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Mathematical modelling and parameter estimation of the Serra da Mesa basin. (English) Zbl 1134.92040

Summary: 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 for developing scenario analysis and managing the real system.

MSC:

92D40 Ecology
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[1] G.M. Masters, Introduction to Environmental Engineering and Science, Prentice-Hall; G.M. Masters, Introduction to Environmental Engineering and Science, Prentice-Hall
[2] Ljung, L., System Identification. Theory for the User (1999), Prentice-Hall PTR
[3] Scheffer, M., Ecology of Shallow Lakes (1998), Chapman and Hall
[4] Murray, J. D., Mathematical Biology (1993), Springer-Verlag · Zbl 0779.92001
[5] Gurney, W. S.C.; Nisbet, R. M., Ecological Dynamics (1998), Oxford University Press · Zbl 0417.92024
[6] R.J. Romanowicz, U. Callies, P.C. Young, Water quality modelling in rivers with limited observational data: River Elbe case study, in: Proceeding of the Int. Conf.: Complexity and Integrated Resource Management, Germany, 14-17 June 2004; R.J. Romanowicz, U. Callies, P.C. Young, Water quality modelling in rivers with limited observational data: River Elbe case study, in: Proceeding of the Int. Conf.: Complexity and Integrated Resource Management, Germany, 14-17 June 2004
[7] Hann, C. E.; Chase, J. G.; Lin, J.; Lotz, T.; Doran, C. V.; Shaw, G. M., Integral-based parameter identification for long-term dynamic verification of a glucose-insulin system model, (Computer Methods and Programs in Biomedicine, vol. 77 (2005)), 259-270
[8] C.E. Hann, J.G. Chase, J. Lin, T. Lotz, K.A. McAuley, J. Wong, S. Andreassen, Integral-based identification of a physiological insulin and glucose model on euglycaemic clamp and IVGTT trials, in: Proceeding of 14th IFAC Symposium on System Identification, Newcastle, Australia, 2006; C.E. Hann, J.G. Chase, J. Lin, T. Lotz, K.A. McAuley, J. Wong, S. Andreassen, Integral-based identification of a physiological insulin and glucose model on euglycaemic clamp and IVGTT trials, in: Proceeding of 14th IFAC Symposium on System Identification, Newcastle, Australia, 2006
[9] Garulli, A.; Mocenni, C.; Vicino, A., Integrating identification and qualitative analysis for the dynamic model of a lagoon, International Journal of Bifurcation and Chaos, 13, 2, 357-374 (2003) · Zbl 1058.92044
[10] Chapelle, A., A preliminary model of nutrient cycling in sediments of a Mediterranean lagoon, Ecological Modelling, 80, 131-147 (1995)
[11] Chapelle, A.; Mè nesguen, A.; Deslous-Paoli, J. M.; Souchu, P.; Mazouni, N.; Vaquer, A.; Millet, B., Modelling nitrogen, primary production and oxygen in a Mediterranean lagoon. Impact of oysters farming and inputs from the watershed, Ecological Modelling, 127, 161-181 (2000)
[12] Norberg, J.; DeAngelis, D., Temperature effects on stocks and stability of a phytoplankton-zooplankton model and the dependence on light and nutrients, Ecological Modelling, 95, 75-86 (1997)
[13] Zaldivar, J. M.; Cattaneo, E.; Plus, M.; Murray, C. N.; Giordani, G.; Viaroli, P., Long-term simulation of main bio-geochemical events in a coastal lagoon: Sacca Di Goro (Northern Adriatic Coast, Italy), Continental Shelf Research, 23, 1847-1875 (2003)
