Thursday, 2 August 2001
Wavelet Approximation in the Computation of Error Covariance Evolution
We present techniques for the approximate evolution of error
correlation 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 apply this technique to an existing constituent
assimilation system and show that the error correlations can be
compressed by about a factor of 50 without loss of localized
information. We also extend this work to non-linear systems using
the extended Kalman Filter (EKF) applied to the one-dimensional
Burgers equation and show that only a small fraction of the wavelet
coefficients are required to capture the covariance dynamics.