Vertical mixing in the atmosphere

The vertical transport of heat and moisture in the atmosphere is accomplished by means of convection, which breaks out spontaneously in various parts of the atmosphere. 

Convection may be dry (in which case it is usually invisible except where it stirs up dust), or it may be moist, in which case its signature is evident in cloud forms. From the ground, convective clouds look lumpy: they are classified as cumulus or cumulonimbus cloud types.  A good example of moist convection as viewed from space is the finely speckled areas over the Southern Ocean in Fig. 4-20 in the center section of the text. 

Convection in the earth's atmosphere may be either shallow (restricted to the lowest 1-2 kilometers) or deep (extending all the way up to the tropopause). Deep convection is always of the moist kind and usually involves cumulonimbus clouds (accompanied by thunder and lightning when they form over land). Shallow convection may be either of the moist or dry type. Shallow moist convection generally involves small, lumpy cumulus clouds or flatter stratocumulus clouds.  Convection makes for bumpy flying. 

Convection is usually made up buoyant, rising plumes of warmer, more moist air known to glider pilots as 'thermals', separated by slowly sinking cooler, dryer air. Thermals start out as "hot spots" in the surface layer close to the ground and they rise until they eventually run out of buoyancy. They expand and cool as they rise, and if they rise high enough, the water vapor in them condenses to form clouds.  The level at which condensation first occurs (i.e. the cloud base) is called the 'lifting condensation level' (LCL). 

Moist thermals that have run out of buoyancy are marked by clouds that have flat tops. In cumulonimbus (the cloud type generally associated with thunderstorms) the flat tops are referred to as "anvils." 

During their life cycle, thermals transport heat and moisture upward from the earth's surface, where they start out, up to the level where they run out of buoyancy. At intermediate levels, warm, moist thermals are going up and cooler, drier air is subsiding in between them.  Thermals that rise all the way up to the upper tropopause lose nearly all their moisture on the way up. The latent heat released by the condensing moisture warms the atmosphere. This latent heat was taken up from the earth's surface wherever the moisture entered the atmosphere via evaporation. 

Convection over land is much more frequent during the day than at night and during spring/summer than in autumn/winter. It occurs only rarely over cold surfaces. 

The description of convection raises a number of questions: 

• Why are thermals buoyant? 
• Why do they cool as they rise? 
• Why does the water vapor begin to condense out of them if they rise high enough? 
• Why do they eventually run out of buoyancy? 

2. Convection in water

Convective plumes form in a pan of water if it is heated from below.  Water (at temperatures above 4°C) expands very slightly when it is heated, much like air does. The water in "hot spots" along the bottom surface of the pan expands just slightly more than the rest of the water along the bottom surface. A given amount of mass of the hotter later occupies more space than a comparable mass of the water that isn't quite as hot. Or equivalently, a given volume of the hotter water contains less mass than a comparable volume of cooler water.  Since it's less dense (i.e. lighter), the warmer water is buoyed (i.e. lifted) by the cooler water that surrounds it. 

The plume will keep rising so long as it remains warmer than the water at the same level. But suppose the water gets warmer toward the top of the pan. In that case, the plume will eventually encounter a level at which it ceases to be warmer than the surrounding water at the same level.  At this level, it runs out of buoyancy and stops rising. Evidently, in a liquid like water convection is suppressed when temperature rises with height: temperature increasing with height constitutes what is referred to as a stable environment.  That's also true in the atmosphere: in "temperature inversions" where temperature increases with height (as it almost always does on cold, still nights over land), convection is strongly suppressed. 
 

3. Convection in a dry atmosphere

Unlike water, gases are compressible: i.e., their volumes expand and contract, not only because of heating and cooling, but also because of changes in pressure. To understand about expansion and compression we need to know a little bit about air pressure. 

Pressure is weight per unit area. Americans express it in terms of pounds per square inch (psi): Our bodies exert pressure on the underlying surface. When we stand up we exert more pressure than when we are lying down because our weight is concentrated in a smaller area.  A petite woman standing on spike heels exerts much more pressure than a heavy man standing on skis or snowshoes. 

The weight of the overlying are exerts pressure on surfaces that the air comes in contact with. Since air is a fluid, it doesn't matter whether the surfaces are horizontal or vertical. The pressure of the overlying atmosphere is equivalent to that exerted by a column of water 38 feet deep or a column of mercury 30 inches deep. It will be demonstrated in class (if we have time) that atmospheric pressure is strong enough to crush a can. It would crush our bodies too if it weren't for the fact that they've adapted to it by exerting an equal outward pressure of their own -- if they were impulsively 'de-pressurized' our lungs would literally explode. 

