Preprint A490/2006
Mathematical Modelling and Parameter Estimation of the Serra da Mesa Basin.

Jorge P. Zubelli | Mocenni, Chiara | Sparacino, Emiliano | Vicino, Antonio

**Keywords: **
Inverse Problems | biomathematics | ecological modelling | biophysical phenomena | environmental studies

This work concerns the development and calibration of several
classes of mathematical models describing ecological and
bio-geochemical aspects of aquatic systems. We focus our
experimental analysis on the Serra da Mesa lake in Brazil, from
which the biological information is extracted by real online
measurements provided by the SIMA monitoring program of the
Brazilian Institute for Space Research (INPE).
A preliminary analysis is carried out so as to define the input-output data to be accounted for by the models. Furthermore, several classes of mathematical models are considered for fitting real data of biological processes.
In order to do that, a two-step parameter identification/validation procedure is applied:
the first step uses the integrals of the differential equations to reduce the nonlinear
estimation problem to a linear least squares one.
The parameter vector resulting from the first step is used for initializing a nonlinear minimization procedure.
The results are discussed to assess the fitting performances of the physical and black-box models proposed in the paper. Several simulations are presented that could be used