Strongly coupled data assimilation using leading averaged coupled covariance (LACC). Part I: Simple model study

This paper studies a new leading averaged coupled covariance (LACC) method for the strongly coupled data assimilation (SCDA). The SCDA not only uses the coupled model to generate the forecast and assimilate observations into multiple model components like the weakly coupled version (WCDA), but also applies a cross update using the coupled covariance between variables from different model components. The cross update could potentially improve the balance and quality of the analysis, but its implementation has remained a great challenge in practice because of different time scales between model components. In a typical extratropical coupled system, the ocean-atmosphere correlation shows a strong asymmetry with the maximum correlation occurring when the atmosphere leads the ocean by about the decorrelation time of the atmosphere. The LACC method utilizes such asymmetric structure by using the leading forecasts and observations of the fast atmospheric variable for cross update, therefore, increasing the coupled correlation and enhancing the signal-to-noise ratio in calculating the coupled covariance. Here it is applied to a simple coupled model with the ensemble Kalman filter (EnKF). With the LACC method, the SCDA reduces the analysis error of the oceanic variable by over 20% compared to the WCDA and 10% compared to the SCDA using simultaneous coupled covariance. The advantage of the LACC method is more notable when the system contains larger errors, such as in the cases with smaller ensemble size, bigger time-scale difference, or model biases.