The Saturated Adiabatic Lapse Rate

1
The Saturated Adiabatic Lapse Rate

• Temperature Changes and Stability Inside Clouds

2
Temperature Changes Inside Clouds

• Two processes occur simultaneously inside clouds
  that affect the temperature.
• Rising air expands, does work and cools
• Condensation releases latent energy which is then
  stored as internal energy and warms the air
  inside the cloud.

3
Temperature Changes Inside Clouds (Cont.)

• Normally, the cooling due to the work of
  expansion is greater than the warming associated
  with the release of latent energy and its
  conversion to internal energy.

4
Temperature Changes Inside Clouds (Cont.)

• Thus, as air rises inside a cloud it still gets
  colder, but it does so at a slower rate than the
  Dry Adiabatic Lapse rate.
• The rate at which rising air inside a cloud cools
  is called the Saturated Adiabatic Lapse Rate
  (SALR).

5
The Saturated Adiabatic Lapse Rate (SALR)

• The derivation of the equation for the SALR
  begins with a form of the First Law of
  Thermodynamics
• dq cpdT - adp

6
The SALR (Cont.)

• In this case the energy gained, dq, is equal to
  the latent energy released when water vapor
  condenses inside the cloud.
• dq -Lvdqv
• where
• Lv is the latent heat of vaporization, and
• dqv is the change of specific humidity of the
  air parcel when water vapor condenses

7
The SALR (Cont.)

• Substitute for dq in the First Law of
  thermodynamics to get
• -Lvdqv cpdT adp
• Add cpdT Lvdqv to both sides to get

8
The SALR (Cont.)

• -cpdT -adp Lvdqv
• Divide by cpdz to get
• -cpdT -adp Lvdqv
• cpdz cpdz cpdz
• Since a 1/? we can write this as

9
The SALR (Cont.)

• -dT - 1 dp Lvdqv
• dz cp? dz cpdz
• From the hydrostatic approximation
• -1 dp g
• ? dz

10
The SALR (Cont.)

• Substitution results in
• -dT g LvdqV Gs
• dz cp cp dz

warming due to latent energy released during
condensation
cooling due to work of expansion

SALR
11
The SALR (Cont.)

• The SALR is always less than the DALR because the
  cooling caused by adiabatic expansion is
  partially offest by the release of latent energy
  during condensation.

12
The SALR (Cont.)

• The SALR is a variable.
• The magnitude of the SALR is determined by the
  amount of water vapor that condenses.

13
The SALR (Cont.)

• When warm moist air rises in a cloud, more water
  vapor condenses and the SALR is smaller.
• When cooler, drier air rises inside a cloud, less
  water vapor condenses and the SALR is larger.

14
SALR 0.5C/ 100 m
more water vapor condenses
less water vapor condenses
SALR 0.9C/100m
warmer moister air
cooler drier air
15
Saturated air rises inside the cloud and the
release of latent energy during condensation
causes it to cool at the SALR
Lifting Condensation Level (LCL)
Unsaturated air rises and cools at the DALR
16
Stability Cases for Clouds

• (1) When the ELR is greater than the SALR, then
  the air inside the cloud is unstable. Unstable
  air moves vertically and we tend to get tall,
  vertical clouds like cumulus and cumulonimbus.

17
Stability Cases for Clouds (Cont.)
cumumlo-nimbus
cumulus
18
Stability Cases for Clouds (Cont.)

• (2) When the ELR is equal to the SALR, then the
  air inside the cloud is neutral.
• (3) When the ELR is less than the SALR, then the
  air inside the cloud is stable.

19
Stability Cases for Clouds (Cont.)

• There is much less vertical motion when air is
  neutral or stable. Thus, when air inside the
  clouds is neutral or stable, the clouds tend to
  have a flat, layered appearance. These types of
  layered clouds are called stratus clouds.

20
Stability Cases for Clouds (Cont.)
stratus
21
Stability Cases for Clouds (Cont.)

• There is a special stability case that occurs
  when the Environmental Lapse Rate is between the
  Dry Adiabatic Lapse Rate and the Saturated
  Adiabatic Lapse Rate.

22
Stability Cases for Clouds (Cont.)

• For example, what if
• DALR 1.00C/100 m
• ELR 0.75C/100 m
• SALR 0.50C/100 m
• If the air is unsaturated ELR lt DALR and the air
  is stable, but if the air is saturated, then ELR
  gt SALR and the air is unstable.

23
Stability Cases for Clouds (Cont.)

• This special case is called conditionally
  unstable, because the air must be lifted until it
  becomes saturated in order for it to become
  unstable

24
DALR 1C/100 m ELR 0.75C/100 m SALR
0.5C/100 m
T 14C, Td 14C
Tenv 13C
2000 m
Air is unstable
1600 m
T 16C, Td 16C
Tenv 16C
Air is neutral
Tenv 22C
T 20C, Td 20C
LCL 800 m
Air is stable
0000 m T 28C, Td 20C
Tenv 28C
25
Stability Cases in Clouds (Cont.)

• When the atmosphere is conditionally unstable it
  can lead to the rapid development of
  thunderstorms when a cold front or other weather
  feature lifts warm moist air in the spring.

26
Stability Cases in Clouds (Cont.)

• The air is stable as long as it isnt lifted high
  enough, but if it is lifted until the parcel is
  warmer than the environment, then the air
  instantaneously becomes unstable and starts
  rising on its own.
• Then thunderstorms can form rapidly.

27
The Effect of Topography on Precipitation Patterns

• Precipitation patterns in mountainous regions
  tend to be closely related to the prevailing wind
  direction.
• Much higher precipitation amounts fall on the
  side of the mountains where the air is rising and
  it is much drier on the side where the air is
  sinking.

28
The Effect of Topography on Precipitation
Patterns (Cont.)

• The process where air is forced to rise up the
  side of a mountain is sometimes called orographic
  lifting.

29
Leeward side
Windward side
wind direction
T 6C, Td 6C
3000 m
Air sinks and warms at the DALR 1C/100 m
Air rises and cools at SALR 0.5C/ 100 m
Air is warm and dry
T 16C, Td 16C LCL
1000 m
T 31C, Td 6C
500 m
T 26C, Td 16C
Air rises and cools at DALR
0 meters
30
The Effect of Topography on Precipitation
Patterns (Cont.)

• Rising motion causes clouds and precipitation on
  the windward side of the mountain range.
• Sinking motion causes warm, dry conditions on the
  leeward side of the mountain.
• The dry area on the leeward side of the mountain
  is called the rain shadow.

31
The Effect of Topography on Precipitation
Patterns (Cont.)

• Since the prevailing wind direction in the middle
  latitudes is from the west, the western sides of
  the mountains along the west coast of the U.S.
  are the rainy sides and the rain shadows occur
  along the eastern slopes of the mountains.