Regime signatures in the phase-space tendencies and PDF of an AGCM

Much of the dynamical behavior of the atmosphere on longer timescales has been interpreted in terms of a linear system. However, there are reasons to believe that this behavior should be fundamentally nonlinear. The phase space behavior of a very long atmospheric general circulation model (AGCM) integration is examined with the aim of determining whether significant departures from linearity can be detected.

Two approaches reveal nonlinear, regime-like behavior of the atmosphere. The probability density function (PDF) of projections onto planes defined by empirical orthogonal functions (EOFs) of the GCM's 500-hPa height field indicate significant departures from Gaussianity though no more than one maximum is found. Regime-like behavior is even more evident in the mean phase space tendencies where in some planes signatures of more than one equilibrium point are distinct (see figure).

The nonlinear structure of the mean tendencies suggests a piecewise linear behavior. It is examined to what degree a local linear decomposition describes this structure and thus justifies a multinormal approximation. The PDF of the geopotential height is decomposed into a sum of component Gaussians which will be related to the piecewise linear fit. Finally, the Fokker-Planck equation is used to relate the PDFs to the mean tendencies of the GCM.

Figure: Mean tendencies with damping removed projected onto the phase space plane spanned by the 1st and 4th EOFs.