Atmospheric Stability

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Atmospheric Stability

• Stability of Dry Air

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Atmospheric Stability

• Atmospheric stability refers to the tendency for
  air parcels to move vertically.

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Atmospheric Stability (Cont.)

• Basic concept when the temperature of the air
  parcel is greater than the temperature of the
  surrounding environment, then it will rise, and
  when the temperature of the air parcel is less
  than the surrounding environment, then it will
  sink.

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Environmental Lapse Rate

• The Environmental Lapse Rate (ELR) is the rate at
  which the measured temperature of the air in the
  environment outside the air parcel decreases with
  height.
• We send up balloons with instrument packages
  called radiosondes to measure the temperature at
  different levels above the Earths surface.

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Environmental Lapse Rate (Cont.)
top
zT 200 m
TT 18C
TB 20C
zB 100 m
bottom
ELR (TB TT) / (zT zB) ELR (20C - 18C) /
(200 m 100 m) ELR 2C / 100 m
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Dry Adiabatic Lapse Rate (DALR)

• Meteorologists normally assume that unsaturated
  air parcels (i.e. air outside clouds) change
  temperature in an adiabatic process as they rise
  or sink.
• The Dry Adiabatic Lapse Rate (DALR) is the rate
  at which an unsaturated air parcel cools as it
  rises.

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DALR (Cont.)

• Why does air cool when it rises?

When air rises is encounters lower pressure
p 990 mb
p 1000 mb
Momentarily, as the air parcel rises it has a
higher pressure than the surrounding molecules.
p 1000 mb
p 1000 mb
This mean that there is more force exerted by the
molecules inside the parcel than is being exerted
by the molecules outside the parcel and the
parcel expands.
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DALR (Cont.)
This means there is more force exerted from
inside the parcel than there is from the outside
and the parcel expands.
p 990 mb
p 990 mb
p 1000 mb
more force
less force
less force
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DALR (Cont.)
In order for the parcel to expand it has to push
away (displace) the surrounding molecules. Thus,
the molecules inside the parcel must some of
their internal energy in order to do this work.
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DALR (Cont.)

• Since the temperature is a function of the
  internal energy, when the internal energy
  decreases, then the temperature decreases.
• Thus, the rising parcel expands and cools.
• This process is called adiabatic cooling.

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Where did the internal energy go?

• When the internal energy was used to displace the
  surrounding molecules so that the air parcel
  could expand, that energy had to go somewhere.
  Where did it go?

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Where did the internal energy go? (Cont.)

• When the molecules inside the parcel collided
  with the molecules outside as the parcel
  expanded, the molecules transferred some of their
  internal energy to the molecules outside the
  parcel.
• In effect the parcel compressed the rest of the
  atmosphere very slightly.

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Where did the internal energy go? (Cont.)

• However, since there is so much mass in the rest
  of the atmosphere, we dont notice the very small
  increase in temperature that occurs outside the
  parcel and the process is labeled as an adiabatic
  process even though it really involves a transfer
  of energy.

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DALR (Cont.)

• We can compute the DALR if we use the form of the
  First Law of Thermodynamics we introduced before.
• dq cpdT adp

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DALR (Cont.)

• In a dry adiabatic process dq 0.
• In this case our equation simplifies to
• 0 cpdT adp
• Subtract cpdT from both sides to get

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DALR (Cont.)

• - cpdT - adp
• Divide both sides by cpdz to get
• - (dT/dz) - (a/cp)(dp/dz)
• Since a 1/?, we can write this as

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DALR (Cont.)

• - (dT/dz) - (1/cp)(1/?)(dp/dz)
• The hydrostatic approximation is
• - (1/?)(dp/dz) g
• so we can write our equation as
• -(dT/dz) g/cp Gd
• where Gd is the Dry Adiabatic Lapse Rate.

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DALR (Cont.)

• If g 9.8 m s-2, and cp 1005 J kg-1 K-1,
• then
• Gd (g/cp) (9.8 m s-2)/(1005 J kg-1 K-1)
• Gd 0.0098 K m-1 1 K / 100 m
• 1C / 100 m

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DALR (Cont.)

• This means that an unsaturated air parcel rising
  in a dry adiabatic process will cool 1C for each
  100 meters it rises.
• Conversely, an unsaturated parcel that is sinking
  in a dry adiabatic process will be compressed by
  the surrounding air, and it will warm 1C for
  each 100 meters it sinks.

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Stability

• Clouds form when rising air cools until it
  becomes saturated.
• The likelihood of the formation of clouds and the
  type of clouds that will form are determined by
  the stability of the air, which tells us the
  tendency for air to move vertically..

