Empirical optimal vertical localization derived from large ensembles

Ensemble-based estimates of error covariances suffer from limited ensemble size due to computational restrictions in data assimilation systems for numerical weather prediction. Localization of error covariances can mitigate sampling errors and is crucial for ensemble-based data assimilation. However, finding optimal localization methods, functions, or scales is challenging. We present a new approach to derive an empirical optimal localization (EOL) from a large ensemble dataset. The EOL allows for a better understanding of localization requirements and can guide toward improved localization.

Our study presents EOL estimates using 40-member subsamples assuming a 1000-member ensemble covariance as truth. The EOL is derived from a 5-day training period. In the presentation, we cover both model and observation space vertical localization and discuss:

• vertical error correlations and EOL estimates for different variables and settings;

• the effect of the EOL compared to common localization approaches, such as distance-dependent localization with a Gaspari-Cohn function;

• and vertical localization of infrared and visible satellite observations in the context of observation space localization.

Proper observation space localization of error covariances between non-local satellite observations and state space is non-trivial and still an open research question. First, we evaluate requirements for optimal localization for different variables and spectral channels. And secondly, we investigate the situation dependence of vertical localization in convection-permitting NWP simulations, which suggests an advantage of using adaptive situation-dependent localization approaches.