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Original Research Papers

Wavelet approximation of error covariance propagation in data assimilation

Author:

Andrew Tangborn

Data Assimilation Office NASA-GSFC, Code 910.3, Greenbelt, MD; JCET, University of Maryland-Baltimore County, Baltimore, MD, US
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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.

How to Cite: Tangborn, A., 2004. Wavelet approximation of error covariance propagation in data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 56(1), pp.16–28. DOI: http://doi.org/10.3402/tellusa.v56i1.14388
  Published on 01 Jan 2004
 Accepted on 19 May 2003            Submitted on 2 May 2002

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