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Tangborn, Andrew (2004)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

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