Root density, soil hydraulic functions, and hydraulic head gradients play an important role in the determination of transpiration-rate-limiting soil water contents. We developed an implicit numerical root water extraction model to solve the Richards equation for the modeling of radial root water extraction. The average soil water content at the moment root water potential dropped below a defined critical value was then estimated. The dependence of average water content at the onset of plant water stress on potential transpiration and root density was compared with an analytical solution for hydraulic conditions in the root sphere. The critical value was a function of potential transpiration rate, soil hydraulic properties, and root density. Matric flux potential appears to be a convenient hydraulic property to determine the onset of limiting hydraulic conditions, as numerical simulations showed that, at onset, matric flux potential vs. distance from the root surface is independent of soil type. This was also determined analytically under the constant-rate assumption. Mean water content occurs at about 0.53 times the half-distance between roots. This allows calculation of the mean limiting soil water content and pressure head from the matric flux potential at this distance, which is a function of transpiration rate and root density only. A nomogram was developed that—given the transpiration rate, the root density, and the soil hydraulic functions—allows determination of the values of mean water content and mean pressure head that occur at the onset of transpiration reduction.

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