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  • 1
    In: Ground Water, July 2010, Vol.48(4), pp.569-579
    Description: In most groundwater applications, measurements of concentration are limited in number and sparsely distributed within the domain of interest. Therefore, interpolation techniques are needed to obtain most likely values of concentration at locations where no measurements are available. For further processing, for example, in environmental risk analysis, interpolated values should be given with uncertainty bounds, so that a geostatistical framework is preferable. Linear interpolation of steady‐state concentration measurements is problematic because the dependence of concentration on the primary uncertain material property, the hydraulic conductivity field, is highly nonlinear, suggesting that the statistical interrelationship between concentration values at different points is also nonlinear. We suggest interpolating steady‐state concentration measurements by conditioning an ensemble of the underlying log‐conductivity field on the available hydrological data in a conditional Monte Carlo approach. Flow and transport simulations for each conditional conductivity field must meet the measurements within their given uncertainty. The ensemble of transport simulations based on the conditional log‐conductivity fields yields conditional statistical distributions of concentration at points between observation points. This method implicitly meets physical bounds of concentration values and non‐Gaussianity of their statistical distributions and obeys the nonlinearity of the underlying processes. We validate our method by artificial test cases and compare the results to kriging estimates assuming different conditional statistical distributions of concentration. Assuming a beta distribution in kriging leads to estimates of concentration with zero probability of concentrations below zero or above the maximal possible value; however, the concentrations are not forced to meet the advection‐dispersion equation.
    Keywords: Hydrogeology -- Analysis ; Hydrogeology -- Models ; Groundwater -- Analysis ; Groundwater -- Models ; Advection (Earth sciences) -- Analysis ; Advection (Earth sciences) -- Models;
    ISSN: 0017-467X
    E-ISSN: 1745-6584
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  • 2
    Language: English
    In: Ground water, 2011, Vol.49(4), pp.491-502
    Description: Infiltrating river water carries the temperature signal of the river into the adjacent aquifer. While the diurnal temperature fluctuations are strongly dampened, the seasonal fluctuations are much less attenuated and can be followed into the aquifer over longer distances. In one-dimensional model with uniform properties, this signal is propagated with a retarded velocity, and its amplitude decreases exponentially with distance. Therefore, time shifts in seasonal temperature signals between rivers and groundwater observation points may be used to estimate infiltration rates and near-river groundwater velocities. As demonstrated in this study, however, the interpretation is nonunique under realistic conditions. We analyze a synthetic test case of a two-dimensional cross section perpendicular to a losing stream, accounting for multi-dimensional flow due to a partially penetrating channel, convective-conductive heat transport within the aquifer, and heat exchange with the underlying aquitard and the land surface. We compare different conceptual simplifications of the domain in order to elaborate on the importance of different system elements. We find that temperature propagation within the shallow aquifer can be highly influenced by conduction through the unsaturated zone and into the underlying aquitard. In contrast, regional groundwater recharge has no major effect on the simulated results. In our setup, multi-dimensionality of the flow field is important only close to the river. We conclude that over-simplistic analytical models can introduce substantial errors if vertical heat exchange at the aquifer boundaries is not accounted for. This has to be considered when using seasonal temperature fluctuations as a natural tracer for bank infiltration.
    Keywords: Models, Theoretical ; Rivers ; Temperature ; Water Cycle
    ISSN: 0017467X
    E-ISSN: 1745-6584
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  • 3
    In: Groundwater, April 2015, Vol.53(S1), pp.139-148
    Description: Numerical and laboratory studies have provided evidence that combining hydraulic tomography with tomographic tracer tests could improve the estimation of hydraulic conductivity compared with using hydraulic data alone. Field demonstrations, however, have been lacking so far, which we attribute to experimental difficulties. In this study, we present a conceptual design and experimental applications of tracer tomography at the field scale using heat as a tracer. In our experimental design, we improve active heat tracer testing by minimizing possible effects of heat losses, buoyancy, viscosity, and changing boundary conditions. We also utilize a cost‐effective approach of measuring temperature changes in situ at high resolution. We apply the presented method to the 8 m thick heterogeneous, sandy gravel, alluvial aquifer at the Lauswiesen Hydrogeological Research Site in Tübingen, Germany. Results of our tomographic heat‐tracer experiments are in line with earlier work on characterizing the aquifer at the test site. We demonstrate from the experimental perspective that tracer tomography is applicable and suitable at the field scale using heat as a tracer. The experimental results also demonstrate the potential of heat‐tracer tomography as a cost‐effective means for characterizing aquifer heterogeneity.
