Correlation-Cutoff Method for Covariance Localization in Strongly Coupled Data Assimilation

Due to its inherent ability to estimate the background error covariances, an ensemble Kalman filter (EnKF) is thought to be a practical approach to the strongly coupled data assimilation problems, where an entire coupled model state is estimated as if it was a single integrated system. However, increased complexity and the multiple time scale of the coupled system aggravate the rank-deficiency and spurious correlation problems caused by limited ensemble size available for the analysis. To alleviate these problems, a distance-independent localization method to systematically select the observations to be assimilated into each model variable has been developed and successfully tested with a nine-variable coupled model with slow and fast modes. This method, called correlation-cutoff method, utilizes the mean squared ensemble error correlation between each observable and model variable to identify where the cross-update should be used, and we cut off the assimilation of observations when the squared error correlation becomes small. To implement the method on a more realistic model, we thoroughly investigate inter-fluid background covariances in an atmosphere-ocean coupled general circulation model where the spatiotemporal scales of coupled dynamics significantly vary by latitudes and driving processes.