Transient Infiltration from Cavities. I: Theory

Abstract

A new method for describing infiltration during filling and draining of cavities such as, for example, irrigation furrows is presented. The model development decomposes in a first step the two‐dimensional (2D) infiltration phenomenon into a series of one‐dimensional (1D) processes, which are described by an extended analytical solution of the 1D Richards equation (which incorporates the varying effect of gravity). A special integration over the wetted perimeter of the cavity includes rigorous description of the filling and draining mechanism of the furrow, thus allowing for accurate modeling of infiltration opportunity times. Then, two higher levels of approximation are still considered. Model version 2 describes with a constant geometry parameter (derived from the curvature of the cavity) the impact of the furrow shape on infiltration; and version 3 finally takes into account that the increasing wetted area around the furrow also affects infiltration. All three model versions employ only physically based parameters. The method decomposes the transient infiltration opportunity times; and the varying effect of gravity along the wetted perimeter are taken into account. The semianalytical character of the new approach avoids expensive and complex numerical solution procedures such as the finite‐difference or finite‐element methods, which recommends its use within a furrow‐irrigation simulation.