In gravity irrigation, how water is distributed in the soil profile makes it necessary to study and develop methodologies to model the process of water infiltration and redistribution. In this work, a model is shown to simulate the advancing front in border irrigation based on the one dimensional equations of Barré de Saint-Venant for the surface flow and the equation of Green and Ampt for the flow in a porous medium. The solutions were obtained numerically using a finite difference Lagrangian scheme for the surface flow and the Raphson method for the subsurface flow. The model was validated with data obtained from the literature from an irrigation test and its predictive capacity was compared with another model and showed excellent results. The hydrodynamic parameters of the soil, necessary to obtain the optimal irrigation discharge, were obtained through the solution of the inverse problem using the Levenberg–Marquardt optimization algorithm. Finally, the results found here allow us to recommend that this model be used to design and model border irrigation, since the infiltration equation uses characteristic parameters of the physical soil.

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Water infiltration is simulated by obtaining the time infiltrated depth evolution and humidity profiles with the numerical solution of the two-dimensional Richards’ equation. The contact time hypothesis is accepted in this study and used to apply a unique form on time of the water depth evolution in the solution domain (furrow), as boundary condition. The specific form of such evolution in time was obtained from results reported in the literature based on the internal numerical full coupling of the Saint-Venant and Richards’ equations in border irrigation. Moreover, the equivalent hydraulic area between the border and the furrow was achieved by scaling the values of water depth. The analysis was made for three contrasting soil textures, and the comparison was done by computing the root mean square error (RMSE) indicator. The comparison was performed from the selection of five finite element meshes with different densities to discretize the solution domain of the two-dimensional Richards’ equation, combined with several time steps. Finally, a comparison was made between infiltrated depth evolution calculated with a constant water depth in the furrow to the one proposed in this work, finding important differences between both approaches. To expand the scope of this study and for a fuller exploration of the subject, the results were compared with results obtained by applying the HYDRUS-2D software. The results confirm that it is important to consider an internal full coupling of the Saint-Venant and Richards´ equations to improve furrow irrigation simulations.

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The second version of the computer program DRENAS (subsurface agricultural drainage) is presented, which includes four analytical solutions and a finite element solution Galerkin type of the differential equation of agricultural drainage in its one-dimensional form and can be run under Windows systems of 32-bit or 64-bit. The analytical and numerical models included in version 1.0 of the program were migrated from Visual Basic 2005 to Visual Basic 2017 and modified to expand and 2020, Instituto Mexicano de Tecnología del Agua Open Access bajo la licencia CC BY-NC-SA 4.0