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

• Published in: Ocean Science
• Main Authors: Sumata, Hiroshi, Kauker, Frank, Gerdes, Rüdiger, Koeberle, Cornelia, Karcher, Michael
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: COPERNICUS GESELLSCHAFT MBH 2013
• Subjects: Sea ice
• Online Access: https://epic.awi.de/id/eprint/33468/; https://epic.awi.de/id/eprint/33468/1/os-9-609-2013.pdf; http://www.ocean-sci.net/9/609/2013/; https://hdl.handle.net/10013/epic.41891; https://hdl.handle.net/10013/epic.41891.d001

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 (\unit{\mu}GA) as an example of a stochastic approach. The opt\imizations 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 \unit{\mu}GA 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 (\unit{\mu}GA) is of practical use for parameter optimization of a coupled ocean--sea ice model with a medium-sized horizontal resolution of 50\,km\,$\times$\,50\,km as used in this study.