A Model‐Averaging Method for Assessing Groundwater Conceptual Model Uncertainty

Ye, Ming; Pohlmann, K.; Chapman, Jenny; Pohll, Greg; Reeves, Donald M.

doi:10.1111/j.1745-6584.2009.00633.x

Cited by 118 publications

(89 citation statements)

References 43 publications

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“…The observation uncertainty stems from a very wide range, including the error caused by the stochastic distribution of the observed variable, the sampling error of the observed variable, indirect measurement error, the error of measuring device, and human recording error, etc. In addition, some authors regarded the uncertainty of model boundary conditions as the fourth uncertainty which is referred as scenario uncertainty [23,24].…”

Section: Sources and Classifications Of The Uncertainty Of Groundwatementioning

confidence: 99%

Review of the uncertainty analysis of groundwater numerical simulation

Zeng

2013

Chin. Sci. Bull.

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Groundwater system is a complex and open system, which is affected by natural conditions and human activities. Natural hydrological processes is conceptualized through relatively simple flow governing equations in groundwater models. Moreover, observation data is always limited in field hydrogeological conditions. Therefore, the predictive results of groundwater simulation often deviate from true values, which is attribute to the uncertainty of groundwater numerical simulation. According to the process of system simulation, the uncertainty sources of groundwater numerical simulation can be divided into model parameters, conceptual model and observation data uncertainties. In addition, the uncertainty stemmed from boundary conditions is sometimes refered as scenario uncertainty. In this paper, the origination and category of groundwater modeling uncertainty are analyzed. The recent progresses on the methods of groundwater modeling uncertainty analysis are reivewed. Furthermore, the researches on the comprehensive analysis of uncertainty sources, and the predictive uncertainty of model outputs are discussed. Finally, several prospects on the deveolpment of groundwater modeling uncetainty analysis are proposed.groundwater modeling, uncertainty analysis, model parameter, conceptual model, observation data Citation:

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Section: Sources and Classifications Of The Uncertainty Of Groundwatementioning

confidence: 99%

Review of the uncertainty analysis of groundwater numerical simulation

Zeng

2013

Chin. Sci. Bull.

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“…In the field of hydrology, metrics such as Akaike's information criterion (AIC) ( Akaike, 1973 ), BIC, and Kashyap's information criterion (KIC) ( Kashyap, 1982 ) are used widely to select the most adequate model ( Li and Tsai, 2009;Marshall et al, 2005;Tsai and Li, 2008;Ye et al, 2010 ). A recent study by Schöniger et al (2014) elucidates that AIC and BIC do a rather poor job in ranking hydrologic models.…”

Section: Introductionmentioning

confidence: 99%

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Brunetti

Linde

Vrugt

2017

Advances in Water Resources

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a b s t r a c tGeophysical data can help to discriminate among multiple competing subsurface hypotheses (conceptual models). Here, we explore the merits of Bayesian model selection in hydrogeophysics using crosshole ground-penetrating radar data from the South Oyster Bacterial Transport Site in Virginia, USA. Implementation of Bayesian model selection requires computation of the marginal likelihood of the measured data, or evidence, for each conceptual model being used. In this paper, we compare three different evidence estimators, including (1) the brute force Monte Carlo method, (2) the Laplace-Metropolis method, and (3) the numerical integration method proposed by Volpi et al. (2016). The three types of subsurface models that we consider differ in their treatment of the porosity distribution and use (a) horizontal layering with fixed layer thicknesses, (b) vertical layering with fixed layer thicknesses and (c) a multi-Gaussian field. Our results demonstrate that all three estimators provide equivalent results in low parameter dimensions, yet in higher dimensions the brute force Monte Carlo method is inefficient. The isotropic multi-Gaussian model is most supported by the travel time data with Bayes factors that are larger than 10 100 compared to conceptual models that assume horizontal or vertical layering of the porosity field.

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“…Model average (MA) can then be calculated by weighting each model through its posterior probability (Ye et al, 2010). The skill of each model and of MA results to interpret the observed data is compared through the following two metrics, i.e., the Normalized Mahalanobis Distance, NMD (Winter 2010 and references therein), and the traditional Mean Square Error,…”

Section: Maximum Likelihood Parameter Estimation and Model Quality Crmentioning

confidence: 99%

Interpretation of two-phase relative permeability curves through multiple formulations and Model Quality criteria

Moghadasi

Guadagnini

Inzoli

et al. 2015

Journal of Petroleum Science and Engineering

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We illustrate the way formal model identification criteria can be employed to rank and evaluate a set of alternative models in the context of the interpretation of laboratory scale experiments yielding two-phase relative permeability curves. We consider a set of empirical twophase relative permeability models (i.e., Corey, Chierici and LET) which are typically employed in industrial applications requiring water/oil relative permeability quantifications. Model uncertainty is quantified through the use of a set of model weights which are rendered by model posterior probabilities conditional on observations. These weights are then employed to (a) rank the models according to their relative skill to interpret the observations and (b) obtain model averaged results which allow accommodating within a unified theoretical framework uncertainties arising from differences amongst model structures. As a test bed for our study, we employ high quality two-phase relative permeability estimates resulting from steady-state imbibition experiments on two diverse porous media, a quartz Sand-pack and a Berea sandstone core, together with additional published datasets. The parameters of each model are estimated within a Maximum Likelihood framework. Our results highlight that in most cases the complexity of the problem appears to justify favoring a model with a high number of uncertain parameters over a simpler model structure. Posterior probabilities reveal that in several cases, most notably for the assessment of oil relative permeabilities, the weights associated with the simplest models is not negligible. This suggests that in these cases uncertainty quantification might benefit from a multi-model analysis, including both low-and high-complexity models. In most of the cases analyzed we find that model averaging leads to interpretations of the available data which are characterized by a higher degree of fidelity than that provided by the most skillful model.

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A Model‐Averaging Method for Assessing Groundwater Conceptual Model Uncertainty

Cited by 118 publications

References 43 publications

Review of the uncertainty analysis of groundwater numerical simulation

Review of the uncertainty analysis of groundwater numerical simulation

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Interpretation of two-phase relative permeability curves through multiple formulations and Model Quality criteria

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