## Stratospheric Sudden Warming

In the polar region of the stratosphere, the temperature in winter can rise by more than 40° K in as little as a week followed by a substantial drop, which is just as fast. The corresponding zonal mean zonal wind, consistent with the thermal wind relationship, can turn easterly in a major warming event. This phenomenon is called "stratospheric sudden warming" (SSW). It may occur more than once during a winter; the last episode, called the "final warming," is often the strongest and precedes the spring flow pattern.

SSW is a catastrophe, due to the interaction between the zonal flow and planetary waves. Chao (1985) proposed a mechanism explaining SSW, as depicted in Fig. 3. This figure depicts the "forcings," or attractions, acting on the zonally averaged zonal wind [w] (the abscissa, i.e., S = [w]) in middle and high latitudes in the stratosphere. The effect of a stationary baroclinic Rossby wave of a zonal wave number on the zonal mean flow is represented by curve B; a positive value denotes westward acceleration. This acceleration occurs when the Rossby waves (i.e. the eddies) carry an upward westward momentum flux that is then deposited in the stratosphere owing to radiative damping in a quasi-equilibrium situation. However, the transient effect of wave-zonal wind interaction (Sec. 12.4 of Holton, 2004)b is prominent during the jump. curve B has a peak at the zonal mean zonal wind speed corresponding to the resonance speed, i.e. c = u — 3/k2 = 0 for the stationary Rossby wave, where c is the phase speed of the Rossby wave, u the zonally averaged zonal wind, k the zonal wavenumber, ¡3 = df/dy; when the phase speed of the Rossby wave matches the speed of the mountain, which is zero. At resonance, the momentum flux due to planetary-scale topography transported upward by the Rossby wave reaches its maximum.

The forcing on [u] due to the meridional gradient of the radiative-convective equilibrium temperature is depicted by line A. Line A pulls [u] toward the state of radiative equilibrium (a positive A represents eastward acceleration), which is represented by the point where line A intersects the x axis, S3. In midwinter, this point has a very high zonal mean zonal wind, and it is the state that exists when there is no topographical forcing (i.e. when curve B is zero) and the high zonal mean zonal wind reflects, through the thermal wind relationship, the large meridional gradient of the radiative equilibrium temperature. In midwinter the state is at S3. As winter progresses toward spring, the zonal mean zonal wind corresponding to the radiative equilibrium meridional temperature gradient becomes smaller, and thus line A moves toward the left in Fig. 3 while retaining its slope. Eventually S2 and S3 merge and both then disappear. At this time, the difference between line A and curve B reflects a westward acceleration of the zonally averaged zonal wind. This difference becomes large as [u] diminishes and approaches the resonance speed. In the meantime, the amplitude of the Rossby wave increases owing to the b Related to A and B being functions of dS/dt, as mentioned in the Introduction.

resonance. Thus, [w] races toward the other equilibrium state, Si. Chao's (1985) model experiments showed S1 to be a quasi-equilibrium state rather than an equilibrium state; in fact, an oscillatory state in the simplified model used. Therefore, Fig. 3 can only serve as a conceptual aid, not an actual depiction of the catastrophe. Owing to the tremendous difference between curve B and line A at resonance, overshooting can occur; thus [w] can pass S1 and, in some extreme cases, become negative. That is why the westerly wind [w] weakens quickly and may even turn easterly; correspondingly, the temperature in the polar region rises rapidly. However, the warmer polar temperature exists only momentarily, since the state of the system soon bounces back from the overshooting. Such bouncing back can be as fast as the overshooting itself; hence, sudden warming is followed immediately by sudden cooling.

The description above is based on a model that has only one zonal wave number (see Chao, 1985, for details). When all zonal wave numbers are included, how the description should be modified still remains to be worked out. Moreover, what is described above explains the final warming well; warmings earlier in the season remain to be explained.

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