A model for the interaction of phytoplankton aggregates and the environment: approximation and parameter estimation. Issue 2 (1st February 2018)

• Record Type: Journal Article
• Authors: Ackleh, Azmy S.; Miller, Robert L.
• Is Part Of: Inverse problems in science and engineering. Volume 26:Issue 2(2018)
• Page Start: 152
• Page End: 182
• Publication Date: 2018-02-01
• Subjects: Phytoplankton -- aggregation -- environment -- finite difference approximation -- parameter estimation; 35Q92 -- 65M06; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2017.1310856
• Languages: English
• ISSNs: 1741-5977

Abstract

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.