ORIGINAL RESEARCH ARTICLE
Modelling of the Svalbard fjord Hornsund
Jaromir Jakacki
a,* , Anna Przyborska
a, Szymon Kosecki
a, Arild Sundfjord
b, Jon Albretsen
caInstituteofOceanology,PolishAcademyofSciences,Sopot,Poland
bNorwegianPolarInstitute,Tromsø,Norway
cInstituteofMarineResearch,Bergen,Norway
Received14July2016;accepted5April2017 Availableonline20May2017
KEYWORDS
Hydrodynamicmodel;
Fjordcirculation;
Heatandsaltcontent andanomalies;
Hornsundmodel
Summary TheArctic Oceaniscurrentlyintransitiontowardsanew, warmerstate.Under- standingthe regionalvariability ofoceanographicconditionsisimportant,sincetheyhavea directimpactonlocalecosystems.Thisworkdiscussestheimplementationofahydrodynamic modelforHornsund,thesouthernmostfjordofwesternSvalbard.Despiteitslocation,Hornsund has astrongerArctic signaturethan other Svalbardfjords.The modelwasvalidatedagainst availabledata,andtheseasonalmeancirculationwasobtainedfromnumericalsimulations.Two main general circulation regimes have been detected in the fjord. The winter circulation representsatypicalclosedfjordsystem,whileinsummerthefreshwaterdischargefromthe catchmentareageneratesasurfacelayerwithanetflowoutofHornsund.Alsodescribedarethe localhydrographic front and itsseasonal variability,as wellastheheat and salt contentin Hornsund.Theintegrationofsaltandheatanomaliesprovidesadditionalinformationaboutthe
Abbreviations: A4,4-kmresolutionPan-Arcticmodel(basedonROMS);ADCP,AcousticDopplercurrentprofiler;AO,ArcticOcean;AW, AtlanticWater;AWAKE,Projects(includingtheAWAKE-2—ArcticClimateSystemStudyofOcean,SeaIceandGlaciersInteractionsinSvalbard Area);GAME,GrowingoftheArcticMarineEcosystemproject;GLAERE,GlaciersasArcticEcosystemRefugiaproject;ERAi,ERA-Interim—a globalatmosphericreanalysis;HOBO,temperatureandpressuresensor;HRM,highresolutionnumericalmodeloftheHornsund;HYCOM,Hybrid CoordinateOceanModel;SCA,SaltContentAnomaly;KNOW,TheLeadingNationalResearchCentre;MIKE,MIKEbyDHI—softwarefromthe DanishHydrologicalInstitute;MIKEHD,MikeFlowModel,Hydrodynamicmodule;NavSim,NavSimPolskasp.zo.o.—PolishDealerofthe Canadianbranchofthismarinesoftwarecompany;ModOIE,MesoscalemodellingofIce,OceanandEcologyoftheArcticOcean;NPI,Norway PolarInstitute;ROMS,RegionalOceanModellingSystem;S800,800mSvalbardareamodel(basedonROMS);SC,SorkappCurrent;TOPEX/
POSEIDON,OceanSurfaceTopographyfromSpace—NASA;TOPAZ4,anocean-seaicedataassimilationsystemfortheNorthAtlanticandArctic globalTPXOmodelofoceantides;WSC,WestSpitsbergenCurrent.
PeerreviewundertheresponsibilityofInstituteofOceanologyofthePolishAcademyofSciences.
* Correspondingauthorat:InstituteofOceanology,PolishAcademyofSciences,PowstańcówWarszawy55,Sopot,Poland.
Tel.:+48587311903.
E-mailaddress:[email protected](J.Jakacki).
Availableonlineatwww.sciencedirect.com
ScienceDirect
jo u rn al ho m e p age : w w w. jo ur na ls .e l se v i er.c o m / o ce an o lo g i a/
http://dx.doi.org/10.1016/j.oceano.2017.04.004
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1. Introduction
Hornsundisafjordinthesouth-westoftheSvalbardarchi- pelago.ItspositionandwideopeningtoGreenlandSeashelf waters(Fig.1),aswellasthelargeareaofcontactbetween thecoastalwatersandtidewaterglacierfronts,exposeitto thestronginfluenceoftheshelfwaters.The fjord's12km widemouthfaceswesttowardstheGreenlandSea.Hornsund is30kmlongwithamaximumdepthofabout260m(average
ca90m)(FrankowskiandZioła-Frankowska,2014),anesti- matedsurfaceareaof275km2andavolumeof23km3.The fjord'scoastlineisverydiverse,withanumberofsmallbays, whicharethemouthsofvalleyswithglaciersflowingintothe sea. Some of these small bays appeared as late as the beginningofthe20thcenturyasaresultofglacierrecession.
The area and coastlineof Hornsundhave been expanding gradually since the retreat of glaciers. The total area of glaciercoverinHornsunddiminished from1899to2010by saltfluxinto theinnermostbasin of thefjord-Brepollenduringthesummer.Extensiveinsitu observationshavebeencollectedinHornsundforthelasttwodecadesbutourhydrodynamicmodel isthefirsteverimplementedforthisarea.Whileatthemomentinsituobservationsbetterrepresent thestateofthisfjord'senvironmentandthelocationofmeasurements,anumericalmodel,despite itsflaws, canprovide amore comprehensive imageof the entirefjord's physical state. In situ observationsandnumericalsimulationsshouldthereforeberegardedascomplementarytools,with modelsenablingabetterinterpretationandunderstandingofexperimentaldata.
©2017InstituteofOceanologyofthePolishAcademyofSciences.ProductionandhostingbyElsevier Sp.zo.o.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.
org/licenses/by-nc-nd/4.0/).
Figure1 Locationofthestudyarea—theHornsundfjord.
