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Open Access 6 Discussions , R. G. Bingham 2 The Cryosphere , and N. Ross 5 , M. J. Siegert 2 , D. M. Rippin 4 5476 5475 , S. L. Cornford 1 , T. A. Jordan 4 , A. M. Le Brocq 1 , F. Ferraccioli 0.3 m of sea-level rise. Significant advancements have been made in our 4 ∼ This discussion paper is/has beenPlease under refer review to for the the corresponding journal final The paper Cryosphere in (TC). TC if available. Geography, College of Life and Environmental Sciences, University of Exeter,Bristol Exeter Glaciology EX4 Centre, School of Geographical Sciences, University ofSchool Bristol, of Bristol, Geosciences, BS8 University ofBritish Edinburgh, Edinburgh Antarctic EH8 Survey, Madingley 9XP, UK Road, High Cross, Cambridge Cambridgeshire CB3Environment Department, 0ET, University of York, Heslington,School York, of YO10 Geography, 5DD, Politics UK and Sociology, Newcastle University, Newcastle Upon Tyne observed in the AmundsenPritchard Sea et region al., (e.g. Payne 2012), et ocean al., modelling 2004; studies Joughin suggest et that al., changes 2010; to current cir- 1 Introduction A recent geophysical surveyinstability has (e.g. highlighted Mercer, the 1978) potential atdell for both Sea a the sector marine-ice-sheet-type Institute ofthe and West bed Möller . topography ice has Near streams beeninland to in observed (Ross the the to et Wed- grounding be al., both lines 2012),ice smooth a of streams and configuration these currently to often ice show deepen called significantly no streams a signs retrograde of slope. While the these dynamic-thinning behaviour that has been ice rises within the Filchner-Ronnepact, Ice however, on Shelf. Rutford, These Carlson same oris perturbations Foundation found ice have to little streams, while im- enter Evansincreased a Ice by Stream phase an order-of-magnitude of from unstable likely retreat present-day values. only after melt at its grounding line has knowledge of both thethus basal enabling an topography assessment and tolection ice be of made ice velocity of streams in the feeding the relative theice Filchner-Ronne sensitivities Weddell sheet Ice of Shelf. Sea model, the Here diverse sector, we whichdynamics, col- use employs the to BISICLES adaptive-mesh carry refinement outface to such and resolve sub-shelf an grounding mass assessment. line balanceindicate The forcing that fields impact both from of the our Institute perturbationsin 2000 yr and basal to “reference” Möller melting model the Ice either run sur- Streams near are to highly their sensitive respective to grounding changes lines, or in the region of the A recent ocean modelling study indicateswarm that possible deep changes in ocean circulation water mayRonne bring ice into streams, direct suggesting the contact potentialalent for with future to ice the losses grounding from this lines sector of equiv- the Filchner- Abstract Sensitivity of the Weddell Seastreams sector to ice sub-shelf melting andaccumulation surface A. P. Wright The Cryosphere Discuss., 7, 5475–5508,www.the-cryosphere-discuss.net/7/5475/2013/ 2013 doi:10.5194/tcd-7-5475-2013 © Author(s) 2013. CC Attribution 3.0 License. F. J. Corr 1 4RJ, UK 2 1SS, UK 3 4 UK 5 6 NE1 7RU, UK Received: 4 July 2013 – Accepted: 12Correspondence August to: 2013 A. – M. Published: Le 19 Brocq November ([email protected]) 2013 Published by Copernicus Publications on behalf of the European Geosciences Union. 5 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 200 km up- ∼ ect the tributary ff 5478 5477 near to the grounding line of Rutford (Jenkins et al., 2006). 1 − Theoretical work has concluded that an idealised marine ice sheet that does not vary The Institute and Möller ice streams are separated by the slow flowing Bungenstock Several modelling studies (Dupont and Alley, 2005; Gagliardini et al., 2010) and a Analysis of the new basal topography from airborne radio-echo sounding has re- cases with two horizontal dimensions however, drag from the channel sides as well as The steep reverse bedfew slopes, pinning points) coupled of with botheven the the a low Institute small and basal increase Möller roughnessto in ice (and thinning streams, melt of suggest therefore at intuitively the the that grounded ice grounding ice shelf, plains line, may resulting or lead in aline. to flotation decrease and a possibly in speed-up unstable buttressing and retreat due thinning of the of grounding the alreadyin lightly the direction transverse to icerests flow on will be a inherently reverse unstable bed when slope the (Schoof, grounding 2007). line When the problem is extended to realistic order of magnitude, towards(Rignot values and currently Jacobs, found 2002). only in the Amundsen SeaIce sector Rise, bothgrounded ice ice streams plain have is a floated for “grounding a zone” period around either 10 side km of wide high where tide the (Brunt et al., 2011). ice streams feeding theCircumpolar Filchner-Ronne Deep Ice Water Shelf. but This itand is water-mass still 2.5 is ma warm cooler enough than toRecent the cause predictions of melt-rates ocean of circulation between models 0.1 future indicate, however, climate that relatively warming modest mightOcean result that in would changes allow to warmershelf circulation deep patterns in ocean in this water the area togrounding Southern penetrate (Hellmer lines across et of the the al., continental Filchner-Ronne 2012). tributaries If would this be were expected to to increase happen by then an melt rates at the in the Amundsen Sea Embaymenthigh region basal of West melt Antarctica ratesdue (Payne et observed to al., beneath the 2004). the incursion The cut Pine of the Island warm continental Ice shelf Circumpolarsalinity Shelf (Jacobs Deep shelf-water et are Water al., is thought along 1996). currently to channels In responsible be which the for cross- Weddell melting Sea sector at the the highest grounding lines of the fast-flowing ice streams is the main cause of the observed dynamic thinning identified thinning of ice shelves and the consequent decrease in buttressing at the mouths of climate. Several linear, glacially eroded basaleach troughs of are