Chaos, Quasiperiodicity, and Interannual Variability: Studies of a Stratospheric Vacillation Model

Abstract

The parameter space of a stratospheric vacillation model is investigated numerically. The model is the quasigeostrophic β-plane model introduced by Holton and Mass with time-independent forcing at the lower boundary. Chaotic and quasiperiodic states, diagnosed by the values of the largest Lyapunov exponents, are found for realistic values of the parameters. The quasiperiodic state branches off the periodic vacillations observed in previous studies through a Hopf bifurcation, and chaotic states appear after additional bifurcations. Defining an appropriate variable, a circle map behavior is revealed and the route to chaos identified as an example of the Ruelle–Takens–Newhouse scenario. The existence of additional bifurcations with constant forcing indicates that the explanation of the stratospheric variability in the Northern Hemisphere does not need to include external factors such as tropospheric variations or variations in the equatorial quasi-biennial oscillation. The bifurcations produce low-frequency components with timescales long enough to interfere with the annual cycle.