Parameter Estimation In A Structured Algal Coagulation-Fragmentation Model

Coagulation of phytoplankton is a fundamental mechanism for vertical flux of carbon in the ocean. This process is dependent on parameters that are not available from experimental data, such as the encounter rate of particles, the contact efficiency of unlike particles and the probability of sticking upon contact. Fragmentation, the breakup of large particles into two smaller ones has been observed in the ocean, but very little modeling effort for incorporating this process in the dynamics of phytoplankton has been attempted. In this paper we incorporate fragmentation process into a nonlinear hyperbolic equation that describes the evolution of a size structured algal population with the aggregation model. We examine through numerical simulation the effect of fragmentation on the dynamics of phytoplankton. We present convergence theory for estimating parameters in this model using nonlinear least squares fit. The least square method is then tested numerically in ideal cases where the dat..