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In the present study, the three-parameter one-dimensional vertical infiltration equation recently proposed by Poulovassilis and Argyrokastritis is examined. The equation includes the saturated hydraulic conductivity (K_s), soil sorptivity (S), and an additional parameter c; it is valid for all infiltration times. The c parameter is a fitting parameter that depends on the type of porous medium. The equation is characterized by the incorporation of the exact contribution of the pressure head gradient to flow during the vertical infiltration process. The application of the equation in eight porous media showed that it approaches to the known two-parameter Green–Ampt infiltration equation for parameter c = 0.300, while it approaches to the two-parameter infiltration equation of Talsma–Parlange for c = 0.750, which are the two extreme limits of the cumulative infiltration of soils. The c parameter value of 0.500 can be representative of the infiltration behavior of many soils for non-ponded conditions, and consequently, the equation can be converted into a two-parameter one. The determination of K_s, S, and c using one-dimensional vertical infiltration data from eight soils was also investigated with the help of the Excel Solver application. The results showed that when all three parameters are considered as adjustment parameters, accurate predictions of S and K_s are not achieved, while if the parameter c is fixed at 0.500, the prediction of S and K_s is very satisfactory. Specifically, in the first case, the maximum relative error values were 33.29% and 39.53% for S and K_s, respectively, while for the second case, the corresponding values were 13.25% and 17.42%. Full article

In the present study, the determination of soil saturated hydraulic conductivity (K_s) and soil sorptivity (S) from one-dimensional vertical infiltration data of eight different soils were investigated using three methodologies. Specifically, the nonlinear optimization procedure with the help of the Excel Solver application using six different two-parameter infiltration equations, as described by Valiantzas, Haverkamp et al. (complete, two and three approximate expansions), Talsma and Parlange and Green and Ampt; the linearization method of cumulative infiltration data by Valiantzas and the method of Latorre et al. were used. The results showed that, in almost all cases, the relative errors in the prediction of S were smaller than those of K_s. The nonlinear optimization procedure using the Valiantzas equation gave the best prediction of S and K_s, with relative errors up to −12.49% and 13.61%, respectively. The two-term approximate expansion of Haverkamp gave the highest relative errors in both S and K_s. The various forms of the Haverkamp equation (complete and three approximate expansion), as well as the Latorre method, gave good predictions of S and K_s in fine-textured soils. In all forms of the Haverkamp equation, when parameter β was considered as an additional adjustment parameter, no improvement in the prediction of the S and K_s values was achieved, so the constant value β = 0.6 was proposed. The relative errors in the prediction of S and K_s resulting from the linearization method of the cumulative infiltration data were similar to those of the Valiantzas equation by the nonlinear optimization procedure. The accuracy in estimating the S and K_s parameters from each equation depends on its infiltration time validity and the soil type. Full article

The infiltration phenomena has been studied by several authors for decades, and numerical and approximate results have been shown through the asymptotic solution in short and long times. In particular, it is worth highlighting the works of Philip and Parlange, who used time and volumetric content as independent variables and space as a dependent variable, and found the solution as a power series in $t^{1/2}$ that is valid for short times. However, several studies show that these models are not applicable to anomalous flows, in which case the application of fractional calculus is needed. In this work, a fractional time derivative of a Caputo type is applied to model anomalous infiltration phenomena. Fractional horizontal infiltration phenomena are studied, and the fractional Boltzmann transform is defined. To study fractional vertical infiltration phenomena, the asymptotic behavior is described for short and long times considering an arbitrary diffusivity and hydraulic conductivity. Finally, considering a constant flux-dependent relation and a relation between diffusivity and hydraulic conductivity, a fractional cumulative infiltration model applicable to various types of soil is built; its solution is expressed as a power series in $t^{\nu /2}$, where $\nu \in (0,2)$ is the order of the fractional derivative. The results show the effect of superdiffusive and subdiffusive flows in different types of soil. Full article

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. Full article