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A parallel-in-time algorithm based on an augmented Lagrangian approach isproposed to solve four-dimensional variational (4D-Var) data assimilationproblems. The assimilation window is divided into multiple sub-intervals thatallows to parallelize cost function and gradient computations. Solutioncontinuity equations across interval boundaries are added as constraints. Theaugmented Lagrangian approach leads to a different formulation of thevariational data assimilation problem than weakly constrained 4D-Var. Acombination of serial and parallel 4D-Vars to increase performance is alsoexplored. The methodology is illustrated on data assimilation problems withLorenz-96 and the shallow water models.

A Time-parallel Approach to Strong-constraint Four-dimensional Variational Data Assimilation