atmos 5140 lecture 7 –chapter 6 - university of...

ATMOS5140Lecture7– Chapter6

• ThermalEmission• BlackbodyRadiation

• Planck’sFunction• Wien’sDisplacementLaw• Stefan-Bolzmann Law

• Emissivity• Greybody Approximation• Kirchhoff’sLaw• BrightnessTemperature

BlackbodyRadiation

• TheoreticalMaximumAmountofRadiationthatcanbeemittedbyanobject

• Perfectemitter– perfectabsorber• Absorptivity=1

Planck’sLaw• Definesthemonochromaticintensityofradiationforablackbody

asafunctionoftemperature.• PhysicalDimensionsofintensity(powerperunitareaperunit

solidangle)perunitwavelength:Wm-2 um-1 sr-1

Where:h=Planck’sconstant=6.626*10-34 Jsk=Bolzmann’s constant=1.381*10-23 J/K

Wien’sDisplacementLaw• ThewavelengthatwhichyoufindmaximumemissionfromablackbodyoftemperatureT

Wherekw =2897umK

Wien’sDisplacementLaw• ThewavelengthatwhichyoufindmaximumemissionfromablackbodyoftemperatureT

Stefan-BoltzmannLaw• Givesthebroadbandfluxemittedbyblackbody• IntegratePlanck’sfunctionoverallwavelengths,andoverahemisphere(2πsteradians ofsolidangle)

=5.67*10-8 Wm-2K-4

Rayleigh-JeansApproximation

• Forwavelengthsof1mmorlonger• Usedcommonlyinmicrowaveband

Where:h=Planck’sconstant=6.626*10-34 JskB=Bolzmann’s constant=1.381*10-23 J/K

Emissivity• Blackbodyisanidealsituation(ε =1)• TypicalInfraredemissivities (%,relativetoblackbody)

–Water=92-96%– Concrete=71-88%– Polishedaluminum=1-5%

“Typicallyshiny,polishedmetalswillhaveaverylowemissivityvaluemakingithardtogetanaccurateinfraredtemperaturereading.Polishedsilver,goldandstainlesssteelareexamplesofsurfaceswithalowemissivity.“

MonochromaticEmissivity

Greybody Emissivity

Assumethereisnowavelengthdependence

Kirchhoff’sLaw

• Emissivity=Absorptivity• Important,itimplieswavelengthdependences• Alsodependsuponviewingdirections(θ, Φ)• Appliesunderconditionsoflocalthermodynamicequilibrium

ThermalImaging

0.1 0.15 0.2 0.3 0.5 1 1.5 2 3 5 10 15 20 30 50 100

λB

λ(T

) (n

orm

aliz

ed

)

Wavelength [µm]

6000 K 250 K300 K(b)

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1e+07

1e+08

0.1 0.15 0.2 0.3 0.5 1 1.5 2 3 5 10 15 20 30 50 100

Bλ(T

) [W

m-2

Sr-1

µm

-1]

Blackbody Emission Curves (Planck’s Function)

6000 K

300 K

250 K

(a)

Wien’s Law

NOTE:Normalized–Relative!Sunemissionismuchgreater.

WhenDoesThermalEmissionMatter?

GeneralRule:4μm isgoodthresholdforseparatingthermalfromsolar

Whyissunyellow?

http://www.iflscience.com/physics/why-sky-blue-and-sun-yellow-ls-currently-working/

BrightnessTemperature

Planck’sfunctiondescribesaone-to-onerelationshipbetweenintensityofradiationemittedbyablackbodyatagivenwavelengthandtheblackbody’stemperature.

BrightnesstemperatureisinverseofPlanck’sfunctionappliedtoobservedradiance.

Thus,whenanobjecthasaemissivity~1,thenthebrightnesstemperatureisveryclosetotheactualtemperature• ExtremelyusefulforremotesensinginThermalIR

BrightnessTemperature

𝑇" = 𝐵%&' 𝜀𝐵% 𝑇

Planck’sFunction–describesadirectrelationshipbetweentemperatureandemittedradiation

Ratioof:ActualemittedradiationEmissionofblackbody

BrightnessTemperature

𝑇" = 𝐵%&' 𝜀𝐵% 𝑇

Planck’sFunction–describesadirectrelationshipbetweentemperatureandemittedradiation

Ratioof:ActualemittedradiationEmissionofblackbody Sowhen

𝜀 =1TB =T

SpectralWindow

AtmosphericInfraredSounder(AIRS)onAQUA

GOES

IRImagingfromSpace

COLDTEMP

HighClouds

BrightnessTemperature

Closeto1,getthetemperatureoftopofcloud

Radiative Equilibrium

FortheMoon– simplesystem

Radiative Equilibrium

Solar Flux S0

Intercepted Flux Φ=S0πRE2

RE

Radiative Equilibrium

IncomingShortwaveRadiation

Outgoing Longwave Radiation

Top-of-theAtmosphereGlobalRadiationBalance

Earthismorecomplicated– yetcanconsiderbalanceatthetop(above)theatmosphere

SimpleRadiativeModeloftheAtmosphereSingleLayer,NonReflectingAtmosphere

Shortwave Longwave

1 3 5 7

2 4 6 8

asw alw Ta

TsA ε

Atmosphere

Surface

Credit: M. Mann modification of a figure from Kump, Kasting, Crane "Earth System"

Longwave/AtmosphericEmissivity

• Greenhouseeffect• Greenhousegasesaretransparentintheshortwave,butstronglyabsorblongwaveradiation

• Thusincreasingvalueof𝛼*+ willshifttheradiativeequilibriumoftheglobetowarmertemperatures.