An in-depth analysis of Markov-Chain Monte Carlo ensemble samplers for inverse vadose zone modeling

Brunetti, Giuseppe; Šimůnek, Jiřı́; Wöhling, Thomas; Stumpp, Christine

doi:10.1016/j.jhydrol.2023.129822

Cited by 5 publications

(4 citation statements)

References 55 publications

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“…MCMC chains typically exhibit a transition period where the samples approach the posterior distribution. The samples of this transition period are discarded as burn-in (Gallagher et al, 2009;Brunetti et al, 2023). GLUE and MLGLUE both result in independent posterior samples, while MCMC and MLDA result in correlated posterior samples.…”

Section: Resultsmentioning

confidence: 99%

“…Various approaches to UQ have been developed and applied in that respect; the Bayesian approach to statistical inversion and UQ, however, is especially popular due to the ability to comprehensively treat uncertainties in state variables, parameters, and model output (Montanari, 2007;Vrugt, 2016;Linde et al, 2017;Page et al, 2023). Gen-eralized Likelihood Uncertainty Estimation (GLUE) (Beven & Binley, 1992Mirzaei et al, 2015) -as an informal Bayesian approach -and Markov-chain Monte Carlo sampling (MCMC) (Gallagher et al, 2009;Vrugt, 2016;Dodwell et al, 2019;Brunetti et al, 2023; -as a formal Bayesian approach -are frequently applied in the environmental sciences for statistical inversion. The Bayesian framework considers model parameters to be random variables that are associated with a prior distribution, which is conditioned on system state observations using a likelihood function to form a posterior distribution.…”

Section: Introductionmentioning

confidence: 99%

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Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

Rudolph,

Wöhling,

Wagener

et al. 2023

Preprint

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Inverse problems are ubiquitous in hydrological modelling for parameter estimation, system understanding, sustainable water resources management, and the operation of digital twins. While statistical inversion is especially popular, its sampling-based nature often inhibits the inversion of computationally costly models, which has compromised the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, e.g., for spatially distributed (partial) differential equation based models. In this study we introduce multilevel GLUE (MLGLUE), which alleviates the computational burden of statistical inversion by utilizing a hierarchy of model resolutions. Inspired by multilevel Monte Carlo, most parameter samples are evaluated on lower levels with computationally cheap low-resolution models and only samples associated with a likelihood above a certain threshold are subsequently passed to higher levels with costly high-resolution models for evaluation. Inferences are made at the level of the highest-resolution model but substantial computational savings are achieved by discarding samples with low likelihood already on levels with low resolution and low computational cost. Two test problems demonstrate the similarity of inferred parameter posteriors and uncertainty estimates of MLGLUE and GLUE as well as increased computational efficiency. Findings are furthermore compared to inversion results from Markov-chain Monte Carlo (MCMC) and from multilevel delayed acceptance MCMC. The computation time of inversion of a groundwater flow model was decreases by ≈45% and ≈57% when using MLGLUE instead of conventional formulations of GLUE and MCMC, respectively.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

Rudolph,

Wöhling,

Wagener

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Similarly, HYDRUS has been coupled externally with Bayesian inference algorithms for calibration and uncertainty assessment purposes (e.g., Brunetti, Šimůnek, et al, 2020;Guo et al, 2020;Schübl et al, 2022;Vrugt et al, 2008;Wöhling & Vrugt, 2011). In this perspective, Brunetti et al (2023) recently compared Markov chain Monte Carlo ensemble samplers for vadose zone inverse modeling, highlighting the advantages and limitations of using these algorithms in conjunction with HYDRUS. Samplers have been embedded into the HYDRUS source code, thus making it possible to incorporate them in the HYDRUS software package.…”

Section: Inverse Problemsmentioning

confidence: 99%

Developments and applications of the HYDRUS computer software packages since 2016

