Wavelet approximation of error covariance propagation in data assimilation

ABSTRACT Estimation of the state of the atmosphere with the Kalman filter remains a distant goal in part because of high computational cost of evolving the error covariance for both linear and non‐linear systems (in this case, the extended Kalman filter). Wavelet approximation is presented here as a...

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Bibliographic Details
Published in:Tellus. Series A, Dynamic meteorology and oceanography Dynamic meteorology and oceanography, 2004-01, Vol.56 (1), p.16-28
Main Author: TANGBORN, ANDREW
Format: Article
Language:English
Subjects:
Approximation
Covariance
Dynamical systems
Earth, ocean, space
Errors
Exact sciences and technology
External geophysics
Marine
Mathematical analysis
Mathematical models
Meteorology
Nonlinear dynamics
Physics of the oceans
Wavelet
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Summary:ABSTRACT Estimation of the state of the atmosphere with the Kalman filter remains a distant goal in part because of high computational cost of evolving the error covariance for both linear and non‐linear systems (in this case, the extended Kalman filter). Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics by implementing a wavelet approximation scheme on the assimilation of the one‐dimensional Burgers' equation. The discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6% of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
ISSN:0280-6495
1600-0870
DOI:10.1111/j.1600-0870.2004.00034.x