H32B-01 INVITED
Role of Optimization in Uncertainty Analysis of Computationally Expensive Simulation Models
Uncertainty Analysis typically requires a large number of model simulations. This is not feasible for computatioally expensive models We discuss how optimization methods can reduce the required computational efforts. We also discuss the use of new response surface optimizatio algorithms that can substantially reduce the number of simulations required. A groundwater application will be discussed.
H32B-02
The Importance of Behavioral Thresholds and Objective Functions in Contaminant Transport Uncertainty Analysis
The TCE release from The Lockformer Company in Lisle Illinois resulted in a plume in a confined aquifer that is more than 4 km long and impacted more than 300 residential wells. Many of the wells are on the fringe of the plume and have concentrations that did not exceed 5 ppb. The settlement for the Chapter 11 bankruptcy protection of Lockformer involved the establishment of a trust fund that compensates individuals with cancers with payments being based on cancer type, estimated TCE concentration in the well and the duration of exposure to TCE. The estimation of early arrival times and hence low likelihood events is critical in the determination of the eligibility of an individual for compensation. Thus, an emphasis must be placed on the accuracy of the leading tail region in the likelihood distribution of possible arrival times at a well. The estimation of TCE arrival time, using a three-dimensional analytical solution, involved parameter estimation and uncertainty analysis. Parameters in the model included TCE source parameters, groundwater velocities, dispersivities and the TCE decay coefficient for both the confining layer and the bedrock aquifer. Numerous objective functions, which include the well-known L2-estimator, robust estimators (L1-estimators and M-estimators), penalty functions, and dead zones, were incorporated in the parameter estimation process to treat insufficiencies in both the model and observational data due to errors, biases, and limitations. The concept of equifinality was adopted and multiple maximum likelihood parameter sets were accepted if pre-defined physical criteria were met. The criteria ensured that a valid solution predicted TCE concentrations for all TCE impacted areas. Monte Carlo samples are found to be inadequate for uncertainty analysis of this case study due to its inability to find parameter sets that meet the predefined physical criteria. Successful results are achieved using a Dynamically-Dimensioned Search sampling methodology that inherently accounts for parameter correlations and does not require assumptions regarding parameter distributions. For uncertainty analysis, multiple parameter sets were obtained using a modified Cauchy's M-estimator. Penalty functions had to be incorporated into the objective function definitions to generate a sufficient number of acceptable parameter sets. The combined effect of optimization and the application of the physical criteria perform the function of behavioral thresholds by reducing anomalies and by removing parameter sets with high objective function values. The factors that are important to the creation of an uncertainty envelope for TCE arrival at wells are outlined in the work. In general, greater uncertainty appears to be present at the tails of the distribution. For a refinement of the uncertainty envelopes, the application of additional physical criteria or behavioral thresholds is recommended.
H32B-03 INVITED
A Systematic Framework for Dealing with Uncertainty in Groundwater Modeling
Engineers and scientists dealing with the modeling and management of subsurface hydrologic systems are routinely confronted with uncertainty caused by incomplete knowledge and/or natural variability. Although considerable advances have been made in the use of geostatistical techniques for quantifying the impacts of spatial variability in hydrogeologic parameters, ad-hoc approaches continue to be used for analyzing the influence of lack-of-knowledge driven parameter uncertainty on numerical model predictions. The objective of our presentation is to describe and illustrate a systematic framework for this purpose. Key elements of such a framework are: (a) uncertainty characterization – which involves fitting and/or assigning marginal and joint distributions to uncertain model inputs, (b) uncertainty propagation – which involves translating the uncertainty in model inputs into uncertainty in model outputs, and (c) uncertainty importance assessment – which involves determining the key drivers of output uncertainty. Additional considerations related to the quantification and propagation of conceptual model uncertainty, as well as conditional uncertainty assessments in the context of model calibration, will also be discussed.
H32B-04
Identification of potential contaminant plume sources under uncertainty
There are various methods that can be applied to identify the potential spatial locations of contaminant sources in regional aquifers. We propose and apply an inverse methodology that takes into account directly the various uncertainties associated with the available hydrogeological information (conceptual uncertainties, observation errors, parameter uncertainties). The technique utilizes a series of forward simulations of probable contaminant transport that encompass predefined uncertainty bounds. The simulations are independent and efficiently performed in parallel. Then the inverse method post processes the results and estimates the spatial distribution of the most probable source locations that are consistent with observations and their uncertainties. In addition, the model predicts the probable contaminant concentrations and their uncertainties. Uncertainties in key model components that impact the results are medium heterogeneity, geochemical processes, and field contaminant concentrations. The analysis will be applied for decision making regarding a next phase of data acquisition. Any new data will be subsequently employed to address the validity of the model predictions and applied methodology.
