Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Ydx_5ln Kdx_ (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, DY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments DY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and DY in a unified and consistent manner has been recently proposed by us. This new `` generalized sub-Gaussian (GSG)'' model has the form Ydx_5Udx_Gdx_ where Gdx_ is (generally, but not necessarily) a multiscale Gaussian random field and Udx_ is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K5eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt5eYt to second order in rYt (the standard deviation of Yt) yields results which approach those we obtain upon perturbing K5eY to second order in rY even as the corresponding series diverges. Our analysis is rendered mathematically tractable by considering mean-uniform steady state flow in an unbounded, twodimensional domain of mildly heterogeneous Y with a single-scale function G having an isotropic exponential covariance. Results consist of expressions for (a) lead-order autocovariance and cross-covariance functions of hydraulic head, velocity, and advective particle displacement and (b) analogues of preasymptotic as well as asymptotic Fickian dispersion coefficients. We compare these theoretically and graphically with corresponding expressions developed in the literature for Gaussian Y. We find the former to differ from the latter by a factor k5hU2 i= hUi 2 (h i denoting ensemble expectation) and the GSG covariance of longitudinal velocity to contain an additional nugget term depending on this same factor. In the limit as Y becomes Gaussian, k reduces to one and the nugget term drops out. Plain Language Summary Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi- Gaussian log hydraulic conductivity fields, Y(x), (x being a position vector). Yet Y, as well as many other variables and their increments DY, are known to be generally non- Gaussian. One common manifestation of non- Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale- dependent distributions of Y and DY in a unified and consistent manner has been recently proposed by us. This new generalized sub- Gaussian (GSG) model has the form Y(x) 5U(x) G(x) where G(x) is (generally, but not necessarily) a multi- scale Gaussian random field and U(x) is a non- negative subordinator independent of G. The purpose of this paper is to explore analytically lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Our analysis is rendered mathematically tractable by considering mean uniform steady state flow in an unbounded, two-dimensional domain of mildly heterogeneous Y.

Hydraulic tomography is a cost -effective technique for characterizing the heterogeneity of hydraulic parameters in the subsurface. During hydraulic tomography surveys, a large number of hydraulic heads (i.e., aquifer responses) are collected from a series of pumping or injection tests in an aquifer. These responses are then used to interpret the spatial distribution of hydraulic parameters of the aquifer using inverse modeling. In this study, we developed an efficient sequential successive linear estimator (SSLE) for interpreting data from transient hydraulic tomography to estimate three-dimensional hydraulic conductivity and specific storage fields of aquifers. We first explored this estimator for transient hydraulic tomography in a hypothetical one-dimensional aquifer. Results show that during a pumping test, transient heads are highly correlated with specific storage at early time but with hydraulic conductivity at late time. Therefore, reliable estimates of both hydraulic conductivity and specific storage must exploit the head data at both early and late times. Our study also shows that the transient heads are highly correlated over time, implying only infrequent head measurements are needed during the estimation. Applying this sampling strategy to a well -posed problem, we show that our SSLE can produce accurate estimates of both hydraulic conductivity and specific storage fields. The benefit of hydraulic tomography for ill -posed problems is then demonstrated. Finally, to affirm the robustness of our SSLE approach, we apply the SSLE approach to transient hydraulic tomography in a hypothetical two- dimensional aquifer with nonstationary hydraulic properties, as well as a hypothetical three-dimensional heterogeneous aquifer.

The purpose of this study was to evaluate the effectiveness of traditional hydrogeologic characterization approaches in a highly heterogeneous glaciofluvial aquifer at the North Campus Research Site (NCRS), situated on the University of Waterloo campus. Continuous soil cores to a depth of approximately 18 m were collected during the installation of the CMT monitoring wells and the multi-screen pumping well. K estimates were obtained for the core by obtaining 471 samples and testing them with a falling head permeameter, as well as by utilizing empirical equations developed to estimate K. A geostatistical analysis performed on the K datasets yielded strongly heterogeneous kriged K fields for the site. K and Ss were also estimated via type curve analysis of slug and pumping test data collected at the site. The various K and Ss estimates were then evaluated by simulating the transient drawdown data using a 3D forward numerical model constructed using Hydrogeosphere (Therrien et al., 2005). Results showed that, while drawdown predictions generally improved as more complexity was introduced into the model, the ability to make accurate drawdown predictions at all of the CMT ports was inconsistent. These results suggest that new techniques may be required to accurately capture subsurface heterogeneity for improved predictions of flow in similar systems.

The purpose of this study was to evaluate the effectiveness of traditional hydrogeologic characterization approaches in a highly heterogeneous glaciofluvial aquifer at the North Campus Research Site (NCRS), situated on the University of Waterloo campus. Continuous soil cores to a depth of approximately 18 m were collected during the installation of the CMT monitoring wells and the multi-screen pumping well. K estimates were obtained for the core by obtaining 471 samples and testing them with a falling head permeameter, as well as by utilizing empirical equations developed to estimate K. A geostatistical analysis performed on the K datasets yielded strongly heterogeneous kriged K fields for the site. K and Ss were also estimated via type curve analysis of slug and pumping test data collected at the site. The various K and Ss estimates were then evaluated by simulating the transient drawdown data using a 3D forward numerical model constructed using Hydrogeosphere (Therrien et al., 2005). Results showed that, while drawdown predictions generally improved as more complexity was introduced into the model, the ability to make accurate drawdown predictions at all of the CMT ports was inconsistent. These results suggest that new techniques may be required to accurately capture subsurface heterogeneity for improved predictions of flow in similar systems.

