Abstract
We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period in 1979 in which several large scale atmospheric blocking regime transitions occurred in the Northern Hemisphere. We examine the role of sampling error and its effect on estimating the flow dependent growing error structures and the associated effects on the respective Kalman gains. We also introduce a Shannon entropy reduction measure and relate it to the spectra of the Kalman gain.
Highlights
A central problem in data assimilation is how best to model the error covariance matrices for the background states and analyses
A major aim of this paper is to examine covariance error estimation comparing the performance of the statistical dynamical filter in which sampling error is eliminated with the results for the ensemble square root (EnSF) and stochastic ensemble Kalman filters (EnKF)
We examine the performance of the ensemble square root filter ensemble square root filter methodology (EnSF) during a 30 day period of 12 hourly data assimilation beginning on the 16th of October 1979
Summary
A central problem in data assimilation is how best to model the error covariance matrices for the background states and analyses. Vidard et al (2003) [77] discuss a variational data assimilation method involving the determination of optimal nudging coefficients (ON) that is shown to be closely related to the Kalman filter In particular they compare the performance of the assimilation when their nudging operator is a full 4D-ON matrix, when it is ”pseudo-diagonal” (correction coefficient varies over observation locations) and when it is a constant coefficient over all spatial points at a given time. Given the background vorticity field the equation for the analysis at time t is again in terms of a linear interpolation between observations and predictions scaled by the Kalman gain K. dk are taken from a nudged integration of a barotropic model but could in general represent the Fourier transform, Eq (3), of observed fields ζ obs.
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