A fractional infiltration model for the simulation of the wetting front in non-saturated soils and its application in a soil column

Many environmental studies require accurate simulation of water and solute fluxes in the unsaturated zone. The present work is an attempt to ascertain whether fractional calculus is suitable as a tool for the simulation of the wetting front in partially saturated porous media. The model is based on the non linear Richards diffusion equation, where the derivative with respect to time is substituted with a fractional derivative of order smaller than one and the fractional Richards equation is solved by the use of a numerical algorithm (i.e. Adams-Bashforth-Moulton method). The behavior of the saturation front as a function of time, space and fractional order and the influence of soil diffusivity on the volumetric moisture content are analyzed through many numerical simulations in order to create a complete description of many phenomena involved in superficial soil layers (as in any porous media) during extreme rain events. Vertical infiltration experiments on a sandy soils have been conducted as well, for the measurement of soil water content at selected times and positions. Preliminary results show the connection between fractional order and hydrologic parameters.