developing a global assimilation and modeling framework to

DevelopingaglobalassimilationandmodelingframeworktoproduceSWOTdataproducts

KostasAndreadis1,DongyueLi2,DennisLettenmaier3,SteveMargulis2

1JetPropulsionLaboratory,CaliforniaInstituteofTechnology2DepartmentofCivilandEnvironmentalEngineering,UniversityofCalifornia,LosAngeles3DepartmentofGeopgraphy,UniversityofCalifornia,LosAngeles

IntroductionandObjectivesAlthoughobservationsfromSWOTwillbetremendouslyimportantforhydrologicscience,therearecertainlimitations.OneisthediscontinuityinspaceandtimeofSWOT-derivedwatersurfaceelevations,dischargeandstoragechange.DuetotheorbitalcharacteristicsofSWOT,waterbodieswillbeobservedbetween2and>10timespercycledependingonlatitude.Forexample,thenumberofobservationsintheAmazonRiverbasinwillrangefrom2-4timesperrepeatcyclewhereastheLenaRiverwillbeobserved4-10times.Thiscouldproveproblematicwhenattemptingtoderiveaggregate(weekly,monthlyorseasonal)estimatesofriverdischargeforinstance,orlake,reservoir,orwetlandstoragechange.Forexample,ifagivenriverissampledonlytwiceperrepeatcycleandthoseobservationscoincidewithpeak(low)flowstherewillbeanover(under)-estimationofdischarge.AmethodologytogenerateproductswithspatiallyandtemporallycontinuousfieldsofSWOTobservableswouldbehighlydesirable.Dataassimilationissuchamethodology;itcanmergeobservationsfromSWOTwithmodelpredictionsinordertoproduceestimatesofquantitiessuchasriverdischarge,storagechange,andwaterheightsforlocationsandtimeswhenthereisnosatelliteoverpassorlayoverrendersthemeasurementunusable.

OurprojectaimstodevelopamodelinganddataassimilationframeworkthatcanbeimplementedefficientlyforgeneratingaSWOTLevel4dataproductsconsistingofcontinuousfieldsofwatersurfaceelevation,discharge,andstoragechangeglobally.Specifically,theobjectivesoftheproposedresearchinclude:1. DevelopaframeworkforgeneratingaLevel4SWOTdataproductthatprovides

continuousfieldsofwatersurfaceelevation,discharge,andstoragechange.2. EvaluatedataassimilationalgorithmsforSWOTobservations.3. QuantifyerrorsinestimatingwateravailabilityfromusingtheLevel3and4

products.4. EvaluatewhetherSWOTobservationscanbeusedtoestimatehumanimpacts

onthewatercycle(e.g.reservoirs,diversions).

5. Deriveadatasetofrunofffieldsanddemonstrateitsvaluebycalibratingahydrologymodelagainstit.

ApproachOuroverallapproachtodevelopingamodelingandassimilationframeworkforgeneratinghigh-levelSWOTdataproductsconsistsofthecouplingofahydrologicandhydrodynamicmodelandtheirmodificationsothatSWOTobservationscanbeassimilated.Theexperimentaldesign(identicaltwinsyntheticexperiment)startswiththecoupledmodelgenerating"true"fieldsofsurfacewatervariables(e.g.waterheight,discharge,storagechange,andrunoff)usingabaselineconfiguration.The"true"fieldsarethenusedtogeneratesyntheticSWOTobservationsoverthestudyareaswiththeproperorbitandaccuracycharacteristics.ThelatteraredefinedusingtheSWOTInstrumentSimulator.A"first-guess"(oropen-loop)simulationwasalsoperformedwiththecoupledmodelusingaconfigurationthatcontainserrorsrepresentingtheimperfectknowledgeofparametersandinputdata.SubsequentlythesyntheticSWOTobservationswereassimilatedintotheopen-loopmodeltoestimatedischargeandstoragechange.Finally,theoutputoftheassimilationmodeliscomparedwiththedesignated“true”fieldsinordertovalidatetheapproach.

