## Dry

Figure 7.3 shows two hypothetical conditions of a dry atmosphere. On the left, the lapse rate

Figure 7.2 Illustration of the foehn effect. There is cooling at 10K/km until cloud base is reached, then cooling at the SALR within the cloud. Once the mountain is surmounted, the descending air first warms at the SALR, using the heat to evaporate cloud droplets. Cloud base is reached when all the droplets have gone, and thereafter there is warming at the DALR. It is assumed that rain falls from the cloud on the windward side of the mountain, so that the cloud on the lee side has less moisture absorbing heat in evaporation than was condensed on the windward side, liberating latent heat. So less heat is absorbed than was previously released. As a result, there is warmer, drier air downwind (Note 7.E).

Figure 7.2 Illustration of the foehn effect. There is cooling at 10K/km until cloud base is reached, then cooling at the SALR within the cloud. Once the mountain is surmounted, the descending air first warms at the SALR, using the heat to evaporate cloud droplets. Cloud base is reached when all the droplets have gone, and thereafter there is warming at the DALR. It is assumed that rain falls from the cloud on the windward side of the mountain, so that the cloud on the lee side has less moisture absorbing heat in evaporation than was condensed on the windward side, liberating latent heat. So less heat is absorbed than was previously released. As a result, there is warmer, drier air downwind (Note 7.E).

is 6 K (i.e. 20-14) in 900 metres (i.e. 6.7 K/ m), whereas it is 13.6 K/km on the right, twice as much. In each case, a parcel of air is shown lifted by 300 m by some means, and the question is, what happens next? In both cases, the parcel has cooled by the dry adiabatic lapse rate of 10 K/km, so that it now has a temperature of 17°C. The parcel on the left finds itself amongst air at 18°C, which is warmer and therefore lighter. As a result, the relatively heavy parcel sinks back to where it was before the temporary nudge upwards. So the situation is stable. However, the uplifted air on the right finds itself within air at only 16°C (i.e. 20- 0.3*13-3), which is cooler than the parcel, i.e. the parcel is less dense. So the lifted parcel on the right now has positive buoyancy and rises spontaneously, without further nudging. When it has risen another 300 m, the parcel has become 2 K warmer than the surroundings (i.e. [17-31-12), so that the buoyancy has actually increased, and ascent consequently accelerates; the initial perturbation has become runaway ascent. This is instability, as described earlier.

The difference between local static stability and instability is seen to be due simply to different environmental lapse rates. The ELR is less than the DALR (or sub-adiabatic, i.e. less than 10 K/km) in a stable environment, shown on the left in Figure 7.3. Or, put differently, the line representing the ELR of a stable atmosphere is oriented clockwise of the DALR line. In some conditions the ELR line is so far clockwise that it implies that the temperature actually increases with height, i.e. there is an inversion. Clearly, inversions are extremely stable.

As regards instability, we have deduced that conditions are locally unstable when the ELR exceeds the DALR, as in the part ab in Figure 7.4, where the ELR line is seen to be relatively anticlockwise, approaching the horizontal. Such a lapse rate is known as super-adiabatic. It is uncommon (except close to the ground when it is heated by sunshine), because the resulting instability leads to a vertical circulation which carries hot air aloft and brings cool air down, automatically changing the temperature profile

Figure 7.3 An illustration of how static stability arises. The vertical axis is height, the horizontal is temperature and the dashed slanted lines represent the DALR (10K/km). The bold sloping lines are different hypothetical soundings, determining the ELR. On the left, the ELR is more vertical than the DALR, since the measured temperature change is only 6K (i.e. 20-14) in 900 m. On the right, the ELR is more horizontal, representing 12K in 900 m. In both cases, two parcels of air are shown (shaded), one on top and one at the bottom of the layer. These parcels are disturbed to the positions of the unshaded ellipses, and their new temperatures are shown, along with their further displacements, according to the difference between each parcel's temperature and that of its new environment.

Figure 7.3 An illustration of how static stability arises. The vertical axis is height, the horizontal is temperature and the dashed slanted lines represent the DALR (10K/km). The bold sloping lines are different hypothetical soundings, determining the ELR. On the left, the ELR is more vertical than the DALR, since the measured temperature change is only 6K (i.e. 20-14) in 900 m. On the right, the ELR is more horizontal, representing 12K in 900 m. In both cases, two parcels of air are shown (shaded), one on top and one at the bottom of the layer. These parcels are disturbed to the positions of the unshaded ellipses, and their new temperatures are shown, along with their further displacements, according to the difference between each parcel's temperature and that of its new environment.

towards that of neutrality, where the ELR equals the DALR.

Another way of expressing the condition for instability is in terms of the potential temperature. A layer of the atmosphere is locally unstable if there is a decrease of potential temperature with elevation. Again, this may be deduced from Figure 7.3; the potential temperature at 600 m is 18°C (i.e. 12+10x0.6) at 600 m on the unstable right, compared with 20°C at sea-level (i.e. there is a positive lapse rate of potential temperature), whereas the potential temperature rises to 22°C (i.e. 16+10x0.6) on the (stable) left.