Atmospheric Stability

Sebastian Hoch / C. David WhitemanAtmos 3200/Geog 3280

Mountain Weather and Climate

1/20/05 at 0900 MST, SLC © CD Whiteman 8/6/06 at 1300 MST near SLC © SW Hoch

Stable Unstable

Stability

Ahrens (1999)

Atmospheric Stability - the degree of resistance of an air parcel to vertical motion.

Stability

ETS Environmental Temperature Sounding

lapse rate = rate of decrease of temperature with height! dT/dz: (temperature change with height)

ELR Environmental Lapse Rate γ (small “gamma”)

dT/dz = 0 C/km

-dT/dz = 0 C/km

T( C)

z (m)

1000

500

dT/dz = -9.8 C/km

-dT/dz = 9.8 C/km = DALR = dΓ

Thermodynamic process

T( C)

z (m)

1500

2515 20

2500 Grandeur Pk

T( C)

z (m)

dT/dz = -5 C/km

-dT/dz = 5 C/km = ELR = γ

2000

1000

155 10

0

dT/dz = 5 C/km

-dT/dz = -5 C/km = ELR = γ

T( C)

z (m)

1000

2000

155 10

0

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:

Ø The parcel expands as it is lifted into the lower pressures encountered at higher levels.

Ø The expansion causes the air in the parcel to cool.

Ø The cooling rate due to the expansion is 9.8°C per kmof lift, so long as no condensation occurs during the parcel’s ascent - i.e., so long as the parcel remains dry.

Ø The cooling rate associated with this process is called the dry adiabatic lapse rate, the DALR.

Thermodynamics / Adiabatic processes

How does the process change when the parcel descends adiabatically?

How does the process differ between saturated and unsaturated parcels?

Adiabatic descent

If a parcel reaches saturation when it is lifted under these same conditions (no mixing or heat exchange with surrounding air):

Ø 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.

Ø Thus, adiabatic ascent of saturated air cools the air at a slowerrate than that associated with unsaturated air.

Ø 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).

Ø 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.

Thermodynamics - moist adiabatic ascent

The moist adiabatic lapse rate MALR in [°C/km] at different pressures and temperatures

Compare with dry adiabatic lapse rate, DALR = 9.8°C/km = 5.4°F/1000 ft.

Moist adiabatic lapse rate (MALR)

Pressure [mbar]

Temperature [ºC]

-40º -20º 0º 20º 40º1000 9.5 8.6 6.4 4.3 3.0800 9.4 8.3 6.0 3.9 2.8600 9.3 7.9 5.4 3.5 2.6400 9.1 7.3 4.6 3.0 2.4

200 8.6 6.0 3.4 2.5 1.0

5

How do we determine Atmospheric Stability from an Environmental temperature sounding (ETS)?Ø Environmental lapse rate (ELR) - actual temperature lapse rate of an

atmospheric layer in the ETS

Ø 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 DALRwhen lifted; if the parcel is saturated it will cool at the MALR.

Ø After lifting, we compare the temperature of the parcel to the temperature of the surrounding air in the ETS at that same height.

1) If the parcel is warmer than the sounding it will accelerate upward and the layer is considered unstable.

2) If the parcel is cooler than the sounding, it will accelerate back downward to its original level and the layer is considered stable.

3) If it has the same temperature as the sounding it will neither accelerate upward nor downward and the layer is considered neutral.

Stability - the degree of resistance of a layer to vertical motion

Stability diagrams

Whiteman (2000)

1. ELR > DALR i.e. air temperature decreases rapidly with height → an unstable atmosphere (favors vertical mixing)

2. ELR < DALR i.e. air temperature 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)

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

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 / moist 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

Indicators of stabilityStable Unstable

Cloud are in layers with little vertical development (stratiform clouds). Mountain wave and lee wave clouds.

Clouds grow vertically (cumuliform clouds).

On the local scale, smoke from elevated stacks remains elevated and only disperses horizontally.

On the local scale, smoke plumes disperse well vertically and horizontally.

On the regional scale, smoke form multiple sources forms stacked layers of pollution in the atmosphere.

On the regional scale, pollution from multiple sources mixes together. The layer is shallow in the morning and deepens during the day.

Poor visibility due to smoke, haze, fog. Good visibility.

Steady winds, usually light. Gusty winds.

Little precipitation, and if, drizzle or light rain.

Showery precipitation, thunderstorms.

Whiteman (2000)

Plume form as a function of stability

Whiteman (2000)

ELR stability regimes

Ø 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)

Ø We could also call any layer with a lapse rate less than the DALR a sub-adiabatic layer.

Superadiabatic and sub-adiabatic layers

Whiteman (2000)

h*

h*

h*

h* indicates the mixing height

Dry adiabatic lapse rate: 9.8 ℃/km

Typical diurnal temperature structure evolution

evening ➜ night

morning ➜ day

superadiabaticlayers

• 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! Let’s call this temperature potential temperature.

Preference for conservative quantities

• 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.• Potential temperature θ is the temperature that a parcel would have

if brought adiabatically to the 1000 mb level.• Then, potential temperature = θ = T (1000/p)0.286 (here T in [K])• 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.

Potential temperature

Stull (2000) Stull (2000)

Comparison of T and θ profiles

FA = free atmosphere EZ = entrainment zone ML = mixed layer SL = superadiabatic layer

Temperature and potential temperature profiles

CI = capping inversionRL = residual layerSBL = stable boundary layer

DALR: 9.8 ℃/km

DALR: 9.8 ℃/km