Download Lecture 09: Atmospheric Stability

Atmospheric Stability
C. David Whiteman
Atmos 3200/Geog 3280
Mountain Weather and Climate
Geisler Group, Dolomite Mtns © CD Whiteman
1/20/05 at 0900 SLC © cd whiteman
Indicators of stability
Table 4.6. Observations that indicate stability.
Stable
Clouds in layers with little vertical
development (stratiform clouds, Section
7.1.1), mountain and lee wave clouds
On the local scale, smoke from elevated
stacks remains elevated and disperses
mostly horizontally.
On the regional scale, smoke from
multiple sources forms stacked layers of
pollution in the atmosphere
Poor visibility due to smoke, haze or fog
Steady winds, usually light
Drizzle or light rain
Unstable
Clouds grow vertically (cumuliform
clouds, Section 7.1.1)
On the local scale, smoke plumes disperse
well vertically and horizontally.
On the regional scale, pollution from
multiple sources mixes together in a layer
near the ground. The layer is shallow in
the morning and deepens during the day.
Good visibility
Gusty winds
Showery precipitation, thunderstorms
z
z
dT/dz = -5°C/km
-dT/dz = 5°C/km = ELR =
dT/dz = 5°C/km
γ
-dT/dz = -5°C/km
ETS
T
T
z
z
dT/dz = 0°C/km
-dT/dz = 0°C/km
dT/dz = -9.8°C/km
-dT/dz = 9.8°C/km = DALR =
Γd
Thermodynamic process
T
T
For a dry parcel:
when the ETS slopes to the left of the DALR, the atmosphere is
unstable
when it slopes to the right of the DALR, the atmosphere is
stable
when it has the same slope as the DALR, the atmosphere is
neutral
For a cloudy parcel:
when the ETS slopes to the left of the MALR, the atmosphere is
unstable
when it slopes to the right of the MALR, the atmosphere is
stable
when it has the same slope as the MALR, the atmosphere is
neutral
Thermodynamics
•
Concept: Take a parcel of air from an environmental
sounding, don’t allow it to mix or exchange heat with the
surrounding air, and lift it to a higher level in the
atmosphere:
•
the parcel expands as it is lifted into the lower pressures
encountered at higher levels
•
•
The expansion causes the air in the parcel to cool
•
The cooling rate associated with this process is called
the dry adiabatic lapse rate, the DALR.
The cooling rate due to the expansion is 9.8°C per km
of lift, so long as no condensation occurs during the
parcel’s ascent - i.e., so long as the parcel remains dry.
Adiabatic descent
•
How does the process change when the
parcel descends adiabatically?
•
How does the process differ between
saturated and unsaturated parcels?
Plume form as a function of stability
Whiteman (2000)
Stability cartoon
Ahrens (1999)
Stability
Stability

Environmental temperature sounding (ETS)
Stability

Environmental temperature sounding (ETS)

Environmental lapse rate (ELR) - actual temp lapse rate of an atmospheric
layer in the ETS
Stability

Environmental temperature sounding (ETS)

Environmental lapse rate (ELR) - actual temp lapse rate of an atmospheric
layer in the ETS

to determine stability we take a parcel from the ETS and lift it an
infinitesimal distance. If the parcel is unsaturated it will cool at the DALR
when lifted; if the parcel is saturated it will cool at the MALR.
Stability

Environmental temperature sounding (ETS)

Environmental lapse rate (ELR) - actual temp lapse rate of an atmospheric
layer in the ETS

to determine stability we take a parcel from the ETS and lift it an
infinitesimal distance. If the parcel is unsaturated it will cool at the DALR
when lifted; if the parcel is saturated it will cool at the MALR.

