Introducing Periodic Parameters in a Marine Ecosystem Model Using Discrete Linear Quadratic Control

Abstract

Abstract. This paper presents the application of the Discrete Linear Quadratic Control (DLQC) method for a parameter optimization problem in a marine ecosystem model. The ecosystem model simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column with temperature and turbulent diffusivity profiles taken from a three-dimensional ocean circulation model. We present the linearization method which is based on the available observations. The linearization is necessary to apply the DLQC method on the nonlinear system of state equations. We show the form of the linearized timevariant problems and the resulting two algebraic Riccati Equations. By using the DLQC method, we are able to introduce temporally varying periodic model parameters and to significantly improve -compared to the use of constant parameters -the fit of the model output to given observational data.

Theoretical Analysis and Optimization of Nonlinear ODE Systems for Marine Ecosystem Models

“…This data is frequently used within optimization approaches of marine ecosystem models, among others the one dimensional version of the NPZD model (see e.g. [9,6,12]). For this study, each profile is vertically averaged from the surface to the respective "mixed layer depth" which is fixed by a temperature decline of more than 0.5…”

“…Since parameter optimization with respect to D1 is subject of [12], we here focus on the optimization using data set D2.…”