Characteristic rate scale and timescale of supply-limited transpiration under a Richards-Cowan framework

Abstract

A combined Richards-Cowan model of transpiration and soil moisture flux is used to analyze the relationship between stage-one (atmosphere limited) and stage-two (stressed) transpiration during a series of simulated dry downs. The duration of stage-one transpiration is found to be controlled by the storage capacity of the root zone, the potential transpiration rate, and the soil desorptivity and drainage properties, which in turn influence the net of upward and downward moisture fluxes through the bottom of the root zone. During stage-two transpiration the root zone lower boundary behaves like a dry surface, and the transpiration rate is supply-limited by the upward flux to this boundary. These findings are combined with a similarity solution for the upward flux rate (including the influence of gravity) in order to derive an analytic approximation for the time to onset of stage-two transpiration. This estimated time to stress t(s), along with a rate scale defined by the time average flux in the root zone prior to stress, can be used to nondimensionalize the relation between stage-two transpiration and time in similar fashion to the bare soil evaporation analysis of Salvucci [1997]. The resulting expressions allow prediction, under simplified event-based initial and boundary conditions, of the second stage of transpiration from soil desorptivity and drainage properties.