Atmospheric--saturated adibatic lapse rate

8/7/2019 Atmospheric--saturated adibatic lapse rate

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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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(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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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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stratus


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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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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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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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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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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.

Atmospheric--saturated adibatic lapse rate

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