    Keywords: Hydrogeology ; Aquifers ; Tracers (Biology) ; Tomography;
    ISSN: 0017-467X
    E-ISSN: 1745-6584
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  • 4
    In: Water Resources Research, May 2014, Vol.50(5), pp.4149-4162
    Description: Models of microbial dynamics coupled to solute transport in aquifers typically require the introduction of a bacterial capacity term to prevent excessive microbial growth close to substrate‐injection boundaries. The factors controlling this carrying capacity, however, are not fully understood. In this study, we propose that grazers or bacteriophages may control the density of bacterial biomass in continuously fed porous media. We conceptualize the flow‐through porous medium as a series of retentostats, in which the dissolved substrate is advected with water flow whereas the biomasses of bacteria and grazers are considered essentially immobile. We first model a single retentostat with Monod kinetics of bacterial growth and a second‐order grazing law, which shows that the system oscillates but approaches a stable steady state with nonzero concentrations of substrate, bacteria, and grazers. The steady state concentration of the bacteria biomass is independent of the substrate concentration in the inflow. When coupling several retentostats in a series to mimic a groundwater column, the steady state bacteria concentrations thus remain at a constant level over a significant travel distance. The one‐dimensional reactive transport model also accounts for substrate dispersion and a random walk of grazers influenced by the bacteria concentration. These dispersive‐diffusive terms affect the oscillations until steady state is reached, but hardly the steady state value itself. We conclude that grazing, or infection by bacteriophages, is a possible explanation of the maximum biomass concentration frequently needed in bioreactive transport models. Its value depends on parameters related to the grazers or bacteriophages and is independent of bacterial growth parameters or substrate concentration, provided that there is enough substrate to sustain bacteria and grazers. One‐dimensional transport model with substrate‐bacteria‐grazer interactions Steady state bacteria concentration is constant over a certain length Grazing may explain the carrying capacity of bacteria in groundwater ecosystems
    Keywords: Groundwater Ecology ; Grazer ; Retentostat ; Reactive Transport ; Microbial Dynamics ; Top‐Down Control ; Linearized Stability Analysis ; Carrying Capacity
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 5
    In: Water Resources Research, January 2015, Vol.51(1), pp.261-280
    Description: Characterizing the topology of three‐dimensional steady‐state flow fields is useful to describe the physical processes controlling the deformation of solute plumes and, consequently, obtain helpful information on mixing processes without solving the transport equation. In this work, we study the topology of flow in three‐dimensional nonstationary anisotropic heterogeneous porous media. In particular, we apply a topological metric, i.e., the helicity density, and two complementary kinematic descriptors of mixing, i.e., stretching and folding, to investigate: (i) the flow field resulting from applying a uniform‐in‐the‐average hydraulic gradient within a fully resolved heterogeneous three‐dimensional porous medium with a nonstationary anisotropic covariance function of the locally isotropic hydraulic log conductivity; (ii) the flow field obtained by averaging a set of Monte Carlo realizations of the former field; (iii) the flow field obtained considering the blockwise uniform anisotropic effective conductivity tensor computed for the fully resolved case. While in the fully resolved case, the local helicity density is zero as a consequence of the local isotropy of hydraulic conductivity, it differs from zero in the other two cases. We show, therefore, that this topological metric is scale dependent and should be computed at the appropriate scale to be informative about the leading patterns of plume deformation. Indeed, streamlines are helical in all three cases at scales larger than the characteristic scale of spatial variability. We apply stretching and folding metrics to investigate the scales at which plume deformation is more influenced by helical motion than by the effect of small‐scale spatial heterogeneity in the hydraulic‐conductivity field. Under steady‐state flow conditions, stretching, which quantifies the increasing length of an interface, dominates at short distances from a given starting plane, while folding, which describes how this interface is bent to fill a finite volume of space, dominates further downstream and can be correlated with the appearance of large‐scale secondary motion. We conclude that three‐dimensional flows in porous media may show a complex topology whose analysis is relevant for the description of plume deformation. These results have important implications for the understanding of mixing processes, as shown in detail in the companion paper focusing on solute transport. Macroscopic helical flow occurs in 3‐D nonstationary isotropic media Helicity density is scale dependent and is used to describe flow topology Stretching and folding metrics are used to describe plume deformation
    Keywords: Topology ; Helicity ; Stretching ; Folding ; Nonstationarity ; Anisotropic Correlation Structure
