4D Variational Data Assimilation for Locally Nested Models : complementary theoretical aspects and application to a 2D shallow water model

Ehouarn Simon 1 Laurent Debreu 2 Eric Blayo 2
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : 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). 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.
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Submitted on : Monday, January 9, 2012 - 9:12:07 PM
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Ehouarn Simon, Laurent Debreu, Eric Blayo. 4D Variational Data Assimilation for Locally Nested Models : complementary theoretical aspects and application to a 2D shallow water model. International Journal for Numerical Methods in Fluids, Wiley, 2011, 66 (2), pp.135-161. ⟨10.1002/fld.2244⟩. ⟨hal-00658105⟩

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