State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems

Sanita Vetra-Carvalho*, Peter Jan van Leeuwen, Lars Nerger, Alexander Barth, M. Umer Altaf, Pierre Brasseur, Paul Kirchgessner, Jean Marie Beckers

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


This paper compares several commonly used state-of-the-art ensemble-based data assimilation methods in a coherent mathematical notation. The study encompasses different methods that are applicable to high-dimensional geophysical systems, like ocean and atmosphere and provide an uncertainty estimate. Most variants of Ensemble Kalman Filters, Particle Filters and second-order exact methods are discussed, including Gaussian Mixture Filters, while methods that require an adjoint model or a tangent linear formulation of the model are excluded. The detailed description of all the methods in a mathematically coherent way provides both novices and experienced researchers with a unique overview and new insight in the workings and relative advantages of each method, theoretically and algorithmically, even leading to new filters. Furthermore, the practical implementation details of all ensemble and particle filter methods are discussed to show similarities and differences in the filters aiding the users in what to use when. Finally, pseudo-codes are provided for all of the methods presented in this paper.

Original languageEnglish (US)
Article number1445364
JournalTellus, Series A: Dynamic Meteorology and Oceanography
Issue number1
StatePublished - Jan 1 2018

Bibliographical note

Publisher Copyright:
© 2018, © 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.


  • data assimilation
  • ensemble Kalman filter
  • high dimension
  • non Gaussian
  • particle filter

ASJC Scopus subject areas

  • Oceanography
  • Atmospheric Science


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