Finding the right balance between groundwater model complexity and experimental effort via Bayesian model selection

Schöniger, Anneli; Illman, Walter A.; Wöhling, Thomas; Nowak, Wolfgang

doi:10.1016/j.jhydrol.2015.07.047

Cited by 44 publications

(133 citation statements)

References 62 publications

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“…The results presented in Section 4 are consistent with what is presented in other groundwater modelling studies (e.g., [11,12,15,[59][60][61]), in that we have obtained posterior model probabilities and a probability distribution of predictions including both parameter and conceptual uncertainty. However, the methods with which these model results have been obtained, differ.…”

Section: Discussionsupporting

confidence: 90%

Hydrogeological Bayesian Hypothesis Testing through Trans-Dimensional Sampling of a Stochastic Water Balance Model

Enemark

Peeters

Mallants

et al. 2019

Water

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Conceptual uncertainty is considered one of the major sources of uncertainty in groundwater flow modelling. In this regard, hypothesis testing is essential to increase system understanding by refuting alternative conceptual models. Often a stepwise approach, with respect to complexity, is promoted but hypothesis testing of simple groundwater models is rarely applied. We present an approach to model-based Bayesian hypothesis testing in a simple groundwater balance model, which involves optimization of a model in function of both parameter values and conceptual model through trans-dimensional sampling. We apply the methodology to the Wildman River area, Northern Territory, Australia, where we set up 32 different conceptual models. A factorial approach to conceptual model development allows for direct attribution of differences in performance to individual uncertain components of the conceptual model. The method provides a screening tool for prioritizing research efforts while also giving more confidence to the predicted water balance compared to a deterministic water balance solution. We show that the testing of alternative conceptual models can be done efficiently with a simple additive and linear groundwater balance model and is best done relatively early in the groundwater modelling workflow.One branch of hypothesis testing is based on the Bayesian probability theory. In Bayesian hypothesis testing, a prior belief about the suitability of a conceptual model is updated to a posterior belief by evaluating the model performance against data. The performance of alternative models are then compared in order to quantitatively rank and potentially reject hypotheses based on the so-called Bayes factor [9,10]. Fields of application in hydrogeology include groundwater modelling [11,12], hydrogeophysics [13,14] and solute transport modelling [15,16]. In many applications, the data is not sufficient to allow for discrimination between the models, in which case Bayesian model averaging is often applied where model predictions are weighed according to their performance against data [17].In hydrogeology, conceptual models are often tested in mathematical models (e.g., [18,19]). Since a model comprises the description of a system as a whole, all assumptions and the interaction of assumptions are tested at once. Also, data that does not directly relate to the conceptually uncertain feature can be integrated because of the holistic testing of the system.A stepwise approach in regards to the complexity of groundwater flow modelling and hypothesis testing is often promoted [20,21]. In this paper the simplicity of a model is defined in terms of setup and run-time. In a stepwise approach, complexity is gradually built up, and involves testing the models in each step to better understand the relative importance of various assumptions. This is opposed to starting with a complex model where all known processes and structural aspects are incorporated "because they exist, not because they matter" [20].Although there seems to be a consensu...

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Section: Discussionsupporting

confidence: 90%

Hydrogeological Bayesian Hypothesis Testing through Trans-Dimensional Sampling of a Stochastic Water Balance Model

Enemark

Peeters

Mallants

et al. 2019

Water

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“…Additionally, the linear model tends to be preferred over the more complex (i.e., with one additional parameter) Freundlich model (when the Langmuir model receives a weight of zero, right edge). This is due to the implicit characteristic of BMS to prefer simpler models under limited data set sizes if differences in performance are reasonably small (e.g., [87]). ] (right axis) plotted over the experimental duration from T = 0 to T = 120 days.…”

