Filchner Ronne Ice Shelf: A coupled model study
Malte Thoma
∗, Jürgen Determann, Klaus Grosfeld, Sebastian Goeller, Hartmut H. Hellmer
AlfredWegenerInstitute,HelmholtzCentreforPolarandMarineResearch,Bussestrasse24,27570Bremerhaven,Germany
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received23December2014
Receivedinrevisedform2September2015 Accepted7September2015
Availableonlinexxxx Editor:J.Lynch-Stieglitz
Keywords:
modellingice–oceaninteraction Filchner–RonneIceShelf impactofclimate/oceanwarming sealevelrise
A general ocean circulation model is coupled with a 3D-thermodynamical ice-sheet/shelf model to simulatetheresponseoftheFilchner–RonneIceShelf(FRIS,Antarctica)andcoastalpartsofitscatchment basin to apostulated inflowof Warm Deep Water into the ice-shelf cavity on a1000-yr timescale.
Prescribedoceanwarming(basedonclimateprojections)enterstheice-shelfcavityintheupto1500 m deep Filchner Troughand penetrates deep into the sub-icecavity. Increasing basal meltrates induce geometry changesofthecavity, whichinturn haveanimpact ontheoceancirculationand therefore the modelledmeltrates.Highestmeltratesofabout 20 m yr−1follow the(upto 180 km)retreating groundingline.Basalmasslossreachesabout250 km3yr−1,doublingthepresent-dayvalue.Themost vulnerable areas below the FRIS are the Bailey Ice Stream and the area between the Institute and MoellerIceStreams,wheretheincreasedmeltingaccountsforabout80 kmofthemodelledgrounding lineretreatonthebackwardslopingbedrock.Thepotentialadditional contributiontotheeustaticsea level riseduetothegrounded-iceloss, simulatedinanensembleapproachagainstatransientcontrol experiment,isabout0.05 mm yr−1duringthefirst500 yrandabout0.17 mm yr−1thereafter.
©2015ElsevierB.V.All rights reserved.
1. Introduction
Ice shelves influence ice-sheet dynamics by contributing a back-stress component(buttressing effect), opposing the ice flux from the continent to the ocean, and thus controlling Antarcti- ca’sgrounded-ice volumewhich affects theglobalsea level(e.g., Dupont and Alley, 2005; Joughin et al., 2012). In particular, for the Filchner–Ronne Ice Shelf (FRIS) cavity, ocean general circu- lation models project a 2 K warming by the end of the 21st century, causing a multifold increase of melting at the base of Antarctica’ssecond biggestice-shelf system(Hellmeretal.,2012;
Timmermann and Hellmer, 2013). The FRIS is fed by a num- ber of ice streams, draining catchment basins of the West and EastAntarcticIce Sheets(Fig. 1b).Increased basal meltingatthe deepestpartsofthefloating iceshelf wouldinducethinning and a decrease in buttressing forces to the grounded ice sheet. On the other hand changes in the ice cavity geometry by melting (freezing) influence the ocean circulation regime with enhanced (reduced) ventilation of the cavity. Due to the weak stratifica- tionin iceshelf cavities the circulationis steered along constant
*
Correspondingauthor.E-mailaddress:Malte.Thoma@awi.de(M. Thoma).
f/H-contours (f Coriolis force, H water column thickness) and therefore is highly sensitive to water column changes (Grosfeld and Sandhäger, 2004). A subsequent retreat of the grounding line would lead to a reduction of the grounded icevolume and thus a further contribution to global sea level rise. Since large parts of the ice sheet in the investigated area are resting on an inland-sloping bedrock (Rosset al., 2012), ice-dynamicprocesses could trigger a marine ice-sheet instability (MISI) (Schoof, 2007;
Gudmundssonetal.,2012).Suchafastandwidespreadgrounding- line retreatmay captureparticularly regions wheregrounded ice is based on bedrock far below sea level. Thishas been assessed fromgeophysical observations(Rossetal., 2012) forMoellerand Institute Ice Streams (Fig. 1). A recent modelling study (Wright et al., 2014) indicates the vulnerability of thisarea. In principle, a grounding-lineretreataffectsicedynamicsduetoachangefrom an ice-sheet to an ice-shelf flow regime. For a given ice geom- etry, this retreat results in a local loss of basal friction, causing higher ice flow velocities and thus favouring increased ice dis- charge. A similar process seems tocontrol the speed-upandthe retreatofthePineIslandGlacier(Favieretal.,2014).Thepotential heatflux,providedbytheoceancurrentsbeneaththeiceshelf,is therefore the principle driverfor icesheet mass lossor instabil- ityinAntarctica, aslongassurface melt processesdo notplay a significantrole.