[14] C. Mocenni, A. Vicino, Modeling the ecological competition between seaweed and seagrass in an aquatic environment: A case study, in: Proceedings of the IFAC SYSID 2006, Newcastle, 29-31 March, 2006; C. Mocenni, A. Vicino, Modeling the ecological competition between seaweed and seagrass in an aquatic environment: A case study, in: Proceedings of the IFAC SYSID 2006, Newcastle, 29-31 March, 2006
[15] C. Mocenni, E. Sparacino, A. Vicino, J. Zubelli, Modelling and parameter identification of an aquatic ecosystem: The Serra da Mesa example, in: Workshop on Mathematical Methods and Modeling of Biophysical Phenomena, Angra dos Reis, Rio de Janeiro, 5-11 March, 2006; C. Mocenni, E. Sparacino, A. Vicino, J. Zubelli, Modelling and parameter identification of an aquatic ecosystem: The Serra da Mesa example, in: Workshop on Mathematical Methods and Modeling of Biophysical Phenomena, Angra dos Reis, Rio de Janeiro, 5-11 March, 2006
[16] Marinov, D.; Zaldivar, J. M.; Norro, A.; Giordani, G.; Viaroli, P., Integrated Modelling in Coastal Lagoons Part B: Lagoon Model Sacca Di Goro Case Study (Italian Adriatic Sea Shoreline) (2005), European Communities
[17] Reynolds, C. S.; Descy, J. P.; Padisàk, J., Are phytoplankton dynamics in rivers so different from those in shallow lakes?, Hydrobiologia, 289, 1-7 (1994)
[18] Smith, E. L., Photosynthesis in relation to light and carbon dioxide, Proceedings of the Natural Academy of Sciences, 22, 504-510 (1936)
[19] Eilers, P. H.C.; Peeters, J. C.H., A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton, Ecological Modelling, 42, 199-215 (1988)
[20] Eppley, R. W.; Rogers, J. B.; MC Carthy, J. J.; Sournia, A., Light/dark periodicity in nitrogen assimilation of the marine phytoplankters Skeletonema costatum and Coccolithus huxley, (N-Limitant Chemostat Culture (1971)), 150-154
[21] Zaldivar, J. M.; Somma, F.; Bouraoui, F.; Austoni, M.; Giordani, G.; Viaroli, P.; Plus, M., Preliminary Study of Spatio-Temporal Data Analysis Tools for the Management of Coastal Lagoons (2004), European Communities
[22] Marinov, D.; Zaldìvar, J. M.; Galbiati, L.; Bouraoui, F.; Sena, F.; Elorza, F. J.; Norro, A.; Giordani, G.; Viaroli, P., Integrated Modelling in Coastal Lagoons Part C: Coupling Watershed-Lagoon Models Sacca Di Goro Case Study (2005), European Communities
[23] Huisman, J.; Weissing, F. J., Light-limited growth and competition for light in well-mixed aquatic environments: An elementary model, Ecology, 75, 507520 (1994)
[24] Van Duin, E. H.S.; Lijklema, L., Modelling photosynthesis and oxygen in a shallow, hypertrophic lake, Ecological Modelling, 45, 4, 243-260 (1989)
[25] Hull, V.; Mocenni, C.; Falcucci, M.; Marchettini, N., A trophodynamic model for the lagoon of Fogliano (Italy) with ecological modifying parameters, Ecological Modelling, 134, 153-167 (2000)
[26] CT Brasil Ministério da Ciência e Tecnologia, Rede Temática de Pesquisa em Modelagem Ambiental da Amazônia (GEOMA). www.geoma.lncc.br; CT Brasil Ministério da Ciência e Tecnologia, Rede Temática de Pesquisa em Modelagem Ambiental da Amazônia (GEOMA). www.geoma.lncc.br
[27] E. Sparacino, Modellistica, identificazione ed analisi dei dati di monitoraggio ambientale per zone umide della regione Amazzonica, Master Thesis in Information Engineering, Università di Siena, 2004-2005; E. Sparacino, Modellistica, identificazione ed analisi dei dati di monitoraggio ambientale per zone umide della regione Amazzonica, Master Thesis in Information Engineering, Università di Siena, 2004-2005
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