The overall goal of this dissertation is to determine and develop optimal strategies for inversely calibrating transmissivities (T), elastic and inelastic skeletal storage coefficients (Ske and Skv) of the developed-zone aquifer and conductance (CR) of the basin-fill faults for the entire Las Vegas basin, and to investigate future trends of land subsidence in Las Vegas Valley. This dissertation consists of three separate stand-alone chapters. Chapter 2 presents a discrete adjoint parameter estimation (APE) algorithm for automatically identifying suitable hydraulic parameter zonations from hydraulic head and subsidence measurements. Chapter 3 compares three different inversion strategies to determine the most accurate and computationally efficient method for estimating T and Ske and Skv at the basin scale: the zonation method (ZM), the adaptive multi-scale method and the Differential Evolution Adaptive Metropolis Markov chain Monte Carlo scheme (DREAM MCMC). Chapter 4 outlines a fine-scale numerical model capable of capturing far more hydrologic detail than any previously developed model of Las Vegas Valley The new model is calibrated using high-resolution InSAR data and hydraulic head data from 1912 to 2010. The calibrated model is used to investigate the influence of faults and their potential role on influencing clay thicknesses and land subsidence distributions, and to investigate future trends of land subsidence in Las Vegas Valley. / Ph. D.

Peatlands are important ecosystems that provide ecohydrological functions related to carbon storage and cycling, water quality, flood attenuation, and groundwater recharge. One key characteristic that gives peatlands these functions is the capacity to swell and shrink upon wetting and drying, commonly referred to as peat volume change. This property of peat volume change is closely related to the fluctuations of the water table and has a buffering effect on the water table depth relative to the peat surface, which acts as an important control on many ecohydrological functions such as carbon cycling, vegetation composition, and biogeochemical processes. In an attempt to fill a gap of knowledge, this thesis investigated peat volume change for multiple Northern peatlands close to Umeå, Sweden, using groundwater level and mire surface level data obtained during the summer of 2021. The objectives were to investigate the temporal trends and characteristics of changes in the water table and peat volume at the studied site and to determine how peat volume change capacity differs for mires of different ages, as well as different land management such as natural, drained and restored peatlands. It was found that old (older than 2000 years) mires have a significantly smaller peat volume change capacity compared to young mires (younger than 1000 years), as well as smaller specific storage, indicating that factors that change as the peatland evolves are important for the ability to expand and contract. It was also found that the relationship between the mire surface and water level was linear for some mires but not for others, including drained and old mires. For the drained mires this could be explained by very deep water tables compared to the natural mires, however, they did not stand out among the natural mires concerning peat volume change capacity. The comparison between a restored mire and a drained gave ambiguous results. It was also found that the specific storage, which is directly related tothe compressibility of the peat, was greater during drying conditions compared to rewetting conditions, highlighting peatlands ability to maintain wet conditions. The study provides a deeper understanding of peat volume change in Northern peatlands and the factors related to this phenomenon, which is crucial for further studying of peatland ecohydrology. / Torvmarker är viktiga ekosystem som bidrar med ekohydrologiska funktioner relaterade till kollagring och kolcykling, vattenkvalitet, minskad översvämningsrisk och grundvattenbildning. En egenskap hos torv som är viktig för dessa funktioner är förmågan att svälla under våta perioder och krympa under torrperioder. Denna torvvolymförändring är relaterad till fluktuationer i grundvattennivå och kan även ha en buffrande effekt på grundvattendjupet (avståndet från markytan till grundvattenytan), vilket påverkar flertalet ekohydrologiska funktioner såsom kolcykling, vegetationssammansättning, och biogeokemiska processer. I ett försök att fylla en lucka i kunskapen kring detta fenomen undersökte detta examensarbete torvvolymförändringar för flera torvmarker, eller myrar, i närheten av Umeå baserat data för grundvattennivåer och nivån på myrars markyta som erhållits under sommaren 2021. Syftet var identifiera trender och egenskaper hos de olika myrarnas förändring i grundvattennivån och myrnivå, samt att ta reda om det finns någon skillnad i torvens kapacitet för att svälla och krypa hos myrar med olika ålder, samt olika markskötsel såsom naturliga, dränerade och restaurerade myrar. Resultatet visade att äldre (äldre än 2000 år) myrar har en betydligt mindre kapacitet att svälla och krympa jämfört med yngre myrar (yngre än 1000 år), samt mindre specifik magasinkoefficient, vilket indikerar att faktorer som förändras när myren blir äldre är viktiga för förmågan att svälla och krympa. Resultatet visade också att förhållandet mellan myrens marknivå och grundvattennivå var linjärt för vissa myrar men inte för andra, inklusive dränerade och gamla myrar. För de dränerade myrarna kunde detta förklaras av mycket djupa grundvattennivåer jämfört med de naturliga myrarna, men de stack inte ut bland de naturliga myrarna vad gäller förmåga att svälla och krympa. Jämförelsen mellan en restaurerad myr och en dränerad gav tvetydiga resultat. Man fann också att den specifika magasinkoefficienten, som är direkt relaterad till torvens kompressabilitet, var större under torra perioder jämfört med våta perioder, vilket visar på myrens förmåga att upprätthålla våta förhållanden. Studien gav en djupare förståelse för myrars förmåga att svälla och krympa och faktorerna relaterade till detta fenomen, vilket är av betydelse för vidare forskning om torvmarkers ekohydrologi.