ThecoupledmodelingframeworkconsistsoftheVariableInfiltrationCapacity(VIC)hydrologymodelandtheLISFLOOD-FPhydrodynamicmodel.VICsolvesthelandsurfaceenergyandwaterbalancesoveragriddeddomainusingasoil-vegetation-atmosphereschemethatmodelshowmoistureandenergyfluxesbetweenlandandatmospherearecontrolledbyvegetationandsoil.Oneofthemodel’sadvantagesisitsrepresentationofsub-gridvariabilityinsoils,vegetationandtopographyviathepartitioningofeachgridcellintotilesofuniformphysiography.AlthoughVICincludesasimpleflowroutingmodelthattransportsthegeneratedrunoffandbaseflowofeachgridcellthroughtherivernetwork,ithascertainlimitationsthatprecludeitfrombeingusedinconjunctionwithSWOTobservations.LISFLOOD-FPovercomestheselimitationsandsimulateswaterflowthrougheachmodelgridcellbysolvingtheinertialmomentumequationthroughasingleexplicitfinitedifferencescheme.Theresultingmodelissimpleyetcontainsenoughphysicstodescribefloodandriverflowprocessesadequatelywhilerequiringanorderofmagnitudefewercomputationaloperationsthanafullshallowwatermodel.

Figure1.MapoftheUpperMississippiRiverbasinanditstopography,alongwiththesimulatedrivers.

ThestudydomainforthefirstexperimentistheUpperMississippiRiverbasin(Figure1),andthecoupledmodelwasusedtosimulatehydrodynamicvariablesat1-kmspatialresolution.The"truth"modelusestheNationalElevationDataset(NED)DEMtoderivetherivernetwork(thresholdedat10,000km2drainage),riverchannelwidthsanddepthfromtheHydroSHEDSdatabase,andinflowssimulatedbyVICusingmeterologicaldata(precipitation,airtemperature,andwindspeed)at1/16o.Theopen-loopsimulationusesaDEMderivedfromtheShuttleRadarTopographyMission(SRTM),andaddserrorstothebankfullwidthsanddepthsaswellastheinflowscreatinganensembleof20modeltrajectories.The"truth"modelsimulationwasabletoreproduceriverdischargewithreasonableaccuracyovera3-yeartimeperiod(selectedtomatchthedesignlifecycleofSWOT).Figure2showsacomparisonofthe"truth"-simulateddischargewithactualmeasurementsfromaUSGSgauge.

Figure2.Validationofthe"truth"-simulated(redline)riverdischargeagainstin-situmeasurements(blueline).

The"truth"watersurfaceelevations(WSE)wereusedasinputstotheSWOTInstrumentSimulatortoproducethesyntheticobservations.Inordertocorrectlyrepresenterrorsfromtopographiclayover(amongothererrors),the1-kmWSEfieldsweredeemedinadequateandweresubsequentlydownscaledtoa30-mspatialresolution.ThesyntheticSWOTobservationsaretheassimilatedintotheopen-loopmodelbyusinganumberofalgorithmsthatarevariantsoftheEnsembleKalmanFilter(EnKF).TheEnKF,andtheKalmanFilteringeneral,solvetheoptimalestimationproblembyupdatingthemodelstatebasedontheerrorsofboththemodelpredictionsandtheobservations.TheuncertaintyinthemodelandtheobservationsisrepresentedthroughanensembleusingaMonteCarloapproachanda-prioriassumptionsaboutthestatisticsoftheseerrors.ThealgorithmstestedincludetheEnKF,thesquare-rootEnKF(SQRTENKF),andtheLocalEnsembleTransformKalmanFilter(LETKF).

AnalysisandAnticipatedResultsTheSWOTInstrumentSimulatorisrelativelyexpensivecomputationally,andgiventhesizeofthestudydomainwearetestinganapproachtoapproximatetheerrorsatthe1-kmscale.Theapproachinvolvestheselectionofrepresentativesubdomains,whichmakerunningtheInstrumentSimulatormoretractable,andthe

derivationofprobabilitydistributionfunctions(PDF)oftheerrors(afterbeingaggregatedto1-km)conditionedtophysiography(topography,riverwidth,landcover).TheerrorPDFsthenareusedtosampleerrorsfortheentiredomain,matchingtheorbitalcharacteristics(i.e.spatialcoverage)ofSWOT.Figure3showsanexampleofthegeneratedsyntheticSWOTobservationsforanumberofpassesoverthestudydomain.

