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Accounting for an imperfect model in 4D‐Var
Author(s) -
Tr'emolet Yannick
Publication year - 2006
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.05.224
Subject(s) - data assimilation , state variable , variable (mathematics) , constraint (computer aided design) , forcing (mathematics) , control variable , representation (politics) , errors in variables models , computer science , mathematics , statistics , meteorology , physics , geometry , politics , political science , law , thermodynamics , mathematical analysis
Abstract In most operational implementations of four‐dimensional variational data assimilation (4D‐Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D‐Var. We present three approaches for the formulation of weak‐constraint 4D‐Var: estimating explicitly a model‐error forcing term, estimating a representation of model bias or, estimating a four‐dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D‐Var are discussed. We show that 4D‐Var with an additional model‐error representation as part of the control variable is essentially an initial‐value problem and that its characteristics are very similar to that of strong constraint 4D‐Var. Taking the four‐dimensional state as the control variable, however, leads to very different properties. In that case, weak‐constraint 4D‐Var can be interpreted as a coupling between successive strong‐constraint assimilation cycles. A possible extension towards long‐window 4D‐Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society