Stability of strongly and weakly coupled data assimilation: error correlation cut-off

Strongly coupled data assimilation (SCDA), where observations of one component of a coupled model are allowed to directly impact the analysis of other components, sometimes fails to improve the analysis accuracy with an ensemble Kalman filter (EnKF) as compared with standard weakly coupled data assimilation (WCDA). This study, Yoshida and Kalnay, 2018, MWR, https://doi.org/10.1175/MWR-D-17-0365.1, derives a method to estimate the reduction of the analysis error variance by using estimates of the cross-covariances between the background errors of the state variables in an idealized situation. It is shown that the reduction of analysis error variance is proportional to the squared background error correlation between the analyzed and observed variables. From this, the authors propose an offline method to systematically select which observations should be assimilated into which model state variable by cutting off the assimilation of observations when the squared background error correlation between the observed and analyzed variables is small. The proposed method is tested with the local ensemble transform Kalman filter (LETKF) and a nine-variable coupled model, in which three Lorenz models with different timescales are coupled with each other. The covariance localization with the correlation-cutoff method achieves an analysis more accurate than either the full SCDA or the WCDA methods, especially with smaller ensemble sizes. We are now thoroughly testing now the correlation cut-off method on a realistic coupled ocean-atmosphere model.