Static Stability and Atmospheric Soundings
Learning Goal 3b. Determine the static stability given temperature
soundings, and describe its effects on air motions and on aviation
Atmospheric stability refers
to whether the air will become or stay turbulent
(unstable static stability)
or will become or stay non-turbulent (stable static stability).
Another word for non-turbulent is "laminar", which implies smooth flow.
Turbulence ranges from small
eddies caused by air flow around a tree or obstacle, through
medium-size eddies (about 2 km in diameter)
associated with warm rising air in "thermals", to large-scale
instability associated with thunderstorms (about 10 to 15 km in
diameter). Turbulence on all scales affects aircraft, sailboats, and
snow-ski races.
Static Stability
The simplest type of stability is called static
stability. It is simple
because it depends only on the temperature layering in the
atmosphere, not on the wind. This stability is related to the
fact that cooler air is denser (heavier) than warmer, less dense
air. You can think of the atmosphere as a layer cake, where each
layer has a different temperature.
If atmospheric structure is such that the cool (heavy) layer of air
is under the warmer (lighter) layer, then that part of the atmosphere
is said to be statically stable.
If there is no wind
shear, then a statically stable region is
non-turbulent, because the air is "happy" where it is. Namely,
the colder air doesn't need to sink because it is already at the bottom
of the layer cake.
But if the warm (lighter, more buoyant) air is under the cooler
denser air, then the atmospheric structure is "unhappy". The
cooler air starts to sink and the warmer air starts to rise (as buoyant
thermals) as it tries to get "happier". In this situation, the
atmospheric structure is statically unstable.
The atmosphere "turns over", where the cooler air
and warmer air change
places is a complex turbulent dance of eddies. It is like when
you cook soup or sauce in a pot on the stove. When the bottom of
the fluid becomes warmer than the top, the fluid in your pot is
statically unstable and becomes turbulent as the warm soup or sauce
tries to rise through the cooler layer.
There is an added complication in the atmosphere that does not
affect liquids such as your soup or sauce. That complication is
that when air rises in the atmosphere, it moves into regions of lower
pressure, which allows the air to expand and get cooler.
Similarly, when air sinks in the atmosphere, it is compressed in the
higher pressure and becomes warmer. This temperature change for
vertically moving blobs of air (air
parcels) is called the adiabatic lapse
rate, and has a value of 9.8°C/km. Namely,
rising air cools about 10°C for each 1 kilometer that it rises, and
sinking air warms at the same rate. This adiabatic temperature change is
normal and happens all the time. But we need to add this effect to
determine static stability.
Here is a tool that you can use to graphically find the
static-stability index, S, if you know the temperatures at the top and
bottom altitudes of a layer of air. (This graphical tool will be provided on the exams if needed to answer any of the exam questions.)
Here is how you interpret "S":
- If S is positive, then the air layer is statically stable,
and the air becomes
non-turbulent (if no wind shear exists)
- If S is zero, then the air is statically neutral
(neither stable nor unstable)
- If S is negative, then the air is statically unstable,
and the air becomes
turbulent
One final trick: Unstable air always wins, if your
computation gives different values of S for the same location.
Solved example
Suppose your layer cake of air has the following temperature
structure:
Top altitude at z = 2 km: T = 5°C
Middle altitude at z = 1 km: T = 15°C
Bottom altitude at z = 0 km: T = 28°C
What is the static stability in each layer (namely, between each pair of altitudes)?
Solution:
For the bottom layer (between the middle and bottom altitudes):
∆T = [ 15°C – 28°C ] = –13°C
∆z = layer thickness = 1 km - 0 km = 1 km.
Using the Stability Tool in the figure above, we find
S = –3°C/km
This is a negative number, therefore the layer is statically unstable.
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For the top layer (between the top and middle altitudes):
∆T = [ 5°C – 15°C ] = –10°C
∆z = layer thickness = 2 km - 1 km = 1 km.
Using the Stability Tool in the figure above, we find
S = 0°C/km
Zero S would mean the air is statically neutral, except don't forget
the "final trick" mentioned above. To address this issue, we need to
also find the static stability between the bottom and the top:
---
For the whole layer cake of air (between the top and bottom altitudes):
S = [ 5°C – 28°C ] = –23°C ∆z = layer thickness = 2 km - 0 km = 2 km.
Using the Stability Tool in the figure above, we find
S = –1.5°C/km
This is a negative number, therefore unstable.
Discussion: Since unstable always wins, in
means
that all three layers are unstable and turbulent. This is typical of
thermals rising on a sunny day over land. Perfect conditions for
sailplanes and birds to soar in the thermal updrafts, but causing a
bumpy ride for light airplanes. So keep the barf bags available for your passengers.
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Static stability affects aviation weather as follows:
In statically stable
conditions:
- Typically forms near the ground at night under clear skies with
calm-to-light winds, when the ground
temperature decreases, and the ground cools the air that touches it.
- Air is usually nonturbulent (a smooth ride in an airplane) if
there is no wind shear.
- But if this air is forced up over a mountain, then on the
downwind side it sinks past its starting altitude (i.e., overshoots
downward), and then starts to rise again and overshoots upward, and
keeps oscillating as a mountain wave.
- Cold air near the ground can drain downhill and can pool in the
valley floor, where frost or fog can form in the cold air.
