Bayesian inversion of Mualem‐van Genuchten parameters in a multilayer soil profile: A data‐driven, assumption‐free likelihood function

Over, M. W.; Wollschläger, Ute; Osorio-Murillo, C. A.; Rubin, Yoram

doi:10.1002/2014wr015252

Cited by 11 publications

(10 citation statements)

References 66 publications

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“…Huisman et al (2010) estimated soil hydraulic properties of a homogeneous dike exploiting flat wire time domain reflectometry (TDR) and electrical resistance tomography (ERT) data recorded during a fluctuating groundwater table experiment. With increasing computational power in recent years, 1-D subsurface architectures were analyzed with ensemble-based parameter estimation methods reaching from Markov chain Monte Carlo (MCMC; e.g., Vrugt et al, 2008b;Scharnagl et al, 2011;Wöhling and Vrugt, 2011) and data assimilation (e.g., Wu and Margulis, 2011;Li and Ren, 2011;Erdal et al, 2014) to data-driven modeling (e.g., Over et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Effect of unrepresented model errors on estimated soil hydraulic material properties

Jaumann¹,

Roth²

2017

Hydrol. Earth Syst. Sci.

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Abstract. Unrepresented model errors influence the estimation of effective soil hydraulic material properties. As the required model complexity for a consistent description of the measurement data is application dependent and unknown a priori, we implemented a structural error analysis based on the inversion of increasingly complex models. We show that the method can indicate unrepresented model errors and quantify their effects on the resulting material properties. To this end, a complicated 2-D subsurface architecture (AS-SESS) was forced with a fluctuating groundwater table while time domain reflectometry (TDR) and hydraulic potential measurement devices monitored the hydraulic state. In this work, we analyze the quantitative effect of unrepresented (i) sensor position uncertainty, (ii) small scale-heterogeneity, and (iii) 2-D flow phenomena on estimated soil hydraulic material properties with a 1-D and a 2-D study. The results of these studies demonstrate three main points: (i) the fewer sensors are available per material, the larger is the effect of unrepresented model errors on the resulting material properties. (ii) The 1-D study yields biased parameters due to unrepresented lateral flow. (iii) Representing and estimating sensor positions as well as small-scale heterogeneity decreased the mean absolute error of the volumetric water content data by more than a factor of 2 to 0.004.

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Section: Introductionmentioning

confidence: 99%

Effect of unrepresented model errors on estimated soil hydraulic material properties

Jaumann¹,

Roth²

2017

Hydrol. Earth Syst. Sci.

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“…This method has several advantages, one of which is that it avoids making strong and sometimes unjustified assumptions about the properties of the residual errors. In practice, however, and because of computational constraints, at least some parametric (Gaussian) assumptions often need to be made about p djh ð Þ a priori [e.g., Murakami et al, 2010;Over et al, 2015]. Another feature of MAD is that it uses basic Monte Carlo simulation to solve for the posterior parameter distribution.…”

Section: Comparison Against the Methods Of Anchored Distributionsmentioning

confidence: 99%

“…This is not very efficient, especially if the posterior distribution constitutes only a small part of the prior distribution. Hence, even with the assumption of a Gaussian distribution for p djh ð Þ, the total number of forward model evaluations required by MAD will typically be on the order of several millions [e.g., Murakami et al, 2010;Over et al, 2015]. This requires the use of many processors on a distributed computing network [on the order of several thousands, e.g., Murakami et al, 2010].…”

Section: Comparison Against the Methods Of Anchored Distributionsmentioning

confidence: 99%

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Laloy

Linde

Jacques

et al. 2015

Water Resources Research

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We present a Bayesian inversion method for the joint inference of high-dimensional multiGaussian hydraulic conductivity fields and associated geostatistical parameters from indirect hydrological data. We combine Gaussian process generation via circulant embedding to decouple the variogram from grid cell specific values, with dimensionality reduction by interpolation to enable Markov chain Monte Carlo (MCMC) simulation. Using the Matern variogram model, this formulation allows inferring the conductivity values simultaneously with the field smoothness (also called Matern shape parameter) and other geostatistical parameters such as the mean, sill, integral scales and anisotropy direction(s) and ratio(s). The proposed dimensionality reduction method systematically honors the underlying variogram and is demonstrated to achieve better performance than the Karhunen-Loè ve expansion. We illustrate our inversion approach using synthetic (error corrupted) data from a tracer experiment in a fairly heterogeneous 10,000-dimensional 2-D conductivity field. A 40-times reduction of the size of the parameter space did not prevent the posterior simulations to appropriately fit the measurement data and the posterior parameter distributions to include the true geostatistical parameter values. Overall, the posterior field realizations covered a wide range of geostatistical models, questioning the common practice of assuming a fixed variogram prior to inference of the hydraulic conductivity values. Our method is shown to be more efficient than sequential Gibbs sampling (SGS) for the considered case study, particularly when implemented on a distributed computing cluster. It is also found to outperform the method of anchored distributions (MAD) for the same computational budget.

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“…As a result, several studies used field soil water content data from different depths for inverse parameter estimations of single 10 domain models (Le Bourgeois et al, 2016;Over et al, 2015;Schelle et al, 2013;Scharnagl et al, 2011;Wollschläger et al, 2009;Ritter et al, 2003). Remote sensing data were also widely used to retrieve soil hydraulic parameters as has been reviewed by Mohanty (2013).…”

mentioning

confidence: 99%

“…Over et al, 2015;Scharnagl et al, 2011;Wollschläger et al, 2009), and could not be avoided in the mesocosms as well, since more extreme soil moisture conditions 5 could have damaged the grasses. If a sufficiently long time series is available an estimate of the effective residual water content may be obtained by using the lowest measured value.…”

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confidence: 99%

Modeling macropore seepage fluxes from soil water content time series by inversion of a dual permeability model

Valle

Potthast

Meyer

et al. 2017

Preprint

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Abstract. Dual permeability models are widely used to simulate water fluxes and solute transport in structured soils. However, so far obtaining necessary data for model calibration is a problem due to the large set of unconstrained parameters. Therefore, this study presents a simplified 1D dual permeability model whose structure is similar to the MACRO model together with a calibration scheme that allows constraining the parameters using time series of soil water content. The inversion scheme consists of four consecutive steps: First, the parameters of three different water retention functions were assessed using vertical 5 soil water content profiles assuming hydraulic equilibrium. Second, the soil sorptivity and diffusivity functions were estimated from Boltzmann-transformed soil water content data of a drying period. Third, the parameters governing macropore flow were determined using the most dynamic part of the soil water content time series during the first 12 h after a precipitation event.The model was calibrated using data of artificial, homogeneous and shallow soils from mesocosms. The resulting retention functions predicted similar values as pedotransfer functions apart from for very dry conditions. The predicted soil water content 10 time series were in good agreement with measurements at 5 and 12 cm soil depth. Predicted macropore seepage fluxes exhibited high uncertainty and differed between water retention functions, but average predictions were close to measurements for two of the three water retention functions.The study demonstrates the feasibility of calibrating a 1D dual permeability model with soil water content time series.

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Bayesian inversion of Mualem‐van Genuchten parameters in a multilayer soil profile: A data‐driven, assumption‐free likelihood function

Cited by 11 publications

References 66 publications

Effect of unrepresented model errors on estimated soil hydraulic material properties

Effect of unrepresented model errors on estimated soil hydraulic material properties

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Modeling macropore seepage fluxes from soil water content time series by inversion of a dual permeability model

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