Source:https://en.wikipedia.org/wiki/Svalbard(OonaRäisänen).
approximately 172km2, the average loss of area being 1.6km2year1. The recession rate increased from 1km2year1 in thefirstdecades of the 20thcentury up to3km2year1in2001—2010(Błaszczyketal.,2013).
AtlanticWater(AW)suppliesthebiggestvolumefluxtothe ArcticOcean(AO)andisoneofthemostimportantfactors shapingtheregion'sclimate(Walczowski,2007,2013).The WestSpitsbergenCurrent(WSC)istheAWbranchthathasthe greatestinfluenceonconditionsinHornsund.TheAWcarried by thiscurrent is characterized as warm and saline(tem- peratureca3.5—6.08Candsalinity>35inthesurfacelayer offtheentrancetoHornsund).Butthereisanothercurrentin theHornsund area thatalso hasa stronginfluenceon the fjord'sstate.ThisistheSorkappCurrent(SC),whichcarries cold,andfresherwaterfromthewesternpartoftheSvalbard Archipelago and the Barents Sea (temperature 1.5 to +1.58C,salinity34.3—34.8)(Cottieretal.,2005;Gluchowska et al.,2016). It is a typical fjordwith an internal Rossby deformation radius representing the ratio of the internal wavespeedtotheCoriolisparameter.InthecaseofHornsund wecanassumethatthemaximumwaterdepthis200m,with asurfacelayer(T=4—78CandS=30—32)thatisca20mthick andlowerlayers(T=0—48CandS=34—35)havinganinternal Rossby deformation radius between 3.5 and 6km (Cottier etal.,2005;Nilsenetal.,2008).WhentheinternalRossby radiusissmallerthanthewidthofthefjord,theinfluenceof the Earth's rotation is not insignificant. This means that variationsintheflowaredrivenbyrotationaldynamics;such fjordsareoftencalled“broad”.
Tidesareanotherprocessthathaveastronginfluenceon thefjord.Generally,tidesarethemainhydrodynamicdriver inthefjord:watercirculationinthefjordisgovernedmainly bytidesandshelfcurrents.Tidesandcurrentshaveastrong influenceon theheat,saltandfresh waterbudgetsinthe fjord.Theamplitudeofthetidalcomponentsvariesbetween 0.75mandthemaincomponentoftidalforcinginthisarea isthesemi-diurnal(M2)constituent(Kowaliketal.,2015).
Other tidal components are considered in the section on validation.
Thestudyareahasbeenexaminedpreviouslyandmany experiments have been done there; indeed, much in situ researchis stillinprogress(mostlyPolish-Norwegiancoop- erative ventures), for example, AWAKE-2 (Arctic Climate SystemStudyof Ocean,SeaIceandGlacierInteractionsin SvalbardArea)project,GAME(GrowingoftheArcticMarine Ecosystem)andGLAERE(GlaciersasArcticEcosystemRefu- gia).Althoughtheseprojectsusuallyfocusoninterdisciplin- arystudies,insitumeasurementsdonotprovideacomplete pictureofthefjord'sphysicalstate.Typically,theobserva- tions are carried out over short timescales (for example, observationsperformedfromaresearchvessel)oras long- terminsitumeasurementsbasedonmoorings.Directmea- surements provide the most accurate results, but making measurements that wouldbe representative of the whole fjordareawouldbeveryexpensiveandlogisticallydifficult (apartfromsatellitemeasurements,butthesecoveronlythe surface). Another approachthatcould providea complete imageof thefjord's physicalstate ismodelling. Thereare alreadymanymodelsembracingHornsund:theHybridCoor- dinateOceanModel(HYCOM)(Chassignetetal.,2006),which hasaspatialresolutionof1/12deg;TOPAZ4(Counillonetal., 2010;Sakovetal.,2012),whichhasahorizontalresolutionof
10—16kmanddoesnottakeintoconsiderationallthemost important factors for studies of water circulation inside fjords (like tides); the Nordic Seas HYCOM model, which hasahorizontalresolutionofabout4km,tonamebutthree.
Theirdomainscovermuchlargerareasandtheirhorizontal resolutionsare insufficient for studyinghydrodynamic pro- cessesinHornsund.Toconclude,wecouldsaythatalthough modellingtools are developing rapidly, no high-resolution hydrodynamic model focused on Hornsund has yet been developed.Boththemodelssupplyinglateralboundarydata covertheHornsundarea(Hattermannetal.,2016),butthe fjordiscoveredbyonlyafewcells,whichareinsufficientfor providingappropriateresults.
Themodelthatweimplementedforthefjordisofhigh resolution, but as boundary condition we used data from another(coveringalargergeographicalarea),lowerresolu- tion model. Our high-resolution model thus extends the existingmodeloftheArcticbyafjord,whichinthelarger modelisnotcorrectlyrepresented.Inourstudy,wedecided tousesoftwarefromtheDanishHydrologicalInstitute(MIKE byDHI,MD)asanadditionaltoolinordertoacquireabetter understandingoftheprocessesthatgovernthebehaviourof thefjord'sphysicalstate.WiththeMDsoftwareonecanuse anunstructuredgrid(alsoknownasameshgrid)thatallowsa modeldomainofvariablespatialresolutionto becreated, whichhasadvantagesinareaswithawiderangeofdepths.
This paper focuses on the implementation of MD for Hornsundandisdividedintofivemainsections.TheIntro- duction is followed by the Model description and Implementation.Generalinformation,suchasthehorizontal andverticalgrids, themodeldomain andbathymetry, are presented here, and all the parameters used (including parameterizations) arelisted inthe table.TheBoundaries section describes the implementation of lateral boundary conditionsandappliedatmosphericforcing.Aseparatesub- sectionaddressestheinclusionoffreshwatersourcesfrom glaciersandthecatchmentarea.Thevalidationprocedures are then described in the next three subsections. Each compares model results with available data for different areas.Becauseoftheextensivelateralboundaries,theshelf area andfjord interior are takenintoaccount separately.
