Bayesian Uncertainty Quantification in Groundwater Modeling

Bayesian uncertainty quantification has emerged as a robust framework for assessing and communicating the confidence in predictions made by groundwater models. By treating model parameters, inputs and even structural choices as random variables, the Bayesian approach updates prior beliefs with observational data to yield posterior distributions that capture all sources of uncertainty. This holistic quantification spans parameter uncertainty, arising from limited or noisy measurements; structural uncertainty, linked to the choice of equations and processes represented; and conceptual uncertainty, reflecting competing hypotheses about subsurface architecture. Computational advances—including Markov Chain Monte Carlo algorithms, adaptive ensemble samplers, nested sampling and surrogate‐model surrogates—have reduced the formidable cost of sampling high‐dimensional posteriors. The resulting probabilistic predictions underpin more informed decision making, from evaluating aquifer recharge rates and contaminant transport to optimising pumping strategies under climate variability. Concrete examples range from quantifying the risk of saltwater intrusion in coastal aquifers to delineating protection zones around public supply wells. By integrating diverse data streams—hydraulic heads, tracer tests, remote-sensing observations—into a coherent inferential framework, Bayesian methods offer transparent, reproducible and actionable insights that directly inform groundwater management at regional and basin scales.

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Bayesian Uncertainty Quantification in Groundwater Modeling publication trend

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Technical terms

Prior distribution: A probabilistic representation of parameter or model uncertainties before accounting for new data.

Likelihood function: A mathematical expression of how probable the observed data are for each parameter configuration.

Posterior distribution: The updated probability distribution of parameters or models after combining the prior with the likelihood.

Markov Chain Monte Carlo (MCMC): A family of algorithms that generate correlated samples from complex posterior distributions.

Bayesian model averaging: A technique that weights multiple models by their posterior probabilities to capture structural uncertainty.

Conceptual uncertainty: Uncertainty arising from competing hypotheses about subsurface structure or process representation.

References

1. Uncertainty-based saltwater intrusion prediction using integrated Bayesian machine learning modeling (IBMLM) in a deep aquifer. Journal of Environmental Management (2024).
2. An in-depth analysis of Markov-Chain Monte Carlo ensemble samplers for inverse vadose zone modeling. Journal of Hydrology (2023).
3. Uncertainty assessment of aquifer hydraulic parameters from pumping test data. Applied Water Science (2024).