use of remote-sensing reflectance to constrain a data

1

Useofremote-sensingreflectancetoconstrainadataassimilatingmarinebiogeochemicalmodeloftheGreatBarrierReef.EmlynM.Jones1,MarkE.Baird1,MathieuMongin1,JohnParslow1,JennySkerratt1,NugzarMargvelashvili1,RichardJ.Matear1,KarenWild-Allen1,BarbaraRobson2,FarhanRizwi1,Peter5Oke1,EdwardKing1,ThomasSchroeder3,AndySteven3andJohnTaylor41CSIROOceansandAtmosphere,Hobart,Australia,7000

2CSIROLandandWater,Canberra,Australia,2601

3CSIROOceansandAtmosphere,Brisbane,Australia,410210

4CSIROData61,Canberra,Australia,2601

Correspondenceto:EmlynM.Jones(emlyn.jones@csiro.au)

Keywords:GreatBarrierReef,DataAssimilation,RemoteSensing,observedOC3M,Reflectances,Biogeochemical(BGC)Model,Chlorophyll15Abstract:Skillfulmarinebiogeochemical(BGC)modelsarerequiredtounderstandarangeofcoastalandglobalphenomenasuchaschangesinnitrogenandcarboncycles.TherefinementofBGCmodelsthroughtheassimilationofvariablescalculatedfromobservedin-waterinherentopticalproperties(IOPs),suchasphytoplanktonabsorption,isproblematic.Empirically-derivedrelationshipsbetweenIOPsandvariablessuchas20Chlorophyll-aconcentration(Chl-a),TotalSuspendedSolids(TSS)andColorDissolvedOrganicMatter(CDOM)havebeenshowntohaveerrorsthatcanexceed100%oftheobservedquantity.Theseerrorsaregreatestinshallowcoastalregions,suchastheGreatBarrierReef(GBR),duetheadditionalsignalfrombottomreflectance.Ratherthanassimilatequantitiescalculatedusingerror-proneIOPalgorithms,thisstudydemonstrates25theadvantagesofassimilatingquantitiescalculateddirectlyfromthelesserror-pronesatelliteremote-sensingreflectance.Theassimilationofadirectly-observedquantity,inthiscaseremote-sensingreflectance,isanalogoustotheassimilationoftemperaturebrightnessinNumericalWeatherPrediction(NWP),oralong-tracksea-surfaceheightinhydrodynamicmodels.Toassimilatetheobservedreflectance,weuseanin-wateropticalmodelto30produceanequivalentsimulatedremote-sensingreflectance,andcalculatethemis-matchbetweentheobservedandsimulatedquantitiestoconstraintheBGCmodelwithaDeterministicEnsembleKalmanFilter(DEnKF).UsingtheassumptionthatsimulatedsurfaceChl-aisequivalenttoremotely-sensedOC3MestimateofChl-aresultedinaforecasterrorofapproximately75%.Alternatively,assimilationofremote-sensingreflectanceresultedina35forecasterroroflessthan40%.Thus,inthecoastalwatersoftheGBR,assimilatingremote-sensingreflectancehalvedtheforecasterrors.Whentheanalysisandforecastfieldsfrom

2

theassimilationsystemarecomparedwiththenon-assimilatingmodel,anindependentcomparisontoin-situobservationsofChl-a,TSS,anddissolvedinorganicnutrients(NO3,NH4andDIP)showthaterrorsarereducedbyupto90%.Inallcases,theassimilationsystemimprovestheresultcomparedtothenon-assimilatingmodel.Thisapproachallowsfortheincorporationofvastquantitiesofremote-sensingobservationsthathaveinthepastbeen5discardedduetoshallowwaterand/orartefactsintroducedbyterrestrially-derivedTSSandCDOM,orthelackofacalibratedregionalIOPalgorithm.

1Introduction:

Aquaticbiogeochemical(BGC)modelshavebeenusedtounderstandarangeofcoastaland10globalphenomenasuchoceanacidification(Monginetal.,2016),nutrientpollution(Skerrattetal.,2013)andcarboncycles,andarecentraltoourpredictionsofglobalclimate(SarmientoandGruber,2006).Atthecoastal/regionalscale,non-linearbiogeochemicalprocessesdrivenbyplanktonicinteractions,aswellasnon-linearcirculationfeaturessuchasmesoscaleeddies,limitthetimescaleoverwhichbiogeochemicalpropertiesare15deterministicallypredictable(Baird,2010).Forthepurposesofprediction,itisthereforenecessarytoassimilateobservationstocorrectformodelerrorsandnon-linearprocesses.Theassimilationofremote-sensingdataintomarinebiogeochemicalmodelshasbeenproblematicduetodifferencesbetweenthevariablesrepresentedinmodelsandthe20variablesthatareroutinelyobserved(Bairdetal.,2016b).Insituobservationsofphytoplanktonpigmentsandmacro-nutrientsaresparseinspaceandtimeduetotheprohibitiveexpenseofcollectingthem.Opticalsensorsonglidersandfloatsprovidehighresolutioninsituobservationsthatareusedtoestimatepigmentandnutrientconcentrations.Nonetheless,theseobservationsinlargepartsoftheoceanremainsparse.25ThemostspatiallycomprehensivedatasetavailableforBGCassimilationisfromoceancolorremotesensing.Itiswellknownthatoceancoloralgorithms,suchasobservedOC3M(ModerateResolutionImagingSpectroradiometer,MODIS,three-bandChl-aalgorithm)thatareoptimizedfor30globalapplicationssufferfromerrorsduetoavarietyofoptically-activeconstituentsincoastalandshelfwaters(Odermattetal.,2012).Furthermore,ithasalsobeennotedthatevengloballythereisanon-uniformdistributionoferror,andsubstantialbias,intheOC3M-derivedchlorophyll-aconcentration(Chl-a).Satellite-derivedoceancolorproductssuchasChl-aareafunctionofobservedsurfacereflectances.Asubstantialeffortisinvestedin35empiricalstudiesthatconvertreflectancetoobservablequantitiessuchasChl-a),TotalSuspendedSolidconcentration(TSS),phytoplanktonfunctionaltypes(PFTs),andColoredDissolvedOrganicMatter(CDOM)(Odermattetal.,2012).Eachoftheseempiricalrelationshipshavedifferingerrormagnitudesstemmingnotonlyfromadifferenceinkind,butalsorepresentationerrors.40Numericalweatherprediction(NWP)overcomeserrorsduetoadifferenceinkindthroughusingthemodeltosimulatedirectlyobservedquantities,suchastemperaturebrightness,inpreferencetoderivingotherquantitiesfrombrightnessmeasurementsandusingthosederivedquantitiesformodeldataassimilation.ThusNWPcommonlyassimilatesbrightness45

3

temperatureinpreferencetotemperatureitself(Deeetal.,2011).Thegoalofthisstudyisapplythisapproachtomarinebiogeochemicalmodelling,assimilatingremote-sensingreflectanceratherthanquantitiescalculatedusingerror-proneIOPalgorithms.TheGreatBarrierReef(GBR)islocatedalongthenortheastcoastlineofAustraliaandis5characterizedbyfringingreefsalongthecontinentalslopethatcreateasemi-connectedinshorelagoonthatspansover3000kmofcoastline(Figure1).TheGBRecosystem,describedasoneofthesevennaturalwondersoftheworld,isunderincreasingpressurefromlocalandglobalanthropogenicstressors(De'athetal.,2012).DecreasingwaterclarityduetonutrientandsedimentpollutionisconsideredaseriousthreattotheGBRecosystem10(Thompsonetal.,2014),withmajorconcernsbeingtheimpactoflowerbenthiclightlevelsoncoralandseagrasscommunities(Collieretal.,2012;Bairdetal.,2016a).ThemanagementofhumanimpactsontheGBRreliesonaccurateestimatesofthebiogeochemicalstateofthecoastalocean.Managementauthoritiesuse,amongother15measures,awaterqualityindexthatcombinesestimatesofconcentrationsofsuspendedsediment,chlorophyll,particulatenitrogenandparticulatephosphorus,aswellasSecchidepth(Schaffelkeetal.,2011).ObservationsofthesequantitiescomefromtensofsitesaroundGBR,whicharealsousedintheskillassessmentofthemodelandassimilationsystem.Nonetheless,witha3000kmcoastline,insituobservationsaresparseand20intermittent.Ultimately,themostaccurate,andbest-resolved,estimateofthebiogeochemicalstateofGBRwillbeobtainedthroughthesynthesisofallinsituandremotely-sensedobservationswithadditionalinformationfrommodelsimulationsusingadataassimilatingsystem.Inthispaper,wemovetowardsthisgoalthroughassimilationofsatellite-derivedremote-sensingreflectance,whilebuildingconfidenceintheapproach25throughwithholdinginsituobservationsforindependentmodelassessment.Thepaperisstructuredinthefollowingmanner,inSection2(Methods)thedataforassimilationandskillassessmentispresented,alongwithadescriptionofthemodelandassimilationmethodsused.Section3containstheresultsfromthecontrol(noassimilation)runofthemodel,andsubsequentdataassimilationexperiments.InSection4wediscussthe30approachusedandimplicationsofthefindingmoregenerally.AndweconcludewithmajorfindingsinSection5.

2Methods:

2.1GBRobservations35

TheIntegratedMarineObservingSystem(IMOS)hasdeployedfluorometersonmoorings,glidersandatYongalaandNorthStradbrokeNationalReferenceStations(NRS).Inthispaperweusethemonthlyobservationsofdissolvedinorganicnutrients(NO3,NH4andDIP)attheNRSsites(Lynchetal.,2014),andIMOSglidertransectsshowthecross-shelfprofile40ofwatercolumnproperties,includingtemperature,salinity,andchlorophyll.TheselocationsareshowninFigure1.

4

TheAustralianInstituteofMarineScience(AIMS)ReefRescuenetwork(Figure1,yellowcircles)contains14sitesininshoreregionsandGBRlagoon,andsamplenutrientsandChl-aextractions3timesayear(Thompsonetal.,2011;RolfeandGreg,2015).ThemooringsweredeployedattheReefRescuesitesfrom2009to2014andincludedaSea-Birdwaterqualitymonitors(WQM)thatmeasurechlorophyllfluorescenceandturbidity(NTU).A5comparisonofthe2011-2014controlrunsimulationagainsttheReefRescueobservations,andotherobservations,isavailableat:https://research.csiro.au/ereefs/models.

2.2MODISobservations

Theobservedremote-sensingreflectanceisobtainedfromusingMODIS-Aquaandan10atmosphericcorrectiondevelopedfortheregion.TheatmosphericcorrectionappliedanArtificialNeuralNetwork(ANN)approachtrainedbyaradiativetransfermodeltoinvertthetopofatmosphere(TOA)signalmeasuredbyMODIS-Aqua.TheANNalgorithmwasadaptedtoanapproachpreviouslydevelopedfortheMEdiumResolutionImagingSpectrometer(MERIS)sensorbutonthebasisofadifferentlearningalgorithm(Schroederetal.,2007).15AlgorithmperformanceisdescribedindetailinGoyensetal.(2013)andKingetal.(2014).SeaDAS-providedLevel-2flagswereusedtoqualitycontroltheobservedremote-sensingreflectanceandtoexcludeerroneousandout-of-rangepixels.Wefilteredthedataforlandandseveresunglintaffectedpixels,cloudcontaminationincludingcloudshadowsand20rejectedpixelswithobservingandsolarzenithanglesabove52°and70°,respectively.Forthecomparisonwithmodeloutput,theobservedremote-sensingreflectanceatthecentreofthe4kmgridcellisobtainedthroughinterpolationfromthe1kmobservations.

