An algorithm for estimation of optimal ‘k’ in Ridge Regression applied in modeling evapotranspiration

Evapotranspiration (ET) is an important parameter in irrigation, water management and hydrology. ET models in use today are based on several approaches. A few are based using ordinary least squares (OLS) using climatic data as predictors. However, multicollinearity may exist among them causing large variances. To offset this limitation of OLS, Ridge Regression (RR) has been used. The estimation of biasing parameter, k (k>;0), has been visually observed in the ridge trace; and using the criterion of mean squared error (MSE), RR has been claimed to be successful. But the unresolved problem in RR is the search for optimal k while ensuring stability of the ridge estimates. This paper describes an algorithm which nearly ensures an optimal k, eliminating subjectivity. This is validated by developing ET model and comparing with other popular ET models as well as with the measured values of ET using climatic data.