This work describes a new taxonomy for elastic, sedimentary porous media. The taxonomy is synthesized for the investigation and characterization of ground-water flow from accumulating developments in the genetic analysis of elastic, sedimentary depositional structures. Genetic analysis recognizes spatial associations of elastic, sedimentary structures imposed during genesis. The taxonomy is a nested hierarchy of discrete elastic, sedimentary structures distinguished by the bounding surfaces created during their emplacement and rearrangement. The investigation and characterization of a specific ground-water flow system in elastic, sedimentary porous media can be improved by imposing a structural context on lithologie observations, geophysical measurements, head measurements, and hydraulic conductivity estimates. Globally-valid and transferable descriptions of structures in the taxonomy from modern exposures, outcrops, and densely sampled subsurface systems are modified to fit site-specific geologic observations and measurements. A specific procedure is developed for applying the taxonomy in the investigation and analysis of ground-water flow. The procedure quantitatively measures the hydraulic validity of alternative geologic interpretations of site-specific data under the taxonomy. The application of the taxonomy and procedure to a typical set of data types, densities, and quality is illustrated with data from a site of ground-water contamination investigation.

This dissertation considers modeling groundwater flow under imprecisely known parameters and managing a plume of contaminant. A new approach has been developed to study the effects of parameters uncertainty on the dependent variable, here the head. The proposed approach is developed based on fuzzy set theory combined with interval analysis. The kind of uncertainty modeled here is the imprecision associated with model parameters as a result of machine or human imprecision or lack of information. In this technique each parameter is described by a membership function. The fuzzy inputs into the model are in the form of intervals so are the outputs. The resulting head interval represents the change in the output due to interval inputs of model parameters. The proposed technique is illustrated using a two dimensional flow problem solved with a finite element technique. Three different cases are studied: homogeneous, mildly heterogeneous and highly heterogeneous transmissivity field. The groundwater flow problem analysis requires interval input values for the parameters, the output may be presented in terms of mean value, upper and lower bounds of the hydraulic head. The width of the resulting head interval can be used as a measure of uncertainty due to imprecise inputs. The degree of uncertainty associated with the predicted hydraulic head is found to increase as the width of the input parameters interval increases. Compared to Monte Carlo simulation approach, the proposed technique requires less computer storage and CPU time, however at this stage autocorrelation and crosscorolation are not configured in the presented formulation. In the plume containment problem two formulations are presented using the hydraulic gradient technique to control the movement of the contaminants. The first one is based on multiobjective analysis and the second, on fuzzy set theory. Multiobjective analysis yields a set of alternative strategies each of which satisfies the multiple objectives to a certain degree. Three different techniques have been used to choose a compromise strategy. Although they follow different principles, the same preferred strategies are selected. It is also noticed that rapid restoration results in a large pumping volumes and high costs. Using a fuzzy formulation for plume containment yields the optimum pumping rates and locations in addition to the membership function at each pumping location. The resulting membership functions at these pumping locations can be used to study the sensitivity of each location to a change in objective function and constraints bounds. Overall, both the fuzzy and multiobjective methodologies, presented in this dissertation, provide new and encouraging approaches to groundwater quality management.

No description available.

This study observes how the size and type of land development can often be limited by the supply of fresh groundwater sources. Multiple-use recharge basins were found to be effective in diverting pollutants around a potable source of groundwater, thus reducing the chances of that source becoming contaminated. A computer-aided numerical model was used to simulate groundwater flow and its responses to recharge basins in a hypothetical situation.Through a series of trials, artifical recharge was able to abate the problem of groundwater contamination in certain geohydrologic conditions. Optimum rates of recharge and discharge were determined to effectively divert contaminated groundwater around several types of developments. From these findings, land use options and development intensities can be safely recommended for areas which otherwise may have been nearly undevelopable. / Department of Landscape Architecture

