ABSTRACT

Biogeochemical processes in sewage plants and lakes are modeled as systems of ordinary or partial differential equations. Both the number of variables and the number of parameters is large (10 -- 50). Because not all variables can be measured, it is not possible to estimate all parameters, but for most parameters there is a reasonable default value. There is thus the problem of selecting some parameters for estimation while keeping the others fixed. This is complicated by the long computing times for the model. We discuss a strategy for solving this problem, based on simple diagnostic coefficients. The fit obtained in this way is sufficient from an engineering point of view, but the residuals show clear systematic deviations. A possible explanation is that some parameters may be time varying. In the second part of the talk, I will therefore discuss models for time varying parameters. In order to estimate these, we use Markov chain Monte Carlo and particle filter methods.