which found ends upstream in ofstream a the raised from basin, bar the indicative present-day of groundingsupport a former line the ice (Ross idea sheet et margin thatbeen al., the 2013). confined West These to Antarctic interpretations Icerently a glaciated Sheet stable basin has, beneath position the underclimate occupying trunks warmer of warming, the past the therefore, Institute may highlands climates, and risk upstream Möller a ice return from streams. of Future the the icegrowing cur- sheet body to of this observational configuration. evidence (e.g. Pritchard et al., 2012) suggest that the shallower on the tonguesAmundsen of Sea, the thus Institute implying andlower that Moller the driving ice bed stresses in streams (Joughining this than also et area they suggests is al., are able that in 2006;sediments, to the the deposited Ross support bed during et significantly of past al., the retreat Robin 2012). Subglacial phases Radio-echo Basin associated sound- is with covered periods with of marine warmer vealed the significance of awhich subglacial has basin a (recently depth namedupstream Robin of from Subglacial around the Basin) 1600 grounding met lines below al., of sea 2012). both level These the at icethe Institute streams a Bungenstock and currently distance Ice discharge Möller less Rise into ice(Fig. than where the 1). streams the 100 ice The km (Ross bed shelf reverse bed on elevationthat slopes either is beneath along side around both Thwaites of 1150 m Glacier. trunks below The are sea ice therefore level comparable stream to surface gradients however, are much Shelf (Hellmer et al.,ice streams 2012). and Such therefore changesmodel the to have parent investigate the the ice possibility mass. that potentialconsequent thinning In to reduction of this the of a Filchner-Ronne paper buttressing ice we atcould shelf, and the employ lead the to grounding an the lines ice loss of sheet of its grounded tributary ice. ice streams, culation patterns may result in greater melting at the base of the Filchner-Ronne Ice 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , even though 1 − ect on grounding ff is calculated using the ) which represents ice ϕ A . An inverse problem is solved to find er substantially. In this paper we aim to ective viscosity calculation incorporates C ff ff 5 km horizontal that are present throughout ∼ 5480 5479 cient , as discussed in Sect. 2.3. ffi ϕ erences and of their causes. and ff C ect of significantly reducing the maximum stable time- ff ect of disrupting the continuity of ice streams produced in the 20 m vertical and ff ∼ 1 and variable coe ect of ice shelves are found to have a stabilising e = ff set to 3. The ice-flow rheological parameter m n erent ice streams in this sector may di ff As is usual for ice sheet models the constitutive relation, which relates the rate of ice The aim of this paper is to assess the sensitivity of the various Filchner-Ronne Ice In addition to enhanced ocean warming and circulation, anthropogenic climate tions of the orderthe of region) had the e Basal topography and initial(Fretwell et ice al., thickness 2013). areet This taken al. includes from (2012) all the ascoverage the in well Bedmap2 data the as compilation collected Weddell several Sea inwas area other the applied (see recent to study Fretwell the et improvements ice area al.,2013). to thicknesssity by A so for the that correction Ross ice floatation for ice (van could firn thickness den be depth routine calculated Broeke, data with 2008). which a The fits single ice den- a surfacenecessary, was as cubic then detail spline modified in by curve the a to Bedmap2 smoothing surface surface topography points (specifically at surface 20 undula- km spacing. This was 2013; Cornford et al.,with 2013). exponent Resistance to basalspatially varying sliding fields is of governed both by a power-law 2.2 Input data and set-up law exponent relation formulated by Pattynby (2003) Pattyn from (2010) a andweakened 3-D by with structural internal an damage. temperature additional Whilevertically field the integrated variable stresses, e produced multiplier the ( componentto of be mass flux neglected due duestep. to The vertical to resulting shearing its model has still e when out-performs compared the to full shelfy-stream Stokes approximation, solutions however, of grounding line problems (Pattyn et al., 2012, tained at grounding lines wherethe the grounding ice velocity line is locationdomain. greater than may 100 sweep ma across a significant proportiondeformation to of the the amount model of force applied, is taken from Glen’s Law with the power the BISICLES mesh evolves during the simulations so that the finest resolution is main- mesh refinement method togrounding line allow than a for higher the rest grid of resolution the ice to sheet. be In applied all the near experiments to presented the here 2.1 Model description We use the BISICLES ice sheetford model, et a al. detailed description (2013). of BISICLESa which is two-dimensional is force given a in balance three Corn- approximation dimensionalfree-surface approach finite-volume problem to model with the which the solution applies rived of addition the of from Stokes a the vertically-integrated model stress of component Schoof de- and Hindmarsh (2010). The model uses an adaptive and location with respect tothe ice di rises within themake ice an shelf assessment suggest of that those the di responses of 2 The BISICLES ice sheet model change is also expected towarmer cause air changes temperatures to are precipitation likelywhich to patterns could mean and, mitigate an in some increase Antarctica, melt-driven in retreat. surface snow accumulation, Shelf tributary ice streams toturbations sub-shelf on melt/freeze-rate the and order surface accumulationThe of per- variations those in predicted geometry, basal to topography, occur catchment area, within grounding the line next melt few rate hundred years. line dynamics even onal., a 2009; retrograde Gudmundson bed et slopethe al., (Dupont stability 2012, of and 2013). paleo-ice Geophysical Alley,dependent 2005; evidence stream on also Goldberg grounding the suggests et line channel