Changes in the state of system that are both rapid and large occur in fact only from time to time. Still, these transitions between states that are far apart in the system's phase space play a major role in its long-term evolution and statistics. In particular, extended-range weather prediction depends in a crucial way on model skill at forecasting the duration of a persistent anomaly, such as blocking, that is under way at initial forecast time. The ability to forecast the subsequent onset of another persistent anomaly -- after the break of the current one -- has proven even more elusive.
The skill of both sequential and variational methods at tracking regime transitions in simple but highly nonlinear models has been explored in the early and mid-1990s. At the same time, our understanding of the dynamics that gives rise to distinct flow regimes in the atmosphere and oceans has improved greatly. It is thus time to investigate how to track regime transitions in increasingly more detailed and realistic models of geophysical flows.
The talk will review the basic concepts of nonlinear dynamics that help explain the existence of multiple flow regimes, as well the results so far in estimating transitions between them in simple and intermediate models. It will also summarize some recent work in progress that applies these concepts to Marshall & Molteni's (1993) three-level quasi-geostrophic model in spherical geometry. This model has been shown to have a fairly realistic climatology and exhibit multiple regimes that bear some resemblance to those found in atmospheric observations. D. Kondrashov, M. Ghil, K. Ide, and R. Todling will present, in a separate paper, the details of tracking regime transitions in that model.
This talk will conclude with a number of open questions that concern the fertile common ground of nonlinear dynamics and sequential estimation. These questions include issues about the dimensionality of the relevant dynamics, as well as the consequences of this dimensionality for the implementation of computationally efficient, near-optimal filters.