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I I remained in the hydrograph fitting and unexplained variance of the regressions were assumed to be mainly sampling error and random fluctuations. It is recognized that spatial variations in rainfall. cover, and other factors constitute the physical reasons for some of the aberrations. I I Need for the Study The design of an ever increasing number of hydraulic structures involves the estimation of flood runoff from srmll watersheds. As road building and headwater flood control programs gain momentum, more and more capital will be involved in culverts I valley fills and small spillways. Most of these struc- tures are not costly enough to warrant detailed indivi- dual hydrologic investigations. Yet the cost of per~ feeting a universal method which could be applied quickly and easily to each field situation would bring about considerable savings. Currently much public and private capital is wasted on hydraulic structures. many of which are either overdesigned or fail due to the underestimation of floods. I I I I By virtue of temporary storage behind road fills and above the spillway level of dams, flood out- lets may sometimes be designed to discharge less than the inflow hydrograph's peak. With a view to such future refinements in design, an estimation pro- cedure which predicts the shape of the hydrograph would be more valuable than one merely giving the peak rate. I I A need also exists to move away from the regional flood frequency approach. Both it and en- velope curves for flood peaks assume adequate spatial sampling and a certain degree of homogeneity through- out the region. Anomolous results will always be pre- sented in the adjacent belts of two such regional syn- theses. Relationships involving the causal elements such as rainfall intensity, land slope and soil pro- perties would be far more realistic. In fact such regressions could reasonably be used beyond the region where the hydrographs were obtained. In the era of American technical aid to underdeveloped countries. such rational methods could be used over- seas. since the topographic, soil and rainfall informa- tion can be obtained far more readily than can flood observations. I I I I Recent Related Studies The most closely related work to the proposed study was reported by Gray (9, 10) in 1960. In that study forty-six watersheds ranging in size from O. 27 to 32.64 square miles were studied from the unit hydrograph approach. Their range in size far ex- ceeded that in the present study. On the other hand Gray's hydrographs came exclusively from Illinois, Iowa, Missouri. Nebraska, Ohio, Wisconsin and North Carolina where the climatic range is far narrower than that encompassed by the present study's watersheds, which represent eleven states. In con- trast to Gray's approach. this investigation does not involve a representative distribution graph for each watershed. Individual differences between hydro- I I I I II graphs observed on the same watershed have been retained here and accounted for by rainfall peculiari- ties. Another difference between the two studies is that Gray employed a two-parameter gamma distribu- tion whereas the present investigation fits a three ~ parameter equation, which should be far more flex- ible, to the observed hydrographs. Benson (2) showed, as has been suggested by Nash (17) and others. that after three or four inde- pendent meteorologic and physiographic variables have been used, further variables do not appreciably decrease the standard error in estimating floods. Benson's analysis eliminates the effect of variation of individual storms since flood peaks, of specified return periods, obtained from a frequency analysis of annual maxima were used as his dependent variable. The main-channel slope was found next in importance to drainage-area size. Benson's study has little application to very small watersheds, since only three of the 170 New England stations which he studied possessed areas of less than ten square miles. Hickok, Keppel and Rafferty (12) made a sig- nificant contribution to hydrograph synthesis. They studied about 130 hydrographs and hyetographs from fourteen watersheds ranging in size from 11 to 790 acres in the arid Southwest. Lag time was related to watershed area, average land slope and drainage density. The estimated lag time was used to predict the hydrograph peak rate for an assumed total vol- ume of runoff. Finally the entire synthesized hydro- graph could be obtained from a generalized hydro- graph, expressed dimensionlessly in terms of lag time and peak rate. Their dimensionless hydrograph appeared to be independent of rainfall pattern and of soil and cover condition. This simplification pro- bably resulted from their four research localities possessing similar climatic and cover conditions. A recent article by Chow (3) presents a method for determining peak discharges from rural watersheds which are smaller than 6000 acres. By trial and error the method enables one to ascertain which duration of rainfall excess gives the maximum rate of runoff and to estimate the latter by applying four charts. The method involves runoff curve num- bers and relationships presented by the U. S. Soil Conservation Service (24). Combined with this is the concept of a peak~reduction factor which is defined as the ratio of the peak discharge to the equilibrium direct discharge. Although the charts presented are exclusively for Illinois, these first two phases of the method are entirely general and could be applied universally with rainfall data (11). To complete the procedure it is necessary to express the peak reduc- tion factor as a function of the ratio of the duration of rainfall excess to lag time. The lag time must there- fore also be estimated from watershed characteristics. Chow obtained these two relationships from fifty- three storms covering twenty small watersheds in the Midwest. Until similar relationships are available for other climatic and topographic areas the method will be regionally restricted. 3