A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography

Ibrahim Hoteit*, D. T. Pham, G. Triantafyllou, G. Korres

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations

Abstract

This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state's probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter's solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.

Original languageEnglish (US)
Pages (from-to)317-334
Number of pages18
JournalMonthly Weather Review
Volume136
Issue number1
DOIs
StatePublished - Jan 1 2008

ASJC Scopus subject areas

  • Atmospheric Science

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