MET4410RemoteSensing:RadarandSatelliteMeteorologyMET5412RemoteSensinginMeteorology

Lecture3:IntroductiontoAtmosphericRadiation(PettyCh1-

2,KidderandVonderHaar Ch3.1)

1

Lec 3:Part1WhatisAtmosphericRadiation?

� Definition:◦ Thestudyofallradiationprocessaffectingtheearth’satmosphere.

� Thedisciplineexamines:◦ Theabsorption,emission,andscatteringofelectromagnetic(EM)radiationwithintheatmosphere;◦ Thenatureanddistributionofincidentsolarradiationatthetopoftheatmosphere;◦ Thereflectionandemissionfromthesurfaceatthebottomoftheatmosphere.

2

WhatisAtmosphericRadiation?(Cont.)

� Twomainareas:◦ Theeffectofradiativeheatingorcoolingontemperature,therebyhelpingtodefinethebasicstructureoftheearth’sclimatesystem.(Thisisnotthefocusofthiscourse)◦ Useoftheinformationcontentinmeasuredradiationtodeducepropertiesoftheatmosphereorsurface-- Remotesensing!

� Energytransferintheatmosphereinvolvesradiationintwodistinctbandsofwavelength:shortwaveandlongwave radiation.

3

Shortwave(Solar)Radiation�

4

Longwave (Thermal)Radiation�

5

PropertiesofRadiation� Electromagnetic(EM)wave:◦ Staticelectricfieldisdeterminedbythedistributionofelectriccharge◦ Staticmagneticfieldisdeterminedbythedistributionofelectriccurrent(movingelectriccharge)intheneighborhood.◦ Relatedlaw:achangingmagneticfieldinducesanelectricfieldthatcandriveacurrent;achangingelectricfieldinducesamagneticfield.◦ EMwave:achangingineitheranelectricormagneticfieldleadstoadisturbancethatisself-perpetuating,whichisanEMwave.◦ Theexampleofmovingamagnetonatableandstickittoarefrigerator(Pettypg.11).

6

EMRadiation(Wave)� Definition:◦ EMwaveconsistsofalternatingelectricandmagneticfields.◦ Theelectricfieldisperpendiculartothemagneticfieldvector,andthedirectionofpropagationisperpendiculartoboth.

7

CharacteristicsofEMwaves� EMwavesalwaystravelinavacuumatanabsolutelyconstantspeed:thespeedoflightc=3x10^8m/s

� EMwavesrequirenomaterialmediuminwhichtopropagate(pondripplesneedapondtopropagate,soundneedsairtopropagate).

� Interactingwithmatters(suchastheatmosphereanditsvariousresidentparticles)makesthepropagationofEMwavesmorecomplexandinteresting.

� EMwavespropagatein3Dspace.Theorientationoftheelectricfieldvectormaylieinanydirection,aslongasitisinaplanenormaltothedirectionofpropagation.

� EMwavesaretransversewaves(soundwavesarelongitudinal).� EMwavescantransportenergy.

8

BasicQuantitiestodescribeEMwaves� Wavelength𝝺 :radiationisspecifiedbyitswavelength,whichisthedistancebetweencrestoftheelectricormagneticfield.Unit:nm(10^-9m);µm(10^-6m);cm(10^-2m)

9

BasicQuantitiestodescribeEMwaves�

10

IndexofRefraction� Indexofrefraction,n,ofasubstanceistheratioofthespeedoflightinavacuumtothespeedwithwhichEMradiationtravelsinthatsubstance.

� Atseaslevel,theindexofrefractionofairisabout1.0003

11

Energy�

12

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.

13

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.

14

SolidAngle� Definitionofsolidangle:Ifonedrawlinesfromthecenteroftheunitspheretoeverypointonthesurfaceofanobject,theareaoftheprojectionontheunitsphereisthesolidangle.Thesolidangleofanobjectthatcompletelysurroundsapointis4 πsteradians (sr).IftheprojectedareaAisonanyspherewithradiusr,thenthesolidangleis:𝜔 = 𝐴/𝑟*

� Solidangleisameasureofhowmuchyourvisualfieldofviewisoccupiedbyanobject.