that locationssubstantially width (Jamieson on et available, reverse al., with slopes 2012). constrained has channels been slowing retreat the buttressing e 5 5 25 15 20 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . Ice vis- C are smoothly ϕ cient . Figure 2 shows 1 ffi − erence between ob- and ff while, away from the equal to 1 everywhere C C ϕ extends further inland than 1 − and of the sliding co-e which can be calculated as a function of ) can be considered as static ice. In the Re- A A 1 . No explicit calving model is used, instead 5482 5481 − 1 − ) are not available we follow the control method ap- to represent damage to the fabric of the ice that has ϕ ( 0.5 ma ϕ ective viscosity, particularly near to shear margins. As ff A ∼ a within ice streams, increasing as an exponential function to 1 and − 1 − C less than 1 (reduced viscosity) are mainly found around shear ϕ er ice is found upstream and in slower tributaries. 0.1 ma ff ∼ equal to 100 Pa m ect of decreasing the e ff C Ice outside the catchment of the Filchner-Ronne Ice Shelf was given zero velocity, This “control problem” involves fitting modelled ice velocities to satellite observations The surface mass balance field used in the model is taken from Arthern et al. (2006). The model domain was chosen to include the entire catchments of the Evans, Carl- a two-part parameterisation ofcontinuous fields the are sub-shelf produced that basal each mass cover the balance entire model is domain, developed. one Two for appli- many of their tributariesice shelf, are values characterised of bymargins while low sti values of 2.4 Sub-shelf mass balance parameterization A 50 yr model runness was held performed constant with thetime-step to grounding of allow line this the location run and ice the ice sheet shelf flux surface thick- divergence geometry within to the relax. ice From shelf the is last retained, and from it zero surface accumulation andboundary condition a at very the ice sticky divide.and As bed an in initial guess order weof set to measured provide velocity where an thethe unchanging ice results flow of speed the is control less problem than after 100 16 ma iterations. The trunks of all ice streams and with the upper andbe lower ice used surface to topographies find fixed.lem the An is best optimization under-constrained. method solution In may to but this iteratively the minimize case two an we unknown objectiveserved use cost-function variables and containing a mean modelled the gradient-based speeds. that di Tikhonov optimization thevariables regularization method prob- penalty are functions also for each includedvarying. of to the enforce a solution where both field measurements of proach of MacAyeal (1992) to invertof the present-day model equations ice using sheet asand input geometry surface measurements (Fretwell velocity et (Rignot et al., al., 2013), 2011). temperature (Pattyn, 2010) the e ice temperature with theinclude Paterson an and additional Budd multiplier (1982) relation. We choose, however, to increase from the calving front ofBedmap2 dataset, the and Filchner-Ronne all Ice ice crossing Shelf this is line fixed is2.3 assumed at to the be Inverse location lost modelling to given of calving. basal in parameters the In order to reproduce thespatially present-day variable ice sheet fields satisfactorily ofcosity it is the is necessary rate dependent to on factor provide Glen’s rate factor covery Ice Stream however, icethe flow model faster domain. than Its 100model. ma behaviour may therefore not be accurately representedWithin in the the model domain this prescribes a roughly uniform south-north accumulation adjusted with the methodlocation of was within Le one Brocq 1 km2011). et grid al. cell of (2010) the to ASAID grounding ensure line that (Bindschadler, et the al., son, grounding Rutford, line Institute, Mollerof and the Foundation Support ice Force and streamsto Recovery as this catchments well study (Fig. as 1).catchment (up the For (where to the lower velocities are time parts 2000 yr) < periods 20 ma relevant we assume that the upper parts of the Support Force ice sheet geometry, ice temperatures,scribed and in satellite Sect. measurements 2.3) ofin is the ice sensitive detail velocity to (de- of thethe surface surface and presence gradient basal of of topographies the basalter caused ice sticky-spots, the smoothing sheet. model which of A to resulted the mismatch erroneously ice in infer surface, discontinuous the ice bed streams. topography Af- (and hence ice thickness) was model. The inverse modelling approach to deriving basal boundary conditions from the 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0 in the forward model 500 m (Cornford et al., = ≤ t cult test of a sharp grounding line ffi . 1 − erence in results with further refinement also 5484 5483 ff 125 m). Initial and final grounding line positions = 200 yr the grounding lines of the Evans, Carlson, Rutford and Founda- = t 4 km) to 5 (minimum cell size = Taking into account the results of this previous work, we chose to use 3 levels of Previous modelling studies have found that, where the transfer to frictionless sliding Using the surface and basal mass balance inputs described in Sect. 2 we ran for- to have a similarStokes grounding solution line (although sensitivity this andtransition). was response That for time result the was to corroborated more a byGlacier di tests high in of the resolution the Amundsen BISICLES full Sea, model whereshape on a Pine was first-order Island found rate of for convergence2013). simulations of with grounding line a finest cell resolution refinement giving a maximum resolutionFig. 