System Response Parameter Calibration Method and its Application on Hydrological Model

The successful application of conceptual hydrological model depends on the choice of model parameters values. The automatic calibration of model parameters can make the model more widely used, which is also beneficial to the further research and development of the model. Most of the current parameter calibration method search the optimal parameter values from the power objective function surface. The most commonly used objective function is the sum of error square function. This kind of method consists of two steps, the construction of the objective function based on error sum of squares and the solution of first derivative of the objective function which is set to zero. It was found that these two steps can increase unrelated local optima for nonlinear models. And the paper also found that the information provided by the parameter function surface is more direct and effective than by the objective function surface. Furthermore, the nonlinear model function can be linearized by the system response relationship between the increment of the dependent variables and the increment of parameters. Based on these researches, this paper proposed one new parameter calibrated method-system response parameter calibration method (SRPCM) based on the parametric function surface. Furthermore, the convergence of the method was theoretically proved. The purpose of this paper is to investigate the usefulness of the SRPCM method in the context of calibrating hydrological models. Two types of analysis were performed. The first refers to an ideal model case free of 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 new proposed method is capable of finding that optimum without producing unrelated local optima. The paper constructed the ideal model of nonlinear Muskingum model. Testing results show that the SRPCM method can converge to the true parameter values in a fast and stable manner, and not affected by the choice of initial parameter values. The second refers to a real case, which was used to further examine the performance of the SRPCM method in model parameter calibration. The Results show that the proposed approach can solve the theoretical problem of unrelated local optima produced in the nonlinear model parameter calibration by using the objective function based on error sum of squares, and has good performance in parameter calibration.