Section: Resultsmentioning

confidence: 99%

“…This optimum state is also shown by the green circles in the ternary plot in Figure 1b The data worth for model choice can be further investigated by asking: how well can a model recognize itself if it had actually generated the data? We refer to this as the self-identification probability (see also Schöniger et al [87]). The models' self-identification probability is shown as a function of experimental duration in Figure 7b.…”

Section: Resultsmentioning

confidence: 99%

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Entropy-Based Experimental Design for Optimal Model Discrimination in the Geosciences

Nowak

Guthke

2016

Entropy

Self Cite

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Abstract:Choosing between competing models lies at the heart of scientific work, and is a frequent motivation for experimentation. Optimal experimental design (OD) methods maximize the benefit of experiments towards a specified goal. We advance and demonstrate an OD approach to maximize the information gained towards model selection. We make use of so-called model choice indicators, which are random variables with an expected value equal to Bayesian model weights. Their uncertainty can be measured with Shannon entropy. Since the experimental data are still random variables in the planning phase of an experiment, we use mutual information (the expected reduction in Shannon entropy) to quantify the information gained from a proposed experimental design. For implementation, we use the Preposterior Data Impact Assessor framework (PreDIA), because it is free of the lower-order approximations of mutual information often found in the geosciences. In comparison to other studies in statistics, our framework is not restricted to sequential design or to discrete-valued data, and it can handle measurement errors. As an application example, we optimize an experiment about the transport of contaminants in clay, featuring the problem of choosing between competing isotherms to describe sorption. We compare the results of optimizing towards maximum model discrimination with an alternative OD approach that minimizes the overall predictive uncertainty under model choice uncertainty.

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“…A number of remediation techniques have been developed to remove dissolved hazardous materials from the groundwater to guarantee the health of the groundwater system and human beings (Boyce et al 2015;Nemecek et al 2015;Maire et al 2015;Paleologos et al 2015). Nevertheless, remediation of contaminated groundwater is costly and timeconsuming compared to that of surface waters (Careghini et al 2015;Schoniger et al 2015;Joodavi et al 2015). To minimize the remediation cost and duration, integrated simulation and optimization approaches have been widely used to assist in developing optimal groundwater remediation management strategies.…”

Section: Introductionmentioning

confidence: 99%

A bilevel groundwater management model with minimization of stochastic health risks at the leader level and remediation cost at the follower level

Chen

et al. 2016

Stoch Environ Res Risk Assess

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Traditional single-objective programs cannot deal with the tradeoffs between the decision makers who represent different perspectives and have inconsistent decision goals. Multi-objective ones can hardly represent a complex dominant-subordinate relationship between the leader and the follower. This study presents a new bilevel programming model with considering leader-follower-related health-risk and economic goals for optimal groundwater remediation management. The bilevel model is formulated by integrating health-risk assessment and environmental standards (the leader or the environmental concern) and remediation cost (the follower or the economic concern) into a general framework. In addition, stochastic uncertainty in health risk assessment is considered into the decision-making process. The developed bilevel model is then applied to a petroleum-contaminated aquifer in Canada. Results indicate that the performance of bilevel programming can not only meet the low remediation cost as the expectation from the follower but also simultaneously conform to the low contamination level as the expectation from the leader. Furthermore, comparative analyses show that the bilevel model with two-level concerns has the advantage of maximizing the interests and satisfaction degrees of decision makers, which can avoid the extreme results generated from the single-level models.

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Finding the right balance between groundwater model complexity and experimental effort via Bayesian model selection

Cited by 44 publications

References 62 publications

Hydrogeological Bayesian Hypothesis Testing through Trans-Dimensional Sampling of a Stochastic Water Balance Model

Hydrogeological Bayesian Hypothesis Testing through Trans-Dimensional Sampling of a Stochastic Water Balance Model

Entropy-Based Experimental Design for Optimal Model Discrimination in the Geosciences

A bilevel groundwater management model with minimization of stochastic health risks at the leader level and remediation cost at the follower level

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