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@ARTICLE{Keller:857132,
      author       = {Keller, Johannes and Hendricks Franssen, Harrie-Jan and
                      Marquart, Gabriele},
      title        = {{C}omparing {S}even {V}ariants of the {E}nsemble {K}alman
                      {F}ilter: {H}ow {M}any {S}ynthetic {E}xperiments {A}re
                      {N}eeded?},
      journal      = {Water resources research},
      volume       = {54},
      number       = {9},
      issn         = {0043-1397},
      address      = {[New York]},
      publisher    = {Wiley},
      reportid     = {FZJ-2018-06376},
      pages        = {6299 - 6318},
      year         = {2018},
      abstract     = {The ensemble Kalman filter (EnKF) is a popular estimation
                      technique in the geosciences. It is used as a numerical tool
                      for state vector prognosis and parameter estimation. The
                      EnKF can, for example, help to evaluate the geothermal
                      potential of an aquifer. In such applications, the EnKF is
                      often used with small or medium ensemble sizes. It is
                      therefore of interest to characterize the EnKF behavior for
                      these ensemble sizes. For seven ensemble sizes (50, 70, 100,
                      250, 500, 1,000, and 2,000) and seven EnKF variants (damped,
                      iterative, local, hybrid, dual, normal score, and classical
                      EnKF), we computed 1,000 synthetic parameter estimation
                      experiments for two setups: a 2‐D tracer transport problem
                      and a 2‐D flow problem with one injection well. For each
                      model, the only difference among synthetic experiments was
                      the generated set of random permeability fields. The 1,000
                      synthetic experiments allow to calculate the probability
                      density function of the root‐mean‐square error (RMSE) of
                      the characterization of the permeability field. Comparing
                      mean RMSEs for different EnKF variants, ensemble sizes and
                      flow/transport setups suggests that multiple synthetic
                      experiments are needed for a solid performance comparison.
                      In this work, 10 synthetic experiments were needed to
                      correctly distinguish RMSE differences between EnKF variants
                      smaller than $10\%.$ For detecting RMSE differences smaller
                      than $2\%,$ 100 synthetic experiments were needed for
                      ensemble sizes 50, 70, 100, and 250. The overall ranking of
                      the EnKF variants is strongly dependent on the physical
                      model setup and the ensemble size.},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {255 - Terrestrial Systems: From Observation to Prediction
                      (POF3-255)},
      pid          = {G:(DE-HGF)POF3-255},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000448088100028},
      doi          = {10.1029/2018WR023374},
      url          = {https://juser.fz-juelich.de/record/857132},
}