� Theunitofsolidangleissteradian (sr).

� Thesolidanglesubtendedbyaninfiniteplaneis2 π sr.

15

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

17

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.

18

MeasuresofEnergy(cont.)� Intensity(orradiance):istheradiantfluxdensity(orfluxforshort)perunitsolidangletravelinginaparticulardirection.Herefluxismeasuredonasurfacenormaltotheradiationbeam.Unit:Wm-2sr-1.

� Visualizingthisdefinitionasfollows:◦ Lookinginaparticulardirection,identifyingaverysmallelementofthescenewithsolidangle𝛿𝜔.◦ Measure,normaltothebeam,theflux𝛿Fofradiationarrivingjustfromthatsmallregion,whichexcludingallothercontributions.◦ Theintensityinthatparticulardirectionisthengivenby:

𝐼 =𝛿𝐹𝛿𝜔

19

ConservationofRadiance(Intensity)� Intensity(orradiance):isindependentofdistancefromanobjectaslongastheviewangleandtheamountofinterveningmatterarenotchanged◦ Considerasatelliteviewingasmallobject.Theirradiance(fluxdensityorflux)reachingthesatellitefromtheobjectwilldecreaseinverselyasthesquareofthedistanceofthesatellite.◦ However,thesolidangleoftheobjectsubtendedatthesatellitewillalsodecreasesinverselyasthesquareofthedistanceofthesatellite.◦ Sincetheradianceoftheobjectasviewedbythesatelliteissimplytheirradiance(flux)dividedbythesolidangle:𝐼 = F

G,sotheradianceisindependentofdistance.

20

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

21

Monochromatic(Spectral)Radiance/Intensity

� MonochromaticIntensity𝐼H:istheenergyperunittimeperunitwavelengthpersolidanglecrossingaunitareaperpendicular tothebeam(orsimplytheradianceorintensityperwavelength).Unit:Wm-2sr-1µm-1.Becausebroadbandradianceorintensityissimplytheintegraloverallwavelengthsofmonochromaticradianceorintensity,wemusthave:

𝐼 = < 𝐼HQ

>𝑑𝜆

� Themostfundamentalradiationunitforsatellitemeteorologyismonochromaticradiance.Thebasicsatelliteinstrument,radiometer,measuresaquantitythatismostcloselyrelatedtomonochromaticradiance.

22

RelationshipbetweenFluxandIntensity

� Thefluxincidenton,passingthrough,oremergingfromanarbitrarysurfaceisgivenbyanintegralovertherelevantrangeofsolidangleoftheintensity(orradiance).

� Tocalculatethefluxemergingupwardfromahorizontalsurface:◦ Itmustbeanintegraloftheintensityoverallpossibledirectionsdirectedskyward,i.e.,into2π Sr ofsolidanglecorrespondingtotheupperhemisphere.◦ Sinceintensityisdefinedintermsoffluxperunitsolidanglenormaltothebeam,wemustweightthecontributionstothefluxbythecosineoftheincidentanglerelativetothenormalvector.

23

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.

25

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 )

26

Polarization� Standardweatherradarequipmenttypicallytransmitscoherentradiation

withlinearpolarization(eitherverticalorhorizontal)andthenmeasuresthebackscatteredradiationwiththesamepolarization.

� Moresophisticatedradars(i.e.,Dual-PolarizationRadar)maytransmitinonepolarizationbutthenseparatelymeasurethereturnedradiationinbothverticalandhorizontalpolarizationsinordertogainadditionalinformationaboutthetargets

� Asageneralrule,naturalemissionsofradiationintheatmospherearecompletelyunpolarized,buttheradiationmaybecomepartiallyorcompletelypolarizedinthecourseofitsinteractionswithparticlesand/orthesurface.

� Inparticular,asmoothsurface,likecalmwater,preferentiallyreflectsradiationhavinghorizontallinearpolarization.Thisisthephenomenonthatmotivatedtheinventionofpolarizedsunglasses,whichblockthereflectedhorizontallypolarizedradiationwhiletransmittingtherest.Itisalsoaphenomenonofgreatpracticalimportanceforsatelliteremotesensinginthemicrowaveband.

27