User’sGuideDatasetname:GriddedSeaSurfaceHeightAnomaliesClimateDataRecordVersionJPL1609AuthorsVictorZlotnicki(1),ZhengQu(2),JoshuaK.Willis(1)

(1) JetPropulsionLaboratory,CaliforniaInstituteofTechnology,PasadenaCA,USA.(2) RaytheonCorp.,PasadenaCA,USA.

AbstractOceantopographygriddedproductsfromnadirsatelliteradaraltimetry,distributedoverthepastnearlytwodecadesbyAVISO,havefoundavarietyofapplications,includingeddytracking,AntarcticCircumpolarCurrentfronts,andestimatingthetransportoftheAtlanticMeridionalOverturningCirculationamongothers.Nonethelesstherewasaneedtoupdatethegriddingprocedures,ascertainsimplificationsimposedbyhistoricalcomputerrestrictionsarenolongernecessary.ThisdocumentdescribesthegriddeddataproductsproducedattheJetPropulsionLaboratory.Thoseproductsare“final”grids,withadelayofafewmonths,andthe“interim”grids,producedinnearrealtime.Onekeymeasureofqualityoftheresultinggridsisacomparisontowithheldaltimetrydata,notonlyintermsofoverallrootmeansquared(RMS)discrepancy,butinassessingthespectralpropertiesofgridsversuswithhelddata.Wefindthatthesegridsbasedontwosatellitesatanyonetime,reproducewavelengthslongerthan350kmneartheEquator(4.3cmRMS),150kmintheAntarcticCircumpolarCurrentregion(4.0cmRMS),and250kmintheGulfStreamregion(9cmRMS).Anotherqualitymeasureisbycomparisonwithasetof61welldistributed,highqualitytidegauges;wefindthatthestandarddeviationofthedetrendeddifferencebetweenourgridsandthetidegaugesis3.1cm,whilethestandarddeviationofthetidegagetimeseriesis7.5cm.Theaboveassessmentappliestothe“final”grids;thereisanoverallRMSdifferenceof2.5cmbetweenfinalandinterimgrids.CreditPleasecitethesedataas:ZlotnickiV.,Z.QuandJ.Willis.2016.GriddedSeaSurfaceHeightAnomaliesClimateDataRecordVersionJPL1609.PO.DAAC,CA,USA.Datasetaccessed[YYYY-MM-DD]athttp://dx.doi.org/10.5067/SLREF-CDRV1Introduction

Inaseriesofpapers(LeTraonetal,1998;Ducetetal,2000;LeTraonandDibarboure,2002),P.Y.LeTraonandcolleaguesestablishedanefficientandaccuratemethodtogridseasurfaceheights(SSH)fromtime-varyingalongtracknadirradaraltimeterdata.TheyshowedthattheirapproachwasanimprovementoverthatproposedbyWunschandZlotnicki(1984),alsousingobjectivemapping(Brethertonetal.,1976),whichfocusedonthetime-averagedseasurfacetopography;theypaidspecialattentiontotheremovaloflongwavelengthalongtrackerror,andascertainedtheaccuracyofthetechniquebysamplingnumericalmodeloutputinthemanneranadiraltimeterdoes,griddingthesampledmodel,andcomparedtothefullmodelgrids.ThegridsproducedbyvariousversionsoftheirtechniquebySSALTO/DUACSanddistributedbyAVISOsponsoredbytheCentreNationaled’EtudesSpatialesofFrancehavebeenwidelyused.ForexampleCheltonetal(2011a)usedthemtotracknonlinearmesoscaleeddiesbasedonclosedcontoursofSSH,itselfadataproductlaterusedinotherstudies(e.g.Cheltonetal,2011b;Samelsonetal,2014);Willis(2010)demonstratedthattheSSHmapstogetherwithArgodatashowedskillinestimatingthetransportoftheupperlimboftheAtlanticMeridionalOverturningCirculationaround41oN;SokolovandRintoul(2007)andThompsonandSallé(2012)usedthesegridstostudyfrontsoftheAntarcticCircumpolarcurrent.Ofcourse,thislistisjustaverysmallsampleofthemanyapplicationsthesemapshavefound.Despitetheirsuccess,AVISOalsosawtheneedtoupdatecertainchoicesmadelongagointhegriddingprocedure,andreleasedanewsetofgridsin2014,labelledDT2014,anddescribedatthe2015OceanSurfaceTopographyScienceTeammeeting(Pujoletal,2015).Thesetofgridsdescribedherealsouseatechniquesimilartoobjectivemapping,calledsimplekrigging(https://en.wikipedia.org/wiki/Kriging;CressieandWikle,2011,chapter4).InputData.Allgridsareconstructedfromtwosimultaneousaltimetricsatellites.OnesatelliteisoneofTOPEX/Poseidon,Jason-1,Jason-2,orJason-3.Theothersatelliteisoneof:ERS-1,ERS-2,Envisat,AltiKa,orCryosat-2.DatafromthefirstsetareobtainedfromthealongtrackdataproductgeneratedbytheGoddardSpaceFlightCenteranddistributedbyPO.DAAC,entitledIntegratedMulti-MissionOceanAltimeterDataforClimateResearch,version3.ThedataforthesecondsetofsatellitesisobtainedfromtheRADSdatabase(rads.tudelft.nl) withdefaultcorrectionsasofMarch2016.Theexactsatelltiesuseddependonthedate,pleaserefertothetablebelow.Date Satellite 1 Date Satellite 2 1992-9-23 to 2002-5-14

