comparison of statistical dynamical, square root and ensemble kalman filters比较统计动力,平方根和集合卡尔曼滤波器.pdf

Entropy 2008, 10, 684-721; DOI: 10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Comparison of Statistical Dynamical, Square Root and Ensemble Kalman Filters Terence J. O’Kane and Jorgen S. Frederiksen Centre for Australian Climate Weather Research, Bureau of Meteorology, Docklands, Australia. E-mail: t.okane@.au. Centre for Australian Climate Weather Research, CSIRO Marine Atmospheric Research, Aspendale, Australia. E-mail: Jorgen.Frederiksen@csiro.au Author to whom correspondence should be addressed. Received: 30 May 2008 / Accepted: 31 October 2008 / Published: 20 November 2008 Abstract: We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covari- ance 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 atmo- spheric 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 struc- tures 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. Keywords: Data assimilation, Entropy, Turbulence closures 1. Introduction A central problem in data assimilation is how best to model the error covariance matrices for the background states and analyses. The aim of data assim