Stability of the atmosphere

Most clouds form as air rises and cools. There are several mechanisms that force surface air to rise. We briefly looked at the most common and important mechanisms that force air to rise. At the moment lets assume that we are in a region of the atmosphere where the surface air is being forced to rise upward. This page explains the concept of atmospheric stability and how it influences the size and shapes of clouds. An important reason for discussing atmospheric stability is that thunderstorms, tornadoes, and hurricanes form when the atmosphere is unstable. The more unstable the atmosphere, the higher the potential for severe weather. There are two general types of clouds:

Stratiform-type clouds
- vertically thin layers of cloud that often cover large horizontal areas
- cloud development is primarily horizontal, rather than vertical
- form under stable environmental conditions, which means the air temperature inside the cloud is colder than the air temperature outside the cloud
Cumuliform-type clouds
- vertically tall clouds, but horizontally not that large, often see clear sky between cloud elements
- cloud development is primarily vertical
- form under unstable environmental conditions, which means the air temperature inside the cloud is warmer than the air temperature outside the cloud

Hand drawn figure of idealized stratiform cloud formation

Hand drawn figure of idealized cumuliform cloud formation

A misleading aspect of the pictures shown above is that they show surface air moving straight upward over a small horizontal area. While this does happen, it is common for a large horizontal layer of air to be forced upward and simultaneously form clouds over a large horizontal area. This will form stratiform clouds in stable environments that can be moved horizontally by the winds at cloud level. In fact the upward moving air often moves along a sloped path upward, rather than just moving stright up. Even in situations of large stratiform cloud formation, there can be small regions where the lifted air becomes unstable, resulting in the formation of cumuliform clouds mixed with the stratus clouds. Finally, clouds can form anywhere air is moving upward, expanding and cooling. The upward moving air does not always begin from the ground surface. For example, if air 4000 meters above the ground is forced upward to 5000 meters above the ground, clouds may form, since upward moving air expands and cools, which will result in the formation of clouds if the air cools to satuaration with respect to water vapor.

Although we are going to spend most of this class talking about the weather that occurs under unstable atmospheric conditions, you should realize that most of the time the atmosphere is not unstable. A good portion of the clouds and precipitation that form on Earth happen when the atmosphere is stable, including many episodes of heavy rain and flooding. We are focusing on unstable conditions since much of the more interesting severe weather, like thunderstorms, tornadoes, lightning, and hurricanes, only happens when the atmosphere is unstable. Please understand that the atmosphere does not need to be unstable for clouds and precipitation to occur and most often the atmosphere is stable. Clouds and precipitation commonly form under stable atmospheric conditions where air is forced upward.

What makes the atmosphere unstable?

If the temperature of the air in a parcel becomes warmer than the surrounding envrionmental air, the air parcel becomes buoyant, and accelerates upward. Again, the surrounding environmental air refers to the air surrounding the parcel, which is at the same pressure and altitude as the parcel. In other words, a warm parcel is less dense than the cooler air surrounding it, so the parcel gets forced upward by the more dense surrounding fluid. When rising air parcels become warmer than the surround air, we say the atmosphere is unstable. Thus, the atmosphere is said to be unstable if the temperature of a lifted parcel becomes warmer than the surrounding air.

This is similar to what happens if you place a block of wood at the bottom of a pool of water and let it go. The block will be forced upward because it is less dense than the surrounding fluid. Parcels which are warmer than the environmental air surrounding them are less dense than the surrounding fluid and are forced to rise upward. We can use the kinetic model of gases to explain why warm parcels are less dense than the cooler air surrounding them. Rememeber gas pressure is caused by collisions of countless numbers of gas molecules on a surface. Consider a parcel of air that is originally at the same temperature and pressure of the air surrounding the parcel. Now heat the air in the parcel. This will temporarily increase the air pressure inside the parcel becuase the gas molecules begin moving faster and thus collide more forcefully with the sides of the parcel. Since the air pressure inside the parcel must always come into balance with the pressure of the air surrounding the parcel, the parcel expands. Now we have the same number of gas molecules in a larger volume, thus the number density of air in the parcel has lowered. This makes the warmer parcel less dense (lighter) than the surrounding air, so it is forced to rise up in the same way that a block of wood rises up when surrounded by a water (a more dense fluid).

