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• Van Genuchten-Mualem soil's steady flux analyzed; analytical solutions developed. • First solution for flow equation without prior assumptions on pressure head's form. • Solution derived using double Maclaurin series and multinomial theorem. • Analytically identify hydraulic parameters, avoiding numerical inverse procedures. Various analytical solutions for steady-state vertical flux through unsaturated soils exist in the literature. These solutions often assume specific hydraulic conductivity forms such as exponential form, rational power form, or power-law form such as the Brooks-Corey model. The van Genuchten-Mualem model is widely used in practical applications of flow through unsaturated soils. It is among the most complicated hydraulic conductivity forms for which no analytical solutions are available. This paper deals with the development of an analytical solution for steady-state vertical flux using van Genuchten-Mualem model. The analytical solution is obtained using Maclaurin series expansions and the multinomial theorem. The general form expresses the depth as a function of pressure head. The analytical solution can be used to model both infiltration (positive flux rate) and evaporation (negative flux rate). The derived analytical solution is compared with numerical results and shows excellent agreement. It can also be used to identify the hydraulic parameters analytically, eliminating the need of a numerical inverse procedure. As far as the author's knowledge, the proposed solution is the first analytical solution dealing with van Genuchten-Mualem model, which is directly derived from the flow equation without any predefined mathematical form of the pressure head. [ABSTRACT FROM AUTHOR]

Highlights • An efficient analytical model for horizontal infiltration in soils is presented. • The model covers many existing realistic models in the literature. • It doesn’t make any prior assumptions about the form of the diffusivity function. • It is useful for studying the effects of soil type and checking numerical schemes. • A new method to predict the distribution of WC and estimate the hydraulic parameters. Abstract An efficient method for nonlinear approximate solutions of the one-dimensional horizontal absorption equation is presented. The method pertains to a semi-infinite soil with uniform initial condition and constant soil water content at the beginning of a soil column. It does not make any prior assumptions about the form of the diffusivity function. The nonlinear solution is of simple combination of power and exponential functions and expresses in explicit form the distance as function of time and soil water content. It involves all the physical parameters and four additional fitting parameters which can be obtained by simple fitting procedure. Algebraic expressions that quantify the main infiltration process are derived from the basic equation. These include the sorptivity, the infiltration rate, the cumulative infiltration rate, and the wetting front. A comparison with exact, numerical and other analytical solutions validates the accuracy of the approximation and shows its advantage to other approximate solutions. The analytical expressions are used to predict experimental soil moisture profiles from simple measurements such as sorptivity, wetting front, and initial and final soil water contents. The method is applied to estimate soil hydraulic properties using horizontal water absorption experiments. The results of the parameter estimation procedure are compared to other existing results and show good agreements. The solution method is also tested to various diffusivity functions and its limitation is discussed in detail. [ABSTRACT FROM AUTHOR]

Summary An analytical solution for one-dimensional steady vertical flux through unsaturated homogeneous soils is presented. The model assumes power law hydraulic conductivity and diffusivity functions. The soil domain is a finite-depth flow medium overlying a water table. A steady constant flux is applied at the top boundary while a constant saturation value is specified at the bottom boundary. The general form of the analytical solution expresses implicitly the depth as function of the liquid water saturation. It can be used to model both infiltration through the soil surface and evaporation from the bottom, depending on the sign of the flux boundary value. The analytical solution takes into account the prediction of a drying front in the case of evaporation from deep water table. Algebraic expressions of practical and theoretical importance are derived in terms of soil water parameters. These expressions include the stored mass in the system at steady state as well as the drying front when it exists. The general form solution can be inverted back to obtain exact explicit solutions when the power law parameters are related. Numerical results show the effects of soil type, surface flux, capillarity, and gravity on the saturation distribution in the soil. The analytical solution is used for comparing between models, validating of numerical solutions, as well as for estimating the hydraulic parameters. [ABSTRACT FROM AUTHOR]

Abstract: In the analysis of the unsaturated zone, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the porous media. Adaptative multi-scale parameterization consists in solving the problem through successive approximations by refining the parameter at the next finer scale all over the domain and stopping the process when the refinement does not induce significant decrease of the objective function any more. In this context, the refinement indicators algorithm provides an adaptive parameterization technique that opens the degrees of freedom in an iterative way driven at first order by the model to locate the discontinuities of the sought parameters. We present a refinement indicators algorithm for adaptive multi-scale parameterization that is applicable to the estimation of multi-dimensional hydraulic parameters in unsaturated soil water flow. Numerical examples are presented which show the efficiency of the algorithm in case of noisy data and missing data. [Copyright &y& Elsevier]