The local ensemble transform Kalman filter (LETKF) with an intermediate atmospheric general circulation model (AGCM) is implemented with the Japanese 10 petaflops (floating point operations per second) "K computer" for large-ensemble simulations of 10,240 members, 2 orders of magnitude greater than the typical ensemble size of about 100. The computational challenge includes the eigenvalue decomposition of 10,240 × 10,240 dense covariance matrices at each grid point. Using the efficient eigenvalue solver for the K computer, the LETKF computations are accelerated by a factor of 8, allowing a 3 week experiment of 10,240-member LETKF with an intermediate AGCM for the first time. The flow-dependent 10,240-member ensemble revealed meaningful long-range error correlations at continental scales. The surface pressure error correlation shows teleconnection patterns like the Pacific North American pattern. Specific humidity error correlation shows continental scale wave trains. Investigations with different ensemble sizes suggest that at least several hundred members be necessary to capture these continental scale error correlations.

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Ensemble data assimilation methods have been improved consistently and have become a viable choice in operational numerical weather prediction. A number of issues for further improvements have been explored, including flow-adaptive covariance localization and advanced covariance inflation methods. Dealing with multi-scale error covariance is among the unresolved issues that would play essential roles in analysis performance. With higher resolution models, generally narrower localization is required to reduce sampling errors in ensemble-based covariance between distant locations. However, such narrow localization limits the use of observations that would have larger-scale information. Previous attempts include successive covariance localization by F. Zhang et al. who proposed applying different localization scales to different subsets of observations. The method aims to use sparse radio sonde observations at a larger scale, while using dense Doppler radar observations at a small scale simultaneously. This study aims to separate scales of the analysis increments, independently of observing systems. Inspired by M. Buehner, we applied two different localization scales to find analysis increments at the two separate scales, and obtained improvements in simulation experiments using an intermediate AGCM known as the SPEEDY model.(Citation: Miyoshi, T., and K. Kondo, 2013: A multi-scale localization approach to an ensemble Kalman filter. SOLA, 9, 170−173,

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