Also,becauseofthedifferentnatureofthedrivingmechan- ism,tidalflowisdealtwithinaseparatevalidationsubsec- tion. The main findings, including a description of typical summer and winter circulation patterns, and the hydro- graphicfront,are presentedinResultsanddiscussion.This section concludes with an analysis of the heat and salt anomalies. Integrated over time, these anomalies reveal thatcirculationinBrepollenisrelativelystableandcanonly bedisturbed bythefreshwaterdischargedfromits catch- mentarea.
2. Model description and implementation
2.1. General informationThenumericalmodelofHornsund(HRM)wassetupbasedon MIKEHD3Dsoftware(MikeFlowModel,Hydrodynamicmod- ule, MH). This model solves Reynolds-averaged Navier—
Stokes(MIKEandDoc,2010—2014)equations(RANS)foran incompressiblemediumwiththeBoussinesqassumptionand
shallowwaterapproximation.Themainpartsofthemodel arethedomain,gridandbathymetry(Fig. 2).Themodel's bathymetry was derived on the basis of electronic charts developedby Primar (international collaboration)and dis- tributedbyNavSimPolskasp.zo.o.(thePolishdealerofthe Canadian branch of this marine software company). The above-mentionedunstructuredgridenables avariablehor- izontal resolution to be used. The model grid consists of 2087elementsand1293nodes (anelementisdefinedasa rectanglecorner,andanodeisthecentreoftherectangle, equivalent to the grid centre in a structured grid). The smallest cell in ourdomain has a horizontal resolution of ca300mandthelargestcellhasadimensionofca3000m.
Theverticaldimension of anaverage cellinthe Hornsund area is ca 2.6m (the average depth of Hornsundis about 90m).Smallernodescoverpartsofthedomainthatconsistof shallower water areas. The mesh grid is also shown in Fig. 2. This figure shows two validation points (points 1and2),andthelocationofthethermistorstringandupward lookingAcoustic Doppler Current Profiler (ADCP, thepoint marked'M').Themodeltimestepissetto30s(thesolution techniquewasselectedasalow-orderfastalgorithm).The modelisbasedonthesigmacoordinatessystemwith35ver- ticallevels.Theinitialtemperatureandsalinityconditions wereconstant,andvelocityandsealevelweresettozero.
2.2. Modelsetup andnumericalparameters
Asmentionedearlier,themodelsolvesthewell-knownRANS equations. However, although these equations are well known, some of the numerical features can vary and are thereforepresentedhere.MikebyDHIisverywelldocumen- ted(MIKEandDoc,2010—2014),soweprovideonlyatable (Table1)withtheparametersusedinthemodel.
2.3. Boundaries
Thelateralboundaryconditionisoneofthemostimportant componentsofthemodel.Ithastocombinetidalforces(the internalrepresentationdoesnotprovidethecorrectampli- tude of sealevel variation,so it has to beapplied as the externalsealevelvariation),velocity,salinityandtempera- ture.Thelineofthelateralboundaryisshownbythethick yellowlinesinFig.2.
Inourcasethreesourcesofdatawereused.Tidalforcesin the Hornsund model were applied as sea level from the globaltidalmodel (datarepresentthe majordiurnal(K1, O1,P1andQ1)andsemidiurnaltidalconstituents(M2,S2,N2 andK2))withaspatialresolutionof0.2580.258basedon TOPEX/POSEIDON altimeter data (MIKE_DHI, 2014). Baro- tropic velocities together with respective sea level and activetracers(temperatureandsalinity)weretakenfrom twoNorwegianmodelsimulations(Hattermannetal.,2016).
Thecoupled ocean andsea ice model is aversion of the Regional Ocean Modelling System (ROMS) (www.myroms.
org; Budgell, 2005; Haidvogel et al., 2008; Shchepetkin andMcWilliams,2009)withtwodifferenthorizontalresolu- tions. The first one, the A4 model, covers a pan-Arctic domain with a 4km resolution, while the second one (high-resolutionmodel(S800,Albretsenetal.,2017))isa one-waynestedsimulationwithan800mresolutionofthe domaincoveringSvalbardandalargepartoftheFramStrait.
Bothmodels(A4andS800)wereforcedbyatmosphericfields derivedfromERAinterimreanalysis(ERAi,Deeetal.,2011).
Inaddition,A4andS800(Hattermannetal.,2016)usedtidal forcesretrievedfromtheglobalTPXOmodelofoceantides (EgbertandErofeeva,2002).
Thebarotropicpartoftheboundarywasspecifiedusing Flather'sboundarycondition(Flather,1976):
Figure2 Modeldomainandbathymetry.Themeshgrid,twovalidationpoints(1and2),thelocationofthethermistorstringand upwardlookingAcousticDopplerCurrentProfiler(ADCP,markedas'M')havebeenmarked.Thesolidyellowlinedelineatesthelateral boundaryandpoint'B'hasbeeninsertedasavalidationboundarypoint.(Forinterpretationofthereferencestocolorinthisfigure legend,thereaderisreferredtothewebversionofthisarticle.)
u¼uext ffiffiffig D r
ðjjextÞ: (1) ComputedfromtheSommerfeldwaveequationandthe continuity equation,thisconditionisoneof themosteffi- cient open boundary conditions (Jeżowiecka-Kabsch and Szewczyk, 2001; Kantha and Clayson, 2000). In Eq. (1) u denotes depth-averagedvelocity, Dis thelocal depthand j represents sea level. The superscript ext links external data.ThebarotropicvelocitiesinEq.(1)wereextractedand interpolatedbasedonan800mROMSsetupthatcoversthe Nordic Seas (Hattermann et al., 2016). In addition, the Dirichletboundarywasappliedtotemperatureandsalinity.
ThedataforthosevariablesweretakenfromtheNordicSeas ROMSmodel(4kmhorizontalresolution;Lienetal.,2013).
