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We develop innovative algorithms for solving the strong-constraintformulation of four-dimensional variational data assimilation in large-scaleapplications. We present a space-time decomposition approach that employsdomain decomposition along both the spatial and temporal directions in theoverlapping case and involves partitioning of both the solution and theoperators. Starting from the global functional defined on the entire domain, weobtain a type of regularized local functionals on the set of subdomainsproviding the order reduction of both the predictive and the data assimilationmodels. We analyze the algorithm convergence and its performance in terms ofreduction of time complexity and algorithmic scalability. The numericalexperiments are carried out on the shallow water equation on the sphereaccording to the setup available at the Ocean Synthesis/Reanalysis Directoryprovided by Hamburg University.

journal of scientific computing

A scalable space-time domain decomposition approach for solving  large-scale nonlinear regularized inverse ill-posed problems in 4D  variational data assimilation