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@ARTICLE{Zhou:16635,
      author       = {Zhou, H. and Gomez-Hernandez, J. and Hendricks Franssen,
                      H.J. and Li, L.},
      title        = {{A}n approach to handling non-{G}aussianity of parameters
                      and state variables in ensemble {K}alman filtering},
      journal      = {Advances in water resources},
      volume       = {34},
      issn         = {0309-1708},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {PreJuSER-16635},
      pages        = {844 - 864},
      year         = {2011},
      note         = {The authors gratefully acknowledge the financial support by
                      ENRESA (project 0079000029). The financial aid from the
                      China Scholarship Council (CSC) to the first author is
                      appreciated and extra travel grants from the Ministry of
                      Education (Spain) awarded to the first and fourth authors
                      are also acknowledged.},
      abstract     = {The ensemble Kalman filter (EnKF) is a commonly used
                      real-time data assimilation algorithm in various
                      disciplines. Here, the EnKF is applied, in a hydrogeological
                      context, to condition log-conductivity realizations on
                      log-conductivity and transient piezometric head data. In
                      this case, the state vector is made up of log-conductivities
                      and piezometric heads over a discretized aquifer domain, the
                      forecast model is a groundwater flow numerical model, and
                      the transient piezometric head data are sequentially
                      assimilated to update the state vector. It is well known
                      that all Kalman filters perform optimally for linear
                      forecast models and a multiGaussian-distributed state
                      vector. Of the different Kalman filters, the EnKF provides a
                      robust solution to address non-linearities: however, it does
                      not handle well non-Gaussian state-vector distributions. In
                      the standard EnKF, as time passes and more state
                      observations are assimilated, the distributions become
                      closer to Gaussian, even if the initial ones are clearly
                      non-Gaussian. A new method is proposed that transforms the
                      original state vector into a new vector that is univariate
                      Gaussian at all times. Back transforming the vector after
                      the filtering ensures that the initial non-Gaussian
                      univariate distributions of the state-vector components are
                      preserved throughout. The proposed method is based in
                      normal-score transforming each variable for all locations
                      and all time steps. This new method, termed the normal-score
                      ensemble Kalman filter (NS-EnKF), is demonstrated in a
                      synthetic bimodal aquifer resembling a fluvial deposit, and
                      it is compared to the standard EnKF. The proposed method
                      performs better than the standard EnKF in all aspects
                      analyzed (log-conductivity characterization and flow and
                      transport predictions). (C) 2011 Elsevier Ltd. All rights
                      reserved.},
      keywords     = {J (WoSType)},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {Terrestrische Umwelt},
      pid          = {G:(DE-Juel1)FUEK407},
      shelfmark    = {Water Resources},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000292801000004},
      doi          = {10.1016/j.advwatres.2011.04.014},
      url          = {https://juser.fz-juelich.de/record/16635},
}