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Notes for the lecture on Wed+Thursday October 11/12
Vertical transport of pollution and inversions

1. A description of convection

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. 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. 

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 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? 
We can answer some of these questions by considering convection in fresh water, which is simpler than its counterpart in the atmosphere but displays many of the same characteristics. 

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). Other commonly used units are millibars or atmospheres. 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. We had a demonstration in class showing 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. 

Air parcels in the atmosphere have three properties which will be useful to understand their vertical motions in the atmosphere:

a) Rising air parcels expand 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. Conversely, sinking air parcels contract as they sink.

b) Rising air parcels cool as they expand. 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
sinking


c) Rising air cools at a rate of 10°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). The lapse rate is the rate at which temperature decreases with increasing height.

adiab

4. Atmospheric stability

We can diagnose whether the atmosphere is stable or unstable with respect to vertical motions by comparing its lapse rate (which we call the environmental 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 10°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 10°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.
  • Finally, if the atmospheric lapse rate is the same as the adiabiatic lapse rate at all heights, then the air parcel will be neutral: it will float.

To understand this concept of stability, you can relate the behavior of the rising air parcel to a marble. If you set a marble in equilibrium on top of an inverted bowl, any motions will make it fall down (unstable). If the marble is at the bottom of a bowl and push it up along the sides of the bowl and let it go, it will come back down to its originial position (stable). Finally, if you set the marble on a flat surface the marble will stay put (neutral). See Figure 5.4 in textbook.

Inversions are cases when the atmospheric lapse rate is negative (temperature is increasing with increasing height). This creates stable conditions. Most parcels cannot rise above an inversion. The picture below shows an inversion.


5. Inversions and air pollution
Inversions occur often in the atmosphere. There are several types of inversions: marine inversions, radiation inversions, and subsidence inversions (see textbook, page 125-128). When they occur,  they can enhance air pollution (remember the Donora smog event!).  Inversions will tend to inhibit vertical excchange of air and pollutants. They will thus trap pollutants near the surface, like a "lid on a pot". Smog events (in L.A., the east coast, and sometimes around Seattle) are often associated with inversions.

inv
To understand why that is the case, recall the box model equation: q = S x tau/V, with q = concentration of pollutant in box, tau = residence time of pollutant, and V = volume of box. From the box model equation you can see that the concentration is inversely proportional to the volume of the box: as the volume decreases, the concentration of pollution will increase. Inversions basically decrease the volume in which the pollutants can mix in. Thus low mixing height (see figure above) will lead to low volumes and high pollutant concentrations, while large mixing heights will lead to large volumes and low pollutant concentrations.

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 Last Updated:
10/05/2006

Contact the instructor at: jaegle@atmos.washington.edu