The overall transport pattern outlined in Figure 6.03 omits an extremely important process for understanding the distribution of ozone in the stratosphere: mixing by large scale weather systems. In Figure 6.13, we can watch the evolution of a large-scale weather system over an 8-day period by watching the effect it has on the total ozone field through mixing processes. The panels show the total ozone field for December 1-8, 1996, over the eastern Pacific and North America.

A very large scale weather system in the upper troposphere pulled high ozone air south and westward from the high latitudes over the course of a week (see red arrows) and pushed that ozone into the tropics during the first week of December 1996. Likewise, low ozone was pulled east and northward by this system out of the lower latitudes and into the higher latitudes (see black arrows). The directions correspond to the air circulation pattern around the low pressure system. The last panel of the figure on December 8, 1996, showed the "wavy" structure in the total ozone field associated with these weather systems. These sorts of weather systems dramatically show how ozone is "mixed" between the high and low latitudes of the northern hemisphere.

The Brewer-Dobson circulation discussed above is in fact induced by the growth and dissipation of these atmospheric waves. These waves can transmit heat and momentum across large distances, and thus their influence can be global. Much like ocean waves, these waves can either temporarily displace trace gas constituents (much like a small boat displaced by a passing ocean wave ), or they can permanently displace trace gas constituents (like a surfer using the wave to move on shore). Without these wave effects, the temperature field in the polar stratosphere would relax to extremely cold temperatures which would follow the seasonal cycle in solar heating (see Chapter 4 and section 3.2 of this Chapter). Therefore, understanding atmospheric waves, and the processes that enhance and dissipate them, is central to understanding ozone transport in the atmosphere.

The waves in the stratosphere are largely composed of waves generated in the troposphere which propagate upward. Tropospheric waves are induced by a variety of processes (see also Chapter 2, section 5.3). We will now review the types of waves most important for stratospheric transport.

4.1 Extratropical Rossby Waves and Gravity Waves

There are two types of waves that are critical for the mixing processes and the Brewer-Dobson circulation: Rossby waves and gravity waves. As noted in section 3.4.1, the Rossby wave exists due to a combination of meridional temperature gradients and the Coriolis force, which arises from the rotation of the planet. The gravity wave, also known as a buoyancy wave, results from the stability or buoyancy of air in a stably stratified atmosphere (see section 2.2 of this Chapter and also Chapter 2, section 5.3.2).

While gravity waves are important for understanding the entire circulation of the stratosphere and mesosphere, Rossby waves are principally responsible for the Brewer-Dobson circulation. This is because it is the very long wavelength Rossby waves induced by topography, known as the stationary planetary waves, that propagate vertically and break (see section 4.1.2) in the stratosphere, causing the wintertime stratospheric sudden warmings in the polar regions that lead to the Brewer-Dobson circulation.

4.1.1 Rossby Waves: An Illustration -- The very long horizontal scales of Rossby waves in the stratosphere is illustrated in Figure 6.14, which shows a weather map for the stratosphere at the 30 mb geopotential height level (about 23 km altitude). The wind tends to blow along the lines of constant geopotential height. (Geopotential height is defined and discussed in Chapter 2.) The top image shows the height field on December 28, 1997. The bottom image of Figure 6.14 shows the same 30 mb geopotential height field on Nov. 18, 1997.

In the top panel image of Figure 6.14, we see the single high-low structure that exists between the Gulf of Alaska and Northern Europe centered roughly along the 60°N latitude. The thick black line highlights the wave structure. Atmospheric scientists refer to this single high-low structure as a planetary wave-1 pattern, since a single wave (one ridge and one trough) straddles the entire planet at that latitude. At 60°N, the wavelength of this wave-1 is 20,000 kilometers. In the bottom panel image, we see two highs and two lows in a double high-low structure extending around the northern high latitudes. It is again centered roughly on 60°N. We refer to this as a planetary wave-2, with a wavelength of 10,000 kilometers at 60°N.

