Analysis of the Magnitude and Frequency of Floods in Colorado
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CROP FOLD LINE CROP MARKS V a i l l , J . E . — A n a l y s i s o f Prepared in cooperation with the t h e Colorado Department of Transportation M a and the Bureau of Land Management g n i t u d e a n d F r e q u e n c y Analysis of the Magnitude and o f F l o o d s Frequency of Floods in Colorado i n C o l o r a d o Water-Resources Investigations Report 99–4190 U S G S / W R I R 9 9 – 4 1 9 U.S. Department of the Interior 0 Printed on recycled paper U.S. Geological Survey CROP CROP FOLD MARKS LINE COVER 1 and 4 - PRINT SOLID Analysis of the Magnitude and Frequency of Floods in Colorado By J.E. Vaill U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 99–4190 Prepared in cooperation with the COLORADO DEPARTMENT OF TRANSPORTATION and the BUREAU OF LAND MANAGEMENT Denver, Colorado 2000 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 Box 25046, Mail Stop 415 Box 25286 Denver Federal Center Federal Center Denver, CO 80225–0046 Denver, CO 80225 CONTENTS Abstract.................................................................................................................................................................................. 1 Introduction............................................................................................................................................................................ 1 Purpose and Scope....................................................................................................................................................... 2 Previous Studies........................................................................................................................................................... 2 Approach...................................................................................................................................................................... 2 Flood-Frequency Analysis at Streamflow-Gaging Stations............................................................................... 2 Regional Flood-Frequency Analysis.................................................................................................................. 4 Regression Analysis............................................................................................................................................................... 7 Multiple Regression and Drainage-Basin Characteristics ........................................................................................... 7 Generalized Least-Squares Regression........................................................................................................................ 7 Limitations and Accuracy of Regression Equations.................................................................................................... 8 Estimating Magnitude of Peak Discharges............................................................................................................................ 8 Gaged Sites .................................................................................................................................................................. 8 Sites near Gaging Stations on the Same Stream.......................................................................................................... 10 Ungaged Sites .............................................................................................................................................................. 10 Summary................................................................................................................................................................................ 11 References Cited.................................................................................................................................................................... 12 Supplemental Data................................................................................................................................................................. 15 FIGURES 1. Map showing boundaries of hydrologic regions and locations of streamflow-gaging stations in Colorado and adjacent States.................................................................................................................................. 3 2. Map showing generalized skew coefficients of the logarithms of annual maximum streamflow for Colorado and adjacent States ................................................................................................................................ 5 3. Graph showing flood-frequency curve for Lake Fork at Gateview, Colorado ............................................................ 6 TABLES 1. Regional flood-frequency equations, Colorado....................................................................................................... 9 2. Basin characteristics and the range of values used in the analysis.......................................................................... 10 3. Drainage-basin characteristics and flood-frequency data at streamflow-gaging stations........................................ 16 CONVERSION FACTORS AND VERTICAL DATUM Multiply By To obtain inch 25.4 millimeter foot (ft) 0.3048 meter mile 1.609 kilometer square mile (mi2) 2.59 square kilometer cubic foot per second (ft3/s) 0.02832 cubic meter per second CONTENTS III Analysis of the Magnitude and Frequency of Floods in Colorado By J.E. Vaill Abstract near gaging stations on the same stream when the ratio of drainage-basin areas is between Regionalized flood-frequency relations about 0.5 and 1.5, and for sites where the drainage need to be updated on a regular basis (about basin crosses a flood-region boundary or a State every 10 years). The latest study on regionalized boundary. Methods are presented for determining flood-frequency equations for Colorado used the magnitude of peak discharges for sites located data collected through water year 1981. A study at gaging stations, for sites located near gaging was begun in 1994 by the U.S. Geological Survey, stations on the same stream when the ratio of in cooperation with the Colorado Department drainage-basin areas is between about 0.5 and 1.5, of Transportation and the Bureau of Land and for sites where the drainage basin crosses a Management, to include streamflow data flood-region boundary or a State boundary. collected since water year 1981 in the regional- ized flood-frequency relations for Colorado. Longer periods of streamflow data and improved statistical analysis methods were used to define INTRODUCTION regression relations for estimating peak In Colorado, various Federal, State, and discharges having recurrence intervals of 2, 5, 10, local governments use hydrologic data collected 25, 50, 100, 200, and 500 years for unregulated and published by the U.S. Geological Survey (USGS) streams in Colorado. The regression relations can be applied to sites of interest on gaged and in making decisions about the cost-effective planning ungaged streams. Ordinary least-squares regres- and design of highway bridges and culverts, flood- sion was used to determine the best explanatory plain management, reservoir management, and other basin or climatic characteristic variables for each water issues. The data are collected from a network peak-discharge characteristic, and generalized of streamflow-gaging stations operated by the USGS, least-squares regression was used to determine and part of that data is used to develop regression the best regression relation. Drainage-basin area, equations for determining the magnitude and mean annual precipitation, and mean basin slope frequency of floods on Colorado streams. were determined to be statistically significant Because of recent improvements in statistical explanatory variables in the regression relations. analysis, longer periods of record at more streamflow- Separate regression relations were developed for gaging stations, and the need to update regression each of five distinct hydrologic regions in the equations regularly (about every 10 years) as State. The mean standard errors of estimate and recommended by the Federal Highway Administration average standard error of prediction associated (FHWA) (L.A. Arneson, Federal Highway with the regression relations generally ranged Administration, oral commun., 1994), in 1994, the from 40 to 80 percent, except for one hydrologic USGS, in cooperation with the Colorado Department region where the errors ranged from about 200 of Transportation (CDOT) and the Bureau of Land to 300 percent. Methods are presented for deter- Management (BLM), developed new regression equa- mining the magnitude of peak discharges for tions for determining flood magnitude and frequency sites located at gaging stations, for sites located on unregulated streams. Abstract 1 Purpose and Scope Colorado. Jarrett and Costa (1988) developed regression equations for a relatively homogeneous This report presents the regression equations hydrologic foothill region in the South Platte River and the methods for determining the magnitude Basin (excluding drainage areas upstream from the and frequency of floods on unregulated streams in South Platte River at South Platte, Colo.). Each of