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A general method for the efficient selection of sampling locations for problems in environmental restoration

Description: Problems in environmental restoration that involve detecting or monitoring contamination or site characterization often benefit from procedures that help select sampling or drilling locations for obtaining meaningful data that support the analysis. One example of this type of procedure is a spatial sampling program that will ``automatically`` (based on the implementation of a computer algorithm) guide an iterative investigation through the process of site characterization at a minimal cost to determine appropriate remediation activities. In order to be effective, such a procedure should translate site and modeling uncertainties into terms that facilitate comparison with regulations and should also provide a methodology that will lead to an efficient sampling plan over the course of the analysis. In this paper, a general framework is given that can accomplish these objectives and can be applied to a wide range of environmental restoration applications. The methodology is illustrated using an example where soil samples support the characterization of a chemical waste landfill area.
Date: March 1, 1996
Creator: Rutherford, B.M.
Partner: UNT Libraries Government Documents Department

The components of geostatistical simulation

Description: There are many approaches to geostatistical simulation that can be used to generate realizations of random fields. These approaches differ fundamentally in a number of ways. First, each approach is inherently different and will produce fields with different statistical and geostatistical properties. Second, the approaches differ with respect to the choice of the features of the region that are to be modeled, and how closely the generated realizations reproduce these features. Some fluctuation in the statistical and geostatistical properties of different realizations of the same random field are natural and desirable, but the proper amount of deviation is an open question. Finally the approaches differ in how the conditioning information is incorporated. Depending on the source of randomness and the uncertainty in the given data, direct conditioning of realizations is not always desirable. In this paper, we discuss and illustrate these differences in order to emphasize the importance of these components in geostatistical simulation.
Date: March 1, 1996
Creator: Gotway, C. A. & Rutherford, B. M.
Partner: UNT Libraries Government Documents Department

Selecting features from spatial data for use in stochastic simulation

Description: An assessment of the long term containment capabilities of a possible nuclear waste disposal site requires both an understanding of the hydrogeology of the region under consideration and an assessment of the uncertainties associated with this understanding. Stochastic simulation - the generation of random {open_quotes}realizations{close_quotes} of the regions hydrogeology, consistent with the available information, provides a way to incorporate various types of uncertainty into a prediction of a complex system response such as site containment capability. One statistical problem in stochastic simulation is: What features of the data should be {open_quotes}mimicked{close_quotes} in the realizations? The answer can depend on the application. A discussion is provided of some of the more common data features used in recent applications. These features include spatial covariance functions and measures of the connectivity of extreme values, as examples. Trends and new directions in this area are summarized including a brief description of some statistics (the features) presently in experimental stages.
Date: August 1, 1994
Creator: Rutherford, B. M. & Gotway, C. A.
Partner: UNT Libraries Government Documents Department

Stochastic simulation for imaging spatial uncertainty: Comparison and evaluation of available algorithms

Description: Stochastic simulation has been suggested as a viable method for characterizing the uncertainty associated with the prediction of a nonlinear function of a spatially-varying parameter. Geostatistical simulation algorithms generate realizations of a random field with specified statistical and geostatistical properties. A nonlinear function is evaluated over each realization to obtain an uncertainty distribution of a system response that reflects the spatial variability and uncertainty in the parameter. Crucial management decisions, such as potential regulatory compliance of proposed nuclear waste facilities and optimal allocation of resources in environmental remediation, are based on the resulting system response uncertainty distribution. Many geostatistical simulation algorithms have been developed to generate the random fields, and each algorithm will produce fields with different statistical properties. These different properties will result in different distributions for system response, and potentially, different managerial decisions. The statistical properties of the resulting system response distributions are not completely understood, nor is the ability of the various algorithms to generate response distributions that adequately reflect the associated uncertainty. This paper reviews several of the algorithms available for generating random fields. Algorithms are compared in a designed experiment using seven exhaustive data sets with different statistical and geostatistical properties. For each exhaustive data set, a number of realizations are generated using each simulation algorithm. The realizations are used with each of several deterministic transfer functions to produce a cumulative uncertainty distribution function of a system response. The uncertainty distributions are then compared to the single value obtained from the corresponding exhaustive data set.
Date: September 1, 1993
Creator: Gotway, C. A. & Rutherford, B. M.
Partner: UNT Libraries Government Documents Department

Statistical analysis of hydrologic data for Yucca Mountain; Yucca Mountain Site Characterization Project

Description: The geologic formations in the unsaturated zone at Yucca Mountain are currently being studied as the host rock for a potential radioactive waste repository. Data from several drill holes have been collected to provide the preliminary information needed for planning site characterization for the Yucca Mountain Project. Hydrologic properties have been measured on the core samples and the variables analyzed here are thought to be important in the determination of groundwater travel times. This report presents a statistical analysis of four hydrologic variables: saturated-matrix hydraulic conductivity, maximum moisture content, suction head, and calculated groundwater travel time. It is important to modelers to have as much information about the distribution of values of these variables as can be obtained from the data. The approach taken in this investigation is to (1) identify regions at the Yucca Mountain site that, according to the data, are distinctly different; (2) estimate the means and variances within these regions; (3) examine the relationships among the variables; and (4) investigate alternative statistical methods that might be applicable when more data become available. The five different functional stratigraphic units at three different locations are compared and grouped into relatively homogeneous regions. Within these regions, the expected values and variances associated with core samples of different sizes are estimated. The results provide a rough estimate of the distribution of hydrologic variables for small core sections within each region.
Date: February 1, 1992
Creator: Rutherford, B.M.; Hall, I.J.; Peters, R.R.; Easterling, R.G. & Klavetter, E.A.
Partner: UNT Libraries Government Documents Department

Uncertainty and error in computational simulations

Description: The present paper addresses the question: ``What are the general classes of uncertainty and error sources in complex, computational simulations?`` This is the first step of a two step process to develop a general methodology for quantitatively estimating the global modeling and simulation uncertainty in computational modeling and simulation. The second step is to develop a general mathematical procedure for representing, combining and propagating all of the individual sources through the simulation. The authors develop a comprehensive view of the general phases of modeling and simulation. The phases proposed are: conceptual modeling of the physical system, mathematical modeling of the system, discretization of the mathematical model, computer programming of the discrete model, numerical solution of the model, and interpretation of the results. This new view is built upon combining phases recognized in the disciplines of operations research and numerical solution methods for partial differential equations. The characteristics and activities of each of these phases is discussed in general, but examples are given for the fields of computational fluid dynamics and heat transfer. They argue that a clear distinction should be made between uncertainty and error that can arise in each of these phases. The present definitions for uncertainty and error are inadequate and. therefore, they propose comprehensive definitions for these terms. Specific classes of uncertainty and error sources are then defined that can occur in each phase of modeling and simulation. The numerical sources of error considered apply regardless of whether the discretization procedure is based on finite elements, finite volumes, or finite differences. To better explain the broad types of sources of uncertainty and error, and the utility of their categorization, they discuss a coupled-physics example simulation.
Date: October 1997
Creator: Oberkampf, W. L.; Diegert, K. V.; Alvin, K. F. & Rutherford, B. M.
Partner: UNT Libraries Government Documents Department