4 at show the that further grounding refinement line continues of to increase 500 the m. sensitivity Our of results the grounding in is gradual, a gridthe size grounding of line less accurately thanet (e.g. al., 1 Vieli km 2009; and Gladstone is Payne, et necessary 2005;et al., in 2010). Pattyn al., In et order 2012) the al., to MISMIP-3D a 2006; intercomparison model BISICLES Durand project movement (Pattyn simulation of with a maximum resolution of 400 m was found of their fjords whereShelf. they The meet Institute the Ice bay Streamconstrained containing has region of advanced the the by bulk Filchner-Ronne between of bay,Stream while 5 has the the and remained grounding Filchner-Ronne 20 stationary. line km In Ice of general, outrefinement the greater into at Moller advances an Ice occur all un- with ice greaterdecreases streams, mesh but as the the di resolutioncreases exponentially improves. with As the the numberan of time optimum levels taken compromise. of to refinement, it perform is a necessary simulation to select in- ward simulations for 200 yrsize with levels of refinementfor each increasing simulation are from shown 0 indomain. Fig. (minimum At 4a–f cell for each oftion the main ice ice streams streams in have the all model advanced by between 40 and 100 km to reach the widening Carlson, Rutford, Institute, Möller andto Foundation cells ice where streams ice and, flow within is these faster areas, than 100 ma imposed at the groundingresolution line to is use chosenincreasing for with levels the of care. grounding refinement. Weby line A investigated half single by the level for conducting appropriate of atdefined a grid least parts refinement series eight reduces of of cells the thecells experiments cell on domain. that with size either Two are levels side of halfreduce of refinement as computation any adds time large grounding a the again lineare parts further to limited within of 4-deep to either specifically the the layer side current domain of grounding of in line which the areas and grid grounding potential refinement line, retreat may paths and occur of so the Evans, on. To 3 Forward model runs 3.1 Model grid refinement The meshes employed all have coarsest resolution of 4 km, but the finest resolution, results of Joughin andice Padman stream (2003) grounding (Fig. lines 3b), andmelt-rate but less combined with freeze-on with slightly in surface greater the accumulation meltingtional centre from near component of Arthern the derived et ice from al.result shelf. the (2006) This in and flux basal an an approximately divergence addi- steady-statethe for ice present-day. grounded These sheet ice input with fields (Fig. awhich then A1) similar perturbations form configuration should can the to be basis that made. of of our reference experiment to away from the grounding line.at The each two new fields time-step arethe (over then grounding a combined line) distance to so of transition that smoothly measurements approximately the 35 indicate km maximum (Rignot melting on and follows the Jacobs,runs the floating 2002). the grounding side combined At line sub-shelf of time as mass satellite balance field (Fig. 3a) shows a similar pattern to the cation near to the grounding line and the other, the ambient field, relevant to floating ice 5 5 25 15 20 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | < 1.0 0.75. 400 yr ψ = = . t ψ 1 2000. The − a = 3 t 3 km ∼ to the basal accumu- ψ 200 yr and = t by the end of the run. This behaviour erent sub-shelf mass balance factors. 1 ff − a 3 5486 5485 8 km 40 km out into an un-topographically constrained ∼ ∼ 2000 the broad front of the ice stream has retreated by = t ect. We prefer this approach to a uniform shift (addition or ff ect of increasing the magnitude of both net ablation in melting areas ff > 1.0) has the e Aside from the application of a multiplying factor to the basal mass balance for float- Our reference run is intended merely as an approximation. It represents the condi- Significant variations in the behaviour of the ice streams become evident during the ψ than in the reference experiment.where The the Institute Ice grounding line Stream provides advances the only exception, et al., 1992). ing ice all other conditionsprevious were section. identical Figure to 6 thement shows reference given equivalent experiment in results described Fig. to in 5In the for those four Fig. for experiments the 6a, with reference di b,Although experi- significant a ice near thickness steady-statedrained increase by ice occurs the in sheet Möller every Ice is catchment Stream, obtained apart grounding lines after from do that 2000 not yr advance with substantially further and net accumulation inwill areas have where the there is oppositesubtraction) freeze-on, e from while the a basal multiplierresulting mass changes 0 balance should < in field fact be asrate crudely it of analogous thermohaline to is convection an likely beneath increasewithin to the or decrease ice the be in shelf cavity more the where increases realistic. more the energetic The rate circulation of sea-ward mass transfer, and vice-versa (Jacobs prediction. 3.3 Perturbations to sub-shelf melting In order toice-shelf investigate mass the balance sensitivity we oflation/ablation chose field the to for various apply floating ice a ice( (shown linear streams in multiplier to Fig. 3a). changes Using in a sub- positive linear multiplier lines of Rutford, Evans, Carlson InletThis and problem Foundation ice inhibits streams our in ability particularreference experiment (Fig. to cannot 5a). make be viewed predictions as andclimate. a The means future reference prediction that run for the a should scenario resultsfrom therefore of be which of constant viewed to the solely assess as the a relative neutral sensitivity starting of point the ice streams to change, and not as a the length of the control run, the result is that thickening occurs near to the grounding- surface velocity to InSARice measurements, fluxes the at model those is ice unable streams to which match flow the through observed well-defined narrow channels. Over suggests that it isaround 1000 not yr, in during equilibriumally which begins with the to the Möller change. forcingbetween Ice By 40 fields. Stream and After appears 80 km an to while it be initial continues stable, period to it lose of tions mass eventu- necessary at to a maintain rate auration of stable as ice possible. In sheet common with withal., as 2011; other close-to Larour ice the et sheet al., present-day modelling 2012) config- studies we (e.g. find Seroussi that, et even after control method matching of the ice tion ice streams, relativelygrounding little lines change advance slightly occurs and between and stabilise, while the the newly inland parts groundedchange of areas very the thicken. catchments little Although during themuch the from Institute their model Ice initial run, state Streamonwards (Fig. its appears with 5a), thickness the it to rate loses and accelerating mass grounding to continuously line from around do not alter the reference experiment, with2000 yr 3 Fig. levels 5 of provideschange refinement, in a ice was summary thickness run and ofand grounding forward this in line Fig. for location experiment. 