Analytical solutions for linearized Richards Equation with arbitrary time‐dependent surface fluxes

Chen, Jiann-Mou; Tan, Yih–Chi; Chen, Chu-Hui; Parlange, J.‐Y.

doi:10.1029/2000wr900406

Cited by 62 publications

(36 citation statements)

References 3 publications

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“…As shown below in Equation (31), P is related to the van Genuchten parameter m. Assuming P = 1, the RE is reduced to a linearized form for which analytical solutions to various flow processes exist [16][17][18]. However, the assumption P = 1 is rarely met under realistic conditions; most soils exhibit a P significantly larger than 1 [33].…”

Section: New Solution To Richards' Equationmentioning

confidence: 99%

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

et al. 2016

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P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar observations, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For this reason, an empirical quadratic function (second order polynomial) is currently applied in the AirMOSS inversion algorithm to retrieve the SMP. The three free parameters of the polynomial are retrieved for each AirMOSS pixel using three backscatter observations (i.e., one frequency at three polarizations of Horizontal-Horizontal, Vertical-Vertical and Horizontal-Vertical). In this paper, a more realistic, physically-based SMP model containing three free parameters is derived, based on a solution to Richards' equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

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Section: New Solution To Richards' Equationmentioning

confidence: 99%

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

et al. 2016

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“…Also important to note is that if the PDE is solved for the moisture content instead of pressure head, a linear PDE occurs naturally without the need for a transformation when using the above assumptions. Chen et al [2001a] can use arbitrary time-dependent surface fluxes when using this moisture-content-based version of Richards' equation. Pullan [1990] gives a great review of papers on the quasi-linear approximation previous to 1990.…”

Section: Previous Workmentioning

confidence: 99%

Clean two‐ and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers

Tracy

2006

Water Resources Research

101

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[1] This technical note derives clean analytical solutions of Richards' equation for threedimensional unsaturated groundwater flow. Clean means that the boundary conditions and steady state solutions are closed form expressions and the transient solutions have relatively simple additional Fourier series terms. Two-dimensional versions of these solutions are also given. The primary purpose for the solutions is to test linear and nonlinear solvers in finite difference/volume/element computer programs for accuracy and scalability using architectures ranging from PCs to parallel high-performance computers. This derivation starts from the quasi-linear assumption of relative hydraulic conductivity varying exponentially with pressure head and the separate approximation that relative hydraulic conductivity varies linearly with moisture content. This allows a transformation to be used to create a linear partial differential equation. Separation of variables and Fourier series are then used to obtain the final solution. Physically reasonable material properties are also used. A total of four solutions are given in this technical note (steady state and transient solutions for two different boundary conditions of the sample problem).

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“…Analytical solutions play an important role in the examination of water infiltration in saturated and unsaturated heterogeneous porous media [5][6][7][8][9][10][11][12][13]. Srivastava and Yeh [5] derived an analytical approach to describe one-dimensional rainfall infiltration towards the water table.…”

Section: Introductionmentioning

confidence: 99%

The Role of Surface Infiltration in Hydromechanical Coupling Effects in an Unsaturated Porous Medium of Semi-Infinite Extent

Selvadurai

Yang

2017

Geofluids

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Rainfall infiltration into an unsaturated region of the earth's surface is a pervasive natural phenomenon. During the rainfall-induced seepage process, the soil skeleton can deform and the permeability can change with the water content in the unsaturated porous medium. A coupled water infiltration and deformation formulation is used to examine a problem related to the mechanics of a two-dimensional region of semi-infinite extent. The van Genuchten model is used to represent the soil-water characteristic curve. The model, incorporating coupled infiltration and deformation, was developed to resolve the coupled problem in a semi-infinite domain based on numerical methods. The numerical solution is verified by the analytical solution when the coupled effects in an unsaturated medium of semi-infinite extent are considered. The computational results show that a numerical procedure can be employed to examine the semi-infinite unsaturated seepage incorporating coupled water infiltration and deformation. The analysis indicates that the coupling effect is significantly influenced by the boundary conditions of the problem and varies with the duration of water infiltration.

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Analytical solutions for linearized Richards Equation with arbitrary time‐dependent surface fluxes

Cited by 62 publications

References 3 publications

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

Clean two‐ and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers

The Role of Surface Infiltration in Hydromechanical Coupling Effects in an Unsaturated Porous Medium of Semi-Infinite Extent

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