hal-00631509, version 1

Some Parameter Estimation Issues in Functional-Structural Plant Modelling

Paul-Henry Cournède () ^1, 2, Veronique Letort () ^1, 2, Amélie Mathieu () ³, Meng Zhen Kang () ⁴, Sébastien Lemaire () ⁵, Samis Trevezas ()^a^, 1, 2, François Houllier ⁶, Philippe De Reffye () ⁶

Mathematical Modelling of Natural Phenomena 6, 2 (2011) 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 serve 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.

a – Université de Technologie de Compiègne
1 : Mathématiques Appliquées aux Systèmes - EA 4037 (MAS)
Ecole Centrale Paris
2 : DIGIPLANTE (INRIA Saclay - Ile de France)
INRIA – Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR – Ecole Centrale Paris
3 : Environnement et Grandes Cultures (EGC)
Institut national de la recherche agronomique (INRA) : UMR1091 – AgroParisTech
4 : Eco-informatics (LIAMA)
Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] – CNRS – Institut national de la recherche agronomique (INRA) – INRIA – Chinese Academy of Science (CAS) – Institute of Automation, Chinese Academy of Sciences
5 : Institut Technique de la Betterave (ITB)
Confédération Générale des Planteurs de Betteraves
6 : BotAnique et BioinforMatique de l'Architecture des Plantes (AMAP)
Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR51 – CNRS : UMR5120 – Institut de recherche pour le développement [IRD] – Institut national de la recherche agronomique (INRA) : UR0931 – Université Montpellier II - Sciences et techniques

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Soumis le : Mercredi 12 Octobre 2011, 15:31:44
Dernière modification le : Jeudi 14 Février 2013, 10:32:57

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DOI : 10.1051/mmnp/20116205

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%% hal-00631509, version 1
%% http://hal-ecp.archives-ouvertes.fr/hal-00631509
@article{cournede:hal-00631509,
    hal_id = {hal-00631509},
    url = {http://hal-ecp.archives-ouvertes.fr/hal-00631509},
    title = {{Some Parameter Estimation Issues in Functional-Structural Plant Modelling}},
    author = {Courn{\`e}de, Paul-Henry and Letort, Veronique and Mathieu, Am{\'e}lie and Kang, Meng Zhen and Lemaire, S{\'e}bastien and Trevezas, Samis and Houllier, Fran{\c c}ois and De Reffye, Philippe},
    abstract = {{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 serve 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.}},
    keywords = {functional-structural plant models; carbon allocation; GreenLab; maximum likelihood estimator; Aitken Estimator; hidden models},
    language = {Anglais},
    affiliation = {Math{\'e}matiques Appliqu{\'e}es aux Syst{\`e}mes - EA 4037 - MAS , DIGIPLANTE - INRIA Saclay - Ile de France , Environnement et Grandes Cultures - EGC , Eco-informatics - LIAMA , Institut Technique de la Betterave - ITB , BotAnique et BioinforMatique de l'Architecture des Plantes - AMAP},
    pages = {133-159},
    journal = {Mathematical Modelling of Natural Phenomena},
    volume = {6},
    number = {2 },
    note = {ACL-11-20 ACL-11-20 },
    audience = {internationale },
    doi = {10.1051/mmnp/20116205 },
    year = {2011},
    pdf = {http://hal-ecp.archives-ouvertes.fr/hal-00631509/PDF/cournede\_etal\_MMNP\_6\_2\_pp133-159.pdf},
}

%F hal-00631509, version 1
%0 Journal Article
%U http://hal-ecp.archives-ouvertes.fr/hal-00631509
%2 MATH:MATH_ST;STAT:TH
%T Some Parameter Estimation Issues in Functional-Structural Plant Modelling
%A Cournède, Paul-Henry
%A Letort, Veronique
%A Mathieu, Amélie
%A Kang, Meng Zhen
%A Lemaire, Sébastien
%A Trevezas, Samis
%A Houllier, François
%A De Reffye, Philippe
%+ Mathématiques Appliquées aux Systèmes - EA 4037 - MAS , DIGIPLANTE - INRIA Saclay - Ile de France , Environnement et Grandes Cultures - EGC , Eco-informatics - LIAMA , Institut Technique de la Betterave - ITB , BotAnique et BioinforMatique de l'Architecture des Plantes - AMAP
%X 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 serve 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.
%G Anglais
%R 10.1051/mmnp/20116205
%J Mathematical Modelling of Natural Phenomena
%2 internationale
%8 2011-00-00
%V 6
%N 2
%P 133-159
%K functional-structural plant models; carbon allocation; GreenLab; maximum likelihood estimator; Aitken Estimator; hidden models
%Z ACL-11-20

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