H32B-05
Nonlinear Dynamic Processes as a Source of Uncertainty for Flow Simulations through Partially Saturated Fractured-Porous Media
The concept of nonlinear dynamics and chaos can be used to provide an alternative explanation for the irreducible uncertainty of seemingly erratic temporal and spatial oscillations of variables characterizing unsaturated flow and transport within fractured-porous media. The goals of this presentation are to discuss the physical processes and to quantify the uncertainty of flow characteristics caused by deterministic-chaotic, nonlinear dynamic processes. The presentation will be based on the results of a series of several infiltration tests, including the time-domain and phase-space interpretation of infiltration and outflow rates, capillary pressure, and dripping-water frequency. It will be shown that the apparent "randomness" of the flow field is caused by the interplay of intrafracture film flow and water dripping, coalescence, divergence, and mixing of multiple flow paths along fracture surfaces. These processes result in chaotic advection, diffusion, mixing, and feedback phenomena. Because direct measurements of variables characterizing a variety of flow and transport processes under field conditions are not technically feasible, only the cumulative effect of these processes can be characterized. The lack of specific measurements leads to a limited knowledge about initial conditions needed for solving deterministic differential or difference-differential equations. This limitation, in turn, leads to the uncertainty in predictions of flow processes. Moreover, it would be difficult, if not impossible, to distinguish between the two components of the total uncertainty—epistemic and aleatoric uncertainties. Quantification of the uncertainty of nonlinear dynamic oscillations caused by both deterministic and random components of time- series data is performed using the cluster analysis, moments analysis and the concept of information entropy. This work was supported by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231.
H32B-06
Uncertainty and the Conceptual Site Model
Our focus is on uncertainties in the underlying conceptual framework upon which all subsequent steps in numerical and/or analytical modeling efforts depend. Experienced environmental modelers recognize the value of selecting an optimal conceptual model from several competing site models, but usually do not formally explore possible alternative models, in part due to incomplete or missing site data, as well as relevant regional data for establishing boundary conditions. The value in and approach for developing alternative conceptual site models (CSM) is demonstrated by analysis of case histories. These studies are based on reported flow or transport modeling in which alternative site models are formulated using data that were not available to, or not used by, the original modelers. An important concept inherent to model abstraction of these alternative conceptual models is that it is "Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise." (Tukey, 1962) The case histories discussed here illustrate the value of formulating alternative models and evaluating them using site-specific data: (1) Charleston Naval Site where seismic characterization data allowed significant revision of the CSM and subsequent contaminant transport modeling; (2) Hanford 300-Area where surface- and ground-water interactions affecting the unsaturated zone suggested an alternative component to the site model; (3) Savannah River C-Area where a characterization report for a waste site within the modeled area was not available to the modelers, but provided significant new information requiring changes to the underlying geologic and hydrogeologic CSM's used; (4) Amargosa Desert Research Site (ADRS) where re-interpretation of resistivity sounding data and water-level data suggested an alternative geologic model. Simple 2-D spreadsheet modeling of the ADRS with the revised CSM provided an improved match to vapor-phase tritium migration. Site-specific monitoring coupled to these alternative CSM's greatly assists in conducting uncertainty assessments. (Work supported by USNRC contract NRC-04-03-061.)
H32B-07
On Model Selection Criteria in Multimodel Analysis
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 (a) rank these models, (b) eliminate some of them and/or (c) 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. In particular, whereas we [Neuman, 2003; Ye et al., 2004, 2005; Meyer et al., 2007] have based our approach to multimodel hydrologic ranking and inference on the Bayesian criterion KIC (which reduces asymptotically to BIC), Poeter and Anderson [2005] have voiced a strong preference for the information-theoretic criterion AICc (which reduces asymptotically to AIC). Their preference stems in part from a perception that KIC and BIC require a "true" or "quasi-true" model to be in the set of alternatives while AIC and AICc are free of such an unreasonable requirement. We examine the model selection literature to find that (a) 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; (b) 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; (c) 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; (d) if a true model is in the set, BIC and KIC select with probability one the true model as sample size increases, a consistency property not shared by AIC and AICc; (e) published comparisons between BIC and AIC (none consider KIC and few consider AICc) tend to rely on the consistency of BIC, which does not apply when a true model is not in the set; and (f) all four criteria have been used with various degrees of success in such situations. 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.