Block iterative correction in strongly coupled data assimilation

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 147; no. 738; pp. 2729 - 2740
• Main Authors: Yaremchuk, Max, Beattie, Christopher, Frolov, Sergey
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.07.2021; Wiley Subscription Services, Inc
• Subjects: Corrections; coupled modeling; Data assimilation; Data collection; Innovation; iterative methods; Numerical experiments; strongly coupled data assimilation; Vectors
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.4047

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. A method of recursive corrections is proposed for transitioning a set of uncoupled data assimilation systems to the strongly coupled formulation. The method is based on applying uncoupled solvers to a sequence of coupled innovation vectors. Testing of the method with the CERA ensemble has shown its fast convergence: The approximation error of the strongly coupled solution drops 5–12‐fold per iteration depending on the location of the uncoupled solution subject to correction. Error reduction in the equatorial region of the Tropical Pacific is shown for two types of the localization kernels used to regularize the background error covariance.