Approximation of internodal conductivities in numerical simulation of one‐dimensional infiltration, drainage, and capillary rise in unsaturated soils

Szymkiewicz, Adam

doi:10.1029/2008wr007654

Cited by 28 publications

(48 citation statements)

References 49 publications

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“…The inter-nodal values of the hydraulic conductivity were calculated as arithmetic averages of the grid point values. We do not insist here on the problem of inter-nodal values calculation (Szymkiewicz 2009) because we are interested in numerical solutions on very fine grids. The numerical strategy used to solve (5) belongs to the class named implicit discretization with explicit linearization (Haverkamp et al 1977).…”

Section: Methodsmentioning

confidence: 99%

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

2011

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The need of accurate and efficient numerical schemes to solve Richards' equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards' equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated-unsaturated soils with hydraulic properties described by van Genuchten-Mualem models. The numerical results obtained are compared with those provided by the modified Picard-preconditioned conjugated gradient (Krylov subspace) approach.

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Section: Methodsmentioning

confidence: 99%

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

2011

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“…These parameters would have great influence on the snow hydraulic conductivity. It could be argued that a piecewise function comprised of individual snow layers' conductivity better describes the vertical pattern of conductivity in the snow pack (Szymkiewicz, 2009). However, when a piecewise function was tested, "dry layers" (that needed prewetting) caused impermeable barriers and caused numerical problems for the simulation.…”

Section: Solving the Richards Equationmentioning

confidence: 99%

Implementation of a physically based water percolation routine in the Crocus/SURFEX (V7.3) snowpack model

et al. 2017

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Abstract. We present a new water percolation routine added to the one-dimensional snowpack model Crocus as an alternative to the empirical bucket routine. This routine solves the Richards equation, which describes flow of water through unsaturated porous snow governed by capillary suction, gravity and hydraulic conductivity of the snow layers. We tested the Richards routine on two data sets, one recorded from an automatic weather station over the winter of 2013-2014 at Filefjell, Norway, and the other an idealized synthetic data set. Model results using the Richards routine generally lead to higher water contents in the snow layers. Snow layers often reached a point at which the ice crystals' surface area is completely covered by a thin film of water (the transition between pendular and funicular regimes), at which feedback from the snow metamorphism and compaction routines are expected to be nonlinear. With the synthetic simulation 18 % of snow layers obtained a saturation of > 10 % and 0.57 % of layers reached saturation of > 15 %. The Richards routine had a maximum liquid water content of 173.6 kg m −3 whereas the bucket routine had a maximum of 42.1 kg m −3 . We found that wet-snow processes, such as wet-snow metamorphism and wet-snow compaction rates, are not accurately represented at higher water contents. These routines feed back on the Richards routines, which rely heavily on grain size and snow density. The parameter sets for the water retention curve and hydraulic conductivity of snow layers, which are used in the Richards routine, do not represent all the snow types that can be found in a natural snowpack. We show that the new routine has been implemented in the Crocus model, but due to feedback amplification and parameter uncertainties, meaningful applicability is limited. Updating or adapting other routines in Crocus, specifically the snow compaction routine and the grain metamorphism routine, is needed before Crocus can accurately simulate the snowpack using the Richards routine.

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“…WGeom satisfies monotonicity conditions derived by Forsyth and Kropinski () and thus can yield oscillation‐free solutions in unsaturated homogeneous soil zones. It is generally more accurate than the upstream mean and more efficient than Szymkiewicz's formula (Szymkiewicz, ). Variably saturated flows are solved in an integrated framework. The proposed framework has a unified treatment to flows in unsaturated zones, saturated zones, transition zones, and ground surface.…”

Section: Introductionmentioning

confidence: 99%

Modeling Variably Saturated Flow in Stratified Soils With Explicit Tracking of Wetting Front and Water Table Locations

Dai

Zhang

Yuan

et al. 2019

Water Resources Research

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The locations of wetting front and water table are key variables in an integrated surface‐groundwater modeling. In current land surface models, they are either diagnosed from pressure head profiles or predicted using certain parameterization schemes. Both approaches need to make assumptions on how pressure head changes vertically and numerical results may have large errors when these assumptions are violated. In this work, we propose a numerical framework, which can explicitly track the locations of wetting front and water table. Existing numerical solvers modeling soil water movement usually use water content, pressure head, or both of them as prognostic variables, while in this framework, two additional prognostic variables representing the locations of wetting front and water table are introduced. Besides, another two improvements are explored to make the framework stable and efficient. First, a new equivalent hydraulic conductivity formula accommodating nonlinear hydraulic curves is proposed. The formula is unconditionally stable and can yield oscillation‐free solution of Richards' equation in unsaturated homogeneous soils. Second, a mixed implicit‐explicit temporal discretization is adopted. It uses an implicit scheme initially at every time step to improve the stability and accuracy, while in case of failure in convergence it replaces the iterations with an explicit scheme to guarantee mass conservation. Based on all these improvements, the framework is potentially used to simulate variably saturated flow in stratified soils in land surface models. Seven numerical tests covering various flow situations, boundary conditions, and soil geometries are carried out and illustrate the characteristics of the proposed framework.

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Approximation of internodal conductivities in numerical simulation of one‐dimensional infiltration, drainage, and capillary rise in unsaturated soils

Cited by 28 publications

References 49 publications

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

Implementation of a physically based water percolation routine in the Crocus/SURFEX (V7.3) snowpack model

Modeling Variably Saturated Flow in Stratified Soils With Explicit Tracking of Wetting Front and Water Table Locations

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