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 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.

Modeling of irrigation and agricultural drainage requires knowledge of the soil hydraulic properties. However, uncertainty in the direct measurement of the saturation moisture content (${\theta }_{\mathrm{s}}$) has been generated in several methodologies for its estimation, such as Pedotransfer Functions (PTFs) and Artificial Neuronal Networks (ANNs). In this work, eight different PTFs were developed for the (${\theta }_{\mathrm{s}}$) estimation, which relate to the proportion of sand and clay, bulk density (BD) as well as the saturated hydraulic conductivity ($K_{\mathrm{s}}$). In addition, ANNs were developed with different combinations of input and hidden layers for the estimation of ${\theta }_{\mathrm{s}}$. The results showed R${}^2$ values from $0.9046\le {\mathrm{R}}^2\le 0.9877$ for the eight different PTFs, while with the ANNs, values of R${}^2>0.9891$ were obtained. Finally, the root-mean-square error (RMSE) was obtained for each ANN configuration, with results ranging from $0.0245\le \mathrm{RMSE}\le 0.0262$. It was found that with particular soil characteristic parameters (% Clay, % Silt, % Sand, BD and $K_{\mathrm{s}}$), accurate estimate of ${\theta }_{\mathrm{s}}$ is obtained. With the development of these models (PTFs and ANNs), high R${}^2$ values were obtained for 10 of the 12 textural classes.

Several studies have assessed crop water requirements based on soil properties, but these have been on a small scale or on soils with similar textures. Here, a data base of soil measurements in the field and laboratory from sites across Irrigation District 023, San Juan del Rio, Queretaro, Mexico was sampled, collected, analyzed, and integrated. The data base, named, NaneSoil, contains information on 900 samples obtained from irrigated plots. NaneSoil cover 10 of the 12 textural classes with the following information: sand, silt, clay contents, bulk density, saturated volumetric water content, field capacity, permanent wilting point and saturated hydraulic conductivity. The aim of this work is to provide the scientific community with sufficient information to perform a large number of analyses, for example, development of pedotransfer functions, calculation of water requirements of plants in soils with similar characteristics, modeling of infiltration, optimal irrigation discharge calculation, among others. The dataset also promotes the scientific community to contribute their own measurements to further strengthen the knowledge of flow in the porous medium.

The overelevation of the water table in surface irrigation plots is one of the main factors affecting salinization in agricultural soils. Therefore, it is necessary to develop simulation models that consider the effect of a shallow water table in the process of advance-infiltration of the water in an irrigation event. This paper, the first in a series of three, develops a simple mathematical model for the advance phase of border irrigation in soils with the presence of a shallow water table. In this study, the hydrodynamic model of the Barré de Saint-Venant equations is used for the water surface flow, and the equations are solved using a Lagrangian finite-differences scheme, while in the subsurface flow, an analytical solution for infiltration in soils with a shallow water table is found using the bisection method to search for roots. In addition, a hydraulic resistance law is used that eliminates the numerical instabilities presented by the Manning–Strickler law. The model results for difference irrigation tests show adjustments with an R² > 0.98 for the cases presented. It is also revealed that, when increasing the time step, the precision is maintained, and it is possible to reduce the computation time by up to 99.45%. Finally, the model proposed here is recommended for studying the advance process during surface irrigation in soils with shallow water tables.