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  • Groundwater Flow
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  • 1
    Language: English
    In: Journal of Hydrology, February 2017, Vol.545, pp.42-54
    Description: Groundwater resources management requires operational, regional-scale groundwater models accounting for dominant spatial variability of aquifer properties and spatiotemporal variability of groundwater recharge. We test the Ensemble Kalman filter (EnKF) to estimate transient hydraulic heads and groundwater recharge, as well as the hydraulic conductivity and specific-yield distributions of a virtual phreatic aquifer. To speed up computation time, we use a coarsened spatial grid in the filter simulations, and reconstruct head measurements at observation points by a local model in the vicinity of the piezometer as part of the observation operator. We show that the EnKF can adequately estimate both the mean and spatial patterns of hydraulic conductivity when assimilating daily values of hydraulic heads from a highly variable initial sample. The filter can also estimate temporally variable recharge to a satisfactory level, as long as the ensemble size is large enough. Constraining the parameters on concentrations of groundwater-age tracers (here: tritium) and transient hydraulic-head observations cannot reasonably be done by the EnKF because the concentrations depend on the recharge history over longer times while the head observations have much shorter temporal support. We thus use a different method, the Kalman Ensemble Generator (KEG), to precondition the initial ensemble of the EnKF on the groundwater-age tracer data and time-averaged hydraulic-head values. The preconditioned initial ensemble exhibits a smaller spread as well as improved means and spatial patterns. The preconditioning improves the EnKF particularly for smaller ensemble sizes, allowing operational data assimilation with reduced computational effort. In a validation scenario of delineating groundwater protection zones, the preconditioned filter performs clearly better than the filter using the original initial ensemble.
    Keywords: Data Assimilation of Hydraulic Heads ; Ensemble Kalman Filter ; Kalman Ensemble Generator ; Groundwater-Age Tracers ; Phreatic Aquifer ; Groundwater Recharge ; Hydraulic Conductivity ; Specific Yield ; Geography
    ISSN: 0022-1694
    E-ISSN: 1879-2707
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  • 2
    Language: English
    In: Water Resources Management, Sept, 2013, Vol.27(12), p.4349(20)
    Description: Byline: Ashutosh Singh (1), Claudius M. Burger (1), Olaf A. Cirpka (1) Keywords: Urban hydrogeology; Groundwater management; MODFLOW; Numerical modeling; Response matrix; Optimization Abstract: In rapidly developing urban areas of emerging countries, increased water demand has led to enormous groundwater withdrawal, calling out for sustainable groundwater management. We suggest implementing a sustainable pumping rate concept based on numerical modeling of the managed aquifer. Sustainability is achieved by constraints regarding (1) a minimum groundwater discharge rate to gaining rivers (ecological constraint) and (2) a maximum drawdown along the city boundaries (social constraints) to prevent excessive groundwater depletion in the neighboring peri-urban and rural areas. The total groundwater extraction is maximized subject to these constraints, leading to specific extraction patterns throughout the city, depending upon the values set for the constraints. The optimization is performed by linear programming. For a given extraction rate, the two constraints can be traded off by the groundwater manager, causing different wells to be activated or deactivated. We demonstrate the applicability of the methodology by the example of the city of Lucknow, India, but it can be transferred to other cities facing conflicts of managing groundwater resources. Author Affiliation: (1) Center for Applied Geoscience (ZAG), University of Tubingen, Holderlinstr. 12, 72074, Tubingen, Germany Article History: Registration Date: 05/08/2013 Received Date: 15/03/2013 Accepted Date: 05/08/2013 Online Date: 18/08/2013
    Keywords: Hydrogeology -- Models ; Water Resource Management -- Models ; Aquifers -- Models ; Groundwater -- Models ; Developing Countries -- Models
    ISSN: 0920-4741
    E-ISSN: 15731650
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  • 3
    Language: English
    In: Advances in Water Resources, April 2017, Vol.102, pp.161-177
    Description: In the geostatistical inverse problem of subsurface hydrology, continuous hydraulic parameter fields, in most cases hydraulic conductivity, are estimated from measurements of dependent variables, such as hydraulic heads, under the assumption that the parameter fields are autocorrelated random space functions. Upon discretization, the continuous fields become large parameter vectors with elements. While cokriging-like inversion methods have been shown to be efficient for highly resolved parameter fields when the number of measurements is small, they require the calculation of the sensitivity of each measurement with respect to all parameters, which may become prohibitive with large sets of measured data such as those arising from transient groundwater flow. We present a Preconditioned Conjugate Gradient method for the geostatistical inverse problem, in which a single adjoint equation needs to be solved to obtain the gradient of the objective function. Using the autocovariance matrix of the parameters as preconditioning matrix, expensive multiplications with its inverse can be avoided, and the number of iterations is significantly reduced. We use a randomized spectral decomposition of the posterior covariance matrix of the parameters to perform a linearized uncertainty quantification of the parameter estimate. The feasibility of the method is tested by virtual examples of head observations in steady-state and transient groundwater flow. These synthetic tests demonstrate that transient data can reduce both parameter uncertainty and time spent conducting experiments, while the presented methods are able to handle the resulting large number of measurements.