5b over a Figure the 2000 time-series yrbasin total 5a of of catchment shows cumulative of constant volume for the conditions change the is total broken-downcatchments). main net by ice drainage streams (including the ice shelf extensionscourse of of those this experiment. In the case of the Evans, Carlson, Rutford and Founda- in terms of the simulation run-time. 3.2 The reference experiment In order to investigate the long-term stability of the Filchner-Ronne tributary ice streams line location, but only by small and decreasing amounts which come at significant cost 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) ω ect ff > 0.9, . 1 − ψ ). This is of am (Fig. 8c, d) or ψ 1 − ) there is very sub- 1 − ect towards reducing 1.75 (equivalent to a ff = ψ cient to stabilise the Institute . Even small increases cause ffi ψ 0.025 m w.e. a 0.0 m w.e. a = ected by increases in basal melt- = ff ω ω ects of the increase in grounding line ff ). At this point a threshold appears to be in a roughly South-North direction. Ligten- 1 0.01 m w.e. for the (IPCC) E1 scenario, and − 1 − ∼ 5488 5487 0.50 ma ∼ to erent multiplying factors to the area near the grounding line 1 ect of increasing the ice thickness in those ice streams that ff − ff cient to fully mitigate the e ffi in surface accumulation has a fairly minimal impact on this result 0.10 ma 1 ∼ (Fig. 8e, f) does have a progressively stronger e − 1 − 0.9. 1.5 and with present-day accumulation ( ≤ = ψ ψ so that we can investigate the sensitivity of our model accordingly. ) and to the area away from the grounding line, or ambient region ( ≤ ω gl At A positive shift in surface accumulation accompanied by no change in sub-shelf melt- As described in section 2.2 the surface mass balance for the reference experiment If the Institute and Möller ice streams seem to be intrinsically unstable for Figure 6c–h show results of incremental changes to 0.04 m w.e. for the A1B scenario. We use these results as a guide to realistic values ψ straightforward to apply di ( the ice sheet, taken asriod (due a to whole, the experiences increased significant accumulation)are while growth in both over continuous the the retreat. Institute Thus modelled andgeometrical we Möller pe- find ice configuration, streams a can situation wherepart experience particular of an basins, a unstable due growing to ice retreat their sheet. even when3.5 they form Grounding line localised vs. “ambient”With or mid-shelf our melting parameterisation of sub-shelf mass balance (described in Sect. 2.4) it is (Fig. 8a, b). Increasing0.05 m the w.e. a accumulation shiftthe to amount of retreatframe, but of is the not su Institutemelt. Figure and 8f Möller demonstrates ice an interesting streams situation within where the the Weddell model Sea time- sector of ing has the predictable e were stable at theirOnly advanced a grounding very small line increase locationsIce in Stream, under surface while accumulation the the is reference Möller su line scenario. Ice location Stream unless does surface not accumulation fully is stabilise increased at by its at current leaststantial grounding 0.05 and m relatively w.e. a rapidof retreat in 0.01 m the w.e. a Weddell Sea sector (Fig. 6e, f). An increase increases up to the year(including 2200 ice that, shelves), when are equivalent averaged∼ to over the entire Antarctic Iceof Sheet berg et al. (2013) and Agosta et al. (2013) describe predictions for future accumulation increases from 3.4 Perturbations to surface mass balance Very little surface meltingConsequently occurs the even surface at mass sea-level balanceareas on is in uniformly the East positive major Antarctica) (excluding and, some Antarctical., at blue-ice ice least 2006). sheets. at To investigate the the model-scale,in smoothly sensitivity surface varying of accumulation (Arthern we the et therefore Filchner-Ronne foundto ice it the most streams base convenient to level apply used changes a in uniform the shift reference ( experiment. behaviour (Fig. 7). Initiallyno showing change very little occurs sensitivity atmelt-rate to this near sub-shelf ice its melt stream grounding rate,reached line right-up almost and any of to further 28 a increase ma in(Fig. value melting 6g, of results h). in a rapid and catastrophic collapse runs. The rate ofthe basal rate melting of at retreat the only(Fig. grounding and 6). not line the In can ultimate contrast therefore positionticular be to at insensitive shown this, which in to the the our ice a experiments, Rutfordpositions sheet remaining Ice even re-stabilises fixed under Stream at quite and their substantial Carlson advanced increases grounding Inlet in line the Glacier melt are ratesand par- at the their Rutford fronts. andrates Carlson at ice their streams grounding lines, are then una demonstrates classic threshold increases in ice thickness and0.5 minor grounding line movements can be obtained using a corresponding acceleration ofOnce retreat retreat has for begun both in the this sector Institute it and continues unabated Möller throughout Ice all Streams. of our model area of the Filchner-Ronne bay. Similarly stable ice sheet configurations with moderate 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ect ff ects of ) to the ff am χ , Henry and ff and Henry Ice Rises and the Doake Ice ff cient to reduce the grounded areas of the ffi 5490 5489 0.50 m w.e.) is necessary to unground the Doake and Henry ice ectively investigate the impact of an increase in sub-shelf melting − ff 0.25 m w.e., while insu = − am = χ am χ In the first group are , Carlson Inlet, , Sup- Rutford, Carlson, Foundation and also