An effective medium approximation and a refined Monte Carlo simulation procedure for solving the stochastic groundwater flow problem are presented. The effective medium approximation permits one to solve the stochastic groundwater flow problem in a single run to generate the expected pressure head field. The proposed effective hydraulic conductivity expression for the effective medium is of the same form as the local Gardner’s equation and is easy to use. The refined Monte Carlo simulation procedure uses analytical means to estimate the sample size by controlling the error incurred in using the sample average in place of its population mean at a chosen confidence level. This estimator consistently performs well. Also, a variance reducing estimator which is different from the simple average for pressure head is developed. This estimator takes advantage of the correlation between the saturated conductivity and the pressure head distribution to reduce the output variance and is unbiased. This reduced variance results in a smaller width of uncertainty about the predicted pressure head. Both the effective medium approximation and the Monte Carlo approaches perform well when applied to several problems. / Ph. D.

A groundwater flow model was constructed for the Rincon Valley area and Mesilla Basin. The system is dominated by the complex interaction of the Rio Grande, canals, laterals, and drains with groundwater pumping. The primary purpose of the model was to aid the New Mexico -Texas Water Commission in assessing options for water resources development in the Lower Rio Grand Basin from Caballo Reservoir in New Mexico to El Paso, Texas. One such assessment was to evaluate the effect of secondary irrigation releases from Caballo Reservoir on the water budget. In addition, the model will eventually be linked to a surface water model (BESTSM) being utilized by the New Mexico -Texas Water Commission to evaluate water supply alternatives for El Paso, Texas. Stress periods were specified on a seasonal basis, a primary irrigation season from March through October and a secondary irrigation season from November through February. Analysis of model output indicates that groundwater pumping decreases Rio Grande flows, secondary irrigation season releases do not alter the water budget significantly, and that recharge and discharge from aquifer storage are strongly related to the season.

This project implements a real application on the Spider II, which is a simulation of Soil Water Movement Model. The main objectives of this project were to develop a parallel and distributed algorithm for the Soil Water Model; implement the Soil Water Movement Simulation model on the Spider II distributed system and to evaluate the performance of simulating the Soil Water Movement Model on Spider II.

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Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or integrate wit resprect to the posterior measure. This calls for sampling or numerical methods which are suitable for infinite dimensional spaces. In this work we focus on Kalman filter techniques based on ensembles or polynomial chaos expansions as well as Markov chain Monte Carlo methods. We analyze the Kalman filters by proving convergence and discussing their applicability in the context of Bayesian inference. Moreover, we develop and study an improved dimension-independent Metropolis-Hastings algorithm. Here, we show geometric ergodicity of the new method by a spectral gap approach using a novel comparison result for spectral gaps. Besides that, we observe and further analyze the robustness of the proposed algorithm with respect to decreasing observational noise. This robustness is another desirable property of numerical methods for Bayesian inference. The work concludes with the application of the discussed methods to a real-world groundwater flow problem illustrating, in particular, the Bayesian approach for uncertainty quantification in practice. / Bayessche Inferenz besteht daraus, vorhandenes a-priori Wissen über unsichere Parameter in mathematischen Modellen mit neuen Beobachtungen messbarer Modellgrößen zusammenzuführen. In dieser Dissertation beschäftigen wir uns mit Modellen, die durch partielle Differentialgleichungen beschrieben sind. Die unbekannten Parameter sind dabei Koeffizientenfunktionen, die aus einem unendlich dimensionalen Funktionenraum kommen. Das Resultat der Bayesschen Inferenz ist dann eine wohldefinierte a-posteriori Wahrscheinlichkeitsverteilung auf diesem Funktionenraum, welche das aktualisierte Wissen über den unsicheren Koeffizienten beschreibt. Für Entscheidungsverfahren oder Postprocessing ist es oft notwendig die a-posteriori Verteilung zu simulieren oder bzgl. dieser zu integrieren. Dies verlangt nach numerischen Verfahren, welche sich zur Simulation in unendlich dimensionalen Räumen eignen. In dieser Arbeit betrachten wir Kalmanfiltertechniken, die auf Ensembles oder polynomiellen Chaosentwicklungen basieren, sowie Markowketten-Monte-Carlo-Methoden. Wir analysieren die erwähnte Kalmanfilter, indem wir deren Konvergenz zeigen und ihre Anwendbarkeit im Kontext Bayesscher Inferenz diskutieren. Weiterhin entwickeln und studieren wir einen verbesserten dimensionsunabhängigen Metropolis-Hastings-Algorithmus. Hierbei weisen wir geometrische Ergodizität mit Hilfe eines neuen Resultates zum Vergleich der Spektrallücken von Markowketten nach. Zusätzlich beobachten und analysieren wir die Robustheit der neuen Methode bzgl. eines fallenden Beobachtungsfehlers. Diese Robustheit ist eine weitere wünschenswerte Eigenschaft numerischer Methoden für Bayessche Inferenz. Den Abschluss der Arbeit bildet die Anwendung der diskutierten Methoden auf ein reales Grundwasserproblem, was insbesondere den Bayesschen Zugang zur Unsicherheitsquantifizierung in der Praxis illustriert.

Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or integrate wit resprect to the posterior measure. This calls for sampling or numerical methods which are suitable for infinite dimensional spaces. In this work we focus on Kalman filter techniques based on ensembles or polynomial chaos expansions as well as Markov chain Monte Carlo methods. We analyze the Kalman filters by proving convergence and discussing their applicability in the context of Bayesian inference. Moreover, we develop and study an improved dimension-independent Metropolis-Hastings algorithm. Here, we show geometric ergodicity of the new method by a spectral gap approach using a novel comparison result for spectral gaps. Besides that, we observe and further analyze the robustness of the proposed algorithm with respect to decreasing observational noise. This robustness is another desirable property of numerical methods for Bayesian inference. The work concludes with the application of the discussed methods to a real-world groundwater flow problem illustrating, in particular, the Bayesian approach for uncertainty quantification in practice. / Bayessche Inferenz besteht daraus, vorhandenes a-priori Wissen über unsichere Parameter in mathematischen Modellen mit neuen Beobachtungen messbarer Modellgrößen zusammenzuführen. In dieser Dissertation beschäftigen wir uns mit Modellen, die durch partielle Differentialgleichungen beschrieben sind. Die unbekannten Parameter sind dabei Koeffizientenfunktionen, die aus einem unendlich dimensionalen Funktionenraum kommen. Das Resultat der Bayesschen Inferenz ist dann eine wohldefinierte a-posteriori Wahrscheinlichkeitsverteilung auf diesem Funktionenraum, welche das aktualisierte Wissen über den unsicheren Koeffizienten beschreibt. Für Entscheidungsverfahren oder Postprocessing ist es oft notwendig die a-posteriori Verteilung zu simulieren oder bzgl. dieser zu integrieren. Dies verlangt nach numerischen Verfahren, welche sich zur Simulation in unendlich dimensionalen Räumen eignen. In dieser Arbeit betrachten wir Kalmanfiltertechniken, die auf Ensembles oder polynomiellen Chaosentwicklungen basieren, sowie Markowketten-Monte-Carlo-Methoden. Wir analysieren die erwähnte Kalmanfilter, indem wir deren Konvergenz zeigen und ihre Anwendbarkeit im Kontext Bayesscher Inferenz diskutieren. Weiterhin entwickeln und studieren wir einen verbesserten dimensionsunabhängigen Metropolis-Hastings-Algorithmus. Hierbei weisen wir geometrische Ergodizität mit Hilfe eines neuen Resultates zum Vergleich der Spektrallücken von Markowketten nach. Zusätzlich beobachten und analysieren wir die Robustheit der neuen Methode bzgl. eines fallenden Beobachtungsfehlers. Diese Robustheit ist eine weitere wünschenswerte Eigenschaft numerischer Methoden für Bayessche Inferenz. Den Abschluss der Arbeit bildet die Anwendung der diskutierten Methoden auf ein reales Grundwasserproblem, was insbesondere den Bayesschen Zugang zur Unsicherheitsquantifizierung in der Praxis illustriert.