Analytical model of infiltration under constant‐concentration boundary conditions

• Published in: Water resources research 2010-03, Vol.46 (3), p.n/a
• Main Authors: Triadis, D, Broadbridge, P
• Format: Article
• Language: English
• Subjects: algorithms; diffusion; hydraulic conductivity; hydrologic models; infiltration; infiltration (hydrology); integrable model; Kummer functions; mathematical models; series methods; similarity solutions; soil water; unsaturated conditions
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2009WR008181

Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C − 1)/(C − theta)2, where theta is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant‐concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C − 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C − 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.