Statistical Tapers for Correlation-Based Localization in Ensemble Data Assimilation

Abstract

Localization is essential in ensemble-based data assimilation because finite ensembles produce noisy covariance estimates, causing spurious updates and excessive loss of ensemble variance. In subsurface applications, localization is usually based on spatial distance, but this criterion can be hard to justify when parameter-data relationships are controlled by flow dynamics, nonlinear operators, non-local parameters, or prior conditioning effects. This work investigates correlation-based localization as an alternative strategy in which tapering coefficients are computed from the statistical reliability of estimated model-data correlations. We interpret localization as a shrinkage problem in correlation space and propose three tapers: a generalized power-law taper motivated by mean-square-error correction, a logistic taper derived from a Bayesian spike-and-slab formulation, and a discrepancy-based taper inspired by Morozov's principle. The tapers are evaluated using synthetic reservoir data assimilation problems involving scalar and grid-based parameters, localized flow responses, non-trivial correlation patterns, and increasing model dimension. The results show that correlation-based localization can suppress spurious correlations while preserving meaningful parameter-data relationships. In several cases, the proposed power-law and logistic tapers retained more posterior ensemble variance than distance-based localization while maintaining acceptable data-match quality. The logistic taper provided the strongest variance preservation, whereas smoother tapers favored better data matches. Overall, the results indicate that correlation-based localization is a statistically motivated alternative to distance-based localization, especially when spatial distance is unavailable or misleading.