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AMSR2

SEAICEALGORITHMTHEORETICALBASISDOCUMENT

WalterN.Meier

ThorstenMarkus

JosefinoComiso

AlvaroIvanoff

JeffreyMiller

NASAGoddardSpaceFlightCenter

CryosphericSciencesLab

Code615

Greenbelt,MD20771

12July2017

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TableofContents

1. Overview 3

2. Background 3

2.1Experimentalobjective 3

2.2Historicalprospective 3

3. TheoreticalBasisofAlgorithm 4

3.1Physicsoftheproblem 4

3.2Mathematicaldescription 5

3.2.1Seaiceconcentration 5

3.2.1.1Implementationoftheconcentrationalgorithm 6

3.2.1.2Landspillovercorrection 11

3.2.1.3Reductionofatmosphericeffects 11

3.2.2Snowdepthonseaice 14

3.2.3Seaicedrift 15

3.2.4Adjustmentstobrightnesstemperatures 17

4. VarianceandUncertaintyEstimates 19

5. ImplementationIssues 19

5.1Computation/programming/proceduralconsideration

5.2Qualitycontrolanddiagnostics

5.3Constraints,limitationsanddiagnostics

6. References 22

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1.Overview

TheAMSR2seaicestandardlevel3productsincludeseaiceconcentration,snowdepthonseaice,andseaicedrift.ItissimilartotheAMSR-Eproducts,withadjustmentsforthechangeinsensor.MuchofthecontenthereisadaptedfromtheAMSR-EATBD.TheAMSR2standardseaiceconcentrationproductisgeneratedusingtheenhancedNASATeam(NT2)algorithmdescribedbyMarkusandCavalieri(2000,2009),thesnowdepthisproducedfromthealgorithmdescribedbyMarkusandCavalieri(1998)forbothhemispheres,butexcludingtheArcticperennialiceregions,andtheseaicedriftisproducedfromanalgorithmdescribedbyLiuandCavalieri(1998).Additionally,thedifferencebetweentheAMSR2Bootstrap(ABA)andtheNT2retrievedconcentrations(ABA-NT2)arearchived.TheseproductstogetherwithAMSR2calibratedbrightnesstemperatures(TBs)aremappedtothesamepolarstereographicprojectionusedforSSMIdatatoprovidetheresearchcommunityconsistencyandcontinuitywiththeexisting32-yearNimbus7SMMRandDMSPSSMIseaiceconcentrationproducts.TheTBgridresolutionsareasfollows:(a)TBsforallAMSR2channels:25-km,(b)TBsforthe18,23,36,and89GHzchannels:12.5-km,(c)TBsforthe89GHzchannels:6.25-km.AlloftheseTBproductsarestoredasacompositeof(i)daily-averagedascendingorbitsonly,(ii)daily-averageddescendingorbitsonly,and(iii)allorbitscreatingafulldailyaverage.Seaiceconcentrationsareproducedat12.5-kmand25-kmresolutionsandstoredasacompositeofdaily-averagedascendingorbits,daily-averageddescendingorbits,andallorbitsforafulldailyaverage,similartotheTBproducts.Snowdepthonseaiceisproducedasa5-dayaverageataresolutionof12.5km.Seaicedriftisalsoafive-dayproductcomputedataresolutionof6.25-km,butmappedataresolutionof100-km.

ThealgorithmsdescribedbelowareessentiallythesameasthosedevelopedforAMSR-E.TheprimarychangeforAMSR2isanadjustmenttotheAMSR2brightnesstemperaturestobeconsistentwiththeAMSR-Evalues.ThisadjustmentissummarizedinSection3.2.4

2.Background

2.1Experimentalobjective

TheobjectiveoftheAMSR2seaiceproductsistoprovidehigh-qualityestimatesofimportantgeophysicalseaiceparameters,including:concentration,snowdepthonseaice,anddrift.ThesefieldswillcontinuethetimeseriesthatbeganwithAMSR-Ein2002.WiththeadditionofcalibratedAMSR2parameters,theAMSR(includingbothAMSR-EandAMSR2)willextentatleast15years,providingahigherqualitycomplementtothelong-termnearly40-yearrecordofpassivemicrowaveseaiceestimatesfromSMMR,SSMI,andSSMIS.

2.2Historicalprospective

Seaiceisakeyclimateindicatorduetoitshighalbedothatreflectsincomingsolarradiation,itsroleasaphysicalbarriertoheatandmoisturetransferbetweentheoceanandatmosphere,and

