Adaptive Correlation- and Distance-Based Localization for Iterative Ensemble Smoothers in a Coupled Nonlinear Multiscale Model

Abstract This paper extends the 2024 study of iterative ensemble smoothers by Evensen et al., who used a sizeable 1000-member ensemble configuration, to now using smaller, more affordable ensemble sizes with localization. As is well known, localization is needed to increase the effective ensemble size and avoid degradation of the smoother solutions by spurious correlations. As an alternative to the standard distance-based localization, we propose a reformulation of an adaptive correlation-based localization method that, in a local update, considers only those observations for which the absolute value of the correlation to the model counterpart is larger than a user-defined threshold. In the standard distance-based localization, we update model variables using only nearby observations in physical distance. In correlation-based localization, we update variables using only observations with small correlation distances. We define the correlation distance as one minus the absolute value of the ensemble correlation between a predicted measurement and the variable we are updating. Using the same formulation and implementation as in the 2024 Evensen et al. study, we compare the performance of the two localization strategies in a coupled nonlinear multiscale model and demonstrate the better or at least comparable performance of the adaptive correlation-based localization. We attribute this to an additional measurement error variance inflation for the measurements with a correlation distance close to the truncation distance, effectively leading to smoother updates. Furthermore, it solves the problem of space–time localization that is hard to solve using localization based on physical distance in ensemble smoothers over longer time windows. We also discuss strategies for the efficient implementation of the correlation-based approach.