A RAINFALL-RUNOFF MODELING PROCEDURE FOR IMPROVING ESTIMATES OF T-YEAR (ANNUAL) FLOODS FOR SMALL DRAINAGE BASINS by R.W. Lichty and F. Liscum Prepared by the U.S. Geological Survey 1978 Water-Resources Investigations 78-7 TABLE OF CONTENTS Abstract Introduction Methods of study     Rainfall-runoff model     Selection of model calibration sites     Synthesis of annual floods     Formulation of multiple-regression model     Regression analysis of synthetic T-year floods-- rural model applications     Effects of imperviousness on synthetic floods     Single-coefficient relation for synthetic T-year floods     Geographic variability of climatic factor, C Map-model estimates of T-year floods at calibration sites     Comparison of observed and map-model flood estimates Accuracy and weighting of observed and map-model T-year floods Summary and conclusions References FIGURES 1. Schematic outline of model structure, showing components, parameters, variables, and input/output data 2. Map showing locations of long-term rainfall, and small streams, calibration sites used in study 3. Relationship between regression constant, ai, and regression coefficient, b2i 4. Relationship between the coefficients ai, and di 5. Contour map showing the geographic variation in the 2-year recurrence interval climatic factor, C2 6. Contour map showing the geographic variation in the 25-year recurrence interval climatic factor, C25 7. Contour map showing the geographic variation in the 100-year recurrence interval climatic factor, C100 8. Scatter diagrams of observed and map-model T-year flood estimates 9. Trends in error-variance components as a function of recurrence interval TABLES 1. Model parameters and variables and their application in the modeling process 2. Long-term recording rainfall sites used in study 3. Streamflow stations used in study 4. Results of multiple-regression analyses for rural model applications 5. Summary and comparison of multiple-regression (m-r) and direct-search (d-s) determinations for the coefficient, ai- 6. Results of the direct-search determinations for the coefficient di for effect of impervious area 7. Standard errors for the single coefficient, synthetic flood relation ABSTRACT The U.S. Geological Survey rainfall-runoff model is used to synthesize a sample of 550 annual-flood series, that are representative of both rural- and impervious-area model applications, using data from each of 36 long-term recording rainfall sites. A flood-frequency curve is developed for each annual-flood series, and a single-coefficient, regression relation for the 2-, 25-, and 100-year floods is developed for each one of the rainfall sites--a generalized definition of the model output as a function of the model parameters for each rainfall sites. The site-to-site variability in the magnitude of the coefficient that characterizes the synthetic T-year (annual) flood relation is interpreted as reflecting the spatially varying influence of local climatic factors, Ci, on the results of synthesis. Three contour maps that depict the geographic variability of the climatic factor were prepared. Estimates of the Ci values taken from these maps were used in conjunction with fitted rainfall-runoff model parameters and the synthetic T-year flood relation to develop map- model, T-year flood estimates for 98 rural-area streamflow stations located in Missouri, Illinois, Tennessee, Mississippi, Alabama, and Georgia. Comparisons of these flood estimates with those based on observed annual floods show that the map-model estimates are generally lower than the observed estimates for return periods greater than the 2-year recurrence interval. This tendency to underestimate the higher recurrence interval floods was removed by use of an average adjustment factor, Bi, and the average accuracy of "unbiased", map-model flood estimates was appraised for the test sample of 98 streamflow stations. The accuracy of the map-model flood estimates are more accurate beyond the 10-year recurrence interval than observed estimates based on a harmonic-mean record length of 13.2 years. Improved T-year flood estimates were computed by weighting observed and map-model estimates, and the accuracy of the improved estimates is appraised as a function of recurrence interval, and in terms of the concept of equivalent length of record. The map-model estimating procedure yields an equivalent length of record that ranges from a low of about 6 years for the 1.25-year flood, up to an ultimate, maximum level of about 30 years of data for estimating the 50- and 100-year recurrence interval floods. LizardTech's Djvu plug-in is needed to view these reports. CLICK HERE TO VIEW THE ENTIRE REPORT For questions or comments, contact K. Van Wilson.