Abstract
The effective action provides an appropriate cost function to determine most 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 variational approximation, which employs simple moment-closures or intuitive guesses 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 to present a serious problem for standard methods of data assimilation. In contrast, it is shown that the effective action for the climate history is already well-approximated by a one-moment closure and that the optimal, minimizing history robustly tracks climate change, even with large observation errors. Furthermore, the Hessian of the effective action provides the ensemble variance as a realistic measure of confidence level in the predicted optimal history.
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Eyink, G.L., Restrepo, J.M. Most Probable Histories for Nonlinear Dynamics: Tracking Climate Transitions. Journal of Statistical Physics 101, 459–472 (2000). https://doi.org/10.1023/A:1026437432570
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DOI: https://doi.org/10.1023/A:1026437432570