Identification of phosphorus dynamics in Kootenay lake, Canada

This paper regards the use of system theory techniques in the development of models describing the phosphorus kinetics in fresh waters with the objective to understand the observed kinetics better in order to obtain indications on the design of future field experiments. Identification techniques have been applied to the data regarding 49 experiments on phosphorus cycling in Kootenay Lake, British Columbia, Canada, in order to determine the minimal number of compartments required to model the phosphorus dynamical behaviour. Canonical state-space models have then been identified both from raw and smoothed data. The parameters in these models do not have a direct physical meaning; they can, however, be identified from the measured data and the obtained models describe with good accuracy the considered kinetics. The identification of physical models has also been performed; in this case, however, only two compartments have been considered according to the results of the identifiability analysis of the complete model parameters. Results give further insight on the phosphorus processes and show that the complete phosphorus cycle through the four compartments described by Lean can be identified only when phosphorus cycles rapidly through the system.