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 radiosonde 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.