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, the Madden-Julien Oscillation, the Atlantic Multidecadal Oscillation, and the Pacific Decadal Oscillation. These climate oscillations have large human impacts and their response to anthropogenic climate change is uncertain. Nonequilibrium steady states can be characterized by persistent currents in phase space and we interpret climate oscillations as the physical space manifestation of those phase space currents. We describe a new diagnostic for phase space currents, the phase space angular momentum, which describes the rotational flow of trajectories in phase space by analogy to the mass angular momentum of a fluid rotating in physical space. One advantage of the phase space angular momentum is that it can be readily calculated from an observed time series with no assumptions about an underlying model. We find that the phase space angular momenta in simple stochastic models of the El-Niño Southern Oscillation and the Madden-Julien Oscillation agree surprisingly well with that seen in observations of the climate system. We propose that the phase space angular momentum might be a useful general metric to describe fluctuations in nonequilibrium steady states.