Assessment of the US Conservation Service method for estimating design floods

New DirectionsforSurface Water ModelingfPmceeàings of the Baltimore Symposium, May 1989) IAHSPubl.no. 181,1989. Assessment of the US Conservation Service method for estimating design floods A.A. Hoesein Fakultas Teknik, Universitas Brawijaya, Malang 65113, Indonesia D.H. Pilgrim School of Civil Engineering, The University of New South Wales, Kensington 2033, Australia G.W. Titmarsh Department of Primary Industries, Queensland, Toowoomba 4350, Australia I. Cordery School of Civil Engineering, The University of New South Wales, Kensington 2033, Australia ABSTRACT The US SCS method has been tested as a design flood procedure in two regions in eastern Australia. Runoff curve numbers have been derived from observed data on a probabilistic rather than an event basis, fitting the design case. Derived values depended on the method for determining time of concentration and the average recurrence interval of the design flood, and to a minor extent on basin characteristics. Values derived by the normal SCS handbook procedure were shown to give very poor estimates of flood frequency values. Mapping of derived values provides a satisfactory basis for flood design. INTRODUCTION The U.S. Soil Conservation Service (SCS) Method is widely used for estimating floods on small to medium sized ungauged drainage basins in the USA and in many other countries. While there is an extensive literature on the method, little quantitative information is available on the data base from which the method was developed, and the manner in which this base was used in the development. Rallison (1980) gives a general description of the origin and evolution of the method from infiltrometer tests. The procedure as currently employed is described by US SCS (1985), and the relationships involved will not be repeated here. The basic relationship in the method is between depths of runoff and rainfall in a flood event, utilizing a runoff curve number CN as a primary variable. An equation involving the calculated runoff depth and lag, time of concentration, and rainfall duration provides an estimate of the peak discharge. Many variations of the procedure have been proposed and employed in practice. A series of papers presented at an international symposium on rainfall-runoff modelling (Singh, 1982) gives a recent review of the method. 283

A. A. Hoesein et al. 284 INTERPRETATION AND TESTING OF THE METHOD As discussed in more detail by Pilgrim (1989), the estimation of design floods on small to medium sized rural drainage basins is of considerable economic importance. Although each individual structure on these basins might be of relatively low cost, the total expenditure on all of these structures is greater than that on any other type of structure for which a design flood provides the basic criterion for sizing and satisfactory performance. It is therefore important that the adequacy of methods such as the SCS procedure should be tested as thoroughly as possible. In addition, designers should understand the method used, its strengths and particularly its weaknesses. As with many other types of flood estimation methods, the SCS method is applied to two quite different types of problems. Although the computational procedure may be virtually the same in both cases, the interpretation of the method, its validity, and the requirements for testing the method are different. The first type of application is where an estimate is required of the depth, and possibly peak rate, of runoff from a particular storm event. This is a deterministic problem and for this case the method is regarded as a deterministic model. The second type is the design case, where a flood of a selected probability of exceedance is derived from a design rainfall of the same probability of exceedance. A probabilistic interpretation of the method is involved, and this is the approach adopted here. Much confusion has arisen through lack of appreciation of the differences in the two approaches, which are discussed in more detail by Pilgrim (1989) in the context of the Rational Method. The SCS method has been tested extensively in the deterministic sense with generally poor results. For example, Wood and Blackburn (1984) using 1600 runoff plots in Nevada, Texas and New Mexico found differences of greater than ±50% in 67% of the results. They found that the assumed antecedent moisture condition had a major effect, and that results were better for bare soil or sparse vegetation than for dense vegetation. Similar findings on the effects of vegetation were reported by Steichen (1983) and Glanville et al. (1984). Hawkins (1980) and Chen (1982) give examples of the sensitivity of runoff estimates to variations in CN. Poor performance as a deterministic model does not necessarily imply that the SCS method is inadequate as a design tool. The requirement here is that the method converts the design rainfall of selected average recurrence interval (ARI) and duration into the runoff depth, or more usually peak rate of flow, of the same ARI. The transformation here is between values of the same ARI from frequency curves of rainfall and floods. This interpretation is the only one that fits the normal design case, and it provides the basis for valid testing of methods for estimating design floods. Some limited testing of the SCS method using this general approach has been carried out by Hiemstra (1968) and Hjelmfelt (1980,1983). This paper reports the results of a more extensive assessment of the method as a design model. DRAINAGE BASINS STUDIED The study covered two regions in eastern Australia. The first involved 43 drainage basins in a 40 000 km 2 region in south eastern

