Free energy of soil water – a superior perspective on storage dynamics and its sensitivity to soil hydraulic properties and topography

Soil moisture measurements are very popular. Yet they provide a very incomplete picture about the state of the partially saturated zone and the capillary binding of soil water. Here we propose that the free energy of the soil water stock offers a superior perspective on storage dynamics, as it combines soil water content, gravity potential and matric potential data. Based on this new state variable, we show that the partially saturated zone is characterized by a system-specific balance of storage and release corresponding to local state of minimum free energy. The latter depends on the soil water retention curve and topography/depth to groundwater. In the absence of an external rainfall or radiative forcing, the system will thus naturally relax back to and persist in this equilibrium. Hydrological systems are however not isolated, they are frequently forced out of their equilibrium either by rainfall or by radiation driven evaporation. Here we show that the corresponding storage dynamics manifests as deviations of the free energy from and relaxations back the local equilibrium and that the latter separates two different regimes, which are either associated with a storage excess and overshoot of potential energy or a storage deficit and overshoot of capillary binding energy. We demonstrate that these pseudo oscillations are distinctly different in different hydrological landscapes. As the free energy state of the soil water stock, the storage equilibrium and the ranges of both storage regimes depend jointly on depth to groundwater and the soil water retention curve, we combine both controls into a hydrological system characteristics we call the ‘energy state function’ of the soil. We show that the latter allows an insightful inter-comparison of storage dynamics with in different hydrological landscapes, and a priory estimate of depth to groundwater, based on available soil moisture and matric potential data. Finally, we demonstrate a threshold-like relation between the free energy of soil water in the riparian zone and streamflow generation, where the tipping points coincides with the transition from a storage deficit to a storage excess.