Methods for estimating magnitude and frequency of floods in the southwestern United States

Abstract

Equations for estimating 2-, 5-, 10-, 25-, 50-, and 100-year peak discharges at ungaged sites in the southwestern United States were developed using generalized least-squares multiple-regression techniques and a hybrid method that was developed in this study. The equations are applicable to unregulated streams that drain basins of less than about 200 square miles. Drainage area, mean basin elevation, mean annual precipitation, mean annual evaporation, latitude, and longitude are the basin and climatic characteristics used in the equations. The study area was divided into 16 flood regions; Region 1 is a high-elevation region that includes the entire study area. Floods in the northern latitudes of the study area generally are much smaller than floods in the southern latitudes. Typical unit peak discharges of record range from 316 cubic feet per second per square mile for sites between 29° and 37° latitude to 26 cubic feet per second per square mile for sites between 41° and 45° latitude. An elevation threshold exists in the study area above which large floods caused by thunderstorms are unlikely to occur. For sites between 29° and 41° latitude, the elevation threshold is approximately 7,500 feet. For sites between 41° and 45° latitude, the elevation threshold decreases in a northward direction at a rate of about 300 feet for each degree of latitude. Detailed flood-frequency analyses were made of more than 1,300 gaging stations with a combined 40,000 station years of annual peak discharges through water year 1986. The log-Pearson Type III distribution and the method of moments were used to define flood-frequency relations. A low-discharge threshold was applied to about one-half of the sites to adjust the relations for low outliers. With few exceptions, the use of the low-discharge threshold resulted in markedly better-appearing fits between the computed relations and the plotted annual peak discharges. After all adjustments were made, 80 percent of the gaging stations were judged to have adequate fits of the computed relations to the plotted data. The individual flood-frequency relations were judged to be unreliable for the remaining 20 percent of the stations because of extremely poor fits of the computed relations to the data, and these relations were not used in the generalized least-squares regional-regression analysis. Most of the stations with unreliable relations were from extremely arid areas with 43 percent of the stations having no flow for more than 25 percent of the years of record. A new regional flood-frequency method, which is named the hybrid method, was developed for those more arid regions. An analysis of regional skew coefficient was made for the study area. The methods of attempting to define the variation in skew by geographic areas or by regression with basin and climatic characteristics all failed to improve on a mean of zero for the sample. The regional skew used in the study, therefore, was the mean of zero with an associated error equal to the sample variance of 0.31 log units. Generalized least-squares regression was used to define the regression models in 12 regions where sufficient data allowed a reasonable regional model to be developed using the flood-frequency relations at gaged sites. Four regions had more than 30 percent of the gaged sites with no defined relations; thus, the regression method was not used because of the large amount of missing information.