Calibration of the soil moisture accounting model using a gradient-type algorithm and analytic derivatives

Abstract

In the pest, derivative-based optimization algorithms have not frequently been used to calibrate conceptual rainfall-runoff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently-developed technique of analytically computing derivatives of a CRR model to a complex, widely-used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative-based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton-Raphson) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the Newton-Raphson algorithm was thought to be due to discontinuities and a rough texture of the response surface.