Modeling dynamic non-equilibrium water flow observations under various boundary conditions

- Dynamic non-equilibrium effects appear in experiments under various boundary conditions.
- We present a non-equilibrium model which macroscopically describes dynamic effects.
- Discussion of possible macroscopic explanations and on theoretical considerations.

SummaryExperimental evidence of variably-saturated flow in soils often shows a non-equilibrium between water content and water potential. Such phenomena, summarized by the term “dynamic effects” often occur in laboratory experiments specifically designed for the identification of soil hydraulic properties which are a mandatory input for water flow simulations at the field scale using the Richards equation. Depending on boundary conditions, dynamic non-equilibrium leads either to a relaxation of pressure head for constant water content or vice versa. Diamantopoulos et al. (2012) presented a model which describes dynamic effects in the case of multistep outflow experiments by assuming that the total water content is portioned into two fractions: one fraction which is in instantaneous equilibrium with the pressure head, and a second fraction for which the equilibration of the water content with the pressure is described by a first-order kinetics which leads to a temporal shift in water content at constant pressure head. In this work we applied this non-equilibrium model to four different observations of dynamic non-equilibrium effects presented in the literature and demonstrate that it successfully describes (1) non-equilibrium in water absorption experiments which results in a non-uniqueness of the diffusivity vs water content function, (2) the flow-rate dependence of soil hydraulic properties, (3) dynamic effects in multistep outflow and (4) dynamic effects in multistep flux experiments. We conclude the article by a discussion of possible macroscopic explanations, the consideration of dynamic effects for modeling water flow at the field scale, the uniqueness of the estimated non-equilibrium parameters among different experiments, and further theoretical considerations concerning dynamic effects.