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GEOG4110/5100AdvancedRemoteSensing
Lecture3
ReviewofRadiometricDistortionRadiometricErrorCorrectionTemperatureRetrievalGeometricDistortion
Relevantreading:Richards,sections2.1– 2.8;2.10-2.15
SignaltoNoiseRatio(SNR)
• Whatisit?• Whydowecare?
DynamicRange
• Whatisit?• Whydowecare?
PossibleCombinationswith:1bit: 0or1 =2or212bits: 0,0,0,11,01,1 =4or223bits: 0,0,00,0,10,1,0,0,1,1 =8or23
1,0,01,0,11,1,01,1,1
Nbits: =2N
GainandOffset(Bias)
GroundSceneBrightness(Input)
ImageBrightness(O
utpu
t)
IdealSensorResponse
ActualSensorResponse
Bias,Offset,DarkCurrent
Gainistheslopeofthesensorresponseline
Ll =(DNxgain)+bias
ContributionstoInstrumentSignal
DistortionDistortion:achange,twist,orexaggerationthatmakessomethingappeardifferentfromthewayitreallyis.
• WhatisRadiometricDistortion?• WhatisGeometricDistortion?
DistortionDistortion:achange,twist,orexaggerationthatmakessomethingappeardifferentfromthewayitreallyis.
• RadiometricDistortion:Errorsinpixelbrightnessvalues– Instrumentation– Wavelengthdependenceofsolarradiation– Effectofatmosphere
• GeometricDistortion:Errorsinimagegeometry,(location,dimensions,etc.)– Platformandinstrumentrelativemotions– Scananglesandscanpatterns– RotationoftheEarth– Attitudeandaltitudevariability
• Irradiance:Theamountofenergyincidentonagivenareaofasurfaceinagivenamountoftime(W/m2).
• Radiance:Theamountofenergyscatteredinaparticulardirection(W/m2/sr).
• Solidangle:Theratiooftheareaofasphericalsurfacetothesquareoftheradius.
Ω=A/r2
Ω
BasicRadiometricTerms
A
r
• SpectralIrradiance:Theamountofenergyavailableacrosswavelengthrange(W/m2/µm).
• Hemisphericalreflectance:Theratiooftheradiantfluxfromasurfacetotheradiantfluxincidenttoit.
• Hemisphericaltransmittance:Theratiooftheradiantfluxtransmittedthroughasurfacetotheradiantfluxincidenttoit.
• Hemisphericalabsorptance:Theratiooftheradiantfluxabsorbedbyasurfacetotheradiantfluxincidenttoit.
BasicRadiometricTerms
AbsenceofanAtmosphereInAbsenceofanatmospheresurfaceirradiancebetweenwavelengthsis
Where:Eλ =solarspectralirradianceattheearth.θ =solarzenithangle.
Formostremotesensingdevicesthewavelengthsaresmallenoughthat:
Wm-2
Wm-2
AbsenceofanAtmosphere
• IfthesurfacehasareflectanceofR,theradiancereflectedbacktotheatmosphereis
• KnowingL,wecandeterminetheIrradianceattheSensorfromadigitalnumberC(e.g.0-255)
L = EΔλcosθ.ΔλRπ
L S=Ck + Lmin
Where: k=(Lmax – Lmin)/Cmax andLmax andLmin arethemaximumandminimummeasureableradiancesasindicatedbytheinstrumentmanufacturer
Wm-2sr-1
Wm-2sr-1
EffectsoftheAtmosphere
BulkAtmosphericCorrection• Oftenitissufficienttoassume
therearepixelvaluesclosetozerointheimagery(e.g.water)
• Inthiscase,anybrightnessobservedwillbearesultofatmosphericcontributions(PrimarilyLP butalsoED)
• Histogramsofeachchannelwillshowanoffsetfromzeroasaresult• Wavelength dependent
• Subtracting thisoffsetfromtheentireimagewillremovethevastmajorityofatmosphericeffects
AbsorptionandAtmosphericWindows
AIRSmeasuresupwellingradiancesin2378spectralchannelscoveringtheIRspectralband,3.74to15.4µm.AsetoffourchannelsintheVisible/Near-IR(VIS)observeswavelengthsfrom0.4to1.0µmtoprovidecloudcoverandspatial-variabilitycharacterization.
