Estimating Selected Parameters for the XAJ Model under Multicollinearity among Watershed Characteristics

Abstract

Because the problem of prediction in ungauged basins (PUB) has become a central theme of hydrological research, there is a clear need to have an effective and efficient method that can help to transfer information from gauged basins to ungauged ones. Previous research relating the parameters of a hydrologic model to physical drainage basin characteristics has had limited success. Conventional regression procedures do not take into account multicollinearity among the basin characteristics, which have a great effect on the stability of regression equations. This study presents an unbiased ridge regression estimate (URR) that can provide robust regression equations in the presence of multicollinearity. The proposed method is applied to estimate parameters of the Xinanjiang model in 20 watersheds located in southeastern China. Compared with conventional estimations, such as ordinary least squares estimate and ordinary ridge regression estimate, the URR was reduced by 78% for root mean square error, 47% for variance, and 13.1% for Akaike’s Information Criterion. The coefficient of determination