Some Parameter Estimation Issues in Functional-Structural Plant Modelling

P.-H. Cournède^1, 2 ; V. Letort^1, 2 ; A. Mathieu³ ; M. Z. Kang⁴ ; S. Lemaire⁵ ; S. Trevezas² ; F. Houllier⁶ ; P. de Reffye^7, 2

¹ Ecole Centrale Paris, MAS, Châtenay-Malabry, France
² INRIA Saclay - Île-de-France, EPI Digiplante, Orsay, France
³ AgroParisTech, UMR EGC, Grignon, France
⁴ CASIA, LIAMA, Beijing, China
⁵ ITB, Paris, France
⁶ INRA, UMR AMAP, Montpellier, France
⁷ CIRAD, UMR AMAP, Montpellier, France

Mathematical modelling of natural phenomena, Tome 6 (2011) no. 2, pp. 133-159.

Résumé

The development of functional-structural plant models has opened interesting perspectives for a better understanding of plant growth as well as for potential applications in breeding or decision aid in farm management. Parameterization of such models is however a difficult issue due to the complexity of the involved biological processes and the interactions between these processes. The estimation of parameters from experimental data by inverse methods is thus a crucial step. This paper presents some results and discussions as first steps towards the construction of a general framework for the parametric estimation of functional-structural plant models. A general family of models of Carbon allocation formalized as dynamic systems serves as the basis for our study. An adaptation of the 2-stage Aitken estimator to this family of model is introduced as well as its numerical implementation, and applied in two different situations: first a morphogenetic model of sugar beet growth with simple plant structure, multi-stage and detailed observations, and second a tree growth model characterized by sparse observations and strong interactions between functioning and organogenesis. The proposed estimation method appears robust, easy to adapt to a wide variety of models, and generally provides a satisfactory goodness-of-fit. However, it does not allow a proper evaluation of estimation uncertainty. Finally some perspectives opened by the theory of hidden models are discussed.

Détail

DOI : 10.1051/mmnp/20116205

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