Doppler on Wheels

DoppleronWheels

• https://www.youtube.com/watch?v=LbFSVG2Xc1o• http://www.pbs.org/wgbh/nova/earth/hunt-for-the-supertwister.html

AtmosphericAerosols

• Size(Volume/Mass,SurfaceArea)• Source

• Primary• Secondary

• ChemicalComposition- PrincipalAerosolSpecies• Concentration• Lifetime

Example8.1Forthedistribution,howmanyparticlesintherangeofdiameter0.1– 0.11umexist?

Example8.1Forthedistribution,howmanyparticlesintherangeofdiameter0.1– 0.11umexist?

13,000um-1 cm-3

Overthatrange.

Multiplebythesizeofthebin(0.01um)

=130particles/cm3

https://youtu.be/H3-I4oLukNk

Köhler Curve

Köhler Curve

A =4𝑀%𝜎%𝑅(𝑇𝜌%

B =6𝑛.𝑀%𝜋𝜌%

ln𝑒. 𝐷4𝑒.∘

=𝐴𝐷4

−𝐵𝐷4:

KelvinEffectCurvatureTerm

Raoult EffectSoluteTerm

Increasesmuchfasterwithdecreasingdropletsize!

Köhler Curve– CriticalDiameter

𝐷4; =:<=

>?⁄

Allcurvespassthroughamaximumandthisisoccursatcriticaldiameter

Koehler curve for two drops: Ns=1x10-17 moles (blue solid line), Ns=5x10-17 moles (red dashed line).

Credit: W. Brune

Note that the supersaturation is less than 0.2% for the smaller particle and less than 0.1% for the larger particle. As cooling occurs, which one will activate first?

Koehler curve for two drops: Ns=1x10-17 moles (blue solid line), Ns=5x10-17 moles (red dashed line).

Credit: W. Brune

Note that the supersaturation is less than 0.2% for the smaller particle and less than 0.1% for the larger particle. As cooling occurs, which one will activate first?

ANSWER: The larger particle, because it has a lower critical supersaturation.

Imagine scenarios with a distribution of cloud condensation nuclei of different sizes and different amounts of solute.

Drops with more solute have lower values for the critical supersaturation and therefore are likely to nucleate first because in an updraft, the lower supersaturation is achieved before the greater supersaturation.

Imagine scenarios with a distribution of cloud condensation nuclei of different sizes and different amounts of solute.

Larger CCN take up the water first and may take up so much water that the ambient supersaturation drops below the critical supersaturation for the smaller CCN. As a result, the larger CCN nucleate cloud drops while the smaller CCN turn into haze.

Time1Time2

Realistic

CloudDropletGrowthCoversReadingMaterialinChapter13.2,13.3

AtmosphericSciences5200PhysicalMeteorologyIII:CloudPhysics

CloudDropletGrowth

• Growthbyvapordeposition/condensation• GrowthbyCollision-Coalescence

Growthbyvapordeposition/condensation

Wherex>r


𝑑𝑀𝑑𝑡 = 4π𝑥E𝐷

𝑑𝜌(𝑑𝑥

Diffusioncoefficientofwatervapor

watervapordensityatadistancex

𝑑𝑀𝑑𝑡 F

𝑑𝑥𝑟E = 4π𝐷F 𝑑𝜌(

HI(K)

HI(M)

NOK

NOM


𝑑𝑀𝑑𝑡 = 4π𝑥E𝐷

𝑑𝜌(𝑑𝑥

Diffusioncoefficientofwatervapor

watervapordensityatadistancex

𝑑𝑀𝑑𝑡 F

𝑑𝑥𝑟E = 4π𝐷F 𝑑𝜌(

HI(K)

HI(M)

NOK

NOM

𝑑𝑀𝑑𝑡 = 4π𝐷𝑟 𝜌( ∞ −𝜌((𝑟)