Evans Ice Streams exhibit the common be- The result of a 2000 yr experiment run with this new sub-shelf melt field is that the Firstly, all grounded parts of the Filchner-Ronne Ice Shelf were manually identified Figure 9 demonstrates that a multiplying factor has minimal impact when applied to high points near to theirStream trough is mouths, the they exception are in very this stable instance in as the the model. water Rutford column Ice below the floating ice in parts of these lastunable two to ice draw streams conclusions fall about their within long-term our behaviour. model domainhaviour and that their we grounding are lines therefore allthe advance early to part the end of of allice their forward respective streams, model fjords runs. during the In water-columnbecome the grounded case depth is of within Carlson, very Foundation the smallresult and (< they floating 50 Evans m ground portions throughout, very and of easily in the in many fjords places the < which model 10 m). and, As once a grounded on bed topographic to the forcing-fields tomelt produce at any their retreat; grounding (2)crease, but lines those only quick and after to a (3) threshold respond those has to been which changes passed. respondport in very Force Ice quickly Stream to and Recovery a Ice Stream. melt We in- note, however, that only the lower melt-rates in the central ice shelf and particularly around the ice rises. 4 Discussion The results of the firstpattern part of of sub-shelf this massthis paper, balance it where were is changes investigated, clear to are that thedivided the summarised into ice magnitude in three streams but Fig. groups: discharging not (1) 7. into the those the From that Filchner-Ronne respond Ice very Shelf slowly can and be require large changes melting (e.g. rises, which then leads rapidly toMöller a sector substantial grounding (Fig. line 10e, retreatthe in f). grounding the These Institute lines experiments and of havecan the a attribute ice component the streams of respective that changes direct is observed melting identical in at to the the model reference to run, the hence “far-field” we e in the model reaching an approximate equilibrium (Fig. 10c, d). A larger increase in ice rises, significantly restrains the advance of the and results Institute Ice Stream advancesDoake grounded out areas. into This the occursity because bay of the to the sub-shelf connect mass iceand with balance aiding rises in the the the is Kor Institute vicin- slightly now Ice Stream overly while to positive, the advance. causingreference behaviour The their run Möller of Ice grounded (Fig. the Stream areas 10a,ambient other also to b). component advances ice increase of The streams the nexton is sub-shelf step the largely various mass was unchanged ice balance, toA streams from in apply of shift the order removing a of to the uniform buttressing investigate shift due the to ( e the grounded ice rises. in the model domainfrom the and calculation the of grounding the“grounding lines line” sub-shelf element mass associated is balance. only with In appliedand the the near not to new ice to the sub-shelf the rises grounding melt ice line removed field of rises. the the main ice sheet the grounding line. Therethe are “ambient” two part reasonsreference of why field this the and should ice (2) be meltbe shelf the in important has the for case: a region buttressing (1) (such of positiveRumples, much as the see or the of Fig. islands Kor 1), near within is the zero subjectfactor. ice to In mass the shelf, order grounding balance which to line may e in multiplier,away rather from the than ice the stream ambient grounding lines a change to the approach was required. the ice streams at/near theirconsequent grounding loss lines of vs. buttressing more and general back-pressure thinning on of ice the stream shelf flow. the and ambient part of thenoted sub-shelf mass in balance the only, and earlier that parts the of ice stream this responses paper are due to increases in melting in the vicinity of interest because it allows us to investigate the relative importance of direct melting of 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | erent ice streams ff ect during retreat (Jamieson et al., 2012). ff 5492 5491 cient to initiate retreat of the grounding line in the ffi ering responses of the ice streams as described above ff , Joughin and Bamber, 2005). It is unique in our model domain 1 − ) melt-rate threshold has been passed (Fig. 7). Evans Ice Stream does 1 36 Gt yr erence between the Institute and Möller ice streams and the other, more − ff ∼ erences in their response to either an increase in melt at their grounding lines or 1.0; Fig. 7), or the partial removal of buttressing due to flotation of the Filchner- Model results indicate that the Institute and Moller ice streams are situated very close Our results also suggest that a substantial increase in surface accumulation would All of the ice streams discussed in this paper have an inverse bed slope with an Evans Ice Stream has one of the smaller catchments of the Filchner-Ronne tribu- The Institute and Möller ice streams comprise the second group, the configurations of 28 m w.e. a ff to a threshold critical for rapid retreat. In our study area they are uniquely sensitive to ments of the ice streamshave feeding used the the Filchner-Ronne most Icetures up-to-date Shelf and measurements in accumulation of rates West to Antarctica. ice producewhich We thickness, surface maintain, flow and as sub-ice-shelf speed, closely mass as tempera- balanceAntarctic possible, fields a Ice steady-state Sheet when applied configuration.were to then Perturbations the made present-day to in order theseto to changes reference-run assess in forcing the sub-shelf relative melt fields away sensitivities near from the of the grounding the grounding lines, di basal lines mass and balance surface on accumulation. the shelf (Fig. 8). 