H13A-0386 1340h
A Systematic Approach for Developing Conceptual Models of Contaminant Transport at the Hanford Site
The U.S. Department of Energy (DOE) faces many decisions regarding future remedial actions and waste disposal at the Hanford Site in southeast Washington State. To support these decisions, DOE recognized the need for a comprehensive and systematic approach to developing and documenting complete, consistent, and defensible conceptual models of contaminant release and migration. After reviewing existing conceptual model development methodologies that might be applicable to environmental assessments at the Hanford Site, DOE initiated efforts to adapt and implement the Features, Events, and Processes (FEP) methodology developed for use in performance assessments of nuclear waste disposal systems by NIREX. In adapting this methodology for use in the environmental assessments at Hanford, the international list of FEPs, compiled from nuclear waste disposal programs, was evaluated to develop a list of potentially relevant Hanford-specific FEPs. The international nuclear waste programs focus on deep geologic disposal while waste disposal at the Hanford Site involves burial in shallow unconsolidated geologic deposits. Thus, a graphical tool called the Process Relationship Diagram (PRD) was created to assist in identifying the international FEPs and additional factors that are relevant to Hanford, and to illustrate the relationships among these factors. The PRD is similar in form and function to the Master Directed Diagram used by NIREX to provide a visual and systematic structure for the FEP methodology. Adaptation of this approach is showing promise in facilitating the development of conceptual models and selection of relevant factors to be incorporated into environmental uncertainty assessments for the Hanford Site.
H13A-0387 1340h
The Role of Monitoring in Risk-Informed Assessments Involving Uncertainty
Research is currently underway to develop a systematic methodology for identifying and assessing uncertainties in ground-water models, focusing on the joint assessment of parameter, conceptual model, and hydrologic scenario uncertainties using a Bayesian model averaging approach. Specially-designed monitoring programs may be useful in this approach in several ways, including (1) developing prior information on parameter and model probabilities, (2) calibration/recalibration of models to provide updated estimates of parameter values/uncertainties and predicted system behavior, including uncertainties, and (3) confirmation/modification of management decisions, including decisions about ongoing monitoring. We outline a framework for making monitoring decisions within the context of a systematic uncertainty assessment. This framework incorporates a number of key concepts. Monitoring needs to support ongoing conceptual model development/refinement, parameter estimation, and hydrologic scenario definition. Since uncertainty is due in part to lack of knowledge of the system's significant features, events, and processes related to flow and transport, monitoring should be focused on improving probabilistic estimates of system performance indicators, such as water and contaminant fluxes. Although monitoring may only directly confirm short-term (e.g., decades) system behavior rather than long-term (e.g., millennia) behavior, insights into long-term prediction uncertainties can be achieved through a Bayesian-based monitoring approach. Furthermore, an ongoing monitoring program focused on identifying and reducing uncertainties can provide information to improve (on a cost or time basis) risk-informed decisions, such as the long-term safety of decommissioning sites or the evaluation of remediation options and closure decisions.
H13A-0388 1340h
Probabilistic Radiological Performance Assessment Modeling and Uncertainty
A generic probabilistic radiological Performance Assessment (PA) model is presented. The model, built using the GoldSim systems simulation software platform, concerns contaminant transport and dose estimation in support of decision making with uncertainty. Both the U.S. Nuclear Regulatory Commission (NRC) and the U.S. Department of Energy (DOE) require assessments of potential future risk to human receptors of disposal of LLW. Commercially operated LLW disposal facilities are licensed by the NRC (or agreement states), and the DOE operates such facilities for disposal of DOE-generated LLW. The type of PA model presented is probabilistic in nature, and hence reflects the current state of knowledge about the site by using probability distributions to capture what is expected (central tendency or average) and the uncertainty (e.g., standard deviation) associated with input parameters, and propagating through the model to arrive at output distributions that reflect expected performance and the overall uncertainty in the system. Estimates of contaminant release rates, concentrations in environmental media, and resulting doses to human receptors well into the future are made by running the model in Monte Carlo fashion, with each realization representing a possible combination of input parameter values. Statistical summaries of the results can be compared to regulatory performance objectives, and decision makers are better informed of the inherently uncertain aspects of the model which supports their decision-making. While this information may make some regulators uncomfortable, they must realize that uncertainties which were hidden in a deterministic analysis are revealed in a probabilistic analysis, and the chance of making a correct decision is now known rather than hoped for. The model includes many typical features and processes that would be part of a PA, but is entirely fictitious. This does not represent any particular site and is meant to be a generic example. A practitioner could, however, start with this model as a GoldSim template and, by adding site specific features and parameter values (distributions), use this model as a starting point for a real model to be used in real decision making.