This can also be easily shown using the gas law. Recall that parcels in the atmosphere adjust their size so that the air pressure inside the parcel equals the air pressure outside the parcel (This is always the case). If the air temperature inside a parcel is warmer than the air temperature of the air surrounding the parcel, the number density inside the parcel is lower than the number density outside the parcel. Thus, the air parcel weighs less than an equal volume of air outside the parcel and it will rise upward (see Figure R).

In the atmosphere, beside the mechanism of surface heating and free convection, the only other way in which parcels become unstable is when the latent heat released during cloud formation (water vapor condensing to liquid cloud droplets) is enough to make the temperature of the parcel warmer than the surrounding environmental air. Meteorologists assess and compute the stability of the atmosphere by lifting hypothetical parcels of air upward from the surface and comparing the parcel temperature with the temperature of the surrounding air. The temperature of the surrounding air from ground level upward is measured twice each day by releasing weather balloons with instruments attached. If the atmosphere is found to be unstable for lifted parcels, there is the possibility of thunderstorms; however, if the atmosphere is found to be stable for lifted parcels, thunderstorms will not form.

In this class, we will illustrate the concepts of cloud formation and stability using simplified numerical examples. The basic problem will be given the vertical temperature structure of the atmosphere and the water vapor content of air at the surface, lift a hypothetical parcel upward to determine (a) at what altitude will a cloud start to form and (b) at what altitude, if at all, will the parcel become unstable.

Recall the rules we already discussed for lifting air parcels:

The starting temperature and water vapor content (use the dew point) of the parcel is taken to be the measured conditions at ground level. You will always be given this information.
As long as the parcel is unsaturated (relative humidity < 100% or whenever the dew point temperature of the parcel less than the temperature of the parcel), the rate of cooling is 10°C for every 1000 meters the parcel is lifted.
As a rising parcel cools, its relative humidity increases. Once the relative humidity reaches 100% (determined when the parcel temperature cools down to its original dew point temperature), further lifting (and cooling) results in net condensation, forming a cloud. 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 remains saturated (relative humidity = 100% and the dew point temperature equals the air temperature inside the parcel).

Now we add the concept of stability. To determine stability, compare the parcel temperature with the temperature of the surrounding air and think about what would happen if the parcel was "let go" or no longer forced upward.

If the parcel temperature is higher than the surrounding air temperature, the parcel is positively buoyant and would tend to move upward if released. This is the unstable situation. The atmosphere is said to be unstable when a lifted parcel reaches a region where it accelerates upward because it has become less dense than the surrounding atmosphere, i.e., push a parcel up and it shoots upward on its own.
If the parcel temperature is lower than the surrounding air temperature, the parcel is negatively buoyant and would tend to move downward if released. This is a stable situation. The atmosphere is said to be stable when a lifted parcel is more dense than the surrounding atmosphere, i.e., push a parcel up and it tends to come back down
If the parcel temperature is equal to the surrounding air temperature, the parcel is said to be neutral and would remain stationary if released. When a parcel becomes neutral, it often signals a transition from stable to unstable or unstable to stable.

Tabular example for Stability

An example of a "blank" table is given below. You are expected to use the rules for moving air parcels to keep track of the temperature and dew point temperature (water vapor content) in an air parcel that is moved upward from 0 meters to 8000 meters above sea level. The designation "neutral" is used to indicate that the parcel temperature is the same as the air temperature of the surrounding atmosphere and thus the parcel is the same density as the surrounding atmosphere.

Altitude (meters above Sea level)	Environmental Temperature (°C)	Stability?	Parcel Temperature (°C)	Parcel Dew Point Temperature (°C)
8000	-15
7000	-12
6000	-9
5000	-2
4000	5
3000	12
2000	20
1000	28
0	35	Neutral	35	25

The rules for keeping track of the temperature and dew point temperature were given on the previous page. Now we add the concept of stability. We are specifically checking to see if a rising parcel becomes warmer than the surrounding environmental air. The next table has been filled in up to the lowest altitude where the air parcel becomes unstable.