2.3TheeReefsmodellingsystem25

WeusedtheeReefscoupledhydrodynamic,sedimentandbiogeochemicalmodellingsystem(Schilleretal2014).Thehydrodynamicmodelisafullythree-dimensionalfinite-differencebaroclinicmodelbasedonthethreedimensionalequationsofmomentum,continuityandconservationofheatandsalt,employingthehydrostaticandBoussinesq30assumptions(Herzfeld2006;HerzfeldandGillibrand2015).Thesedimenttransportmodeladdsamultilayersedimentbedtothehydrodynamicmodelgridandsimulatessinking,depositionandresuspensionofmultiplesize-classesofsuspendedsediment.

(Margvelashvili2008).Thecomplexbiogeochemicalmodelsimulatesoptical,nutrient,plankton,benthicorganisms(seagrassmacroalgaeandcoral),detritus,chemicaland35sedimentdynamicsacrossthewholeGBRregion,spanningestuarinesystemstooligotrophicoffshorereefs(Bairdetal.,2016b).Thebiogeochemicalmodelconsidersfourgroupsofmicroalgae(smallandlargephytoplankton,Trichodesmiumandmicrophytobenthos),2zooplanktongroups,threemacrophytestypes(seagrasstypescorrespondingtoZosteraandHalophila,macroalgae)andcoralcommunities.40Photosyntheticgrowthisdeterminedbyconcentrationsofdissolvednutrients(nitrogenandphosphate)andphotosyntheticallyactiveradiation.Microalgaecontaintwopigments(chl-aandanassessorypigment),andhavevariablecarbon:pigmentratiosdeterminedusinga

5

photoadaptationmodel(describedinBairdetal.,2013).Overall,themodelcontains23optically-activeconstituents(AppendixA).Themodelisforcedwithfreshwaterinputsat21riversalongtheGBRandtheFlyRiverinsouthwestPapuaNewGuinea.Riverflowsinputintothemodelareobtainedfromthe5DERM(DepartmentofEnvironmentandResourceManagement)gaugingnetwork.Algorithmicrelationshipsareusedtoaccountfornutrientandsedimentinputsfromriversintothemodel(statisticalrelationshipsbetweenriverflowandnutrientconcentrations(Furnas2003,Furnasetal2011).NutrientconcentrationsflowinginfromtheoceanboundarieswereobtainedfromtheCSIROAtlasofRegionalSeas(CARS)2009climatology10(Ridgwayetal.,2002).

2.4Calculationofremote-sensingreflectancefrombiogeochemicalstate

Themodelcontains23optically-activeconstituents(AppendixA).Tocalculatetheremote-sensingreflectanceatthesurface,weneedtoconsiderthelightreturningfrommultiple15depths,andfromthebottom.Ratherthanusingacomputationally-expensiveradiativetransfermodel,weapproximatesurfacereflectancebasedonanoptical-depthweightedscheme(Bairdetal.,2016b).Theratioofthebackscatteringcoefficienttothesumofbackscatteringandabsorptioncoefficientsforthewholewatercolumnatwavelength,λ,is:20𝐮𝛌 =

𝐰𝛌,𝐳(𝐛𝐛,𝛌,𝐳(𝐚𝛌,𝐳(+𝐛𝐛,𝛌,𝐳(

𝐝𝐳′𝐳𝟎 Eq1

wherewλ,z’isaweightingrepresentingthecomponentoftheremote-sensingreflectanceduetotheabsorptionandscatteringatdepthz’,andzisthebottomdepth.25Theweightingfractionisgivenby:𝐰𝛌,𝐳 =

𝟏𝐳𝟏0𝐳𝟎

𝐞𝐱𝐩 −𝟐𝐊𝛌,𝐳( 𝐝𝐳′𝐳𝟏𝐳𝟎

Eq2

whereKλistheverticalattenuationcoefficientatwavelengthλandthefactorof2accounts30forthepathlengthofbothdownwellingandupwellinglight.Theverticalattenuationcoefficientiscalculatedfromthesumoftheabsorptionandscatteringpropertiesofeachoftheoptically-activeconstituents,andthezenithangle(foreachoftheserelationships,andmoreinformation,seeBairdetal.,2016).35Theintegralofwλ,z’toinfinitedepthis1.Inareaswherelightreachesthebottom,theintegralofwλ,z’tothebottomislessthanone,andbenthicreflectanceisimportant.Thesub-surfaceremote-sensingreflectance,rrs,isgivenby:40𝐫𝐫𝐬 = 𝐠𝟎𝐮𝛌 + 𝐠𝟏𝐮𝛌𝟐 Eq3whereg0=0.0895andg1=0.1247arecoefficientsforthenadir-viewinoceanicwatersthatvarywithwavelengthandotheropticalproperties(Moreletal.,2012),butcanbe

6

approximatedasconstants(Leeetal.,2002).Theconstantsresultinachangeofunitsfromtheunitlessutoaperunitofsolidangle,sr-1,quantity,rrs.Theabove-surfaceremote-sensingreflectanceisgivenby(Leeetal.,2002):5𝐑𝐫𝐬,𝛌 =

𝟎.𝟓𝟐𝐫𝐫𝐬,𝛌𝟏0𝟏.𝟕𝐫𝐫𝐬

Eq4

Thus,theabove-surfaceremote-sensingreflectanceiscalculatedfromtheinherentopticalpropertiesoftheoptically-activeconstituentsinthebiogeochemicalmodel.

2.5DataAssimilationSystem10

TheDataAssimilation(DA)algorithmusedinthisstudyistheDeterministicEnsembleKalmanFilter(DEnKF;SakovandOke,2008).Thefullbiogeochemicalstatevariablelistcontainsover1302Dand3Dvariables,andincludingalloftheseintheassimilationsystemisimpracticalduetomemoryconstraints,butwealsoacknowledgethatformanyvariables15theobservationswillbeuninformative,andthereforenotgoodcandidatestoincludeintheassimilationstatevector.WethereforelimitthevariablesthatareupdatedwithinthesystemtoaselectsubsetthataredetailedinSection2.4.2.

2.5.1DataAssimilationAlgorithm20

TheDEnKFisbasedontheKalmanfilteranalysisequation,ofwhichvariousflavourshavehadgeneralsuccessinstateestimationinothermarineBGCdataassimilationproblems(e.g.Huetal.,2012,Ciavattaetal.,2016).ThederivationoftheDEnKFisgiveninSakovandOke(2008)andisamodificationtothetraditionalKalmanfilterequation:25𝐱𝐚 = 𝐱𝐟 + 𝐊(𝐘 − 𝐇𝐱𝐟) Eq5Wherexisthemodelstate,Yisthevectorofobservations,Histheobservationoperator,andthesuperscriptsofaandfdenotetheanalysisandforecastfieldsrespectively.Inthis30study,weonlyuseasubsetofthestatevariablesintheDEnKFupdate,thosevariablesnotincludedinthestatevectorsdenotedinTable1arenotalteredbythestateupdate.TheForecastInnovations(FI)aredefinedby:𝑭𝑰 = (𝒀 − 𝑯𝒙𝒇) Eq635TheKalmangainmatrix,K,isgivenby:𝑲 = 𝒍𝑷𝒇𝑯𝑻 𝑯𝑷𝒇𝑯𝑻 + 𝑹 0𝟏

Eq740Wherelisthelocalizationoperator,andRisobservationerrorcovariancematrix.Thebackgrounderrorcovariancematrix,P,isgivenby:

7

𝑷𝒇 = 𝟏𝒎0𝟏

(𝑿𝒊𝒇 − 𝒙𝒇)(𝑿𝒊

𝒇 − 𝒙𝒇)𝑻𝒎𝒊R𝟏 = 𝟏

𝒎0𝟏𝑨𝑨𝑻 Eq8

wheremistheensemblesize,andidenotestheithmemberoftheensemble.GiventhatweareusingaflavoroftheensembleKalmanfilter,thebackgrounderrorcovarianceisapproximatedbya36memberdynamicensemblewhereby𝑿T

Uistheithensemblemember,5andxistheensemblemean.Toavoidnegativevaluesandnormalizethestate,welog-transformthestatebeforeformingthestatevector.Thebackgrounderrorcovariancematrixisneveractuallycomputed,ratheraseriesofanomalyfieldsareconstructedanddenotedbyA.WethenconstructtheKalmangainmatrixintheobservationsubspaceasperSakovandOke(2008)10𝑨 = [𝑨𝟏 …𝑨𝒎] Eq9wheretheithanomalyfieldisgivenby:𝑨𝒊 = 𝑿𝒊

𝒇 − 𝒙𝒇 Eq1015wherexisthetheensemblemeanandisupdatedviaEq5,eachanomalyfieldisupdatedby:𝑨𝒂 = 𝑨𝒇 − 𝟏

𝟐𝑲𝑯𝑨𝒇 Eq1120

Thefullanalyzedensembleisthengivenby:𝑿𝒂 = 𝑨𝒂 + [𝒙𝒂, … , 𝒙𝒂] Eq1225Theassimilationsystemiteratesthroughtimeusingafivedayforecastlength.Theassimilationsystemiscycledbycalculatingtheanalysisfieldsattimet,usingtheforecastfromthepreviouscycle,Xf(t),andobservationsY(t)attime(t+/-3hrs).ThenumericalmodeisinitializedusingtheanalysisfieldsXa(t)andthenextfivedayforecastismade.Thisforecastatt+5days,Xf(t+5),isthenusedinthenextassimilationcycle.30TheDEnKFrequirestheensembletobeperturbedinsuchawaythatiscapturesthemainsourceoferror.Theseperturbationsareintroducedinawaythatcapturesourpriorunderstandingofthethedominanterrors.InthissystemweexpectthaterrorswillstemfromuncertaintyintheInitialConditions(ICs)aspermostassimilationsystem.Additional35sourcesoferrorcanstemfromuncertaintyassociatedwithBGCprocessparameters,whichhasbeendiscussedatlengthinParslowetal.(2013),andriverboundaryconditions(BCs).Inthecontextofthisstudy,wehaveintroducedperturbationstotheensemblebysamplinginitialconditionsrandomlyforafouryearrunoftheBGCmodel:40𝑿(𝒕 = 𝟎)𝒊~𝑼𝒏𝒊𝒇𝒐𝒓𝒎 𝑿(𝒕 = 𝟎) , 𝑿(𝒕 = 𝑻) 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq13WhereX(t=0)iistheinitialconditionforthemodelstatefortheithmembersampledfora45uniformdistributionwithnoreplacement.WhereX(t=0)i=1istheensemblemean.Sensitivity

8

experimentshaveshownthemodelissensitivetoperturbationinthequadraticzooplanktonmortalityrateforlarge(mQ,ZS)andsmallzooplankton(mQ,ZL)withunitsofd-1(mgNm-3)-1.Theseareconsideredsystemparameters,andareassuchuncertain.Tothisendwehaveperturbedtheensemble,bysamplingspaceandtimeinvariantparametersfrom:5𝒎𝒒,𝒁𝑳,𝒊~𝑳𝑵 𝟎. 𝟎𝟏𝟐, 𝟏 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq14𝒎𝒒,𝒁𝑺,𝒊~𝑳𝑵 𝟎. 𝟎𝟎𝟕, 𝟏 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq15WhereLNisalog-normaldistribution.Therivernutrientandsedimentloadswerealtered10byatimeinvariantscalingfactor(𝜃)toallrivers:𝜽𝑵𝑶𝟑,𝒊~𝑵 𝟏, 𝟎. 𝟑 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq16𝜽𝑵𝑯𝟒,𝒊~𝑵 𝟏, 𝟎. 𝟑 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq17𝜽𝑫𝑰𝑷,𝒊~𝑵 𝟏, 𝟎. 𝟑 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq1815𝜽𝑭𝒊𝒏𝒆𝑺𝒆𝒅,𝒊~𝑵 𝟏, 𝟎. 𝟑 𝒇𝒐𝒓𝒊 = 𝟐…𝒎 Eq19WhereNisanormaldistributiontruncatedat0.Eachensemblememberhastheirload(Qi)scaledaccordingto:20𝑸𝒊 = 𝜽𝒊𝑸𝒄𝒐𝒏𝒕𝒓𝒐𝒍 Eq20where𝑄pqrstqu istheloadenteringthecontrolrun.

