Regional Hydrologic Analysis: 1. Ordinary, Weighted, and Generalized Least Squares Compared

TLDR: In this paper, the authors compared the performance of ordinary, weighted, and generalized least squares estimators of the parameters of such regional hydrologic relationships in situations where the available Streamflow records at gaged sites can be of different and widely varying lengths and concurrent flows at different sites are cross-correlated.

Abstract: Streamflow gaging networks provide hydrologic information which is often used to derive relationships between physiographic variables and Streamflow statistics. This paper compares the performance of ordinary, weighted, and generalized least squares estimators of the parameters of such regional hydrologic relationships in situations where the available Streamflow records at gaged sites can be of different and widely varying lengths and concurrent flows at different sites are cross-correlated. A Monte Carlo study illustrates the performance of an ordinary least squares (OLS) procedure and an operational generalized least squares (GLS) procedure which accounts for and directly estimates the precision of the predictive model being fit. The GLS procedure provided (1) more accurate parameter estimates, (2) better estimates of the accuracy with which the regression model's parameters were being estimated, and (3) almost unbiased estimates of the model error. The OLS approach can provide very distorted estimates of the model's predictive precision (model error) and the precision with which the regression model's parameters are being estimated. A weighted least squares procedure which neglects the cross correlations among concurrent flows does as well as the GLS procedure when the cross correlation among concurrent flows is relatively modest. The Monte Carlo examples also explore the value of Streamflow records of different lengths in regionalization studies.