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itsroleinbiogeochemicalcycles.ItisalsoplaysamajorroleinpolarecosystemsandinlivesofindigenouspeoplesoftheArctic.ChangesinArcticseaiceoverthepastnearlyfourdecadeshavebeendramatic,withalossofoverathirdofsummericecover,alargedeclineinicethickness,andanearly-completelossofoldice.Satelliteremotesensinghasbeentheprimarytoolformappingseaiceconcentration,extent,andagesincethelate1970s.Theconsistentandcontinuouslong-termmultichannelmicrowaveradiometerseaicerecordbeganinOctober1978withtheScanningMultichannelMicrowaveRadiometer(SMMR)ontheNASANimbus-5satellite,followedbyaseriesofSpecialSensorMicrowaveImagers(SSMI)andSpecialSensorMicrowaveImager/Sounders(SSMIS)instrumentsonU.S.DefenseMeteorologicalSatelliteProgram(DMSP)platforms.TheSSMIandSSMISrecordbeganinJuly1987andcontinuestoday(throughmid-2017).Thesesensorsprovidethecontinuousandconsistentlong-termrecordofseaicethatisnownearly40yearslong.Startingin2002,theAdvancedMicrowaveScanningRadiometerfortheEarthObservingSystem(AMSR-E),aJAXAsensorlaunchedontheNASAAquasatellite,providesimprovedspatialresolutionandotheradvancesovertheSMMR-SSMI-SSMISrecord.TheAdvancedMicrowaveSoundingRadiometer2(AMSR2)onboardthefirstGlobalChangeObservationMission–Water(GCOM-W1)satelliteincludessimilarcharacteristicsasAMSR-Ewithslightlybetterspatialresolutionandotherimprovements.TheAMSR-EandAMSR2sensorprovidea15+yearrecordofenhancedseaiceretrievalsthatcomplementthelongerrecord.

3.TheoreticalBasisofAlgorithm

3.1Physicsoftheproblem

PassivemicrowaveradiationisnaturallyemittedbytheEarth’ssurfaceandoverlyingatmosphere.Thisemissionisacomplexfunctionofthemicrowaveradiativepropertiesoftheemittingbody(HallikainenandWinebrenner,1992).However,forthepurposesofmicrowaveremotesensing,therelationshipcanbedescribedasasimplefunctionofthephysicaltemperature(T)oftheemittingbodyandtheemissivity(ε)ofthebody.

TB=ε*T(1)

TBisthebrightnesstemperatureandistheparameter(aftercalibrations)retrievedbysatellitesensorsandistheinputparametertopassivemicrowaveseaiceconcentrationalgorithms.

Themicrowaveelectromagneticpropertiesofseaiceareafunctionofthephysicalpropertiesoftheice,suchascrystalstructure,salinity,temperature,orsnowcover.Inaddition,openwatertypicallyhasanelectromagneticemissionsignaturethatisdistinctfromseaiceemission(Eppleretal.,1992).Thesepropertiesformthebasisforpassivemicrowaveretrievalofseaiceconcentrations.

Specifically,theunfrozenwatersurfaceishighlyreflectiveinmuchofthemicrowaveregime,resultinginlowemission(Figure5).Inaddition,emissionfromliquidwaterishighlypolarized.

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Whensaltwaterinitiallyfreezesintofirst-year(FY)ice(icethathasformedsincetheendofthepreviousmeltseason),themicrowaveemissionchangessubstantially;thesurfaceemissionincreasesandisonlyweaklypolarized.Overtimeasfreezingcontinues,brinepocketswithintheseaicedrain,particularlyiftheseaicesurvivesasummermeltseasonwhenmuchofthebrineisflushedbymeltwater.Thismulti-year(MY)icehasamorecomplexsignaturewithcharacteristicsgenerallybetweenwaterandfirst-yearice.Othersurfacefeaturescanmodifythemicrowaveemission,particularlysnowcover,whichcanscattertheicesurfaceemissionand/oremitradiationfromwithinthesnowpack.Atmosphericemissionalsocontributestoanysignalreceivedbyasatellitesensor.Theseissuesresultinuncertaintiesintheretrievedconcentrations,whicharediscussedfurtherbelow.

Becauseofthecomplexitiesoftheseaicesurfaceaswellassurfaceandatmosphericemissionandscattering,directphysicalrelationshipsbetweenthemicrowaveemissionandthephysicalseaiceconcentrationarenotfeasible.Thus,thestandardapproachistoderiveconcentrationthroughempiricalrelationships.Theseempirically-derivedalgorithmstakeadvantageofthefactthatbrightnesstemperatureinmicrowavefrequenciestendtoclusteraroundconsistentvaluesforpuresurfacetypes(100%wateror100%seaice).Concentrationcanthenbederivedusingasimplelinearmixingequation(Zwallyetal.,1983)foranybrightnesstemperaturethatfallsbetweenthetwopuresurfacevalues:

TB=TICI+TO(1-CI)(2)

WhereTBistheobservedbrightnesstemperature,TIisthebrightnesstemperaturefor100%seaice,TOisthebrightnesstemperatureforopenwater,andCIistheseaiceconcentration.

Inreality,suchanapproachislimitedbythesurfaceambiguitiesandatmosphericemission.Usingcombinationsofmorethanonefrequencyandpolarizationlimitstheseeffects,resultinginbetterdiscriminationbetweenwateranddifferenticetypesandamoreaccurateconcentrationestimate.

3.2Mathematicaldescription

3.2.1Seaiceconcentration

ThetworatiosofbrightnesstemperaturesusedintheoriginalNASATeamalgorithm(Cavalierietal.1984;GloersenandCavalieri1986;Cavalierietal.1995)aswellasintheNT2approacharethepolarization

PR(ν)=[TB(νV)−TB(ν)]/[TB(νV)+TB(νH)] (3)

andthespectralgradientratio

GR(ν1pν2p)=TB(ν1p)−TB(ν2p)]/[TB(ν1p)+TB(ν2p)] (4)

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whereTBisthebrightnesstemperatureatfrequencyνforthepolarizedcomponentp(vertical(V)orhorizontal(H)).

