Stratospheric Sudden Warmings as Self-Tuning Resonances. Part I: Vortex Splitting Events

Abstract

The fundamental dynamics of ''vortex splitting'' stratospheric sudden warmings (SSWs), which are known to be predominantly barotropic in nature, are reexamined using an idealized single-layer f-plane model of the polar vortex. The aim is to elucidate the conditions under which a stationary topographic forcing causes the model vortex to split, and to express the splitting condition as a function of the model parameters determining the topography and circulation.For a specified topographic forcing profile the model behavior is governed by two nondimensional parameters: the topographic forcing height M and a surf-zone potential vorticity parameter V. For relatively low M, vortex splits similar to observed SSWs occur only for a narrow range of V values. Further, a bifurcation in parameter space is observed: a small change in V (or M) beyond a critical value can lead to an abrupt transition between a state with low-amplitude vortex Rossby waves and a sudden vortex split. The model behavior can be fully understood using two nonlinear analytical reductions: the Kida model of elliptical vortex motion in a uniform strain flow and a forced nonlinear oscillator equation. The abrupt transition in behavior is a feature of both reductions and corresponds to the onset of a nonlinear (self-tuning) resonance. The results add an important new aspect to the ''resonant excitation'' theory of SSWs. Under this paradigm, it is not necessary to invoke an anomalous tropospheric planetary wave source, or unusually favorable conditions for upward wave propagation, in order to explain the occurrence of SSWs. 1 The present study casts doubt on the accuracy of quasi-linear wave-mean models such as that used by Smith, as it is shown explicitly in section 4d that the interaction of weakly nonlinear vortex Rossby waves with their second harmonic is equally important as their interaction with the zonal mean flow.

Vortex Preconditioning due to Planetary and Gravity Waves prior to Sudden Stratospheric Warmings

“…The fact that there is a multiday time lag between when the vortex begins to split and when the largest wave fluxes appear seems to support the contention put forth by Matthewman and Esler (2011) that split-type SSWs are characterized by nonlinear wave growth (i.e., a wave-amplitude bifurcation) rather than anomalous tropospheric wave forcing. The key but subtle implication to this idea is that, while an SSW is indeed characterized by a large-amplitude wave-2 vortex event, the anomalously large wave fluxes themselves are the result, not the cause, of the SSW.…”

“…In contrast to the concept of anomalous wavetriggered SSWs, recent theoretical SSW studies have suggested that anomalous tropospheric upward wave fluxes are not necessary for triggering an SSW (Esler and Scott 2005;Scott and Polvani 2006;Matthewman and Esler 2011;Esler and Matthewman 2011). These studies suggest that the explosive growth of wave amplitude that occurs during an SSW is instead representative of nonlinear resonance that is triggered by the modulation of key geometric vortex parameters that are defined based on whether a split or displacement-type warming (Charlton and Polvani 2007) is under consideration.…”

“…Triggering an SSW via resonance was suggested at least as far back as Clark (1974), and has been discussed by numerous authors since that time (Tung and Lindzen 1979a,b;Plumb 1981;Haynes 1985;Smith and Avery 1987;Smith 1989;Esler and Scott 2005;Matthewman and Esler 2011;Esler and Matthewman 2011). In a broad sense, there are two types of resonance that are relevant for SSWs.…”

“…The first circumstance is a local external mode where a ''perfect'' vertical waveguide supplies the horizontal nodal structure. This is the idea envisioned by Matthewman and Esler (2011), who modeled such a waveguide by employing a sharp stepwise increase in PV between the surf zone and the interior of the polar vortex. The second type of external Rossby wave arises as a global normal mode where Earth's poles provide the horizontal nodal structure.…”

“…In doing so, we focus particular attention on split-type SSWs for two reasons. First, the notions of precursor wave events and vortex preconditioning are observed to occur largely for the case of split SSWs (Labitzke 1977;Schoeberl 1978;Labitzke 1981;McIntyre 1982;Charlton and Polvani 2007); thus, the analysis of split SSWs provides a natural starting point for comparing the recent nonlinear resonance ideas of Matthewman and Esler (2011) and Esler and Matthewman (2011) to observational/reanalysis data. Second, from a practical standpoint, the dynamics of resonance due to the first baroclinic mode that is thought to be responsible for displacement SSWs is significantly more complicated ; thus, we defer detailed analysis of displacement SSWs in reanalysis data to a future study.…”