http://dx.doi.org/10.1016/j.epsl.2015.09.013 0012-821X/©2015ElsevierB.V.All rights reserved.
Fig. 1.a) MapofWeddellSeasectorofAntarctica.Redboxmarkstheregionofthecoupledice-sheet/shelf–oceanmodel.b)Oceancavitygeometry,1000 yearsafter initiatingoceanwarming.Colour scaleindicatesnegativebedrockandcontoursindicatewatercolumnthickness.Thebathymetricdepression,FilchnerTrough,actsasinflow regionforwarmoceancurrents.Browndotsindicatepositionoftheshelficefront(after1000 years);redlineshowsinitialiceshelfedges(includinggroundinglineposition).
TheyellowlineindicatesthelocationofthetemperaturesectionshowninFig. 2.NamesindicateicestreamsfeedingtheFRIS.
Most studies investigating the impact of climate warming on icesheet–iceshelf systems,implya steady-stateinitial condition.
This is achievedby tuning the model’s boundary conditions and parameters until themodel is ableto reproduce thepresent day observations as close as possible. However, it is arguable if the presentdayice sheetscan be considered to be in asteady state atall,ratherthaninatransitionaladjustmentphasesincethelast deglaciation.Therefore,wetakeadifferentapproachhere:Instead oftuningour coupledmodeltowards thepresentdayconditions, weuseanensembleapproachtoestimatethepotentialimpactof oceanwarmingonthesealevelrise.
Inour study,we analyse theimpact ofocean warming ofthe FRIS cavity and the corresponding contribution to sea level rise witha fullycoupled icesheet/shelf –ocean model.For thispur- pose we introduce the applied models and their coupling (Sec- tion 2) before we present the results (Section 3). Finally (Sec- tion4),wediscusstheimplicationsandcompareourresultswith otherfindings.
2. Modelsetup
We coupledtheice-flow modelRimbay1 (Thomaet al., 2014), andtheregionaloceancirculationmodelRombax2 (Grosfeldetal., 1997; Thomaetal.,2006,2014)inordertoinvestigategrounding- linemigrationandgrounded-icevolumechangesintheFRISregion withina centennialtimescale followingtheonsetofahigh-melt mode.The asynchronous coupling-procedurewithRiRoCo3 isde- scribed in detail in Thoma et al. (2010). Rombax provides heat fluxesnecessarytoquantifymeltratesattheice-shelfbasebysim- ulatingthethermohalinecirculationwithintheice-shelfcavityand theadjacentocean.Ourice-model domaincomprisesthepresent- dayareaofFRISaswell asnear-shorepartsofitscatchmentarea, totalling1.4×106 km2(Fig. 1a).
2.1. Ice-sheet–ice-shelfmodel
The3-dice-flowmodelRimbay(Thomaetal.,2014) isapplied withahorizontalresolutionof10 km.Themodelusestheshallow- iceapproximation(SIA)torepresentice-sheet flowdominatedby vertical shear, andthe shallow-shelf approximation (SSA), which
1 RevisedIcesheetModelBasedonfrAnkpattYn.
2 RevisedOceanModelBasedonBryAnandCoX.
3 Rimbay–Rombax–Coupler.
utilises longitudinal stresses to simulate ice-shelf spreading. Up- stream of the grounding line, a transition zone of 40 km width allows a numerically smooth change frompure ice-sheet flow to pure ice-shelf flow by interpolating both solutions. The ice rhe- ology, which links the deviatoric stress with the strain rate, is described byGlen’s(isotropic)flow lawwiththeexponentn=3.
