The distribution of states in phase space produced by nonlinear systems can possess local maxima and the trajectories traced out through phase space by such systems can be markedly nonrandom. Detecting this kind of organized behavior for the atmosphere could help uncover dynamical processes not now recognized as contributing to its evolution, but searches have been frustrated by the limited duration of the observational record. As a means of determining what kind of phase space organization one might expect to find in nature, this study examines properties of the phase space of a one million day integration of a perpetual January R15 general circulation model.
Just as is true for nature, to a first approximation the probability density functions and mean trajectories for this GCM have the characteristics of a linear system. But careful analysis shows a very distinct influence by nonlinearity on the phase space behavior of the system. Nongaussianity of PDFs, as determined via mixture modeling, is one indication of nonlinearity, but even more compelling is the organization of the mean system trajectories. In some planes trajectories indicate oscillatory behavior with the equilibrium point of the oscillation being near the mean GCM state. In other planes very distinct multiple equilibrium points are evident in plots of mean trajectories. Highly organized and significant trajectory behavior of this kind has not been detected in systems with the complexity of a GCM before because of the need to sample many locations in phase space, a problem overcome by our dataset size.
To highlight the nonlinearity of the presented results, they are compared to the PDFs and trajectories that result from linearizing the GCM's equations of motion and that result from linear models that are optimally fit to the GCM simulation. Our results indicate that stochastically forced linear equations are a useful null hypothesis for our PDFs and phase space trajectories, but many features can only be understood in terms of departures from this null model, departures resulting from nonlinearity.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics