ATMO 171 Introduction to Meteorology and Climatology

10/11/99

CLOUD FORMATION

Since the relative humidity of air near the surface of the earth is usually less than 100 %, the condensation of water vapor required to form the liquid water droplets that make up a cloud must take place by first cooling this air. Once the air is cooled to its dewpoint temperature, the RH = 100 % and condensation can take place.
Recall back in the beginning of the class we associated the presence of clouds with rising motion. For example, the convergence of air at a low pressure center and the lifting of air with the passage of warm fronts and cold fronts led to cloudy conditions being observed. The relationship between rising air motions and cloudiness comes from the fact that rising air cools.
The dry adiabatic lapse rate

The process by which rising air cools is called adiabatic expansion. It can be understood in terms of the ideal gas law, wich states that the air pressure is the product of the air's density and temperature. First, let's imagine we have an imaginary block of air that is surrounded by a flexible but impenetrable boundary. No air molecules can pass across this boundary, so that the mass of the "air parcel" remains constant. Also, no heat energy can pass through this boundary, so the parcel is effectively insulated from its environment. Any changes in the temperature of the air inside this parcel of air will only be due to changes in the internal state of the parcel. This is what we mean by adiabatic.
Say the parcel of air sits just above the earth's surface. The pressure of the air inside the parcel is equal to the outside pressure, which is 1000 millibars. Initially, the air inside the parcel has a temperature of 10 degrees C, and a dew point temperature of -8 degrees C (the parcel is considered to be unsaturated. Why?) If we lift this parcel up to a higher level in the atmosphere, what will happen to it?
If we lift the parcel up to the 800 millibar pressure level, the pressure inside the parcel (= 1000 millibars initially) will be greater than the surrounding air pressure. This will cause the parcel to expand. As the parcel expands, its volume increases, but the mass of the parcel remains the same (remember that the walls of this imaginary parcel do not allow heat or mass to pass into or out of the parcel). The expansion of the parcel causes its density to decrease (can you see why?). At the same time, the temeprature of the air inside the parcel also decreases. Another way to say this is that the average kinetic energy of the air molecules inside the parcel decreases. Where did this energy go? It went into the work required to push the sides of the parcel out - i.e. the work required to make the parcel expand.
The ideal gas law states that if the air's density and temperature both decrease, then the air pressure must also decrease. In fact, as the air parcel rises in the atmosphere, it will expand and cool until the pressure inside the parcel equals the pressure outside the parcel. In our example of an air parcel begin lifted from 1000 millibars (the surface) to the 800 millibars (about 1800 meters in altitude), the parcel will expand and cool until its internal pressure equals 800 millibars. How much will the parcel cool as it rises? For a parcel whose RH is < 100 % (i.e. it is unsaturated) it will cool off 9.8 C for every kilometer it rises (1 kilometer = 1000 meters), or about 5.4 F for every 1000 feet. Thus the parcel cools by about 18 degrees C, or about 33 degrees F.
The rate of cooling of an unsaturated air parcel that does not exchange heat with its surroundings is called the adiabatic lapse rate, and it is equal to 9.8 Degrees C per kilometer. Any rising air parcel whose RH < 100 % will cool at this rate. It is important to note that any sinking air parcel will warm at this same rate.

10/13/99
The moist adiabatic lapse rate

The whole idea behind cloud formation is that rising air cools to the point where it becomes saturated (i.e., the air temperature equals its dew point temperature, and the RH = 100 %). We know how much an unsaturated ("dry") parcel cools as it rises and expands - but how does the parcel's temperature change once it becomes saturated?
Remember that when water changes phase from a solid to a liquid (melting) or from a liquid to a gas (evaporation) energy is required, and this energy comes from the surrounding environment. Thus a process like evaporation cools the environment in which it takes place (like your skin or the air being blown through your swamp cooler). On the other hand, condensation of water vapor (going from gas to liquid) releases energy ("latent heat"), and thus warms the environment. Figure 2.9 on page 43 in Danielson summarizes this nicely.
So what happens as we lift our air parcel up from the surface? Assuming it is initially unsaturated (RH < 100 %, air temperature greater than dew point temperature) it will expand and cool at the dry adiabatic lapse rate. At some point, the parcel will cool to its dew point temperature, and then become saturated. The altitude at which this occurs is called the condensation level (CL) . When this occurs, water vapor begins to condense. This condensation will warm the air parcel. If the air parcel keeps rising past its CL, it will still expand and cool, but it will cool at a lesser rate because of the heat released by condensation. This new cooling rate is called the moist adiabatic lapse rate, and it ranges in value from 4 to 7 degrees C per kilometer.
The condensation level, or CL, marks the base of a cloud. Above the CL, within the cloud, the RH is 100 %. As a parcel continues to rise above the CL, cooling at the moist adiabatic rate, more and more water vapor will condense into liquid. This will reduce the amount of water vapor in the parcel, and so the dew point temperature must decrease. [Another way to look at this is to recognize that if the RH within the cloud is 100 %, then the air temperature and the dew point temperature are equal. If a parcel's air temperature decreases as it rises, the dew point temperature must also decrease to keep RH = 100 %. Rarely does the atmosphere become supersaturated - RH greater than 100 %]. Also, as more and more water vapor condenses, more and more latent heat is released. This is important when we consider atmospheric stability next.