On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
Abstract: This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed whose practical performance is compared to that of other formulations. This comparison is conducted on two data assimilation instances (Burgers equation and the Quasi-Geostrophic model), using two different assumptions on parallel computing environment. Because these variants essentially retain the parallelization advantages of the original proposal, they often --- but not always --- perform best, even for moderate numbers of computing processes.
Keywords: data assimilation, variational methods, weakly-constrained 4D-VAR, saddle formulation, parallel computing
Category 1: Applications -- Science and Engineering (Basic Sciences Applications )
Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )
Category 3: Nonlinear Optimization (Unconstrained Optimization )
Citation: Technical Report, NAXYS, University of Namur, September 2017.
Entry Submitted: 09/19/2017
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