Figure 4.2 provides mean geopotential height fields at the 30 hPa level for the four mid-season months. In winter, as illustrated by January, the height field points to strong westerlies in the middle and upper stratosphere flowing around a deep cold vortex. Above 40 km (3 hPa, not shown) there is a polar night westerly jet stream in mid-latitudes. Peak mean zonal winds of 80 m s-1 actually occur around 60-70 km altitude (0.3-0.1 hPa). The winter mean stratospheric vortex is broadly symmetric, but less so than its Antarctic counterpart. There are troughs over eastern Asia and eastern North America and a weak ridge located over western North America. In spring, illustrated by the April field, the vortex center has shifted well off the Pole to north-central Eurasia. In summer and above about 20 km (as seen in the July field), the cyclonic vortex has broken down. There is polar easterly flow around a highly symmetric warm polar anticyclone. Summer sees an easterly jet of about 60 m s-1 at 0.1 hPa located around 50-60° N. The October field illustrates the transition back toward winter conditions.
As discussed by Holton (2004) and Andrews et al. (1987), if there were no transports arising from the breaking of atmospheric waves propagating upwards from the troposphere, the zonal mean temperature of the stratosphere would relax to a radia-tively determined state, with the temperature distribution corresponding to an annually varying thermal equilibrium that follows the annual cycle in solar heating. The circulation would hence represent a zonal-mean zonal flow in balance with the meridional temperature gradient (a thermal wind balance), with essentially no meridional or vertical circulation and no stratosphere-troposphere exchange. While, as just discussed, the existence of a westerly vortex in winter and an easterly vortex in summer is qualitatively that expected from radiative equilibrium, the winter season actually shows considerable departures from the radiatively determined state. In the 30-60 km region, the change in temperature from the winter pole to the summer pole is much smaller than the radiatively determined gradient. This is due to eddy transports that drive the flow away from a state of radiative balance. By contrast, the departure from radiative equilibrium in summer is small, implying a reduction in transports.
In the troposphere, these eddy transports are largely associated with traveling, synoptic-scale waves (which we associate with migrating cyclones and anticyclones
at the surface). By contrast, winter transports in the stratosphere are associated with the long planetary waves, especially wavenumbers 1 and 2, which can penetrate into the stratosphere under certain conditions. Wavenumber refers to the number of atmospheric waves around a latitude circle. For any given day, Fourier transform methods can be used to break down the total circulation at a given level in the atmosphere with respect to the relative contributions of long planetary waves (low wavenumbers), which move only slowly or remain stationary with respect to the Earth's surface, and shorter traveling waves (higher wavenumbers). A strong wavenumber 2 component, for example, would have a pronounced expression of two ridges and two troughs, each separated by 180° longitude. If we look at the circulation on a typical winter day, we find that while the troposphere has a strong contribution from the higher wavenumbers, the circulation of the stratosphere is more symmetric, indicating that the shorter waves are not readily penetrating into the stratosphere. For long time averages, the effects of the shorter waves cancel out. But even with such time averaging, the winter circulation of the stratosphere (Figure 4.2) is more symmetric than that of the troposphere
(compare with Figure 4.8, which we will describe later). At 60° N, the mean January field in Figure 4.2 shows strong contributions from wavenumbers 1 and 2. This can be related to the impacts of orography and land-sea thermal contrasts (Pawson and Kubitz, 1996).
While a full explanation is beyond the scope of this textbook (see Holton, 2004, for further reading), it can be shown that waves will penetrate (vertically propagate) into the stratosphere provided that the zonal-mean wind is positive (the wind averaged around a latitude circle blows from west to east) but less than a critical value that depends strongly on the length of the waves. The longer the wave (that is, the lower the wavenumber), the stronger the zonal wind can be and still allow for vertical propagation. Since the zonal wind tends to be at a maximum near the tropopause in middle and high latitudes (much lower in altitude than the winter stratospheric jet), the shorter waves in winter tend to be "trapped" in the troposphere. In summer, the zonal-mean zonal winds in the stratosphere are negative (easterly, see the July field in Figure 4.2). There can be no vertical propagation of waves in these conditions. This is consistent with the fact that the summer stratospheric circulation is highly symmetric with a thermal structure close to that expected from radiative equilibrium.
The typical thermal structure of the winter stratosphere features low temperatures in the vortex core of the lower stratosphere that increase outward from the axis of rotation. Conversely, there are high temperatures in the vortex core of the upper stratosphere and lower mesosphere that decrease outward. This is illustrated schematically in Figure 4.3. This vertical change in the temperature structure is attributed to warming through large-scale subsidence in the mesosphere and radiative cooling in the lower stratosphere during the polar night (Gerrard et al., 2002). The stratospheric jet maximum is located at the level of the temperature transition region in the vertical (10 to 1 hPa). Positive potential vorticity (PV) anomalies are found in the vortex core at the level of the thermal transition zone, with a cold trough below and warm dome above. The vortex winds, which are formed between the two thermal regimes, circulate around the core. Potential vorticity represents the specific volume (volume per unit mass of air) times the scalar product of the absolute vorticity (the sum of relative and planetary vorticity) and the gradient of potential temperature. The PV maximum shown in Figure 4.3 arises from the low density of the air at stratospheric levels (specific volume is large), the strong increase of potential temperature with height (strong stability) and the positive absolute vorticity.
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