Maximization of water storage in backfilled and lined: Channels and dimples subject to evaporation and leakage

A channel or axisymmetric dimple filled with a coarse porous material and aimed at a temporary storage of infiltrated water as a perched water table aquifer is studied. The bottom shape is varied based on the criterion of maximal water storage after a certain period of drainage and evaporation. Leakage into the vadose zone through a thin liner occurs with a specific discharge proportional to the pressure drop across the liner. Evaporation through a horizontal shrinking water table is spatially uniform. An ordinary differential equation, which follows from the mass balance condition, is solved either explicitly or numerically. The class of triangular, polynomial, and conical sections is studied. The shape of maximal water retention is calculated for a given initial stored water volume or water table width, evaporation intensity, liner thickness and conductivity, vadose zone pressure beneath the liner, and selected time interval between two sequential infiltration events.