Modelstudiesindicate thatintroducingan enhancementfactorto this empirical relationship improves the modelled ice velocities withrespecttoobservations.Weapplytwodifferentenhancement factors for the ice sheet andice shelf (4.5 and 0.5, respectively, consistent with Martin et al., 2011), which reflect the different anisotropiccharacteristicswithintheseicebodies(Maetal.,2010).
In general, a horizontal resolution of 10 km is considered to be toocoarse to representalldetails ofgrounding linemigration (e.g.,Pattynetal.,2013).Ifthegridresolutionisinthesameorder ofmagnitudethan theexpectedgroundinglinemigration,details of themigration cannaturally not be resolved (Levermann etal., 2014).However, ifthegroundinglinemovesoverlarge distances, this limitation becomes lessrestrictive. This has been shownfor Rimbay in Thoma et al. (2014, Section 6.3), where parts of the first MISMIP (Marine IceSheetModel IntercomparisonProject) ex- periment (Pattyn et al., 2012) were successfully repeated. They demonstrated that a 10 km andeven a 20 km gridresolution is sufficient to reproduce a reversible grounding line migration of about730 km.Also,Pollardetal. (2015)showedthatforglacial/in- terglacialclimate-forcings thedifferencesbetween10 km,20 km, and 40 km grid resolution are negligible in the context of the modelled impact on sea-levelrise. In the second MISMIP bench- mark(MISMIP-3D,Pattynetal.,2013),wheretheGRLmovesonly about18 km,itwasdemonstratedthatRimbayisabletosimulate a reversible grounding line migration and to estimate diagnostic horizontal velocities within acceptable limits, given the low grid resolutionandthecomparableimmobileGRL.
A second issue in the context of grounding line migration modelling is the difference between a coupled SIA/SSA model and higher order models. According to Pattyn et al. (2013) and Feldmann etal. (2014)the responsetime of SIA/SSA andhigher- order models differs. However, with respect to the centennial timescales,onwhichthe icesheet/shelfresponds toclimateforc- ing, thedecadal-scaledifferencesbetweenSIA/SSAandhigheror- der models have only a minor influence on our results (Mengel andLevermann,2014).
Thomaetal. (2014)showedinanextendedversionoftheMIS- MIPexperiment(Pattynetal., 2012) withanestedhigherorderor FullStokesphysicszone aroundthegroundinglinethatRimbayre-
shelves.
For capturing the dynamics of grounded ice flow, basal slid- ing is taken into account by the Weertman sliding mechanism (e.g., Cuffey and Paterson, 2010) with a constant basal friction coefficient. Vertically, 41 terrain-following layers resolve the ice- sheet flow with the highestresolution near the lower boundary.
Themodelledice-flux divergence,surface accumulation (Le Brocq et al., 2010), and basal melting or freezing at floating parts (as modelledby the ocean model) determine projected ice-thickness changeswithinthesystem.Thesurface accumulationiskeptcon- stantinallexperimentsdescribedhere.AccordingtoWrightetal.
(2014), it would have to increase significantly more than prog- nosedinclimate scenarios tocounteract increasedbasalmelting.
Calvingis notexplicitlymodelled here,insteadtheice-fluxis ex- portedvirtually atthe ice shelf front. However, Rimbay allows a shelfretreatfora negativeflux balanceattheiceshelf front,i.e., ifbasal meltingsurmountsother fluxcomponents.Basal topogra- phyand ice thickness (ALBMAP, Le Brocq et al., 2010) yield the positionofthegroundingline(bymeansoftheflotationcriterion), whichbecomes the southern boundaryofthe ocean-model com- ponent.Onthelateralmodelboundaries,whicharenotconsistent withthe drainage basin ofthe FRIS, thevelocities are estimated accordingtothelocallydefinedSIA,andicethicknessisassumed to be constant. The latter simplification is justified for the only several-century-longice-sheetevolutionevaluatedinthisstudy,as icethicknessalongtheedgesofthemodeldomaindecreasesonly byafewmeters(lessthan1%),whichcanbeignored inthecon- textofsea-levelrise.WiththissetupRimbayisabletomodelthe generalfeaturesoftheobservedflowpattern(Rignotetal.,2011) without anyadditional tuning within acceptable limits(see sup- plementalmaterial).
