why is stability important? and cloud...

AT 350 Introduction to Weather and Climate Atmospheric Stability and Vertical Motion

Scott Denning CSU Atmospheric Science Spring 2008 1

StabilityStabilityand Cloud Developmentand Cloud Development

Please read Chapter 6 in Ahrens

Why is stability important?Why is stability important?

• Vertical motions in the atmosphere are acritical part of energy transport andstrongly influence the hydrologic cycle

• Without vertical motion, there would be noprecipitation, no mixing of pollutants awayfrom ground level - weather as we know itwould simply not exist.

• There are two types of vertical motion:– forced motion such as forcing air up over a hill, over colder

air, or from horizontal convergence– buoyant motion in which the air rises because it is less

dense than its surroundings - stability is especiallyimportant here

Stability & InstabilityStability & Instability

A rock, like a parcel of air, that is in stable equilibriumwill return to its original position when pushed.

If the rock instead accelerates in the direction of thepush, it was in unstable equilibrium.

Stability in the atmosphereStability in the atmosphere

Stable Unstable Neutral

If an air parcel is displaced from its original height it can:Return to its original height - StableAccelerate upward because it is buoyant - UnstableStay at the place to which it was displaced - Neutral

An InitialPerturbation



BuoyancyBuoyancy• An air parcel rises in the atmosphere when it’s density

is less than its surroundings• Let ρenv be the density of the environment. From the

Equation of State/Ideal Gas Lawρenv = P/RTenv

• Let ρparcel be the density of an air parcel. Thenρparcel = P/RTparcel

• Since both the parcel and the environment at the sameheight are at the same pressure– when Tparcel > Tenv ρparcel < ρenv (positive buoyancy)– when Tparcel < Tenv ρparcel > ρenv (negative buoyancy)

Vertical Motion and TemperatureVertical Motion and Temperature

Rising airRising airexpands, usingexpands, usingenergy to pushenergy to pushoutward againstoutward againstits environment,its environment,adiabaticallyadiabaticallycooling the aircooling the air

A parcel of airA parcel of airmay be forced tomay be forced torise or sink, andrise or sink, andchangechangetemperaturetemperaturerelative torelative toenvironmental airenvironmental air

““Lapse rateLapse rate””

• The lapse rate is the change oftemperature with height in theatmosphere

• There are two kinds of lapse rates:– Environmental Lapse Rate

• What you would measure with a weather balloon– Parcel Lapse Rate

• The change of temperature that an air parcelwould experience when it is displaced vertically

• This is assumed to be an adiabatic process(no heat exchange occurs across parcel boundary)

Trading Height for HeatTrading Height for Heat

There are two kinds of “static” energy inthe parcel: potential energy (due to itsheight) and enthalpy (due to the motionsof the molecules that make it up)

pS c T g z! = ! + !

Change instatic energy

Change inenthalpy

Change ingravitationalpotential energy



Trading Height for Heat (contTrading Height for Heat (cont’’d)d)• Suppose a parcel exchanges no energy

with its surroundings … we call thisstate adiabatic, meaning, “not gainingor losing energy”

0 pc T g z= ! + !

pc T g z! = " !

21

1 1

(9.81 )9.8

(1004 )p

T g msK km

z c J K kg

!

!

! !

"= ! = ! = !

"

“Dry adiabatic lapse rate”

Stability and theStability and thedry adiabatic lapse ratedry adiabatic lapse rate

• Atmospheric stabilitydepends on theenvironmental lapse rate– A rising unsaturated air

parcel cools according tothe dry adiabatic lapserate

– If this air parcel is• warmer than surrounding

air it is less dense andbuoyancy accelerates theparcel upward

• colder than surroundingair it is more dense andbuoyancy forces opposethe rising motion

A saturated rising air parcel coolsA saturated rising air parcel coolsless than an unsaturated parcelless than an unsaturated parcel

• If a rising air parcel becomes saturatedcondensation occurs

• Condensation warms the air parcel due tothe release of latent heat

• So, a rising parcel cools less if it issaturated

• Define a moist adiabatic lapse rate– ~ 6 C/1000 m– Not constant (varies from ~ 3-9 C)– depends on T and P

Stability and theStability and themoist adiabatic lapse ratemoist adiabatic lapse rate

• Atmospheric stabilitydepends on theenvironmental lapse rate– A rising saturated air parcel

cools according to the moistadiabatic lapse rate

– When the environmental lapserate is smaller than the moistadiabatic lapse rate, theatmosphere is termedabsolutely stable

• Recall that the dry adiabaticlapse rate is larger than themoist

– What types of clouds do youexpect to form if saturatedair is forced to rise in anabsolutely stableatmosphere?

dry



What conditions contribute to aWhat conditions contribute to astable atmosphere?stable atmosphere?

