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4D variational data assimilation for locally nested models: Complementary theoretical aspects and application to a 2D shallow water model
Author(s) -
Simon Ehouarn,
Debreu Laurent,
Blayo Eric
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2244
Subject(s) - data assimilation , polygon mesh , grid , shallow water equations , mathematics , computer science , algorithm , focus (optics) , covariance , mathematical optimization , domain (mathematical analysis) , geometry , mathematical analysis , physics , statistics , computer graphics (images) , meteorology , optics
We consider the application of a four‐dimensional variational data assimilation method to a numerical model, which employs local mesh refinement to improve its solution. We focus on structured meshes where a high‐resolution grid is embedded in a coarser resolution one, which covers the entire domain. The formulation of the nested variational data assimilation algorithm was derived in a preliminary work ( Int. J. Numer. Meth. Fluids 2008; under review). We are interested here in complementary theoretical aspects. We present first a model for the multi‐grid background error covariance matrix. Then, we propose a variant of our algorithms based on the addition of control variables in the inter‐grid transfers in order to allow for a reduction of the errors linked to the interactions between the grids. These formulations are illustrated and discussed in the test case experiment of a 2D shallow water model. Copyright © 2010 John Wiley & Sons, Ltd.