5 Conclusions This paper has described an application of the BISICLES ice sheet model to the catch- shown to have a close linkreverse-bed to slope ice stream a stability. Even narrowing underincrease conditions of in of the lateral a drag, continuous available have width a for stabilising e the icebe stream necessary can, to through counteractespecially a so moderate because increase theity in impact experiments of grounding is fairly increasing line uniformevenly surface melt distributed, whereas accumulation due rate. the to in This the impact our di of is sensitiv- sub-shelf melt increases is un- average gradient of 0.004–0.009 slopinggrounding inland line for and a distance withoutdi of topographic 100–200 highs km to from the provideto potential a pinning-points. reduction The invariations buttressing in due basal to ice topography rises within therefore, the is trough. unlikely to Trough width be explained has by previously been taries but, due toume its of ice higher ( ratefor of its surface rapid accumulation, response discharges∼ to the increases largest in vol- basalflow melting within that a occur fjord, only2011). and once At has a the a (fairly mouth particularly high true of right well its bank defined (by trough set the however,tic Haag of the Peninsula Nunataks) side tributaries ice than (Fig. by (Rignot stream 1) the and et is subduedbetween this al., better topography stability may on go and constrained the some sensitivity. on Antarc- way to its explaining its behaviour midway fjord. The horizontal boundariesgrounded of well the below Institute seaBungenstock and Ice level Rise). Möller rather The are than consequentmargins with lack may substantial explain of slow-flowing their bedrock buttressing ice sensitivity due topography to to changing (e.g. conditions lateral at the drag the at base their of the ice shelf. which appear to place themcollapse. near to A a small critical thresholdψ increase between in advance and their unstable Ronne relatively ice modest rises grounding (Fig.model. 10e, line Once f), melt this is has su rates begunposition (e.g. neither within the ice period stream of findsA our a marked model new runs, di equilibrium irrespective of groundingstable the line size tributaries of the of perturbation. the Filchner-Ronne Ice Shelf is their absence of a constraining Rutford fjord, however, is the longest,tributaries narrowest and and the deepest glacier ofbuttressing is all the well this Filchner-Ronne constrained provides within mayreverse steep bed explain walls slope on its throughout both much apparent margins. of stability its The length. in the model despite the its fjord is around 500 m deep (Johnson and Smith, 1997; Fretwell et al., 2013). The 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 2009. , 2010. , 2011. ect of but- ff 10.5194/tc-6- , 2005. 10.1029/2008JF001227 10.1029/2009JF001615 10.5194/tc-5-569-2011 ect the responses of ice streams to ff 10.1029/2004GL022024 5494 5493 , 2010. , 2006. , 2013. , 2009. Funding for this work was provided by UK NERC AFI grant 10.1029/2010GL043334 10.1029/2004JD005667 , 2012. 10.5194/tc-7-375-2013 erent responses of the various ice streams cannot be explained entirely by ff 10.1029/2008JF001170 The di In contrast, the Rutford, Carlson and Foundation ice streams appear to be quite re- grounding lines on retrograde slopes, The Cryosphere, 6, 1497–1505, doi: ing in marine ice sheets, J. Geophys. Res., 114, F04026, doi: 1497-2012 mesh ice sheet model, J. Geophys. Res., 115, F04014, doi: R., Fricker, H., Hall, M., Hindmarsh, R.,S., Kohler, Vornberger, J., P., Padman, and L., Young, Rack, N.: W., Rotschky, Getting G., Urbini, around Antarctica: new high-resolution mappings Shelf, Antarctica, using ICESat laser altimetry, J. Glaciol., 57, 965–975,Payne, 2011. A. J., Ng,marine ice E. sheets, J. G., Comp. and Phys., 232, Lipscomb 529–549, 2013. W.sheet H.: flow, Geophys. Adaptive Res. mesh, Lett., 32, finite L04503, volume doi: modelingsheet of dynamics:doi: Hysteresis and neutral equilibrium,C., J. Bingham, R. Geophys. G., Res.,Cook, Blankenship, D. A. D., 114, J., Casassa, Corr, G., F03009, Gim, H. Catania, Y., F. Gogineni, G., J., P., Callens, Griggs, Damaske, D.,R. J. D., Conway, A., H., Damm, W., Hindmarsh, V., Jenkins, R. Ferraccioli, A.,M., C. F., Forsberg, Langley, A., Jokat, K. R., Holmlund, A., W., P., Fujita, Leitchenkov, Holt,J., Jordan, G., S., J. Leuschen, Nitsche, T., W., C., F. Jacobel, King, Luyendyk, O., B. E.Roberts, Nogi, P., Matsuoka, C., Y., J., K., Nost, Ross, Kohler, Mouginot, O. J., N.,Tinto, A., B. Krabill, Siegert, K., Popov, Welch, S. W., M. B. V., Riger-Kusk, J., C.,improved Rignot, Wilson, ice Smith, D., E., Young, bed, A. D. Rippin, A., surface M.,393, Xiangbin, D. and C., doi: Steinhage, M., and thickness D., Rivera, Zirizzotti, datasets A.: Studinger, A., for Bedmap2: M., Antarctica, Sun, The B., Cryosphere,shelf 7, melting 375– and buttressing37, is L14501, a doi: key process in ice-sheet dynamics, Geophys. Res. Lett., of the groundedInternational and Polar Year, freely-floating The Cryosphere, boundaries 5, of 569–588, doi: the Antarctic ice sheet created for the Antarctic surface mass balance, applicationcenturies. for Clim. the Dyn., twentieth, 1–14, twenty doi:10.1007/s00382-013-1903-9, first 2013. and twenty second using polarization ofD06107, doi: 4.3-cm wavelength microwave emission, J. Geophys. Res., 111, the relative vulnerability of Antarctic ice streams to climate change induced retreat. to the surface and sub-shelf massthat balances. unstable Evans retreat ice stream will is occur uniquepassed. only in Model after this results a sector indicate in threshold that groundingof this line magnitude threshold melt-rate increase is has quite in been high, the likely present-day requiring grounding an line order melt-rate tofeatures initiate of retreat. the basal topographytressing within at their lateral troughs. margins Fjord andchanges width in at and their ice the forcing. e rises These also factors a must all be taken into account when assessing the region of themodel fails ice to find rises a incontinue new to equilibrium the lose position Filchner-Ronne mass for the throughout Ice grounding the Shelf. line 2000 yr and Once the period retreat ice ofsistant streams the begins to model either the runs. retreat or significant advance even with fairly substantial perturbations both increased melting at their respective grounding lines