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Procedures are defined for estimating the magnitude and frequency of future flood peaks and flood volumes and for estimating the expected hydrograph shape of rainfall-induced runoff of small streams in South Dakota. The procedures are applicable to flood flows that are not significantly affected by artificial storage or other manmade activities. For 115 gaged sites within the State, the estimates are from the frequency curves defined from the gaging records. Flood-frequency estimates are made for ungaged sites by using regression relations that require evaluation of the size, main channel slope, and a soil-infiltration index for the drainage basin. Regression relations are considered applicable for estimating flood peaks at sites on basins draining 0.05 to 100 square miles and for estimating flood volumes at sites on basins draining from 0.05 to 15 square miles. Limitations on use of the regression relations and the reliability of regression estimates are discussed. A method is indicated for using the estimating procedure and embankment ponding to design smaller highway culverts. The procedures were developed from analysis of flood records of 123 gaged sites in South Dakota and adjacent States. For 66 sites, short-term records were extended on the basis of longterm climatic records and a rainfall-runoff model. Linear leastsquares regression analyses were used with logarithmic transformation of variables to relate flood magnitudes as dependent variables to indexes describing the drainage basins as independent variables. A dimensionless hydrograph shape was found appropriate for rainfall-runoff hydrographs in South Dakota. INTRODUCTION The magnitude and frequency of flood flows need to be considered in the design of highway structures such as bridges and culverts, in land-use planning, in establishing rates for flood insurance, or in formulating emergency evacuation plans for flood-prone areas. A regional flood-frequency analysis, which provides techniques for estimating peaks with recurrence intervals of as much as 100 years at most ungaged sites located in unregulated drainage basins, has been made for South Dakota 1 (Becker, 1974). However, the magnitude of flood volumes and the characteristic shape of flood hydrographs to be expected must also be known if embankment ponding is to be considered as a design factor and used to reduce required culvert size. In order to determine flood-flow characteristics in unregulated drainage basins with areas less than 10 mi 2, the U.S. Geological Survey, in cooperation with the South Dakota Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration, conducted an investigation to: (1) Determine the magnitude and frequency of flood peaks and volumes in small, unregulated drainage basins, (2) define the characteristic shape of flood hydrographs, and (3) develop a method for using embankment ponding in culvert design. This is the final report resulting from the investigation and supplements earlier reports by Becker (1973, 1974). The report presents flood frequency information at gaged sites; a simple, practical method for estimating flood peaks and volumes at ungaged sites; a method for estimating flood volumes based on known flood peaks; a method for determining the shape of flood hydrographs; and a method for using embankment ponding in reducing culvert size. The opinions, findings, and conclusions presented in this report are those of the U.S. Geological Survey and are not necessarily those of the cooperating agencies. The report is organized so that the estimating relations, their accuracy and limitations, and examples of their use; and a method regarding use of embankment ponding are presented first. These items are followed by a documentation of the data available and of the procedures used in the data analysis including aspects of rainfall-runoff modeling, flood-frequency analysis, regression analysis, and determination of hydrograph shape. Approach The approach to this research has been to collect and analyze data on flood peaks and flood volumes on a sample of streams draining basins with areas generally less than 10 mi 2. These data were augmented by peak-flow data from a crest-stage gaging program that were collected on basins of between 10 and 150 mi 2 in area. Analysis included defining relationships between magnitude and frequency of flood peaks and flood volumes for gaged sites. Because reliability of that frequency relationship increases with record length, a rainfall-runoff model was used to synthesize long-term flood records from available long-term climatological records. Multiple-regression analysis defined relations for estimating the magnitude-frequency relation for both flood peaks and flood volumes at ungaged sites. The average time-distribution (hydrograph) of observed rainstorm floods also was defined. 2 Acknowledgments Long-term daily precipitation records and 5-minute incremental storm-rainfall data were obtained from the National Oceanic and Atmospheric Administration, Environmental Data Service, National Climatic Center, at Asheville, N.C. D. M. Thomas and G. R. Dempster, Jr., of the U.S. Geological Survey, provided technical advice and assistance needed to apply the rainfall-runoff model to hydrologic conditions in South Dakota and to refine the model to meet specific project objectives. ESTIMATING RELATIONS The most reliable estimators of future floods generally are the frequency analyses of gaging-station records. Streamflow characteristics listed in tables 4 and 5 at the back of the report under the heading "Supplemental Information" may provide satisfactory estimates for planning and design of bridges and culverts at or near gaged sites, particularly where long-term records are available. Therefore, the estimating technique includes a search for available flood-frequency data for the desired site. Estimating peak discharges and runoff volumes at ungaged sites or at gaged sites with short-term records where floodflow is virtually natural involves solving mathematical equations relating flow magnitude to basin characteristics. The equations are: Qt = aAbScSid (peak discharge), (1) Vt = aAbSic (runoff volume), (2) where Q = peak discharge, in cubic feet per second; V = runoff volume, in acre-feet; t = flood recurrence interval, in years; a = regression constant; b, c, and d = regression coefficients; A = contributing drainage area upstream from site, in square miles; S = main channel slope, in feet per mile; and Si = soil-infiltration index, in inches.

Techniques for estimating flood peaks, volumes and hydrographs on small streams in South Dakota