Comparison of Newton-type and SCE optimisation algorithms for the calibration of conceptual hydrological models

Abstract

Hydrological model calibration has benefited from improved optimisation algorithms and advances in computing power over the last few decades. Stochastic optimisation methods have received particular attention, the SCE search has emerged as one of the best performing global optimisation algorithms for a single objective function. However, the improved robustness of stochastic optimisation usually comes at a considerable computational cost as the number of calibrated parameters increases. This work revisits the use of modern gradient-based algorithms. We investigate the performance of quasi-Newton and Gauss–Newton algorithms using SIMHYD and FUSE-536 calibrated to three Australian catchments. Analysis of the objective function surfaces detects micro-scale roughness and parameter insensitivity in both SIMHYD and FUSE-536. The SCE search provides the most robust performance for calibrating SIMHYD, but, somewhat surprisingly, struggles in the case of FUSE-536. In terms of computational costs, the Newton-type algorithms require about 20 times fewer objective function evaluations than the SCE search for SIMHYD and 50 times fewer evaluations for FUSE-536. Considering the chance of converging to the global optimum and the computational cost, we suggest that modern Newton-type algorithms may be competitive with, or even outperform, the SCE search. Improvements in the robustness of Newton-type algorithms should further increase their competitiveness.

Keywords:

• Model calibration
• parameter optimisation
• Newton-type algorithms
• SCE search