StripinginImagery
SouthernMaruitania neartheSenegalborder,October10,1980,LANDSAT4Multi-SpectralScanner(MSS). Themajorityoftheland-coverconsistsofriparianvegetation,poorgrassland,andbarrenground
Band1 NDVI
Striping
• Idealradiationdetectorhasaconsistenttransferfunction(radiationinà radiationout)
• Inreality,differentdetectorshavedifferenttransferfunctions– Sameirradiancecausesdifferentbrightnessvaluesindifferent
detectors– 6detectorsonMSS,16onTM,6000onSPOTHRV
TransferCharacteristics
Mismatchesbetweendetectors
Destriping
• Correctionofradiometricmismatchescanbemadebyadoptingonesensorasareferencesensor,andadjustingtheoffsetsoftheotherstomatchit
Wherex =oldbrightnessofapixely =new(destriped)brightnesssd =referencevaluestandarddeviationsi =standarddeviationofdetectorunderconsiderationmd =referencevaluemeanbrightnessmi =meanbrightnessofdetectorunderconsideration
Assumesbrightnessvaluesdon’tchangesignificantlyoverdistanceequivalenttoonescanofdetectors(474m forLandsats 1,2,and3)
€
y =σ d
σ i
x + md −σ d
σ i
mi
Destriping
OriginalBand1 Band1afterdestriping
Fig.2.2ReducingsensorinducedstripingnoiseinaLandsatMSSimage:aoriginalimage,andbafterdestriping bymatchingsensorstatistics
ExamplefromRichardsText
ApparentSurfaceTemperature
25
Bias
DigitalNumber
Radian
tIntensity
Gain
Offset
InputSignal(RadiantIntensity)
Outpu
tSigna
l(DN
)
TransferFunction
InstrumentCharacteristics ImageCharacteristics
RadiometricResolution/Dynamic
Range
L=Bias+(Gain× DN)
Lmin Lmax 0 2550
255
Lmin
Lmax
Bias=LMIN
Gain=
TrueSurfaceTemperature• Mustcorrectforatmosphericcontribution
– Attenuationofsurfacesignal– Additionofatmosphericsignal– Differsfromvisibleinthatwecan’tdoabulkcorrectionfordarkest
pixel:Why?
• Varioustechniques– Splitwindow:uses2channels(windows)thatoverlapinspectral
sensitivity– Dualwindow:uses2channelsthatdonotoverlap– Triplewindow:Uses3channels
• WewillfocusonAVHRRseasurfacetemperature– Globalcoverage– Goodresolution– Nearly30yearsofdata– Reasonablystablesurfaceemissivitycharacteristics– Channel3:3.55-3.93µm;Channel4:10.3-11.3µm;Channel5:11.5-
12.5µm26
TransmissionfromGroundtotheTopoftheAtmosphere(TOA)
27
1
2
3
4
5
I0
I0t’+ I1
(I0t’ + I1)t’+ I2
[(I0t’ + I1)t’ + I2]t’+ I3
{[(I0t’ + I1)t’ + I2]t’+ I3}t’+ I4
({[(I0 t’ + I1)t’ + I2]t’+ I3}t’+ I4)t’+ I5
I5 = I0 (t’)5 + I1(t’)4 + I2(t’)3
+ I3(t’)2+ I4t’+ I5
€
Ii = Iiτ 'n− i( )
0
n
∑ + In
TemperatureRetrieval• Exploitthefactthatattenuationandemissioncharacteristicsare
differentfordifferentwavelengths• Thermalradiationemittedbythesurfaceisabsorbedby
atmosphericconstituentsandre-emittedatalllevelsofheatmosphere– Primaryfactoratwavelengthsweconsideriswatervapor
SpectralIrradianceatsensor
SpectralRadiancefrom
surface
AtmosphericTransmittance
SpectralRadiancefromTopofAtmos.
