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An investigation of incremental 4D‐Var using non‐tangent linear models
Author(s) -
Lawless A. S.,
Gratton S.,
Nichols N. K.
Publication year - 2005
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.04.20
Subject(s) - tangent , data assimilation , mathematics , rate of convergence , perturbation (astronomy) , convergence (economics) , mathematical optimization , computer science , geometry , meteorology , physics , computer network , channel (broadcasting) , quantum mechanics , economics , economic growth
We investigate the convergence of incremental four‐dimensional variational data assimilation (4D‐Var) when an approximation to the tangent linear model is used within the inner loop. Using a semi‐implicit semi‐Lagrangian model of the one‐dimensional shallow water equations, we perform data assimilation experiments using an exact tangent linear model and using an inexact linear model (a perturbation forecast model). We find that the two assimilations converge at a similar rate and the analyses are also similar, with the difference between them dependent on the amount of noise in the observations. To understand the numerical results, we present the incremental 4D‐Var algorithm as a Gauss–Newton iteration for solving a least‐squares problem and consider its fixed points. Copyright © 2005 Royal Meteorological Society.