𝑑𝑟𝑑𝑡 =

𝐷𝑟𝜌Q

𝜌( ∞ −𝜌((𝑟)

Substitutein𝑀 =

43 𝜋𝑟

:𝜌Q

Growthbyvapordeposition/condensation𝑑𝑟𝑑𝑡 =

𝐷𝑟𝜌Q

𝜌( ∞ −𝜌((𝑟)

𝑑𝑟𝑑𝑡 =

𝐷𝜌( ∞𝑟𝜌Q𝑒 ∞

𝑒 ∞ − 𝑒(𝑟)

Substituteintheidealgasequationforwatervaporandcompletesomealgebraicmanipulations

𝑒 ∞ − 𝑒(𝑟)𝑒 ∞ = S

Where

𝑑𝑟𝑑𝑡 =

𝐷𝜌( ∞𝑟𝜌Q

𝑆



𝑆

ThegrowthrateisproportionaltoS.

Physically,thisstatementmeansthat thegreaterthedifferencebetweenthesupersaturationintheenvironmentandsupersaturationattheparticle’ssurface,thefasterwatervaporwilldiffuseandstickonthesurface.

Forinstance,ifsenv equaledsk,thentheevaporationandcondensationofwaterontheparticle’ssurfacewouldbeequalandtherewouldbenomassgrowth.

TakeHomeMessage#1

𝑑𝑟𝑑𝑡 =

1𝑟 𝐺Q𝑆

Where

𝐺Q =𝐷𝜌( ∞𝜌Q

Coefficientthatisafunctionoftemperatureandpressure



𝑆

Gl incorporatestheeffectsofthemasstransportofwatervapormoleculestothesurfaceandthetransportofheatgeneratedoncondensationawayfromtheparticlesurface.

TakeHomeMessage#2

𝑑𝑟𝑑𝑡 =

1𝑟 𝐺Q𝑆

Where



VaporDeposition •As water vapor diffuses to the drop and forms water, energy is released (i.e., latent heat of condensation) and this raises the temperature of the cloud drop surface so that Tsfc > Tenv.

•But an outward energy flow occurs and is proportional to Tsfc -Tenv.

•Physically, this statement means that the particle and the air molecules around it are warmed by latent heat release. These warmer molecules lose some of this energy by colliding with the cooler molecules further away from the particle, and warm them by increasing their kinetic energy

Schematic of the two physical processes in the growth of a cloud drop by vapor deposition. One is vapor deposition and

the other is the transfer of condensational heating to the atmosphere;

Credit: W. Brune (after Lamb and Verlinde)



𝑆

Dropradiusgrowsasthesquarerootofaconstanttimestime.

TakeHomeMessage#3

𝑑𝑟𝑑𝑡 =

1𝑟 𝐺Q𝑆

Where



𝑟 = (𝐶𝑡𝑖𝑚𝑒)Z E[


Growth of a cloud drop by vapor deposition as a function of time. Dashed lines indicate drop size after the typical cloud lifetime.

Credit: W. Brune

Physicalexplanation:• Thenucleatedclouddropradiusincreasesfairlyrapidlyatthebeginning,butwithinminutesslowsdownbecauseofthesquarerootdependenceontime.

• So,clouddropscangrowto10-20μm in15orsominutes,butthengrowbiggermuchmoreslowly.

• Sinceatypicalcloudonlylasts10sofminutes,itisnotpossibleforclouddropstogrowintoraindropsbyvapordepositionalone.

• CCNnucleationfollowedbyvapordepositioncanmakeclouds,butitcan’tmakethemrain.

Conclusion:• Weneedotherprocessestogetclouddropsbigenoughtoformprecipitation,eitherliquidorsolid.


Rate of Drop Growth

• Rain drops form in around 30 minutes.

• Condensation41,000s = 11.4 hours

• Something else must be happening.