http://www.neptuneandco.com/goldsim/generic/
H13A-0389 1340h
Environmental Modeling and Bayesian Analysis for Assessing Human Health Impacts from Radioactive Waste Disposal
Bayesian decision analysis provides a unified framework for coherent decision-making. Two key components of Bayesian decision analysis are probability distributions and utility functions. Calculating posterior distributions and performing decision analysis can be computationally challenging, especially for complex environmental models. In addition, probability distributions and utility functions for environmental models must be specified through expert elicitation, stakeholder consensus, or data collection, all of which have their own set of technical and political challenges. Nevertheless, a grand appeal of the Bayesian approach for environmental decision- making is the explicit treatment of uncertainty, including expert judgment. The impact of expert judgment on the environmental decision process, though integral, goes largely unassessed. Regulations and orders of the Environmental Protection Agency, Department Of Energy, and Nuclear Regulatory Agency orders require assessing the impact on human health of radioactive waste contamination over periods of up to ten thousand years. Towards this end complex environmental simulation models are used to assess "risk" to human and ecological health from migration of radioactive waste. As the computational burden of environmental modeling is continually reduced probabilistic process modeling using Monte Carlo simulation is becoming routinely used to propagate uncertainty from model inputs through model predictions. The utility of a Bayesian approach to environmental decision-making is discussed within the context of a buried radioactive waste example. This example highlights the desirability and difficulties of merging the cost of monitoring, the cost of the decision analysis, the cost and viability of clean up, and the probability of human health impacts within a rigorous decision framework.
H13A-0390 1340h
Uncertainty in Hydrodynamic Dispersion: Using Data Quality Weights and Statistical Techniques to Develop Parameter Estimates and Distributions.
Hydrodynamic dispersion is dependent on the size of a plume and the distance of transport. As a result, it is helpful to know the expected distances of contaminant transport a priori to best assess the range of dispersion values that would be most appropriate for modeling efforts. For large-scale models (scales of several km), with multiple point sources, uncertainty in longitudinal dispersion values is hard to constrain and can be difficult to implement. Data from field tracer tests and contaminated sites was collected, from published literature, to update the data set published by Gelhar et al. (1992). Data quality ranks were assigned based on data collection and interpretation methods. Data were then carefully evaluated to determine if individual data points were providing an undue influence on the distribution of the data. Two approaches were then tested to provide an appropriate model to quantify the uncertainty in longitudinal dispersivity values for transport distances for up to 20 km. The first approach is a probabilistic model where many discrete bins were formed to describe different scales of longitudinal dispersivity data collection, a CDF was fit to each bin. The resulting mixture distribution can then be sampled to obtain the range of values needed for a sensitivity analysis based on scale (travel distance) of the specific simulation. The second approach utilized a linear regression model where a single linear model of longitudinal dispersion was developed as a function of (log-transformed) scale that can be sampled for the observed residuals to complete an uncertainty analysis for transport models. The idea was to fit a linear regression line that can predict longitudinal dispersivity based on scale. Then, for sensitivity analyses, add a quantity based on the empirical distribution of the regression residuals to the linearly predicted value. Both of these approaches were evaluated using not only the typical goodness of fit measures, but also Monte Carlo simulations that were designed to demonstrate the effectiveness of the final models as well how these models reproduce the original data sets.
