## Thermal wind applied

 B. Geerts and E. Linacre 5/'98

Strong westerly winds blow in the upper troposphere and lower stratosphere of the midlatitudes. In Note 12.F we explained how these winds were consistent with the meridional temperature variation: near the surface it is warmer near the equator than at the poles. We first repeat the explanation, in more simple terms, and then apply the concept to the observed atmosphere.

Explanation

In Fig 1 the low-level (1000-700 hPa) air on the left is warmer than that on the right, corresponding respectively to equatorial and polar latitudes, for instance. Warming implies vertical expansion (Note 12.E), as shown on the left. The result is that the air above is lifted, and the level rises at which the pressure is 700 hPa. In other words, the isobaric surface becomes tilted, as on the top of the illustrated segment of the atmosphere. It can be seen that the slope is greater for the isobaric surface at 700 hPa than for the one at 900 hPa, i.e. the slope increases with height, as long as the temperature gradient exists.

Fig 1. The effect of differential warming on the slope of the isobaric surfaces (highly exaggerated). Some height contours are shown on the 700 hPa surface. It is assumed that the 1,000 hPa surface is level, i.e. there is no wind.

If now we compare pressures at two places of equal height, we see that there is a difference. This difference is 100 hPa in the case of A and B in Fig 1. This would drive a wind from A towards B, except that the Coriolis effect turns it parallel to the contour lines which are shown. It is called a ‘thermal wind’ because it is due to the gradient of temperature. The strength of the wind is proportional to the pressure gradient between A & B, i.e. to 100/AB, where 100 hPa is the pressure difference and AB the horizontal distance. However, the same discussion applies to a comparison of pressures at C & D, where the gradient is 100/CD. But 100/AB is greater than 100/CD, because CD is seen to be a distance greater than AB. In other words, the thermal wind increases with height, in accord with the greater slope of the isobaric surface.

This principle, the thermal wind balance, explains why the strongest westerlies occur at the top of the troposphere. Likewise the explanation of a strong jet above a strong, deep cold front (Fig 13.4).

Application

As an example we test whether the observed zonal wind in a cross section of the troposphere through western Australia and eastern Siberia, during the southern summer, is in thermal wind balance with the observed meridional temperature field (Fig 2).

 Fig 2. Mean meridional temperature profile at 120° E in January, for longterm data (1968-'96). The colour bar below indicates the temperature (° C) (from (1)). Fig 3. Mean meridional profile of zonal wind at 120° E in January, for longterm data (1968-'96). The colour bar below indicates the wind speed (m/s). Negative values are easterly winds, positive values westerly (from (1)).

A careful comparison between the temperature cross section and the zonal (east-west) wind cross section (Fig 3) shows that a strong poleward cooling implies a large positive wind shear, i.e. a rapid increase of westerly winds with height. For instance, there is a strong westerly jet at 200 hPa (an altitude of about 12 km) at 30° N. This jet is found above a region with tightly packed, steeply sloping isotherms (Fig 2). This same jet weakens in the stratosphere, because the meridional temperature gradient there has reversed: at 100 hPa it is -75° C near the equator and -55° C at 45° N. Strong winds continue at higher latitude (50° N) in the stratosphere at 50 hPa (19 to 20 km), the top of Fig 3, because the wintertime polar stratosphere is very cold (Fig 2). This is the polar night jet, which obviously is absent in the southern hemisphere, where it is summer at this time.

The southern hemisphere jet is weaker at this time and longitude because the meridional temperature gradient is smaller. Both jets are westerly because the Coriolis force acts in opposite directions in the two hemispheres. Thermal wind balance does not apply near the equator because the Coriolis force there is too weak. The easterly winds in the equatorial upper troposphere (Fig 3) are not the result of a meridional temperature gradient. One way to explain these winds is the fact that the global atmosphere does not move relative to the rotating Earth. The easterly momentum over the equator compensates for the net westerly momentum in the midlatitude belt.

Reference

(1) Data source: NCEP/NCAR Reanalysis Electronic Atlas