2.5.2Assimilationsystemexperimentsandconfiguration

25Inallexperimentswehavegeneratedasetofsuper-observations(Cummingsetal,2005;Okeetal.,2008)bycombiningtheobservedatmospherically-correctedremote-sensingreflectance(Schroederetal.,2008)at443,488and551nmintoasingleobservationusingtheOC3Malgorithm:30𝑶𝑪𝟑𝑴 =𝟏𝟎(𝒂𝟎+𝒂𝟏.𝑩+𝒂𝟐.𝑩𝟐+𝒂𝟑.𝑩𝟑+𝒂𝟒.𝑩𝟒) Eq21Wherea0,a1,…a4areasetofempiricallydeterminedcoefficients(e.g.NOMADversion2,http://seabass.gsfc.nasa.gov/wiki/article.cgi?article=NOMAD)andBis:35𝑩 = 𝒍𝒐𝒈𝟏𝟎(

𝑹𝒓𝒔,𝝀𝟏𝑹𝒓𝒔,𝝀𝟐

) Eq22

𝑅t},~�and𝑅t},~�aredeterminedbytheabsolutemagnitudeoftheremote-sensingreflectance,and𝑅t},~�iseitherthebandcentredon443nmor488nmand𝑅t},~�isthebandcentredon551nm.WeapplytheOC3Malgorithm(Eq.21)toboththeobservedand40simulatedremote-sensingreflectances.ThuswhenwecomparetheobservedandsimulatedOC3M,wearecomparingtwofieldsthatcontainthesameerrorcharacteristics.TheuseoftheobservedOC3Msuperobservationfieldisadvantageousfortworeason:1.)givenoursystemislimitedbymemory,wecanuse3timesmorespatiallocationsifwe

9

assimilatethesuper-observationOC3M,asopposedtoworkingwiththeindividualspectralbands;and2.)ptherelationshipbetweenindividualstatevariablesandremote-sensingreflectancesisattimesnon-linear,thusviolatingtheoneoftheunderlyingassumptionsoftheDEnKF.Incontrast,therelationshipbetweensimulatedandobservedOC3Mislinear.Additionally,therearestrongcross-correlationsbetweenthebands.Forexample,the5reflectanceat443nmisstronglycorrelatedwiththereflectanceat488nm.Therefore,theobservationsofadjacentbandsarenolongerindependentanditislikelythattheassumptionthattheoffdiagonalelementsoftheobservationerrorcovariancematrix(R),needstobereconsidered.Usingonesuper-observationseliminatesthepossibilityofcross-correlation.10Fourexperimentswerethenundertakentodeterminetheforecastskilloffourdifferentassimilationsystemconfigurationsusingasubsetofstatevariablesintheassimilationstatevector,andcorrespondingdiagonalelementsoftheobservationerrorcovariancematrix(R).Weonlyallowtheobservationstoupdatethevariablescontainedintheassimilationstate15vector.Theanalysedassimilationstatevectoristheninsertedintothefullmodelstatevector.InEXP1,wemaketheassumptionthattheobservedOC3MisequivalenttothesimulatedsurfaceChl-aandusethisastheinputintotheobservationoperator.InEXP2-4weassume20thatthesimulatedOC3MisequivalenttotheobservedOC3Manditisusedasinputintotheobservationoperator.Theassimilationsystempreservesthestoichiometryofthesmallandlargephytoplanktonasfollows.Inthebiogeochemicalmodel,eachphytoplanktoncell(small,large,benthicor25Trichodesmium)isrepresentedbyaquantityofstructuralmaterial,B,andreservesofnitrogen,RN,reservesofphosphorus,RP,reservesofenergy,RI,andanintracellularchlorophyll-aconcentration,ci.Ourintentionintheassimilationistochangethenumberofcells,asquantifiedbyB,notthephysiologicalstatusofthecell,asrepresentedbyRN,RP,RI,andci.Sincethereservesarequantifiedasthetotalofthesereservesacrosstheentire30population,eachofthereservesischangedbythesameproportionasthebiomass.Thus,forexample,thenitrogenreserveofanindividualcell,RN/B,isunchanged.Oncetheanalyzedquantityofciisdetermined(e.g.PhyL_Chl-aandPhyS_Chl-a),thequantitiesofRN,RP,RIandBareupdatedsuchthattherespectiveratiospriortoassimilationarepreserved.35

3Results:

3.1ControlRun

Themodellingsystemhasbeendesignedtorepresentthespatially-resolvedwaterqualitydynamics(phytoplankton,nutrients,turbidityandoxygen)oftheGBRWorldHeritageArea40forinformedmanagement.Anumberofindicatorshavebeenusedtoassesstheskillofthemodel,includingRMSerrors,Pearson’scorrelationcoefficients,Wilmott’sskillindicators(Wilmottetal.,1985;https://research.csiro.au/ereefs/models).

10

Thesimulatedstatevariableconcentrationsresembleboththeregionalclimatologyforoffshore-reef,lagoon-reefandnear-shorezonesandwaterqualityobservationsundercontrastingseasons/loadsandfloodevents[notshownhere,butdetailedathttps://research.csiro.au/ereefs/models,withoptical(Bairdetal.,2016b)andcarbon5chemistry(Monginetal.,2016)skillassessmentpublishedelsewhere].Asmentionedabove,themodelsimulatesremote-sensingreflectance.Itisthereforepossibletoincorporatethesereflectancesintostandard,well-recognizedremote-sensingproducts.Figure2presentsasnapshotofsimulatedsurfaceChl-aandthesimulatedOC3M,aswellasremotely-sensedproducts(regionalANN-observedOC3MandNASA-observedOC3M).10ThetwopanelsontherightsideofFigure2representthesimulated(top)andremotely-sensed(bottom)OC3MestimateofChl-a.Bothcombineindividualbandremote-sensingreflectanceintoproxiesforChl-ausingtheOC3Malgorithm.OC3MpoorlyrepresentssurfaceChl-aclosetothecoastwhereCDOMabsorptiondominates).Bycomparingthetwo15panels,wecanconcludethatthemodelrepresentsaccuratelythegeneraldistributionofChl-athroughouttheregion,withhighvaluesalongthecoastandaboveeachreefsystems,andlowconcentrationsoffshore.ThesimulatedsurfaceChl-ainsidethecoastalbandishigherthanintheremotely-sensedobservation.20ThetwopanelsontheleftofFigure2representsimulatedsurfaceChl-a(top)andOC3Mbasedontheregionally-optimizedremote-sensingreflectance(ANN-observedOC3M).SimilartoNASA-observedOC3M,butlookinginsidethecoastalbandthistime,thegeneralgradientofconcentrationsaresimilarinboththesimulatedOC3M(Figure2,topright)andtheremotely-sensingestimate(Figure2,bottomleft),butthemodelslightlyoverestimates25OC3M.

3.2Assimilationsystemconfigurationexperiments

30Tochoosethebestconfigurationfortheassimilationofremote-sensingreflectanceintoacoastalbiogeochemicalmodel,fourexperimentswereundertakenusingavarietyofstatevariablesinthestatevector(X,Table1),andbyalteringthediagonalelementsoftheobservationerrorcovariancematrix(R,Eq7).Theforecastinnovations(Eq6)forthefourassimilationsystemconfigurationexperimentsdescribedbelowareshowninFigure3:35

EXP1(greenlines,Figure3):Theerror-proneassumptionthattotalsurfaceChl-aisequivalenttoobservedOC3Mismadeandisusedtocalculatetheforecastinnovations,whicharethenusedtoupdatesmallandlargephytoplanktonChl-a.An80%errorintheANN-observedOC3MisprescribedonthediagonalelementsofR.40EXP2(redline,Figure3):SimulatedOC3M(calculatedfromsimulatedremote-sensingreflectanceatseveralwavelengths,asdescribedbyBairdetal.,2016b)isusedtocalculatetheforecastinnovations.ThestatevariableandobservationerrorsarethesameasEXP1.EXP3(blackline,Figure3):ThesameconfigurationasEXP2,withareducedobservederrorimposedonthediagonaloftheobservationerrorcovariancematrix.45

11

EXP4(blueline,Figure3):Additionalvariablesareincludedintheassimilationstatevector,whichnowcomprisesofsmallandlargephytoplankton,ammonia,nitrateandtotalsuspendedsolidsconcentrations.TheobservationerroristhesameasEXP3.

Theforecastinnovation(Eq6)statisticsfromeachexperiment(Figure3)provideinsightinto5theassimilationsystemperformance.Anoptimalassimilationsystemshouldresultinmeanforecastinnovations(mismatchesbetweenobservationsandthemodel)ofcloseto0,andlowmeanabsoluteinnovations.TheassimilationsystemwheretheobservationoperatorassumedthattherewasadirectrelationshipbetweensimulatedsurfaceChl-aandANN-observedOC3M(EXP1,Figure3greenline),performedverypoorlyandwasdiscontinued10after9cycles;themodelattimesbecamenumericallystiff,requiringtheadaptiveODEintegratortotakeprogressivelysmallersteps.TheinnovationstatisticsforEXP1suggestedthemodelwasconstantlyover-predictingChl-awiththemeanabsoluteinnovationexceeding0.7morethan50%ofthetime.CalculatingtheforecastinnovationswithsimulatedOC3MandANN-observedOC3MratherthansimulatedsurfaceChl-aand15observedANN-observedOC3Mimprovedinnovationstatisticsdramatically(EXP2-EXP4,Figure3).TheconfigurationusedforEXP4(Figure3,blueline)gavethebestperformance.AllsubsequentresultspresentedinthisstudyusetheEXP4assimilationsystemconfiguration,andweonlyrefertotheANN-observedOC3M.

3.3Assimilationsystemforecasterrorsinpreferredsystem(EXP4configuration).20

Theassimilationsystemwasrunwitha5-dayforecastcycle.Usingtheforecastatt+5daysandcomparingthetemporalmeanoftheRootMeanSquareDifference(RMSD)andPercentageErroragainstobservationsprovidesinsightintothevalueoftheassimilationsystem,whencomparedwithanon-assimilatingsystem.Bycomparingtheforecastfields25againstobservations,weareprovidinganindependentestimateofforecastskill,astheseobservationsatt+5dayshavenotyetbeenassimilatedbytheDAsystem.Additionally,bycomparingtheforecastagainstthepersistedanalysisfieldfromthepreviousanalysiscycle,itcanbedeterminedifthedynamicmodelisaddingskilltotheforecast.