    Keywords: Inverse Modeling ; Geostatistical Inversion ; Uncertainty Quantification ; Nonlinear Conjugate Gradients ; Preconditioning ; Engineering
    ISSN: 0309-1708
    E-ISSN: 1872-9657
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  • 4
    Language: English
    In: Computers and Geosciences, July, 2012, Vol.44, p.78(8)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.cageo.2012.03.014 Byline: Ronnie L. Schwede (a), Adrian Ngo (b), Peter Bastian (b), Olaf Ippisch (b), Wei Li (a), Olaf A. Cirpka (a) Abstract: Hydraulic conductivity is a key parameter for the simulation of groundwater flow and transport. Typically, it is highly variable in space and difficult to determine by direct methods. The most common approach is to infer hydraulic-conductivity values from measurements of dependent quantities, such as hydraulic head and concentration. In geostatistical inversion, the parameters are estimated as continuous, spatially auto-correlated fields, the most likely values of which are obtained by conditioning on the indirect data. In order to identify small-scaled features, a fine three-dimensional discretization of the domain is needed. This leads to high computational demands in the solution of the forward problem and the calculation of sensitivities. In realistic three-dimensional settings with many measurements parallel computing becomes mandatory. In the present study, we investigate how parallelization of the quasi-linear geostatistical approach of inversion can be made most efficient. We suggest a two-level approach of parallelization, in which the computational domain is subdivided and the evaluation of sensitivities is also parallelized. We analyze how these two levels of parallelization should be balanced to optimally exploit a given number of computing nodes. Author Affiliation: (a) University of Tubingen, Center for Applied Geoscience, Holderlinstr. 12, 72074 Tubingen, Germany (b) University of Heidelberg, Interdisciplinary Center of Scientific Computing, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany Article History: Received 20 December 2011; Revised 24 February 2012; Accepted 19 March 2012
    Keywords: Hydrogeology -- Analysis ; Groundwater Flow -- Analysis ; Hydraulic Flow -- Analysis ; Groundwater -- Analysis ; Geostatistics -- Analysis
    ISSN: 0098-3004
    Source: Cengage Learning, Inc.
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  • 5
    Language: English
    In: Journal of Contaminant Hydrology, 2010, Vol.111(1), pp.36-47
    Description: The contaminant mass discharge crossing a control plane is an important metric in the assessment of natural attenuation at contaminated sites. For risk-assessment purposes, the mass discharge must be estimated together with a level of uncertainty. We present a conditional Monte Carlo approach that allows estimating the statistical distribution of mass discharge. The approach is based on conditioning multiple realizations of the hydraulic conductivity field on all data available. We jointly determine a first-order decay coefficient in each realization, leading to conditional statistical distributions of all estimated parameters and the total mass discharge. The resulting statistical distribution of contaminant mass discharges can be used in the assessment of risks at the contaminated site. The method is applied to data of hypothetical test cases, which gives the opportunity to compare estimation results to the true field. As concentration data, we account for pointlike measurements obtained in multi-level sampling wells. The obtained empirical distribution of mass discharge crossing the multi-level sampling fence could be well fitted by a log-normal distribution.
    Keywords: Groundwater ; Steady-State Concentration ; Mass Discharge Distribution ; Bayesian Inference ; Engineering ; Environmental Sciences ; Geography
    ISSN: 0169-7722
    E-ISSN: 1873-6009
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  • 6
    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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  • 7
    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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  • 8
    Language: English
    In: Journal of contaminant hydrology, 2012, Vol.140, pp.95-106
    Description: Compound-specific stable isotope analysis (CSIA) has increasingly been used as a tool to assess intrinsic biodegradation at contaminated field sites. Typically, the Rayleigh equation is used to estimate the extent of biodegradation from measured isotope ratios of the contaminant. However, if the rate-limiting step in overall degradation is not the microbial reaction itself, the Rayleigh equation may no more be applicable. In this study we simulate biodegradation of continuously emitted petroleum hydrocarbons in groundwater systems. These contaminants are effectively degraded at the plume fringe where transverse dispersion makes them mix with dissolved electron acceptors present in the ambient groundwater. We simulate reactive transport to study the coupled effects of transverse mixing and biodegradation on the spatial patterns of carbon isotope signatures and their interpretation based on depth-integrated sampling which represents the most common setup in the assessment of contaminated sites. We present scenarios mimicking a hydraulically uniform laboratory experiment and a field-scale application considering heterogeneous conductivity fields. We compare cases in which isotopologue-specific transverse dispersion is considered to those where this additional fractionation process is neglected. We show that these effects cause significant shifts in the isotopic signals and may lead to overestimation of biodegradation. Moreover, our results provide evidence that the rate-limiting effect of transverse mixing on the overall degradation spatially varies along the length of a steady-state contaminant plume. The control of biodegradation by transverse dispersion and the fractionating effect of dispersion modulate the fractionation caused by the microbial reaction alone. As a consequence, significantly nonlinear isotopic patterns are observed in a Rayleigh plot. Simulations in heterogeneous flow domains show that these effects persist at larger field scales and are sensitive to the degree of mixing enhancement, determined by the heterogeneity of the hydraulic conductivity fields, and to the groundwater flow velocity. ; p. 95-106.
