A multi-scale localization method was developed

We developed a new approach to error-covariance localization that considers multi-scale structure of the forecast error covariance in ensemble data assimilation methods. We found that this new approach is practical and very effective in improving accuracy of ensemble data assimilation.

With higher-resolution models, we tend to have more sampling noise in the shorter range due to limited ensemble size. This limits the use of observation data only in a limited range even though the data should impact a larger area. The figure above illustrates how the proposed multi-scale localization works. The patterns indicate what impact the observation data at the star point have. We mix the shorter-range impact (top left) with the longer-range impact (bottom left) to obtain a hybrid of both (right). This way, we preserve more structure in the shorter range, while we still include impact on an extended area using the smoothed error covariance (or smoothed ensemble perturbations). For more details, please refer to our recent publications:

• Miyoshi, T. and K. Kondo, 2013: A multi-scale localization approach to an ensemble Kalman filter. SOLA, 9, 170-173. doi:10.2151/sola.2013-038
• Kondo, K., T. Miyoshi and H. L. Tanaka, 2013: Parameter sensitivities of the dual-localization approach in the local ensemble transform Kalman filter SOLA, 9, 174-177. doi:10.2151/sola.2013-039