Modeling tree crown dynamics with 3D partial differential equations

Robert Beyer 1, 2, * Véronique Letort 3 Paul-Henry Cournède 4
* Corresponding author
2 DIGIPLANTE - Modélisation de la croissance et de l'architecture des plantes
MAS - Mathématiques Appliquées aux Systèmes - EA 4037, Inria Saclay - Ile de France, Ecole Centrale Paris, CIRAD - Centre de Coopération Internationale en Recherche Agronomique pour le Développement
Abstract : We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.
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Robert Beyer, Véronique Letort, Paul-Henry Cournède. Modeling tree crown dynamics with 3D partial differential equations. Frontiers in Plant Science, Frontiers, 2014, 5, pp.329. ⟨10.3389/fpls.2014.00329⟩. ⟨hal-01272213⟩

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