AtmosphericEmissivity
= +( ( ( () ) ))Ii =Llst +Lli(1-t)
Ifweconsidertheatmosphereasawhole,therelationshiponthepreviouspagecanbecondensedforanarrowwavelengthbandto:
Atmosphericreflectanceisnegligibleatthermalwavelengths
TemperatureRetrieval:BasicConcepts
29
TemperatureRetrieval:BasicConcepts
30
€
Ii = Bλ(Ts)[ ](Δλ)τλ + Bλ(Ti)[ ](Δλ)(1− τλ)
Ii = Bλ (Ts )[ ]τ λ dλ + Bλ (Ti )[ ](1−τ λ )dλλ1
λ2∫λ1
λ2∫
Ii =Llst +Lli(1-t)
TemperatureRetrieval
BrightnessTemperature:Brightnesstemperatureisthetemperatureofablackbodyinthermalequilibriumwithitssurroundingswouldhavetobetoduplicatetheobservedintensityofagreybodyobjectatagivenwavelength
SplitWindow:Atechniqueusedtocalculatelandandseasurfacetemperatures,wherecorrectionsaremadefortheatmosphericmodificationofupwellingradiationfromthesurface.Whileasingle-channeldoesnotallowresolutionofambiguitybetweensurfacetemperatureandatmosphericcontributionstoasignal,twochannelscan.
31
TemperatureRetrieval
Ifweusechannelsthatarecloseinthespectralrange,aswiththesplitwindow,thepreviousrelationshipcanbeinvertedtosolveforsurfacetemperature
WhereT4 andT5 arethebrightnesstemperaturesofchannels4and5respectively,andk4 andk5 aretheeffectiveabsorptioncoefficientsatwavelengthsinchannels4and5.
Thek andt termsarecalculatedwithradiativetransfermodelsforavarietyofconditions,andregressedagainsttemperaturedatafrombuoystoprovidearelationshipbetweenTsandthecombinationofT4 andT5.Theyarewavelength-dependent
32
Ts = T4 + [k4/(k4-k5)](T4-T5)
CloudFiltering• MaximumTemperature
– allobservationsofasmallsurfaceareaoverarelativelyshortperiodoftimearecompared.
– Thehighesttemperatureisretainedasthebestestimateoftemperatureinthatarea.• oceansurfacefeaturesaremorepersistentthanclouds• cloudsarecolderthanthesurface.• Caveat:Thismethodworkspoorlyforpersistent,thinclouds.
• TwoWavelengthInfrared– comparetemperaturesfrom3.7µmand10.5µm
• 3.7µmsensitivetowatervapor– Ifthetemperaturesarethesame,thenwecanassumethemeasuredsignal
camefrom• theseasurface,OR• uniformclouds,whichwillprobablybedetectedinavisualimageoftheareaof
interest.– Ifthetemperaturesatthetwowavelengthsaredifferent,thenthereare
scattered,undetectedcloudsinthescene.
CloudFiltering• InfraredVariability
– temperaturesofcloudstendtobemuchmorevariableinspacethantemperatureoftheseasurface
– allareashavingasmalldeviationfromameanbrightnesstemperatureclosetothatexpectedoftheseaintheregionareacceptedasgoodvalues.
• TwoWavelengthVisible-Infrared– usesreflectedsunlighttodetectcloudsontheassumptionthattheseais
muchdarkerinvisiblewavelengthsthanclouds
Oncecloud-freepixelshavebeenidentified,theinfraredradianceoftheremainingpixelsmustbecorrectedfortheinfluenceofwatervaporandaerosolsintheatmosphereinordertoobtainaccuratevaluesforSST.