H13A-0391 1340h
Protection of installations for potable water abstraction against hazardous environmental influences in bedrock media
Contaminated groundwater of abandoned hazardous sites are leading to significant ecological damages in the adjacent reservoirs. Especially explosive composites and their metabolites of armament industry are toxic. The direct vicinity of the abandoned defence industry site of Stadtallendorf (Hesse, Germany) to the water supply company of a great catchment area is a severe hazard for the water supply of the whole region. It is a prerequisite to determine the behaviour of flow and transport in the local aquifer to assess the status of the site. A sustainable protection of the reservoir is only feasible with predictions of a flow- and transport model of the local aquifer. Local geology includes bedrock media, faults and a diversified stratigraphy. To describe transport in the aquifers, one has to take into consideration interaction between advective transport in fractures and diffusion in porous bulk. Onsite investigations are carried out to make predictions of advection, dispersion and attributes of the fractures (strike, slip, hydraulic aperture, density, length). Laboratory tests reveal data concerning matrix diffusion and adsorptive character of the media. Also environmental dependent transformation rates are considered to assess natural attenuation processes. Bulkdiffusion has been identified as an important component of contaminant retardation. Porous bulk acts as a store of pollutants. Even after remediation of the site, diffusion controls the decrease of pollutant concentration in water. The determined parameters of the investigations are incorporated into a flow model and later on into a transport model.
H13A-0392 1340h
Calibration of a Heterogeneous Flow Simulation of the Western San Joaquin Valley
A stochastic alluvial aquifer model was developed for the Westside of the San Joaquin Valley. Based on extensive analysis of well-logs, we determined sub-regional transition probability models of the major alluvial facies. The spatially varying geostatistical models were integrated into a non-stationary stochastic model of the aquifer structure using conditional sequential simulation. The hydraulic conductivities of the major facies are calibrated against a deterministic model representation of the regional fluxes across the land surface, of subflow across the eastern aquifer boundary, and of leakage across the bottom aquifer boundary. Weights for the individual calibration targets are assigned based on an approximation of the measurement errors underlying the calibration of the deterministic model, as well as potential modeling errors in the deterministic model. Our work addresses the overall issue of calibrating regional stochastic models to existing measurement data at relatively small scales as well as to derived data about the regional hydrologic water balance.
H13A-0393 1340h
Stochastic Approach for Modeling of DNAPL Migration in Heterogeneous Aquifers: Model Development and Experimental Data Generation
Modeling of the complex behavior of DNAPLs in naturally heterogeneous subsurface formations poses many challenges. Even though considerable progress have been made in developing improved numerical schemes to solve the governing partial differential equations, most of these methods still rely on deterministic description of the processes. This research explores the use of stochastic differential equations to model multiphase flow in heterogeneous aquifers, specifically the flow of DNAPLs in saturated soils. The models developed are evaluated using experimental data generated in two-dimensional test systems. A fundamental assumption used in the model formulation is that the movement of a fluid particle in each phase is described by a stochastic process and that the positions of all fluid particles over time are governed by a specific law. It is this law, which we seek to determine. The approach results in a nonlinear stochastic differential equation describing the position of the non-wetting phase fluid particle. The nonlinearity in the stochastic differential equation arises because both the drift and diffusion coefficients depend on the volumetric fraction of the phase, which in turn depends on the position of the fluid particles in the problem domain. The concept of a fluid particle is central to the development of the proposed model. Expressions for both saturation and volumetric fraction are developed using this concept of fluid particle. Darcy's law and the continuity equation are used to derive a Fokker-Planck equation governing flow. The Ito calculus is then applied to derive a stochastic differential equation(SDE) for the non-wetting phase. This SDE has both drift and diffusion terms which depend on the volumetric fraction of the non-wetting phase. Standard stochastic theories based on the Ito calculus and the Wiener process and the equivalent Fokker-Planck PDE's are typically used to model diffusion processes. However, these models, in their usual form, cannot represent barrier effects that occur at the interfaces of the soil layers with different characteristics. For example, in tracking a DNAPL plume, the behavior of the plume at an interface depends on the pressure-saturation relationships of the two soils forming the interface. In the model, the control of the flow of DNAPL particles across an interface is accomplished using a jump term, which derives from the Ito formula. The jump term is based on capillary diffusivity and the pressure-saturation curves of the two soils forming the interface. A series of laboratory spill experiments in two-dimensional test cells were conducted to create a comprehensive database to evaluate the model under development. These experiments utilized five well-characterized test sands that are used to create different heterogeneous packing configurations. The experiments that have been completed used horizontal and dipping capillarity barriers. The propagation of the spill was monitored using an automated X-ray photon attenuation system that accurately measures the DNAPL and water saturations. The computational aspects of the modeling approach, experimental results and preliminary analysis that were conducted to validate the new modeling method are presented.