    Keywords: Groundwater ; Biodegradation ; Isotope Fractionation ; Dispersions ; Carbon ; Hydrocarbons ; Petroleum ; Equations ; Hydraulic Conductivity ; Stable Isotopes ; Electrons ; Groundwater Flow
    ISSN: 0169-7722
    Source: AGRIS (Food and Agriculture Organization of the United Nations)
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  • 9
    Language: English
    In: Journal of Contaminant Hydrology, Oct, 2012, Vol.140-141, p.95(12)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jconhyd.2012.08.010 Byline: Dominik Eckert, Massimo Rolle, Olaf A. Cirpka Keywords: Isotope fractionation; Rayleigh equation; Mixing; Transverse dispersion; Biodegradation Abstract: Compound-specific stable isotope analysis (CSIA) has increasingly been used as a tool to assess intrinsic biodegradation at contaminated field sites. Typically, the Rayleigh equation is used to estimate the extent of biodegradation from measured isotope ratios of the contaminant. However, if the rate-limiting step in overall degradation is not the microbial reaction itself, the Rayleigh equation may no more be applicable. In this study we simulate biodegradation of continuously emitted petroleum hydrocarbons in groundwater systems. These contaminants are effectively degraded at the plume fringe where transverse dispersion makes them mix with dissolved electron acceptors present in the ambient groundwater. We simulate reactive transport to study the coupled effects of transverse mixing and biodegradation on the spatial patterns of carbon isotope signatures and their interpretation based on depth-integrated sampling which represents the most common setup in the assessment of contaminated sites. We present scenarios mimicking a hydraulically uniform laboratory experiment and a field-scale application considering heterogeneous conductivity fields. We compare cases in which isotopologue-specific transverse dispersion is considered to those where this additional fractionation process is neglected. We show that these effects cause significant shifts in the isotopic signals and may lead to overestimation of biodegradation. Moreover, our results provide evidence that the rate-limiting effect of transverse mixing on the overall degradation spatially varies along the length of a steady-state contaminant plume. The control of biodegradation by transverse dispersion and the fractionating effect of dispersion modulate the fractionation caused by the microbial reaction alone. As a consequence, significantly nonlinear isotopic patterns are observed in a Rayleigh plot. Simulations in heterogeneous flow domains show that these effects persist at larger field scales and are sensitive to the degree of mixing enhancement, determined by the heterogeneity of the hydraulic conductivity fields, and to the groundwater flow velocity. Article History: Received 10 February 2012; Revised 9 August 2012; Accepted 10 August 2012
    Keywords: Groundwater Flow -- Analysis ; Hydrogeology -- Analysis ; Groundwater -- Analysis ; Biodegradation -- Analysis
    ISSN: 0169-7722
    Source: Cengage Learning, Inc.
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  • 10
    Language: English
    In: Advances in Water Resources, November 2014, Vol.73, pp.134-143
    Description: Flows showing complex topology are ubiquitous in natural systems. However, contrasting evidence exists on the helical nature of flow in porous media and on the occurrence of groundwater whirls. We analyze the topology of steady-state flow fields in porous media, highlighting the importance of considering the three-dimensionality of the flow field to properly capture the complexity of the system dynamics controlling the deformation of material surfaces, which is widely recognized as the main driver of mixing. We use the helicity density as topological measure and investigate the necessary and sufficient conditions to obtain non-zero helicity density for Darcy flow. We show that helical groundwater flow can develop in both homogeneous and heterogeneous porous media, provided that the hydraulic conductivity is anisotropic. In the homogeneous case, the additional condition of non-vanishing mixed second spatial derivatives of hydraulic head is required, while in heterogeneous media, helical flow may occur even when the hydraulic gradient is uniform. We present illustrative examples of complex flow topology in three-dimensional porous media and discuss the computed streamline patterns and their potential implications for mixing processes.
    Keywords: Helicity ; Anisotropy ; Porous Media ; Streamlines ; Groundwater Whirls ; Mixing ; Engineering
    ISSN: 0309-1708
    E-ISSN: 1872-9657
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