met 4410 remote sensing: radar and satellite meteorology...
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MET4410RemoteSensing:RadarandSatelliteMeteorologyMET5412RemoteSensinginMeteorology
Lecture3:IntroductiontoAtmosphericRadiation(PettyCh1-
2,KidderandVonderHaar Ch3.1)
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Lec 3:Part1WhatisAtmosphericRadiation?
� Definition:◦ Thestudyofallradiationprocessaffectingtheearth’satmosphere.
� Thedisciplineexamines:◦ Theabsorption,emission,andscatteringofelectromagnetic(EM)radiationwithintheatmosphere;◦ Thenatureanddistributionofincidentsolarradiationatthetopoftheatmosphere;◦ Thereflectionandemissionfromthesurfaceatthebottomoftheatmosphere.
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WhatisAtmosphericRadiation?(Cont.)
� Twomainareas:◦ Theeffectofradiativeheatingorcoolingontemperature,therebyhelpingtodefinethebasicstructureoftheearth’sclimatesystem.(Thisisnotthefocusofthiscourse)◦ Useoftheinformationcontentinmeasuredradiationtodeducepropertiesoftheatmosphereorsurface-- Remotesensing!
� Energytransferintheatmosphereinvolvesradiationintwodistinctbandsofwavelength:shortwaveandlongwave radiation.
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Shortwave(Solar)Radiation�
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Longwave (Thermal)Radiation�
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PropertiesofRadiation� Electromagnetic(EM)wave:◦ Staticelectricfieldisdeterminedbythedistributionofelectriccharge◦ Staticmagneticfieldisdeterminedbythedistributionofelectriccurrent(movingelectriccharge)intheneighborhood.◦ Relatedlaw:achangingmagneticfieldinducesanelectricfieldthatcandriveacurrent;achangingelectricfieldinducesamagneticfield.◦ EMwave:achangingineitheranelectricormagneticfieldleadstoadisturbancethatisself-perpetuating,whichisanEMwave.◦ Theexampleofmovingamagnetonatableandstickittoarefrigerator(Pettypg.11).
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EMRadiation(Wave)� Definition:◦ EMwaveconsistsofalternatingelectricandmagneticfields.◦ Theelectricfieldisperpendiculartothemagneticfieldvector,andthedirectionofpropagationisperpendiculartoboth.
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CharacteristicsofEMwaves� EMwavesalwaystravelinavacuumatanabsolutelyconstantspeed:thespeedoflightc=3x10^8m/s
� EMwavesrequirenomaterialmediuminwhichtopropagate(pondripplesneedapondtopropagate,soundneedsairtopropagate).
� Interactingwithmatters(suchastheatmosphereanditsvariousresidentparticles)makesthepropagationofEMwavesmorecomplexandinteresting.
� EMwavespropagatein3Dspace.Theorientationoftheelectricfieldvectormaylieinanydirection,aslongasitisinaplanenormaltothedirectionofpropagation.
� EMwavesaretransversewaves(soundwavesarelongitudinal).� EMwavescantransportenergy.
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BasicQuantitiestodescribeEMwaves� Wavelength𝝺 :radiationisspecifiedbyitswavelength,whichisthedistancebetweencrestoftheelectricormagneticfield.Unit:nm(10^-9m);µm(10^-6m);cm(10^-2m)
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BasicQuantitiestodescribeEMwaves�
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IndexofRefraction� Indexofrefraction,n,ofasubstanceistheratioofthespeedoflightinavacuumtothespeedwithwhichEMradiationtravelsinthatsubstance.
� Atseaslevel,theindexofrefractionofairisabout1.0003
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Energy�
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Lec 3:Part2MeasuresofEnergy
� RadiantEnergy:Unit:Joule(J)� Power(rateofenergytransfer,somebookscallit“radiantflux”,buttovoidconfusionwiththe“fluxdensity”below,wewillcallitpower):istheradiantenergyperunittime.Unit:Watts(W)=J/s
� Fluxdensity(orfluxforshort):istheradiantpowerperunitarea.Unit:W/m2.Accordingtowhichwaytheenergyistraveling,fluxissubdividedinto:◦ Radiantexitance:isradiantfluxdensityemergingfromanarea◦ Irradiance:isradiantfluxdensityincidentanarea
� Intensity:isthemostimportantmeasureofradiationenergy.Itincludesthedirectioninformation.Itwillbedefinedafterweintroducesolidangle.
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SphericalPolarCoordinates� ZenithAngle𝜃:measurestheanglefromthelocalvertical.Therangeof𝜃 isonlyfrom0toπ (notfrom0to2 π)◦ 𝜃=0° directlyoverhead,vertical◦ 𝜃=90°,horizon◦ 90° < 𝜃<180°,directionbelowhorizon◦ 𝜃=180°,nadir
� AzimuthalAngle𝜑:measurestheanglecounterclockwisefromareferencepointonthehorizon.Therangeof𝜑 isonlyfrom0to2 π.
