Formulation of root water uptake in a multi-layer soil-plant model: does van den Honert's equation hold?

摘要

The withdrawal of water from soil by vegetation, which insteady state conditions is equivalent to the transpiration rate, can be written in termsof water potential in the form of an Ohm's law analogy, known as van den Honert'sequation: The difference between an effective soil water potential and the bulk canopywater potential is divided by an effective soil-plant resistance. This equation iscommonly used, but little is known about the precise definition of its parameters. Theissue of this paper is to bridge the gap between the bulk approach and a multi-layerdescription of soil-plant water transfer by interpreting the bulk parameters in terms ofthe characteristics of the multi-layer approach. Water flow through an elementary pathwithin the soil or the root is assumed to follow an Ohm's law analogy, and the soil androot characterisics are allowed to vary with depth. Starting from the basic equations ofthe multi-layer approach, it is proved that the total rate of transpiration can also beexpressed in the form of an Ohm's law analogy. This means that van den Honert's equationholds at canopy scale, insofar as the assumptions made on the physics of root water uptakehold. In the bulk formulation derived, the effective soil-plant resistance appears as acombination of the elementary resistances making up the multi-layer model; and theeffective soil water potential is a weighted mean of the water potentials in each soillayer, the weighting system involving the complete set of elementary resistances. Simplerrepresentations of soil-plant interaction leading to Ohm's law type formulations are alsoexamined: a simplified multi-layer model, in which xylem (root axial) resistance isneglected, and a bulk approach, in which soil-root interaction is represented by only onelayer. Numerical simulations performed in different standard conditions show that thesesimpler representations do not provide accurate estimates of the transpiration rate, whencompared to the values obtained by the complete algorithm.