Figure1(top)showsatypicalscatterplotofPR(19)versusGR(37V19V)forSeptemberconditionsintheWeddellSea.TheNTalgorithmidentifiestwoicetypesthatareassociatedwithfirst-yearandmultiyeariceintheArcticandicetypesAandBintheAntarctic(asshowninFigure1(top)).TheA-Blinerepresents100%iceconcentration.Thedistancefromtheopenwaterpoint(OW)tolineA-Bisameasureoftheiceconcentration.Inthisalgorithm,theprimarysourceoferrorisattributedtoconditionsinthesurfacelayersuchassurfaceglazeandlayering(Comisoetal.1997),whichcansignificantlyaffectthehorizontallypolarized19GHzbrightnesstemperature(Matzleretal.1984)leadingtoincreasedPR(19)valuesandthusanunderestimateoficeconcentration.Inthefollowingdiscussion,wewillrefertotheseeffectsassurfaceeffects.InFigure1(top),pixelswithsignificantsurfaceeffectstendtoclusterasacloudofpoints(labeledC)awayfromthe100%iceconcentrationlineA-BresultinginanunderestimateoficeconcentrationbytheNTalgorithm.Theuseofhorizontallypolarizedchannelsmakesitimperativetoresolveathirdicetypetoovercomethedifficultyofsurfaceeffectsontheemissivityofthehorizontallypolarizedcomponentofthebrightnesstemperature.

WemakeuseofGR(89V19V)andGR(89H19H)toresolvetheambiguitybetweenpixelswithtruelowiceconcentrationandpixelswithsignificantsurfaceeffects.AplotofthesetworatiosarefoundtoformnarrowclustersexceptforareaswheresurfaceeffectsdecreaseTB(19H)andconsequentlyincreaseGR(89H19H)(Figure1(bottom)).ValuesofhighGR(89V19V)andhighGR(89H19H)areindicativeofopenwater.TherangeofGR(89H19H)valuesislargerbecauseofthegreaterdynamicrangebetweeniceandwaterforthehorizontallypolarizedcomponents.Withincreasingiceconcentration,thetworatioshavemoresimilarvalues.ThenarrowclusterofpixelsadjacenttothediagonalshowninFigure1(bottom)represents100%iceconcentrationwithdifferentGRvaluescorrespondingtodifferenticetypes.Whensurfaceeffectscomeintoplay,pointsdeviatefromthisnarrowclustertowardsincreasedGR(89H19H)values(cloudofpointstotherightofthediagonal)whileGR(89V19V)changeslittleorremainsconstant.ThiscloudofpointslabeledCinFigure3(bottom)alsocorrespondstotheclusterofpointslabeledCinFigure3(top).Thedifference,therefore,betweenthesetwoGRs(ΔGR)isusedasameasureofthemagnitudeofsurfaceeffects.BasedonthisanalysisweintroduceanewicetypeC,whichrepresentsicehavingsignificantsurfaceeffects.ForcomputationalreasonswerotatetheaxesinPR-GRspace(Figure1(top))byanangleφsotheA-Blineisvertical.ThismakestherotatedPRs(PRR(19)andPRR(89))independentoficetypesAandB(first-yearandmultiyearfortheArctic).Theuseofthe89GHzdatarequiresacorrectionforatmosphericeffects.ThisisaccomplishedthroughanadditionalAMSR2variable,PR(89).

Theresponseofthebrightnesstemperaturestodifferentweatherconditionsiscalculatedusinganatmosphericradiativetransfermodel(Kummerow1993).Inputdataintothemodelaretheemissivitiesoffirst-yearseaiceunderwinterconditionstakenfromEppleretal.(1992)with

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modificationstoachieveagreementbetweenmodeledandobservedratios.Atmosphericprofilesusedasanotherindependentvariableinthealgorithm,havingdifferentcloudproperties,specificallycloudbase,cloudtop,cloudliquidwateraretakenfromFraseretal.(1975)andaverageatmospherictemperaturesandhumidityprofilesforsummerandwinterconditionsaretakenfromAntarcticresearchstations.Theseatmosphericprofilesarebasedonclimatologyandareassumedvalidforbothhemispheres.

Figure1:Top:GR(37V19V)versusPR(19)fortheWeddellSeaonSeptember15,1992.ThegraycirclesrepresentthetiepointsfortheicetypesAandBaswellasforopenwaterasusedbytheNTalgorithm.LabelCindicatespixelswithsignificantsurfaceeffects.Φistheanglebetweenthey-axisandtheA-Bline.Bottom:GR(85V19V)versusGR(85H19H).TheicetypesAandBareclosetothediagonal.TheamountoflayeringcorrespondstothehorizontaldeviationfromthislinetowardslabelC.TakenfromMarkusandCavalieri[2000].

TheplotsofΔGRversusPRR(19)(Figure2a)andΔGRversusPRR(89)(Figure2b)illustratethealgorithmdomain.Thegraysymbolsindicatethetie-pointswiththedifferentatmospheresforthethreesurfacetypes(A,C,andOW).Theyalsoillustratethattheeffectofweatheriswellmodeled.Forexample,theclusterofopenwatervaluesismainlytheresultofchangingatmosphericconditions.ThemodeledatmospheresadequatelyspanthelengthsoftheOWclusters.AcomparisonofFiguresB4aandB4balsoshowshowmuchmorethe89GHzdataareaffectedbytheatmospherecomparedtothe19GHzdata.

