Consequences of Nonlinearities on the Low-Frequency Behavior of an ACGM

Although there is agreement that the atmosphere is fundamentally nonlinear, much of the behavior on longer timescales has been interpreted in terms of a linear system. A thorough analysis of the consequences of the nonlinearities is often hampered by the data requirements for such a study. With this issue in mind, an exceptionally long atmospheric general circulation model integration of NCAR's CCM0 is studied to examine the influence of nonlinearities on low-frequency behavior.

Two approaches reveal nonlinear behavior of this atmosphere: The probability density function (PDF) of projections onto planes and cubes defined by EOFs of the GCM's 500-hPa height field indicate significant departures from Gaussianity though no more than one maximum is found. Nonlinear behavior is even more evident in the mean phase space tendencies. In some subspaces these tendencies together with the trajectories they imply produce distinct signatures of more than one equilibrium point.

To quantify in which ways the detected deterministic nonlinearities produce different behavior than would occur in a system with deterministic dynamics that was linear, linear and nonlinear stochastic models are built using the mean tendency fields derived from the GCM dataset. The nonlinearities are found to markedly affect the PDF of such models even when they are highly truncated. Indeed, the nonlinearities produce non-Gaussian distributions very similar to those found in the GCM generated data. The impact of external forcing acting in conjunction with the observed nonlinearities is also quantified in terms of its influence on the PDFs of the truncated model.

Finally, an empirical nonlinear/linear hybrid-model is developed to compare its response to anomalous forcing, like the forcing associated with tropical sea surface temperature anomalies, to the response of a purely linear empirical model. In this hybrid model the dynamics in those phase space directions in which marked nonlinearities were found in the earlier part of the study are defined to be the analyzed mean GCM tendencies, while the dynamics of all other components are derived using the linear regression approach commonly used in inverse models.