30AcomparisonofsimulatedOC3MandobservedOC3Mforthenon-assimilatingcontrolrungivesadomainwidemedianerror(range)of0.32(0.27–0.48)mgm-3(Figure4).Thisisapproximatelyequivalenttoadomain-widemedianpercentageerror(range)of100%(80%-130%)(Figure4).Thedataassimilationsystemreducestheforecasterrorsandpercentageerrorstoamedianvalue(range)of0.23(0.20–0.30)mgm-3and55%(43%-63%)35respectively.Theanalysiserrorsareagainreducedwhenobservationsareassimilated,withmedianandpercentageerrors(range)of0.19(0.14–0.23)mgm-3and39%(37%-42%)respectively.Whentheanalysisfieldfromthepreviousassimilationcycleispersistedforward,theerrors(andpercentageerrors)slightlyexceedthatoftheforecastfieldwithvaluesof0.26(0.21–0.29)mgm-3and52%(44%-65%)respectively.However,itisnot40expectedthattheseerrorstatisticsarespatiallyuniformgiventhelargepercentageofareathatisdominatedbydeepoceanicwaters.Tounderstandthespatialvariabilityoftheforecasterrorstatistics,thewholedomainisdividedintothreeregionsrepresentingshallowcoastalwaters(depth<30m),lagoonandshelfwaters(30m<depth<500m),anddeepoceanicwaters(depth>500m).45

12

Inshallowcoastalareas,thenon-assimilatingcontrolrunhasamedianerror(range)of1.35(1.1–2.45)mgm-3,whichcorrespondstoapercentageerror(range)of130(105–180)%.Thedistributionofcontrolrunerrorsinthecoastalzoneispositivelyskewed,withthemeanvalueofthedistributionsittingsomewayfromthemedian.Theassimilationsystemmarginallyreducesthemedianforecasterrorwhencomparedwiththecontrolrun,though5mostnotably,itreducesthemedianpercentageerrorandassociatedvariability.Theforecastalsobeatspersistenceinthisregion.Thereisamarkedimprovementforlagoonandshelfwaterswiththeassimilationsystemreducingthemedianerrorfrom0.34to0.25mgm-3,whichcorrespondstoareductioninpercentageerrorfrom96%to48%.Intheoceanicregionsofthedomain,theassimilationsystemreducestheerrorfrom0.16to0.1010mgm-3,correspondingtoapercentageerrorreductionfrom91%to45%.Inallcasestheforecastfieldsbeatpersistence.AsummaryoftheresultscanbefoundinTable2andTable3.

3.3.1Forecast,IncrementandAnalysisFields15

ThesumofthesurfaceTrichodesmiumChl-a,SmallPhytoplankton(PhyS)Chl-aandLargePhytoplankton(PhyL)Chl-abiomassdifferssubstantiallyfromthesimulatedOC3MasshowninFigure5.Theassimilationsystemupdatesallofthestatevariablesincludedintheassimilationstatevector.SimulatedOC3Misadiagnosticvariablethatisafunctionofallthe20optically-activedynamicstatevariablesasdescribedinSection2.TodemonstratetheimpactonthedynamicvariablesofPhySandPhyL,resultsfromtheforecaststep,andtheassimilationupdate,arepresentedinFigure5,Figure6andFigure7.

ThesimulatedOC3Mforecastfieldforcycle22(12thSeptember2013)displayselevated25OC3MintheshallownearshoreenvironmentthroughoutthewholeofGBRregionandsouthernshelfofPapuaNewGuinea(PNG)(Figure5).AdditionalfeaturesareelevatedOC3Minthevicinityofthecentralandsouthernfringingreefs,andaplumeoriginatingfromtheeasternregionofPNG.OffshoreoceanicwatersgenerallyhavelowOC3Mof0.2mgm-3orless.Thereissomeevidenceofmesoscalebloomsinthenorthernandsouthern30sectionsofthedomain.ObservedOC3MisoverlaidonFigure5(left).Wherethereisadifferenceincolour,thesimulatedOC3MdiffersfromtheobservedOC3M.

TheforecastsurfacelayerfieldsforPhySandPhyLappearsubstantiallydifferenttothesimulatedOC3Mfield(Figure5).TherearesubstantialdifferencesnearthecoastwhereTSS35andCDOMareknowntocauseartefactsinOC3M.Whiletherearepatchybloomsofsmallphytoplanktonatvariouslocationswithinthedomain,rarelydoesthePhySChl-aexceed0.5mgm-3.TheexceptiontothisintheinnercentralcoastalregionoftheGBRandinthevicinityoftheFlyRiverplumeonthesouthcoastofPNG.Similarly,thePhyLChl-aremainsverylowforlargeareasofthedomain,howeverinregionswithadditionalnutrientsupply40(e.g.inupwellingregions,mesoscaleeddiesandsomerivermouths)bloomsdooccur.WhentheobservedOC3Misassimilated,incrementfieldsarecalculatedusingEquation5andarepresentedinFigure6forsimulatedOC3M,PhySChl-aandPhyLChl-a.TheinnovationsareoverlaidontheincrementfieldforOC3Mtogiveanindicationofhowwell45wearefittingtheobservations.InareaswherethemodelisoverpredictingOC3M,the

13

incrementswillbenegative.InareaswherethemodelisunderpredictingtheOC3M,theincrementswillbepositive.Theincrementsandinnovationsherearepresentedasafractionalchangewithrespecttothebackground(forecast)field.Forthisparticularanalysiscycle,itappearsthatthemodelisunderestimatinginshoreOC3M5byupto10-30%andoverestimatingOC3Mbyupwardsof50%offshore(Figure6,left).Byusingthebackgroundensemblecorrelationstructure,theincrementsappliedtoPhySbiomassaretoincreaseitsconcentrationintheinnerlagoonbyupto20%,butsubstantiallyincreasethePhySbiomassoffshoreofthecentralouterreefsbymorethan50%(Figure6,centre).Itshouldbenotedthattheincrementsbeingappliedtothebackgroundfields10containmesoandsub-mesoscaleinformation.Significantly,featuressuchasupwellingfilaments,eddiesandplumesaremaintainedthroughtheassimilationprocedure,demonstratingthattheyareallowedtodynamicallyevolveintheassimilationsystem.TheincrementsappliedtoPhyLbiomass(Figure6,right).differsubstantiallytothoseofPhySbiomass(Figure6,centre).Forlargeareasofthedomain,theassimilationsystemdecreases15thePhyLbiomassbyupto50%,whereastherearesomeareasthatitincreases.Theseareascorrespondtoregionswhereabloommaybeoccurring.Theincrementappliedtothecentralregionofthedomain,offshoreoftheouterreefs,islinearandcoherentandlikelyaresultofshiftingadynamicfeaturesuchasanupwelling-inducedbloomtobettermatchobservations.20 WhentheincrementscontainedinFigure6areappliedtotheforecastfields,theresultinganalysisfieldforsimulatedOC3MbetterfitstheobservedOC3M,withasubstantiallyreducederrorinshoreandinthevicinityoftheouterreefs(Figure7).ThedifferencebetweensimulatedandobservedOC3Missmallinthedeeperoffshoreregionsandshallow25sectionsofthelagoon.ThegreatesterrorinOC3Moccursinthecentrallagoonandtheouterreefswherespatialvariabilityishighest.ThecorrespondinganalysisfieldsforsmallphytoplanktonandlargephytoplanktonarecontainedinFigure6.Thereareelevatedconcentrationsofsmallphytoplanktonbiomassinthenearshoreregionnearrivermouthsandtheouterfringingreefs.Thelargephytoplanktonbiomassisconcentratedintheregion30ofBroadSound,theFlyRiverplume,andthePapuaNewGuineaupwelling.Eachofthesefeatureswaspredictedbytheforecast,aslittlebiomassisaddedorsubtractedbytheassimilationupdate.However,thereissubstantialremovaloflargephytoplanktonbiomassfromthenorthernandcentraloffshoreregions.Thisleavesverylittlelargephytoplanktonbiomasspresentinsubstantialareasofthedomainduringthisparticularanalysiscycle.35

3.3.2Independentassimilationsystemassessment:Glider

Thecontrolandassimilatingrunswerecomparedwithanoceangliderthatwasdeployedon26May2013,andrecoveredonthefourthofAugust2013.Theglidertracklargelyfollowedtheshelfbreakandheadedinasouth-easterlydirection.Tomakeacomparisonbetween40gliderobservationsandthemodel,wetakeasubsampleofgliderobservationscentredatthetimeofmodeloutput,withatimewindowoftwohours.Foreachgliderobservationthatfallswithinthistimeperiod,wefindacorresponding3-Dcellfromthemodelandextracttheequivalentmodelsolution.No3-Dinterpolationisperformedasthenon-interpolatedsolutionwillyieldinsightintotheunresolvedsubgridscalevariability.The45

14

unresolvedsubgridscalevariabilityisthenaccountedforintherepresentationerrorofthedataassimilationsystem.

Apersistentfeatureseeingintheobservedrecord(Figure8)istherelativelylowChl-aintheupper100mofwatercolumn.Formuchoftherecord,thereisapersistentdeep5chlorophyllmax(DCM)thatiscentredatbetween80and120mdepth.Rarelydoconcentrationsintheupper80mexceed0.5mg/m³.Whenthecontrolrunisexamined,Chl-ainthetop80mregularlyexceeds1mg/m³,DCMswhentheyexist,arelocatedbetween30and60mdeep.AdetailedanalysisofthecontrolrundemonstratesthemodelisabletoreliablyproducedDCMs,however,inthisparticularlocationintimeandspace,themodel10doesnotgenerateoneconsistentwiththeobservations.Theassimilationsystemimprovesthecontrolwhencomparedtotheglider,howeveritcannotplacetheDCMinthecorrectlocationbecausetheremotesensingobservationsprovidenoinformationaboutsuchadeepfeature.Theremotesensingobservationsdoremovethebiasintheupper80mwithconcentrationsintheassimilatingrunningrangingbetween0.1-0.3mg/m³.15Acomparisonbetweenindividualprofilesfromthegliderandequivalentsamplingofthemodelshowssubstantialunresolvedvariability.Figure9Ashowsthatatabout70mtheobservedChl-aasmeasuredbythefluorometerrangesbetween0.14and0.25mg/m³,withameanvalueof0.18mg/m³.Thesegliderprofilesfallwithintwoadjacentmodelcells.The20controlrungaveindistinguishablesolutionsinthesetwocells,whereastheassimilatingrunwasdifferentby0.3mg/m³betweenthesetwocells.Therangeinunresolvedvariabilityisthereforeapproximately50%ofthemeanvalue.Similarpatternsareseenacrossmostprofiles,asubsampleofwhicharegiveninFigures9b-f.Themagnitudeoftheunresolvedvariabilityrangesfrom5to40%.InallcasestheassimilationofobservedOC3Mhas25reducedtheerrorinthesimulatedChl-awhenassessedagainstindependentgliderdata.TheRMSDwhencalculatingforeachlayerofthemodel,andaggregatedintimeforallgliderobservations,isshowninFigure10.Above80m,thereisasubstantialreductioninRMSDbetweenthecontrolandassimilatingruns.TheassimilatingrunhasanRMSDofbetween300.10and0.17mgm-3comparedwith0.30to0.41mgm-3inthecontrolrun.Below80m,theRMSDprofileisverysimilarbetweenthecontrolandassimilatingrun.TheobservedOC3Mconstrainstheupper80m,anddoesnotdegradethesolutionbelow80m.

