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about Atmospheric Stability

Atmospheric Stability
Perhaps one of the most confusing aspects of meteorology for most beginning students is the concept of atmospheric stability.

Atmospheric stability is certainly a complex concept! Stability in the atmosphere is usually described in terms of 'lapse rates'. An understanding of latent heat is also imperative to conceptualizing atmospheric stability, therefore this page will focus on both lapse rates and latent heat as precursors to our understanding of atmospheric stability.

Even before we begin here, it is highly recommended that you visit our "Water & Weather" page. There you will learn some of the important properties of water that will greatly enhance your understanding of atmospheric stability here.

Lapse Rates
Lapse rate defines the way in which temperature varies with altitude. Lapse rates come in two
general flavors: The Environmental Lapse Rate (ELR) and The Adiabatic Lapse Rates. The latter
comes in two flavors of its own: The Dry Adiabatic Lapse Rate (DALR) and The Saturated
Adiabatic Lapse Rate (SALR) sometimes called The Wet Adiabatic Lapse Rate (WALR) and sometimes it is also called The Moist Adiabatic Lapse Rate (MALR)! Ugggg! We'll just call it SALR.

The ELR is the actual variation of temperature with height at a certain time and place. It varies from place to place and from time to time so there really is no fixed rate. Meteorologists measure temperatures through a vertical profile by releasing weather balloons with mini-weather stations attached to them called radiosondes. Sometimes, meteorologists drop these mini-weather stations from a plane at high altitude with a parachute attached. These latter type of measuring devices are called dropsondes.

The word 'adiabatic' refers to a thermodynamic process in which heat neither enters nor leaves the system in question. Yet temperatures drop with altitude in the troposphere. Why is that? Considering the fact that no heat leaves the system, how is it possible that air gets cooler with altitude?

The following illustration shows how pressure decreases with increasing altitude. The reason pressure is lower with altitude is due to the fact that there are fewer 'air molecules' at altitude than there are closer to Earth. Air becomes thinner (air molecules become increasingly scarce) as you go up. As a result, air expands. The following illustration opens in separate window. Be sure to close the window to return to this page!
See Illustration

This is a good point to list a couple important laws of physics! These links will open in a new window, so just close the windows when you are ready to return to this page!
The Law of Adiabatic Expansion/Compression
The Law of Hydrostatic Balance

Since pressure decreases with elevation, rising air parcels (see Law of Buoyancy) will expand. There will be less inward pressure relative to outward pressure exerted on that parcel. The process of expansion effectively takes up some internal energy of that parcel; this energy is heat energy, therefore the result is removal of heat translating in lower temperatures. The energy is still there (it is neither created or destroyed). It is simply not detectable by measuring instruments (thermometers)!
Check out The Ideal Gas Law!

Temperature doesn't just suddenly drop. It drops at a rate (-deg/elev) known generically as the Adiabatic Lapse Rate. So what is this rate? It depends on whether the air parcel ascending into the sky is saturated or not. If it is 'dry' (not saturated), it will rise and expand experiencing temperature drop as heat energy is absorbed during the expansion process. If, on the other hand, it is saturated, then it will rise, expand and reach its dew point temperature causing the water vapor in it to condense on condensation nuclei.

During condensation, water vapor is undergoing a phase change from gas to liquid requiring that every gram of water vapor release 539 calories of heat energy (read more about this in our "Weather's Water" section). This heat energy is released thus lowering the rate at which the air parcel cools as it ascends. For example: if air cooled 10 units per 1000 feet (lost 10 units of heat), then condensed and released 3 units of heat, then we would subtract 3 units from the original 10 giving us a slower rate of 7 units per 1000 feet.

The dry adiabatic lapse rate is 9.8ºC per kilometer (9.8ºC/km). This rate is constant until the air parcel in ascent becomes saturated (reaches its dew point temperature). As explained above, once dew point is reached (saturation), latent heat is released as a result of condensation (gas to liquid change of state of water) and the rate drops.

The saturated adiabatic lapse rate is variable since it largely depends on how much latent heat is made available within the air parcel as its moisture condenses. Generally, the higher the parcel ascends, the greater the amount of heat released by condensation since expansion is more pronounced (pressure decreases with elevation). Temperature will also affect this rate. Another thing to keep in mind is that as the parcel condenses and continues its ascent, less and less water vapor will remain to be condensed meaning that less heat energy will be released. In the lower elevations the SALR varies from about 3.9ºC/1km when ambient temperature is around 26ºC to about 7.2ºC/1km when ambient temperature is around -10ºC.

Considering the fact that less water vapor is available for condensation after prolonged ascent, the SALR will eventually increase to the point where it is almost identical to the DALR (9.8ºC/1km)! This is most likely to occur at very high elevations where ambient temperature can drop below -40ºC!  That sounds pretty cold eh?! Consider that when you fly across country, the air temperature outside your window is probably around -100ºF! Chilly!

I should note here that in a beginning course, you will probably be taught the average SALR, which is between or at 5-6ºC/1km, an approximate average of the extremes.

