Divergence of the Ensemble Transform Kalman Filter (LETKF) by Nonlocal Observations

Abstract

Ensemble Kalman filters are powerful tools to merge model dynamics and observation data. For large system models, they are known to diverge due to subsampling errors at small ensemble size and thus possible spurious correlations in forecast error covariances. The Local Ensemble Transform Kalman filter (LETKF) remedies these disadvantages by localization in observation space. However, its application to nonlocal observations is still under debate since it is still not clear how to optimally localize nonlocal observations. The present work studies intermittent divergence of filter innovations and shows that it increases forecast errors. Nonlocal observations enhance such innovation divergence under certain conditions, whereas similar localization radius and sensitivity function width of nonlocal observations minimizes the divergence rate. The analysis of the LETKF reveals inconsistencies in the assimilation of observed and unobserved model grid points which may yield detrimental effects. These inconsistencies inter alia indicate that the localization radius should be larger than the sensitivity function width if spatially synchronized system activity is expected. Moreover, the shift of observation power from observed to unobserved grid points hypothesized in the context of catastrophic filter divergence is supported for intermittent innovation divergence. Further possible mechanisms yielding such innovation divergence are ensemble member alignment and a novel covariation between background perturbations in location and observation space.