Abstract
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.
Highlights
Sea ice plays an important role in shaping the climate system in the Arctic Ocean by altering heat, momentum and material exchanges between the atmosphere and ocean (e.g., Wadhams, 2000; McPhee, 2008; Thomas and Dieckmann, 2009)
In order to provide a suitable optimization method, we introduce a cost function composed of model–data misfit of ice concentration, ice drift velocity and ice thickness
The paper is organized as follows: in Sect. 2 we describe the experiment design, which is composed of a brief introduction of the coupled ocean–sea ice model, sea ice data used in this study, definition of the cost function, a description of two types of optimization methods and a description of optimization experiments
Summary
Sea ice plays an important role in shaping the climate system in the Arctic Ocean by altering heat, momentum and material exchanges between the atmosphere and ocean (e.g., Wadhams, 2000; McPhee, 2008; Thomas and Dieckmann, 2009). Other than sea ice models, such methods for model’s parameter optimizations can be found in numerous atmospheric and oceanic studies (e.g., Garcia-Gorriz et al, 2003; Menemenlis et al, 2005; Mochizuki et al, 2007; Bocquet, 2012) These approaches provided effective methods to perform a multivariate parameter optimization, problems could arise if the model exhibits a nonlinear response to control parameters, resulting in a complicated shape of the cost function (Evensen and Fario, 1997; Mazzega, 2000). One has to perform multiple individual optimizations starting from a variety of initial parameter guesses to find the global minimum Another problem may arise from a micro-scale structure of the cost function, because gradient descent approaches can only be reasonably applied if the cost is a smooth function of control parameters.
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