In this work we develop and analyze algorithms motivated by the parameter estimation problem corresponding to a multilayer aquifer/interbed groundwater flow model. The parameter estimation problem is formulated as an optimization problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and differentiability properties of the map. For differentiability, we expand existing results on Fréchet sensitivity analysis to convection diffusion equations and groundwater flow equations. This is achieved by proving that the Fréchet  derivative of the solution operator is Hilbert-Schmidt, under smoothness assumptions for the parameter space. In addition, we approximate this operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant changes in the solutions, as well as applications to uncertainty quantification. Numerical results complement our theoretical findings. / Ph. D.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24892号 / 工博第5172号 / 新制||工||1988(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 渦岡 良介, 教授 安原 英明, 教授 肥後 陽介 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

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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.

Deep injection wells (DIW) in Florida are regulated by the U.S. Environmental Protection Agency (USEPA) and the state of Florida through the Underground Injection Control regulations contained within the Safe Drinking Water Act. Underground injection is defined as the injection of hazardous waste, nonhazardous waste, or municipal waste below the lowermost formation containing an underground source of drinking water within one-quarter mile of the wellbore. Municipalities in Florida have been using underground injection as an alternative to surface disposal of treated domestic wastewater for nearly 40 years. The research involved collecting data as of September, 2007 on all the Class I DIWs in the state of Florida and evaluating the differences between them. The analysis found regional differences in deep well practice and canonical correlation analyses concluded that depth below the USDW is the most significant factor to prevent upward migration of the injected fluid. / by Jie Gao. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

The Barton Springs Segment, part of the karstic Edwards aquifer in Central Texas, is a Sole Source aquifer, is habitat to rare karst species, and provides water to a well-loved municipal swimming pool, yet its hydrogeologic properties remain insufficiently understood. For this study, the hydrogeologic characteristics of the Barton Springs Segment were investigated using several approaches, including mapping of hydrostratigraphic units and faults, measurement of upland infiltration, groundwater traces, and aquifer tests. The depositional environment, diagenesis, fracturing, down-dropped and dipping faulted blocks, and subsequent dissolution were determined to play important roles in controlling groundwater flow-path development within the Barton Springs Segment. In particular, downdropped fault blocks create groundwater gradients to the southeast that influence flow in the Edwards outcrop area. Upland internal drainage basins were found to be extremely efficient at conveying recharge to the underlying aquifer. The maturity of natural internal drainage sinkholes can be measured by its bowl volume, which grows in proportion to the catchment area it captures. A 19-hectare internal drainage basin, HQ Flat sinkhole, was monitored for rainfall, evapotranspiration, soil moisture, and discrete runoff to the cave drain. During a 505-day period, 5.5% of measured rainfall entered the cave drain as discrete recharge, 26% of measured rainfall infiltrated through soils on the slopes, and the remaining 68% was lost through evapotranspiration. This amount of upland infiltration is consistent with infiltration measurements in other karst areas and is much larger than the 1% upland recharge of rainfall that was previously estimated. A chloride mass balance indicates that at the adjacent Tabor research site, about 50% of rainfall infiltrates to a 6-meter depth. Dye-tracing and pump tests demonstrated that primary and secondary groundwater flow paths are the major influence on transmissivity within the Barton Springs Segment. Groundwater tracing breakthroughs reveal very high advection and relatively low dispersion. Drawdown response to pump tests indicates a very high degree of anisotropy, controlled by location of groundwater flow paths. Overall the Barton Springs Segment is a mature karst aquifer with highly developed rapid, discrete network for both recharge and groundwater-flow. / text

published_or_final_version / Earth Sciences / Doctoral / Doctor of Philosophy