2.2.Oceanmodel
Weusetheprimitiveequation,generalcirculationoceanmodel Rombax,which hasbeenusedin severalapplicationstosimulate thecirculation andice–oceaninteraction inice-shelf cavitiesand theadjacentocean(DetermannandGerdes,1994; Grosfeld etal., 1997; GrosfeldandSandhäger,2004; Thomaetal.,2006,2014).In thecurrentstudy,Rombaxisapplied ina horizontalresolutionof 0.1◦×0.3◦,correspondingtogridcells ofabout11 km×8 km at 75◦S.Inthevertical,15terrain-following layersresolvethewater columnwithintheiceshelfcavity,andfouradditionalsurfacelay- ersofconstantthickness(each25 m)intheopenoceanpreventa pressuregradienterroratthesteepicefront(Grosfeldetal.,1997).
Theminimumlayerthicknesswithin thecavityisforcedtobeat least1 m, butmostlayers are in theorder of10 to50 m thick.
Themaximumlayer thicknessisabout102 m.Northofthe calv- ingfront, Rombax’s modeldomainisextended by an open-ocean regionofabout50to100 kmwidth(Fig. 1).
Atthe northern edgeof theocean domain an open boundary serves as a gate for the climate signal by prescribed inflow of awarm ocean current. At inflow regions,ocean temperature and saltare restored(nudged) toprescribed conditionsand advected
nual cyclesareexpectedto be asecondary effectonly,compared to the impact of thestrong and warm inflow atthe open-ocean boundaryanalysedinthisstudy.
In general, the major driving mechanism for ice–ocean inter- actionwithin the ice-shelfcavityisthe heatexchange across the ice–oceanboundary(e.g.,LewisandPerkin,1986).Relativelywarm currents with respect to the in-situ freezing point (Foldvik and Kvinge, 1974) provide heatformelting,becomefresherandmore buoyantandtendto riseintoshallowerareas.Here, beingsuper- cooled withrespectto thein-situfreezingpoint ofthisless-deep boundary,thewaterhasthepotentialtoformiceplatelets,which accreteattheice-shelfbase.InRombax,the processofice–ocean interactionisparametrised accordingtoathree-equationformula- tion(e.g.,HollandandJenkins,1999).
TheFilchnerTroughservesasthemainexchangerouteforwa- termassesof theWeddell Seaslope currentandthe FRIS cavity.
Thetroughendsatthecontinentalshelfbreakwitha600 mdeep sill, where presently Ice Shelf Water (ISW) colder than −1.9◦C leavesthetroughatthebottomofitswesternflank(e.g.,Grosfeld et al., 2001; Foldvik et al., 2004). Modified Warm Deep Water (MWDW) enters the Filchner Trough at its eastern flank with a seasonalcycle,rangingfrom0◦Cduringsummerto−1.5◦C during winter (Årthun et al., 2012). Recent findings derived from CTD- sectionsandmooringdatabyDareliusetal. (2014)andmodelling effortsbyMakinsonetal. (2011)suggestthattheclassicalviewof adeepcycloniccirculationofIceShelfWater(ISW)(Carmackand Foster,1975) mightbe revisedintoa flow whichturns eastward, leavingtheice-shelfcavity,andcrossesthesillattheeasternflank oftheFilchnerTrough.
As a responseto climate warming,according tothe IPCC AR4 (Bernstein et al., 2007) scenario A1B (atmospheric CO2 reaches 700 ppm by the year2100),ocean-model simulations projectthe intrusionofWarmDeep Water(WDW)ofcircumpolarorigininto the Filchner Trough at rates of 2.5–4.0 Sv (1 Sv=106m3s−1).
