Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas Using an L-moment-Based, PRESS-Minimized, Residual-Adjusted Approach

Abstract

Annual peak-streamflow frequency estimates are needed for flood-plain management; for objective assessment of flood risk; for cost-effective design of dams, levees, and other flood-control structures; and for design of roads, bridges, and culverts. Annual peak-streamflow frequency represents the peak streamflow for nine recurrence intervals of 2, 5, 10, 25, 50, 100, 200, 250, and 500 years. Common methods for estimation of peak-streamflow frequency for ungaged or unmonitored watersheds are regression equations for each recurrence interval developed for one or more regions; such regional equations are the subject of this report. The method is based on analysis of annual peak-streamflow data from U.S. Geological Survey streamflow-gaging stations (stations). Beginning in 2007, the U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, began a 3-year investigation concerning the development of regional equations to estimate annual peak-streamflow frequency for undeveloped watersheds in Texas. The investigation focuses primarily on 638 stations with 8 or more years of data from undeveloped watersheds and other criteria. The general approach is explicitly limited to the use of L-moment statistics, which are used in conjunction with a technique of multi-linear regression referred to as PRESS minimization. The approach used to develop the regional equations, which was refined during the investigation, is referred to as the “L-moment-based, PRESS-minimized, residual-adjusted approach.” For the approach, seven unique distributions are fit to the sample L-moments of the data for each of 638 stations and trimmed means of the seven results of the distributions for each recurrence interval are used to define the station-specific, peak-streamflow frequency. As a first iteration of regression, nine weighted-least-squares, PRESS-minimized, multi-linear regression equations are computed using the watershed characteristics of drainage area, dimensionless main-channel slope, and mean annual precipitation. The residuals of the nine equations are spatially mapped, and residuals for the 10-year recurrence interval are selected for generalization to 1-degree latitude and longitude quadrangles. The generalized residual is referred to as the OmegaEM parameter and represents a generalized terrain and climate index that expresses peak-streamflow potential not otherwise represented in the three watershed characteristics. The OmegaEM parameter was assigned to each station, and using OmegaEM, nine additional regression equations are computed. Because of favorable diagnostics, the OmegaEM equations are expected to be generally reliable estimators of peak-streamflow frequency for undeveloped and ungaged stream locations in Texas. The mean residual standard error, adjusted R-squared, and percentage reduction of PRESS by use of OmegaEM are 0.30 log10, 0.86, and −21 percent, respectively. Inclusion of the OmegaEM parameter provides a substantial reduction in the PRESS statistic of the regression equations and removes considerable spatial dependency in regression residuals. Although the OmegaEM parameter requires interpretation on the part of analysts and the potential exists that different analysts could estimate different values for a given watershed, the authors suggest that typical uncertainty in the OmegaEM estimate might be about ±0.10 log10. Finally, given the two ensembles of equations reported herein and those in previous reports, hydrologic design engineers and other analysts have several different methods, which represent different analytical tracks, to make comparisons of peak-streamflow frequency estimates for ungaged watersheds in the study area.