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 ≤ T_e. The extinction time T_e 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.