If we look closely at these fields, we can see other bumps and wiggles on the contours (e.g., on the Dec. 28 image, there is a distinct variation of the black line near the Caspian Sea at about 60°E, 40°N). These smaller scale features are also waves, but their horizontal dimensions are only a couple of thousand kilometers. So while waves-1 and 2 dominate on these two days shown, we can see other, smaller scale waves that have horizontal dimensions of 1,000 to 4,000 kilometers. These waves are referred to as synoptic scales waves. The collection of all of these Rossby waves is known as the Rossby wave spectrum.

4.1.2 Wave Theory -- Because these waves drive the Brewer-Dobson circulation, affect mixing processes, and control the wind and temperature distributions in the stratosphere, they are extremely important to understand and predict. The development and movement of these waves remains an area of research in the atmospheric sciences. In this section, we will briefly discuss where these Rossby waves originate, how they move into the stratosphere, and where they are dissipated.

(a) Origin of planetary wave forcing -- As noted previously in this chapter, planetary scale Rossby waves are forced by topography, specifically, the large-scale features like the Rockies and the Himalaya-Tibet complex. They are also forced by land-ocean heating contrasts. These are fixed features, and the waves forced by them are thus stationary or standing ones. Rossby waves may also be induced by instabilities arising from horizontal and/or vertical gradients in the temperature and wind distributions.

Because of the hemispheric asymmetries of the wave forcing mechanisms (such as the much greater land area and the larger, more extensive mountain ranges in the northern hemisphere), this wave energy is significantly larger in the northern stratosphere than the southern stratosphere. This is seen in Figure 6.15, which shows the climatological average winter geopotential height distribution for the northern hemisphere (January) and the southern hemisphere (July) at 10 mb or about 32 km altitude. The northern winter is based on 1979-1998 January data, and the southern winter is based on 1979-1997 July data.

In the top panel image, we see that in the northern hemisphere, a localized maximum in the height field exists in the North Pacific ocean between 40°N-60°N around the International Dateline (180° longitude). This is referred to as the Aleutian anticyclone . Recall that there is a clockwise circulation around anticyclones (high pressure areas) in the northern hemisphere. As a result of this planetary wave feature, the polar vortex is displaced off of the North Pole and is centered just north of Scandinavia near Spitzbergen Island (shown by the deep green-blue colors).

By contrast, in the bottom panel image, we see that in the southern hemisphere, there are only small planetary wave features. The polar vortex appears to be centered right on the South Pole. This interhemispheric asymmetry has a profound effect on the distribution of ozone and other trace gases in the two hemispheres. Note that in the summer hemisphere, there are virtually no stratospheric waves in the geopotential field.

These large scale waves have the largest influence in the winter hemisphere stratosphere outside of the equatorial region. Figure 6.16 shows the average monthly amplitudes (in terms of geopotential height deviations) of these waves in the 10 mb geopotential height field over the course of the year for the northern hemisphere (top panel) and southern hemisphere (bottom panel). The time axis is labeled in months. The top panel begins with month 7 (July), the bottom with month 1 (January). This allows us to observe a complete winter cycle centered at the middle of the images. The northern hemisphere time axis has been shifted by six months for comparison to the southern hemisphere.

In Figure 6.16, we see that the northern hemisphere wave amplitudes peak in the northern midwinter (January) and have considerably larger values than the corresponding peak period in the southern hemisphere. The southern hemisphere wave amplitude peaks in late winter/early southern spring (September-October). The early spring peak in southern hemisphere wave activity corresponds to the time when the more isolated southern polar vortex breaks down.

These stronger northern hemisphere waves produce a stronger Brewer-Dobson circulation, a weaker polar vortex, warmer polar temperatures in response to the stronger Brewer-Dobson circulation, and an earlier breakup of the polar vortex. In addition, because of the stronger Brewer-Dobson circulation, more ozone is transported to the northern polar lower stratosphere, leading to higher ozone levels in the northern hemisphere. This hemispheric asymmetry in wave activity thus has a profound effect on the distribution and mixing processes of ozone and other trace gases between the two hemispheres.

