Water Balance in Surface Soil: Analytical Solutions of Flow Equations and Measurements in the Alpine Toce Valley

Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions

“…Medium 0.1 5 · 10 À6 1 5 0-5 5567.6 -0.090 0.068 0.061 0.022 0.007 2 Medium 0.1 À5 · 10 À6 1 5 5-10 -21,430.5 0.000 0.029 0.017 À0.029 0.012 b = V 2 /(4 AE D) because in this case the solution of the Richards equation is much more simple than in the general case with b assuming any other positive value (Menziani et al, 2005). In this example the hydraulic characteristics of the soil #2 (medium) have been used.…”

“…the space and time evolution of the soil water content is given by the sum of two solutions (Menziani et al, 2005):…”

Water dynamics in a gradually nonhomogeneous soil described by the linearized Richards equation

“…With a different approach, following the original works by Philip [1973] and Knight and Philip [1974], exact solutions have been found for power law soil hydraulic constitutive laws [ Sander et al , 1988], that allow to reduce the Richards equation to a Burgers equation [ Hills and Warrick , 1993; Warrick and Parkin , 1995; Schwartzendruber , 2002]. By linearizing the Richards equation through Gardner's constitutive relationships, analytical solutions were found following the original applications by Gardner [1958] both for a homogeneous [ Wooding , 1968; Basha , 1999, 2000; Menziani et al , 2005] and a nonhomogeneous porous medium [ Philip , 1972; Srivastava and Yeh , 1991; Shan and Stephens , 1995; Warrick and Knight , 2003; Chen and Gallipoli , 2004].…”