The role of cross‐domain error correlations in strongly coupled 4D‐Var atmosphere–ocean data assimilation

Abstract

Strongly coupled atmosphere-ocean data assimilation offers the ability to improve information exchange across the modelled air-sea interface by enabling observations in one domain to have a direct influence on the analysis in the other. For incremental 4D-Var assimilation a strongly coupled approach enables both domains to be updated at the beginning of the assimilation window, whether they are observed or not, and is hence more likely to produce consistent initial model states. This is made possible by the explicit inclusion of cross-domain forecast error covariance information in the coupled forecast error covariance matrix. In this study we use an idealised 1D single-column coupled atmosphere-ocean model to examine the extent to which explicit cross-domain forecast error covariances play a role in shaping the coupled analysis increments compared to those implicitly generated in the inner-loop of the incremental formulation of the 4D-Var algorithm. This is done via a set of single-observation experiments with and without initial cross-domain forecast error covariances prescribed. Using single observations allows us to obtain explicit expressions for the atmosphere and ocean analysis updates, separating out the individual effects of the explicitly prescribed and implicitly generated cross-domain covariances. Our experiments show that when only one domain is observed, including explicit cross-domain error covariances allows more consistent adjustment of the unobserved domain. Neglecting the cross-domain terms and relying solely on the covariances implicitly generated by the coupled tangent linear and adjoint models restricts the ability of the covariance matrix to impose balance between the two domains. In this case the coupling is essentially one-way; the update to the observed domain is independent of the unobserved domain and so is likely to produce atmosphere and ocean updates that are inconsistent with one another.As we show, this has important consequences for the balance of the coupled analysis state. K E Y W O R D S 4D-Var, coupled data assimilation, cross-correlations, error covariancesThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz ’96 system

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