Petty Fig. 2.3:The relationship between Cartesian and spherical coordinates.
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SolidAngle� Definitionofsolidangle:Ifonedrawlinesfromthecenteroftheunitspheretoeverypointonthesurfaceofanobject,theareaoftheprojectionontheunitsphereisthesolidangle.Thesolidangleofanobjectthatcompletelysurroundsapointis4 πsteradians (sr).IftheprojectedareaAisonanyspherewithradiusr,thenthesolidangleis:𝜔 = 𝐴/𝑟*
� Solidangleisameasureofhowmuchyourvisualfieldofviewisoccupiedbyanobject.
� Theunitofsolidangleissteradian (sr).
� Thesolidanglesubtendedbyaninfiniteplaneis2 π sr.
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UnderstandingSolidAngle� Solidangleisto“regular”angleasareatolength.� Steradian issomethinglike“squareradian”or“squaredegree”.Solidangleis
like“2Dangulardimension”.� Mathematically,recallthedefinitionofregularangleinradian,whichis:
𝜃 = +, ,forawholecircle,𝑙 = 2𝜋𝑟,then
𝜃 = *0,, = 2𝜋
� Analogically,solidangle
𝜔 =𝐴𝑟*
WhereAisthecross-sectionalareaoftheobject,andristhedistancefromtheorigin(ortheobservationpoint).� Forawholesphere,A = 4𝜋𝑟2,then
𝜔 =4𝜋𝑟2
𝑟2 = 4𝜋16
DifferentialElementofSolidAngle� Ifyoupaintaninfinitesimalrectangleonthesurfaceofasphere,andithasangulardimensionsd 𝜃 (zenithangle)and𝑑𝜑(azimuthalangle),andispositionedat𝜃,thentheinfinitesimalincrementofsolidangleisasfollow:𝑑𝜔 = 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑
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Derivation� Theareaofinfinitesimalrectangleis:
𝑑𝐴 = (𝑟𝑑𝜃) : (𝑟𝑠𝑖𝑛𝜃𝑑𝜑)� Thentheinfinitesimalincrementofsolidangleis:
𝑑𝜔 =𝑑𝐴𝑟* = 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑
� Todemonstratethattheexpectedsolidangleoftheentiresphereis4𝜋𝑠𝑟:
< 𝑑𝜔=0
= < < 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑 = 2𝜋0
>< 𝑠𝑖𝑛𝜃𝑑𝜃 = −2𝜋< 𝑑𝑐𝑜𝑠𝜃
0
>= −2𝜋 𝑐𝑜𝑠𝜋 − 𝑐𝑜𝑠0 = 4𝜋
0
>
*0
>
� Tounderstandwhydoes𝑠𝑖𝑛𝜃 appearin𝑑𝜔 = 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑:◦ Thisisforthesamereasonthata1x1boxissmallerneartheNorthpolethanneartheequator.
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MeasuresofEnergy(cont.)� Intensity(orradiance):istheradiantfluxdensity(orfluxforshort)perunitsolidangletravelinginaparticulardirection.Herefluxismeasuredonasurfacenormaltotheradiationbeam.Unit:Wm-2sr-1.
� Visualizingthisdefinitionasfollows:◦ Lookinginaparticulardirection,identifyingaverysmallelementofthescenewithsolidangle𝛿𝜔.◦ Measure,normaltothebeam,theflux𝛿Fofradiationarrivingjustfromthatsmallregion,whichexcludingallothercontributions.◦ Theintensityinthatparticulardirectionisthengivenby:
𝐼 =𝛿𝐹𝛿𝜔
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ConservationofRadiance(Intensity)� Intensity(orradiance):isindependentofdistancefromanobjectaslongastheviewangleandtheamountofinterveningmatterarenotchanged◦ Considerasatelliteviewingasmallobject.Theirradiance(fluxdensityorflux)reachingthesatellitefromtheobjectwilldecreaseinverselyasthesquareofthedistanceofthesatellite.◦ However,thesolidangleoftheobjectsubtendedatthesatellitewillalsodecreasesinverselyasthesquareofthedistanceofthesatellite.◦ Sincetheradianceoftheobjectasviewedbythesatelliteissimplytheirradiance(flux)dividedbythesolidangle:𝐼 = F
G,sotheradianceisindependentofdistance.
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Broadbandvs.MonochromaticRadiation� EMradiationcomposedentirelyofasinglefrequencyistermedmonochromatic (“onecolor”),alsocalledcoherent.
� Radiationthatconsistsofamixtureofawiderangeoffrequencyiscalledbroadband radiation,alsocalledincoherent.
