Linear and nonlinear signatures in the planetary wave dynamics of an AGCM: Probability density functions

There is no evidence of multiple maxima in the full PDF, but the radial ridges lead to three distinct modes in the distribution of circulation patterns. It is demonstrated that these key aspects of non-Gaussianity are captured by a two-Gaussian mixture model fitted in four dimensions. The two circulation states at the centroids of the component Gaussians are very similar to those associated with two nonlinear features identified by Branstator and Berner in their analysis of the trajectories of the GCM.

These two dynamical features are locally linear, so it is concluded that the behavior of planetary waves can be conceptualized as being approximately piecewise-linear, leading to a two-Gaussian mixture with three preferred patterns.