Air is considered to be stable if it descends to its original level after an initial vertical displacement. Rising air parcels are considered to be unstable, and can sometimes result in impressive cumulonimbus clouds! You may have heard the term 'thermal' used before. A thermal is simply a term given to a rising parcel of air. From this point on we will refer to rising air parcels simply as thermals.

We know thermals won't ascend into space! So how far do they get? It depends on numerous factors. We will start with the very basic concept before we get into other factors. Let's begin with a hypothetical example:

If a thermal's temperature near Earth's surface is say, 29ºC, and ambient air temperature has been measured at 26ºC, and we have determined by reading the data from the radiosonde we released into the air that the environmental lapse rate (the actual temperature through a vertical column of air) is 5.8ºC/1km, then we should have no problem determining the point at which the thermal's ascent will stop. For simplicity, let's say the thermal rises only at the DALR (9.8ºC/1km).

The thermal will stop its ascent as soon as its temperature equals the ambient air temperature around it! After the first kilometer, the thermal will have cooled due to expansion by 9.8ºC (the DALR). Meanwhile, air around it will have cooled 6.8ºC (the ELR). This means the thermal will be 19.2ºC and ambient air temperature will also be 19.2ºC. At equal temperatures, the thermal no longer rises, and stabilizes at 1km of elevation! If you have the free Flash plug-in from www.macromedia.com, you can see an example of what we just went over by clicking>> here. If the window is blank, you need to download the free Flash plug-in!

Though a bubble was used to represent the thermal, the more likely 'shape' of a thermal would be like this >>> THERMAL.  For simplicity, a bubble is used to illustrate thermal ascent.

Now let's throw in another variable: momentum. The momentum of any object is just its mass multiplied by its velocity, or mv. Momentum expresses the persistence of movement, or inertia, of a body in motion. The pressure exerted by a gas (in this case air of a thermal) is related to the molecular motion of the gas molecules. When a molecule collides with a surface (another molecule) it produces a force on that surface. That force multiplied by the by the time duration of the collision is called the impulse. Impulse is related to momentum (both are properties of mass).

It is likely that the thermal will have momentum on its side as it ascends. So even if it reaches a temperature equal to that of surrounding air, it may still ascend another 300 meters or so just from momentum! In this scenario, the thermal will become slightly cooler than surrounding air, but this makes it denser than surrounding air and it will soon descend. Though, it is likely to have momentum on its side as it descends now! In which case it will simply descend below the level at which its temperature equals the temperature of surrounding air and heat adiabatically causing it to become slightly warmer than surrounding air. Again, it will begin to rise and may pass the point again, each time having less and less momentum. See it here>> click here

Okay, now let's throw another factor into the mix: moisture! We discussed the SALR earlier, and learned that it is lower than the DALR due to release of latent heat as water vapor condenses.

We'll focus on what its predicted temperature should be at a given altitude. Let's say the thermal has a temperature of 25ºC at Earth's surface, and we have determined that SALR is 5.5ºC/1km (average rate taught in most courses). What would the thermal's temperature be at 2km above Earth's surface if it rises at the DALR for the first kilometer, and at the SALR for the second kilometer? Check your answer here

We have covered DALR, ELR, and SALR, now let's add one more: Dew Point Lapse Rate. Again, the exact rate varies depending on atmospheric conditions, but the range is relatively small nevertheless. NOAA meteorologist, Thomas Schlatter, performed numerous calculations of dew point lapse rate under various conditions and found that values range from 1.6
ºC/1km to nearly 1.9ºC/1km.

Let's refer to dew point lapse rate simply as DPLR. Okay, quick recap before we move on:
DALR = dry adiabatic lapse rate = 9.8ºC/1km
SALR = saturated adiabatic lapse rate = 3.9ºC/1km - 7.2ºC/1km
ELR = varies from place to place and from time to time...
DPLR = 1.6ºC/1km - 1.9ºC/1km

It is important to know dew point changes slightly with altitude since it affects the level at which condensation occurs. This level is officially termed the condensation level by meteorologists or lifting condensation level (LCL). What is condensation level?

Condensation level is the level at which moisture in rising air (thermals) starts to condense and form droplets of cloud. It is the point at which dew point temperature and air temperature become equal. You should already be aware that dew point temperature is the temperature to which air must be cooled to become saturated with water vapor. Further cooling leads to the formation of cloud droplets or fog in the atmosphere or the deposit of dew on surfaces. If air temperature equals dew point temperature, relative humidity equals 100%.

Condensation level is very nearly the base of any cumulus cloud. You can indirectly see it best when there are large cumulonimbus or towering cumulus clouds in the sky. Their flat bases are very nearly indicative of condensation level! You'll notice there aren't any clouds below this level.

