@article{359dfcae6e31490d910f4249fe888e33,
title = "A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem",
abstract = "We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the above-mentioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallow-water model. ",
keywords = " empirical orthogonal functions, SEEK filter",
author = "Serge Gratton and Patrick Laloyaux and Annick Sartenaer and {Tshimanga Ilunga}, Jean",
year = "2011",
language = "English",
pages = "452--466",
journal = "Quarterly Journal of the Royal Meteorological Society",
issn = "1477-870X",
publisher = "John Wiley and Sons Ltd",
number = "137",
}