Averaged water potentials in soil water and groundwater, and their connection to menisci in soil pores, field-scale flow phenomena, and simple groundwater flows

Abstract. The movement of subsurface water is mostly studied at the pore scale and the Darcian scale, but the field and regional scales are of much larger societal interest. Volume-averaging has provided equations at these larger scales, but the required restrictions rendered them of little practical interest. Others hypothesized a direct connection at hydrostatic equilibrium between the average matric potential of a subsurface body of water and the average pressure drop over the menisci in the soil pores. The link between the volume-averaged potential energy of subsurface water bodies and large-scale fluxes remains largely unexplored. This paper treats the effect of menisci on the potential energy of the water behind them in some detail, and discusses some field-scale effects of pore-scale processes. Then, various published expressions for volume-averaged subsurface water potentials are compared. The intrinsic phase average is deemed the best choice. The hypothesized relationship between average matric potential and average meniscus curvature is found to be valid for unit gradient flow instead of hydrostatic equilibrium. Still, this restriction makes the relationship hold only for a specific depth range in the unsaturated zone under specific conditions, and certainly not for entire fields or catchments. In the groundwater, volume-averaged potential energy is of more use: for linearized, steady flows with flow lines that are parallel, radially diverging, and radially converging, proofs are derived for proportionality between averaged hydraulic potentials and fluxes towards open water at a fixed potential. For parallel flow, a simplified but relevant transient flow case also exhibits this proportionality.