Moving Air Parcels Up and Down in the Atmosphere

Brief Review of Cloud Fomation

Clouds typically form where air is rising upward in the atmosphere. As air rises, it expands and cools. As it cools, the air's capacity for water vapor (its saturation mixing ratio) decreases. If the air cools to its dew point temperature (in other words if it reaches saturation with respect to water vapor), condensation is forced and some of the water vapor in the air condenses into liquid water droplets. We will now take a more quantitative look at the process of cloud formation by tracking what happens to the temperature and water vapor content (measured by the dew point temperature) in parcels of air as they are raised and lowered in the atmosphere.

Rules for moving air parcels up and down in the atmosphere

1. The starting temperature and water vapor content of the parcel is taken to be the measured conditions at ground level. We will use the dew point temperature of the air in the parcel to keep track of the water vapor content. You will generally be given this information.
2. As long as the parcel is unsaturated (i.e., when the relative humidity < 100% or whenever the dew point temperature of the air inside the parcel is lower than the temperature of the air inside the parcel), the rate of cooling is 10°C for every 1000 meters the parcel is lifted. The parcel temperature decreases as it rises upward because the parcel is expanding. The dew point temperature of the air in a rising parcel does not change until the parcel cools to saturation. Since the dew point temperature is a measure of the amount of water vapor in the air, this means that the water vapor in the parcel at ground level is moving upward with the parcel.

3. As a rising parcel cools, its relative humidity increases because the air temperature is getting closer to the dew point temperature. Once the relative humidity reaches 100% (determined when the parcel temperature cools down to equal its original dew point temperature), further lifting (and cooling) results in net condensation, forming a cloud. Remember that an air parcel will never contain more water vapor than its capacity or saturation mixing ratio. In other words, the dew point temperature of the air in the parcel will never be greater than the temperature of the air in the parcel because that would make the relative humidity greater than 100%, which does not happen. Instead condensation happens so that the air never contains more water vapor than the saturation amount at the lower temperature.

   Since condensation releases latent heat within the parcel, the rate of cooling is slower. Parcels which are saturated cool at a rate of 6°C for every 1000 meters the parcel is lifted. Also keep in mind that once a cloud begins to develop in a parcel, just enough water vapor will condense into liquid water so that the air in the parcel will have a relative humidity of exactly 100%, but not over 100%. This means that once a cloud begins to form in a rising parcel, the amount of water vapor that condenses into liquid drops is exactly enough that the dew point temperature of the air in the parcel remains the same as the air temperature .

   Once condensation begins in a rising parcel of air, there become two factors that influence the temperature of the air within the parcel. The parcel continues to expand as it rises upward, which lowers the temperature of the air inside the parcel, but now there is condensation happening (cloud formation), which releases heat and warms the air inside the pacel. The expansion wins out and the rising parcel still gets colder, but accounting for the latent heat release during condensation, a saturated, rising parcel cools at a slower rate than a rising parcel that is unsaturated and not forming a cloud by condensation.

4. When lowering an air parcel in the atmosphere, the temperature changes are reversed. If there is no cloud (liquid water) in the parcel, the air temperature in the parcel increases at a rate of 10°C for every 1000 meters the parcel moves downward in the atmosphere. The increase in temperature happens because the parcel is being compressed by increasing air pressure as it moves downward. When there is no cloud of liquid water drops (or ice crystals), the water vapor content and dew point temperature of the air in the parcel stays the same as it moves downward in the atmosphere.

   If there is liquid water in a parcel (cloud droplets or raindrops) that is moving downward, the liquid will evaporate because as the parcel warms its capacity for water vapor increases. As long as there is liquid water (cloud or rain) in the downward moving parcel, just enough water will evaporate to keep the relative humidity at 100%. Thus, for parcels of air that contain liquid water, the dew point temperature will increase to remain equal to the air temperature inside the parcel. Parcels which contain an evaporating cloud warm at a rate of 6°C for every 1000 meters the parcel is lowered until the entire cloud has evaporated. There are now two processes that influence the temperature of the air inside the parcel. The parcel will warm as it gets compressed, but the evaporation of liquid water is a cooling process because the liquid water absorbs heat from the air inside the parcel as it evaporates. The compression wins out and sinking parcels containing liquid water still warm, but accounting for the latent heat absorbed during evaporation, the rate of warming is slower than for a sinking parcel that does not contain liquid water.

Tabular example for raising an air parcel

You are expected to apply the rules above to fill in tables that keep track of the air temperature and dew point temperature of the air in a parcel that is moving up or down in the atmosphere. An example of a "blank" table is given below. You are expected to fill in the missing values in the table for a parcel of air forced to move upward from 0 meters to 6000 meters above sea level.

The first thing to do is move the parcel upward until it cools to its dew point temperature or reaches saturation with respect to water vapor. Rising parcels that are unsaturated cool at a rate of 10° C per 1000 meters they are lifted. Note that the dew point temperature remains constant until saturation is reached. Since the dew point temperature is a measure of the amount of water vapor in the parcel, it does not change unless there is a phase change of water happening in the parcel.

In this example, the parcel cools to saturation after it has been moved up to 3000 meters above sea level. This is the altitude where a cloud will start to form in the parcel. Once saturation is reached, condensation occurs as the parcel continues upward. Now the rate of temperature decrease becomes 6° C per 1000 meters of lifting due to the release of latent heat by condensation. Once condensation begins there are two influences on the temperature of the air within a rising parcel, cooling because the parcel is expanding as it rises and warming due to the release of latent heat during cloud formation (condesation from water vapor to liquid). Overall the rising parcel still cools, but the rate of parcel cooling as it is lifted is now slower. Because the dew point temperature keeps track of the amount of water vapor in the parcel, it must decrease once a cloud begins to form by condensation (water vapor condensing to the tiny liquid droplets that make up a cloud). The decrease in the dew point temperature indicates that there is a decreasing amount of water vapor in the air parcel. The water does not disappear though, it is condensing into the liquid that is the cloud. You should realize that once a cloud begins to form that the dew point temperature in a rising air parcel will remain the same as the air temperature so that the relative humidity in the parcel stays at 100%.

Additional Numerical example for raising an air parcel

Another numerical example is contained in the link below. The image of the link contains two tables. The first table is mostly blank and shows you the information you would be given about the atmosphere before lifting a surface parcel upward. You wll have to determine at what altitude a cloud will form by filling in the blanks. The second table shows the solution. NOTE: Please do not worry about the columns labeled environmental temperature and stability, we have not covered that material yet. You will be expected to do similar in homework and exam questions. Click Here to view the example.

Discussion

Although the instructive method of filling in a table to keep track of what happens to air parcels as they rise is somewhat simplified, I believe it is very helpful in getting a first-order understanding of how clouds form. You will have to perform similar exercises in both homework problems and exams, so you should understand how to do it and the reasoning behind the rules for doing it.

This instructive method ignores some of the complicating details. For example, air parcels do not remain completely isolated from the surrounding air, since some mixing of the air inside the parcel with the air outside the parcel does occur. Although the rate of cooling of rising unsaturated parcels is always about 10°C per 1000 meters in Earth's atmosphere, the rate of cooling of saturated parcels is not always 6°C per 1000 meters (as this is only an average). The actual cooling rate depends on how much water vapor condenses, which changes as the saturation mixing ratios change. Another detail is that the dew point temperature of rising parcels does not remain constant prior to saturation, but actually decreases slightly. You are not expected to consider these details for homework or exam questions. A good understanding of the basic processes involved can be gained using our simplified method.