Southern Hemisphere winter conditions tend to be unfavorable for strong wave prop- agation and sudden warmings, as observations of the Southern Hemisphere as well as model studies presented here and elsewhere show. Winter 2002 was very disturbed
long before the warming (Figure 4-1), and Northern Hemisphere stratospheric dy- namics show that even for less weakening of the mean flow, precursor structures are common if not necessary for a sudden warming to occur. The precursor structures in winter 2002 may have allowed the waves to propagate through the weakened winds. It is however still a matter of ongoing research to explain the exact causes for that special warming.
Despite the fact that no sudden warmings were observed in the control run, a sudden warming caused by the traveling waves observed in the stratosphere may not be impossible. A similar long (10,000 days) model run by Kushner and Polvani (2005) in a spectral core model with no longitudinally varying forcing and no truncation of synoptic waves exhibited a single sudden stratospheric warming which they found to exhibit similar characteristics to the warming observed in the Southern Hemi- sphere in 2002. They ascribed the generation of the waves responsible for the major stratospheric warming to the Scinocca and Haynes (1998) mechanism, however the possibility of tropospheric instability to long waves was not considered. In addition, a weaker vortex (γ = 2 K/km as compared to γ = 4 K/km in the present run) was used in their run, which yields conditions more favorable for wave propagation. Examining the likelihood of such an extreme event for both vortex strengths γ = 2 K/km, which yielded their warming, to γ = 4 K/km, which was used in the present model run, they find that warm events are exponentially distributed (with their event located at 6 standard deviations), with similar slopes of the distribution for the γ = 2 K/km and the γ = 4 K/km event, but with a strong decrease in variance for γ = 4 K/km. Con- cluding, internal atmospheric variability is able to force extreme events in atmospheric models.
4.4.3
Sudden Warmings Forced by a Single Wave Number
In addition to the above results, a comparison of the two truncated runs gives im- portant insights into the internal dynamics of the stratosphere. The truncated runs differ from each other only in the wave numbers which are allowed to propagate: one run allows propagation of both zonal wave-1 and wave-2, while the other run
allows propagation of wave-2 only. Since these waves amplify and propagate into the stratosphere, it will be elucidating to investigate wave-wave interaction in the stratosphere.
In order to understand if and how a single planetary wave number is able to produce sudden warmings, various studies with simple 1- and 2-dimensional models have looked at the propagation of a single wave number and found that it is able to induce significant variability in a 1- or 2-dimensional model atmosphere. The most prominent example is the study by Holton and Mass (1976), who used a quasi- geostrophic β-plane model including a single wave number and a mean flow as well as a relaxation to a mean temperature profile. They showed that for sufficiently large forcing the stratosphere exhibits strong stratospheric vacillations in time despite the time-independence of the forcing. These vacillations were shown to be caused by the interaction of the wave with the mean flow in the stratosphere.
A similar behavior has been observed in more complex models: A three dimen- sional dynamical core model run by Scott and Polvani (2004) has shown that propa- gation of a single planetary wave number into the stratosphere can cause significant stratospheric variability: They force a zonal wave-1 pattern by a time-independent heat source in the lower troposphere, while damping all waves except for wave-1 in the troposphere (below 200 hPa) and relaxing the tropospheric mean flow to a prescribed westerly wind profile in order to ensure the possibility for the wave to propagate. In addition to damping the synoptic eddies, they eliminate the meridional temperature gradient in the troposphere (below 200 hPa), i.e. baroclinic instability as observed in our truncated model run is inhibited. This troposphere is designed merely as a provider of wave-1 flux to the stratosphere, comparable to the Holton and Mass (1976) study. They find that despite the time-independent nature of the forcing, the stratosphere exhibits a highly variable state with an interchange between sudden warmings and a subsequent relaxation to radiative mean conditions. In addition to sudden warmings, Scott and Polvani (2004) also find downward propagation of the stratospheric anomalies into the lower stratosphere. As described in Section 5.4.2, we find the same for the run truncated to wave-2.
The above results indicate that in our model, we may be able to assume that the wave flux provided by baroclinic instability is approximately constant in time, while internal stratospheric dynamics is responsible for the strong time-dependence in the upward wave flux as well as the stratospheric flow variability. This will however be difficult to verify, as the flux entering the stratosphere does not represent the wave flux provided by the troposphere, but rather the amount of wave flux that the stratosphere allows in.
Our research confirms and expands the results by Scott and Polvani (2004). They had shown that forcing a single wave number in the troposphere, while damping all other wave numbers in the troposphere, can yield significant stratospheric variability. It is from the Scott and Polvani (2004) run, however, not clear if a single forced wave number could have induced a stratospheric warming without wave-wave interaction between different wave numbers in the stratosphere. Our results show that even when setting all other wave numbers to zero throughout the entire atmosphere, stratospheric variability is significant and sudden warmings are possible.