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

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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)

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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.

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TemperatureRetrieval

Ifweusechannelsthatarecloseinthespectralrange,aswiththesplitwindow,thepreviousrelationshipcanbeinvertedtosolveforsurfacetemperature

WhereT4 andT5 arethebrightnesstemperaturesofchannels4and5respectively,andk4 andk5 aretheeffectiveabsorptioncoefficientsatwavelengthsinchannels4and5.

Thek andt termsarecalculatedwithradiativetransfermodelsforavarietyofconditions,andregressedagainsttemperaturedatafrombuoystoprovidearelationshipbetweenTsandthecombinationofT4 andT5.Theyarewavelength-dependent

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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.