Modeling Tree Water Flow as an Unsaturated Flow through a Porous Medium

Aumann, Craig; Ford, E. David

doi:10.1006/jtbi.2002.3061

Cited by 34 publications

(21 citation statements)

References 47 publications

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“…Instead, we will attempt to take account of the complex structure of the entire water transport medium by modelling it as a porous medium; the distinction is discussed further in Vilagrosa et al [18]. Porous-medium-type flow models in plants are discussed in recent studies [19,20], where the need for numerical simulations in twoand three-dimensions as well as hydraulic functions dependent on water saturation are highlighted. The hydraulic system of trees is also studied in Frü h & Kurth [21], where porous medium flow is combined with a water storage model, with architectural parameters of trees used as inputs to the model.…”

Section: Introductionmentioning

confidence: 99%

Impact of plant shoot architecture on leaf cooling: a coupled heat and mass transfer model

Bridge

Franklin

Homer

2013

J. R. Soc. Interface.

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Plants display a range of striking architectural adaptations when grown at elevated temperatures. In the model plant Arabidopsis thaliana, these include elongation of petioles, and increased petiole and leaf angles from the soil surface. The potential physiological significance of these architectural changes remains speculative. We address this issue computationally by formulating a mathematical model and performing numerical simulations, testing the hypothesis that elongated and elevated plant configurations may reflect a leaf-cooling strategy. This sets in place a new basic model of plant water use and interaction with the surrounding air, which couples heat and mass transfer within a plant to water vapour diffusion in the air, using a transpiration term that depends on saturation, temperature and vapour concentration. A two-dimensional, multi-petiole shoot geometry is considered, with added leaf-blade shape detail. Our simulations show that increased petiole length and angle generally result in enhanced transpiration rates and reduced leaf temperatures in well-watered conditions. Furthermore, our computations also reveal plant configurations for which elongation may result in decreased transpiration rate owing to decreased leaf liquid saturation. We offer further qualitative and quantitative insights into the role of architectural parameters as key determinants of leaf-cooling capacity.

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Section: Introductionmentioning

confidence: 99%

Impact of plant shoot architecture on leaf cooling: a coupled heat and mass transfer model

Bridge

Franklin

Homer

2013

J. R. Soc. Interface.

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“…The model extends previous approaches that were developed to describe hydro-dynamics in above-ground plants (Früh and Kurth 1999;Aumann and Ford 2002;Bohrer et al 2005) by additionally including the hydraulic root system architecture in combination with a soil water flow model. In this way a complete water flow model for the whole soil-plant system is obtained, which then vice versa extends existing root water uptake modelling approaches (Doussan et al 1998;Javaux et al 2008) by including the above-ground water dynamics of the plant.…”

Section: Discussionmentioning

confidence: 92%

“…Only recently, this approach was further improved by substituting the electrical circuit analogy by a porous media description for sap flow in wood that is based on Darcy's law and includes a water capacity term to better account for the dynamic behaviour of the hydraulic storage in trees in a way that mass conservation is considered, e.g. by Bohrer et al (2005), see also Arbogast et al (1993), Früh and Kurth (1999), Kumagai (2001) and Aumann and Ford (2002). This avoids calculations of negative water contents and unlimited water withdrawal from the tree as occurring with applications of the electrical circuit model (Chuang et al 2006).…”

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confidence: 99%

A one-dimensional model of water flow in soil-plant systems based on plant architecture

et al. 2010

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The estimation of root water uptake and water flow in plants is crucial to quantify transpiration and hence the water exchange between land surface and atmosphere. In particular the soil water extraction by plant roots which provides the water supply of plants is a highly dynamic and non-linear process interacting with soil transport processes that are mainly determined by the natural soil variability at different scales. To better consider this root-soil interaction we extended and further developed a finite element tree hydrodynamics model based on the one-dimensional (1D) porous media equation. This is achieved by including in addition to the explicit three- dimensional (3D) architectural representation of the tree crown a corresponding 3D characterisation of the root system. This 1D xylem water flow model was then coupled to a soil water flow model derived also from the 1D porous media equation. We apply the new model to conduct sensitivity analysis of root water uptake and transpiration dynamics and compare the results to simulation results obtained by using a 3D model of soil water flow and root water uptake. Based on data from lysimeter experiments with young European beech trees (Fagus silvatica L.) is shown, that the model is able to correctly describe transpiration and soil water flow. In conclusion, compared to a fully 3D model the 1D porous media approach provides a computationally efficient alternative, able to reproduce the main mechanisms of plant hydro-dynamics including root water uptake from soil.

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“…Another approach in modelling the xylem transport in plant tissues is based on the fluid percolation in a non-uniform anisotropic porous medium, which is propelled by the gradient of water potential. The governing equation is [2]:…”

Section: Biophysical Theories Of Water Motion and Exchange In Plantsmentioning

confidence: 99%

“…When Q = Φ, (22)- (23) gives the following values which differ from Θ P by a constant (for Θ (1) and Θ (2) ), by a geometry-independent term (for Θ (3) ), or by a term that in the case of the sap flow in the leaf veins (| l |≤ 0.5) gives…”

Section: Model Of An Optimal Pipeline With Permeable Wallsmentioning

confidence: 99%

Long-distance liquid transport in plants

Kizilova¹

2008

Proc. Estonian Acad. Sci.

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Abstract. A brief review of the thermodynamic and fluid dynamic problems related to long-distance liquid flow and signalling in plants is presented. Geometrical parameters of the plant leaf venation are measured and the general relationships between the diameters and lengths of the veins, branching angles at the vein bifurcations, and the corresponding drainage areas are obtained. The same relationships had been obtained before for the bifurcations of the pathways in the arterial and bronchial systems of mammals and humans; tree trunks, branches and roots; and river basins. The identity of the principle of design of the transportation systems in the nature can be understood on the concept of optimal networks that provide liquid delivery at total minimal energy costs. The corresponding models of the optimal vessels and branching systems of vessels with impermeable and permeable walls are presented and discussed.

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Modeling Tree Water Flow as an Unsaturated Flow through a Porous Medium

Cited by 34 publications

References 47 publications

Impact of plant shoot architecture on leaf cooling: a coupled heat and mass transfer model

Impact of plant shoot architecture on leaf cooling: a coupled heat and mass transfer model

A one-dimensional model of water flow in soil-plant systems based on plant architecture

Long-distance liquid transport in plants

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