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 6
    In: Water Resources Research, June 2017, Vol.53(6), pp.4984-5001
    Description: The complexity of hyporheic flow paths requires reach‐scale models of solute transport in streams that are flexible in their representation of the hyporheic passage. We use a model that couples advective‐dispersive in‐stream transport to hyporheic exchange with a shape‐free distribution of hyporheic travel times. The model also accounts for two‐site sorption and transformation of reactive solutes. The coefficients of the model are determined by fitting concurrent stream‐tracer tests of conservative (fluorescein) and reactive (resazurin/resorufin) compounds. The flexibility of the shape‐free models give rise to multiple local minima of the objective function in parameter estimation, thus requiring global‐search algorithms, which is hindered by the large number of parameter values to be estimated. We present a local‐in‐global optimization approach, in which we use a Markov‐Chain Monte Carlo method as global‐search method to estimate a set of in‐stream and hyporheic parameters. Nested therein, we infer the shape‐free distribution of hyporheic travel times by a local Gauss‐Newton method. The overall approach is independent of the initial guess and provides the joint posterior distribution of all parameters. We apply the described local‐in‐global optimization method to recorded tracer breakthrough curves of three consecutive stream sections, and infer section‐wise hydraulic parameter distributions to analyze how hyporheic exchange processes differ between the stream sections. Compounds, dissolved in river water, are transported along the river, but also to some extent into the sediments and back into the river. While being in the sediments, they may react. In reactive stream‐tracer tests, we add easy‐to‐detect reactive compounds into a stream and measure time‐series of concentration in the river further downstream. We present an approach of analyzing such tracer tests in a flexible, yet reliable manner, which also provides the uncertainty of our interpretation. This can be useful in the assessment of river‐water quality The estimation of transport parameters is coupled with the inference of a continuous travel time distribution The nested local‐in‐global approach provides the joint posterior distribution of all parameters The presented approach is applied to reactive stream‐tracer data to determine hyporheic exchange processes
    Keywords: Hyporheic Travel Time Distribution ; Local‐In‐Global Estimation ; Reactive Tracer Test ; Markov‐Chain Monte Carlo
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 7
    In: Water Resources Research, April 2017, Vol.53(4), pp.2813-2832
    Description: The spatial variability of hydraulic conductivity is known to have a strong impact on solute spreading and mixing. In most investigations, its local anisotropy has been neglected. Recent studies have shown that spatially varying orientation in sedimentary anisotropy can lead to twisting flow enhancing transverse mixing, but most of these studies used geologically implausible geometries. We use an object‐based approach to generate stacked scour‐pool structures with either isotropic or anisotropic filling which are typically reported in glacial outwash deposits. We analyze how spatially variable isotropic conductivity and variation of internal anisotropy in these features impacts transverse plume deformation and both longitudinal and transverse spreading and mixing. In five test cases, either the scalar values of conductivity or the spatial orientation of its anisotropy is varied between the scour‐pool structures. Based on 100 random configurations, we compare the variability of velocity components, stretching and folding metrics, advective travel‐time distributions, one and two‐particle statistics in advective‐dispersive transport, and the flux‐related dilution indices for steady state advective‐dispersive transport among the five test cases. Variation in the orientation of internal anisotropy causes strong variability in the lateral velocity components, which leads to deformation in transverse directions and enhances transverse mixing, whereas it hardly affects the variability of the longitudinal velocity component and thus longitudinal spreading and mixing. The latter is controlled by the spatial variability in the scalar values of hydraulic conductivity. Our results demonstrate that sedimentary anisotropy is important for transverse mixing, whereas it may be neglected when considering longitudinal spreading and mixing. When sediments are deposited in stream channels they retain the “imprint” of the stream flow that deposited them. Groundwater flows more easily along the path of this streamflow imprint than against it—this is called anisotropy. Many groundwater systems are made up of deposits from many different streams and so will have many different imprints, even when the deposits are close to each other. We found that this can cause groundwater to flow along complicated and tangled paths. These tangled groundwater paths can change the way that compounds move through the system, especially at right angles to the main groundwater flow direction. This is important because groundwater scientists often do not think about the imprint, or anisotropy, of the sediments in their studies, and perhaps they should. Internal anisotropy in realistic glacial outwash deposits causes complex three‐dimensional groundwater flow patterns Dilution of steady state plumes in anisotropic test cases is not adequately characterized by two‐particle statistics Sedimentary anisotropy is of critical importance when considering contaminant plumes controlled by transverse mixing
