Reducing fisheries model complexity using a finite Fourier series reparameterization

Quantifying fish stocks through modeling involves estimating time-varying parameters such as growth, stock recruitment, mortality rates and fishing levels. Each of these parameters vary non-uniformly and non-smoothly with time. For a given parameter, e.g., growth, the standard approach has been to estimate a single value of the parameter per time-step. When the modeling spans several time-steps this compounds the complexity of the model by increasing the dimension of the parameter space.This paper presents a method for reducing model complexity by effective reparameterization of selected time-varying parameters. The method involves representing the parameters by truncated (i.e., a finite) Fourier series, where the dimension of the Fourier coefficients is very much less than the number of time-steps in the modeling.Example results are presented, which show that the reparameterization can lead to over 40% decrease in the number of model parameters associated with fishing levels, growth and stock recruitment. We illustrate using time-varying parameters associated with fishing levels, growth and stock recruitment, derived from an optimized biological model. The input data for the biological model is based on landed catch-data of Northeast Arctic cod (Gadus morhua).