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Wavelet Approximation in Data AssimilationEstimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, 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.
Document ID
20020080877
Acquisition Source
Goddard Space Flight Center
Document Type
Preprint (Draft being sent to journal)
Authors
Tangborn, Andrew (NASA Goddard Space Flight Center Greenbelt, MD United States)
Atlas, Robert
Date Acquired
September 7, 2013
Publication Date
January 1, 2002
Subject Category
Geophysics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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