Estimation of Unit Hydrograph by Ridge Least-Squares Method

Abstract

Least squares (LS) methods are frequently used to determine an optimal unit hydrograph (UH) for a watershed. However, the conventionally used ordinary LS method could potentially produce a UH with unwanted fluctuation among hydrograph ordinates. When that occurs, the ridge LS method can be used to reduce noise fluctuation in a derived UH. In the framework of the ridge LS method, a UH can be obtained by minimizing the mean-squared error (MSE) of the estimated UH or direct runoff hydrograph (DRH). Therefore, the ridge LS method theoretically would enhance the predictability of the derived UH. This paper describes methodologies of obtaining the optimal ridge parameter for use in the ridge LS method to estimate a UH. Furthermore, the unit volume constraint is considered in the determination of the optimal ridge parameter. A statistical validation study is also conducted to show that a UH obtained by the ridge LS method has a better predictive capability than the one derived by the ordinary LS method.