285 Assessment of the SCS method for estimating design floods New South Wales, mostly with areas of 0.1-240 km 2 and either forest or pasture cover. The second region was larger, with 96 drainage basins over an area of 150 000 km 2 in and adjacent to south eastern Queensland with areas mostly in the range 0.01-500 km 2. As well as forest and pasture cover, some basins had large areas of cultivation. In both regions, all of the gauged rural basins were used that were of small to medium size and that had at least 10 years of recorded streamflows. DERIVATION OF CN VALUES FROM RECORDED DATA As the SCS method was being tested as a design procedure, conventional design rainfalls from intensity-frequency-duration data derived by the Bureau of Meteorology (Inst. Engrs Aust., 1987) were calculated for each drainage basin for a range of ARIs. A frequency analysis of observed floods was carried out for each basin, using the partial series of floods. Flood peaks were only estimated for ARIs up to or a little beyond the length of record In each case. As very little extrapolation of data was involved, log Pearson ill distributions were fitted by moments to the partial series of floods purely as a curve fitting or smoothing procedure, using the same number of floods in the series as the number of years of record to give the best fit to the data (McDermott Pilgrim, 1982). Values of CN were then derived to make the peak discharges estimated from the design rainfalls equal to the peak discharges determined from the frequency analyses of observed floods. The estimated peak discharges were calculated by the formula based on a triangular hydrograph shape. As the values of design rainfall and the peak discharge from the flood frequency curve for a given basin were different for the various ARIs, the values of CN derived in this way were different for each ARI. EFFECT OF METHOD OF DETERMINING TIME OF CONCENTRATION In the SCS method, the rainfall duration depends on an estimated value of the time of concentration(t ). The design rainfall depth on a given basin for a particular ARI is calculated from the intensityfrequency-duration relation for the region, and CN will therefore depend on the method used to calculate t. In general, a longer t_ leads to a lower design rainfall and hence a larger value of CN. For south eastern New South Wales, the effects of five methods of estimating t were investigated. Four of these involved formulae for calculating t c directly from catchment characteristics. These were the Bransby Williams formula using the length and slope definitions of the Institution of Engineers Australia (1987), a simple power function of area derived by McDermott Pilgrim (1982), the Ramser-Kirpich formula (Kirpich, 1940), and a variation of this (Midgley 5 Schultz, 1956) using a different measure of slope. The fifth method was that given by the US SCS (1985) where t c is related to stream length, slope and potential Infiltration. This last value Is a function of CN, so that in deriving the CN value from observed flood data, a trial and error procedure was required. For south eastern Queensland, a similar range of methods was tested, but with parameters for many of the formulae derived from local data. Table 1 shows values of CN for an ARI of 10 years [CN(10)] derived from the observed flood data on two drainage basins In south eastern

A. A. Hoesein et al. 286 New South Wales using design rainfalls with durations derived from t c values given by each of the five procedures. The variations are typical of those for the remainder of the basins in both regions. They demonstrate that the appropriate value of CN for a given basin depends on the manner in which the rainfall duration is determined, which must also be used in application of the derived CN values in design if the observed flood data are to be reproduced. TABLE 1 Variation of derived CN(iO) with method of estimating t c Basin Method of estimating t c gauging TïrluTsTyy McDermott Ramser- Midgley SCS triallj stn Natl No. Williams Pilgrim Kirpich Schultz error 401006 73.4 70.5 69.7 69.7 76.6 410063 89.2 79.1 82.6 81.1 93.0 VARIATION OF DERIVED CN WITH ARI As noted previously, different values of CN were derived on each basin for each different value of ARI. CN remains almost constant in very few cases. However, the direction and magnitude of change with increasing ARI vary considerably for different basins, and also vary on most basins with the different methods of estimating t c. For this latter effect, the differences in CN values for the different t methods increase with increasing ARI. Tables 2 and 3 show the differences between the 1 and 10 year, and 10 and 50 year ARI values of CN for 30 of the basins in south eastern New South Wales. There are feiver values in Table 3 because CN(50) was not derived for basins with relatively short records. The tables illustrate the differences in the variation of CN with ARI for the different methods of estimating t c. For the first four methods in which t~ is estimated directly from basin characteristics, there is a greater variation of CN for low ARIs between 1 and 10 years than for higher ARIs above 10 years. For all but the Bransby Williams method, CN values seem to reach a minimum on average at an ARI of about 10 years. CN values derived using the SCS method for estimating t c tend to vary randomly with little trend. TABLE 2 [CN (1) - CN (10)] - south eastern New South Wales Number of stations with CN difference Method for ^ m ^ÏQ -5 g- ^7j t c to -5 to 0 to 5 to 10 Bransby Williams 4 9 7 7 2 1 McDermott Pilgrim 6 10 9 4 1 0 Ramser Kirpich 6 10 7 9 4 0 Midgley Schultz 7 11 8 3 1 0 SCS trial error 1 5 10 11 1 1 TABLE 3 [CN (10) - CN (50)] - south eastern New South Wales Method for t Bransby Williams McDermott %, Pilgrim Ramser % Kirpich Midgley Schultz SCS trial error <-10 2 1 1 1 0 Number of stations with CN difference -10-5 0 5 >10 to - 5 to 0 to 5 to 10 2 5 2 3 0 1 3 5 4 0 1 3 5 4 0 1 3 5 4 0 4 6 2 2 0