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Stability (Cont.)

• In order to determine the stability of the air we
  compare the Environmental Lapse R ate (ELR) to
  the Dry Adiabatic Lapse Rate (DALR).

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Case 1 ELR lt DALR
ELR 0.5C / 100 m
z 400 m T 13.0C
T 13.0C
z 300 m T 13.5C
T 14.0C
z 200 m T 14.0C
z 100 m T 14.5C
T 14C
z 0 m T 15.0C
T 15C
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Stable Case

• This situation is called the stable case because
  air does not tend to move vertically.
• Stable air parcels tend to return to their
  original levels.
• Unsaturated air is unstable whenever the
• ELR is less than the DALR.

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Stable Case (Cont.)

• There is little vertical mixing when air is
  stable and air quality tends to be worse when
  stable conditions exist.
• Air is stable most often at night when the
  cooling of the Earths surface decreases the ELR.

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Temperature Inversions

• A temperature inversion exists when the
  temperature of the environmental air increases
  with height, which is the opposite (i.e. the
  inverse) of the pattern we normally observe in
  the troposphere.
• A temperature inversion is an extremely stable
  situation.

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Temperature Inversion
ELR - 0.5C / 100 m
z 400 m T 17.0C
T 17.0C
z 300 m T 16.5C
T 18.0C
z 200 m T 16.0C
z 100 m T 15.5C
T 14C
z 0 m T 15.0C
T 15C
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Case 2 ELR DALR
ELR 1.0C / 100 m
z 400 m T 11.0C
T 11.0C
z 300 m T 12.0C
T 12.0C
z 200 m T 13.0C
z 100 m T 14.0C
T 14C
z 0 m T 15.0C
T 15C
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Neutral Case

• This situation is called the neutral case because
  will not move vertically on its own, but it can
  be moved vertically by external forces.
• Unsaturated air is neutral when the ELR is equal
  to the DALR.
• Some vertical mixing occurs when air is neutral.

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Neutral Case (Cont.)

• Air is typically neutral for periods in the
  morning and evening.

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Case 3 ELR gt DALR
ELR 1.5C / 100 m
z 400 m T 9.0C
T 11.0C
T 9.0C
z 300 m T 10.5C
T 10.0C
T 12.0C
z 200 m T 12.0C
T 11.0C
T 13.0C
z 100 m T 13.5C
T 12.0C
T 14C
z 0 m T 15.0C
T 15C
T 13.0C
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Unstable Case

• This situation is called the unstable case
  because when air is moved vertically, it tends to
  keep going in the same direction.
• Unsaturated air is unstable when the ELE is
  greater than the DALR.
• There is a lot of vertical mixing when the air is
  unstable because of all of the rising and sinking
  air parcels.

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Unstable Case (Cont.)

• Air is most often unstable in the afternoon when
  solar radiation is absorbed by the Earths
  surface and the ELR increases.
• Air quality is usually best when air is unstable
  due to all of the mixing that occurs then.

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Unsaturated sir is stable when the
ELR is to the right of the DALR.
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Unsaturated air is neutral when the ELR
is on the DALR.
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Unsaturated air is unstable when the ELR is to
the left of the DALR.
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Potential Temperature

• The potential temperature is the temperature that
  air would have if it were moved to a pressure of
  100,000 Pa (1000 mb) during a dry adiabatic
  process.

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Potential Temperature (Cont.)

• ? T (100,000 Pa / p).286
• where
• ? is the potential temperature
• T is the temperature in Kelvins
• p is the pressure in Pascals

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Potential Temperature (Cont.)

• If the temperature is 288 K and the pressure is
  85,000 Pa, what is the potential temperature?
• ? 288 K (100,000 Pa / 85,000 Pa).286
• ? 301.7 K

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U.S. Standard Atmosphere

• The U.S. Standard Atmosphere represents the
  average conditions over the U.S. and it is used a
  a standard reference set of conditions for some
  meteorological calculations.

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U.S. Standard Atmosphere (Cont.)

• The U.S. Standard Atmosphere assumes
• an atmosphere of pure dry air with a
• constant composition
• (2) the atmosphere is an ideal gas
• (3) the gravitational acceleration is a constant
  (g 9.80665 m s-2)
• (4) the hydrostatic approximation is valid

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U.S. Standard Atmosphere Assumptions (Cont.)

• (5) the pressure at sea level is 101325 Pa
• (1013.25 mb) and the temperature at sea
• level is 288.65 K (15.5C)
• (6) from 0 to 11,000 meters above sea level
• the ELR is 0.0065 K m-1 (0.65C/100 m)
• (7) additional assumptions about higher
• layers in the atmosphere.

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