Collinearity and stability in the estimation of rainfall-runoff model parameters

The common use of statistical rainfall-runoff models of the regressive type lead to the problem of handling the unavoidable correlation existing between the explanatory variables of these models. The above collinearity problem is treated using ridge regression techniques. This powerful regression method is extensively presented and discussed. Examples show that collinearity has significant effects on values of rainfall-runoff model parameters and that ridge regression effectively deals with the problem, leading to well behaved model coefficients. The important issue of parameter stability is also addressed using both ridge regression and Kalman filtering as estimation procedures. It is shown that considerable data are required before parameter stability is achieved casting serious doubts on the predictive capability of models developed with usually limited historical data. Although a powerful methodology, Kalman filtering exhibited disturbing instability and lack of convergence unless special algorithms of high numerical accuracy are used.