287 Assessment of the SCS method for estimating design floods For the CN values derived with the McDermott Pilgrim method of estimating t, linear regressions were derived for CN(Y) against C(10) for each of the ARIs of Y = 1, 2, S, 20, 50 and 100 years. The number of CN values decreased as ARI increased. The coefficient of determination (r 2 ) was in the range 0.70 to 0.98 for all regressions, and the correlations were significant at probability levels considerably less than 1% in all cases. Table 4 shows the CN values given by the regressions for each of the ARIs noted above corresponding to CN(10) values of 60, 80 and 90, covering the approximate range of derived values. This shows that the magnitude of CN has a considerable effect on the manner in which the CN values vary with ARI. For basins with CN(10) of 60, the derived CN values tend to decrease rapidly with increasing ARI. There is a very slight decrease, and a small increase for values of CN(10) of 80 and 90 respectively. The results represented only apply to this region and to CN values derived using t c calculated from the McDermott Pilgrim formula. They would not necessarily apply to other t c procedures or other regions. TABLE 4 CN(10) CN values given by regressions of CN(Y) on CN(10) - south eastern NSW using McDermott Pilgrim t c CN(Y) given by regressions CN(1) CNC2) CN(5) CNC2ÏÏ) CN(50) CNTTÔÔY"' (r 2 =0.702) (r 2 =0.873) (r 2 =0.981) (r 2 =0.985) ( r 2 =0.890) (r 2 =0.858) 60 75 69 63 57 52 51 80 84 82 80 80 81 80 _90 89 89 89 91 96 95 Similar variations of derived CN values with ARI were found for south eastern Queensland as are discussed above for south eastern New South Wales, In summary, derived values of CN vary with ARI on a given drainage basin. However from the results in this study, the manner and magnitude of variation depend on the particular region, the method of determining t c for the rainfall duration, and the magnitude of CN. To be useful for design, the effects of ARI need to be investigated in the region of interest. VARIATION OF DERIVED CN VALUES WITH BASIN CHARACTERISTICS Relationships between the derived CN values and a large number of drainage basin characteristics were investigated for both regions. Unless otherwise stated, the details of the following discussion apply to the south eastern Queensland region, with CN values derived from design rainfalls with durations estimated by the SCS procedure for t, but with locally derived parameters. Only a few basin characteristics had significant effects. The percentage of area cultivated had the greatest effect. Although there was a large scatter of data, increasing percentages produced significant increases in derived CN values, with r 2 = 0.35 for the 69 basins with the most reliable records. CN(10) values from the regression fitted to the data increased from 78 to 92 as area cultivated increased from 0 to 100%. The effect was most pronounced for ARIs up to 10 years, with lesser effects for the larger floods. The results here agree with those obtained deterministically for individual events, for example by Freebairn Boughton (1981), Rawls Richardson (1983) and Steichen (1983).

A. A. Hoesein et al. 288 Increasing basin size produced small variations in opposite directions in the derived CN values in the two regions. In south eastern New South Walesj basin size had no effect up to an ARI of 20 years, but beyond this CN increased with size. This could have resulted by chance from the small sample. In south eastern Queensland, CN decreased slightly with increasing basin size, possibly because the smaller gauged basins are generally on clays as these are the most important agriculturally. Overall, the results indicate that basin size probably had little effect on CN, and that the variations that did occur may have resulted from other causes. The only other basin characteristics showing any significant relation with CN were soil type and crop management. Average values of CN(10) decreasing by only 9 for soils with the lowest to the highest expected final infiltration rates respectively. Values of CN were influenced by crop management practices for small floods with ARIs up to 5 years. Overall, the derived values of CN varied over a much smaller range than the recommended values published by the US SCS (1985), and they were related to a much smaller number of basin characteristics. COMPARISON WITH CN VALUES ESTIMATED FROM BASIN CHARACTERISTICS A basic aspect of the SCS procedure as normally applied in practice is the estimation of a value of CN from basin characteristics. Tabulated values are given for three antecedent moisture conditions, for land use or cover, treatment or practice, hydrologie condition of soil cover, and four soil types. Values of CN were estimated by this handbook procedure for each of the drainage basins in the two regions. These values were then compared with those derived probabilistically from observed data. The results for both regions are typified by Fig. 1, showing derived CN(10) values plotted against estimated values for all 96 basins in the south eastern Queensland region. The line of equality is also shown. The very large scatter shows that the handbook procedure for estimating CN from basin characteristics is highly inaccurate. Poor estimates of the observed flood characteristics would result. Fig. 1 Estimated CN value Fig. 1 Comparison of derived and estimated CN values, south eastern Queensland.

