| 13 Apr 2026
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.
This is a well-written paper (albeit using ChatGPT) that addresses important deficiencies of the Richards’ equation, which is widely used for soil water simulations at scales from global to local. The paper is well referenced and written with clarity. It does a good job in explaining some of the issues and highlighting the fact that discrepancies in behaviour arise in slow as well as fast flow processes.
However, the paper does not consider several other common complications in the use of the Richards’ equation. One is the effects of phase change, e.g. freeze-thaw processes; a second is the effect of geochemical interactions between the solid soil and the liquid solutes. A third is the case of fracture flow with solid phase interactions. These effects are often neglected in Richards’ equation applications.
In my opinion, the paper makes a useful contribution to the discussion of soil water flow processes and their modelling, but I suggest the authors clarify the scope of the comparison and spend a little space to note the issues that have not been considered, and which also need to be addressed.
Points of detail:
Line 190 mentions increasing or decreasing pressure head, but line 198 only mentions water leaving the soil column. Clarification is needed. Maybe edit line 192, replacing change by decrease.
The figures are so small that it is very difficult to distinguish the symbols. In fig 2b I can’t see a green line, which is referred to in the caption or the symbols, and what is the dotted blue line? Fig 5 green dashed line is undefined. Fig 6c is confusing. Why is the equilibrium retention line shown in red, which denotes the non-equilibrium model?
l353 apparent reference error