    Keywords: Sedimentary Anisotropy ; Transverse Mixing ; Glacial Outwash Deposits ; Dilution ; Two‐Particle Moments ; Flow Topology
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 8
    In: Water Resources Research, January 2015, Vol.51(1), pp.241-260
    Description: Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two‐dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady‐state flows. In three‐dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady‐state groundwater whirls. We analyze steady‐state solute transport in three‐dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse‐dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log‐hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two‐point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two‐particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux‐related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy. Natural sediments exhibit nonstationary anisotropic structures Nonstationary anisotropy causes secondary groundwater motion Secondary motion enhances transverse mixing and dilution
    Keywords: Nonstationarity ; Anisotropic Correlation Structure ; Secondary Motion ; Mixing ; Dilution
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 9
    In: Water Resources Research, December 2016, Vol.52(12), pp.9218-9227
    Description: While stochastic subsurface hydrology has been tremendously successful in understanding how the spatial variability of hydraulic conductivity affects conservative solute transport in idealized settings, it has gained little impact in practice. This is the case because typical assumptions needed for the derivation of analytical expressions are too restrictive for practical applications and often geologically implausible, small‐scale variation of hydraulic conductivity is by far not the only cause of uncertainty when considering the fate and remediation of pollutants, and the research community has not developed enough methods that can directly be used by practitioners. To overcome these shortcomings, we propose putting more emphasis on providing easy‐to‐use tools to generate realistic realizations of subsurface properties that are conditioned on all data measured at a site, extending the focus from hydraulic conductivity only to all parameters and processes relevant for reactive transport, making use of self‐organizing principles of reactive transport to conceptually simplify the problem, and addressing conceptual uncertainty by stochastic methods. Stochastic methods have rarely been used in practice Assumptions of closed‐form expressions are too restrictive More useful tools for practitioners are needed
    Keywords: Stochastic Subsurface Hydrology ; Contaminant Transport ; Mixing ; Reactive Transport ; Uncertainty
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 10
    In: Water Resources Research, December 2016, Vol.52(12), pp.9390-9411
    Description: We present a semianalytical model for the transport of solutes being subject to sorption in porous aquifers. We couple a travel time‐based model of advective transport with a spherical diffusion model of kinetic sorption in nonuniform material mixtures. The model is formulated in the Laplace domain and transformed to the time domain by numerical inversion. By this, three‐dimensional transport of solutes undergoing mass transfer between aqueous and solid phases can be simulated very efficiently. The model addresses both hydraulic and reactive heterogeneity of porous aquifers by means of hydrofacies, which function as homogeneous but nonuniform subunits. The total exposure time to each of these subunits controls the magnitude of sorption effects, whereas the particular sequence of facies through which the solute passes is irrelevant. We apply the model to simulate the transport of phenanthrene in a fluvio‐glacial aquifer, for which the hydrofacies distribution is known at high resolution, the lithological composition of each facies has been analyzed, and sorption properties of the lithological components are available. Taking the fully resolved hydrofacies model as reference, we evaluate different approximations referring to lower information levels, reflecting shortcomings in typical modeling projects. The most important feature for a good description of both the main breakthrough and tailing of phenanthrene is the nonuniformity of the porous medium. While spatial heterogeneity of chemical properties might be neglected without introducing a large error, an approximation of the facies' composition in terms of a uniform substitute material considerably compromises the quality of the modeling result. Efficient semianalytical transport model for sorbing solutes in heterogeneous porous media Hydraulic and reactive heterogeneity are considered by spatially distributed nonuniform hydrofacies Results show major significance of facies nonuniformity to accuracy of simulated solute breakthrough
    Keywords: Mathematical Model ; Solute Transport ; Kinetic Sorption ; Aquifer Heterogeneity
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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