Development of a Numerical Model for Furrow Irrigation by Coupling 1D Saint-Venant and 3D Richards’ Equations

Development of numerical models for management and assessment of irrigation systems is an important step for establishing farm decision support systems. In this study, a coupled model has been developed for simulation of furrow irrigation using 1D fully hydrodynamic form of Saint-Venant equations and 3D fully-form of Richards’ equation. The Saint-Venant equations have been discretized by an explicit scheme while the Richards’ equation has been solved by an implicit scheme. Furthermore, coordinate transformation technique was employed to handle non-orthogonal grids of 3D Richards’ equation. The model was subsequently validated using experimental and numerical data and in all cases acceptable accuracy was observed. Root mean square error and mean absolute error for the advance phase were 0.63 and 2.63 sec, respectively. Furthermore, the maximum root mean square error and the mean absolute error for pressure head distribution were obtained 0.24 and 0.45 m, respectively.  Finally, the proposed model was employed to simulate furrow irrigation for five irrigation events and the results were analyzed. The results showed that the proposed model is able to simulate advance phase of furrow irrigation.