A model for the interaction of phytoplankton aggregates and the environment: approximation and parameter estimation

Abstract

We present a model for the dynamics of phytoplankton aggregates and their interaction with the environment in a well-mixed reactor or surface layer of a water column. The biophysical problem yields a nonlinear partial differential equation coupled with a general system of ordinary differential equations. We first develop a finite difference scheme for approximating the solution of this model. Then convergence results are established for the finite difference method and existence-uniqueness of solutions are obtained. A least-squares parameter estimation method is presented to illustrate the performance of the model against a real dataset, and to highlight the effects of aggregate growth on algal bloom dynamics and nutrient consumption rates. The model is well-suited to complement microcosm studies and can accommodate the effects of a wide range of environmental conditions.