On the validity of Richards' equation under dynamic flow conditions

Abstract. Richards' equation is currently applied to simulate water flow in soils over a wide range of spatial scales, from the centimeter to the kilometer scale. A key assumption of Richards' equation is that water content and matric potential are at an equilibrium which is described by the water retention curve. However, numerous observations have called this assumption into question, particularly under conditions of fast water flow. In this mini-review, we present six experiments in which the equilibrium assumption is violated and which therefore cannot be adequately described by Richards' equation: multistep outflow/inflow, continuous outflow/inflow, multistep flux, capillary rise, evaporation and, transpiration. These experiments span a wide range of experimental conditions, from fast to very slow water flow and apply both pressure head and flux boundary conditions. Although it is in most cases unknown which exact physical processes are responsible for these effects, a simple flow model, which extends the Richards equation by a partial decoupling of pressure head and water content under dynamic flow conditions, can describe the observed relaxation of water content or pressure head well. Notably, this represents the first demonstration of a non-equilibrium model for all six types of non-equilibrium observations. We discuss implications, theoretical limitations, and future perspectives on researching dynamic nonequilibrium in variably-saturated flow in soils, as well as potential improvements of modeling concepts necessary to describe non-equilibrium during variably-saturated flow at different scales and under different boundary conditions.