Varying localization scales based upon observation impact in a serial ensemble filter

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Tuesday, 6 January 2015
Jeffrey S., Whitaker, NOAA/ESRL/PSD, Boulder, CO ; and L. Lei

Optimal covariance localization length scales typically vary with observation density in ensemble Kalman filter based data assimilation systems. Where observations are very dense, smaller localization radii are usually needed relative to regions with sparse observations. This is because the uncertainty in the ensemble mean analysis, as represented by the ensemble perturbations, tend to be smaller scale in regions with dense observations. In regions with very few or no observations, the scale of the ensemble perturbations is larger, and tends towards the climatological variability of the forecast model. In this talk we will present a scheme that calculates the localization radius based upon the predicted ensemble variance reduction in observation space in a serial ensemble filter. As the observations are assimilated, they are sorted in order of increasing posterior/prior variance in observation space. This means that the next observation assimilated is always the one which will produce the largest ensemble variance reduction. The localization radii are calculated for each observation as a function of ensemble variance reduction, so that observations with larger variance reduction can have a loarge impact on the model state than those with smaller variance reduction. This has the desired effect of reducing the average localization radius in regions of dense observations relative to regions of sparse observations. The scheme is tested with a simple two-level model and with the NCEP global forecast system model using real observations. In both cases, the scheme is found to outperform a baseline configuration using a constant localization radius in situations where the observation network is very inhomogeneous.