A NEW APPROACH OF DATA ASSIMILATION METHODS: THE SADDLE POINT ALGORITHMS

Abstract

The goal of data assimilation is to provide as accurate as possible estimations of the physical state of numerical models based on all available information. In this thesis, a number of theoretical and technical improvements are proposed in this recent and ever growing field of study. First, a new graphic formalism that is able to describe a majority of methods is proposed. This new approach gives a good understanding of the structure of the data assimilation methods which enables the development of new ones. A new mathematical tool has also been introduced: the use of the Legendre transform on convex functions in order to describe the ``dual'' algorithms in a more general case than the Gaussian statistics.

These tools have enabled us to derive a new class of data assimilation methods: the saddle point algorithms, that include and generalize the already known methods. A numerical comparison between three algorithms has been made in order to compare their relative performances. These three algorithms leads to the same solution by different ways. The first one is a 4D-Var with the imperfect model assumption, the second one is its dual algorithm (which is implemented for the second time in this work), and the third one is a saddle point algorithm which has been discovered and tested for the first time here. It has been shown that the saddle point methods were technically possible, and that they could run twice as fast as than the classical methods.

In conclusion, some interesting ways have been opened by this work: in the technical field, new techniques able to accelerate the analysis are given, and in the theoretical field, a new kind of variational algorithm is proposed as well as a new formulation of the Kalman smoother.

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Last update : 26 mai 2003, Nicolas Daget.