Altitude (meters above Sea level)	Environmental Temperature (°C)	Stability?	Parcel Temperature (°C)	Parcel Dew Point Temperature (°C)
8000	-15
7000	-12
6000	-9
5000	-2
4000	6	Unstable	7	7
3000	14	Stable	13	13
2000	21	Stable	19	19
1000	28	Stable	25	25
0	35	Neutral	35	25

You should realize that the rising parcel reaches saturation (its temperature cooled to equal its dew point temperature) at an altitude of 1000 meters. This is the level where a cloud would start to form in the parcel. You should realize that once condensation begins and a cloud starts to form, the rate of cooling changes from 10°C per 1000 meters to 6°C per 1000 meters to account for the latent heat realeased by the condensation of cloud formation. At an altitude of 4000 meters, the temperature of the air in the lifted parcel is warmer than the temperature of the air surrounding the parcel, which is specified in the column "Environmental Temperature." This is the unstable situation for a parcel moving upward. For the atmospheric coniditions specified in the table, if an air parcel were forced upward to 4000 meters, it would become unstable, i.e., warmer and less dense than the surrounding air. An unstable parcel will accelerate upward as long as it remains warmer and less dense than the surrounding air. The remainder of the table is filled in below.

Altitude (meters above Sea level)	Environmental Temperature (°C)	Stability?	Parcel Temperature (°C)	Parcel Dew Point Temperature (°C)
8000	-15	Stable	-17	-17
7000	-12	Unstable	-11	-11
6000	-9	Unstable	-5	-5
5000	-2	Unstable	1	1
4000	6	Unstable	7	7
3000	14	Stable	13	13
2000	21	Stable	19	19
1000	28	Stable	25	25
0	35	Neutral	35	25

Note that the parcel was unstable over the altitude range from 4000 to 7000 meters above sea level and then it became stable again. If an air parcel were forced up to 4000 meters, it would then accelerate upward from 4000 to 7000 meters over the altitude range where it is warmer than the surrounding air, and stop accelerating upward by 8000 meters when the parcel becomes colder and more dense than the surrounding air.

Additional example for computing stability

Here is another numerical example. The first table shows you what you would know about the atmosphere before performing the stability analysis. You would have to fill in the blanks. The second table shows the solution. You will be asked to perform similar problems in homework. Click Here to view the example.

Videos of cloud and thunderstorm formation

When the atmospheric is unstable, time-lapse videos of developing clouds can be quite interesting. The videos placed under the link below are quite large (file size), and if you cannot view them that is ok. I suggest looking at the one dated 20070823 as a good example of a day when it was unstable and storms formed. Once parcels are pushed up to the level where they become unstable, they accelerate upward, trailing towers of cumulus clouds.
(Cloud annimation videos taken from the roof of the PAS building at the University of Arizona

Some notes on Predicting Violent Storms

Meteorologists use a similar method to assess the potential for thunderstorms and severe weather:

Lift parcels upward to see if they become unstable. This must be done for the current measured atmospheric conditions as well as for forecasted conditions in the future.
The more unstable the atmosphere, the greater the potential for violent storms

The depth of the unstable layer is important, i.e., how many thousands of meters does the parcel remain warmer than the surrounding air?
The greater the positive difference between the parcel temperature and the surrounding air temperature, the more unstable the atmosphere.

Question to answer. If the atmosphere is unstable, will parcels be lifted high enough (by one of the four mechanisms that cause air to rise) to reach the unstable layer? This must occur to "release the instability" if storms are to occur.

If analysis shows that the atmosphere is unstable, it means that there is the potential for thunderstorms to form, however, it does not guarantee that thunderstorms will form. An unstable atmosphere means that there is potential energy available for thunderstorms to develop, but this potential energy will not be realized unless air parcels are lifted up to the altitude where they become unstable. When thunderstorms do form, this potential energy is converted to kinetic energy. This is why some meteorologist say that a lifting mechanism is required to "release the instabily" or unleash the potential energy available under the given atmospheric conditions.