Joint data assimilation and parameter inference in spaces without a natural metric

Investigate methodologies for joint state–parameter data assimilation in spaces lacking a natural spatial metric, and assess the comparative effectiveness of structure-agnostic covariance estimation techniques relative to distance-based localization and hybrid estimators in such settings.

Background

The test problems in the paper possess underlying spatial structure, which likely favors distance-based localization and climatology-informed hybrid estimators. The authors note that structure-agnostic approaches (e.g., correlation-based methods) are competitive even in these settings, suggesting potential advantages in non-metric spaces.

They explicitly raise unresolved questions about how to approach joint data assimilation and parameter inference when no natural notion of distance exists and state that they leave these questions for future work.