H13A-0394 1340h
Combining Data and Process Models to Characterize Non-point source Pollution to Shallow Ground Water from an Irrigated Dairy Farm
The objective of our work is to characterize non-point source nitrate leaching from a dairy farm located in a relatively vulnerable hydrogeologic region of California. We consider sub-management unit, management unit (fields, corrals and ponds) and farm scale processes. Available data consists of measured fluxes/heads and nitrogen concentrations in a tile drainage and monitoring well network. Of concern is that there are several scales of measurements and processes that are difficult to relate due to high spatial and temporal variability of the leaching processes and the varying area represented by each of the measurements (measurement support). The focus of our modelling approach therefore lays on the development of several three-dimensional process based groundwater flow and transport models that are jointly capable of characterizing in-farm pollution variability and accommodating different types of data with varying measurement support for their calibration and validation. Estimated average leaching is 486 kg/ha/yr, 695 kg/ha/yr and 807 kg/ha/yr for field, corrals and ponds respectively. Aggregated results of the simulations are also compared to field and farm scale nitrogen balances and nitrogen discharges from tile drains and assessed in relation to their data requirement and measurement support scale.
H13A-0395 1340h
A Gibbs Sampler for Constrained Geostatistical Interpolation and Inverse Modeling
Interpolation and inverse modeling techniques are gaining increased exposure as researchers and practitioners strive to make optimal use of limited data. In stochastic approaches, unknown parameters are described through statistical distributions, and meaningful uncertainty bounds can often be identified. One of the challenges of stochastic approaches is the need to select a statistical model that is consistent with our conceptual understanding of the problem. In addition, for most environmental applications, data are limited and any information available about an unknown parameter or function should be used to improve the analysis. One useful piece of information is that, in many cases, the unknown parameter has known physical constraints. Examples from environmental applications include solubility limits for chemical concentrations, nonnegativity constraints on hydraulic conductivity, and minimum or maximum hydraulic head constraints when screened portions of sampling wells do not capture the location of the water table. Geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters, but these methods typically cannot enforce physical constraints, instead imposing an assumption of Gaussianity on estimates, confidence bounds and conditional simulations. This presentation describes a novel, mathematically rigorous and computationally efficient Gibbs sampler (a Markov chain Monte Carlo technique) which allows for multiple and variable physical constraints to be enforced within a geostatistical framework. Sample interpolation and inverse modeling applications confirm that estimates, uncertainty bounds and conditional simulations reflect the specified constraints, leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters to be estimated. In addition, especially in inverse modeling applications, a posteriori confidence bounds are narrower even in areas where constraints are not imposed, as a result of the additional information introduced into the system. Finally, the method can be directly applied in multiple dimensions and with any variogram model, without sacrificing the statistical rigor of the geostatistical approach.
