Multi-scale data assimilation in SPEEDY-LETKF

In ensemble-based data assimilation, the forecast error covariance is estimated from ensemble forecasts. Here, sampling errors due to a limited ensemble size may be problematic, and we usually apply localization techniques to remove the sampling errors in distant locations. However, larger scale structures than the localization scale are also removed due to the localization. To retain the larger-scale structures with a limited ensemble size, we propose a multi-localization approach that considers the multi-scale error covariance. We separate the error covariance into a high frequency part and a low frequency part. For the high frequency part, a smaller-scale structure of the covariance is analyzed by using the high resolution model outputs and a narrow localization scale. For the low frequency part, we apply a spatial smoothing to the model outputs and use a large localization scale, so that larger-scale covariance structures are analyzed, and that more distant observations are assimilated without contaminated by the sampling error. This approach uses two localization scales simultaneously, so we call it the dual-localization approach. Here, we investigated the parameter sensitivity to the two localization scales in SPEEDY-LETKF. Using the dual-localization approach, we obtained a significant improvement.