Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

Zha, Yuanyuan; Yang, Jinzhong; Zeng, Jicai; Tso, Chak-Hau Michael; Zeng, Wenzhi; Shi, Liangsheng

doi:10.1002/wat2.1364

Cited by 82 publications

(69 citation statements)

References 168 publications

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“…Lots of models are used to study groundwater dynamics in such systems, but Richards equation-based models are widespread for saturated/unsaturated flows. As a consequence, subsurface hydrogeology community has good numerical experience about solution of Richards equation [1,2]. The present work is the continuation of a first paper [3] and enters into a long-term research project aiming to provide insight into the groundwater circulation due to wave action on sandy beaches.…”

Section: Introductionmentioning

confidence: 93%

Adaptive Discontinuous Galerkin Method for Richards Equation

Clément¹,

Golay²,

Ersoy³

et al. 2020

Topical Problems of Fluid Mechanics 2020

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This paper deals with the numerical simulation of time-dependant flows in partially saturated porous media modelled by Richards equation. A Discontinuous Galerkin method together with an implicit scheme are used to approximate the solution. The mathematical framework and a procedure for solving this nonlinear equation are presented. In particular, treatment of seepage boundary condition and adaptive time step are underlined. An adaptive mesh refinement technique is also outlined in order to capture wetting front efficiently. Some numerical simulations are performed to illustrate the performance of the method.

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Section: Introductionmentioning

confidence: 93%

Adaptive Discontinuous Galerkin Method for Richards Equation

Clément¹,

Golay²,

Ersoy³

et al. 2020

Topical Problems of Fluid Mechanics 2020

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“…Numerical solution of flow and transport equations in unsaturated porous media is a challenging problem [30][31][32]. The systems of equations in both linear transport and mobile-immobile transport cases are solved with the standard finite volume method.…”

Section: Numerical Modelmentioning

confidence: 99%

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Younès

Zaouali

Kanzari

et al. 2019

Water

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Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations.

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“…The purpose of this study was not simply comparing the differences of their performance in the circumstance of infusing various data into a soil water system but also contemplating the necessity of introducing advanced nonlinear approach or whether a straightforward sampling approach or linear filter is adequate. As suggested by Zhou et al (2014), “…the best inverse model should be the one that is stochastic, is capable of dealing with multiple sources of state data governed by a complex state equation, is not limited to multi‐Gaussian realizations, and can weight in prior information.” Considering the inherent nonlinearity of soil water flow (Zha et al, 2019), it will be interesting to investigate the capability of typical data assimilation methods in dealing with different data with a probability distribution and representative scale (e.g., pressure head and soil water content, averaged surface soil water content, and groundwater level data). The motivation of this work was thus to investigate the performance of three different data assimilation approaches (i.e., EnKF, MCMC, and EnRML) for estimating soil hydraulic parameters in a one‐dimensional soil column using three different observations (i.e., surface soil water content, soil water pressure head, and groundwater level).…”

mentioning

confidence: 99%

Investigation of Data Assimilation Methods for Soil Parameter Estimation with Different Types of Data

Zhu

Zhang

Zhu

et al. 2019

Vadose Zone Journal

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Groundwater level data require EnRML for better interpretation. Different methods perform similarly when assimilating surface soil moisture data. Soil water pressure head data are the most valuable in terms of parameter estimation. MCMC performs well in homogeneous soil but degrades in heterogeneous soil. The EnKF method relies more on a relatively large number of ensembles than does EnRML. In the past few decades, different data assimilation methods have been proposed to estimate soil parameters. It is not clear whether a straightforward sampling approach is sufficient or whether a linear filter or even an advanced nonlinear filter is needed to interpret the potential information carried by different data types (e.g., pressure head and water content data from multiple depths, easily available surface soil moisture data, and groundwater level data). In this study, three classical data assimilation methods, i.e., the ensemble Kalman filter (EnKF), the ensemble randomized maximum likelihood filter (EnRML), and the Markov chain Monte Carlo (MCMC), were investigated numerically in terms of the utility to cope with three different types of observations. Results show that, compared with the EnKF approach, EnRML is a superior method to extract the parameter information from observations. The MCMC approach performs well in homogeneous soil but not in heterogeneous soil. Regardless of the data assimilation methods and the soil heterogeneity, point‐scale soil water pressure head data are the most valuable in terms of soil parameter estimation, followed by groundwater level data, which require a nonlinear filter to interpret. A smaller observation error for groundwater level data leads to obviously improved parameter estimates by using EnRML with a slight improvement by using EnKF. The stable performance of the EnKF method relies more heavily on a relatively large number of ensembles than the EnRML method, whereas only a few ensemble members are needed for EnRML in a homogeneous soil column.

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Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

Cited by 82 publications

References 168 publications

Adaptive Discontinuous Galerkin Method for Richards Equation

Adaptive Discontinuous Galerkin Method for Richards Equation

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Investigation of Data Assimilation Methods for Soil Parameter Estimation with Different Types of Data

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