The recent development of accurate coupled models of the Earth system and enhanced computation power have enabled numerical prediction with the coupled models in weather, sub-seasonal, seasonal, and interannual time scales as well as climate projection. In the shorter timescales, the initial condition, or the estimate of the present state of the system, is essential for accurate prediction. Coupled data assimilation (DA) based on an ensemble of forecasts seems to be a promising approach for this state estimate due to its inherent ability to estimate flow-dependent error covariance.

Strongly coupled DA tries to incorporate more observations of the other subsystems into an analysis (e.g., ocean observations into the atmospheric analysis) using the coupled error covariances; the covariance is estimated with a finite ensemble, and spurious covariance must be eliminated by localization. Because the coupling strength between subsystems of the Earth is not a simple function of a distance, we develop a better localization strategy than the distance-dependent localization.

Based on the estimated benefit of each observation into each analysis variable, we first propose the correlation-cutoff method, where localization of strongly coupled DA is guided by ensemble correlations of an offline DA cycle. The method achieves improved analysis accuracy when tested with a simple coupled model of the atmosphere and ocean.

As a related topic, error growth and predictability of a coupled dynamical system with multiple timescales are explored using a simple chaotic model of the atmosphere and ocean. A discontinuous response of the attractor's characteristics to the coupling strength is reported.

The characteristic of global atmosphere-ocean coupled error correlation is investigated using two sets of ensemble DA systems. This knowledge is essential for effectively implementing global strongly coupled atmosphere-ocean DA. We report and discuss common and uncommon features, and the importance of ocean model resolution is stressed.

Finally, the correlation-cutoff method is realized for global atmosphere-ocean strongly coupled DA with neural networks. The combination of static information provided by the neural networks and flow-dependent error covariance estimated by the ensemble improves the atmospheric analysis in our proof-of-concept experiment. The neural networks' ability to reproduce the error statistics, computation cost in a DA system, as well as analysis quality are evaluated.