Parallelization in the time dimension of four‐dimensional variational data assimilation

The current evolution of computer architectures towards increasing parallelism requires a corresponding evolution towards more parallel data assimilation algorithms. In this article, we consider parallelization of weak-constraint four-dimensional variational data assimilation (4D-Var) in the time dimension. We categorize algorithms according to whether or not they admit such parallelization and introduce a new, highly parallel weak-constraint 4D-Var algorithm based on a saddle-point representation of the underlying optimization problem. The potential benefits of the new saddle-point formulation are illustrated with a simple two-level quasi-geostrophic model.