On the Selection of Localization Radius in Ensemble Filtering for Multiscale Quasigeostrophic Dynamics

Covariance localization in ensemble filtering can reduce sampling errors due to limited ensemble size. The search for an optimal localization radius seeks essentially the balance between removing sampling error and reducing information loss. The optimal localization is suggested in previous studies to be dependent on ensemble size, observation density and uncertainties, as well as the underlying correlation scale that is determined by the model dynamics. However, the relative importance of these factors under complex multiscale dynamical system remains an active area of research. Based on a two-layer quasi-geostrophic model, this study systematically evaluates the sensitivity of ensemble filter performance to the choice of covariance localization under different model and ensemble configurations. Results show that when the ensemble size is sufficiently large, the best localization radius increases with increasing ensemble size, increasing mean physical correlation length scale, and/or increasing observation error due to a sparser or less accurate observing network. The sensitivity, however, is found to be small when a relatively small sampling error is present, namely a wide range of localization radius is suitable in this case. However, when the ensemble size is small, the mean physical correlation length scale of the multi-scale model becomes a more dominant factor in the choice of the best-performance localization radius. Findings from these sensitivity experiments provide a practical guidance for the selection of localization distance in complex multiscale dynamical systems, and for the future development of adaptive localization algorithms.