The following animation will illustrate an air parcel's orographic ascent up a mountain slope, reaching condensation level, then proceeding up the slope and descending the other side. This example is commonly used in the classroom because it not only illustrates DALR and SALR, but it also shows condensation level and DPLR as well! It also effectively illustrates the cause of rain shadow desert environments.
See it here >>click here

Having watched the animation at the link above, you are now aware of the lifting condensation level, and how it can be considered to be the boundary delimiting areas where a thermal will rise at DALR and where it will rise at SALR. You have also learned that lifting condensation level is very nearly located at the base of any CB (cumulonimbus) or TCU (towering cumulus) cloud. If you have the free Flash plug-in, then check out the following interactive animation depicting linear relationships between DPLR, SALR, DALR and LCL! It opens in a new window, click here
 

As weather observers, there are times when we want to know how high the base of these clouds are, especially for purposes of aviation.

One way of course is to use special instrumentation, such as a ceilometer used at Pierce College and at the Van Nuys airport. However, there are times when no such instrument is available, or there is a patch of blue sky over the ceilometer so that the ceilometer thinks it's clear weather.

The way to determine cloud base without such instrumentation available is to use a simple psychrometer. We can calculate cloud base for cumulus clouds by basing our calculations on Normand's Theorem. Simply multiply the difference between ambient air temperature and dew point temperature by 400. Your answer will be cloud base in feet above ground level. For example, if you take the following measurements:
If,
          Air Temperature:  13.9
ºC
          Dew Point:  6.1ºC
then,
          13.9 - 6.1 = 7.8
          7.8 * 400 = 3120
therefore,
          cloud base is approximately 3,120 feet above ground level.

It should be noted here that this is restricted to morning to noon when sunshine is warming the ground and the air in contact with it. It is also restricted to cumulus and low stratus clouds. Beyond noon, and with any other cloud, this equation only tells you the minimum level a cloud base will be, but gives no indication of how high bases actually are.

Here in the San Fernando Valley, I generally restrict this equation to times between sunrise and about 10 to 11am when reporting cloud bases to aircraft.

We have covered DALR, SALR, DPLR, LCL and ELR. Now let's look at inversions or as they are sometimes referred to as inversion layers.

An inversion is where air temperature increases with altitude rather than the normal decrease in temperature in the troposphere. Normally, the environmental lapse rate (ELR) shows us a decrease in temperature with height. Earlier we learned that ELR is variable from place to place and from time to time depending on conditions, but that it is often defined as cooling with elevation as a result of adiabatic cooling processes.

However, an inversion is where this cooling stops, and a warming trend with height occurs. The following illustration is adapted from the animation on the previous page you looked at showing lapse rates' relationships with lifting condensation level. The following illustration shows SALR, DALR, DPLR, and LCL, but it also shows a new element: the ELR. It illustrates on one of seemingly infinite amounts of possibilities available in nature!

The inversion in the above illustration begins at 2,000 meters above the ground. From that point upward, the actual air temperature increases with altitude. This increase in temperature with elevation makes the atmosphere above 2,000 meters very stable. This layer, or inversion layer as it is called, acts as a 'lid' restricting the height to which a thermal can rise. The thermal's temperature is relatively cooler than ambient temperatures in the inversion layer, therefore the thermal is technically denser than air in the inversion. As such, the thermal will no longer be displaced by denser air around it and will subsequently cease its ascent.

Anvil tops on cumulonimbus clouds most often are a result of the cloud reaching an inversion layer. The inversion layer for the really huge cumulonimbus clouds is the stratosphere where ozone's absorption of solar radiation creates an inversion layer many kilometers thick! Not all tops of clouds are necessarily the base of inversions. Cut-off cloud tops may also be from wind shear aloft.

Okay, now the part you've all been waiting for...

Atmospheric stability comes in several "flavors". They include Absolute Instability, Neutral Stability, Conditional Instability, Absolute Stability, and Potential Instability.

Absolute Instability
Absolute instability occurs when ELR is greater than DALR. We have learned that DALR is 9.8ºC/1km, therefore we can conclude that absolute instability exists when ELR is 9.9ºC/1km or greater. Meteorologists call this a "super-adiabatic lapse rate" since heat loss with elevation is so rapid.

Neutral Stability
Neutral stability occurs when ELR and DALR are equal. That is, when ELR is 9.8ºC/1km. It is called 'neutral' because the thermal keeps its initial momentum and does not accelerate or slow down.

Conditional Instability
Conditional Instability occurs when ELR is less than DALR but more than SALR. In other words, it is when ELR is between SALR (which varies between 3.9ºC/1km to 7.2ºC/1km) and DALR (which is 9.8ºC/1km). The 'condition' for instability is only when the thermal becomes saturated, not before.

Absolute Stability
Absolute stability occurs when ELR is less than SALR (and therefore less than DALR). This means that ELR must be lower than SALR (which varies between 3.9ºC/1km and 7.2ºC/1km) which will never be more than 7.1ºC/1km (if SALR is at its maximum).

Potential Instability
Potential Instability occurs when air at low levels (near the ground) is moist, but is dryer higher up. The wet bulb temperature (on a psychrometer) must decrease faster than the SALR. The potential for instability is only realized when the thermal ascends, most often up a slope of a mountain (orographic uplift), up a an air mass front (frontal lifting), or by convergence at Earth's surface, and reaches saturation. If you didn't see the animation on rain shadow effect earlier, you can see an example of orographic uplift by clicking >>here.

 

-by Steve W. Woodruff