Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

Abstract

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.