  A parallel-in-time algorithm based on an augmented Lagrangian approach is
proposed to solve four-dimensional variational (4D-Var) data assimilation
problems. The assimilation window is divided into multiple sub-intervals that
allows to parallelize cost function and gradient computations. Solution
continuity equations across interval boundaries are added as constraints. The
augmented Lagrangian approach leads to a different formulation of the
variational data assimilation problem than weakly constrained 4D-Var. A
combination of serial and parallel 4D-Vars to increase performance is also
explored. The methodology is illustrated on data assimilation problems with
Lorenz-96 and the shallow water models.