TOPEX/Poseidon ERS-1

2002-5-14 to 2008-7-2

Jason-1 ERS-2

2008-7-2 to present Jason-2 Envisat Future Jason-3 AltiKa CryoSat-2

Method.First,acovariancefunctionforeachlocationovertheglobaloceanswasobtainedasfollows.TheanalyticalfunctionCij=var*b*exp(-a*rij-(dtij/Lt)^2)=<h(xi,yi,ti)h((xj,yj,tj)>isused,where:<>isanexpectedvalueoperator,h(x,y,t)istheseasurfaceheightathorizontalpositionx,y,timet,Lt=10daysforlatitudesupto5o,15daysforlatitudeshigherthan10o,andlinearlyinbetweena=3.3369,b=1+r+r2/6-r3/6r=√(((dx-Cx*dt)/Lx)2+((dy-Cy*dt)/Ly)2),dx=xi-xj,likewisefordyanddt.var=squaredrootmeansquaredhfromTOPEXandJasonalongtrackdata1993-2014.LxandLyarelengthscalesinthezonalandmeridionaldirectionsdeterminedbyfittingtheabovefunctiontoalongtrackcovariancefunctionsdeterminedfromhistoricalalongtrackrepeataltimetrydataalongtheTOPEXandJason-1and-2tracks,thenrotatedusingJacobs(2013)estimateoftheratioofzonalandmeridionallengthscales.CxandCyaredriftvelocitycomponents,determinedasfollows:inafirststep,Cx,Cyaresettozeroandthecompletedatasetisusedtogenerategridssampledevery1/6degreeand5days.Inasecondstep,CxandCyaredeterminedfromsuccessivegridsbydecomposingintocircles,whoseradiusisthezerocrossingofthecorrelationfunction(Figure2),shiftingtwocorrespondingboxesby1degreeoffsetinalldirections,andcomputingtheircorrelationcoefficient,finallydeterminingCxandCyfromtherelativepositionofthetwoboxeswithmaximumcrosscorrelation.ThethirdsteprerunsthewholegriddingcomputationusingtheCxandCymapsthusdetermined.

Figure2:zerocrossingdistanceoftheautocovariancefunction,estimatedfromalongtrackaltimetrydata.

Figure1aandb:alongtrackcorrelationsestimatedfromourdata,andfromLeTraonetal

a b

Figure3:Top:LxfromGregJacobs,2014,pers.Comm..Bottom:theratioLx/Lyfromthesamesource.

Figure4:propagationsvelocitycomponentsCxandCyfor2010-01-05(anewsetofCx,Cyiscomputedforeach5daymap).Giventheabovecovariancefunction,theestimationofh(P),P=(x,y,t)isthelinearcombinationh(P)=sum(h(Qi)wi(P,Qi))wherethevectorwofweightswiisestimatedbyleastsquaresas𝑤𝜇 = 𝐷 1

1 0'( 𝐶

1 whereCisthesetofCijbetweenthepositionofinterpolationi(gridnode)andeachofthesurroundingdatapointsj;D=C’+EisthesumofthematrixofC’ikbetweenanytwodatapointsiandkandtheexpectederrorcovarianceEikbetweenthosetwopositions.Eikisdiagonal,exceptwhentwodatapointsareonthesamegroundtrack,whereabiaserrorisallowedandsolvedfor.ThistrackbiasisassumedtobezerofortheTOPEX,Jason-1,-2,-3satellites,butnonzerofortheERS-1,-2,Envisat,AltiKasatellites.

Thematricesdonotcontainalltheglobaldatadistribution,butonlydataintwowindows:theinnerwindowhasa400kmradius,theouterwindow1050kmradius,thetimewindow15days.Alldataintheinnerwindowareused,1datapointevery3intheouterwindowareused.Thematrixisinvertedforallpointsinsidea1oboxinbothlatitudeandlongitude.AccuracyAssessmentAgainstAltimetry.Accuracyhasbeenassessedbywithholdingdatafromonealtimeter(oftheT/P,J-1,J-2series)foroneday,thencomparingtheresultinggridstothewithhelddata.Thisproducesanupperboundontheerror,sincethefinalgridsincludealldata.Thedatawerecomparedbothspatiallyandspectrally.Thefiguresbelowshowthespatialpowerspectrumofthewithheldalongtrackdata,ofthegriddedproductinterpolatedlinearlytothepositionofthealongtrackdata,andthespectrumofthedifference.Seecaptionfordetails.