3.3.3Independentassimilationsystemassessment:In-situbottlesamples

35TheAIMSReefRescue(RR)mooringsweredeployedat14sitesintheshallowinshoreregionsoftheGreatBarrierReefLagoon(Figure1).ThecontrolruntypicallyhadRMSDsofbetween0.4and0.6mg/m3ofinsituChl-a(Figure11),withtheexceptionbeingGeoffreyBay,whichisknowntobeproblematicduetothepoorspatialresolutioninthisarea.InmostcasestheassimilatingrunreducedtheRMSDofinsituChl-aby10to0%.40

TheTSSRMSDvarieswidelyacrossalltheRRsites(Figure11),drivenbythestrongvariationinmagnitudeofthespring–neaptidalforcing.Thecombinationofperturbedforcing,andtheinclusionoftheTSSconstituentsinthestatevectorintheassimilatingmodel,hasgeneratedrealistictimevaryingcorrelationsbetweentheobservedOC3MandinshoreTSS.45Thesecross-correlationsallowforthecorrectionofsimulatedTSSfromOC3Mobservations.

15

TheTSSRMSDatallsitesfortheassimilatingrunislessthan5to20%thatofthecontrolrun.WithintheGBRregion,therearetwoIMOSNRSsites(YongalaandNorthStradbroke,NS,Figure1).ThedissolvedinorganicnutrientsofNO3,NH4andDIParetakenmonthly.At5Yongala,watersamplesaretakenatthesurface(0m),10m,20mandbottom(26m).AtNS,samplesaretakenatthesurface(0m),10m,20m,30m,40mand50m.Itshouldbenotedthatthereareonly3to4samplesperdepthateachsiteduringthesimulationperiod..AtYongala,typicalRMSDsforNO3rangefrom5to12mg/m³.TheimprovementatNSisconfinedtoshallowlayersabove20m.Below20mtheassimilationsystemdegrades10thesolutionby5to15%.

WiththeexceptionofthesurfacesamplesatYongala,theassimilationsystemimprovedthepredictionofNH4atalldepthsforeachsite.Mostnotablywasthe70to90%reductioninRMSDatthedeeperlocationsatYongala.ThereweremarginalimprovementstoDIP,which15displayeda0to30%reductioninRMSDacrossallsites.

4Discussion

Intheoptically-complexwatersoftheGBR,theuseofobservedremote-sensingreflectancetoconstraintheBGCmodelsubstantiallyreducestheerrorsinOC3MandinsituChl-a,TSSandnutrients.Thishasbeenachievedbyexplicitlyassimilatinglike-for-likevariables.The20dataassimilationisconstrainedbythemis-matchbetweensimulatedandobservedOC3M.Ourapproachofsimulatingtheobservationistheoppositetotheconversionofobservedremote-sensingreflectancesintomodelledvariables,e.g.theassimilationofphytoplanktonfunctionaltypes,TSS,CDOMandChl-a.Theconversionofreflectancesintoderivedvariables(e.g.Chl-a,PFTs)haveassociatederrorsthatareaslargeas200%issomelocations,andcan25bebiasedbyupto70%.Theseerrorsattimesaredifficulttocharacteriseinthedataassimilationsystems,andtheanalysisfieldscontainerrorsthatarelargerthantheforecastorfreerunmodelfields.Oursystemavoidstheseerrors.OneofthemostsignificantsourcesoferrorsinalgorithmssuchasOC3Misthatthey30produceasinglevalueforeachhorizontalpixel,generallyconsideredtoberepresentativeofthefirstopticaldepthofthewatercolumn.Ifthisistobecomparedtoasinglevalueinbiogeochemicalmodel,thenitmustbeassumedthatthewatercolumniswell-mixedtotheopticaldepth,andthatthereisanequalopticaldepthofeachofthewavebandsusedinthealgorithm.Bothoftheseconditionsarerarelymetincoastalwaters.Matchingremote-35sensingreflectancerequiresnoassumptionsaboutthestructureofthewatercolumn,oroftheverticaldistributionoftheoptically-activeconstituents,becausebothobservedandmodelledquantitiesaretwodimensionalfields.Inordertovisualisetheimpactoftheassimilationsystemonthepredictionofwaterclarity,40wecomparetheobservedtruecolour(Figure13)withthesimulatedtruecolourofthecontrolrun(Figure14,topleft)andtheassimilatedrun(Figure14,topright).Simulatedtruecolourimagesaregeneratedfromtheremote-sensingreflectanceatthered,greenandbluewavelengthscalculatedusingtheopticalmodelandthethreedimensionalfieldsofmodel-predicted23optically-activeconstituents.45

16

Theobservedtruecolourimageonthe12Sep2013showsbrown/yellowfeaturesassociatedwithhighsuspendedsedimentconcentrations.Astheseconcentrationsbecomemorediluted,andmixedwithphytoplankton,thewaterappearsmoregreenishblue.Offshorereefs,withclearwaterabovewhitesubstrates,appearaslightbluefeatures,with5theintensitydependingonthereefdepth.Qualitatively,thecontrolrun(Figure14,topleft)doesareasonablygoodjobofreproducingtheobservedtruecolour.Thequantificationofthismismatchcanalsobedoneonindividualcolorbands(Bairdetal.,2016b).Qualitatively,thecontrolrundoesnothaveenoughsuspendedsolidsinthesurfacewaterinthemouthofBroadSound(22.2°S,149.5°E),andhastoohighphytoplanktonconcentrationsoffshore,10especiallyinafeaturecentredat23°S,151.5°E.Theassimilatedrun,whilenotthatdifferenttothecontrolrun,correctssomeoftheseerrors.Toapproximatelyquantifyimpactsoftheassimilationofwaterclarity,itispossibleconsiderthecolouroftheadded(andsubtracted)constituentsintheassimilationprocedure.To15avoidconfusionwiththephrases‘falsely-coloured’or‘negative’,whichhavedistinctmeaningsinvisualisationscience,buttostillprovideaphrasefortruecolourerror,weusetheterm“off-colour”,anddistinguishbetweenoff-colourthatrequirescorrectionthroughaddition(Figure14,bottomleft)andsubtraction(Figure14,bottomright).Theassimilationprocedureaddedyellowcolours(suspendedsediment)withinBroadSoundandgreen20colours(phytoplankton)inthemouth.Offshoretheassimilationremovedgreen,particularly,asnotedaboveat23°S,151.5°E.Byremovinggreenitmadethewatermoreblue(Figure14,topright).Thegeneralmethodologypresentedinthisstudyissimilartothatusedinnumerical25weatherprediction(NWP).Theapproachtakenhereistoavoidtheuseofanempirical/statisticalinversemodel,anduseaphysics-basedforwardmodeltopredictremote-sensingreflectancecentredattheMODISbandwidths.Wethenpost-processthesesimulatedremote-sensingreflectancesintoasimulatedOC3M.ThesimulatedOC3MisdirectlycomparabletotheobservedOC3Mwithbothcontainingsourcesoferrorderived30frombottomreflectance,andturbidcoastalwaters.WehavetakenthefinalstepofconvertingthesimulatedremotesensingreflectancesintosimulatedOC3Masitremovesanumberofnon-linaritesassociatedwithworkingonrawreflectances,andtheassociatedcorrelatedobservationerrors.Additionally,itreducesthesizeofobservationvectorbyafactorofthree,allowingforagreaternumberofspatialpointstobeassimilated.Byavoiding35theuseofaninverseempiricalstatisticalmodel,wearepresentingaBGCDAapproachthathadbeenadoptedbytheNWPcommunitydecadesago(Deeetal.,2015).ByavoidingtheuseofIOP/AOPbasedempirical/statisticalproducts,thisapproachcantakeadvantagenon-ocean-colorspecificmissionssuchasHimawari8.ThespectralresolutioncanbealteredtosimulatereflectancesattheHimawari8truecolourbands.IftheHimawari408datacanbeassimilateditwillprovideastepchangeinthedataavailableforareassuchastheGBR,duetothehighspatialresolution(nominally500m)andtemporalresolution(every30minutes).Thisdatadensityfarexceedsthatavailablefromorbitingsatellites,andwillprovidecoveragesimilartotheproductsbeingassimilatedinNWPsystems.

45Theunderlyingconfigurationofthedataassimilationpresentedinthisstudyrequiresthedominanterrorsub-spacetobespannedbytheensemble.Pragmaticchoiceshavebeen

17

madetoallowthesystemtorunontheavailablecomputeresources.Tothisendwehaveperturbed2sensitivemodelparameters,andriverloadsofnutrientsandsediments.Thedistributionsthathavebeensampledtoperturbthezooplanktonmortalityratesand𝜃T alongwiththeirrespectiveshapeparameterscouldbeconsideredasubjectivechoice.ThereissubstantialscopeheretorecasttheproblemwithaBayesianHierarchicalModelling5(BHM)framework(asinParslowetal.,2013;andDowdetal.,2014),wherebythepriordistributionareassignedtouncertainparameters,andathoroughmeta-analysisoftheliteraturecouldbeusedtoconstructinformativedistributions.Theobservationscouldthenbeusedtoconstructnotonlyaposterioroverthestate,butafulljointposterioroverthestateandparameters.Furthermore,wehavenotalloweduncertaintyinthephysicsto10propagateintotheBGCsolution.Werecognisethisisashortcomingofthestudy,however,giventhecomputationalconstraints,wearenotinapositiontoexpandtheensembletoincludephysicsperturbations(whichwouldrequireanensemblethatisuptoanorderofmagnitudelarger).Asmorecomputingpowerbecomesavailable,ensemblesizescouldbeincreased,stochasticparameterisationsintroduced(Garnieretal.,2016),andDAmethods15withlessparametricassumptions(e.g.Parslowetal.,2013),couldbeadopted. TherehasbeentworecentdiscussionpapersreleasedthatdetailthepathwaytowardsoperationalisingBGCforecastingsystems(Gehlenetal.,2015;andFordetal.,2016),analogoustothecurrentNWPandhydrodynamicpredictionssystemthatroutinelyrunat20numerousoperationalcentres.Ithasbeenacknowledgedthatsatelliteremotesensingwillplayakeyroleinsuchsystems,thereappearstobetwodivergentpathwaystoachievethisvision.Fordetal.,(2016)advocatefortheassimilationofempiricalstatisticalproductssuchasChl-a,diffuseattenuationcoefficientsandPhytoplanktonFunctionalTypes(PFTs),withthealternativebeingtheassimilationofAOPssuchremote-sensingreflectances(or25subsequentfunctionalderivatives).Forcomplexcoastalregionsthataredominatedbycase2waters,theassimilationofremote-sensingreflectancesavoidsthecostlyrequirementofcalibratingaempirical/statisticalalgorithmthatisregionally-specific.Weadvocateathirdapproach–theassimilationofremote-sensedreflectance.

5Conclusion30

Inthisstudywehaveusedaspectrally-resolvedopticalmodelcoupledtoaBGCmodeltosimulatetheremote-sensingreflectancescentredattheMODISoceancolourbands.Thenon-linearobservationoperatorintheassimilationsystemsubsequentlyconvertedremote-sensingreflectanceintoasimulatedOC3MapproximationofChl-a.ObservedOC3Misthenassimilatedintothemodel,whichreducesthedomain-wideforecasterrorsinChl-afrom35100%to55%whencomparedtothenon-assimilatingmodel.Byusingafunctionalderivationoftheremote-sensingreflectances(OC3M),wehalvetheforecasterrorcomparedtosimplyassumingtheOC3MisdirectlyrelatedtothemodelpredictionofsurfacetotalChl-a.Acomparisonagainstin-situobservationsofNO3,NH4,DIPandTSSshowstheassimilatingmodelreducestheMAPEfrom90%tolessthan20%atmost40stations.ByusingaforwardmodelthatincludesamajorityoferrorsourcespresentintheobservedOC3M,wehaveshownthattheassimilationofremotely-sensedproductsinopticallycomplexcase2waterscanbeachieved,andaddssubstantialpredictiveskillwhencomparedtothenon-assimilatingmodel.Furthermore,thisapproachcanbegeneralizedto

18

nonocean–colourspecificmissionsliberatingavastquantityofdatathatcannotbeusedusingtraditionalBGCassimilationsystems.

