Seepage-evaporation controlled depletion of initially water-filled reservoirs on Earth and Mars: Analytic versus HYDRUS modeling

Analytical solutions are obtained for water extinction from an axisymmetric crater, filled at t < 0 and depleted by evaporation and transient infiltration into a Gardner or capillarity-free homogeneous soil during the time interval 0 ≤ t ≤ Te. The extinction time Te is found for crater beds, the shapes of which are shallow cones, spherical, spheroidal, and paraboloidal caps. An instantaneous seepage flow rate, Q(t), is approximated by truncated two-term formulae of Wooding for a zero-depth disk in Gardner's soil or Hunt for paraboloidal craters (soils with no capillarity). The instantaneous evaporation losses are the product of a constant A-pan evaporation rate and the shrinking area of a flat horizontal disk of the free water, which dwindles in the crater. In HYDRUS simulations of a van Genuchten soil, the Reservoir Boundary Condition is used for a falling water level in the ponded depressions. Cones and paraboloids are selected as craters, initially fully or partially filled with free water at t = 0, and infiltrating until extinction. The results are presented as drawdown curves and – for shallow craters - attest a good match between analytical approximations and HYDRUS numerical simulations. Experiments with the extinction of water from small axisymmetric ponds in dune sand are also carried out. They allow blitz-evaluation of hydraulic parameters of the subjacent sand. Hydrological implications for commingling surface-subsurface (pore) water entities in terrestrial and Martian environments are discussed.