The2Dfieldwasinterpolatedforthetopboundarylayer.
The model does notrequire any atmospheric data, but in ordertoreplicaterealisticconditions,weappliedthefollow- ingatmosphericdata:
—Meansealevelpressure,
—Windspeedanddirection,
—2mpotentialtemperature,
—Cloudiness,
—Precipitation,
—Seaiceconcentration,
—Seaicethickness.
AtmosphericfieldswerepreparedonthebasisoftheERA Interimreanalysis dataset (fromthe EuropeanCentre for
Medium-Range Weather Forecasts) and ice coverage was takenfromtheS800model.
2.4. Freshwatersources
Fresh water sources are an important part of the fjord ecosystem.The main ones include directprecipitation on to the fjord surface (taken into account as atmospheric forcing),tidewaterglacierablationandcalving,meltingof fastice andsea ice,and land/riverine outflow.The fresh watersourcesfortheHornsundareaandacompilationofthe availabledatawerepresentedattheMareNorSymposiumon theEcologyofFjordsandCoastalwaters(Węsławskietal., 1995).This is summarizedin Fig. 3. The percentages and quantitative contributions of all fresh water components (ablation, precipitation, snow and rivers) were estimated onthebasisofFig.3aandb.Next,thepercentagecontribu- tionofeachsourcewasestimatedonthebasisofthatreport andFig.3b.Then,thequantitativecontributionofthefresh water component for each location shown in Fig. 3b was adopted from Węsławski's results (Węsławski et al.,1995;
Fig.3a).Wealsointroducedatimeshiftbetweenthewestern and eastern parts of the fjord, because of the melting processesthatoccurinthecatchmentarea.Movingthetime periodoficemeltisbasedonanobservationprovidedbythe PolishPolarStationinHornsund.Meltingalwaysbeginsinthe shelfareaandthenmoveseastwards.Thetimeshiftbetween theeasternandwesternpartsisaboutonemonthanditisnot visibleinthefigure(Fig.3c).AlthoughtheAWAKE2project run by the Institute of Oceanology, Sopot, had one work Table1 Parametersusedinthemodel.
Parameter Value Modeloptionorcomments(ifneeded)
Generalinformation
Horizontalresolution Sizeofcell(max,min)=(300,3000) MeshgridpresentedinFig.2 Verticalcoordinates 35verticallevels,min=0.2m,
max=40m
Sigmacoordinates Simulationperiods 01.2005—06.2010
Maximumtimestep 30s
Bathymetrysource NavSim(basedonElectronicNavigationalCharts—ENC)
Floodanddry Included
Horizontalturbulencemodel Smagorinsky Verticalturbulencemodel k—e
Bedfriction Constantindomain,butdependsoncellthickness
Floodanddry Included
Density Salinityandtemperaturedependent Coriolisforcing Included
Atmosphericforcing Included BasedonERAi:
—Meansealevelpressure
—Windspeedanddirection
—2mpotentialtemperature
—Cloudiness
—Precipitation
—Windspeed
Icethicknessandconcentration Included BasedonS800model
CriticalCFLvalue 0.8 Courant—Friedrichs—Lewynumber
Initialconditions Initializationfromcoldstart
Surfacelevel 0m
Velocities 0ms1
Figure3 SourcesoffreshwaterandtheirtimedependenceinHornsundbasedonWęsławski,1995(a);theversionimplementedfor themodel(b)representstheestimatedpercentagecontributionofeachsource;thetimevariabilityofeachsource(c).
Figure4 (a)Timeseriesofthemodelled(HRM,redline)andmeasured(blackline)seasurfacelevel,(b)powerspectrumdensity derivedfromthetimeseriesshownin(a).Theupper,blacklineimagestandsfortheexperimentalresultsandthelower,redline representsthespectrumofHRMsealevel;(c)comparisonbetweenmeasured(verticalaxis)andHRM(horizontalaxis)sealevelswitha filteredM2(semi-diurnal,redpoints)component.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis referredtothewebversionofthisarticle.)
packagefocusedonestimatingfresh watersourcesinthat area,theresultsarestillnotavailable.Becausethereareno otherdatathatcouldrepresentfreshwaterfromtheHorn- sunddrainagebasin,wedecidedtoutilizethesourcesfrom Fig.3(Węsławskietal.,1995)inthemodelfor thewhole simulation.
3. Model validation
The validation procedure depends on the area and local forces. As validation of tidal forces requires different
methods from temperature or salinity variation, it was dividedintothreeparts:
—Tides;
—Theshelfarea;
—Thefjord'sinterior.
3.1. Tidevalidation
The lack of experimental data does not permit long-term validation, so weused short-term measurementsfrom the
Figure5 ComparisonofbarotropiccurrentvelocityatthetwolocationsintheshelfareashowninFig.2(theupperimagerepresents point1(a)andtheloweronepoint2(b);theblueandredlinesrepresenttheHRMandS800modelsrespectively).(Forinterpretationof thereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
Figure6 Comparisonofthecurrentvelocityforonepointlocatedontheboundary(south-east,yellowboundaryline—point'B'in Fig.2).TheblueandredlinesrepresenttheHRMandS800modelsrespectively.Thelinearregressionforthisseriesisshownonthe lowerpanel.CorrelationcoefficientR0.91.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle.)
area in front of the Hansbreen Glacier measured by the Institute of Geophysicsof the Polish Academy of Sciences (IGF).Theinsitumeasurementsweremadebetween9and 15August2011usingaSchlumbergerMini-Diver.Thisinstru- mentwasequippedwithapressuresensor,andtheduration ofmeasurements waslimitedby itsmemory capacity.Our modeldoes notprovideresultsforthose dates,but inthe caseof tidesthere willonlybeaphase shiftbetweenthe data.Fig.4ashowsasealeveltimeseriesasmeasuredbythe Mini-Diver andthe modelled one. The spectral analysis of thesesignalsisshowninFig.4b.Thepowerspectraldensity wasnormalizedtothemaximumofbothsignals(inthiscase tothemeasuredmaximumsealevel)forbetterclarity.Sea levelswithafilteredM2componentarecomparedinFig.4c.
