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@ARTICLE{Schoniger:21348,
      author       = {Schoniger, A. and Nowak, W. and Hendricks-Franssen, H.J.},
      title        = {{P}arameter estimation by ensemble {K}alman filters with
                      transformed data: {A}pproach and application to hydraulic
                      tomography},
      journal      = {Water resources research},
      volume       = {48},
      issn         = {0043-1397},
      address      = {Washington, DC},
      publisher    = {AGU},
      reportid     = {PreJuSER-21348},
      pages        = {W04502},
      year         = {2012},
      note         = {The authors would like to thank the German Research
                      Foundation (DFG) for financial support of the project within
                      the Cluster of Excellence in Simulation Technology (EXC
                      310/1) and within the International Research Training Group
                      "Nonlinearities and upscaling in porous media" (NUPUS, IRTG
                      1398) at the University of Stuttgart.},
      abstract     = {Ensemble Kalman filters (EnKFs) are a successful tool for
                      estimating state variables in atmospheric and oceanic
                      sciences. Recent research has prepared the EnKF for
                      parameter estimation in groundwater applications. EnKFs are
                      optimal in the sense of Bayesian updating only if all
                      involved variables are multivariate Gaussian. Subsurface
                      flow and transport state variables, however, generally do
                      not show Gaussian dependence on hydraulic log conductivity
                      and among each other, even if log conductivity is
                      multi-Gaussian. To improve EnKFs in this context, we apply
                      nonlinear, monotonic transformations to the observed states,
                      rendering them Gaussian (Gaussian anamorphosis, GA). Similar
                      ideas have recently been presented by Beal et al. (2010) in
                      the context of state estimation. Our work transfers and
                      adapts this methodology to parameter estimation.
                      Additionally, we address the treatment of measurement errors
                      in the transformation and provide several multivariate
                      analysis tools to evaluate the expected usefulness of GA
                      beforehand. For illustration, we present a first-time
                      application of an EnKF to parameter estimation from 3-D
                      hydraulic tomography in multi-Gaussian log conductivity
                      fields. Results show that (1) GA achieves an implicit
                      pseudolinearization of drawdown data as a function of log
                      conductivity and (2) this makes both parameter
                      identification and prediction of flow and transport more
                      accurate. Combining EnKFs with GA yields a computationally
                      efficient tool for nonlinear inversion of data with improved
                      accuracy. This is an attractive benefit, given that
                      linearization-free methods such as particle filters are
                      computationally extremely demanding.},
      keywords     = {J (WoSType)},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {Terrestrische Umwelt},
      pid          = {G:(DE-Juel1)FUEK407},
      shelfmark    = {Environmental Sciences / Limnology / Water Resources},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000302531800001},
      doi          = {10.1029/2011WR010462},
      url          = {https://juser.fz-juelich.de/record/21348},
}