Figure3.ExampleelevationmapsoverUpperMississippiRiverbasinfordifferentsatelliteoverpasses.

Animportantaspectofthedataassimilationalgorithmsisthedefinitionoftheobservationoperator(i.e.themappingfunctionalbetweenthepredictedvariablesandobservations).Inthecaseofhydrodynamicmodeling,thisbecomescomplicatedduetotheerrorsinrivertopologybetweenthe"truth"andopen-loopsimulations.Inaddition,theexperimentaldesignintroducederrorsinmultipleparameters(inflows,channelwidthanddepth,roughness)makingtheassessmentofSWOTdataassimilationmorerealisticthanpreviousandcurrentwork.Inordertoaccountforthedifferingrivertopology,weperformedtheassimilationin"reprojected"coordinatesexpressingthevariablesintermsofflowdistance.

Figure4showsacomparisonofthethreedataassimilationalgorithmswiththeopen-loopand"truth"simulationsintermsofthedownstreamprofileofWSEofariverreachoftheMisouriRiver.TheLETKFappearstooutperformtheothertwoKalmanfiltervariantsbybetterreproducingthepools,whichcouldbeattributedtothelocalizationinherentinthealgorithm.Nonetheless,allassimilationalgorithmsimprovetheestimationofWSEovertheentirelengthoftheriverreach,whencomparedwiththepriorestimate.

Figure4.ComparisonofalgorithmsassimilatingsyntheticSWOTobservationswithrespecttowatersurfaceelevationspatialprofilesoverareachoftheMissouriRiveronspecificdate.

WeexpecttotestandestablisharobustmodelingandassimilationframeworkforSWOTobservations,anddemonstrateitsfeasibilityforoperationalimplementationovercontinental-scaleriverbasinsaswellasglobally.Theaddedvalueofthehigher-levelversustheinstantaneous(Level2)dataproductwillbeassessedbycalculatingandthencomparingtemporally-aggregateddischargeandstoragechangeforweekly,monthly,andseasonalperiods.Theevaluationoftheproductwillalsobeperformedseparatelyforrivers,lakes,wetlandsandreservoirsandtheerrorswillbelinkedtocharacteristicssuchasbasinphysiography,riverchannelwidth/slopeetc.providingsomeinsightintotheexpectederrorsinareasotherthanourtestcases.

TheframeworkwearedevelopingwillproducetemporallycontinuousestimatesofdischargethatcanalsobeusedtocalibratetheVIChydrologymodel.Streamflowistheresponseoftheintegrationofrunoffinspaceandtime(mathematicallyrepresentedbytheroutingmodel).Hence,runofffieldscanalsobeusedtocalibratehydrologicmodels(onagridcellbygridcellbasisforspatiallydistributedmodels).ThederivationofrunofffieldsfromSWOTobservationscouldgreatlyfacilitatehydrologicmodelcalibration,whichisinmanyrespectstheAchillesHeelofhydrologicmodeling.Runoff,thekeyquantityproducedbyspatiallydistributedmodels,isnotdirectlyobserved,andinsteadstreamflowmeasurementsaretypicallyused,whichhasmanydrawbacks(includingpoorlyposedmodelidentification,whichcanresult,forinstance,in“cliffs”atbasinboundaries.Streamflowisanintegratedmeasureofthehydrologicprocessesoftheriverbasin;hencethehydrologicsignalattheoutlet(orstreamflowmeasurementlocation)losesanyspatialandtemporalinformationupstreamatsmallerorshorterscales.Theworkofthisprojectcouldalleviatetheselimitationsbyfacilitatingandallowing

theestimationofspatiallydistributedmodelparametersaswellasatungaugedbasins.