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Four‐dimensional variational data assimilation: A new formulation of the background‐error covariance matrix based on a potential‐vorticity representation
Author(s) -
Cullen M. J. P.
Publication year - 2003
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.02.10
Subject(s) - data assimilation , robustness (evolution) , potential vorticity , covariance matrix , numerical weather prediction , covariance , mathematics , meteorology , minification , uncorrelated , vorticity , computer science , mathematical optimization , algorithm , statistics , physics , biochemistry , chemistry , vortex , gene
All variational data assimilation schemes use some form of mass–wind coupling in their definitions of the control variables used in the minimization of the cost function. At the European Centre for Medium‐Range Weather Forecasts, the statistical coupling developed by Parrish and Derber (1992) is used. This is simple and robust. The robustness is obtained by calculating the mass–wind correlations from a dataset representing short‐range forecast errors. A potential disadvantage of this method is that, if the calibration dataset is not well balanced, there will be little mass–wind coupling in the analysis procedure. An alternative procedure is to assume that the balanced part of the errors, represented in this case by potential‐vorticity errors, is uncorrelated with the unbalanced part of the error. This would be natural for a linear model. A simple potential‐vorticity based method is developed and tested. It is shown that the strong scale dependence of the gravity‐wave speed introduces significant numerical difficulties. However, with care, good results can be obtained. Copyright © 2003 Royal Meteorological Society