In order to trigger a high-melt phase in our simulations, we in- stantly raise potential temperatures of the deep inflow to 0.1◦C and salinity to 34.75, following the projections of two coupled sea–ice–ocean models (Hellmer et al., 2012; Timmermann and Hellmer,2013).A prescribedmasstransportof3.0 Svatthenorth- ern boundary off the Filchner Trough induces a southward flow of these warm waters, guiding them through the trough under- neath the iceshelf (Fig. 2b). To the west, in front of the Ronne Ice Shelf, only a θ, S-restoring to climatological values is per- formed.Ingeneral,themodelledcirculationbeneaththeFRIS(not shown)isinagreementwiththeresultspresentedbyGrosfeldand Gerdes (1998)andGerdesetal. (1999),whousedapredecessorof Rombax. By neglecting the influence ofwind and sea-ice effects, all changes in theocean–ice-shelf interaction can be tracedback tothepostulatedwarmflowintotheFilchnerTrough.
2.3. Modelcoupling,modelspin-upand ensemblemeanapproach Before the ice sheet is allowed to evolve freely, Rimbay is run for 1000 years with a fixed geometry to adjust the thermal
Fig. 2.Transect of potential temperature along the yellow line shown inFig. 1during the first 1000 years (left) and after warming occurred for 900 years.
regime within the ice to the given boundary conditions. After- wards,thefullcouplingbetweentheicesheet/shelfmodelRimbay andtheoceanmodelRombaxisperformedbythecouplerRiRoCo (Thoma et al., 2010):After50years(orevenlessfortheearlycy- cles) ofice thicknessevolution, thecavity geometryis passed to theocean model Rombax, whichis integratedforabout8 model years until a quasi steady state of the basal melting is reached.
TheestimatedbasalmassbalanceispassedbackviaRiRoCotothe ice model Rimbay, which now evolves according to the updated boundaryconditions.Thisasynchronouscouplingprocedureissuf- ficient as ice and ocean models evolve on different time scales.
A similar approach has been applied by Grosfeld andSandhäger (2004),whomodelledanidealised coupledice–oceansystem.The exacttiming ofthegroundinglinemigration (retreat)isofminor importance for the potential of additional sea-level contribution, therefore, we choose coupling cycles between 10 and 50 years.
Fig. 3ashowsdiscontinuous changesinbasalmassbalanceinthe order of10 km3/yr, whichis less than 10% of the total amount.
Thefigure alsoshowsan asymptoticbehaviourof thebasalmass balancechangeduringtheevolution(lowerstepstowardstheend ofthesimulation)andasmoothevolutionoftheiceshelfareaand icevolume.Thisindicatesthatthechoiceofthecouplingcyclesis sufficient.
To estimate the impact of ocean warming on the fully cou- pled system, the unwarmed controlrun is continued until model year2200. Anensembleofnineclimatesensitivityexperimentsis createdby inducingocean warming accordingtothe methodde- scribedinSection 2.2,every 100yearsbetweenmodelyear1100 and1900.Theensemblemembersdifferbytheirinitialstate(e.g., ice volume, grounding line position). A comparison betweenthe controlrun(Fig. 3a)andthewarmingscenarios forcorresponding yearsafter thewarming hasbeeninitiated, allows to projectthe climate impact on the ice shelf, while the FRIS is ina transient state(seeSection3).
3. Results
PreviousapplicationswiththepredecessorofRombax(Grosfeld and Gerdes, 1998; Gerdes et al., 1999) showed that the mod- elled basal mass balance of FRIS is consistent with evidence of marine ice beneath the ice shelf (e.g., Grosfeld et al., 1998;
Sandhägeretal.,2004).The spatialpatternandthemagnitudeof the basal mass balance of the control experiment (Fig. 4a)is in agreement with these earlier studies and with recent results of thefiniteelementoceanmodelFESOM(Timmermannetal.,2012;
Timmermann and Hellmer, 2013). Highest melt rates occur near theFilchner IceShelf front andnearthegrounding linesofdeep troughs, corresponding to ice stream estuaries. However, in our modelthisicelossisonlypartlycompensatedbysurfaceaccumu- lationandice fluxfrom theinner icesheet. Since itis unknown whethertheFRISisinsteadystateornotwerunourmodelwith-
out anytuningofbasal slidingoriceviscosity.(Recent massbal- ance estimates derivea slightlypositive mass balance,e.g., Paolo etal.,2015.)Thesimulatedvolumeandiceshelf areaareincreas- ingslightlybyabout3.3%and6.9%within1000 years,respectively (Fig. 3a).ThisisingeneralagreementwiththeresultsofWrightet al. (2014),whomodelledthesameregion,butwithaverydifferent approach(seediscussioninSection4).Notethatinthecontrolrun, the initialbasal melting(model year1000)issignificantly higher thanaftersomecouplingcycles,duetoanicethinningandacor- respondingadjustmentoftheoceancirculation(Fig. 3a).
After ocean warming at the inflow of the Filchner Trough is initiated, accordingto projectedclimate changeimpacts (Hellmer etal., 2012; TimmermannandHellmer,2013), meltingattheice shelfbaseincreasesdramatically(Figs.3a,band4b).Theimpactof oceanwarmingonthecoupledice–oceansystemcanbeevaluated by comparingthewarming experimentswiththe(unwarmed,but coupled) control experiment after corresponding years of evolu- tion.Fig. 3showsthetransientcontrol experimentandanomalies between the ensemble mean results plus the standard deviation for the individual ensemble members. Thus, the impact of the warming signal can be separated fromthe transient state of the coupledsystem.
The ocean warming results ina distinct increase of the basal masslossbyabout125 km3/yr(i.e.,doublingtheformervalue)for about 500 years (Fig. 3a,b andFig. 4).This reverses the volume gain of about0.33% within the first 100 years of the control ex- perimentto avolumelossofabout0.75%within100 yearsofthe warming experiments andhasconsequences forthe ice-shelfge- ometry(Fig. 5a)andice-flowvelocities(Fig. 5b)ofthecoupledice- sheet/shelfsystem. Becauseofoceanwarming,thegroundingline retreats faster between Moeller and Institute Ice Streams (com- pare Fig. 1), possibly reaching an ancient position, as suggested by Ross et al. (2012). Observed sediment layers in this subma- rine basinindicate a formerdeglaciationof thearea. Theregions withhighestbasal meltratesfollowtheretreatinggroundingline (Figs. 2 and 4).TheFRISareaincreasesbyabout25 000 km2within 700 years (Fig. 3c), representinga growthof about6% compared tothepresent-dayvalueofabout435 000 km2(compareFig. 3aat thebeginningofcouplingcycles).Thisincreaseistwiceasmuchas wasanticipatedbyestimatesofhistoricalgrounding-line positions accordingtothebedrockcharacteristicsoftheconcerned reverse- slope basin (Ross et al., 2012). The only other region, where a significant grounding line retreat takes place is further north in theareaoftheBaileyIceStream.
Compared to the control run, the ice thickness decreases by morethan 100 mwithinlarge partsoftheFilchner IceShelfand more than 1000 m in thenewly formed ice shelf areasbetween theMoeller–InstituteIceStreamsandattheFoundationandBailey Ice Streams(Fig. 5a). The changefromgrounded ice(withveloc- ities of lessthan50 m yr−1) towards floating iceis accompanied byan iceflowaccelerationofmorethan500 m yr−1,demonstrat-
Fig. 3.a)Timeevolutionoficevolume(blue),iceshelfarea(black),andbasalmassbalance(red)oftheFRIS-areaforthecontrolexperiment.Stepsinthebasalmassbalance indicatecouplingcycles.b–d)Differencesbetweensensitivityexperimentsandcontrolexperiment(a),showingtheimpactofoceanwarmingonbasalmassbalance,iceshelf area,andcorrespondingeustaticsea-levelrise.Theshadedareaindicatesthestandarddeviationofthewarmingscenarioensemblemembers,startingatdifferentyearsof thecontrolexperiment.
