Two models are compared for Darcian flows in a vadose zone and shallow unconfined aquifer with an intensive evapotranspiration, common for hyperarid climates. An analytical 2-D Dupuit-Forchheimer approximation, in which the vadose zone is considered as a “distributed sink” (similar to a standard “distributed source” which models recharge to the water table in humid climates), is collated with HYDRUS3D. In a planar domain, a vertically-averaged flow from a constant piezometric head contour (seepage from ditches or trenches) is studied and integral criteria (the volume of the saturated zone and the area of unsaturated lacuna) are either evaluated or estimated by the Pòlya and Szegö isoperimetric inequalities. Mixed BVPs for Richards’ equation in cylindrical domains are numerically solved and give the pressure head, moisture content, and velocity fields, streamlines and criteria. Implicaitons for urban hydrology and ecohydrology of water logged drylands are discussed.