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Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

Scientific Investigations Report 2008-5084

Prepared in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University
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Abstract

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

Additional Publication Details

Publication type:
Report
Publication Subtype:
USGS Numbered Series
Title:
Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization
Series title:
Scientific Investigations Report
Series number:
2008-5084
Edition:
Version 1.0
Year Published:
2008
Language:
ENGLISH
Publisher:
Geological Survey (U.S.)
Contributing office(s):
Texas Water Science Center
Description:
iv, 40 p.