Ensemble estimation of balanced dynamics

In deriving basic understanding of geophysical flows, the analysis often revolves around discovering and exploiting relationships between fields (e.g. wind and mass through geostrophic balance) and between locations (e.g. tropics and extratropics through Rossby wave propagation). Observationally, such relationships have been determined by sampling methods over long periods of time, such as multiple case studies, composites, and time-series analysis. Theoretical progress derives mainly from scaling arguments and asymptotic expansions of the governing equations. In both cases, the relationships are usually deterministic.

Here we propose an alternative, probabilistic, approach to understanding dynamics that derives from state estimation using the ensemble Kalman filter. Probabilistic state estimates from such a filter offer the opportunity to establish non-stationary balance relationships. For example, state-dependent inversion operators for Ertel potential vorticity may be determined statistically. The range and null space of these statistical operators provide a convenient framework for defining the balanced and unbalanced part of the state, respectively. Such definitions are attractive because they hold for arbitrary departures from states of rest. Illustrative examples will be given for idealized and observed cases.