- If there is wind shear in a statically stable region, then
turbulence can form, along with breaking atmospheric waves called
Kelvin Helmholtz waves (see Learning Goal 1b).
In statically neutral
conditions:
- Typically forms in overcast conditions (day or night) when the
wind is moderate or strong.
- Air can be nonturbulent, but the slightest wind shear can create
dynamic instability and turbulence.
- Neutral air hitting a mountain creates obstacle wake turbulence
downwind of the mountain.
In statically unstable
conditions:
- Typically occurs in sunny days over land when the average winds
are relatively light.
- It can be caused when the sun heats the
land and the land warms the bottom layer of air.
- Thermals of warm air rise with cooler descending air between the
thermals.
- Cumulus clouds might form at the top of the thermals if the
thermals are humid enough and the unstable air is deep enough.
- If the unstable air extends over most of the depth of the
troposphere, then thunderstorms
can form (with many flight hazards).
Thunderstorm Stability Indices
As thunderstorms are hazardous to flight, many additional stability
indices are have been devised for thunderstorms. Two of those
indices are described here, because they are used in Learning Goals
4a-h about thunderstorms. These indices don't tell us if a
thunderstorm will form - - they tell us only how strong the storm might
be if it forms.
Convective Available Potential Energy (
CAPE)
is one index. It is a measure of the accumulated buoyant energy
of a rising blob of warm humid air relative to the cooler surrounding
environment that it is rising through. More violent storms are
associated with larger values of CAPE. There are different ways
to estimate CAPE - - the table below uses "most unstable" CAPE.
CAPE (J/kg)
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Interpretation
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1750
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Ordinary thunderstorm
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1850
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Marginal supercell thunderstorm
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1950
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Supercell thunderstorm, but no
tornado
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2150
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Supercell thunderstorm with weak
(EF0 to EF1) tornado
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2850
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Supercell thunderstorm with
strong (EF2 to EF5) tornado
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An older measure is called the
K Index.
It looks at temperature and dew-point (humidity) of the environment at
just a few key altitudes, and is useful for indicating rain intensity
in thunderstorms (see table below).
K Index (°C)
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Interpretion
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less than 20
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Thunderstorm unlikely
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20 to 30
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Chance of scattered thunderstorms
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30 to 40
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Many thunderstorms likely, some
with heavy rain
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greater than 40
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Many thunderstorms with very
heavy rain
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We don't need to know how to calcualte CAPE and K indices, because they
are automatically calculated from upper air soundings. However, the
tables above guide us in interpreting the results.
Temperature Soundings (Upper air Soundings)
To determine the stability, we need weather conditions (temperature,
wind, etc.) at many different heights. This is called a sounding.
While climbing or descending in your aircraft, if you record the
outside air temperature at a bunch of different altitudes, then you
have made a sounding. Modern commercial aircraft have automated systems
(AMDAR - click on this link to download a tutorial movie) on board to
make these measurements and
relay them by radio or satellite
to government weather centers.
Also, most countries have national weather services that launch
weather ballons called rawinsondes.
These small helium-filled latex balloons (first photo below) have a
small sensor package (second photo below) and radio transmitter hanging
from the bottom of the balloon.
— Environment Canada rawinsonde balloon launch at
UBC in 2011.
— Example of a sonde (i.e., the sensor
package). The dime is shown for scale.
As the balloon rises, the sensor package measures temperature,
humidity, and pressure. Also, modern sondes have GPS, so they can also
measure altitude, and can
infer the wind by recording the balloon location as it blows downwind.
Eventually at high altitude, the balloon bursts and the sensor package
gently falls by small parachute to earth. These are expendible and are
launched twice each day (00 UTC and 12 UTC) from "upper air" sites
around the
world (see next figure).
— Radiosonde (upper air) launch sites around the
world. (Courtesy of NOAA).
There is no routine sounding site in Greater Vancouver. The closest
one is Quillayute, WA (station identifier = UIL), southwest of UBC on
the Olympic
peninsula of Washington State. Next is Port Hardy, BC (station
identifier = YZT), northwest
of UBC near the northern tip of Vancouver Island. To the east
of UBC is Kelowna, BC (station identifier = WLW).
You can retrieve current soundings from a very nice Upper
Air site at the University of Wyoming. For example, below is a
sounding I retrieved for Port Hardy, where PRES = pressure, HGT =
height or altitude, TEMP = temperature, DWPT = dew-point temperature (a
measure of humidity), RELH = relative humidity, MIXR = mixing ratio
(another measure of humidity), DRCT = wind direction, SKNT = wind
speed. You can also get the spreadsheet of that data here.
Here are videos of balloon launches:
As part of the ATSC 303 Meteorological Methods (Weather Instruments)
course in 2011, we launched
one from the Thunderbird Stadium parking lot at
UBC.
Key words: atmospheric stability, laminar,
turbulence, static stability, air parcels, adiabatic lapse rate,
sounding, rawinsondes, stable, neutral, unstable, CAPE, K index
Xtra info for Experts
The stability index "S" is actually the vertical gradient of potential temperature, defined by
Where S is the static stability, T is temperature, z is altitude.
This equation was used to produce the static-stability tool shown earlier in this web page.
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Image credits. All the photos were taken by Roland
Stull, and the drawings were made by Roland Stull, and all are
copyright by him and
used with his permission.