This study evaluates alternative groundwater models with different recharge and geologic components at the northern Yucca Flat area of the Death Valley Regional Flow System (DVRFS), USA. Recharge over the DVRFS has been estimated using five methods, and five geological interpretations are available at the northern Yucca Flat area. Combining the recharge and geological components together with additional modeling components that represent other hydrogeological conditions yields a total of 25 groundwater flow models. As all the models are plausible given available data and information, evaluating model uncertainty becomes inevitable. On the other hand, hydraulic parameters (e.g., hydraulic conductivity) are uncertain in each model, giving rise to parametric uncertainty. Propagation of the uncertainty in the models and model parameters through groundwater modeling causes predictive uncertainty in model predictions (e.g., hydraulic head and flow). Parametric uncertainty within each model is assessed using Monte Carlo simulation, and model uncertainty is evaluated using the model averaging method. Two model-averaging techniques (on the basis of information criteria and GLUE) are discussed. This study shows that contribution of model uncertainty to predictive uncertainty is significantly larger than that of parametric uncertainty. For the recharge and geological components, uncertainty in the geological interpretations has more significant effect on model predictions than uncertainty in the recharge estimates. In addition, weighted residuals vary more for the different geological models than for different recharge models. Most of the calibrated observations are not important for discriminating between the alternative models, because their weighted residuals vary only slightly from one model to another.

[1] Previous application of maximum likelihood Bayesian model averaging (MLBMA, Neuman (2002) to alternative variogram models of log air permeability data in fractured tuff has demonstrated its effectiveness in quantifying conceptual model uncertainty and enhancing predictive capability (Ye et al., 2004). A question remained how best to ascribe prior probabilities to competing models. In this paper we examine the extent to which lead statistics of posterior log permeability predictions are sensitive to prior probabilities of seven corresponding variogram models. We then explore the feasibility of quantifying prior model probabilities by (1) maximizing Shannon's entropy H (Shannon, 1948) subject to constraints reflecting a single analyst's (or a group of analysts') prior perception about how plausible each alternative model (or a group of models) is relative to others, and (2) selecting a posteriori the most likely among such maxima corresponding to alternative prior perceptions of various analysts or groups of analysts. Another way to select among alternative prior model probability sets, which, however, is not guaranteed to yield optimum predictive performance (though it did so in our example) and would therefore not be our preferred option, is a minimum-maximum approach according to which one selects a priori the set corresponding to the smallest value of maximum entropy. Whereas maximizing H subject to the prior perception of a single analyst (or group) maximizes the potential for further information gain through conditioning, selecting the smallest among such maxima gives preference to the most informed prior perception among those of several analysts (or groups). We use the same variogram models and log permeability data as Ye et al. (2004) to demonstrate that our proposed approach yields the least amount of posterior entropy (residual uncertainty after conditioning) and enhances predictive model performance as compared to (1) the noninformative neutral case in which all prior model probabilities are set equal to each other and (2) an informed case that nevertheless violates the principle of parsimony.Citation: Ye, M., S. P. Neuman, P. D. Meyer, and K. Pohlmann (2005), Sensitivity analysis and assessment of prior model probabilities in MLBMA with application to unsaturated fractured tuff, Water Resour.

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Detailed numerical flow and radionuclide simulations are used to predict the flux of radionuclides from three underground nuclear tests located in the Climax granite stock on the Nevada Test Site. The numerical modeling approach consists of both a regional-scale and local-scale flow model. The regional-scale model incorporates conceptual model uncertainty through the inclusion of five models of hydrostratigraphy and five models describing recharge processes for a total of 25 hydrostratigraphic-recharge combinations. Uncertainty from each of the 25 models is propagated to the local-scale model through constant head boundary conditions that transfer hydraulic gradients and flow patterns from each of the model alternatives in the vicinity of the Climax stock, a fluid flux calibration target, and model weights that describe the plausibility of each conceptual model.The local-scale model utilizes an upscaled discrete fracture network methodology where fluid flow and radionuclides are restricted to an interconnected network of fracture zones mapped onto a continuum grid. Standard Monte Carlo techniques are used to generate 200 random fracture zone networks for each of the 25 conceptual models for a total of 5,000 local-scale flow and transport realizations. Parameters of the fracture zone networks are based on statistical analysis of site-specific fracture data, with the exclusion of fracture density, which was calibrated to match the amount of fluid flux simulated through the Climax stock by the regional-scale models. Radionuclide transport is simulated according to a random walk particle method that tracks particle trajectories through the fracture continuum flow fields according to advection, dispersion and diffusional mass exchange between fractures and matrix. The breakthrough of a conservative radionuclide with a long half-life is used to evaluate the influence of conceptual and parametric uncertainty on radionuclide mass flux estimates. The fluid flux calibration target was found to correlate with fracture density, and particle breakthroughs were generally found to increase with increases in fracture density. Boundary conditions extrapolated from the regional-scale model exerted a secondary influence on radionuclide breakthrough for models with equal fracture density. The incorporation of weights into radionuclide flux estimates resulted in both noise about the original (unweighted) mass flux curves and decreases in the variance and expected value of radionuclide mass flux.

Carroll, Rosemary W.H., Greg Pohll, David McGraw, Chris Garner, Anna Knust, Doug Boyle, Tim Minor, Scott Bassett, and Karl Pohlmann, 2010. Mason Valley Groundwater Model: Linking Surface Water and Groundwater in the Walker River Basin, Nevada. Journal of the American Water Resources Association (JAWRA) 46(3):554‐573. DOI: http://dx.doi.org/10.1111/j.1752-1688.2010.00434.x Abstract:  An integrated surface water and groundwater model of Mason Valley, Nevada is constructed to replicate the movement of water throughout the different components of the demand side of water resources in the Walker River system. The Mason Valley groundwater surface water model (MVGSM) couples the river/drain network with agricultural demand areas and the groundwater system using MODFLOW, MODFLOW’s streamflow routing package, as well as a surface water linking algorithm developed for the project. The MVGSM is capable of simulating complex feedback mechanisms between the groundwater and surface water system that is not dependent on linearity among the related variables. The spatial scale captures important hydrologic components while the monthly stress periods allow for seasonal evaluation. A simulation spanning an 11‐year record shows the methodology is robust under diverse climatic conditions. The basin‐wide modeling approach predicts a river system generally gaining during the summer irrigation period but losing during winter months and extended periods of drought. River losses to the groundwater system approach 25% of the river’s annual budget. Reducing diversions to hydrologic response units will increase river flows exiting the model domain, but also has the potential to increase losses from the river to groundwater storage.

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