Acknowledgements

ThemodelsimulationsweredevelopedaspartoftheeReefsproject,apublic-privatecollaborationbetweenAustralia'sleadingoperationalandscientificresearchagencies,5government,andcorporateAustralia(research.csiro.au/ereefs).Atmospherically-correctedMODISproductsweresourcedfromNASAandtheIntegratedMarineObservingSystem(IMOS)-IMOSissupportedbytheAustralianGovernmentthroughtheNationalCollaborativeResearchInfrastructureStrategy(NCRIS)andtheSuperScienceInitiative.Simulationsandtheprocessingoftheremotesensingdatawasundertakenwiththe10assistanceofresourcesfromtheNationalComputationalInfrastructure(NCI),whichissupportedbytheAustralianGovernmentviaNCRIS.WethankthemanycolleaguesinvolvedindevelopingtheeReefsmodel,particularlyMikeHerzfeld,JohnAndrewartha,PhilipGillibrand,CedricRobillotandRichardBrinkman.MarkBairdwasadditionallyfundedbytheCSIROWealthfromOceansFlagship,theGasIndustrySocial&EnvironmentalResearch15Alliance(GISERA),CSSFSPandtheCSIROCoastalCarbonCluster.RiverflowdataandinformationusedtospecifyrivernutrientandsedimentloadswereprovidedbytheGovernmentofQueensland.

References

20Ariathurai,R.&Krone,R.B.1976.Finiteelementmodelforcohesivesedimenttransport.JournaloftheHydraulicsDivision,ASCE,104,HY2,323–328.Baird,M.E.(2010)Limitstopredictioninasize-resolvedpelagicecosystemmodel.J.PlanktonRes.32,1131-1146.25Baird,M.E.,M.P.Adams,R.C.Babcock,K.Oubelkheir,M.Mongin,K.A.Wild-Allen,J.Skerratt,B.J.Robson,K.Petrou,P.J.Ralph,K.R.O'Brien,A.B.Carter,J.C.Jarvis,M.A.Rasheed(2016a)Abiophysicalrepresentationofseagrassgrowthforapplicationinacomplexshallow-waterbiogeochemicalmodelEcol.Mod.325:13-27.30Baird,M.E.,N.Cherukuru,E.Jones,N.Margvelashvili,M.Mongin,K.Oubelkheir,P.J.Ralph,F.Rizwi,B.J.Robson,T.Schroeder,J.Skerratt,A.D.L.StevenandK.A.Wild-Allen(2016b)Remote-sensingreflectanceandtruecolourproducedbyacoupledhydrodynamic,optical,sediment,biogeochemicalmodeloftheGreatBarrierReef,Australia:comparisonwith35satellitedata.Env.Model.Software78:79-96.

19

Baird,M.E.,P.J.Ralph,K.Wild-Allen,F.RizwiandA.D.L.Steven(2013).Adynamicmodelofthecellularcarbontochlorophyllratioappliedtoabatchcultureandacontinentalshelfecosystem.Limnol.Oceanogr.58,1215-1226.

Ciavatta,S.,Kay,S.,Saux-Picart,S.,Butenschön,M.andAllen,J.I.,2016.DecadalreanalysisofbiogeochemicalindicatorsandfluxesintheNorthWestEuropeanshelf-sea5ecosystem.JournalofGeophysicalResearch:Oceans.121,1824-1845

Collier,C.J.,Waycott,M.,McKenzie,L.J.,2012.LightthresholdsderivedfromseagrasslossinthecoastalzoneofthenorthernGreatBarrierReef,Australia.Ecol.Indic.23,211-219.Cummings,J.A.,2005.Operationalmultivariateoceandataassimilation.QuarterlyJournalof10theRoyalMeteorologicalSociety,131(613),pp.3583-3604.De'ath,G.K.E.Fabricius,H.SweatmanandM.Puotinen(2012)The27-yeardeclineofcoralcoverontheGreatBarrierReefanditscauses.PNAS109,17995-17999.15Dee,D.P.etal.(2011)TheERA-Interimreanalysis:configurationandperformanceofthedataassimilationsystem.Q.J.R.Meteorol.Soc.137:553–597.Dowd,M.,Jones,E.andParslow,J.,2014.Astatisticaloverviewandperspectivesondataassimilationformarinebiogeochemicalmodels.Environmetrics,25(4),pp.203-213.20Egbert,G.D.andErofeeva,S.Y.,2002.Efficientinversemodelingofbarotropicoceantides.JournalofAtmosphericandOceanicTechnology,19(2),pp.183-204.25Furnas,M.2003.Catchmentsandcorals:terrestrialrunofftotheGreatBarrierReef.AustralianInstituteofMarineScience,Queensland.,334p.Garnier,F.,Brankart,J.M.,Brasseur,P.andCosme,E.,2016.Stochasticparameterizationsofbiogeochemicaluncertaintiesina1/4°NEMO/PISCESmodelforprobabilisticcomparisons30withoceancolordata.JournalofMarineSystems,155,pp.59-72.Gaspari,G.andCohn,S.E.,1999.Constructionofcorrelationfunctionsintwoandthreedimensions.QuarterlyJournaloftheRoyalMeteorologicalSociety,125(554),pp.723-757.35Gehlen,M.,Barciela,R.,Bertino,L.,Brasseur,P.,Butenschön,M.,Chai,F.,Crise,A.,Drillet,Y.,Ford,D.,Lavoie,D.andLehodey,P.,2015.Buildingthecapacityforforecastingmarinebiogeochemistryandecosystems:recentadvancesandfuturedevelopments.JournalofOperationalOceanography,8(sup1),pp.s168-s187.

20

Gillibrand,P.A.andHerzfeld,M.,2016.Amass-conservingadvectionschemeforofflinesimulationofscalartransportincoastaloceanmodels.OceanModelling,101,pp.1-16.Goyens,C.,Jamet,C.,Schroeder,T.,2013.Evaluationoffouratmosphericcorrection5algorithmsforMODIS-Aquaimagesovercontrastedcoastalwaters.Rem.Sens.Env.131,63-75.Gregg,W.W.,2008.AssimilationofSeaWiFSoceanchlorophylldataintoathree-dimensionalglobaloceanmodel.JournalofMarineSystems,69(3),pp.205-225.10Herzfeld,M.2006,Analternativecoordinatesystemforsolvingfinitedifferenceoceanmodels.,OceanModelling,14,174-196.Hu,J.,Fennel,K.,Mattern,J.P.andWilkin,J.,2012.DataassimilationwithalocalEnsemble15KalmanFilterappliedtoathree-dimensionalbiologicalmodeloftheMiddleAtlanticBight.JournalofMarineSystems,94,pp.145-156.King,E.A.,Schroeder,T.,Brando,V.E.,Suber,K.,2014.Apre-operationalSystemforSatelliteMonitoringoftheGreatBarrierReefMarineWaterQuality.Tech.rep.,CSIRO20Report,pp56.LynchTP,MorelloEB,EvansK,RichardsonAJ,RochesterW,etal.(2014)IMOSNationalReferenceStations:AContinental-WidePhysical,ChemicalandBiologicalCoastalObservingSystem.PLoSONE9(12):e113652.doi:10.1371/journal.pone.0113652.25Madsen,O.S.,1994.Spectralwave-currentbottomboundarylayerflows,inCoastalEngineering1994Proceedings,24thInternationalConferenceCoastalEngineeringResearchCouncil/ASCE,pp.384-398.30Margvelashvili,N.,Saint-Cast,F.,Condie,S.,2008.NumericalmodellingofthesuspendedsedimenttransportinTorresStrait.ContinentalShelfResearch28,2241-2256.

Mattern,J.P.,Fennel,K.andDowd,M.,2014.Periodictime-dependentparametersimprovingforecastingabilitiesofbiologicaloceanmodels.GeophysicalResearch35Letters,41(19),pp.6848-6854

Mongin,M.,M.E.Baird,B.Tilbrook,R.J.Matear,A.Lenton,M.Herzfeld,K.A.Wild-Allen,J.Skerratt,N.Margvelashvili,B.J.Robson,C.M.Duarte,M.S.M.Gustafsson,P.J.Ralph,A.D.

21

L.Steven(2016).TheexposureoftheGreatBarrierReeftooceanacidification.NatureCommunications7,10732.MorelloEB,PlagányiÉE,BabcockRC,SweatmanH,HillaryR,PuntAE(2014)Modeltomanageandreducecrown-of-thornsstarfishoutbreaks.Mar.Ecol.Prog.Ser.512:167-1835Oke,P.R.,Brassington,G.B.,Griffin,D.A.andSchiller,A.,2008.TheBluelinkoceandataassimilationsystem(BODAS).OceanModelling,21(1),pp.46-70.Odermatt,D.,Gitelson,A.,Brando,V.E.andSchaepman,M.,2012.Reviewofconstituent10retrievalinopticallydeepandcomplexwatersfromsatelliteimagery.Remotesensingofenvironment,118,pp.116-126.Oke,P.R.andSakov,P.,2008.Representationerrorofoceanicobservationsfordataassimilation.JournalofAtmosphericandOceanicTechnology,25(6),pp.1004-1017.15Parslow,J.S.,Cressie,N.,Campbell,E.,Jones.E.M.,andMurray,L.2013.Bayesianlearningandpredictabilityinastochasticnonlineardynamicalmodel.EcologicalApplications23:4,679-69820RidgwayK.R.,J.R.Dunn,andJ.L.Wilkin2002Oceaninterpolationbyfour-dimensionalleastsquares-ApplicationtothewatersaroundAustralia.J.Atmos.Ocean.Tech.,19,1357-1375.Robson,B.J.,Baird,M.andWild-Allen,K.,2013.Aphysiologicalmodelforthemarinecyanobacteria,Trichodesmium.InMODSIM2013,20thInternationalCongressonModelling25andSimulation.ModellingandSimulationSocietyofAustraliaandNewZealand,ISBN(pp.978-0).Rolfe,J.andGregg,D.,2015.FactorsaffectingadoptionofimprovedmanagementpracticesinthepastoralindustryinGreatBarrierReefcatchments.Journalofenvironmental30management,157,pp.182-193.Sakov,P.andOke,P.R.,2008.AdeterministicformulationoftheensembleKalmanfilter:analternativetoensemblesquarerootfilters.TellusA,60(2),pp.361-371.35SchaffelkeB,CarletonJ,DoyleJ,FurnasM,GunnK,SkuzaM,WrightM,ZagorskisI(2011)ReefRescueMarineMonitoringProgram.FinalReportofAIMSActivities2010/11-InshoreWaterQualityMonitoring.ReportfortheGreatBarrierReefMarineParkAuthority.AustralianInstituteofMarineScience,Townsville.(83p.)40

