Toward a strongly coupled assimilation in the Earth System Prediction Capability system

We assess a possibility to efficiently represent the strongly coupled increment in an ocean-atmosphere coupled data assimilation (DA) system by applying an iterative procedure involving uncoupled solvers and the weakly coupled analysis as a first guess approximation to the strongly coupled increment. Using the output of the ensemble-based weakly coupled DA system, we explore convergence of the approximations to the strongly coupled DA solution by applying the uncoupled solver to a sequence of innovation vectors at various spacetime locations over the global ocean grid. The results demonstrate that, in general, fewer than two iterations are required to approximate the coupled increment in the majority of the locations tested with sufficient (3%) accuracy given the uncertainty of the background error covariance estimated from the limited number of the ensemble members. We assess the impact of data thinning and hybridization of the background error covariance model on the convergence of the iterative approximations to the strongly coupled increment. An empirical relationship between the spectral radius of the expansion matrix and convergence rate is obtained.