Because of thedifferent time series, thephase shift is visiblein Fig.4cas acircle (orellipse)formedby thered points.Despitetheshortperiodcoveredbytheinsitudata, the results providequite a good comparison between the measured and modelled amplitudes and frequencies. One maximumshowninFig.4b(periodcloseto12h)represents thesemidiurnaltidalconstituent(M2,althoughtherearealso othersemidiurnalconstituentsinthisarea),theother(close to24h)relatestodiurnalcomponents.However,forashort timeseriesitisimpossibletoseparateallthesemidiurnaland diurnalconstituents.
3.2. The shelfarea
Inthesecondstepofthevalidationwecomparedourmodel datawiththedataprovidedbytheS800andA4models.For thispurposewecompared thebarotropiccurrent velocity, salinityandtemperaturederivedfromourHornsundmodel withtheresultsofmodelsimplementedaslateralboundary conditions(thecomparisonwasperformedforthetwopoints showninFig.2).Fig.5comparesthetemporalvariabilityof thecurrentspeedderivedfromS800 modelwiththatfrom theHRMmodel.Themaindifferencescanbeexplainedbythe bathymetry.Allthemodelsusedifferentsourcesofbottom topography;inthecaseofthebarotropicvelocityitisthe main reason for these differences. Linear correlation between these series yields low values of the coefficient that are close to 0.3. This might suggest that the lateral boundary condition has been implemented incorrectly.
Exceptforthepointlocatedonthesouth-eastboundaryline (point'B')ontheyellowlineinFig.2,thecorrelationismuch better.Thevalueofthecoefficientisabout0.91andisshown inFig.6.Thisconfirmstheearliersuggestionthatthediffer- encesbetweenS800andHRMintheshelfareamostlyresult fromdifferencesinbathymetries.
Fig. 7 shows atime series of surfacesalinity and tem- peraturederivedfromtheHRMandA4models.Thesolidlines
Figure7 Comparisonoftemperatureandsalinityinthesurfacelayer(theuppergraphrepresentspoint1(a),thelowergraphpoint2 (b);theredandbluelinesrepresenttemperatureandsalinityrespectively;thedashedlinesrepresentmodelA4,thesolidlinesHRM).
(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
refertoourHRMmodel.Thecomparisonforthesurfacelayer looksquitegood.ModelA4hasa4kmresolution,sothefjord hasonlyseveralpointsinit.Inourcasethemaindifferences are between May and October, when fresh water sources were active throughout the fjord. Moreover, it is plainly evidentthatthemodelreproduces theseasonal variability oftheshelfarea.Fig. 8showsasimilargraph,butforthe bottommost layer. Here, there is also good agreement betweentheresultsofthetwo models,althoughthetem- peratureisa littlehigherfor thesecondpointin summer.
Both models (A4 and HRM) are quite different, so a comparison between them yields different resultsfor the bottom layers. Nonetheless,HRM still reproduces seasonal variability(whichisstrongerinthiscase)andexceptforthe summer,thetimeseriesareveryclose.Insummerthereisa visibleinfluenceofthefreshwatersourcesontheshelfarea, butintheotherseasonsthevariabilityfrombothmodelsis very similar. A simple linear correlation yields the coeffi- cientsshowninTable2.
Thebestcorrelationcoefficientsareforthesurfacelayer.
This is the result of the similar atmospheric fluxesimple- mentedin both models(S800, A4andHRM used thesame sourceofatmospheric forces,sowehadexpectedto geta goodcorrelation)andalso becausetheforcingattheopen boundaries is similar (HRM uses boundary conditions from S800 andS800 fromA4).The influenceofthefjordisalso clear in summer. The differences, visible mostly on the temperaturecurves,aredrivenbyfreshwatersources.
3.3. Thefjord interior
Thelimitedavailabilityofexperimentaldatadoesnothelpto carryoutadetailedvalidationofthefjordinterior.Mostdata Figure8 Comparisonoftemperatureandsalinityinthebottomlayer(theuppergraphrepresentspoint1(a),thelowergraph point2(b);theredandbluelinesrepresenttemperatureandsalinityrespectively;thedashedlinesrepresentmodelA4,thesolid linesHRM).(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthis article.)
Table2 Correlationcoefficientcalculatedfortemperature andsalinityforpoints1and2.
Point1 Point2
Surfacelayer
Temperature 0.80 0.88
Salinity 0.85 0.65
Bottomlayer
Temperature 0.91 0.49
Salinity 0.43 0.22
areavailablefromtheAWAKEprojects(includingtheAWAKE- 2—ArcticClimateSystemStudyofOcean,SeaIceandGlacier InteractionsintheSvalbardArea)managedbytheInstituteof Oceanologyandimplementedwithin theframeworkofPol- ish-Norwegiancollaboration.Themostimportanttimeseries areprovidedbytheNorwayPolarInstitute's(NPI)instrument mooring located at the silled entrance to Brepollen (76.9850N 16.1728E, see Fig. 2). They were collected between September 2013 and June 2014. The mooring, equipped with a profiling current metre and a string of
thermistors,wasdeployedatadepthof76monthesillat theentrancetoBrepollenandwasinoperationfrom5Sep- tember 2013 to 5 July 2014. An AADI RDCP600 Acoustic DopplerCurrent Profilerwas usedto measure 3Dcurrents.
Thisinstrumentwasmountedinabottomframeandcovered therangefrom72mupwardswith1mverticalresolution.
