Application of Linearized Calibration Method for Vertically Mixed Runoff Model Parameters

Abstract

Objective functions are the most important information source for parameter calibration. Current parameter calibration methods mostly employ error sum of squares as the objective function and depend on the information provided by the objective function to search the parameter optima. This kind of method can increase unrelated local optima for nonlinear models. In order to solve the problem, the linearized calibration method of nonlinear model parameters was developed. The purpose of this paper is to investigate the usefulness of the linearized calibration method in the context of calibrating rainfall-runoff models. The new method was first introduced and then used to calibrate vertically mixed runoff model parameters. Two types of analysis were performed. The first refers to an ideal model case free of data and model errors in which the true optimum set of parameter values was known by assumption. The ideal model case was used to examine whether the linearized calibration method is capable of finding that optimum without producing unrelated local optima. Furthermore, it was also applied to validating the advantages and effectiveness of the proposed method through comparison with the shuffled complex evolution (SCE-UA) method and the simplex method. The second refers to a real case in which the data were from four real catchments. It was used to further examine the performance of the linearized calibration method in model parameter calibration. The results show that the linearized calibration method is always able to find the unique global optima with a fast convergence rate and performs better than the SCE-UA method and the simplex method, which demonstrates that the linearized calibration method is an effective parameter optimization technique.