A comparison between gradient descent and stochastic approaches for parameter optimization of a sea ice model

Abstract

Two types of optimization methods were applied to a parameter optimization problem in a coupled ocean–sea ice model of the Arctic, and applicability and efficiency of the respective methods were examined. One optimization utilizes a finite difference (FD) method based on a traditional gradient descent approach, while the other adopts a micro-genetic algorithm (μGA) as an example of a stochastic approach. The optimizations were performed by minimizing a cost function composed of model–data misfit of ice concentration, ice drift velocity and ice thickness. A series of optimizations were conducted that differ in the model formulation ("smoothed code" versus standard code) with respect to the FD method and in the population size and number of possibilities with respect to the μGA method. The FD method fails to estimate optimal parameters due to the ill-shaped nature of the cost function caused by the strong non-linearity of the system, whereas the genetic algorithms can effectively estimate near optimal parameters. The results of the study indicate that the sophisticated stochastic approach (μGA) is of practical use for parameter optimization of a coupled ocean–sea ice model with a medium-sized horizontal resolution of 50 km × 50 km as used in this study.