Monserrat Rincon Camacho : August 31, 2012

In order to solve a large-scale data assimilation problem by an incremental four-dimensional variational technique (4D-Var), we propose to decompose it into a collection of subproblems whose associated non-linear least-square problems are ``less costly" to solve. The construction of the subproblems relies on a hierarchical decomposition of the set of observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, we adaptively add observations accordingly to a derived a posteriori error estimator. A recursive trust-region method is integrated to the resulting collection of nonlinear square problems. The particular structure of the sequence of linear systems associated to the successive linearization of the problems allows a variant of the conjugate gradient algorithm more efficient when the set of physical observations is smaller than the size of the unknown vector in the 4D-Var model. Such variation on the conjugate gradient algorithm specially benefits from the hierarchical decomposition of the set of observations. The method is tested by the Lorenz-96 system due to its low dimension and similarity characteristics to NWP systems where it is possible to include more realistic scenario for the observations distribution.