Biogeochemical model of Lake Zürich: sensitivity, identifiability and uncertainty analysis

A model for the description of nutrient, oxygen and plankton dynamics in Lake Zürich, Switzerland has recently been developed. Because, with this model, an attempt is made to describe mechanistically the most important mass fluxes and conversion processes in the water column and sediment of the lake, it is already too complicated to allow all of its parameters to be identifiable from the monthly measured profiles. This raises the questions of how to select a subset of model parameters to be included in a formal parameter estimation process and how to estimate model prediction uncertainty. In this paper, a systematic approach to tackle this problem is applied to this model. The technique consists of the combination of an analysis of the sensitivity of model results to single parameters with an analysis of the approximate linear dependence of sensitivity functions of parameter subsets. It is demonstrated that the most severe parameter identifiability problems are caused by the parameterization of light dependence of algae growth, by competing effects of production, respiration and death of algae and zooplankton, and by the interactions between algae and zooplankton. The dynamics of dissolved variables is much easier to describe. The results of the analysis are used to select a parameter subset for a fit with measured data, to analyse the effect of other, fixed parameters on the estimates of the selected parameters, and to estimate the uncertainty of model predictions.