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Figure2(a)ΔGRversusPRR(19)and(b)ΔGRversusPRR(89)forSeptember15,2008.ThegraysymbolsrepresenttheNT2tie

We,then,calculatebrightnesstemperaturesforallpossibleiceconcentrationcombinationsin1%incrementsandforeachofthosesolutionscalculatetheratiosPRR(19),PRR(89),andΔGR.Thiscreatesaprisminwhicheachelementcontainsavectorwiththethreeratios(Figure3).ForeachAMSR2pixelPRR(19),PRR(89),andΔGRarecalculatedfromtheobservedbrightnesstemperatures.Next,wemovethroughthisprismcomparingtheobservedthreeratioswiththemodeledones.Theindiceswherethedifferencesaresmallestwilldeterminethefinaliceconcentrationcombinationandweatherindex.Thenextsectionwillprovidedetailedinformationabouttheimplementation.

Becauseoftheuniquesignatureofnewiceinthemicrowaverange,wesolvefornewiceinsteadoficetypeCforselectedpixels.UsingaGR(37V19V)thresholdof–0.02weeitherresolveicetypeC(forpixelswhereGR(37V19V)isbelowthisthreshold)orthinice(forpixelswhereGR(37V19V)isabovethisthreshold).AreasoficetypeCandthinicearemutuallyexclusivebecausethinicehaslittle,ifany,snowcover.Alimitation,ofcourse,isthatwecannotresolvemixturesofthiniceandthickericewithlayeringinitssnowcover.

3.2.1.1Implementationoftheconcentrationalgorithm

Incontrasttootheroperationalseaiceconcentrationalgorithmsusingdailyaveragedbrightnesstemperaturesasinput,theAMSR-ENT2concentrationsarecalculatedfromindividualswath(Level2)datafromwhichdailymapsaremadebyaveragingtheseswathiceconcentrations.UsingswathbrightnesstemperaturesisparticularlycriticalfortheNT2algorithmanditsatmosphericcorrection.Theatmosphericinfluenceonthebrightness

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temperaturesisnonlinearandbyusingaveragebrightnesstemperatureswewoulddilutetheatmosphericsignal.Theiceconcentrationalgorithmisimplementedasfollows:

1.Generatelook-uptables:ForeachAMSRchannelwithfrequencyνandpolarizationpcalculatebrightnesstemperatureforeachiceconcentration-weathercombination(usingTBow,TBA/FY,TBC/thinasgivenintheAppendixofMarkusandCavalieri(2009)):

TBca,cc,wx(νp)=(1−CA−CC)•TBow(νpWx)+CA•TBA/FY(νpWx)+CC•TBC/thin(νpWx) (5)

whereCAreferstotheicetypeA/Bconcentration(FY/MYforArctic),CCtoicetypeCconcentration,andWxtotheweatherindex.Iceconcentrationsarebetween0and100in1%increments,weatherindicesarebetween1and12correspondingtothetablesintheAppendixofMarkusandCavalieri(2009).

Figure3.FlowdiagramoftheNT2algorithm(fromMarkusandDokken2002).

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2.FromtheseTBscalculateratioscreatingthelook---uptables,e.g.LUTPR19(CA,CC,Wx)etc.:

LUTPR19(CA,CC,Wx)=[TBca,cc,wx(37V)−TBca,cc,wx(19V)]xsinφ19/[TBca,cc,wx(37V)+TBca,cc,wx(19V)]+[TBca,cc,wx(19V)−TBca,cc,wx(19H)]xcosφ19/[TBca,cc,wx(19V)+TBca,cc,wx(19H)] (6)

LUTPR89(ca,cc,wx)=[TBca,cc,wx(37V)−TBca,cc,wx(19V)]xsinφ89TBca,cc,wx(37V)+TBca,cc,wx(19V)+[TBca,cc,wx(89V)−TBca,cc,wx(89H)]xcosφ89/[TBca,cc,wx(89V)+TBca,cc,wx(89H)] (7)

IfGR(37V19V)<-0.02wesolveforicetypeCusingΔGRasourthirdvariable,i.e.,

LUTdGR(ca,cc,wx)=[TBca,cc,wx(89H)−TBca,cc,wx(19H)]/[TBca,cc,wx(89H)+TBca,cc,wx(19H)] −[TBca,cc,wx(89V)−TBca,cc,wx(19V)]/[TBca,cc,wx(89V)+TBca,cc,wx(19V)] (8)

WhereasforpixelswhereGR(37V19V)>-0.02wesolveforthiniceusingthestandardGR(37V19V)assuggestedbyCavalieri(1994),i.e.,

LUTdGR(ca,cc,wx)=[TBca,cc,wx(37V)−TBca,cc,wx(19V)]/[TBca,cc,wx(37V) +TBca,cc,wx(19V)] (9)

Eachofthesearrayshasthedimensionsof101x101x12where,ofcourse,thetotaliceconcentration(ca+cc)cannotexceed100.

3.ForeachpixeliwehavetheactualmeasuredAMSR-Ebrightnesstemperatures(TBi(νp))

4.Calculatesameratiosfromthesebrightnesstemperaturesasinstep2(PRi(19),etc.).