http://www-personal.engin.umich.edu/~amichala/
H13A-0396 1340h
Parsimonious PARMA Models and Their Application to Modeling of Riverflows
For analysis and design of water resources systems, it is sometimes required to synthetically generate riverflow data with high resolution (that is, weekly or daily values). Periodic AutoRegressive Moving Average models provides a powerful tool for modeling such riverflow time series, which are often periodically stationary. The innovations algorithm can be used to obtain parameter estimates for PARMA models with finite fourth moment as well as infinite fourth moment but finite variance. Fitting the PARMA model to historical weekly or daily data, however, requires estimation of too many parameters, which violates the principle of parsimony. In an effort to obtain a parsimonious model representing periodically stationary series, we develop the asymptotic distribution of the discrete Fourier transform of the innovation estimates and then determine those statistically significant Fourier coefficients. We also extend these results to other periodic model parameters. We demonstrate the effectiveness of the technique using simulated data from different PARMA models. An application of the technique is demonstrated through the analysis of a daily riverflow series for the Fraser River in British Columbia.
H13A-0397 1340h
Estimating Prior Model Probabilities Using an Entropy Principle
Considering conceptual model uncertainty is an important process in environmental uncertainty/risk analyses. Bayesian Model Averaging (BMA) (Hoeting et al., 1999) and its Maximum Likelihood version, MLBMA, (Neuman, 2003) jointly assess predictive uncertainty of competing alternative models to avoid bias and underestimation of uncertainty caused by relying on one single model. These methods provide posterior distribution (or, equivalently, leading moments) of quantities of interests for decision-making. One important step of these methods is to specify prior probabilities of alternative models for the calculation of posterior model probabilities. This problem, however, has not been satisfactorily resolved and equally likely prior model probabilities are usually accepted as a neutral choice. Ye et al. (2004) have shown that whereas using equally likely prior model probabilities has led to acceptable geostatistical estimates of log air permeability data from fractured unsaturated tuff at the Apache Leap Research Site (ALRS) in Arizona, identifying more accurate prior probabilities can improve these estimates. In this paper we present a new methodology to evaluate prior model probabilities by maximizing Shannon's entropy with restrictions postulated a priori based on model plausibility relationships. It yields optimum prior model probabilities conditional on prior information used to postulate the restrictions. The restrictions and corresponding prior probabilities can be modified as more information becomes available. The proposed method is relatively easy to use in practice as it is generally less difficult for experts to postulate relationships between models than to specify numerical prior model probability values. Log score, mean square prediction error (MSPE) and mean absolute predictive error (MAPE) criteria consistently show that applying our new method to the ALRS data reduces geostatistical estimation errors provided relationships between models are postulated correctly. We illustrate our method further by using it to assess the comparative conceptual uncertainty of five recharge models developed by three independent parties for the Nevada Test Site. Influence of the recharge model uncertainty to predictive uncertainty of the flow model is explored.
H13A-0398 1340h
General approach for evaluation parameter uncertainty based on inverse model sensitivities
In the most general case, inverse model sensitivities represent partial derivatives of inverse estimates of model parameters in respect to various other parameters related to underlying conceptual, numerical and inverse models. In this definition, we distinguish two separate sets of model parameters: the former set represents parameters estimated in the inverse process; the latter set represents parameters that are excluded from the inverse process; however these parameters impact the inverse estimates and we have some knowledge about their uncertainty. The latter set of parameters can include calibration targets, computational grid resolution, accuracy of the numerical solver, priors, boundary condition terms, etc. The uncertainties in these parameters can be efficiently propagated to the uncertainty of inverse estimates using the inverse model sensitivities approach (Vesselinov, 2004). In this case a covariance matrix of estimation errors is computed based on Jacobian matrix consisting of inverse model sensitivities and a covariance matrix of errors of the unestimated model parameters. The proposed methodology can be applied for problems related to model development, optimization of data collection strategies, design of monitoring networks, etc. Its implementation is computationally intensive but can be performed efficiently through parallelization. Results based on synthetic and real case inverse problems are presented and discussed.
