Science and Literature Susan Matthews RE 5140 April 27, 2010.
ATMOS 5140 Lecture 7 –Chapter 6 - University of...
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ATMOS 5140 Lecture 7 – Chapter 6 • Thermal Emission • Blackbody Radiation • Planck’s Function • Wien’s Displacement Law • Stefan-Bolzmann Law • Emissivity • Greybody Approximation • Kirchhoff’s Law • Brightness Temperature
Transcript of 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.
