The use of GLS regression in regional hydrologic analyses

Abstract

Summary To estimate flood quantiles and other statistics at ungauged sites, many organizations employ an iterative generalized least squares (GLS) regression procedure to estimate the parameters of a model of the statistic of interest as a function of basin characteristics. The GLS regression procedure accounts for differences in available record lengths and spatial correlation in concurrent events by using an estimator of the sampling covariance matrix of available flood quantiles. Previous studies by the US Geological Survey using the LP3 distribution have neglected the impact of uncertainty in the weighted skew on quantile precision. The needed relationship is developed here and its use is illustrated in a regional flood study with 162 sites from South Carolina. The performance of a pooled regression model is compared to separate models for each hydrologic region: statistical tests recommend an interesting hybrid of the two which is both surprising and hydrologically reasonable. The statistical analysis is augmented with new diagnostic metrics including a condition number to check for multicollinearity, a new pseudo- R ¯ 2 appropriate for use with GLS regression, and two error variance ratios. GLS regression for the standard deviation demonstrates that again a hybrid model is attractive, and that GLS rather than an OLS or WLS analysis is appropriate for the development of regional standard deviation models.