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

The withdrawal of water from soil by vegetation, which in steady state cond itions is equivalent to the transpiration rate, can be written in terms of R-ater potential in the form of an Ohm's law analogy, known as van den Hone rt's equation. The difference between an effective soil water potential and the bulk canopy water potential is divided by an effective soil-plant resi stance. This equation is commonly used, but little is known about the preci se definition of its parameters. The issue of this paper is to bridge the g ap between the bulk approach and a multi-layer description of soil-plant wa ter transfer by interpreting the bulk parameters in terms of the characteri stics of the multi-layer approach. Water flow through an elementary path wi thin the soil or the root is assumed to follow an Ohm's law analogy, and th e soil and root characterisies are allowed to vary with depth. Starting fro m the basic equations of the multi-layer approach, it is proved that the to tal rate of transpiration can also be expressed in the form of an Ohm's law analogy. This means that van den Honert's equation holds at canopy scale, insofar as the assumptions made on the physics of root water uptake hold. I n the bulk formulation derived, the effective soil-plane resistance appears as a combination of the elementary resistances making up the multi-layer m odel; and the effective soil water potential is a weighted mean of the wate r potentials in each soil layer, the weighting system involving the complet e set of elementary resistances. Simpler representations of soil-plant inte raction leading to Ohm's law type formulations are also examined: a simplif ied multi-layer model, in which xylem (root axial) resistance is neglected, and a bulk approach, in which soil-root interaction is represented by only one layer. Numerical simulations performed in different standard condition s show that these simpler representations do not provide accurate estimates of the transpiration rate, when compared to the values obtained by the com plete algorithm.