Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances

Mickaël David Chekroun, J. David Neelin, Dmitri Kondrashov, James C. McWilliams, and Michael Ghil, 2012:
Proc. Nat. Acd. Sci., 111 (5) 1684-1690, doi: 10.1073/pnas.1321816111.
PNAS journal link.

Main paper and supplement.
© Copyright 2013 by the National Academy of Sciences.

Abstract. Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them as filtered through an observable of the system is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap defined as the distance between the subdominant RP resonance and the unit circle plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

Citation.Chekroun, M. D., J. D. Neelin, D. Kondrashov, J. C. McWilliams1, and M. Ghil, 2014: Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances Proc. Nat. Acd. Sci., 111 (5) 1684—1690, doi: 10.1073/pnas.1321816111.


Acknowledgments. M.D.C. thanks Honghu Liu for help in preparing Fig. S1 and Joyce Meyerson for help in preparing Figs. 1-3. This study was supported by National Science Foundation Grants DMS 1049253 and AGS-1102838, Office of Naval Research Grant N00014-12-1-0911, and Department of Energy Grant DE-SC0006739.