Fig. 4.Basalmeltratesandgroundinglinepositionestimatedwiththecoupledice-sheet/shelf–oceansystemafter2200yr(1200yrofdynamicicesheet/shelfevolution).
Thegreenlinesindicatetheinitialgroundinglineposition.a)Controlexperiment,b)Warming(initiatedafter1100modelyears)experiment.
ingtheresponseoficedynamicsonamelt-inducedgrounding-line retreat(Fig. 5b).
4. Discussionand conclusion
Acommonapproachwhenmodellingtheimpactofclimate(in thiscaseocean)warming on theclimate system(in thiscaseon theFRIS andits hinterland) isto start froma quasisteady state,
whichrepresentsthecurrentconditionsascloseaspossibletoob- servations, and to analyse the deviationin response to changing boundaryconditions.However,thisassumptionmightbeproblem- aticfortworeasons.First,ifanumericalmodeldoesnotreproduce thecurrentobservedstateofaconsideredsystemwithitsinherent physicsandhastobeforcedtowardsitbytuningofmodelparam- eters(whichismostoftenthecase),thereisnoguaranteethat(a) theseparameters are alsovalid fordifferentboundary conditions
Fig. 5.Simulatedchangesoficethickness(left)andice-flowvelocities(right)after1000 yearsofoceanwarming.Thegroundinglineisindicatedbythegreenline(initial positionuntilmodelyear1000),thedarkgreenline(positionincontrolexperimentafter2200 years),andtheblackline(positionafter2200yearswhenwarmingstartedat year1100).
and(b)the model’sresponse tochanging boundaryconditionsis correct. Second, for slowly varying systems like ice bodies it is notcleariftheyare inasteadystateinthefirstplace atall. Ad- justmentprocessesof icedynamics,sealevel,andsolid Earthon glacial-interglacial time scales, especially in response to changes since thelast deglaciation, are long-termtransient processes and cannot beconsideredascompleted.
Inthiscontext, we wouldliketo referto thestudyof Wright et al. (2014), who modelled the same region (FRIS) with the same question (impact of ocean warming), but with a very dif- ferentapproach:Wrightetal. (2014)tunedtheir icemodel(BISI- CLES) by inverting observed surface velocities and a prescribed 3D-temperature field fromPattyn (2010) forthe effectiveviscos- ityand basal traction. The basal mass balance fortheir ice shelf isthenderivedfrommassdivergence,assuming steadystate con- ditions. In addition, BISICLES uses an adaptive mesh refinement around the grounding line to representits possible migration as goodaspossible.Becauseoftheappliedinversion,theirmodelled icevelocities are ingood agreementwithobservations. However, despiteall theseefforts,the initial (observed)groundinglinepo- sition is not stable and significant ice thickness adjustments of several hundred meters occur during their 2000-year model run (see Fig. 5a inWright etal., 2014). This isin generalagreement withourfindings, asforournot-tunedicemodelRimbaytheini- tial FRIS domain is not in steady state for the currentboundary conditions,too.
Thismightindicate,thateither(a)theappliedboundarycondi- tions (e.g.,surface massbalance, surface temperature, basalmass balance,bedrock topography)havedeficits,(b) themodelphysics andparameterisations (which are quitedifferent inboth models) donotrepresentthereal-worldphysicssufficiently,or(c)thecur- rentlyobservedFRISisnotinsteadystatebutratherinatransition phase.
Nevertheless,despiteall modellimitations,itispossibletoes- timatetheimpactofclimatechangeontheFRIS domainbycom- paringwarmingscenarioswithanun-warmedcontrolexperiment.