H13A-0399 1340h
Parameter Uncertainty Analysis of a Regional Subsurface Water Flow Model Using Single and Multi-Objective Calibration
Regional-scale modeling of variably-saturated subsurface water flow is affected by uncertainties associated with the model parameters and the appropriate model structure. These uncertainties may be reduced by comparing the model predictions to measurements using inverse modeling, resulting in posterior parameter distributions that are conditioned on the data used in the calibration. We present the calibration of a regional distributed subsurface water flow model for a 1,400 km2 irrigated agricultural area in the western San Joaquin Valley of California. Two global optimization algorithms were used to identify optimal parameter values and their uncertainties using data on spatially distributed local water table depth measurements, district-average groundwater pumping and district-average subsurface drainage data. Using the single objective function approach, the three measurement types were weighted into a single objective function for global optimization purposes. Additionally, a three-objective multi-criteria optimization problem was formulated in which no prior weighting of the individual objectives was specified. The single-objective optimization approach resulted in identifiable parameters with relatively small uncertainties, however, most likely values for various optimized parameter approached the outer bounds of their physical-realistic ranges. In the multi-objective approach, the objective function of each measurement type was treated independently, so that no subjective preferences were assigned a priori. The estimated Pareto set exhibited large parameter uncertainty, indicating possible model structural inadequacies.
H13A-0400 1340h
Evaluation of Net Infiltration Uncertainty for Multiple Uncertain Input Parameters Using Latin Hypercube Sampling
To assess, via numerical simulation, the effect of 12 uncertain input parameters (characterizing soil and rock properties and boundary [meteorological] conditions), on net infiltration uncertainty, the Latin Hypercube Sampling (LHS) technique (a modified Monte Carlo approach using a form of stratified sampling) was used. Each uncertain input parameter is presented using a probability distribution function, characterizing the epistemic uncertainty (which arises from the lack of knowledge about parameters-an uncertainty that can be reduced as new information becomes available). One hundred LHS realizations (using the code LHS V2.50 developed at Sandia National Laboratories) of the uncertain input parameters were used to simulate the net infiltration over the Yucca Mountain repository footprint. Simulations were carried out using the code INFIL VA-2.a1 (a modified USGS code INFIL V2.0). The results of simulations were then used to determine the net infiltration probability distribution function. According to theoretical considerations, for 12 uncertain input parameters, from 15 to 36 realizations using the LHS technique should be sufficient to get meaningful results. In this presentation, we will show that the theoretical considerations may significantly underestimate the required number of realizations for the evaluation of the correlation between the net infiltration and uncertain input parameters. We will demonstrate that the calculated net infiltration rate (presented as a probability distribution function) oscillates as a function of simulation runs, and that the correlation between net infiltration rate and the uncertain input parameters depends on the number of simulation runs. For example, the correlation coefficient between the soil (or rock) permeability and net infiltration stabilizes only after 60-80 realizations. The results of the correlation analysis show that the correlation to net infiltration is highest for precipitation, bedrock permeability (positively correlated), soil depth, and potential evapotranspiration (negatively correlated).
H13A-0401 1340h
Refined Estimate of Total Variation Enables a More Accurate Parameter and Uncertainty Estimation, as Well as a new Model Selection Procedure
In almost every field of science and engineering nonlinear equations are increasingly used to model experimental measurements. In this context, we address the problem of accurately estimating the model parameters and their uncertainty. For that, it is essential to correctly take into account the stochastic measurement uncertainties. For instance, if the measurements are subject to individual errors, the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods generally assume that the errors on the independent variable(s), also called "input", are negligible, which is often not true in reality. We propose a refinement of the abovementioned parameter and uncertainty estimation methods, which generalises their applicability to cases where input noise is not negligible. An advantage of this method is that the input noise is transformed into output noise, which allows to keep the traditional WLS formalism (and software). The refined methods are evaluated and compared to the original procedures. The results reveal an improved consistency of the refined WLS estimator compared to the original one. An additional advantage of the refined WLS cost function is that its residual value can be interpreted as a sample from a chi square distribution. This property is useful because it enables an internal quality control of the results. In addition, this property allows an objective procedure to select the most appropriate model for describing the data under study, when several competing models are available. The parameter uncertainty estimation is also clearly improved by applying the refined method. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. Therefore, without the refinement, the parameter uncertainties are systematically underestimated. Using the refined method, this systematic error disappears.