum infiltration

505

rates, and (3) evaluation of proper antecedent moisture conditions and criteria for distinguishing different AMC. The initial abstraction coefficient was assumed equal to 0.2 S for which the curve numbers have been defined (USDA, 1971).

Based on a soil map of the watershed, the soils were classified according to the four hydrologic groups. The soil cover complexes for the entire watershed were determined by super- imposing the land-use map on the soil map. The conservation and management practice was obtained for each soil cover complex. Three “seasons,” based on climate, vegetation, ground conditions, farming stages, and management practices, were defined for calibration: Season 1 - April to May, Sea- son 2 - June to July, and Season 3 - August to September. The period between October to March was not considered since the watershed was covered with snow. The calibration was carried out in three phases: a preliminary study, a least square analysis, and a trial and error procedure. Eleven storms were selected for the calibration. The results are presented in Table 1.

heliminary Study

In the preliminary phase of the calibration, the values of AMC, MIR, and CNs were determined following the SCS guidelines (USDA, 1971). The lumped curve number for the entire watershed was computed by weighting each soil cover complex by area. Runoff for the eleven storms was computed using the SCS method. Computed runoffs were comparedwith observed; the agreement for most storms was poor for assumed values of AMC and MIR, as shown in Table 1. Revised values of AMC and MIR to obtain better agreement between observed and computed runoffs were determined by a least squares procedure.

Least Squares Analysis The runoff for each storm was computed for all possible

combinitions of lumped curve number, AMC, and MIR. The combination that resulted in the least sum of the squares of errors was chosen. The error is defined as the difference between the observed and computed runoffs. The results are shown in Table 1. Comparison of the results of the least square analysis with those of the preliminary study, show that the AMC in least square analysis was, in general, increased to the next higher potential runoff. The MIR varied from season to season, with the lowest in Season 2 and the highest in Sea- son 3. However, the problem of “colinear stability” seems to occur when different storms were included in each season. This condition is not totally unexpected, since small data sets were used. Therefore, this technique was not given full considera- tion and a trial and error procedure was adopted as an alter- native.

lHal and Error Rocedure In the trial and error procedure, the curve numbers for each

soil cover complex in the watershed, instead of the lumped curve number of the entire watershed, were optimized. The comparison between predicted and observed runoffs for the final calibration is shown in Figure 2, which indicates a

WATER RESOURCES BULLETIN

Kumar and Jain

TABLE 1. Catibration Results.

ReJiminary Study Least Square Analysis Trial and Erroz Rocedure

Total Observed Antecedent Redicted R e d i C t e d Predicted Storm Rainfall Runoff Rainfall MIR Runoff MIR Runoff MIR Runoff

No. Date (inches) (inches) (inches) AMC (inhr) (inches) AMC (in/hr) (inches) AMC On/hr) (inches)

Total Five-Day

1 2 3

4 5 6 7 8

9 10 11

April 28,1974 April 20,1973 April 16,1972

June 22,1974 July 17, 1972 June 1-2,1970 June 29,1969 July 7,1969

August 12,1974

September 7, 1970 August 5-6, 1972

2.462 1.5 89 2.033

1.260 4.099 1.566 1.483 3.097

1.670 2.501 4.072

0.910 0.570 0.608

0.277 1.791 0.184 0.422 1.076

0.382 0.909 1.109

(A) SEASON 1 - DORMANT 0.45 1 0.10 0.039 0.78 2 0.10 0.100 1.10 2 0.10 0.210

(B) SEASON 2 - GROWING 2.05 3 0.10 0.24 0.65 1 0.10 0.40 0.189 1 0.10 0.002 2.78 3 0.10 0.382 1.45 2 0.10 0.82

(C) SEASON 3 - GROWING

2.10 3 0.23 0.37 1.50 2 0.23 0.41 3.77 3 0.23 1.8

2 0.09 3 0.09 3 0.09

2 0.05 2 0.05 2 0.05 2 0.05 2 0.05

3 0.23 2 0.23 3 0.23

0.604 0.685 0.706

0.099 1.786 0.189 0.156 1.115

0.42 1 .oo 1.20

2 0.10 3 0.10 3 0.10

3 0.07 2 0.07 2 0.07 3 0.07 2 0.07

3 0.23 2 0.23 3 0.23

0.390 0.490 0.570

0.250 1.43 0.093 0.390 0.85

0.38 1.04 1.10

satisfactory fit. Figure 3 is the revised criteria to determine the proper AMC, and is obtained by plotting the five-day antecedent rainfall with the revised AMC determined by trial and error. The revised curve numbers for various soil cover complexes are listed in Table 2, and are slightly different than those recommended by USDA (1971). The values of MIR were subjectively selected by comparing the results of the preliminary study and the least square analysis. In general, moderate variations in MIR did not significantly change the results. The seasonal variations in MIR were observed by Hor- ton (1933). He found that MIR for the North Concho River basin in Texas varied as a bell shaped function. The peak rate occurred during June and July, and decayed to almost half the peak for January and December. Horton attributed the varia- tion to changes in temperature, evaporation, vegetation, farming practice, and biological activity. In the present study, a different trend was observed. However, if the MIR for Sea- son 2 is assumed to be approximately the same as Season l , then it is probable that the MIR increases to a peak in Season 3 and subsequently decays for the remaining period. It should also be noted that the ground is generally frozen from Novem- ber to March and the effect of this condition on MIR is not clear.

