Block iterative correction in strongly coupled data assimilation

The ongoing transition to coupled data assimilation (DA) systems encounters substantial technical difficulties associated with the need to merge together different elements of atmospheric and ocean DA systems that typically have had independent development paths for decades. In this study, we consider the incorporation of strong coupling in the observation space via successive corrections that involve the application of only uncoupled solvers to a sequence of innovation vectors. The coupled increment is then obtained by projecting a coupled innovation vector on the grid using coupled ensemble correlations. The proposed approach is motivated by the classic block Jacobi matrix iteration applied to the coupled system using the uncoupled solvers as a preconditioner. The method is tested via numerical experiments with the CERA ensemble in a simplified setting.