(b) Movement -- After being generated in the troposphere, planetary waves propagate into the stratosphere, growing in size as they move upward (because of decreasing air density in the stratosphere). This process is illustrated in Figure 6.17, which shows the polar night jet averaged from 19 years of data (1979-1997).

In Figure, 6.17, the tropopause is shown by the thin white line under 16 km altitude. The propagation of a planetary wave is schematically illustrated by the thick black arrow. The wave develops in the troposphere, propagates vertically into the stratosphere along the axis of the jet core, eventually bending towards the tropics. The wave decelerates the polar night jet (in the region encircled by the blue line) by depositing easterly momentum into the fast moving westerly jet. As explained in Section 3.4, the Brewer-Dobson circulation (shown as the white arrow) is induced by this wave deceleration and the accompanying stratospheric sudden warming. As for the red arrow in the figure, it is discussed in section 4.2.

(c) Wave growth and dissipation -- The growth and dissipation of atmospheric waves results in meridional exchange or transport of air in the stratosphere. Periods of rapid growth of extratropical planetary waves, referred to as wave transience, are most common in northern high latitudes during the northern winter. This rapid wave growth can lead to sudden and dramatic changes in the temperature and circulation structure (and hence the ozone distribution) in the stratosphere. This is the stratospheric sudden warming phenomenon already discussed in this chapter and in Chapter 2. Wave growth also occurs in the southern high latitudes during the southern late winter and spring, although it is less dramatic than its northern hemisphere counterpart. It is this wave transience in the southern hemisphere that is responsible for the breakup of the polar vortex and the Antarctic ozone hole during the early spring there.

Wave dissipation has two main causes. These are thermal dissipation and wave breaking. Thermal dissipation occurs through radiative processes, while wave breaking refers to a rapid mixing of air parcels from different regions. Both processes are detailed below.

(1) Thermal dissipation -- Thermal dissipation refers to the process of wave dissipation in which radiative heating and cooling lessen the temperature differences that are associated with Rossby wave formation. These Rossby waves have associated large scale areas of warm and cold temperature perturbations. The warm regions will radiatively cool to space at greater rates than the colder regions and restore the atmosphere to a more uniform temperature field (see Chapter 4). In general, this thermal damping process becomes more significant with increasing altitude in the stratosphere.

(2) Wave breaking -- Wave dissipation or damping also occurs by a process referred to as wave breaking. Much like ocean waves breaking on the beach, atmospheric waves grow to large amplitudes and break, thereby causing rapid meridional mixing. This process is particularly evident in the winter middle latitudes. Waves propagate vertically from the troposphere into the stratosphere, and then equatorward into the subtropics. As the wave moves upward, the density of the atmosphere decreases, and the strength of the wave consequently grows. This eventually leads to wave "breaking," in which air parcels undergo large and rapid latitudinal excursions causing them to undergo strong, irreversible, meridional mixing. As a result, material (i.e., long-lived tracers) becomes thoroughly mixed throughout the subtropics and lower middle latitudes.

The strength of the mixing is directly related to the strength of the waves (see Fig. 6.17). This means that greater mixing occurs during the northern midwinter than during the southern midwinter. The well-mixed region occurs on the equatorward side of the polar night jet. This is the "surf zone" that we discussed in Section 2.4.2-b, where the name "surf zone" is used as an analogy to the surf breaking on a beach. Such ocean wave breaking is characterized by overturning and mixing of water. The wave dissipation occurs as energy is transferred from the larger wave scales to smaller wave scales (finer features), which are thermally dissipated. The planetary wave breaking generally occurs when a wave propagates into a region where the wave speed matches the mean flow.

Wave breaking processes not only occur for stratospheric planetary waves, but also occur for very small scale gravity waves. Gravity waves (see Chapter 2, section 5.3.2) result from the buoyancy of the atmosphere. Breaking gravity waves are important in the mesosphere where gravity wave amplitudes become large enough to generate convective instability, overturning, and rapid vertical mixing of air parcels. These gravity waves are also thought to decelerate the mean flow in the upper stratosphere and mesosphere, and hence, also affect the mean circulation.

