Shape Factors for Elements of the Infiltration Profile in Surface Irrigation: Generic Approach

Advanced mathematical models of surface irrigation use the equations of motion applied to a series of cells comprising the surface stream and an infiltration profile. In the simulation, a mass balance must be preserved among the inflow, surface stream, infiltrated profile, and runoff volumes. The shapes of the profiles are not known a priori, yet the curvature of the element boundaries influences the calculation of the volume contained therein, especially near the front of the irrigation stream. This paper presents a focus on the shape of the subsurface volume elements comprising the infiltration profile. Previous calculations of shape factors documenting departures from assumed first-order approximations (trapezoidal shapes) have been on the basis of empirical equations selected to describe infiltration as a function of wetting time. Modern simulations are not always on the basis of empirical formulas but increasingly rely on solutions of physically based approaches, such as the Green-Ampt or Richard's equation. These solutions provide only tabulated values of infiltration and infiltration rates along the profile. The proposed generic approach calculates shape factors for each cell of the profile on the basis of the calculated change in infiltration rates on the two sides of the cell.