Most probable histories for nonlinear dynamics: Tracking climate transitions

The effective action provides an appropriate cost function to determine mos t probable (or optimal) histories for nonlinear dynamics with strong noise. In such strong-coupling problems, a nonperturbative technique is required to calculate the effective action. We have proposed a Rayleigh-Ritz variati onal approximation, which employs simple moment-closures or intuitive guess es of the statistics to calculate the effective action. We consider here an application to climate dynamics, within a simple "bimodal" Langevin model similar to that proposed by C. Nicolis and G. Nicolis [Tellus 33:225 (1981) ]. Capturing climate state transitions even in this simple model is known t o present a serious problem for standard methods of data assimilation. In c ontrast, it is shown that the effective action for the climate history is a lready well-approximated by a one-moment closure and that the optimal, mini mizing history robustly tracks climate change, even with large observation errors. Furthermore, the Hessian of the effective action provides the ensem ble variance as a realistic measure of confidence level in the predicted op timal history.