Itisimportantto addthatthesignal-to-noiseratioofindi- vidualcurrentmeasurementsdecayswithdistancefromthe instrument and the upper part of the data shown in the following has large uncertainty and is included only for Figure9 (a)DepthprofileoftheaveragecurrentmagnitudemeasuredbyADCP(thinbluelinewithredcircles)andHRMmodeldata (thickblueline).(b)Average(for2006—2009)temporalvariabilityofverticalprofileofcurrentdirectedintoBrepollen(positivevalue means'into').(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthis article.)
illustrationalpurposes.TheRDCP600wasalsoequippedwith apressuresensorandatemperaturesensor.TinyTagAquatic2 thermistorswereinstalledat5mintervalsfrom27to67m depth.Onthesamerope,aHOBOU20-001-03temperature andpressuresensorwasattachedat22mdepth.Thepres- suresensorshowedmodestvariationduringthedeployment, indicatingthatthethermistorchainwasnotseriouslysub- ductedbystrongcurrents.Because wehadno modelinte- grations for that year, we will make a comparison for differentyears.
Fig.9ashowsacomparisonbetweentheaveragemodelled current magnitude (HRM model, thick blue line) and that measuredbytheADCP (left)fordifferent depthsrecorded duringthisexperiment.Theresultshowsgoodcompatibility between the measured and modelled velocity profile. It shows the minimum current velocity located at around 40—50mdepth.Thisminimumexistsbecauseoftheinternal tideoscillations.
Inordertoobtainabroaderimageofinflowsandoutflows atthislocationwecalculatedthethree-yearaveragetem- poral variability of currents into Brepollen (Fig. 9b — a positivevelocitymeans'intoBrepollen').Twomainregimes arevisible.ThefirstoneisbetweenMarchandJuly.During thistimetheinflowintoBrepollenisinthelowerlayerand theoutflowintheupperlayer.Inthesecondone(between AugustandDecember)theinflowintoBrepollentakesplace inthe upper layers (mostly below30m).The first regime ensuesfromthetypicalcirculationwhenlighterfreshwater isflowingoutintheupperlayers.Thesecondonecomesinto existencewhenthevolumeoffreshwaterisnegligible.This situationistypicalofnarrowfjords,i.e.whentheinternal Rossbydeformation radiusis bigger than thewidth ofthe fjord.Inasuchsituation,waterflowsintothefjordinthe
upperlayers and outin thelower layers or vice versa. At middledepths,theinternaltidalmotionisbidirectionaland itsaverageconstitutesthelocalminimumofthemagnitude.
Fig.10illustratesthe9months'variabilityoftemperature forthreedepths:27,47and67m.Althoughthedifferences between the modelled andmeasured temperatures some- times exceed 2 degrees, the model appearsto reproduce seasonal variabilityquitewell. Correlationcoefficientsare mostly over 0.8; they are smaller only for the shallowest depths.Thelowercorrelationcoefficientsfor27mdepthcan beexplainedbythelow-resolutionatmosphericdatafocused on large-scale variability (ERAi). In addition, large scale reanalysis such as ERAi does notfocus on localscale pro- cesses.
4. Results and discussion
4.1. GeneralcirculationAsmentionedbefore,rotationaleffectsinfluencethegeneral circulationinHornsund: thisis presentedinFig. 11astwo typicalcirculationregimes.Thefiguresrepresenttheaver- agecirculationfor thewholedomain(temporalanddepth mean)forJanuaryandJuly2008,whichisequivalenttothe winterandsummerstates.Forgreaterclaritywehaveused streamlinesinsteadofvectors.
Themaincirculationpattern(showninFig.11)represents theresidualcurrentthatentersthefjordonthesouthernside and then recirculates along its northern part. In summer, watersofshelforiginpenetratemuchfartherintothefjord's mainbasinandreachtheentranceoftheinnerbasincalled Brepollen. In winter, fresh water sources are limited to Figure10 Temporalvariabilityoftemperaturefrominsitumeasurementsandmodelsimulations:red—fromthethermistorstring, blueandgreen—theHRMmodel(2006—2007and2007—2008respectively).ThelocationofthemooringismarkedinFig.2by'M'.Linear correlationcoefficientsareinsertedoneachfigure.ThecorrelationcoefficientsbetweentemperaturesfromthethermistorsandHRM for2006—2007aremarkedinblue,andthecorrelationcoefficientsbetweentemperaturesfromthethermistorsandHRMfor2007— 2008ingreen.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthis article.)
meltwaterfrommarineterminatingglaciers,thustheresi- dualcirculationpatternissimilarbutthevolumeexchange between the fjord and the shelf is much smaller than in summer(MIKEDHIdoesnothaveanyassimilationdatamod- uleorparameterizationofocean-glacierinteractionsuchas surfacemeltingorsubmergedplumedischarge,sotherepre- sentationofunderwaterglaciersisnotpossible).Acyclonic circulationisobservedinthecentralareaofthefjordmostly duringtheperiodswhenfreshwaterinputsarethesmallest.
In summer this cyclonic flow is disrupted by an intense
circulationdrivenbyfreshwaterfromterrestrialandglacial sources.ThecirculationinBrepollen,theeasternmostpartof thefjord,isalsocharacterizedbyseasonalvariability,with the main winter circulation pattern significantly different from thatin July. Small-scale eddies in Brepollen, Samar- invagen and Burgerbukta are also more abundant in July.
Increasedfreshwaterdischargeinsummerresultsinstronger stratificationinthefjord; asaconsequence,submesoscale eddiesaregeneratedowingtotheinternalRossbydeforma- tionradius.
Figure11 Streamlines(whitelines)andcurrentspeed(colour-coded)overdomainandtimeaveragedinHornsundforJanuary(a) andJuly2008(b).
Figure12 Averageseasurfacesalinity(aandb)andtemperature(candd)retrievedforJanuary(candd)andJuly(aandb)2009.
