Transpiration reduction functions are often used in hydrological modeling to estimate actual transpiration as a function of soil water status. Empirical reduction functions are most frequently used due to the higher data needs and computational requirements of mechanistic models. Empirical models, however, lack a description of physical mechanisms and their parameters require extensive calibration. We derive a process-based reduction function predicting system potentials, resistances, and water flows. An analytical solution for a special case of Brooks and Corey soils is presented. A numerical version of the reduction function for van Genuchten soils was implemented in the Soil–Water–Atmosphere–Plant (SWAP) hydrological model, allowing predictions for layered soil profiles and root length density variations over depth. The analytical and numerical versions of the model allow an increasingly quantitative insight into the mechanism of root water uptake, such as the existence of a maximum root water uptake rate as a function of soil water status, soil hydraulic properties, root length density, and root radius, in addition to the fact that sensitivity of simulated root water uptake to the radial root conductivity and axial conductance decrease when root length density increases. The approach can be used for the estimation of threshold values for empirical reduction functions.

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