On uncertainty quantification in hydrogeology and hydrogeophysics

Linde, Niklas; Ginsbourger, David; Irving, James; Nobile, Fabio; Doucet, Arnaud

doi:10.1016/j.advwatres.2017.10.014

Cited by 103 publications

(100 citation statements)

References 169 publications

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“…In doing so, we always keep the error of the RB 1 order of magnitude smaller than the above uncertainty (more details in section ). We acknowledge that other strategies to account for modeling uncertainties in Bayesian inversions could also be considered (see Linde et al, , for a review), for instance, via a full covariance matrix defining model errors (see also a discussion in Afonso, Fullea, Griffin, et al, , and Afonso, Fullea, Yang, et al, ). Another option could be to assign priors to these errors and let them be modeled as part of a hierarchical Bayesian inversion (Malinverno & Briggs, ; Titus et al, ).…”

Section: Preliminary Numerical Considerationsmentioning

confidence: 99%

Fast Stokes Flow Simulations for Geophysical‐Geodynamic Inverse Problems and Sensitivity Analyses Based On Reduced Order Modeling

et al. 2020

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Markov chain Monte Carlo (MCMC) methods have become standard in Bayesian inference and multi‐observable inversions in almost every discipline of the Earth sciences. In the case of geodynamic and/or coupled geophysical‐geodynamic inverse problems, however, the computational cost associated with the solution of large‐scale 3‐D Stokes forward problems has rendered probabilistic formulations impractical. Here we present a novel and extremely efficient method to produce ultrafast solutions of the 3‐D Stokes problem for MCMC simulations. Our approach combines the individual benefits of Reduced Basis techniques, goal‐oriented error formulations, and MCMC algorithms to produce an accurate and computationally efficient surrogate for the forward problem. Importantly, the surrogate adapts itself during the MCMC simulation according to the history of the chain and the goals of the inversion. This maximizes the efficiency of the forward problem and removes the need for preinversion off‐line computations to build a surrogate. We demonstrate the benefits and limitations of the method with several numerical examples and show that in all cases the computational cost is of the order of <1% compared to a traditional MCMC approach. The method is general enough to be applied to a range of problems, including uncertainty quantification/propagation, adjoint‐based geodynamic inversions, sensitivity analyses in mantle convection problems, and in the creating surrogate models for complex forward problems (e.g., heat transfer, seismic tomography, and magnetotellurics).

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Section: Preliminary Numerical Considerationsmentioning

confidence: 99%

Fast Stokes Flow Simulations for Geophysical‐Geodynamic Inverse Problems and Sensitivity Analyses Based On Reduced Order Modeling

et al. 2020

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“…This vector was estimated using a Bayesian inversion to obtain the joint posterior probability distribution functions (jpdfs). These functions were evaluated using the DREAM (ZS) [46] MCMC sampler, which was largely used in sub-surface hydrology e.g., [9,15,16,[46][47][48]. DREAM (ZS) generates random parameter set sequences which converge asymptotically to the target solution [49].…”

Section: Bayesian Parameter Inferencementioning

confidence: 99%

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

Younès

Shao

Mara

et al. 2020

Water

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Accurate simulation of flow and contaminant transport processes through unsaturated soils requires adequate knowledge of the soil parameters. This study deals with the hydraulic characterization of soils using laboratory experiments. A new strategy is developed by combining global sensitivity analysis (GSA) and Bayesian data-worth analysis (DWA) to obtain efficient data that ensure a good estimation of the soil properties. The strategy is applied for the estimation of soil properties from a laboratory infiltration experiment. Results of this study show that GSA allows identification of regions and periods of high sensitivity of each parameter and thereby, the observations prone to contain information for a successful calibration. Further, the sensitivity depicts a nonlinear behavior with regions of high influence and regions of weak influence inside the parameter space. Bayesian DWA, performed a priori, allows to quantify the improvement of the posterior uncertainty of the estimated parameters when adding a type of measurement. The results reveal that an accurate estimation of the soil properties can be obtained if the target parameter values are located in the regions of high influence in the parameter space.Water 2020, 12, 736 2 of 15 and evaporation experiments [13], unsaturated transport experiments [14][15][16][17], and hydrogeophysical experiments [18,19].Laboratory experiments are often time consuming, expensive, and tricky because of the risk of non-identifiability of the accepted parameters which depends on the measured data. Global sensitivity analysis (GSA) has been employed by Younes et al., [7] to help assess unsaturated soil hydraulic parameters. The GSA evaluates how output uncertainties are related to input parameter uncertainties with all the variation of inputs. In the last decades, GSA has been largely used for unsaturated flow in porous media. For instance, in Pan et al. [20], GSA has been conducted to assess the relative contribution of parameter uncertainties to the flow and transport uncertainties in a layered heterogeneous system. Brunetti et al. [21] used GSA to investigate the influence of soil hydraulic parameters on the behavior of a permeable pavement. Younes et al. [19] used GSA to investigate the influence of hydraulic and geophysical parameters on the streaming potential signals. In van Griensven et al. [22], GSA has been used to reduce the number of parameters and thus reduce over-parametrization of the numerical model.GSA allows to quantify the impact changes of parameters have on the model output. By this way, GSA enables the detection of the important parameters, their regions, and periods of influence [23]. This can facilitate the experimental procedure by identifying strategic measurements that could be relevant for soil characterization. However, collecting new output observations even when the output is highly sensitive to the parameters may not reduce parameter uncertainties if the information contained in the new observations are already contained in the previous observat...

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“…In the following, the pdfs are inferred using DREAM (ZS) software [39] based on the Markov chain Monte Carlo (MCMC) method. The MCMC method has been used by several authors in hydrogeology, e.g., [11,[40][41][42][43][44]. With MCMC, random sequences of parameter sets are generated and converge asymptotically toward the target distribution [45].…”

Section: Bayesian Parameter Inferencementioning

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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On uncertainty quantification in hydrogeology and hydrogeophysics

Cited by 103 publications

References 169 publications

Fast Stokes Flow Simulations for Geophysical‐Geodynamic Inverse Problems and Sensitivity Analyses Based On Reduced Order Modeling

Fast Stokes Flow Simulations for Geophysical‐Geodynamic Inverse Problems and Sensitivity Analyses Based On Reduced Order Modeling

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

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

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