4.2. Hydrologicalfront
The fjord's dynamics andfresh waterfrom the catchment area (including the underwater glaciers, which are not includedinthemodel)generateahydrologicalfrontmostly at the mixed layer depth. Fronts, natural boundaries betweenwatersofdifferentproperties, affectmixingpro- cesses,whichoccurinthewaterinboththehorizontaland vertical.Dramaticchanges inthepropertiesof waterscan resultintheformationofvariouseddies,whichaffectlocal windconditions,coastalupwelling,intrusionsofintermedi- ate waters andsea ice. The fronts may bevisible on the surfaceasdemarcationlines,colourchanges,foamaccumu- lationorchoppywaters.Thebestindicatorsofthespreadof riverinewatersintheseaaredensityandsalinity(Fedorov, 1986;GinzburgandKostianoy,2009),buthereweusetem- peratureandsalinity.
Thefrontisrepresentedbystrongtemperatureandsali- nitygradients(Fig.12).Freshwaterfromthecatchmentarea leavesthenorthernareaofthemainfjordandoceanicwater entersthefjordthroughthesouthernpartofthemouth.The shapeandgradientofthefrontdependsmostlyonthefresh watercontentinthesurfacelayersofthefjord.
Inwinterthisfrontalsoexistsbutthesalinityandtem- perature gradients are much weaker andthey are clearly symmetrical.The temperatureandsalinity distributions in thefjordaremorehomogeneousatthattimeandthefjord watersaregenerallyseparatedfromtheAWoftheWSCbythe front,yetitsshape,locationandphysicalpropertiesstrongly dependontheseason.Theshapeofthesurfacetemperature and salinity fields result from the dynamic impact of the Earth's rotationon thefjord.The typicalbaroclinicRossby deformationradiusis3.5—6kmfortheSvalbardfjords(Cot- tieretal.,2010).TheouterpartofHornsundis30kmwide, whichis5—10timesgreaterthantheinternaldeformation radius.Theeffectofrotationisbettervisibleinthesummer months, since in the warm season the strongly, vertically
stratifiedwaterstend toreducetheinternalRossbydefor- mationradius,sotheCoriolisforceismorepronouncedand canactmoreeffectivelyinthenarrowerpartsofthefjordas well.Fig.13b—fshowsthesectionsmarkedinFig.13a.The firstone(IP1-IP2-IP3-IP4-IP5)isalongthefjord(wecallitthe along-fjordsection(HS)),whilethesecondoneisacrossthe fjordentrance(A-A0,the cross-section(VS)). AttheHS an areaisvisibleinthemiddledepthswithastrongsalinityand temperaturegradient (at about 20m depth) —above this depththefreshwaterfromthecatchmentareaflowsoutin thesurfacelayersofthefjord.Thewatersaremixed,andthe degreeofmixingdepends onthedistancefrom thesource andlocaldynamicconditions. TheVSsshowthatthemain core of theshelf waters entersthe southern mouth area.
Moreover, the image showing the velocities of VS (which representsthevelocityof inflow—apositivevaluemeans thattheflowisdirectedintothefjord)confirmsthatthemain outflowareaisintheupperandlowerlayersandiscloserto the northern part of the fjord. As mentioned earlier, the shapeofthefrontdependsonthefreshwatercontentinthe fjordandcouldbeveryusefulforestimatingtheamountof freshwaterfromglaciersandthecatchmentarea.Wewillbe abletoformulatemoregeneralconclusionsaboutthehydro- logicalfrontandtheimpactofotherfactorsonfrontforma- tionfollowingadetailedanalysisofthefrontoveralonger periodoftime;thisisplannedforthenearfuture.
4.3. Saltandheatcontentanditsanomalyofthe mainfjord andBrepollen
The fjord's dynamics strongly depend on the season. The annualvariabilitycould berepresented bythefjord'sheat and salt content. Furthermore, the fjord is known tobe under the strong influence of shelf waters consisting of WSCandSC,anditisimpossibletoseparatethembecause thesetwo currentsmixat the fjord'smouth (Gluchowska etal., 2016; Walczowski, 2013). Analysis of the salt and Figure12. (Continued).
Figure13 Verticalsectionsofsalinity,temperatureandvelocitytowardsthefjordforJuly;(a)locationsofthesections;sectionIP1- IP2-IP3-IP4-IP5ofsalinity(b)andtemperature(c);sectionsA-A0ofsalinity(d),temperature(e)andvelocitydirectedtowardsthefjord (f).SectionIP1-IP2-IP3-IP4-IP5iscalledalong-fjord(HS),sectionsA-A0andB-B0arecalledcross-sections(VS).Cross-sectionsareshown withnorthontheleft-handside(i.e.pointsAorBfrompanela)).Positivevelocityonthesubplot(f)isdirectedintothefjord.Sections A-A0andB-B0arealsopresentedfordiscussioninthesubsection'SaltandheatcontentanditsanomalyinthemainfjordandBrepollen' andinFig.16.
Figure13. (Continued).
heat contentin the whole fjordshowsthe clearly visible seasonal variability in the heat and salt content of the entirefjord and Brepollen (Fig. 14) (note: the reference temperaturefortheheatcontentwastakentobe0.18C).
Moreover,anyincreaseinthesaltcontentduringanypart oftheyear,exceptduringperiodsofdecreasingcatchment areaactivity,whichbeginsinmid-July(seeFig.4c),means thatitismostlyundertheinfluenceofWSC.Fig.15shows thesaltcontentanomaly(SCA)integratedovertime.The anomalywasintegrated becausethis process removesall small oscillations. For example, if the anomaly is repre- sentedbyasimplesine function,throughoscillation,the timeintegrated sine will yieldzero in the long-term. On the other hand, it works like a low pass filter. The salt anomalyintegratedovertime(anditsderivative—Eqs.(2) and(3)fortheentirefjordprovidesnoevidencethatonly WSCoronlySC(Fig.15)exertaninfluencethere.However, Fig. 16 shows that the method detects inflows of more salineorfresherwaterintothefjordorBrepollen,butitis stilldifficultto say whetherHornsundis under the influ- enceofonly one ofthem.
