Climate variability: a manifestation of fluctuations in a nonequilibrium steady-state

The climate system is forced by incoming solar radiation, is damped by outgoing long-wave radiation and is, apart from time-dependent natural and anthropogenic forcing, approximately in a nonequilibrium steady-state. The natural variability about the time-mean climate state takes the form of coherent, preferred, spatio-temporal patterns with names such as the El-Niño Southern Oscillation (ENSO), the Madden-Julien Oscillation (MJO), the Atlantic Multidecadal Oscillation, and the Pacific Decadal Oscillation. Climate oscillations have large human impacts and their response to anthropogenic climate change is difficult to predict. Nonequilibrium steady-states can be characterized by persistent phase space currents and we interpret climate oscillations as the physical space manifestation of those currents. We describe a diagnostic for phase space currents, the phase space angular momentum, closely related to the Lévy stochastic area. The phase space angular momentum describes the rotational flow of trajectories in phase space by analogy to the mass angular momentum of a fluid rotating in physical space. An advantage of the phase space angular momentum and stochastic area over other measures of nonequilibrium currents, such as entropy production, is that they can be readily calculated from an observed time series with no assumptions about an underlying model. We find that the phase space angular momentum in simple stochastic models of ENSO and the MJO agree surprisingly well with that seen in observations of the climate system, providing additional evidence for its utility in quantifying nonequilibrium steady-states. We propose that the phase space angular momentum and the Lévy stochastic area are useful diagnostics to intercompare climate models and to compare climate models with observations of the climate system.