22

Sarmiento,J.LandN.Gruber(2006)OceanBiogeochemicalDynamics.PrincetonUniversityPress.ISBN:9780691017075.528pp.Schiller,A.,Herzfeld,M.,Brinkman,R.,Stuart,G.,Jan.2014.Monitoring,predictingandmanagingoneofthesevennaturalwondersoftheworld.Bull.Am.Meteor.Soc.23-30.5Schroeder,T.,Behnert,I.,Schaale,M.,Fischer,J.,Doerer,R.,2007.AtmosphericcorrectionalgorithmforMERISaboveCase-2water.J.Int.RemoteSens.28,1469-1486.Skerratt,J.,Wild-Allen,K.,Rizwi,F.,Whitehead,J.andCoughanowr,C.,2013.Useofahigh10resolution3Dfullycoupledhydrodynamic,sedimentandbiogeochemicalmodeltounderstandestuarinenutrientdynamicsundervariouswaterqualityscenarios.Ocean&coastalmanagement,83,pp.52-66.Thompson,A.,Costello,P.,Davidson,J.,Logan,M.,Schaffelke,B.,Uthicke,S.andTakahashi,15M.,2011.Reefrescuemarinemonitoringprogram.ReportofAIMSActivities–Inshorecoralreefmonitoring,p.128.Thompson,A.,Schroeder,T.,Brando,V.E.,Schaffelke,B.,2014.Coralcommunityresponsestodecliningwaterquality:WhitsundayIslands,GreatBarrierReef,Australia.CoralReefs33,20923-938.Willmott,C.J.,AcklesonSG,DavisRE,FeddemaJJ,KlinkKM,LegatesDR,ODonnellJ,RoweCM.1985.Statisticsfortheevaluationofmodelperformance.JournalofGeophysicalResearch90:8995-9005.25

AppendixA:DetaileddescriptionoftheeReefsmodellingsystem

TheeReefsmodellingsystemisasuiteofcoupledhydrodynamic,sediment,opticalandbiogeochemicalmodelsspecificallytailoredtotheGreatBarrierReef.Thehydrodynamicmodelisathree-dimensional,finite-difference,baroclinicmodelbasedonthethree-30dimensionalequationsofmomentum,continuityandconservationofheatandsalt,employingthehydrostaticandBoussinesqassumptions(Herzfeldetal.,2006,Schilleretal.,2015).Theequationsofmotionarediscretizedonafinite-differencestencilcorrespondingtotheArakawaCgrid.Intheverticalz-coordinatescheme,thereare47fixedz-levels.Theatmosphericforcingproducts(wind,pressure,rainandheatfluxes)aresuppliedbyBureau35ofMeteorology(BOM)reanalysisproducts.Atidalsignalwassuperimposedonthelow-frequencysealeveloscillationprovidedbyBRAN2.3(Okeetal.,2008)ontheregionalgridopenboundary.Thistidalsignalwasintroducedviaalocalfluxadjustment.TheOTIStidalmodel(EgbertandErofeeva,2002)wasusedtogeneratethetidalsignalfromamplitudeandphaseinformationfor8constituents.Thelocalgridopenboundarywasforcedwith40temperature,salinityandvelocity(withlocalfluxadjustment)derivedfromtheregional

23

grid.Amassconservingflux-basedadvectionschemeisusedtotransportsedimentandbiogeochemicaltracers.Thesedimenttransportmodeladdsamultilayersedimentbedtothehydrodynamicmodelgridandsimulatessinking,depositionandresuspensionofmultiplysize-classesof5suspendedsediment(Margvelashvilietal.,2008).Themodelsolvesadvection-diffusionequationsofthemassconservationofsuspendedandbottomsedimentsandisparticularlysuitableforrepresentingfinesedimentdynamics,includingresuspensionandtransportofbiogeochemicalparticles.Themodelisinitialisedwiththeobserveddistributionofgravel,sandandmudintheseabedoftheshelfregion.Sedimentparticlessettleontheseabeddue10togravityandresuspendintothewatercolumnwheneverthebottomshearstress,exertedbywavesandcurrents,exceedsthecriticalshearstressoferosion.TheresuspensionanddepositionfluxesareparameterisedwiththeAriathuraiandKrone(1976)formula.Thebottomfrictionundercombinedwavesandcurrentsisestimatedthroughthenonlinearbottomboundarylayermodel(Madsen,1994).15

Sedimentsinbenthiclayersundergoverticalmixingduetobioturbation,representedbylocaldiffusion.Thecorrespondingdiffusioncoefficientscaleswiththesedimentdepthsothatthebioturbationceasestooperatebeneaththebiologicallyactivelayer.Theresistanceofsedimentstoresuspensionalsovarieswiththesedimentdepthtoreflectthe20consolidatednatureofdeepsediments.Thenumericalgridforsedimentvariablesinthewatercolumncoincideswiththenumericalgridforthehydrodynamicmodel.Withinthebottomsediments,themodelutilisesatime-varyingsediment-thickness-adaptedgrid,wherethethicknessofsedimentlayersvarieswithtimetoaccommodatethedepositedsediment.Horizontalresolutionwithinsedimentsfollowstheresolutionofthewater25columngrid.Thebiogeochemicalmodelisorganisedinto3zones:pelagic,epibenthicandsediment.Theepibenthiczoneoverlapswiththelowestpelagiclayerandthetopsedimentlayer,sharingthesamedissolvedandsuspendedparticulatematerialfields.Dissolvedandparticulate30biogeochemicaltracersareadvectedanddiffusedthroughoutthemodeldomain.Additionally,biogeochemicalparticulatesubstancessinkandareresuspendedinthesamewayassedimentparticles.Biogeochemicalprocessesareorganizedintopelagicprocessesofphytoplanktonandzooplanktongrowthandmortality,remineralisationofparticulateandorganicmaterial,andfluxesofdissolvedoxygen,nitrogen,phosphorusandcarbon35(includingnitrogenfixation,phosphorusadsorptionanddesorption,surfacegasexchanges,respirationandphorosythensis,andfluxestoandfrombioticpools);epibenthicprocessesofgrowthandmortalityofmacroalgae,seagrassandcorals,andsedimentbasedprocessesofphytoplanktonmortality,microphytobenthosgrowth,detritalremineralisationandfluxesofdissolvedsubstances(Fig.2).40

Thebiogeochemicalmodelincludesfourgroupsofmicroalgae(smallandlargephytoplankton,Trichodesmiumandmicrophytobenthos)andthreemacrophytestypes(seagrasstypescorrespondingtoZosteraandHalophila,macroalgaeandcoralcommunities).Photosyntheticgrowthisdeterminedbyconcentrationsofdissolved45nutrients(nitrogenandphosphate)andphotosyntheticallyactiveradiation.Autotrophstakeupdissolvedammonium,nitrate,phosphateandinorganiccarbon,andinthecaseof

24

Trichodesmium,fixatmosphericnitrogen(Robsonetal.,2014).Microalgaeincorporatecarbon(C),nitrogen(N)andphosphorus(P)attheRedfieldratio(106C:16N:1P,Redfield1963)whilemacrophytesdosoattheAtkinsonratio(550C:30N:1P,Atkinson1983).Microalgaecontaintwopigments(chlorophyll-aandanaccessorypigment),andhavevariablecarbon:pigmentratiosdeterminedusingaphotoadaptationmodel(describedin5Bairdetal.,2013).Micro-zooplanktongrazeonsmallphytoplanktonandmeso-zooplanktongrazeonlargephytoplanktonandmicrozooplankton,atratesdeterminedbyparticleencounterratesandmaximumingestionrates.Ofthegrazedmaterialthatisnotincorporatedintozooplankton10biomass,halfisreleasedasdissolvedandparticulatecarbon,nitrogenandphosphate,withtheremainderformingdetritus.Additionaldetritusaccumulatesbymortality.Detritusanddissolvedorganicsubstancesareremineralisedintoinorganiccarbon,nitrogenandphosphatewithlabiledetritustransformedmostrapidly(days),refractorydetritusslower(months)anddissolvedorganicmaterialtransformedoverthelongesttimescales(years).15Theproduction(byphotosynthesis)andconsumption(byrespirationandremineralisation)ofdissolvedoxygenisalsoincludedinthemodelanddependingonprevailingconcentrations,facilitatesorinhibitstheoxidationofammoniatonitrateanditssubsequentdenitrification(inthesediment)todi-nitrogengaswhichisthenlostfromthesystem.FulldetailsofequationsusedinthebiogeochemicalmodelaregivenbyBairdetal.(2016b)and20detailsofparametervaluesandimplementationfortheGreatBarrierReefaregivenbyHerzfeldetal.2016Themodelisforcedusingflowandconcentrationsofdissolvedandparticulateconstituentsfrom21riversalongtheQueenslandcoast(northtosouth:Normanby,Daintree,Barron,25combinedMulgrave+Russell,Johnstone,Tully,Herbert,Haughton,Burdekin,Don,O'Connell,Pioneer,Fitzroy,Burnett,Mary,Calliope,Boyne,Caboolture,Pine,combinedBrisbane+Bremer,andcombinedLogan+Albert)andtheFlyRiverinPapuaNewGuinea(Herzfeldetal.,2015).Todetermineriverconcentrations,sedimentandnutrientobservationswerestatisticallyevaluatedover10years(Furnas2003).Separateanalysiswas30undertakenforwet-(theFly,andthenorthernmost6riversinQueensland)anddry-(remainder)catchmentrivers.Volume-averagedwetseasonexportcoefficientsbasedonthisobserveddatasetwerederivedforwet-anddry-catchmentrivertypes,andmeanflow-weightedconcentrationsdetermined.Theseconstantconcentrationsaremultipliedbyhigherfrequency(daily)observeddischargedatatocalculatethefluxofconstituentsatthe35rivermouths.

TheeReefsBGCandsedimentmodelhas3openoceanboundaries.NutrientconcentrationsflowinginfromtheboundarieswereobtainedfromtheCSIROAtlasofRegionalSeas(CARS)2009climatology(Ridgwayetal.,2003)andempiricalnutrient-40temperaturerelationships.TheinitialconditionsarespecifiedbyageneralisedempiricalrelationshipandscalednutrientprofilesonthemodeldensityprofilespecifyingtopandbottomwatercolumnvaluesfromCARSoceanatlas.SurfaceNO3isusuallylow(<3mgm-

3).Indeeperwatersnutrientconcentrationsincreasefrom0to1500mdepthandthenremainconstantdowntotheoceanfloor(4000mdepth,500mgm-3).Theinitialconditions45formostothertracerswerenotspatiallyresolved,sinceobservationsfortheouterreefandCoralSeaarelimitedtemporallyandspatially.

25

Tables:Table1:Thesubsetofstatevariablesincludedinthestatevectorandcorrespondingobservationerrorstandarddeviationsusedforfourassimilationsystemconfigurations.Theboldvariablesinthestatevectorareusedintheinput5totheobservationoperator.Itshouldbenotedthanthestatevariablesaretransformedbytakingthenaturallogarithmofthevariables.Theobservationerroristhenappliedtothelog-transformedstatevector.