QAðtÞ¼ Z t
0ðQðt0ÞQÞdt0; (2)
Q0AðtÞ¼dQA
dt ; (3)
whereQisthetracer,tthetime,anduthetimeaveraged tracer.
Separating the inflows of WSC and SC in Hornsund appearstobeimpossible.ButforBrepollentheanomalies arevery stable andthere is astrong seasonalvariability.
Theinference is that the circulation is stablebut that it canbedisturbedbyfreshwaterfromthecatchmentarea and glaciers. Consequently, at this time scale, the circulationsuppliesadditionalheatandtransferssaltfrom the shelf area into Brepollen and the entire fjord.
Furthermore, it transfers additional salt and heat to the main fjord area, but this is small compared to the short time scale of natural variability associated with inflows fromthe shelf.As showninFig.15, thevariabilityin the Figure14 Heatandsaltcontentfortheentirefjord(a)andBrepollen(b)fortheperiod01.01.2006—31.12.2009.
saltcontentisrelatedtoinflowsofmoresalineorfresher water into Brepollen. The atmospheric influence on the saltcontent can beneglected. Precipitation represents a verysmallamountofthefreshwaterfromthecatchment area,and otheratmosphericfactors areunrelated tothe integrated salt content. Other factors that could have some influence on the salt content are underwater gla- ciers.Butaswestatedabove,weareunabletoconstruct evenasimplerepresentationof theglacier,sowe should not analyze the influence of heat content. SCA in the Brepollen shows a strong seasonal variability which depends strongly on freshwater discharge. Althoughthe freshwaterdischargeforeveryyearisidentical,theSCAs are different (Fig. 15). As mentioned above, we do not think that atmospheric factors could havea strong influ- ence on this. Only shelf waters consisting of mixed WSC and SC could change the shape of SCA. Fig. 16 shows sections B-B0 (shown in Fig. 13a) on the positive and negative representation of SCA(alsofor thepositive and negativetimederivativeofSCA).Itisclearthatincreasing (as wellas decreasing) SCAis caused by inflowsof more
salinewatersfromthe mainfjordtoBrepollen. Thetime derivativeofSCAismoresensitivethanSCAanditismuch easiertodetect inflowsof moresaline(orfresher) water intoBrepollen.
5. Concluding remarks
Ahydrodynamicmodelhasbeenimplementedforthewest SvalbardfjordHornsund.HRMreproducesseasonalvariability ofthefjordproperly. Validationof themodel showsquite goodagreementbetweentheavailabledataandthemodel results.Thegeneralcirculationisshown,basedonthemodel integrations.Generally,thefjordcirculationcanbedivided intotwo regimes, onerepresentingthewintercirculation, theother being related to summer andstrongly linked to fresh water discharges. Furthermore, the fjord's hydrody- namicfronthasbeendocumented.Seasonalvariabilityisalso presented for the heat and salt content. Analysis of the integratedsalt content anomaly suggests that apart from thestrongseasonalperiodicitydrivenbyshelfwaters,rela- Figure15 TheSCA(overtime)anditsderivativefortheentirefjord(a)andtheBrepollenarea(b)fortheperiod01.01.2006— 31.12.2009.
Figure16 Zoomed,time-integratedsaltanomalyfortheentirefjordandtheBrepollenarea,andsections(c,d,e,f)representing theinflowsofsalineandfreshwater(thetimelocationonthechartisalsomarkedonsubplots(a)and(b)),sectionsaremarkedin Fig.13a(A-A0 andB-B0).Theresultsarefor2007.
Figure16. (Continued).
tively largeamounts of saltandheatare transported into Brepollenwhen waterfrom the catchmentarea is carried intothefjord.
Themodelhasalsosomedrawbacks.Itdoesnotincorpo- rateanyicemodel,soitusesonlyexternaldata.Thismeans thereis no freshwater generatedduringicemelting. The sameproblemalsoariseswheniceforms.Freezingdoesnot introduceanysalinewaterintothefjord.Ice coverinthe model is treated only as a barrier between atmospheric forces and the fjord surface, modifying only momentum andheatfluxes.Furthermore,inanArcticfjorditisimpor- tanttoincludeunderwaterglaciers.ButDHIdoesnotprovide anymodulethatcouldhelpcreatesuchglacierwallsinthe model. The inclusion of these processes would probably decreaseheatcontentinthefjordandwouldincreasesalt content.Wethinkthatitcouldalsohavesomeinfluenceon thegeneralcirculationofthefjordaswellasontheshape, salinityandtemperaturegradientinthehydrologicalfront.
Weareplanningtoincludeinourfutureworkunderwater glaciers(inthefirststepinbasicformasanunderwaterwall thathasnosalinityorfreezingtemperature).Afterthatwe intend to investigate the hydrological front more deeply, includemore realistic winds (data from ECMWF are close tothegeostrophicwind,butthemainwindintheHornsund areaapproximatesaseabreeze)andanalyzetheinfluenceof factorsaffectingclimatechange.
Acknowledgements
WeareverygratefultoProf.AndrzejJankowskiforhisadvice andthehelpful,stimulatingdiscussion.
Theprojectwasco-financedfromthefundsoftheLeading NationalResearchCentre(KNOW)receivedbytheCentrefor PolarStudiesfortheperiod2014—2018.
Thisworkwasalsopartiallycarriedoutwithintheframe- work of projects GAME (DEC-2012/04/A/NZ8/00661) and AWAKE2(Pol-Nor/198675/17/2013).
Data fromtheA4andS800 modelsweremadeavailable through the Fram Centre 'Arctic Ocean' flagship project 'ModOIE'.
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