atmospheric--saturated adibatic lapse rate
TRANSCRIPT
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The Saturated Adiabatic
Lapse RateTemperature Changes and
Stability Inside Clouds
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Temperature Changes InsideClouds
Two processes occur simultaneously insideclouds that affect the temperature.
(1) Rising air expands, does work andcools;
(2) Condensation releases latent energywhich is then stored as internalenergy and warms the air inside thecloud.
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Temperature Changes InsideClouds (Cont.)
Normally, the cooling due to the work ofexpansion is greater than the warmingassociated with the release of latentenergy and its conversion to internalenergy.
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Temperature Changes InsideClouds (Cont.)
Thus, as air rises inside a cloud it still getscolder , but it does so at a slower rate thanthe Dry Adiabatic Lapse rate.
The rate at which rising air inside a cloudcools is called the Saturated AdiabaticLapse Rate (SALR) .
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The Saturated Adiabatic LapseRate (SALR)
The derivation of the equation for the SALRbegins with a form of the First Law ofThermodynamics
dq = c pdT - dp
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The SALR (Cont.)
In this case the energy gained, dq , is equalto the latent energy released when watervapor condenses inside the cloud.
dq = -L vdq vwhere
Lv is the latent heat of vaporization, anddq v is the change of specific humidity of the
air parcel when water vapor condenses
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The SALR (Cont.)
Substitute for dq in the First Law ofthermodynamics to get
-Lvdq v = c pdT dp
Add c pdT + L vdq v to both sides to get
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The SALR (Cont.)
-c pdT = - dp + L vdq v
Divide by cpdz to get
-c pdT = - dp + L vdq vc
pdz c
pdz c
pdz
Since = 1/ we can write this as
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The SALR (Cont.)
-dT = - 1 dp + L vdq vdz c p dz c pdz
From the hydrostatic approximation
-1 dp = g dz
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The SALR (Cont.)
Substitution results in
-dT = g + L vdq V =
sdz c p c p dz
SALR =
coolingdue towork ofexpansion +
warming due tolatent energyreleased duringcondensation
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The SALR (Cont.)
The SALR is always less than the DALRbecause the cooling caused byadiabatic expansion is partially offest by the release of latent energy during condensation .
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The SALR (Cont.)
The SALR is a variable.
The magnitude of the SALR isdetermined by the amount of water vapor that condenses .
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The SALR (Cont.)
When warm moist air rises in a cloud, morewater vapor condenses and the SALR issmaller .
When cooler, drier air rises inside a cloud,less water vapor condenses and theSALR is larger .
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cooler drier air warmer moister air
SALR =0.9 C/100mless watervaporcondenses
more watervaporcondenses
SALR = 0.5 C/ 100 m
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Unsaturated air rises andcools at the DALR
LiftingCondensationLevel (LCL)
Saturated air risesinside the cloud andthe release of latentenergy during
condensation causesit to cool at the SALR
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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 tendto get tall, vertical clouds like cumulusand cumulonimbus .
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Stability Cases for Clouds (Cont.)
cumulus
cumumlo-
nimbus
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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 .
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Stability Cases for Clouds (Cont.)
There is much less vertical motion when airis neutral or stable. Thus, when air insidethe clouds is neutral or stable, the cloudstend to have a flat, layered appearance .These types of layered clouds are calledstratus clouds .
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Stability Cases for Clouds (Cont.)
stratus
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Stability Cases for Clouds (Cont.)
There is a special stability case that occurswhen the Environmental Lapse Rate isbetween the Dry Adiabatic Lapse Rateand the Saturated Adiabatic Lapse Rate.
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Stability Cases for Clouds (Cont.)
For example, what ifDALR = 1.00 C/100 m
ELR = 0.75 C/100 mSALR = 0.50 C/100 m
If the air is unsaturated ELR < DALR andthe air is stable, but if the air is saturated,then ELR > SALR and the air is unstable.
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Stability Cases for Clouds (Cont.)
This special case is called conditionallyunstable , because the air must be lifteduntil it becomes saturated in order for it tobecome unstable
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0000 m T = 28 C, Td = 20 C Tenv = 28 C
LCL = 800 m T = 20C , Td = 20 C Tenv = 22 C
Air is stable
1600 m T = 16 C, Td = 16 C Tenv = 16 CAir is neutral
2000 m T = 14 C, Td = 14 C Tenv = 13 C
Air is unstable
DALR = 1 C/100 m
ELR = 0.75 C/100 m
SALR = 0.5 C/100 m
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Stability Cases in Clouds (Cont.)
When the atmosphere is conditionallyunstable it can lead to the rapiddevelopment of thunderstorms when acold front or other weather feature liftswarm moist air in the spring.
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Stability Cases in Clouds (Cont.)
The air is stable as long as it isnt lifted highenough, but if it is lifted until the parcel iswarmer than the environment, then the airinstantaneously becomes unstable andstarts rising on its own.
Then thunderstorms can form rapidly.
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The Effect of Topography onPrecipitation Patterns
Precipitation patterns in mountainousregions tend to be closely related to theprevailing wind direction.
Much higher precipitation amounts fall onthe side of the mountains where the air isrising and it is much drier on the sidewhere the air is sinking.
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The Effect of Topography onPrecipitation Patterns (Cont.)
The process where air is forced to rise upthe side of a mountain is sometimes calledorographic lifting .
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0 meters
T = 26 C, Td = 16 CAir rises and
cools atDALR
T = 16 C, Td
= 16 C LCL 1000 m
Air rises and cools atSALR = 0.5 C/ 100 m
3000 mT = 6 C, Td = 6 C
Air sinks and warms at
the DALR = 1 C/100 m
500 mT = 31 C, Td = 6 C
Air is warm and dry
Windward side Leeward side
wind direction
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The Effect of Topography onPrecipitation Patterns (Cont.)
Rising motion causes clouds andprecipitation on the windward side of themountain range.
Sinking motion causes warm, dry conditionson the leeward side of the mountain.
The dry area on the leeward side of themountain is called the rain shadow .
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The Effect of Topography onPrecipitation Patterns (Cont.)
Since the prevailing wind direction in themiddle latitudes is from the west, thewestern sides of the mountains along thewest coast of the U.S. are the rainy sidesand the rain shadows occur along theeastern slopes of the mountains.