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@ARTICLE{Keller:902846,
      author       = {Keller, Johannes and Hendricks-Franssen, Harrie-Jan and
                      Nowak, Wolfgang},
      title        = {{I}nvestigating the pilot point ensemble {K}alman filter
                      for geostatistical inversion and data assimilation},
      journal      = {Advances in water resources},
      volume       = {155},
      issn         = {0309-1708},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {FZJ-2021-04603},
      pages        = {104010 -},
      year         = {2021},
      abstract     = {Parameter estimation has a high importance in the
                      geosciences. The ensemble Kalman filter (EnKF) allows
                      parameter estimation for large, time-dependent systems. For
                      large systems, the EnKF is applied using small ensembles,
                      which may lead to spurious correlations and, ultimately, to
                      filter divergence. We present a thorough evaluation of the
                      pilot point ensemble Kalman filter (PP-EnKF), a variant of
                      the ensemble Kalman filter for parameter estimation. In this
                      evaluation, we explicitly state the update equations of the
                      PP-EnKF, discuss the differences of this update equation
                      compared to the update equations of similar EnKF methods,
                      and perform an extensive performance comparison. The
                      performance of the PP-EnKF is tested and compared to the
                      performance of seven other EnKF methods in two model setups,
                      a tracer setup and a well setup. In both setups, the PP-EnKF
                      performs well, ranking better than the classical EnKF. For
                      the tracer setup, the PP-EnKF ranks third out of eight
                      methods. At the same time, the PP-EnKF yields estimates of
                      the ensemble variance that are close to EnKF results from a
                      very large-ensemble reference, suggesting that it is not
                      affected by underestimation of the ensemble variance. In a
                      comparison of the ensemble variances, the PP-EnKF ranks
                      first and third out of eight methods. Additionally, for the
                      well model and ensemble size 50, the PP-EnKF yields
                      correlation structures significantly closer to a reference
                      than the classical EnKF, an indication of the method’s
                      skill to suppress spurious correlations for small ensemble
                      sizes.},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {2173 - Agro-biogeosystems: controls, feedbacks and impact
                      (POF4-217) / DFG project 238370553 - Ensemble Kalman Filter
                      zur Parameterschätzung in geklüfteten und fluviatilen
                      geothermischen Reservoiren},
      pid          = {G:(DE-HGF)POF4-2173 / G:(GEPRIS)238370553},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000696986200008},
      doi          = {10.1016/j.advwatres.2021.104010},
      url          = {https://juser.fz-juelich.de/record/902846},
}