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Assimilation Techniques: Approximate
Kalman Filters and Singular Vectors
April 2001
By Mike Fisher
European Centre for Medium-Range Weather
Forecasts.
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1 . Introduction
For a perfect, linear model and linear observation operators, both 4dVar and the Kalman filter give the same values for the model variables at the end of the 4dVar assimilation window, provided that both systems start with the same covariance matrices at the beginning of the window. The fundamental difference between the Kalman filter and 4dVar is that the former explicitly evolves the covariance matrix, whereas the covariance evolution in 4dVar is implicit. This means that when we come to perform another cycle of analysis, the Kalman filter provides us with both a model state (background) and its covariance matrix. 4dVar does not provide the covariance matrix.
The aim of this lecture is to describe some approaches to Kalman filterering for very large systems. Particular emphasis is placed on describing the ECMWF "reduced rank" Kalman filter. This is under development as a possible replacement for the current 4dVar system.
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07.06.2002 |
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