Furrow Irrigation Advance Simulation Using a Surface–Subsurface Interaction Model

Abstract

A model for the simulation of furrow irrigation advance was developed based on the Saint-Venant equations for the one-dimensional surface flow and the two-dimensional Richards equation for porous media flow. Solutions are computed numerically using finite differences for the surface flow and finite elements for the subsurface flow. Computations are internally coupled through an iterative procedure. Infiltration is computed with the Richards equation every five nodes used in the surface flow computations and by linear interpolation at the remaining nodes. In addition, the Richards equation is solved at the boundaries of the surface flow domain and in the vicinity of the wave front. The time step is calculated using the Courant–Friedrich–Lewy condition and a stability criterion that accounts for friction effects. This combined criterion prevents numerical instabilities and convergence problems, especially in cases of high friction coefficient, low discharge rates, and/or high infiltration rates resulting generally in low flow depth and slow irrigation advance. The model was evaluated against an approach involving high resolution correspondence used in both surface and subsurface flow, using different soil types, inflow discharge, and stability criteria.