A "Typical" and "Atypical" Application of Ensemble Filtering

In typical applications of ensemble Kalman filtering, a numerical model is used to evolve the probability distribution though time by operating on an ensemble of state vectors. The covariance structures on which one draws during the update-step arise naturally from the dynamics of the numerical model. Here we present a text-book application of the ensemble Kalman filter, in which we assimilate observations of SST in the tropical Pacific to make state-estimates of the interannual (ENSO-related) modes of ocean/atmosphere variability. Our results illuminate some pitfalls of naively chosen localization functions, in particular how the dynamical structure of the numerical model must be taken into consideration when applying localization.
The second part of this talk is concerned with a less-typical use of ensemble filtering, where I will discuss its application to historical reconstructions. Historical reconstructions are typically done in the absence of a numerical model, where parametric forms of the covariance structure are assumed stationary and are modeled from a finite and fixed ensemble of modern data. I will briefly present the problem of SST reconstruction from the traditional (Bayesian, parametric) perspective, and demonstrate how ensemble methods can be used to do non-parametric reconstruction in a straightforward way. I will also mention some ideas for extending this framework into a non-parametric approach to "evolving" the covariance model.
An overview of challenges in the field of ensemble filtering will be briefly discussed at the close.