289 Assessment of the SCS method for estimating design floods shows that the estimated values are too low on average, but this could result from the procedure used to estimate t c in calculating the derived values. In fact, as the derived values depend on the method used for estimating t c, exact correspondence of the two sets of CN values is of little importance. However, a consistent relation between the two sets would be necessary to make it possible for the estimated CN values to give accurate discharge values that reflect basin records. It is the scatter on Fig. 1 that indicates the poor accuracy of the handbook type procedure for estimating CN, and its inadequacy as a design procedure. MAPPING OF CN VALUES FOR DESIGN Mapping of the values of CN(10) derived from observed data was suggested by the similar procedure that was used by McDermott Pilgrim (1982) for probabilistic runoff coefficients for the Rational Method. It was also supported by the relation of CN values to soil type and percentage of area cultivated which are related to location. Values of CN(10) were plotted on maps and contours were sketched in. These were drawn subjectively, but account was taken of patterns of average annual rainfall and short duration design intensities, and of topography, geology and soil types. Reliability of gauging station records was also assessed and considered in the drawing of the contours. Fig. 2 shows a map of CN(10) for the south eastern New South Wales region. Some scatter of the values from the contours is to be expected due to the random errors and relatively small sample sizes of the recorded flood data, and to a lesser extent the design rainfalls. In general, the contours agree well with the plotted values, and are smooth, consistent and of reasonable shape. For both regions studied, the maps provide a sound basis for practical design and should give results that match the frequency curves of observed floods as well as possible. This is the objective of design. For application it would be essential to use the same design rainfall data and t c estimation procedure as was used in deriving the values. To determine CN values of other ARIs for design purposes, relations between these values and CN(10) are required. As discussed previously, N I- 100 Fig. 2 Map of design CN(10) values, south eastern New South Wales.

A. A. Hoesein et al. 290 linear regressions were derived between CN(Y) and CN(10) for each of the regions for ARIs of Y = 1, 2, 5, 20, 50 and 100 years. Some values from the regressions for south eastern New South Wales are shown in Table 4. These relations would complete the design procedures for the two regions. CONCLUSION Values of curve number (CN) for use in the SCS method as a design procedure should be derived probabilistically from observed data so that they reproduce values given by flood frequency curves, when they are applied to design rainfalls. This exactly matches the design procedure, in contrast to the usual approach of deriving CN values deterministically on an event basis. Probabilistic values of CN have been derived for large numbers of drainage basins in two regions in eastern Australia. The values of CN are not fixed or constant for a given basin as is implied in the normal handbook approach. They depend on the method used for estimating t in determining the rainfall duration and on the ARI of the flood considered, but their variation with these factors differed in the two regions. The CN values were fairly weakly related to some basin characteristics, but with a much smaller range of values than indicated by the SCS recommendations. There was a very poor relationship between CN values estimated from basin characteristics by the SCS handbook recommendations and the values derived from observed data. The former values would give inaccurate estimates of design runoff and flood peaks in both regions. Mapping of the derived values provided a sound basis for design in both regions. REFERENCES Chen, C.L. (1982) An evaluation of the mathematics and physical significance of the Soil Conservation Service curve number procedure for estimating runoff volume. In: Runoff-Rainfall Relationship (Proc. Internat. Symp. on Rainfall-Runoff Modeling, ed. by V.P. "Singh), 387-415. Water Resources Publ., Littleton, Colo. Freebairn, D.M. & Boughton, W.C. (1981) Surface runoff experiments on the eastern Darling Downs. Aust J. Soil Res. 19, 133-146. Glanville, S.F., Freebairn, D.M. Silburn, D.M. (1984) Using curve numbers from simulated rainfall to describe runoff characteristics of contour bay catchments. Agric. Engg Conf., Bundaberg 1984, Inst. Engrs Aust., Natl. Conf. Publ. 84/6, 304-307. Hawkins, R.H. (1980) Infiltration and curve numbers: some pragmatic and theoretic relationships. Proc. Symp. on Watershed Management 1980, Boise Idaho, Vol. II. Am. Soc. Civil Engrs. 925-937. Hiemstra, L.A.V. (1968) Modifications on the "Soil Conservation Service Method" for the estimation of design floods on very small catchments in the arid western part of the United States of America. Colo. State Univ., Civil Engg Dept, Tech. Report. Contract No. 14-11-008-2812. Hjelmfelt, A.T. (1980) Empirical investigation of curve number technique. Proc. Am. Soc.

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