In the present work, we construct several artificial neural networks (varying the input data) to calculate the saturated hydraulic conductivity (K${}_{\mathrm{S}}$) using a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. All of them were constructed using two hidden layers, a back-propagation algorithm for the learning process, and a logistic function as a nonlinear transfer function. In order to explore different arrays for neurons into hidden layers, we performed the bootstrap technique for each neural network and selected the one with the least Root Mean Square Error (RMSE) value. We also compared these results with pedotransfer functions and another neural networks from the literature. The results show that our artificial neural networks obtained from 0.0459 to 0.0413 in the RMSE measurement, and 0.9725 to 0.9780 for R${}^2$, which are in good agreement with other works. We also found that reducing the amount of the input data offered us better results.

The aim of this study is the deduction of an analytic representation of the optimal irrigation flow depending on the border length, hydrodynamic properties, and soil moisture constants, with high values of the coefficient of uniformity. In order not to be limited to the simplified models, the linear relationship of the numerical simulation with the hydrodynamic model, formed by the coupled equations of Barré de Saint-Venant and Richards, was established. Sample records for 10 soil types of contrasting texture were used and were applied to three water depths. On the other hand, the analytical representation of the linear relationship using the Parlange theory of infiltration proposed for integrating the differential equation of one-dimensional vertical infiltration was established. The obtained formula for calculating the optimal unitary discharge is a function of the border strip length, the net depth, the characteristic infiltration parameters (capillary forces, sorptivity, and gravitational forces), the saturated hydraulic conductivity, and a shape parameter of the hydrodynamic characteristics. The good accordance between the numerical and analytical results allows us to recommend the formula for the design of gravity irrigation.

Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation.

In recent years, groundwater levels have been decreasing due to the demand in agricultural and industrial activities, as well as the population that has grown exponentially in cities. One method of controlling the progressive lowering of the water table is the artificial recharge of water through wells. With this practice, it is possible to control the amount of water that enters the aquifer through field measurements. However, the construction of these wells is costly in some areas, in addition to the fact that most models only simulate the well as if it were a homogeneous profile and the base equations are restricted. In this work, the amount of infiltrated water by a well is modeled using a stratified media of the porous media methodology. The results obtained can help decision-making by evaluating the cost benefit of the construction of wells to a certain location for the recharge of aquifers.

In the study of water transference in soil according to Darcy law, the knowledge of hydrodynamic characteristics, formed by the water retention curve θ(ψ), and the hydraulic conductivity curve K(ψ) are of great importance. The first one relates the water volumetric content (θ) with the water-soil pressure (ψ); the second one, the hydraulic conductivity (K) with the water-soil pressure. The objective of this work is to establish relationships between both curves using concepts of probability theory and fractal geometry in order to reduce the number of unknown functions. The introduction of four definitions used at the literature of the pore effective radius that is involve in the general model has permitted to establish four new specials models to predict the relative hydraulic conductivity. Some additional considerations related to the definitions of flow effective area and the tortuosity factor have allow us to deduce four classical models that are extensively used in different studies. In particular, we have given some interpretations of its empirical parameters in the fractal geometry context. The resulting functions for hydrodynamic characteristics can be utilized in many studies of water movement in the soil.

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.