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Unbiased ensemble square root filters
Author(s) -
Dance S. L.,
Livings D. M.,
Nichols N. K.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700603
Subject(s) - square root , data assimilation , mean squared error , ensemble learning , covariance , mathematics , root mean square , ensemble forecasting , algorithm , covariance matrix , set (abstract data type) , implementation , computer science , statistics , artificial intelligence , meteorology , engineering , physics , geometry , electrical engineering , programming language
Ensemble square root filters are a method of data assimilation, where model forecasts are combined with observations to produce an improved state estimate, or analysis. There are a number of different algorithms in the literature and it is not clear which of these is the best for any given application. This work shows that in some implementations there can be a systematic bias in the analysis ensemble mean and consequently an accompanying shortfall in the spread of the analysis ensemble as expressed by the ensemble covariance matrix. We have established a set of necessary and sufficient conditions for the scheme to be unbiased. While these conditions are not a cure‐all and cannot deal with independent sources of bias such as model and observation errors, they should be useful to designers of ensemble square root filters in the future. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)