4.2 Wave Transport

As discussed previously, wave growth and dissipation generates meridional mass transport by two processes. First, the Brewer-Dobson circulation results from these waves because of the transfer of easterly momentum and energy via waves from the troposphere to the stratosphere, which act as a break on the westerly polar night jet, creating first a radiative and then a mass imbalance. Secondly, meridional exchange of mass occurs as waves dissipate in the atmosphere, producing a meridional stirring of air. This stirring or mixing tends to occur approximately on isentropic surfaces. Returning to Figure 6.17, these two processes are schematically shown by the white arrow (the Brewer-Dobson circulation) and the double-arrowed red line (mixing).

4.2.1 Wave Mixing -- Planetary or synoptic scale waves can cause irreversible changes in ozone concentration. Figure 6.18 shows northern hemisphere ozone mixing ratios from a 3-dimensional transport model on the 417 K (144°C or 291°F) isentropic surface for December 29, 1991 (left) and December 31, 1991 (right). The high ozone levels over the polar region are within the polar vortex which persists throughout the winter. These high concentrations are maintained by the combination of the downward component of the Brewer-Dobson circulation, which brings ozone-rich air downward and poleward, and wind patterns which isolate the vortex from middle latitude air. Between the tropics (black-purple colored values) and the polar vortex (red-orange colors), there is a tremendous amount of structure in the ozone field, similar to the stirring patterns in a paint bucket with two colors. It is here that wave mixing occurs, stirring up air parcels and redistributing trace gas constituents.

A particular event is revealed in Figure 6.18 that occurs over this two day period. Large changes in ozone occur over eastern Scandinavia as a wave distorts the polar vortex and moves a tongue of high ozone air over the region. As the shape of the polar vortex continues to change (not shown), repeated penetrations of tongues of low ozone middle latitude air are seen entering into and out of the polar vortex. As low ozone air moves into the vortex, high ozone air moves south out of the vortex and into the middle latitudes. This exchange of air mixes up ozone amounts in the middle latitudes. Eventually, as the year progresses, a climax is reached when the vortex completely breaks apart in the spring period. Once the vortex breaks, it will not reform until the fall. As the vortex breaks up, low ozone air is mixed with high ozone air. The polar region considerably warms, which is why we refer to this breakup as the final warming.

4.2.2 The Stratospheric Surf Zone -- As previously noted, the stratosphere is divided into three latitudinal regions between the equator and the pole. The tropics, the polar vortex, and the midlatitude "surf zone". Figure 6.18 shows these regions distinctly, with low ozone tropical air, high ozone polar air inside the polar vortex, and the complicated fine structure of high and low ozone air mixing inside the middle latitude surf zone region. (See sections 2.4.2-b and 4.1.2-c for overview of surf zone terminology.)

4.2.3 Wave Influence On Mean Circulation -- These planetary wave induced ozone changes that are illustrated in Figure 6.18 create a high degree of ozone variability across the globe, but this variability does not contribute to the global average of ozone on time scales of months or longer. Rather, the global average of ozone is primarily driven by the Brewer-Dobson circulation. This circulation decreases ozone levels in the tropics by lifting low ozone from low altitudes (see Figure 6.03) and increases ozone in middle to high latitudes by pulling high ozone down from higher altitudes. This circulation produces the observed ozone gradient of elevated extratropical latitude stratospheric ozone and low tropical stratospheric ozone. Mixing by waves acts to flatten out this gradient. These wave events are continually pulling low ozone air from the tropics into the extratropical region and high ozone extratropical air into the tropical region.

Figure 6.18 shows thin filaments of high ozone air from the polar vortex that are pulled into the middle latitudes over central Asia and the Eastern Pacific. These filaments get thinner and elongate with time. Eventually, they are irreversibly mixed into the middle latitude surf zone, never to retreat back into the polar vortex. The net effect of this irreversible process is to weaken the latitudinal (meridional) gradient of ozone between the polar vortex and the middle latitudes and the tropics that was created by the Brewer-Dobson circulation.