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.
|Number of pages||15|
|Journal||Quarterly Journal of the Royal Meteorological Society|
|Publication status||Published - 2011|
- empirical orthogonal functions
- SEEK filter
Gratton, S., Laloyaux, P., Sartenaer, A., & Tshimanga Ilunga, J. (2011). A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem. Quarterly Journal of the Royal Meteorological Society, (137), 452-466.