5.Comparetheseobservedratioswitheachoftheratiosinthelook-uptablesloopingthroughalliceconcentration-weathercombinations,i.e.,

δ=(PRi(19)−LUTPR19(ca,cc,wx))2+(PRi(89)−LUTPR89(ca,cc,wx))2 +(ΔGRi−LUTdGR(ca,cc,wx))2 (10)

6.Theindicesca,cc,wxwhereδisminimaldeterminetheiceconcentration(andweatherindex),i.e.:

CT=CAminδ+CCminδ (11)

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3.2.1.2LandSpilloverCorrection

Althoughalandmaskisappliedtotheiceconcentrationmaps,landspilloverstillleadstoerroneousiceconcentrationsalongthecoastlinesadjacenttoopenwater.Thismakesoperationalusageofthesemapscumbersome.Therefore,weapplyalandspillovercorrectionschemeonthemaps.Thedifficultyistodeleteallclearlyerroneousiceconcentrationwhileatthesametimepreservingactualiceconcentrations,asforexample,alongthemarginsofcoastalpolynyas.Weapplyafive-stepprocedure.

1.Classifyallpixelsofthepolar-stereographicgridwithrespecttothedistancetocoast.Oceanpixelsdirectlyalongthecoastareclassifiedby1,whereaspixelsfartherawayare2and3.Openoceanpixelsarezero.Landpixelsdirectlyalongthecoastareclassifiedas4andpixelsfartherawayhaveincreasingvalues.

2.Allpixelswithclasses1or2willbeassessedforerroneousseaiceconcentrationsduetolandspilloverbyanalyzingthe7by7pixelneighborhood.Theareaoftheneighborhood(7pixelsor87.5km)needstobegreaterthantheAMSR2antennapattern.Pixelswithvaluesof3and0willnotbechanged.

3.Checkwhetherallclass3pixelsin7-pixelneighborhoodareopenwater(ifso,seticeconcentrationto0).

4.Calculateanaverageseaiceconcentrationforthe7by7pixelboxassumingalloceanpixelshavezeroiceconcentrationandalllandpixelshaveaniceconcentrationof90%.Thisapproximatesatheoreticalconcentrationcausedbylandspilloveronly.

5.IftheAMSR2iceconcentrationislessthanorequaltothisvalue,setpixelatcenterofboxtoopenwater.

Figure4showsanexampleiceconcentrationwithandwithoutthelandspillovercorrection.

3.2.1.3ReductionofAtmosphericEffects

TheNT2algorithmhasanatmosphericcorrectionschemeasaninherentpartofthealgorithm.Itprovidesweather-correctedseaiceconcentrationsthroughtheutilizationofaforwardatmosphericradiativetransfer(RT)model.However,toeliminateremainingsevereweathereffectsoveropenocean,twoweatherfiltersbasedonthespectralgradientratioareimplementedusingthresholdvaluessimilartothoseusedbytheNTalgorithm(GloersenandCavalieri1986;Cavalierietal.1995).However,theadvantageoftheRTatmosphericcorrectionisthatnotonlyarespuriousiceconcentrationsovertheopenoceanremoved,butatmosphericcorrectionsareappliedtoicecoveredportionsoftheocean.

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Figure4.Mapoficeconcentrationwithandwithoutlandspillovercorrection.

Figure5showsAMSR-EseaiceconcentrationmapsfortheSeaofOkhotsk.Figure5ashowstheiceconcentrationmapifPRR(19),PRR(89),andΔGRareusedwithoutanyweathercorrection.Figure5bshowstheiceconcentrationmapwiththeNT2weathercorrection.ThedifferencesbetweenFigure5aand5bareshowninFigure5dandillustratetheeffectoftheweathercorrectionnotonlyovertheopenocean,butalsoovertheseaice.Moresevereweathereffectsovertheopenocean(forexample,inthebottomrightcorner)arefinallyremovedbytheNTweatherfilters(Figure5c).ThethresholdfortheGR(37V19V)NTweatherfilter(GloersenandCavalieri1986)is0.05,wherethethresholdfortheGR(22V19V)NTweatherfilter(Cavalierietal.1995)is0.045.IftherespectiveGRvaluesexceedthesethresholds,theseaiceconcentrationsaresettozero.Figure5eshowsthedifferenceiniceconcentrationsbetweentheretrievalsusingonlytheNT2weathercorrectionandtheretrievalsusingboththeNT2correctionandtheNTfilters.Aslightchangealongtheiceedgeisobserved.

EvenwithboththeatmosphericcorrectionschemeandtheGRfilters,westillhadproblemswithresidualweathercontaminationparticularlyatlowlatitudes.Afilterbasedonmonthlyclimatologicalseasurfacetemperatures(SSTs)fromtheNationalOceanicandAtmosphericAdministration(NOAA)oceanatlas,usedearlierbyCavalierietal.(1999),wasemployedtoeliminatetheselow-latitudespuriousiceconcentrations.IntheNorthernHemisphere,anypixelwherethemonthlySSTisgreaterthan278K,theiceconcentrationissettozerothroughoutthemonth;whereasintheSouthernHemisphere,whereverthemonthlySSTisgreaterthan275K,theiceconcentrationissettozerothroughoutthemonth.ThehigherSSTthreshold

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valueintheNorthernHemisphereisneededbecausethe275KisothermusedintheSouthernHemisphereistooclosetotheiceedgeinthenorth.Theclosestdistancethethresholdisothermsaretotheiceedgeismorethan400km(Cavalierietal.1999).