� Naturalradiationisbroadbandandincoherent.� Radiationfromartificialsourcesusedinremotesensingismonochromaticandcoherent.
� Thefluxandintensityofnatural(incoherent)radiationexpressedsimplyinWm-2andWm-2sr-1mustbeabroadbandquantity.
� Monochromatic(spectral)flux𝐹H:shouldbepowerperunitareaperunitwavelength:Wm-2µm-1.Broadbandfluxbetweenarangeofwavelength[𝜆K, 𝜆*] is:
𝐹(𝜆K, 𝜆*) = ∫ 𝐹HHOHP
𝑑𝜆
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Monochromatic(Spectral)Radiance/Intensity
� MonochromaticIntensity𝐼H:istheenergyperunittimeperunitwavelengthpersolidanglecrossingaunitareaperpendicular tothebeam(orsimplytheradianceorintensityperwavelength).Unit:Wm-2sr-1µm-1.Becausebroadbandradianceorintensityissimplytheintegraloverallwavelengthsofmonochromaticradianceorintensity,wemusthave:
𝐼 = < 𝐼HQ
>𝑑𝜆
� Themostfundamentalradiationunitforsatellitemeteorologyismonochromaticradiance.Thebasicsatelliteinstrument,radiometer,measuresaquantitythatismostcloselyrelatedtomonochromaticradiance.
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RelationshipbetweenFluxandIntensity
� Thefluxincidenton,passingthrough,oremergingfromanarbitrarysurfaceisgivenbyanintegralovertherelevantrangeofsolidangleoftheintensity(orradiance).
� Tocalculatethefluxemergingupwardfromahorizontalsurface:◦ Itmustbeanintegraloftheintensityoverallpossibledirectionsdirectedskyward,i.e.,into2π Sr ofsolidanglecorrespondingtotheupperhemisphere.◦ Sinceintensityisdefinedintermsoffluxperunitsolidanglenormaltothebeam,wemustweightthecontributionstothefluxbythecosineoftheincidentanglerelativetothenormalvector.
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RelationshipbetweenFluxandIntensity� Therefore,theupward-directedflux:
𝐹↑ = < 𝐼↑(𝜃, 𝜑)𝑐𝑜𝑠𝜃𝑑𝜔*0
>
𝐹↑ = < < 𝐼↑(𝜃, 𝜑)0/*
>𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜃
*0
>𝑑𝜃𝑑𝜑
� Forthedownwardflux,weintegrateoverthelowerhemisphere:
𝐹↓
= −< < 𝐼↓(𝜃, 𝜑)0
0/*𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜃
*0
>𝑑𝜃𝑑𝜑
� Forisotropicradiation(i.e.,iftheradiance/intensityisindependentofdirection):
𝐹↓ = 𝐹↑ = 𝜋𝐼 24
Polarization� TheorientationoftheoscillatingelectricfieldvectorinaEMwavecanbeanydirectionthatisperpendiculartothedirectionofpropagation.
� Polarization:istokeeptrackofthatorientationandhowitevolvesoverthecourseofacompletecycle.
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Polarization� Incoherentradiation,thereisaunique,repeatingpatterntotheoscillatingelectricfieldvector whenviewedalongthedirectionofpropagation.
� LinearPolarization:Itvibratesbackandforthinafixedplane,likeapendulumorpluckedguitarstring:(a)–(c). (a)isverticalpolarization,(b)ishorizontalpolarization.
� CircularPolarization:Itvibratesinaspiralfashionaboutthedirectionofpropagation,eitherclockwiseorcounterclockwise:(f)
� EllipticalPolarization:isahybridofthefirsttwo(d)-(e)
(a) (b) (c)
(d) (e) (f )
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Polarization� Standardweatherradarequipmenttypicallytransmitscoherentradiation
withlinearpolarization(eitherverticalorhorizontal)andthenmeasuresthebackscatteredradiationwiththesamepolarization.
� Moresophisticatedradars(i.e.,Dual-PolarizationRadar)maytransmitinonepolarizationbutthenseparatelymeasurethereturnedradiationinbothverticalandhorizontalpolarizationsinordertogainadditionalinformationaboutthetargets
� Asageneralrule,naturalemissionsofradiationintheatmospherearecompletelyunpolarized,buttheradiationmaybecomepartiallyorcompletelypolarizedinthecourseofitsinteractionswithparticlesand/orthesurface.
� Inparticular,asmoothsurface,likecalmwater,preferentiallyreflectsradiationhavinghorizontallinearpolarization.Thisisthephenomenonthatmotivatedtheinventionofpolarizedsunglasses,whichblockthereflectedhorizontallypolarizedradiationwhiletransmittingtherest.Itisalsoaphenomenonofgreatpracticalimportanceforsatelliteremotesensinginthemicrowaveband.
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