CloudDropletGrowth• GrowthbyCollision–Coalescence

• FocusingonWarmCloudprocesses(fornow)• Mostprecipitationcomesfromthisprocess

https://youtu.be/DS6k3MkNfV0

CollisionsCollisionsoccurinbothcoldandwarmcloudsandcaninvolveeitherliquiddropsorsolidparticlesorboth.• Collision-Coalescence: Largeliquiddropscavengessmallerliquiddropsasitfalls.

• Riming: Fallingicecollectsliquidwater,whichfreezesonitssurface.• CaptureNucleation: Largeliquiddropcapturessmalliceparticle,whichactsasanicenucleiandcausesthelargedroptofreeze.Theparticlethatiscollectedcanbeeitheranicenuclei(IN)orapieceofice,whichalsoisagoodicenuclei.Ineithercase,thesupercooled liquiddropfreezesoncontactwiththeIN.

• Aggregation: Fallingsnowflakescavengesothersnowflakesthataggregatetomakealargersnowflakebundle.

CollisionsCollisionsoccurinbothcoldandwarmcloudsandcaninvolveeitherliquiddropsorsolidparticlesorboth.• Collision-Coalescence: Largeliquiddropscavengessmallerliquiddropsasitfalls.

• Riming: Fallingicecollectsliquidwater,whichfreezesonitssurface.• CaptureNucleation: Largeliquiddropcapturessmalliceparticle,whichactsasanicenucleiandcausesthelargedroptofreeze.Theparticlethatiscollectedcanbeeitheranicenuclei(IN)orapieceofice,whichalsoisagoodicenuclei.Ineithercase,thesupercooled liquiddropfreezesoncontactwiththeIN.

• Aggregation: Fallingsnowflakescavengesothersnowflakesthataggregatetomakealargersnowflakebundle.

WARMCLOUDPROCESS!!

COLDCLOUD

PROCESS!!

Air flow around a falling particle. The shaded area is the cross

sectional area of the particle. Note the movement of air around the

particle. Only the air in innermost streamline collides with the

particle; the rest goes around it.Credit: W. Brune (after Lamb and

Verlinde)

terminal velocity of a 10 µm cloud drop is about 1 mm s-1, while the terminal velocity for a 100 µm drop is about 1 m s-1.

Thegrowthofaclouddropintoaprecipitationdropbycollision-coalescenceisgivenbytheequation:

\]^\_

=AreasweptoutxefficiencyofcollectionxvelocitydifferencexLWC𝑑𝑚Q𝑑𝑡 = 𝐴` a 𝐸; a (𝑣Q − 𝑣.) a 𝐿𝑊𝐶

𝑑𝑚Q𝑑𝑡 = 𝜋(𝑟Q+𝑟.)E a 𝐸; a (𝑣Q − 𝑣.) a 𝐿𝑊𝐶

• mL isthemassofthelargedropthatisfalling,• Ag isthegeometriccross-sectionalareaforwhichcollisionsbetweenthefallinglargedropandthemanydropsbelowispossible,

• Ec isthecollision-coalescenceefficiency(i.e.,acollectionefficiency),whichisthefractionoftheactualcrosssectionalareathatissweptoutcomparedtothecrosssectionalareathatisgeometricallypossible(smallerdropscanfollowairstreamlinesandgoaroundthebigdrop)(seethefigurebelow),

• vL isthevelocityofthelargedropandvs isthevelocityofthesmaller,slowerfallingdropsbelow,

• andLWCistheliquidwatercontent.

Schematic of the maximum possible

geometric cross-section of a large and

small drop and the actual cross-section

due to particles following air

streamlines around the big particle.

Credit: W. Brune (after Lamb and Verlinde)

Collision-collectionefficienciesfortwodrops,withthepercentcollisionefficiencyonthey-axis,theratiooftheradiusofthesmalldrop,rs,totheradiusofthelargedrop,rL,withlinesforindividuallargedropradii.Credit:W.Brune (afterRogersandYau)

Documents

Doppler on Wheels