Insummary,theorderofprocessingisasfollows:

1.Calculateseaiceconcentrationswithatmosphericcorrection.2.ApplyGRfilters.3.ApplySSTmask.4.Applylandspillovercorrection.

Figure5.AMSR-EseaiceconcentrationsforMarch1,2007.(a)IceconcentrationscalculatedusingPRR(19),PRR(89),andΔGRwithoutapplyinganatmosphericcorrection;(b)iceconcentrationwithatmosphericcorrection;(c)finaliceconcentrationwithadditionalclean-upovertheopenoceanbyapplyingthestandardNASATeamGRweatherfilters;(d)differencebetween(a)and(b);(e)differencebetween(b)and(c).Differencesgreaterthan10%havebeentruncatedfortheerroneousseaiceconcentrationsinthelowerrightcorner.

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3.2.2Snowdepthonseaice

TheAMSR-Esnow-depth-on-sea-icealgorithmwasdevelopedusingDMSPSSMIdata(MarkusandCavalieri1998)toestimatesnowdepthonseaicefromspace.Thesnowdepthonseaiceiscalculatedusingthespectralgradientratioofthe18.7GHzand37GHzverticalpolarizationchannels,

hs=a1+a2GRV(ice) (12)

wherehsisthesnowdepthinmeters,anda1=2.9anda2=-782arecoefficientsderivedfromthelinearregressionofinsitusnowdepthmeasurementsonmicrowavedata.GRV(ice)isthespectralgradientratiocorrectedfortheseaiceconcentration,C,asfollows

GRV(ice)=[TB(37V)-TB(19V)-k1(1-C)]/[TB(37V)+TB(19V)-k2(1-C)] (13)

withk1=TBO(37V)-TBO(19V)andk2=TBO(37V)+TBO(19V).Theopenwaterbrightnesstemperatures,TBO,areaveragevaluesfromopenoceanareasandareusedasconstants.TheprincipalideaofthealgorithmissimilartotheAMSR-Esnow-on-landalgorithm(Kellyetal.2003)utilizingtheassumptionsthatscatteringincreaseswithincreasingsnowdepthandthatthescatteringefficiencyisgreaterat37GHzthanat19GHz.Forsnow-freeseaice,thegradientratioisclosetozeroanditbecomesmoreandmorenegativeasthesnowdepth(andgrainsize)increases.Thecorrelationofregionalinsitusnowdepthdistributionsandsatellite-derivedsnowdepthdistributionsis0.81(Figure6).Theupperlimitforsnowdepthretrievalsis50cm,whichisaresultofthelimitedpenetrationdeptha19and37GHz.

Thealgorithmisapplicabletodrysnowconditionsonly.Attheonsetofmelt,theemissivityofboththe19GHzandthe37GHzchannelsapproachunity(thatofablackbody)andthegradientratioapproacheszeroinitiallybeforebecomingpositive.Thus,snowdepthisindeterminateunderwetsnowconditions.Snow,whichiswetduringtheday,frequentlyrefreezesduringthenight.Thisrefreezingresultsinverylargegrainsizes(Colbeck1982)whichleadstoareducedemissivityat37GHzrelativeto19GHztherebydecreasingGRV(ice)andthusleadstoanoverestimateofsnowdepth.Thesethaw-freezeevents,therefore,causelargetemporalvariationsinthesnowdepthretrievals.Thistemporalinformationisusedinthealgorithmtoflagthesnowdepthsasunretrievablefromthoseperiodswithlargefluctuations.

Asgrainsizeinsitumeasurementsareevenlessfrequentlycollectedthansnowdepthmeasurements,theinfluenceofgrainsizevariationscouldnotbeincorporatedintothealgorithm.Becauseoftheuncertaintiesingrainsizeanddensityvariationsaswellassporadicweathereffects,AMSR-Esnowdepthproductswillbe5-dayaveragessimilartothesnow-on-landproduct.

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SnowdepthsareretrievedfortheentireSouthernOcean,butonlyfortheseasonalseaicezonesintheArctic,becausethemicrowavesignatureofsnowisverysimilartothemultiyearicesignaturesothatsnowdepthonmultiyearicecannotberetrievedunambiguously.Tothisend,weuseadynamicmultiyearicemaskbasedonathresholdinGRwhichevolvesonaday-to-daybasisstartingfromOctober1ofeachyearuntiltheonsetofmelt.

Figure6:Comparisonofin-situandSSM/I-derivedsnowdepthdistributions[fromMarkusandCavalieri1998].

3.2.3Seaicedrift

ThemethodtoestimateseaicedriftistheMaximumCross-Correlationfeature-trackingalgorithmdevelopedattheUniversityofColorado(CU)(Emeryetal.,1995).Thebasicmethodologyofthealgorithmisfairlysimple.Twospatiallycoincidentimagesareobtained,separatedbysomeperiodoftime.Atargetarea,whichmaybedefinedbyapixeloragroupofpixels,ischoseninthefirst(older)image.Then,asearchareasurroundingthetargetareaischoseninthesecond(newer)image(Figure1).Correlationswiththetargetareainthefirstimagearecomparedwithallregions(ofthetargetarea’ssize)inthesearchareainthesecondimage.Theregionwiththehighestcorrelationisdeterminedtobethelocationwherethe

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targetmoved(Figure2).Afilteringalgorithmisthenemployedtoremoveatleastsomeofthequestionablematches.