The distributed watershed model (Jain, et a l , 1981) with the modified SCS model was tested for the August 5-6, 1972, storm and the August 12, 1974 storm. The comparison between computed and observed hydrographs is shown in Figure 4. The fit for both storms is satisfactory.

graphs. Hourly runoff and loss rates were computed using the SCS model. The precipitation in five-minute intervals was superimposed on the hourly loss rate. The hourly loss rates were then adjusted such that the volume of rainfall excess computed using five-minute data agrees with the hourly runoff predicted by the modified SCS model.

2.0 I 1 I

- 1.5 z Y

LL 0 Z X

a

m W v)

0 0.5

PREDICTED RUNOFF (IN.)

Figure 2. Results of Trial and Error Calibration. SUMMARY AND CONCLUSIONS

The SCS infiltration model was modified to suit the type of rainfall data needed for predicting overland flood hydro-


Application of SCS Witration Model

- OBSERVED HYDROGRAPH

- -- PREDICTED HYDROGRAPH -

0 I 2 3 TOTAL 5-DAY bNTECEDENT RAIN-

FALL IN INCHES

- AYC (US0.A.. 19711

SEASON I - --

SEASON 3

Figure 3. Ettimation of AMC for Watershed of the North Branch of the Ralston Chek.

TABLE 2. Curve Number Definition for Average Watershed conditions.

<kne Number for Average Watershed condition

Land Land Hydrologic uee Treatmmt conditions AMCI AMCII AMCIII

Yard f i b e r Corn Golf counre Alfalfa Cemetery Garden G i O W o a t s Fallow

- - - - - -

Contoured

Contoured

Contoured Contoured Contoured

- - - - - -

- - -

FaL Average Good Poor Good Average Good Good Good

52 71 42 62 57 75 58 76 52 71 54 72 58 76 53 12 53 72 70 85

86 79 88 89 86 87 89 86 86 94

A trial and error procedure was adopted to determine the curve number, AMC, and MIR for the distributed watershed. The AMC criterion recommended in the SCS method was revised to obtain a good fit between observed and predicted runoff. The MIR showed an increasing trend from Season 1 to Season 3. Since the volume of runoff and rainfall excess hyetograph is sensitive to AMC, it is felt that the index for estimating AMC and the number of divisions in AMC should be improved. A moderate amount of subjective decisions were made in assigning curve numbers, especially in determining the various hydrologic conditions, i.e., to distinguish between poor, average, and good hydrologic conditions.

The complete distributed watershed model including the modified SCS model was tested for two storms. The results indicate that the infiltration model satisfactorily describes the distribution of losses and that the technique of calculating rainfall excess hyetograph to develop overland flood hydrographs is adequate.

LJTFXATURE CITED

Aron, G., k C. Miller. JI., and D. F. Lakatos, 1977. Infiltration Model Based on SCS Curve Number. J. of Irrigation and Drainage, ASCE IR4.

Holtan, H. N., 1961. A Concept for Witration Estimates in watershed Engineering. Agriculture Reaearch Service, U.S Department of Agriculture.

Horton, R. E, 1940. An Approach Toward physical Inteapretatbn of Jnfiltration Capadty. Roc. Soil Science Society of America 5399- 417.

Jain, S. C, S. Kumat, G. Whelm, and T. E. Croley I& 1981. IMR Dis- tributed Parameter Watershed Model. IMR Report No. 236. Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City. Iowa.

KostiaLov, k N., 1932. On the Dynamics of the @efficient of Water Percolation in Soils and on the Necessity for Studying it from the Dynamic Point of View for Purposes of Amelioration. Interna- tional Society of Sod sdence.

Philip, J. R, 1957. The Theory of Infitration: The Infiltration Equp tion and Its Solution, Part I. Soil Science 83(5):345-357.

U.S. Bureau of Reclamation, 1974. Design of Small Dams. A Water Resources Technical Publication, U.S. Government Rinting Office, Washington. D.C., pp. 527-544.

U.S. Department of Agriculture, 1971. Hydrology Guide for Use in Watershed Planning. National Engineering Handbook, Section 4, !hpplement A, Soif Conservation Service.

MINUTES 250 I I I I I 1

- W

AUG. 12, ‘74 STORM - r

-

-

MINUTES

Figure 4. Comparison Betwecn Obwrvad and predicted mood Hydrograpb.


APPLICATION OF SCS INFILTRATION MODEL

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