Global Modeling and Assimilation Office/GSFC/NASA
University of Maryland Baltimore County
We present techniques for the approximate evolution of error covariance statistics used in atmospheric data assimilation. This step dominates the computational requirements of the Kalman filter, and is therefore a logical and frequent target of approximation methods. Error correlations needed by assimilation systems are influenced by the observing network, model errors and propagation due to atmospheric winds, and therefore tend to become highly localized. Wavelet functions are an efficient way to represent localized information and therefore have the potential transform the error correlations into a low dimensional system.
We will present some basic theory of compactly supported wavelet functions, and apply the wavelet transform to the extended Kalman filter for Burger's equation, and to a global constituent assimilation system. We show that as much as 95% of coefficients can be discarded without significant loss of accuracy.