Atmospheric pressure decreases with height as the pressure of the overlying air decreases. At sea level it decreases by ~1% for each 80 m-- it decreases by 3-4% riding up in the elevator to the top of a tall office building like the Columbia Tower; by 15% driving up to Chinook Pass, and by 40% climbing to the top of Mr. Rainier.  Sometimes we feel pressure in our ears while our bodies are adjusting to changes in altitude. If it weren't for the fact that passenger cabins on high flying aircraft are pressurized, these pressure  changes would be much more painful than they are. 

Rising and sinking air parcels expand (contract) in response to changes in atmospheric pressure. For example, the volume of a weather balloon increases by nearly a factor of 100 as it rises from sea-level to the 30 km level, where it's above 99% of the mass of the atmosphere. The so called 'adiabatic (without the addition or removal of heat) expansion' of the air as it rises affects its behavior. 

Whereas the rising plume of water considered in the previous section maintained its temperature as it ascended, a rising thermal cools as a result of adiabatic expansion, just as the air escaping from an aerosol can or a tire valve cools. It isn't possible to explain this cooling without delving deeper into the science of thermodynamics than we have time to do in this course, so we'll just accept it as fact. Rising air cools at a rate of 9.8 °C per kilometer. This rate of temperature decrease with height is called the dry adiabatic lapse rate.  (In this context, dry means not saturated with water vapor.)  At this rate an air parcel originating at sea level with a typical winter temperature of 10°C (50°F) would cool to a temperature of about -3°C by the time it ascended to an altitude comparable to Stevens Pass (1300 m). 

We can deduce the conditions under which the atmospheric lapse rate (remember that the lapse rate is the rate at which temperature decreases with increasing altitude) is stable by considering how much the air in a hot air balloon would have to be heated in order to keep it rising.  The more stable the atmosphere, the more heating is required.  Suppose that the actual lapse rate is isothermal (i.e., that temperature is neither increasing nor decreasing with height). If the balloon starts off just a degree warmer than the surrounding air and is heated just enough to maintain this small differential, it will have to be heated 9.8°C to keep it rising up to the 1 km level. If the heater were turned off part way up and the balloon forcibly lifted the rest of the way and then released, it would find itself colder and denser than the surrounding air and therefore negatively buoyant. This negative buoyancy would cause it to sink back to near the altitude at which the heater was turned off, where it was more or less in equilibrium with the surrounding air. Hence, an isothermal lapse rate represents a stable condition in which an unheated balloon (or air parcel) perturbed about its equilibrium level will experience a restoring force tending to return it to that level. 

Now if, instead of isothermal, the observed lapse rate is a more typical 6°C per km, the balloon will still need to be heated in order to keep it rising, but in this case it will only need to be warmed by 9.8 - 6.0 = 3.8°C per km. The lapse rate remains stable (i.e., heat will still need to be applied) so long as the lapse rate remains less than the dry adiabatic lapse rate of 9.8°C per km. As in the water tank, if the atmosphere is heated from below (and or cooled from above) strongly enough and for a long enough time, the lapse rate will eventually reach this critical value and convection will ensue.  If the heating and/or cooling continues, convection will transport enough heat upward to keep the lapse rate from increasing any further. Hence, the hot air balloonist doesn't have to worry about encountering unstable conditions in which the balloon could start to rise uncontrollably.

More generally, one can diagnose whether the atmosphere is stable or unstable with respect to vertical motions by comparing its lapse rate to the adiabatic lapse rate of 9.8°C/km:

•  If the rate of decrease of atmospheric temperature (the lapse rate) is larger than the adiabatic lapse rate, then the atmosphere is unstable and convection will take place readily: as a bubble of warm air rises, its temperature will decrease at a rate of 9.8°C/km while the temperature of the surrounding air will decrease at a more rapid rate. As a result, the rising bubble of air will always be warmer than the surrounding air and will be buoyant.
• If the atmospheric lapse rate  is smaller than 9.8°C/km, then the atmosphere is stable and convection will not take place.  If you move a bubble of warm air at higher altitude, it will cool faster than the surrounding air and will thus be cooler (and denser), and sink.  It will return to its starting level.

 Last Updated:
10/16/2001