• Radiative coolingof surface atnight

• Advection of coldair near thesurface

• Air moving over acold surface(e.g., snow)

• Adiabatic warmingdue tocompression fromsubsidence(sinking)

Absolute instabilityAbsolute instability

• The atmosphere is absolutely unstable if theenvironmental lapse rate exceeds the moistand dry adiabatic lapse rates

• This situation is not long-lived– Usually results from surface heating and is

confined to a shallow layer near the surface– Vertical mixing can eliminate it

• Mixing results in a dry adiabatic lapse rate inthe mixed layer, unless condensation (cloudformation) occurs (in which case it is moistadiabatic)

Absolute instability (examples)Absolute instability (examples) Conditionally unstable airConditionally unstable air• What if the

environmental lapserate falls between themoist and dryadiabatic lapse rates?– The atmosphere is

unstable for saturatedair parcels but stablefor unsaturated airparcels

– This situation istermed conditionallyunstable

• This is the typicalsituation in theatmosphere



What conditions enhanceWhat conditions enhanceatmospheric instability?atmospheric instability?

• Cooling of air aloft– Cold advection aloft– Radiative cooling of

air/clouds aloft• Warming of surface air

– Solar heating of ground– Warm advection near

surface– Air moving over a warm

surface (e.g., a warm body ofwater)

• Contributes to lake effectsnow

• Lifting of an air layer andassociated vertical“stretching”– Especially if bottom of layer

is moist and top is dry

Cloud developmentCloud development

• Clouds form as airrises, expandsand cools

• Most clouds formby– Surface heating

and freeconvection

– Lifting of air overtopography

– Widespread airlifting due tosurfaceconvergence

– Lifting alongweather fronts

Fair weather cumulusFair weather cumuluscloud developmentcloud development

• Air rises due tosurface heating

• RH rises as risingparcel cools

• Cloud forms at RH ~ 100%

• Rising is stronglysuppressed at base ofsubsidence inversionproduced from sinkingmotion associated withhigh pressure system

• Sinking air is foundbetween cloudelements– Why?

Fair weather cumulus cloudFair weather cumulus clouddevelopment schematicdevelopment schematic



What conditions support tallerWhat conditions support tallercumulus development ?cumulus development ?

• A less stable atmospheric (steeper lapse rate)profile permits greater vertical motion

• Lots of low-level moisture permits latentheating to warm parcel, accelerating it upward

Determining ConvectiveDetermining ConvectiveCloud BasesCloud Bases

• Dry air parcels cool at the dry adiabatic rate(about 10oC/km)

• Dew point decreases at a rate of ~ 2oC/km• This means that the dew point approaches the air

parcel temperature at a rate of about 8oC/km• If the dew point depression were 4oC at the surface,

a cloud base would appear at a height of 500 meters– Cloud base occurs when dew point = temp (100% RH)

• Each one degree difference between the surfacetemperature and the dew point will produce anincrease in the elevation of cloud base of 125 meters

Drier air produces higher cloud bases; moist air produces lower cloud bases

d

d

Dry adiabats

Determining convective cloud topDetermining convective cloud top

• Cloud top is defined by the upper limit to air parcelrise

• The area between the dry/moist adiabatic lapserate, showing an air parcel’s temperature duringascent, and the environmental lapse rate, can bedivided into two parts– A positive acceleration part where the parcel is

warmer than the environment– A negative acceleration part where the parcel is

colder than the environment• The approximate cloud top height will be that

altitude where the negative acceleration area isequal to the positive acceleration area



Orographic cloudsOrographic clouds

• Forced liftingalong a topographicbarrier causes airparcel expansionand cooling

• Clouds andprecipitation oftendevelop on upwindside of obstacle

• Air dries furtherduring descent ondownwind side

Lenticular Lenticular cloudsclouds• Stable air flowing over a

mountain range oftenforms a series of waves– Think of water waves

formed downstream of asubmerged boulder

• Air cools during risingportion of wave and warmsduring descent

• Clouds form near peaks ofwaves

• A large swirling eddyforms beneath the leewave cloud– Observed in formation of

rotor cloud– Very dangerous for

aircraft

Cumulus Clouds & Clear SkyCumulus Clouds & Clear Sky



Cumulus to CumulonimbusCumulus to CumulonimbusChanging cloudChanging cloud

formsforms

• Differential heating/coolingof top and bottom of acontinuous cloud layer cancause it to break up intosmaller cloud elements– Cloud top absorbs solar

radiation but cools morequickly by radiative cooling

– Bottom of cloud warms bynet absorption of IRradiation from below

– The result is that the layerwithin the cloud becomesless stable and convectionmay ensue

why is stability important? and cloud...

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