Figure5:spectraofwithheldalongtrackT/PorJ-1orJ-2data,spectraofthemapwithoutthesedata,interpolatedtothetimeandpositionofthealongtrackdata,andspectraofthedifference.Ascanbeseen,theinterpolationretrievesintheACCregionwavelengthslongerthan150kmwith4cmoverallRMS,intheGulfStreamregionwavelengthslongerthan225kmwith9.5cmRMS,andintheequatorialregionwavelengthslongerthan350kmwith4.4cmRMS.

Wehavenotcarriedoutadetailederrorassessmentnearcoasts,wherealtimetererrorsincrease,eitherduetolandcontaminationoftheradiometeroraltimeter,orincreaseduncertaintyofthetidalcorrection,orthefactthatdatafromdeeperwaterareincludedintheinterpolationduetothesearchradiiandtheabsenceofdataononesideofthesearchbox.Usersareurgedcautionininterpretingnearcoastaldata.Theauthorswouldwelcomeanyfindingsontheiraccuracy(pleaseemailvictor.zlotnicki[at]jpl.nasa.gov).Accuracyassessmentagainsttidegauges.Thegridswerecomparedagainstasetof61tidegaugeswithlongtimeseriescoveringtheperiodofthegrids(RichardRay,2016,pers.Comm.).Thedistributionofthetidegaugesisshowninfigure6,whileafewtimeseriesareshowninfigure7.

Figure6:(TOP)spatialdistributionofthe61tidegaugesusedinthiscomparison.Bottom:globalaverageofthedifferencebetweenaltimetricgridandtidegauges.The‘drop’before1998isanow-well-knownfeaturerelatedtoaninaccurateTOPEXcorrection.

Figure7.Sampletimeseriesofaltimetricgrid(blue)andtidegauge(red).Notetheexcellentagreement;thediscrepancyattheendoftheNaurutimeserieshasbeenfoundtobeatidegaugeerror.Thecombinedstandarddeviation(SD)ofthetidegaugesis7.5cm,theSDofthedetrendeddifferencebetweenJPLaltimetryandtidegaugesis3.1cm.WealsocomparedthelatestversionoftheAVISO2-satellitegridstothesamesetoftidegages.TheSDoftheirdifferencewas2.5cm.ThenatureofthedifferenceisassociatedwithshortperiodnoiseintheJPLgrids.Differencebetween“final”and“interim”gridsThedifferencebetween“final”grids,computedexactlyasdescribedabove,and“interim”gridsisthis:thedatasourcefortheJasonseriesofsatellitesinsteadofbeingtheGoddardSpaceFlightCenterprocesseddata,whichisusuallydelayedbyafewmonthsinordertoyieldthehighestaccuracyproduct,isobtainedfromtheRADSsystem(Scharrooetal,2016)innearreal

time.ThedifferencebetweenthesetwosetsofgridsisillustratedinFigure8,withaglobally-averagedrootmeansquareddifferenceof25mm.

Figure8.RMSdifferencebetween“final”and“interim”gridsCoverageandresolution:Thegridsaregivenevery5daysand1/6degreespatialsampling.Theactualresolutionisasillustratedinthe“accuracyassessment”section.Interim:Thereisalonglagofwhenfullyprocesseddataareavailableforthisdataset.Toalleviatethegapofwhenthedataaremeasuredandthefinalversionareavailableaninterimdatasetisprovided.TheinterimgridsaregeneratedentirelyfromnearrealtimeRADSdata,bothfortheJasonseriesaswellasforthesecondsatellite.Format:Thefilenamesareoftheformssh_grids_v1609_1992100712.nc,wherethedateofthemidpointoftheinterpolationisyear1992,month10,day07,hour12noon.Theextension‘nc’referstothenetCDFformat.Theinterimgridsareidentifiedbythestring‘_i’followingthedateinthefilename,asinssh_grids_v1609_1992100712_i.nc.Theversionidrefertotheyearandmonthwhenthecodewasfrozen.ThedatafilesarenetCDF,CFcompliant.Thecontentscanbeseenbelow:netcdfssh_grids_1993020412{dimensions: Longitude=2160; Latitude=960;

Time=UNLIMITED;//(1currently)variables: floatLongitude(Longitude); Longitude:units="degrees_east"; Longitude:long_name="longitude"; Longitude:standard_name="longitude"; Longitude:point_spacing="even"; floatLatitude(Latitude); Latitude:units="degrees_north"; Latitude:long_name="latitude"; Latitude:standard_name="latitude"; Latitude:point_spacing="even"; floatTime(Time); Time:units="Dayssince1985-01-01"; Time:long_name="Time"; Time:calendar="standard"; floatSLA_ERR(Time,Longitude,Latitude); SLA_ERR:units="m"; SLA_ERR:_FillValue=NaNf; SLA_ERR:long_name="SeaLevelAnomalyErrorEstimate"; floatSLA(Time,Longitude,Latitude); SLA:units="m"; SLA:_FillValue=NaNf; SLA:long_name="SeaLevelAnomalyEstimate";//globalattributes: :DATE_CREATION="2015-11-06"; :Institution="JetPropulsionLaboratory"; :Conventions="CF-1.5";}References

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