Wright et al. (2014) scaled the present day basal mass balance bysimplelinearmultiplicationofthepresent-daybasalmassbal- ancepatternandbyextrapolationintoformerlygroundedareasto simulateocean warming. However, thisapproach is limited asit cannot represent the dynamic response of the ocean to a modi- fiedcavitygeometry,whichleads to apatternshift.Furthermore,
formerfreezingareasmightnotsurviveiftheamountofprovided heat exceedsthe meltingcapabilitynearthedeepgroundingline orareasofmeltingmightturnintofreezingareas(Fig. 4). There- fore,thecomplex3D-geometrybeneaththeFRISdemandsahighly resolved (intheorderof10 km) oceanmodeltoderive thebasal melt (andfreeze)pattern, whichisinteractivelycoupledwiththe overlying ice shelf. Our coupled modelling approach shows that ocean circulationand melt regions follow a migrating grounding line. Thiskey process ofamarine-based ice-sheeterosioncannot be mapped by any simpleparametrisation of sub-ice-shelf melt- ing which ignores the highly dynamic feedback betweeniceand oceanasmentionedabove.Thiskindofparametrisation mightre- solvean averagebasalmeltratebutfailstofindandquantifyhot spotsatpotentiallyvulnerableareaslikethegroundingline.Also,a parametrisation whichneglectsthefeedbackofmeltwateronthe circulationmighttendtooverestimatethetotalmeltvolume.
Thestrongestimpactofoceanwarmingisfoundintheareasof Bailey andFoundationIceStreamsaswell asintheareabetween MoellerandInstitute IceStreams,wherethe icethicknessreduc- tion of(formerly)groundediceisaccompanied by anincrease of icevelocity,drainingthehinterland.
Theimpact onsealevelriseζ (t)duetoanicevolumechange (V) can be estimatedfrom the changes in icethickness (H), withspecialconsiderationofgroundedicebelowsealevelwhere bedrock(B)isnegative:
ζ (
t) = − ρ
Iρ
Ox
y A0
H if B
≥
0H
+
ρρOIB if B<
0 (1) withthedensities ofice(ρ
I) andocean (ρ
O),the oceanarea A0, andthehorizontalgriddimensionsxandy.Theimpactofthe ice loss, resulting fromocean warming, is shown in Fig. 3d. We estimate an additionalsea level rise of about 5 mm per 100 yr for the first 500 years, and a distinct increase of about 17 mm per 100 yr thereafter. This substantial increase results from the icethicknessreductionbetweenMoellerandInstituteIceStreams causedbythegroundinglineretreatinthisarea(Figs.5aand3b).ThesevaluesaresimilartotheresultsofWrightetal. (2014),who concluded that the FRIS sector hasthe potential to contribute to sea levelraiseby about0.3 m in2000 yr,which isequivalent to 15 mmper100 yr.
Wewouldliketoemphasise thatahigherice- andoceanmodel resolution,inparticularinthevicinityoftheGRLwouldcertainly
and MoellerIce Streams)under the FRIS catchment. At present, theWeddellSeasectoroftheWestAntarcticIceSheetmightrep- resentan intermediatestate betweena glacialandaninterglacial extent.Current climate change will last at leastfor severalhun- dredyears (e.g.,Solomon etal., 2009), butit needsto be proven whetherprolongedhigh-meltconditionsunderFRIS mightleadto adisintegrationofvastareasoftheWestAntarcticIceSheet.Inany case,ourstudycalls forfullycoupledicesheet/shelf–oceanmod- elsprovidingtheabilitytoincludethefullfeedbackofthecoupled climatesystem.
Acknowledgements
Thiswork was funded by theDFG through grant TH 1136/1-1 andpartiallysupportedbyfundingtotheice2seaprogrammefrom theEuropeanUnion7thFrameworkProgramme,grantNo.226375.
Here itis ice2sea publication numberice2sea161. Thiswork also contributestotheHelmholtzClimateInitiativeREKLIM(RegionalCli- mateChange),ajointresearchprojectoftheHelmholtzAssociation of German Research Centres (HGF). The authors wish to thank Ralph Timmermann for fruitful discussions, Rüdiger Gerdes for hissupport,andtwo anonymousreviewersforhelpfulcomments whichimprovedthequalityofthemanuscript.
Appendix A. Supplementarymaterial
Supplementarymaterialrelatedtothisarticlecanbefoundon- lineathttp://dx.doi.org/10.1016/j.epsl.2015.09.013.
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Furtherreading
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