Šimůnek,

Brunetti,

Jacques

et al. 2024

Vadose Zone Journal

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The HYDRUS codes have become standard tools for addressing many soil, agricultural, environmental, and hydrological problems requiring the evaluation of various subsurface physical, chemical, and biological processes. There are now many thousands of HYDRUS users worldwide, with thousands of applications of the HYDRUS models appearing in the peer‐reviewed literature. In this manuscript, we provide an overview of the capabilities of the most recent Version 5 of HYDRUS, focusing primarily on features implemented since 2016. We briefly describe the standard HYDRUS model and its standard and nonstandard specialized add‐on modules that significantly expand the capabilities of the software packages. The standard add‐on modules include HPx, UNSATCHEM, Wetland, Furrow, PFAS, COSMIC, DPU, SLOPE Cube, and Particle Tracking. Recent developments of the HYDRUS Package for MODFLOW are also described, along with additional capabilities incorporated into the graphical user interface supporting HYDRUS. Also discussed are new or improved options to simulate the fate and transport of environmental isotopes, multi‐cropping systems, compensated root water uptake, and hydraulic redistribution within the rootzone, which will be implemented in upcoming add‐on modules. Another objective is to review selected applications of the HYDRUS models, such as evaluations of various irrigation, low‐impact development (LID), and managed aquifer recharge (MAR) schemes.

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“…Various approaches to UQ have been developed and applied in that respect; the Bayesian approach to statistical inversion and UQ, however, is especially popular due to the ability to comprehensively treat uncertainties in state variables, parameters, and model output (Montanari, 2007;Vrugt, 2016;Linde et al, 2017;Page et al, 2023). Generalized Likelihood Uncertainty Estimation (GLUE) (Beven & Binley, 1992 -as an informal Bayesian approach -and Markov-chain Monte Carlo sampling (MCMC) (Gallagher et al, 2009;Vrugt, 2016;Dodwell et al, 2019;Brunetti et al, 2023;Lykkegaard et al, 2023;Cui et al, 2024) -as a formal Bayesian approach -are frequently applied in the environmental sciences for statistical inversion. The Bayesian framework considers model parameters to be random variables that are associated with prior distributions, which are conditioned on system state observations using a likelihood function to posterior distributions.…”

Section: Introductionmentioning

confidence: 99%

Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

Rudolph,

Wöhling,

Wagener

et al. 2024

Preprint

View full text Add to dashboard Cite

Inverse problems are ubiquitous in hydrological modelling for parameter estimation, system understanding, sustainable water resources management, and the operation of digital twins. While statistical inversion is especially popular, its sampling-based nature often inhibits its application to computationally costly models, which has compromised the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, e.g., for spatially distributed (partial) differential equation based models. In this study we introduce multilevel GLUE (MLGLUE), which alleviates the computational burden of statistical inversion by utilizing a hierarchy of model resolutions. Inspired by multilevel Monte Carlo, most parameter samples are evaluated on lower levels with computationally cheap low-resolution models and only samples associated with a likelihood above a certain threshold are subsequently passed to higher levels with costly high-resolution models for evaluation. Inferences are made at the level of the highest-resolution model but substantial computational savings are achieved by discarding samples with low likelihood already on levels with low resolution and low computational cost. Two example inverse problems, using a rainfall-runoff model and groundwater flow model, demonstrate the substantially increased computational efficiency of MLGLUE compared to GLUE as well as the similarity of inversion results. Findings are furthermore compared to inversion results from Markov-chain Monte Carlo (MCMC) and multilevel delayed acceptance MCMC, a corresponding multilevel variant, to compare the effects of the multilevel extension. All examples demonstrate the wide-range suitability of the approach and include guidelines for practical applications.

show abstract

An in-depth analysis of Markov-Chain Monte Carlo ensemble samplers for inverse vadose zone modeling

Cited by 5 publications

References 55 publications

Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

Developments and applications of the HYDRUS computer software packages since 2016

Extending GLUE with Multilevel Methods to Accelerate Statistical Inversion of Hydrological Models

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