GriddedLevel3dailycompositebrightnesstemperaturesat12.5kmonthepolarstereographicgridareusedasinputintothemotionalgorithm.Icemotionsarecalculatedfromtwocompositeimagesusingtheslidingwindowtofindthecorrelationpeak,whichdeterminesthedistanceafeaturehasmoved.Thedriftisthencomputedbydividingthedistancebythetimeseparation(24hours).Aseaicemaskisappliedtoonlyretrieveicemotionwhereconcentrationisabovethestandardseaiceextentthresholdof15%concentration.Falsecorrelationscanoccurduetocloudsorvariabilityoficesurfacefeatures.Toeliminatethis,firstaminimumcorrelationthresholdof0.7isappliedtoeliminateweakmatches.Nextapost-processingfilterprogramisruntoremoveatleastsomequestionableanderroneousmotions.Thisusesthefactthatmotionishighlyspatiallycorrelatedandrequiresthateachvectorbereasonablyconsistentinspeedanddirectionwithatleasttwoneighboringmotionestimates.

TheCUalgorithmissimpletoimplementandwidelyvalidated.Ithasbeenwidelyusedonavarietyofimagery,includingAMSR-E(e.g.,MeierandDai2006)andiscurrentlythebasisforalong-termseaicedriftproduct(Tschudietal.2016)attheNationalSnowandIceDataCenter.Intheorytheaccuracyofthealgorithmislimitedbythegriddedspatialresolutionoftheinputdata–i.e.,aseaiceparceleitherstaysinitscurrentgridcellormovestoasurroundinggridcell.Thiswouldlimittheaccuracyto~12.5kmperday.Therearealsoadditionalerrorsourcessuchasfalsecorrelationsfromcloudsoricesurfacechanges,sotheuncertaintywouldbeevenmorethan12.5kmperday.However,thealgorithmincludesa4Xoversamplingroutinetoyieldatheoreticalaccuracyofupto3.125kmperday.ValidationstudiesofAMSR-Emotionsincomparisonwithbuoy-derivedmotions(MeierandDai2006)showanRMSerrorof4.5–5.0kmperdayforeachvelocitycomponentwithnegligiblebias.ThisisconsistentwithpreviousstudiesusingSSMI-derivedmotions,giventheincreasedresolutionofAMSR-E(Meieretal.,2000).Errorsarelowestinthecentralicepackduringwinter.Highererrorsoccurneartheiceedgeduetogrowthandmeltoficeandthinicecondition,duringsummermeltduetoliquidwateronthesurfaceobscuringpossiblecorrelation,andnearthecoastduetothespatialresolutionlimitations.

3.2.4Adjustmentofbrightnesstemperatures

Asnotedabove,theseaicealgorithmsforAMSR2arethesameasthoseusedforAMSR-E.TheonlysubstantialdifferenceisthatAMSR2brightnesstemperaturesareadjusted–i.e.,intercalibrated–tomatchAMSR-EsothatthealgorithmcoefficientscanremainthesameandobtainconsistentgeophysicalestimatesfrombothAMSR-EandAMSR2.

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Mostintercalibrationeffortsuseoverlapbetweensensorstomakeadjustmentstothesensordata.ThiswasnotpossibleherebecausetherewasnooverlapbetweenAMSR2andthefully-operationalAMSR-E.However,AMSR-Edidoperateinaslowrotationmode.ThisallowedanintercalibrationacrosscommonpointsofAMSR2andtheslow-rotationAMSR-Ebrightnesstemperatures.RegressionswereperformedforthesecommonpointsoverafullyearandaveragedtodevelopregressionequationstoadjustAMSR2brightnesstemperaturesinto“pseudo-AMSR-E”brightnesstemperaturesthatwouldbeconsistentwiththeAMSR-Ealgorithms;regressionsweredoneindependentlyforboththeArcticandtheAntarctic.ThevaluesusedintheAMSR2processingareprovidedinTable1below.TheseregressionequationsareappliedtotheAMSR2brightnesstemperaturesbeforetheyarefedintothesubsequentgeophysicalalgorithms.

TableIAverageregressionandcorrelationcoefficientsforAMSR2Tbs,basedoncomparisonwith2rpmAMSR-ETbsforJanuary–December2013(FromMeierandIvanoff2017)

NorthernHemisphere SouthernHemisphere

Channel Slope Intercept Correlation Slope Intercept Correlation

18V 1.031 -9.710 0.9984 1.032 -10.013 0.9982

18H 1.001 -1.104 0.9985 1.000 -1.320 0.9983

23V 0.999 -1.706 0.9979 0.993 -0.987 0.9976

36V 0.997 -2.610 0.9916 0.995 -2.400 0.9919

36H 0.996 -2.687 0.9938 0.994 -2.415 0.9932

89V 0.989 0.677 0.9766 0.975 4.239 0.9619

89H 0.977 3.184 0.9621 0.969 4.935 0.9549

Overall,theregressionsshowedverygoodconsistencybetweenAMSR2andtheslow-rotationAMSR-E.Themostnotabledifferenceisfoundinthe18GHzVpolarizationchannel,whichhasslopesslightlyofffrom1andhigherinterceptvalues.The89GHzchannelsalsoshowlessagreementthantheotherchannels,likelyduetothegreateratmosphericemissionat89GHz.

