Modeling Tree Crown Dynamics with 3D Partial Differential Equations
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 locall...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2014-07-01
|
| Series: | Frontiers in Plant Science |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fpls.2014.00329/full |
| _version_ | 1811200180819591168 |
|---|---|
| author | Robert eBeyer Véronique eLetort Paul-Henry eCournède |
| author_facet | Robert eBeyer Véronique eLetort Paul-Henry eCournède |
| author_sort | Robert eBeyer |
| collection | DOAJ |
| description | 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 towards 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. |
| first_indexed | 2024-04-12T02:00:29Z |
| format | Article |
| id | doaj.art-97250e83cf65446eb220f0f10c0f9f46 |
| institution | Directory Open Access Journal |
| issn | 1664-462X |
| language | English |
| last_indexed | 2024-04-12T02:00:29Z |
| publishDate | 2014-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Plant Science |
| spelling | doaj.art-97250e83cf65446eb220f0f10c0f9f462022-12-22T03:52:41ZengFrontiers Media S.A.Frontiers in Plant Science1664-462X2014-07-01510.3389/fpls.2014.0032967205Modeling Tree Crown Dynamics with 3D Partial Differential EquationsRobert eBeyer0Véronique eLetort1Paul-Henry eCournède2Ecole Centrale ParisEcole Centrale ParisEcole Centrale ParisWe 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 towards 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.http://journal.frontiersin.org/Journal/10.3389/fpls.2014.00329/fullleaf area densityfunctional-structural plant modelcrown plasticitycompetition for lightBeer-Lambert's lawcontinuity equation |
| spellingShingle | Robert eBeyer Véronique eLetort Paul-Henry eCournède Modeling Tree Crown Dynamics with 3D Partial Differential Equations Frontiers in Plant Science leaf area density functional-structural plant model crown plasticity competition for light Beer-Lambert's law continuity equation |
| title | Modeling Tree Crown Dynamics with 3D Partial Differential Equations |
| title_full | Modeling Tree Crown Dynamics with 3D Partial Differential Equations |
| title_fullStr | Modeling Tree Crown Dynamics with 3D Partial Differential Equations |
| title_full_unstemmed | Modeling Tree Crown Dynamics with 3D Partial Differential Equations |
| title_short | Modeling Tree Crown Dynamics with 3D Partial Differential Equations |
| title_sort | modeling tree crown dynamics with 3d partial differential equations |
| topic | leaf area density functional-structural plant model crown plasticity competition for light Beer-Lambert's law continuity equation |
| url | http://journal.frontiersin.org/Journal/10.3389/fpls.2014.00329/full |
| work_keys_str_mv | AT robertebeyer modelingtreecrowndynamicswith3dpartialdifferentialequations AT veroniqueeletort modelingtreecrowndynamicswith3dpartialdifferentialequations AT paulhenryecournede modelingtreecrowndynamicswith3dpartialdifferentialequations |