Nonequilibrium oscillations, probability angular momentum, and the climate system

The climate system is, apart from anthropogenic forcing and other external perturbations, in a thermodynamically nonequilibrium steady-state. A major difference between fluctuations in nonequilibrium and equilibrium steady-states is that noneqilibrium steady-states violate time reversal symmetry. One manifestation is the presence of persistent probability currents, which form closed loops. In this paper, we regard the natural variability of the climate system as an expression of nonequilibrium fluctuations within the statistically steady-state and study the consequences of such persistent current loops. In particular, they give rise to preferred spatio-temporal patterns of natural climate variability that take the form of climate oscillations such as the El-Niño Southern Oscillation (ENSO) and the Madden-Julien Oscillation (MJO). In the phase space of climate indices, we observe persistent currents and define a new diagnostic for these currents: the probability angular momentum (Lτ ). Using the climate time series of ENSO and MJO, we compute both the averages and the Nonequilibrium oscillations 2 distributions of Lτ . These results are in good agreement with the analysis from a linear Gaussian model. We propose that probability angular momentum provides a new quantification of climate oscillations across models and observations. Submitted to: Dynamics and Statistics of the Climate System, Dec. 14, 2016 Nonequilibrium oscillations 3