A thermodynamic formulation of root water uptake

By extracting bound water from the soil and lifting it to the canopy, root systems of vegetation perform work. Here we describe how the energetics involved in root water uptake can be quantified. The illustration is done using a simple, four-box model of the soil-root system to represent heterogeneity and a parameterization in which root water uptake is driven by the xylem potential of the plant with a fixed flux boundary condition. We use this approach to evaluate the effects of soil moisture heterogeneity and root system properties on the dissipative losses and export of energy involved in root water uptake. For this, we derive an expression that relates the energy export at the root collar to a sum of terms that reflect all fluxes and storage changes along the flow path in thermodynamic terms. We conclude that such a thermodynamic evaluation of root water uptake conveniently provides insights into the impediments of different processes along the entire flow path and explicitly accounting not only for the resistances along the flow path and those imposed by soil drying but especially the role of heterogenous soil water distribution. The results show that least energy needs to be exported and dissipative losses are minimized by a root system if it extracts water uniformly from the soil. This has implications for plant water relations in forests where canopies generate heterogenous input patterns. Our diagnostic in the energy domain should be useful in future model applications for quantifying how plants can evolve towards greater efficiency in their structure and function, particularly in heterogenous soil environments. Generally, this approach may help to better describe heterogeneous processes in the soil in a simple, yet physically-based way