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  • 1
    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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  • 2
    Language: English
    In: Mathematics and Computers in Simulation, 2011, Vol.81(10), pp.2051-2061
    Description: For the simulation of transport processes in porous media effective parameters for the physical processes on the target scale are required. Numerical upscaling, as well as multiscale approaches can help where experiments are not possible, or hard to conduct. In 2009, Bastian and Engwer proposed an Unfitted Discontinuous Galerkin (UDG) method for solving PDEs in complex domains, e.g. on the pore scale. We apply this method to a parabolic test problem. Convergence studies show the expected second order convergence. As an application example solute transport in a porous medium at the pore scale is simulated. Macroscopic breakthrough curves are computed using direct simulations. The method allows finite element meshes which are significantly coarser then those required by standard conforming finite element approaches. Thus it is possible to obtain reliable numerical results for macroscopic parameter already for a relatively coarse grid.
    Keywords: Discontinuous Galerkin Method ; Higher Order ; Unfitted Finite Elements ; Numerical Upscaling ; Flows in Porous Media ; Convection–Diffusion-Problems ; Parabolic Equations ; Computer Science
    ISSN: 0378-4754
    E-ISSN: 1872-7166
    Source: ScienceDirect Journals (Elsevier)
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  • 3
    Language: English
    In: Computers and Geosciences, July 2012, Vol.44, pp.78-85
    Description: 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. ► Parallel geostatistical inversion. ► Two level parallelization. ► Efficient C++ programming.
    Keywords: Parallel Computing ; Geostatistical Inversion ; Adjoint ; Parallelization ; Geology
    ISSN: 0098-3004
    E-ISSN: 1873-7803
    Source: ScienceDirect Journals (Elsevier)
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  • 4
    Language: English
    In: Geomorphology, 2008, Vol.95(1), pp.61-73
    Description: Mud boils, a form of non-sorted circles, cover the ground surface in many periglacial landscapes. The vegetation-covered trough acts as an effective buffer to the downward movement of water and chemicals, while the bare center experiences larger fluxes of heat and mass. Since dissolved ions affect the electric conductivity of the soil solution, measurements of the bulk soil electric conductivity offer potential for estimating solute concentration. Since 1998, bulk soil electric conductivity has been measured automatically and hourly using 32 time domain reflectometry probes over an approximately 1 m diameter mud boil close to Ny Ålesund, Spitsbergen. Soil water electric conductivity was calculated from bulk soil electric conductivity using volumetric soil water content and a calibration parameter. The seasonal and spatial behaviour of water, temperature and solute concentration within two profiles of this mud boil were analyzed. Concentrations of estimated soil water electric conductivity were highest during the summer period when the active layer was thawed. Thermodynamic equilibrium modelling of the soil solution during freezing suggests that precipitation of dissolved species leads to the observed decrease in electric conductivity. There is a pronounced vertical solute concentration gradient in both profiles, while there is little evidence for horizontal solute concentration gradients beneath the mudboil.
    Keywords: Permafrost ; Freezing ; Geophysical Methods ; Electric Conductivity ; Solute Dynamics ; Patterned Ground ; Geography ; Geology
    ISSN: 0169-555X
    E-ISSN: 1872-695X
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