After lifting, we compare the temperature of the parcel to the
temperature of the surrounding air in the ETS at that same height. If the
parcel is warmer than the sounding it will accelerate upward and the layer
is considered unstable. If the parcel is cooler than the sounding, it will
accelerate back downward to its original level and the layer is considered
stable. If it has the same temperature as the sounding it will neither
accelerate upward nor downward and the layer is considered neutral.
Stability diagrams
Stability - the degree of
resistance of a layer to
vertical motion
Whiteman (2000)
Thermodynamics - moist adiabatic ascent
•
If a parcel reaches saturation when it is lifted under these same
conditions:
•
The rate of cooling during ascent will be reduced by the release of
latent heat into the parcel as the water vapor in the parcel
condenses to form cloud droplets or precipitation
•
Thus, adiabatic ascent of saturated air cools the air at a slower rate
than that associated with unsaturated air.
•
The rate of cooling with height associated with this process, the
moist adiabatic lapse rate, MALR, is not constant and depends on
the pressure and temperature of the parcel (which govern the
parcel’s moisture content).
•
If the saturated parcel has a high vapor content the MALR will be
much smaller than the DALR. If the saturated parcel has a low
vapor content (example, very cold air) the MALR will approach the
DALR.
Moist adiabatic lapse rate
Table 4.6. The moist adiabatic lapse rate at different pressures
and temperatures in °C/km and °F/1000 ft.
Pressure
(mb)
1000
800
600
400
200
Temperature (°C)
-40
9.5
9.4
9.3
9.1
8.6
-20
8.6
8.3
7.9
7.3
6.0
0
6.4
6.0
5.4
4.6
3.4
Temperature (°F)
20
4.3
3.9
3.5
3.0
2.5
40
3.0
2.8
2.6
2.4
2.0
-40
5.2
5.2
5.1
5.0
4.7
-20
4.7
4.6
4.4
4.0
3.3
0
3.5
3.3
3.0
2.5
1.9
DALR = 9.8°C/km = 5.4°F/1000 ft.
20
2.4
2.2
1.9
1.6
1.4
40
1.6
1.5
1.4
1.3
1.1
Stability
It should become apparent, after a few applications of the parcel method for determining
stability, that the stability of the layer can be determined simply by comparing
the ELR to the DALR (for unsaturated layers) or the MALR (for saturated layers).
For example, for an unsaturated layer:
For a saturated layer, the appropriate comparison is between the ELR and the MALR
Stability
It should become apparent, after a few applications of the parcel method for determining
stability, that the stability of the layer can be determined simply by comparing
the ELR to the DALR (for unsaturated layers) or the MALR (for saturated layers).
For example, for an unsaturated layer:
1.
ELR > DALR i.e. air temp decreases rapidly with height → an
unstable atmosphere (favors vertical mixing)
For a saturated layer, the appropriate comparison is between the ELR and the MALR
Stability
It should become apparent, after a few applications of the parcel method for determining
stability, that the stability of the layer can be determined simply by comparing
the ELR to the DALR (for unsaturated layers) or the MALR (for saturated layers).
For example, for an unsaturated layer:
1.
ELR > DALR i.e. air temp decreases rapidly with height → an
unstable atmosphere (favors vertical mixing)
2. ELR < DALR i.e. air temp decreases slowly with height or may
increase with height (i.e. an inversion) → the atmosphere is
stable (strongly resists vertical mixing)
For a saturated layer, the appropriate comparison is between the ELR and the MALR
Stability
It should become apparent, after a few applications of the parcel method for determining
stability, that the stability of the layer can be determined simply by comparing
the ELR to the DALR (for unsaturated layers) or the MALR (for saturated layers).
For example, for an unsaturated layer:
1.
ELR > DALR i.e. air temp decreases rapidly with height → an
unstable atmosphere (favors vertical mixing)
2. ELR < DALR i.e. air temp decreases slowly with height or may
increase with height (i.e. an inversion) → the atmosphere is
stable (strongly resists vertical mixing)
3. ELR = DALR i.e. air temp decreases at the rate of about 9.8oC/km
→ the atmosphere is neutral (no relative tendency for the air
parcel to rise or sink)
For a saturated layer, the appropriate comparison is between the ELR and the MALR
For you to think about
•
There are situations (see E in the previous
figure) in which the layer is stable if
unsaturated but unstable if saturated. This
situation is called conditional instability, since
the stability depends on the moisture
condition of the layer.
Superadiabatic and sub-adiabatic layers
•
A layer in the atmosphere having a lapse rate
greater than the DALR is called a
superadiabatic layer. Such layers are usually
ground-based (but they can sometimes be
seen as elevated layers)
•
We could also call any layer with a lapse rate
less than the DALR a sub-adiabatic layer.
Preference for conservative quantities
♦ The temperature of an unsaturated parcel changes as it
ascends or descends in the atmosphere. Wouldn’t it be nice if
we had some other temperature-like variable that was
conservative (i.e., didn’t change as the parcel ascended or
descended)?
♦ We could come up with such a variable! It’s easy. Measure the
parcel’s temperature at its current height z and then calculate
the temperature that the parcel would have if at sea level.
♦ TSL = T(z) + Γd z
♦ No matter what height the unsaturated parcel has in the
atmosphere (assume no mixing) it will always have this same
temperature when brought to sea level! We could call this
temperature, say, ‘potential temperature’.
Potential temperature
•
The above method is actually used. But, why did we choose sea level? We
could have chosen any height zA in the atmosphere for this definition. The
equation would then change to TPOT = T(z) + Γd (z - zA).
•
We often deal with pressure coordinates in atmospheric work. The usual
definition of potential temperature assumes that the parcel starts at a
certain T and p, rather than a certain T and z.
•
•
•
Then, potential temperature = θ = T (1000/p).286
•
So long as the parcel doesn’t mix with its environment or exchange heat
with its surroundings, the parcel will maintain this potential temperature no
matter where it is carried in the atmosphere. θ, like r (the mixing ratio) is a
conservative quantity. The values of θ and r can be used as air motion tracers.
•
We can plot soundings of θ vs z, just as we can plot T vs z.
For this equation to work, T must be in Kelvins.
Potential temperature θ is the temperature that a parcel would have if
brought adiabatically to the 1000 mb level.
Temperature and pot temperature profiles
Stull (2000)
Stull (2000)
Compare T and θ soundings
FA = free atmosphere; EZ = entrainment zone; ML = mixed layer, SL = superadiabatic layer;
CI = capping inversion; RL = residual layer; SBL = stable boundary layer