[1] Hydrologic systems are open and complex, rendering them prone to multiple conceptualizations and mathematical descriptions. There has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to (1) rank these models, (2) eliminate some of them, and/or (3) weigh and average predictions and statistics generated by multiple models. This has led to some debate among hydrogeologists about the merits and demerits of common model selection (also known as model discrimination or information) criteria such as AIC, AICc, BIC, and KIC and some lack of clarity about the proper interpretation and mathematical representation of each criterion. We examine the model selection literature to find that (1) all published rigorous derivations of AIC and AICc require that the (true) model having generated the observational data be in the set of candidate models; (2) though BIC and KIC were originally derived by assuming that such a model is in the set, BIC has been rederived by Cavanaugh and Neath (1999) without the need for such an assumption; and (3) KIC reduces to BIC as the number of observations becomes large relative to the number of adjustable model parameters, implying that it likewise does not require the existence of a true model in the set of alternatives. We explain why KIC is the only criterion accounting validly for the likelihood of prior parameter estimates, elucidate the unique role that the Fisher information matrix plays in KIC, and demonstrate through an example that it imbues KIC with desirable model selection properties not shared by AIC, AICc, or BIC. Our example appears to provide the first comprehensive test of how AIC, AICc, BIC, and KIC weigh and rank alternative models in light of the models' predictive performance under cross validation with real hydrologic data.

[1] Hydrologic analyses typically rely on a single conceptual-mathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. Bayesian model averaging (BMA) [Hoeting et al., 1999] provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty. However, it tends to be computationally demanding and relies heavily on prior information about model parameters. Neuman [2002, 2003] proposed a maximum likelihood version (MLBMA) of BMA to render it computationally feasible and to allow dealing with cases where reliable prior information is lacking. We apply MLBMA to seven alternative variogram models of log air permeability data from single-hole pneumatic injection tests in six boreholes at the Apache Leap Research Site (ALRS) in central Arizona. Unbiased ML estimates of variogram and drift parameters are obtained using adjoint state maximum likelihood cross validation [Samper and Neuman, 1989a] in conjunction with universal kriging and generalized least squares. Standard information criteria provide an ambiguous ranking of the models, which does not justify selecting one of them and discarding all others as is commonly done in practice. Instead, we eliminate some of the models based on their negligibly small posterior probabilities and use the rest to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. We then average these four projections and associated kriging variances, using the posterior probability of each model as weight. Finally, we cross validate the results by eliminating from consideration all data from one borehole at a time, repeating the above process and comparing the predictive capability of MLBMA with that of each individual model. We find that MLBMA is superior to any individual geostatistical model of log permeability among those we consider at the ALRS.

DISCLAIMER'letter reporting refinement of flammable gas generatiodretention models using void meter and retained gas sampling data."The data obtained from operating the void fraction instrument 0 (Stewart et al. 1996a), and retained gas sampler (RGS) (Shekarriz et al. 1997) have determined the amount and composition of gas retained in the wastes in the six double-shell tanks on the Flammable Gas Watch List (Johnson et al: 1997). The interpretation of those data and the models for gas retention and release developed or improved as a result represent significant progress toward an adequate understanding of the mechanisms of gas generation, retention, and release. This report summarizes the VFI and RGS data and presents the models these data have enabled us to develop.. iii AbstractThis report describes the current understanding of flammable gas retention and release in Hanford double-shell waste tanks AN-103, AN-104, AN-105 The applicable data available from the void fraction instrument, retained gas sampler, ball rheometer, tank characterization, and field monitoring are summarized. Retained gas volumes and void fractions are updated with these new data -Using the retained gas compositions from the retained gas sampler, peak dome pressures during a gas burn are calculated as a function of the fraction of retained gas hypothetically released instantaneously into the tank head space. Models and criteria are given for gas generation, initiation of buoyant displacement, and resulting gas release; and predictions are compared with observed tank behavior. V Summary .The gas retention and release behaviors of Hanford double-shell tanks (DSTs) on the Hammable Gas Watch List (FGWL), were characterized in detail using the ball rheometer and void fraction instrument 0 from December 1994 to May 1996. These are reported in Stewart et al. (1996a). Additional data on gas .composition and void fraction have since become available on four of these tanks (AW-101, AN-103, AN-104, and AN-105) using the retained gas sampler (RGS) from March through September 1996 and are described in Shekarriz et al. (1997).The main objective of the work presented in this report is improving the models for gas retention and release based on these data and updating the original gas retention and release calculations with the new RGS and core sample data-Because of this extensive characterization effort, we have a better knowledge and understanding of these DSTs than of any other Hanford tanks. We include models that help explain current gas retention and release behavior and examine the potential for other tanks to exhibit hazardous episodic gas releases. The models developed for gas generation based on waste sample testing are also summarized. While none of these models have been formally ve$i,ed and validated for safety analysis, they are consistent with the extant body of data and observations. The updates to earlier calculations and improvements to gas generation, retention, and release models are summarized below. G a s Generation Models and ...

This paper provides a simple way to convert Brooks‐Corey (BC) parameters to van Genuchten (vG) parameters and vice versa, for use primarily in situations where saturated conditions are likely to be encountered. Essential in this conversion is the preservation of the maximum value of a physical characteristic, the “effective capillary drive” HcM [Morel‐Seytoux and Khanji, 1974], defined with a good approximation for a soil water and air system as HcM = ∫0∞ krw dhc, where krw is relative permeability (or conductivity) to water and hc is capillary pressure (head), a positive quantity. With this conversion, infiltration calculations are essentially insensitive to the model used to represent the soil hydraulic properties. It is strictly a matter of convenience for the user which expression is used. On the other hand, the paper shows that other equivalences may lead to great variations in predictions of infiltration capacity. Consequently, the choice of the proper equivalence to use in calculations for rainfall‐runoff modeling or for low‐level radioactive waste disposal design is a serious matter.

The design of a monitoring network to provide initial detection of groundwater contamination at a waste disposal facility is complicated by uncertainty in both the characterization of the subsurface and the nature of the contaminant source. In addition, monitoring network design requires the resolution of multiple conflicting objectives. A method is presented that incorporates system uncertainty in monitoring network design and provides network alternatives that are noninferior with respect to several objectives. Monte Carlo simulation of groundwater contaminant transport is the method of uncertainty analysis. The random inputs to the simulation are the hydraulic conductivity field and the contaminant source location. The design objectives considered are (1) minimize the number of monitoring wells, (2) maximize the probability of detecting a contaminant leak, and (3) minimize the expected area of contamination at the time of detection. The network design problem is formulated as a multiobjective, integer programming problem and is solved using simulated annealing. An application of the method illustrates the configurations of noninferior network solutions and the trade‐offs between objectives. The probability of detection can be increased either by using more monitoring wells or by locating the wells farther from the source. The latter case results in an increase in the average area of the detected contaminant plumes at the time of initial detection. If monitoring is carried out very close to the contaminant source to reduce the expected area of a detected plume, a large number of wells are required to provide a high probability of detection. A sensitivity analysis showed that the predicted performance of a given number of wells decreases significantly as the heterogeneity of the porous medium increases. In addition, a poor estimate of hydraulic conductivity was shown to result in optimistic estimates of network performance. In general, the trade‐offs between monitoring objectives are an important factor in network design unless the cost (as expressed by the number of monitoring wells) is of limited concern.