AssimilationStateVector(X) ObservationError(R)

EXP1 Log(SurfaceTotalChl-a,PhySChl-a,PhyLChl-a) 0.8EXP2 Log(SimulatedOC3M,PhySChl-a,PhyLChl-a) 0.8EXP3 Log(SimulatedOC3M,PhySChl-a,PhyLChl-a) 0.4EXP4 Log(SimulatedOC3M,PhySChl-a,PhyLChl-a,NO3,NH4,TSS) 0.4Table2:ForecasterrorstatisticsforEXP4byregion(inshore,lagoon,offshore)fortheControl(C),Forecast(F),Analysis(A)andPersistence(P)fields.10

RegionField C F A P C F A P C F A P C F A PMedian 0.32 0.23 0.19 0.26 1.35 1.29 1.12 1.46 0.34 0.25 0.19 0.25 0.16 0.1 0.06 0.11Mean 0.37 0.24 0.2 0.27 1.92 1.37 1.25 1.46 0.38 0.24 0.2 0.25 0.16 0.1 0.06 0.1125%Quartile 0.27 0.2 0.14 0.21 1.1 0.95 0.92 0.94 0.29 0.16 0.14 0.21 0.14 0.08 0.04 0.775%Quartile 0.48 0.3 0.23 0.29 2.45 1.87 1.64 1.08 0.43 0.29 0.22 0.29 0.19 0.13 0.08 0.12

WholeofDomain Coastal LagoonandShelf Oceanic

Table3:ForecastPercentageerrorsforEXP4byregion(inshore,lagoon,offshore)fortheControl(C),Forecast(F),Analysis(A)andPersistence(P)fields.

RegionField C F A P C F A P C F A P C F A PMedian 100 53 39 53 130 95 90 105 95 47 38 52 93 48 31 48Mean 107 54 38 55 180 97 90 107 102 51 37 56 96 50 31 5125%Quartile 81 41 35 42 105 105 95 74 75 43 36 41 71 44 35 3975%Quartile 131 61 41 62 181 85 81 145 118 62 42 62 126 55 30 62

WholeofDomain Coastal LagoonandShelf Oceanic

15 Figures:20

26

Figure1:AmapoftheGreatBarrierReefregion,withthecolorbardenotingthewaterdepth,markersdenotethepopulationcentres(redtriangles),IMOSNRSsites(yellowtriangles),ReefRescueWQMs(yellowcircles)andpointsofinterestreferredtointhetext(redcircles),withthe5glidertrack(whitelineadjacenttoLizardIsland).Thein-situsamplinglocationsandgliderobservationsareusedtoassessthedataassimilationsystemperformance,usingtheEXP4configuration.

27

Figure2:SimulatedsurfaceChl-a(mgm-3)ofthenon-assimilatingcontrolrun(topleft)andthesimulatedOC3M(topright)derivedfromthesimulatedremote-sensingreflectanceforthe14/7/2013.TheobservedOC3MwithANN-derivedobservedremote-sensingreflectance(bottomleft)andNASA-derivedobservedremote-sensingreflectance(bottomright).5

28

Figure3:Comparisonofinnovationstatisticsforthefourassimilationexperimentsundertaken,where0indicatesperfectagreementbetweenmodelandobservations.Thetoppanelplotsthemeaninnovationforeachassimilationcycle.Thelowerpanelplotsthemeanabsoluteinnovationagainstassimilationcycle.Thefollowingcolourscorrespondto:green(EXP1),red(EXP2),black5(EXP3)andblue(EXP4).Thevariablesinthelegendcorrespondtotheobservationerror(R)andtheassimilationstatevector(X).

29

Figure4:BoxandwhiskerplotsofRMSD(toprow)andMAPE(bottomrow)ofthemis-matchbetweensimulatedOC3MandANN-observedOC3M.Eachpanelcontainsthecontrolrun(C)andEXP4showingforecast(F),persistence(P)andanalysis(A).Presentedarestatisticsforthewholedomain(leftcolumn),andforspecificdepthranges(threerightmostcolumns).5

Figure5:Simulated(forecast)OC3M(left)forcycle22(12thSeptember2013)withobservationsoverlaid,surfaceSmallPhytoplankton(PhyS)Chl-a(centre)andsurfaceLargePhytoplankton(PhyL)Chl-a(right).

30

Figure6:IncrementsthatareaddedtotheforecastfieldsgeneratedbytheassimilationsystemforsimulatedOC3Mwithinnovationsoverlaid(left),andtheprognosticvariablesofsurfacesmallphytoplanktonChl-a(centre)andsurfacelargephytoplanktonChl-a(right).

5

Figure7:TheresultinganalysisfieldsforsimulatedOC3MandwithheldANNOC3Mobservationsoverlaid(left),andtheanalysisfieldsfortheprognosticvariablesofsmallphytoplankton(centre)andlargephytoplankton(right)forthe12thSeptember,2013.

31

Figure8:ComparisonagainstindependentIMOSgliderobservations,withtheobservedsectionofChl-aderivedfromtheonboardfluorescencesensor.Thecomparisonisundertakeninmodelspace,wherebyallgliderdatathatfallwithina1hourwindoweithersideofwhenthereisa3Dmodeloutputavailableisextracted,andequivalentsimulatedChl-aareextractedfromthemodel.Thegliderandmodeldataisthenspatiallyaggregatedandinterpolatedontothevertical5modelgrid.Theresultingsectionfortheglider(top),andthesimulatedglidersectionsfromthenon-assimilatingmodel(centre)andassimilatingmodel(bottom).

Figure9:Comparisonofdepth-resolvedChl-aagainstsixindividualgliderprofilesusingthemethoddescribedinthecaptionofFigure8.Gliderobservationsareblack,thenon-assimilatingcontrolrunprofilesareblue,andtheassimilating10runprofilesarered.

26/05/13 05/06/13 15/06/13 25/06/13 05/07/13 15/07/13 25/07/13 04/08/13−200

−150

−100

−50

0

Dept

h (m

)

Observed

26/05/13 05/06/13 15/06/13 25/06/13 05/07/13 15/07/13 25/07/13 04/08/13−200

−150

−100

−50

0

Dept

h (m

)

Control

26/05/13 05/06/13 15/06/13 25/06/13 05/07/13 15/07/13 25/07/13 04/08/13−200

−150

−100

−50

0

Dept

h (m

)

Assimilating

Chl−

a (m

g m−3

)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5−450

−400

−350

−300

−250

−200

−150

−100

−50

0Date = 26/05/13

Dep

th (m

)

Chl−a (mg m−3)0 0.1 0.2 0.3 0.4 0.5 0.6

−900

−800

−700

−600

−500

−400

−300

−200

−100

0Date = 19/06/13

Dep

th (m

)

Chl−a (mg m−3)0 0.1 0.2 0.3 0.4 0.5 0.6

−1000

−900

−800

−700

−600

−500

−400

−300

−200

−100

0Date = 26/06/13

Dep

th (m

)

Chl−a (mg m−3)

0 0.2 0.4 0.6 0.8 1−1000

−900

−800

−700

−600

−500

−400

−300

−200

−100

0Date = 03/07/13

Dep

th (m

)

Chl−a (mg m−3)0 0.1 0.2 0.3 0.4

−1000

−900

−800

−700

−600

−500

−400

−300

−200

−100

0Date = 02/08/13

Dep

th (m

)

Chl−a (mg m−3)0 0.1 0.2 0.3 0.4 0.5 0.6

−1000

−900

−800

−700

−600

−500

−400

−300

−200

−100

0Date = 05/08/13

Dep

th (m

)

Chl−a (mg m−3)

a. b. c.

d. e. f.

32

Figure10:AprofileofthetemporalmeanChl-aRMSDbetweenthegliderobservationspresentedinFigure8andthenon-assimilating(blue)andassimilating(red)runs.

Figure11:AcomparisonofChl-aandTSSRMSDsbetweenthein-situAIMSReefRescuemooringsforthenon-5assimilating(blue)andassimilating(red)modelruns,theReefRescuesitesaredenotedbytheyellowcirclesinFigure1.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−200

−180

−160

−140

−120

−100

−80

−60

−40

−20

0

RMSD Chl−a (mg m−3)

Dep

th (m

)

ControlAssimilating

Snap_5m Fitz_5m High_5m Russell_5m Dunk859_5m Pelorus_5m Pandora_5m GeoffreyBay336_5mDoubleCone_5m Daydream_5m Pine_5m Barren_5m Pelican_5m Humpy_5m0

0.5

1

1.5

Chl−a

RM

SD (m

g m−3

)

ControlAssimilating

Snap_5m Fitz_5m High_5m Russell_5m Dunk859_5m Pelorus_5m Pandora_5m GeoffreyBay336_5mDoubleCone_5m Daydream_5m Pine_5m Barren_5m Pelican_5m Humpy_5m0

0.005

0.01

0.015

0.02

0.025

TSS

RM

SD (m

g m−3

)

ControlAssimilating

33

Figure12:AcomparisonofRMSDofsimulatednutrientswithin-situbottlesamplesforthenon-assimilating(blue)andassimilating(red)modelruns.ObservationsareobtainedattheQueenslandIMOSsite(yellowtrianglesinFigure1)atYongala(Y)andNorthStradbroke(NS)Island.Y_0aretheYongalasurfacesamples,whileY_26arethesamplestakenfrom26mdepth.5

Figure13:Observedtrue-colourimageonthe12Sep2013obtainedfrom1kmresolution,atmospherically-correctedANNremote-sensingreflectance.TheRGBwavelengthsusedwere667,551and488nmandprocessedusingtheMODIS

Y_0 Y_10 Y_20 Y_26 NS_0 NS_10 NS_20 NS_30 NS_40 NS_500

10

20

30

40

NO3

RMSD

(mg

m−3

)

Y_0 Y_10 Y_20 Y_26 NS_0 NS_10 NS_20 NS_30 NS_40 NS_500

5

10

NH4

RMSD

(mg

m−3

)

Y_0 Y_10 Y_20 Y_26 NS_0 NS_10 NS_20 NS_30 NS_40 NS_500

2

4

6

DIP

RMSD

(mg

m−3

)

Control Assimilating

34

truecolouralgorithm(Gumleyetetal.,2010;Bairdetal.,2016).Thewhitepixelsareclouds,greyisland.Simulatedtruecolourimagesarenotfalsely-coloured,thusdonotrequireacolourmap,norarethey2Dastheyhaveadepthoffield,beingbasedonreflectancefrommultipledepthsandthebottom(Bairdetal.,2016a).Thussimulatedtruecolourcanbeconsideredaphotographoftheopticalstateofthedifferentmodelruns,and,likeobservedtruecolour,apowerfulandintuitivevisualisationtoolforwaterclarityinbiogeochemicalmodels.5

Figure14:Thesimulatedtrue-colourimageonthe12Sep2013ofthecontrolrun(topleft)andassimilationrun(topright).Thedifferencebetweentheremote-sensingreflectanceinthecontrolandassimilatedrunswasusedtoquantifythecolour(referredtoasoff-colour)added(i.e.greatersurfaceexpression,bottomleft)andsubtracted(i.e.lesssurface10expression,bottomright)duetotheupdatingofoptically-activeconstituentsintheassimilationrun(seeFig.13formoredetails).Notethattheoff-colourimageshaveasmallerbrighteningfactorastheMODIStruecolourstretchsaturatesthefeaturesthatareofmostinterest.

35

Figure15:TheeReefsmodellingsystemwithoptically-activecomponentsidentifiedwithbeigecolouringandanasterisk,withthenumberofasterisksdenotingthenumberofdifferentoptically-activeelementswiththiscomponent.Thus,eachofthefourmicroalgaemicroalgaehavetwopigmenttypes,oneabsorbinglikedivinylchlorophyll-a,andthe5otherlikephotosyntheticcarotenoids;therearetwoseagrasstypes,coralshavebothskeletonsandzooxanthellae;threetypesofdetritusabsorbandscatter,andthesedimentmodelcontainsasuspendedfractionandfour(mixed)sedimentcompositions.Additionally,pureseawaterbothabsorbsandscatterslight.