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# Combined Estimation of Hydrogeologic Conceptual Model and Parameter Uncertainty (NUREG/CR-6843, PNNL-14534)

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## Publication Information

**Manuscript Completed:** October 2003**Date Published:** March 2004

**Prepared by:** P.D. Meyer, M. Ye, K.J. Cantrell Pacific Northwest National Laboratory (Primary Contractor) P.O. Box 999 Richland, Washington 99352 

S.P. Neuman Department of Hydrology and Water Resources University of Arizona (Subcontractor) Tucson, Arizona 85721

T.J. Nicholson, NRC Project Manager

**Prepared for:** Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001

NRC Job Code Y6465

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## Abstract

The objective of the research described in this report is the development and application of a methodology for comprehensively assessing the hydrogeologic uncertainties involved in dose assessment, including uncertainties associated with conceptual models, parameters, and scenarios. This report describes and applies a statistical method, Maximum Likelihood Bayesian Model Averaging (MLBMA), to quantitatively estimate the combined uncertainty in model predictions arising from conceptual model and parameter uncertainties. The method relies on model averaging to combine the predictions of a set of alternative models. Implementation is driven by the available data. When there is minimal site-specific data the method can be carried out with prior parameter estimates based on generic data and subjective prior model probabilities. For sites with observations of system behavior (and optionally data characterizing model parameters), the method uses model calibration to update the prior parameter estimates and model probabilities based on the correspondence between model predictions and site observations. The set of model alternatives can contain both simplified and complex models, with the requirement that all models be based on the same set of data.

MLBMA was applied to the geostatistical modeling of air permeability at a fractured rock site. Seven alternative variogram models of log air permeability were considered to represent data from single-hole pneumatic injection tests in six boreholes at the site. Unbiased maximum likelihood estimates of variogram and drift parameters were obtained for each model. Standard information criteria provided an ambiguous ranking of the models, which would not justify selecting one of them and discarding all others as is commonly done in practice. Instead, some of the models were eliminated based on their negligibly small updated probabilities and the rest were used to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. These four projections, and associated kriging variances, were averaged using the posterior model probabilities as weights. Finally, cross-validation was conducted by eliminating from consideration all data from one borehole at a time, repeating the above process, and comparing the predictive capability of the model-averaged result with that of each individual model. Using two quantitative measures of comparison, the model-averaged result was superior to any individual geostatistical model of log permeability considered.

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