Sudden Stratospheric Warmings as Catastrophes

Abstract

In this conceptual and numerical study, sudden stratospheric warnings (SSW) are identified as catastrophes. A catastrophe is the transition toward a separate new equilibrium after the original stable equilibrium state of a dynamical system terminates as an external parameter changes smoothly and slowly across a critical value. Many qualitative results of some previous modeling studies of SSW are interpreted in light of catastrophe theory. For example, the cutoff amplitudes in wave forcing as functions of initial conditions determined by Holton and Dunkerton are shown to be in the loci of unstable equilibria in a bifurcation diagram. Also the stage of warmest polar temperature represents the peak of the overshooting in a catastrophe. Moreover, the rapid restoration of westerlies corresponds to the return from the overshooting, Basic concepts in catastrophe theory related to SSW-for example, hysteresis, cusp and triggering-are demonstrated in a numerical study using the Holton-Mass model. The transition from the steady regime to the vacillation regime in the Holton-Mass model, i.e., SSW, is explained conceptually in terms of the topographically induced Rossby wave instability. The multiple equilibria involved owe their existence to the resonant response of the system to bottom forcing. The suddenness of SSW is due to the resonant increase of wave amplitude and its positive feedback on the mean flow. The model, as well as the conceptual explanation, gives a resonant buildup of the planetary wave, followed quickly by its decay and then by the warming peak, a scenario corresponding well with observations. A surge of wave amplitude at upper tropospheric levels prior to the warming peak is a result of the instability and, as such, should not be used as a trigger td instigate SSW as in many previous mechanistic models. Implications of the catastrophic nature of SSW for simulation and forecasting efforts are discussed. An additional and perhaps more difficult challenge in the SSW forecasting effort comes when the initial planetary wave amplitude is not yet in the rapid building-up phase; i.e., before the instability occurs.