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Estimating the Magnitude and Frequency of Floods in Rural Basins of North Carolina

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Estimating the Magnitude and Frequency of Floods in Rural Basins of North Carolina Estimating the Magnitude and Frequency of Floods in Rural Basins of North Carolina By Benjamin F. Pope and Gary D. Tasker U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 99–4114 Prepared in cooperation with the North Carolina Department of Transportation Raleigh, North Carolina 1999 U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary U.S. GEOLOGICAL SURVEY Charles G. Groat, Director The use of firm, trade, and brand names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey. For additional information write to: Copies of this report can be purchased from: District Chief U.S. Geological Survey U.S. Geological Survey Information Services 3916 Sunset Ridge Road Federal Center, Box 25286 Raleigh, NC 27607-6416 Denver, CO 80225 CONTENTS Abstract ................................................................................................................................................................................. 1 Introduction........................................................................................................................................................................... 1 Purpose and scope....................................................................................................................................................... 2 Approach..................................................................................................................................................................... 2 Data compilation ......................................................................................................................................................... 3 Acknowledgments....................................................................................................................................................... 3 Basin characteristics.............................................................................................................................................................. 6 Estimation of flood magnitude and frequency at gaged sites................................................................................................ 7 Estimation of flood magnitude and frequency at ungaged sites............................................................................................ 10 Regional regression analysis ....................................................................................................................................... 10 Region-of-influence analysis....................................................................................................................................... 13 Comparison of results ................................................................................................................................................. 14 Use of computer software ........................................................................................................................................... 15 Application of methods......................................................................................................................................................... 15 Summary ............................................................................................................................................................................... 16 References............................................................................................................................................................................. 17 Appendix............................................................................................................................................................................... 43 FIGURES 1. Locations of gaged rural sites in North Carolina ...................................................................................................... 4 TABLES 1. Map identification numbers and descriptions of gaged rural sites in North Carolina with annual peak-flow record ................................................................................................................................ 19 2. Recurrence interval discharges and basin characteristics for gaged rural sites in North Carolina ................................................................................................................................................... 31 3. Basin characteristics that were used in the North Carolina flood-frequency regionalization study .............................................................................................................................................. 6 4. Generalized skew coefficient and associated mean square error for rural North Carolina gaging sites ................................................................................................................................... 9 5. North Carolina rural flood-frequency equations .................................................................................................... 11 6. Average predictive errors and equivalent years of record associated with North Carolina rural flood-frequency equations .............................................................................................................. 12 7. Root mean square error for the regional regression and region-of-influence methods, presented by hydrologic area and recurrence interval ............................................................................................ 14 Contents III Estimating the Magnitude and Frequency of Floods in Rural Basins of North Carolina By Benjamin F. Pope and Gary D. Tasker ABSTRACT between flood discharge and basin characteristics for a subset of gaged sites with similar basin A statewide study was conducted to develop characteristics. This, then, can be used to estimate two methods for estimating the magnitude and flood discharges at ungaged sites. Because the frequency of floods in rural ungaged basins in computations required for this method are North Carolina. Flood-frequency estimates for somewhat complex, a computer application was gaged sites in North Carolina were computed by developed that performs the computations and fitting the annual peak flows for each site to a log- compares the predictive errors for this method. Pearson Type III distribution. As part of the The computer application also includes the option computation of flood-frequency estimates for of using the regression equations to compute gaged sites, new values for generalized skew estimated flood discharges and errors of prediction coefficients were developed. Basin characteristics specific to each ungaged site. for these gaged sites were computed by using a Root mean square errors, computed for each geographic information system and automated recurrence interval and hydrologic area, are computer algorithms. Flood-frequency estimates generally only slightly lower for the region-of- and basin characteristics for 317 gaged sites were influence method than for the regression equations combined to form the data base that was used for and do not provide sufficient basis for this analysis. recommending one method over the other. In Regional regression analysis, using addition, the region-of-influence method is a new generalized least-squares regression, was used to method that is still being improved. As a result, the develop a set of predictive equations that can be regional regression equations are considered to be used to estimate the 2-, 5-, 10-, 25-, 50-, 100-, the primary method for computing flood- 200-, and 500-year recurrence interval discharges frequency estimates at ungaged sites. for rural ungaged basins in the Blue Ridge- Piedmont, Coastal Plain, and Sand Hills hydrologic areas. The predictive equations are all INTRODUCTION functions of drainage area. Average errors of prediction for these regression equations range Reliable estimates of the magnitude and from 38 to 56 percent. frequency of floods are needed by State and local designers and managers. The design of highway and A region-of-influence method also was railroad stream crossings, delineation of flood plains developed that interactively estimates recurrence and flood-prone areas, management of water-control interval discharges for rural ungaged basins in the structures, and management of water supplies are all Blue Ridge-Piedmont and Coastal Plain activities that require estimates of the frequency hydrologic areas of North Carolina. Regression distribution of flood events. Such estimates can be techniques are used to develop a unique relation computed directly by using statistical methods at gaged Abstract 1 sites that have at least 10 years of annual peak record; performed by a computer application that is discussed the longer the record of annual peak flows, the more later in this report. Because only gaged sites with reliable the estimate. It is not feasible, however, to similar basin characteristics are used to estimate flows collect 10 years of annual peak record for every at ungaged sites, there is less chance of extrapolation location where an estimate of the flood-frequency beyond the limits of the explanatory data. Tests of this distribution is needed, nor is it reasonable to wait approach in Texas (Tasker and Slade, 1994) and in 10 years for an estimate once a site has been identified. Arkansas (Hodge and Tasker, 1995) yielded estimates Estimates that are derived solely from gage with lower prediction errors than those produced by records do not provide
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