Abstract
A detailed analysis of the bifurcation structure of a two-level, quasigeostrophic model is made by a combined use of a continuation algorithm and extensive time integrations. The model is formulated on a sphere with realistic Northern Hemisphere topography and is driven by Newtonian relaxation to axisymmetric radiative-equilibrium temperature that represents the equator-to-pole contrast of the diabatic heating. The strength of this heating contrast is varied as a primary control parameter. Bifurcations of not only stationary but also periodic, doubly periodic (quasi periodic), and chaotic solutions are followed for the model with triangular 15 (T15) horizontal resolution, corresponding to the number of (real) spherical harmonic coefficients, 240.
It is found that the model possesses multiple attractors for a fairly broad, but realistic, range in the parameter space. Characteristic oscillatory modes are associated with each one of these attractors. Two frequency bands, one in synoptic and the other in intraseasonal timescales, are dominant in such oscillations. These attractors keep their identity even when the system is perturbed by stochastic forcing of fairly large amplitude. Furthermore, when some parameters are changed to make the system more turbulent, it is observed that the system starts transiting among the ruins of attractors that used to be stable, a behavior reminiscent of the transitions among different flow regimes observed in the real atmosphere. Such behavior, called chaotic itinerancy, has recently attracted much attention as a characteristic of chaos in physical systems with many degrees of freedom. Chaotic itinerancy in the present model appears to be more complicated than the examples reported so far in that it consists of attractors with no obvious spatial symmetry and that preferred routes of transitions are observed. Evidences of multiple attractors and chaotic itinerancy are found in higher resolutions up to T21.
Discussions are made about implications of such model behavior to the understanding of observed low-frequency variability.