Forseaice,theadjustmentsareevaluatedintermsofminimizingthedifferenceinextent,area,andconcentration.ThiswasnotexplicitlypossibleherebecausethereisnotcompletecoveragetocalculatetheseparametersfromtheAMSR-Eslowrotationdata.Inordertoexaminethese

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variables,abridgeconcentrationdatasetwasused,basedonSSMISbrightnesstemperatures.ThisbridgedatasetspannedafullyearofAMSR-EandAMSR2(2010–2013).DifferencesinextentandareabetweeneachsensorandSSMISwerecalculated.Thesetwofieldswerethendifferencedtoobtainadouble-differenceAMSR2-AMSREextentandareadifference.Fromthis,andexaminationoftheconcentrationfields,itwasfoundthatanadjustmentintheGR3619weatherfilter,from0.050to0.046,wasneededtooptimizetheseaiceconcentrationfields.

Thedouble-differencefieldsandsubsequentGR3619adjustmentdecreasedtheextentbiasbetweenAMSR2andAMSR-Efrom~200,000squarekilometersto<10,000squarekilometers(Figure7).Thisisasgoodorbetterthanpreviousseaiceextentsensorintercalibrations(e.g.,Cavalierietal.2012;Meieretal.2011).ThefullmethodologyforderivingtheregressioncoefficientsandtheadjustmenttoAMSR2brightnesstemperaturesfortheseaicealgorithmsisdescribedinMeierandIvanoff(2017).

4.VarianceandUncertaintyEstimates

TheseaiceproductshavebeenthoroughlyvalidatedinpreviousstudiesusingAMSR-E(e.g.,MarkusandCavalieri2000;MarkusandCavalieri2009;MarkusandCavalieri1998;LiuandCavalieri1998).FurthercomparisonshavebeenmadeforAMSR2seaiceconcentrationinMeieretal.(2017).ThesecomparedAMSR2concentrationestimateswithconcentrationsderivedfromvisibleimageryobtainedfromtheSuomiVisibleandInfraredImagingRadiometerSuite(VIIRS).

Thisvalidationshowedaconcentrationbiasof3.9%andanRMSEof11.0%intheArctic(Figure8),andabiasof4.45%andanRMSEof8.8%intheAntarctic.ThesevaluesareconsistentwithpreviousvalidationstudiesofAMSR-Eseaiceconcentrations.ThereisconsiderablevariationthoughintheaccuracyofAMSR2concentration,dependingonseaiceconditions.Errorsarelowforhighconcentrationregions,butarehigherinregionswithlowerconcentrations,suchasthemarginalicezone.Again,thisperformanceistypicalforpassivemicrowaveretrievalsandhasbeenfoundinnumerousotherstudies.

5.Implementationissues

5.1Computation/programming/proceduralconsideration

5.2Qualitycontrolanddiagnostics

5.3Constraints,limitationsanddiagnostics

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ThebasiclimitationsoficeconcentrationdatafromAMSR2includerelativelycoarseresolutionandtheinabilitytounambiguouslyidentifyareascoveredbythinice,pancakeiceandmeltpondedice.Thinice,pancakeiceandmeltpondedicecanhaveemissivitiesintermediatetothoseofopenwateranddrythickiceandcouldcontributetosignificantuncertaintiesintheretrievaloficeconcentration.Agoodschemethatenablesclassificationofeachdataelementintodifferentsurfacetypeswouldhelpminimizeuncertainties.

Fig.7.(a)Arcticand(b)Antarcticextentdoubledifferences,(AMSR2–SSMIS)–(AMSR-E–SSMIS)fororiginalAMSR2(green),regressedAMSR2(purple),andregressedAMSR2withGRadjustment(blue).FromMeierandIvanoff(2017).

!0.4%

!0.2%

0%

0.2%

0.4%

0.6%

0.8%

1%

1.2%

J% F% M% A% M% J% J% A% S% O% N% D%

Extent%Differen

ce%(1

06%km

2 )%

Date,%2010%&%2013%

ArcCc%NT2%AMSR2!AMSRE%Extent%%Double%Difference,%2010%&%2013%

AMSR2%NT2(Original)!AMSRE%NT2%

AMSR2%NT2(Regressed)!AMSRE%NT2%

AMSR2%NT2(GR%Adjusted)!AMSRE%NT2%

!0.2%

0%

0.2%

0.4%

0.6%

0.8%

1%

1.2%

J% F% M% A% M% J% J% A% S% O% N% D%

Extent%Differen

ce%(1

06%km

2 )%

Date,%2010%&%2013%

AntarcCc%NT2%AMSR2!AMSRE%Extent%%Double%Difference,%2010%&%2013%

AMSR2%NT2(Original)!AMSRE%NT2%

AMSR2%NT2(Regressed)!AMSRE%NT2%

AMSR2%NT2(GR%Adjusted)!AMSRE%NT2%

(a)

(b)

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Fig.8.ComparisonofAMSR2minusVIIRSiceconcentrationsfordifferentAMSR2iceconcentrationranges/binsintheArctic.TheAMSR2concentrationiscomputedwiththeNASATeam2algorithm.Notethatthey-axisrangeisdifferentfor"All","90-100%",andtheotherplots.FromMeieretal.(2017).

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