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Volume 22, issue 6 | Copyright
Nonlin. Processes Geophys., 22, 645-662, 2015
https://doi.org/10.5194/npg-22-645-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 03 Nov 2015

Research article | 03 Nov 2015

Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation

M. Bocquet1, P. N. Raanes2,3, and A. Hannart4 M. Bocquet et al.
  • 1CEREA, Joint laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
  • 2Nansen Environmental and Remote Sensing Center, Bergen, Norway
  • 3Mathematical Institute, University of Oxford, Oxford, UK
  • 4IFAECI, CNRS-CONICET-UBA, Buenos Aires, Argentina

Abstract. The ensemble Kalman filter (EnKF) is a powerful data assimilation method meant for high-dimensional nonlinear systems. But its implementation requires somewhat ad hoc procedures such as localization and inflation. The recently developed finite-size ensemble Kalman filter (EnKF-N) does not require multiplicative inflation meant to counteract sampling errors. Aside from the practical interest in avoiding the tuning of inflation in perfect model data assimilation experiments, it also offers theoretical insights and a unique perspective on the EnKF. Here, we revisit, clarify and correct several key points of the EnKF-N derivation. This simplifies the use of the method, and expands its validity. The EnKF is shown to not only rely on the observations and the forecast ensemble, but also on an implicit prior assumption, termed hyperprior, that fills in the gap of missing information. In the EnKF-N framework, this assumption is made explicit through a Bayesian hierarchy. This hyperprior has so far been chosen to be the uninformative Jeffreys prior. Here, this choice is revisited to improve the performance of the EnKF-N in the regime where the analysis is strongly dominated by the prior. Moreover, it is shown that the EnKF-N can be extended with a normal-inverse Wishart informative hyperprior that introduces additional information on error statistics. This can be identified as a hybrid EnKF–3D-Var counterpart to the EnKF-N.

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The popular data assimilation technique known as the ensemble Kalman filter (EnKF) suffers from sampling errors due to the limited size of the ensemble. This deficiency is usually cured by inflating the sampled error covariances and by using localization. This paper further develops and discusses the finite-size EnKF, or EnKF-N, a variant of the EnKF that does not require inflation. It expands the use of the EnKF-N to a wider range of dynamical regimes.
The popular data assimilation technique known as the ensemble Kalman filter (EnKF) suffers from...
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