and to elevated melting in Gudmundsson, G. H., Krug, J., Durand, G., Favier, L., and Gagliardini, O.: The stability of Goldberg, D., Holland, D. M., and Schoof, C.: Grounding line movement and ice shelf buttress- Gladstone, R. M., Lee, V., Vieli, A., and Payne, A. J.: Grounding line migration in an adaptive Bindschadler, R., Choi, H., Wichlacz, A., Bingham, R., Bohlander, J., Brunt, K., Corr, H., Drews, Cornford, S. L., Martin, D. F., Graves, D. T., Ranken, D. F., LeBrocq,Dupont, A. T. M., K. Gladstone, and R. M., Alley, R. B.: AssessmentDurand, of G., the importance Gagliardini, of ice-shelf O., buttressing to de ice- Fleurian,Fretwell, P., Pritchard, B., H. D., Zwinger, Vaughan, D. T., G., Bamber, and J. L., LeMeur, Barrand, N. E.:Marine E., Bell, R., ice Bianchi, Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R. C. A., and Le Meur, E.: Coupling of ice- Brunt, K. E., Fricker, H. A., and Padman, L.:Analysis of ice plains of the Filchner-Ronne Ice Arthern, R. J., Winebrenner, D. P., and Vaughan, D. G.: Antarctic snow accumulation mapped Agosta, C., Favier, V., Krinner, G., Gallée, H., and Genthon, C.: High-resolution modelling of the References Acknowledgements. NE/G013071/1. 5 5 30 10 20 25 25 15 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , 2006. 10.5194/essd- , 1996. 10.1029/2005GL023844 , 2003. ect: A threat of disaster, Nature, ff 10.1029/2005JF000394 , 2013. , 2012. 10.1029/96GL00723 greenhouse e 2 , 2011. 5496 5495 10.1029/2003GL016941 , 2003. , 2012. , 2012. 10.5194/tc-7-647-2013 , 2012. , 2012. 10.1029/2011JF002140 10.1126/science.1208336 10.1029/2002JB002329 10.1038/nature10968 10.1038/nature11064 , 2010. 10.5194/tc-6-573-2012 10.1038/NGEO1600 1427–1430, doi: D. M., Young, D. A., Blankenship, D. D., and Siegert, M. J.: Steep reverse bed slope at ing lines, Science, 296, 2020–2023, 2002. of largest West Antarcticdoi:10.1029/2004GL021284, ice 2004 stream triggered by oceans, Geophys. Res.and Lett., Padman, 31, L.: L23401 Antarctic ice-sheet502–505, loss doi: driven by basal melting of ice shelves, Nature, 484, G., Gagliardini, O., Gladstone, R.,V., Nick, Goldberg, D., F. Gudmundsson, M., G.Marine Payne, H., A. Ice Huybrechts, J., P., Sheet Lee, Pollard,doi: Model D., Rybak, Intercomparison O., Project, Saito, MISMIP, F., The and Cryosphere, Vieli, 6, A.: 573–588, Results of the tica, Geophys. Res. Lett., 30, 1477, doi: spatial resolution, ice sheet modelling usingRes., the 117, Ice Sheet F01022, System doi: Model (ISSM), J. Geophys. jgaard, E.: Future surface mass balance of the Antarctic ice sheet and its influence on sea sensitivity, ice stream development and108, 2382, ice doi: flow across subglacial lakes, J. Geophys.ice Res., sheet dynamics, J. Geophys. Res., 111, F02004, doi: Integrating satellite observations withIce modelling: Streams, Phil. Basal Trans. R. shear Soc.: stress Math. of Phys. Eng. the Sci., Filchner-Ronne 364, 1795–1814, 2006. merical ice sheet models (ALBMAP v1),2-247-2010 Earth Syst. Sci. Data, 2, 247–260, doi: Earth Planet. Sci. Lett., 295, 451–461, 2010. Ronne Ice Shelf, Antarctica. Geophys.2005. Res. Lett., 32, L17503, doi: methods, J. Geophys. Res., 97, 595–603, 1992. 271, 321–325, 1978. Tech., 6, 175–177, 1982. Ice Shelf, derived from seismic surveys, Ant. Sci., 9, 201–208, 1997. level change, simulated by adoi:10.1007/s00382-013-1749-1, regional 2013. atmospheric climate model. Clim. Dyn., 41, 867–884, Pacific, Geophys. Res. Lett., 23, 957–960, doi: and Dowdeswell J. A.: Ice-streamdoi: stability on a reverse bed slope, Nat. Geosci., 5, 799–802, tween ice and ocean observed withing phase-sensitive line, radar J. near Glaciol., an 52, Antarctic ice-shelf 325–346, ground- 2006. 225–228, doi: shelves and the mass balance of Antarctica, J. Glaciol., 38, 375–387, 1992. warming of a large Antarctic ice-shelf cavity by a re-directed coastal current, Nature, 485, Cryosphere, 7, 647–655, doi: Pattyn, F.: A new three-dimensional higher-order thermomechanical ice sheet model: basic Pattyn, F.: Antarctic subglacial conditions inferred from a hybrid ice sheet/ice stream model, Paterson, W. S. B. and Budd, W. F.: Flow parameters for ice sheet modelling, Cold Reg. Sci. Mercer, J. H.: West Antarctic Ice Sheet and CO MacAyeal, D. R.: The basal stress distribution of Ice Stream E, Antarctica, inferred by control Ross, N., Bingham, R., Corr, H. F. J., Ferracciolo F., Jordan, T. A., LeBrocq, A. M., Rippin, Rignot, E., Mouginot, J., and Scheuchl, B.: Ice flow of the Antarctic Ice Sheet, Science, 333, Rignot, E. and Jacobs S. S.: Rapid bottom melting widespread near Antarctic ice sheet ground- Pritchard, H. D., Ligtenberg, S. R. M., Fricker, H. A., Vaughan, D. G., van den Broeke, M. R., Payne, A. J., Vieli, A., Shepherd, A. P.,Wingham, D. J., and Rignot, E.: Recent dramatic thinning Pattyn, F., Schoof, C., Perichon, L., Hindmarsh, R. C. A., Bueler, E., de Fleurian, B., Durand, Ligtenberg, S. R. M., van de Berg, W. J., van den Brooke, M. R., Rae, J. G. L., and van Mei- Pattyn, F., Huyghe, A., Brabander, S. D., and Smedt, B. D.: Role of transition zones in marine Lerour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale, high order, high Joughin, I. and Padman, L.: Melting and freezing beneath the Filchner-RonneLe Ice Brocq, Shelf, A. Antarc- M., Payne, A. J., and Vieli, A.: An improved Antarctic dataset for high resolution nu- Joughin, I., Bamber, J. L., Scambos, T., Tulaczyk, S., Fahnestock, M., and MacAyeal, D. R.: Joughin, I. and Bamber, J. L.: Thickening of the ice stream catchments feeding the Filchner- Johnson, M. R. and Smith, A. M.: Seabed topography under the southern and western Ronne Jamieson, S. S. R, Vieli, A., Livingstone S. J., ÓJenkins, Cofaigh, A., C., Corr, Stokes, H. C., F. J., Hillenbrand, Nicholls, K. C. W., D., Stewart, C. L., and Doake, C. S. M.: Interactions be- Jacobs, S. S., Hellmer, H. H., and Jenkins, A.: Antarctic Ice Sheet melting in the Southeast Hellmer, H. H., Kauker, F., Timmermann, R., Determann J., and Rae,Jacobs, J.: S. Twenty-first-century S., Hellmer, H. H., Doake, C. S. M., Jenkins, A., and Frolich, R. M.: Melting of ice Gudmundsson G. H.: Ice-shelf buttressing and the stability of marine ice sheets, The 5 5 30 25 20 30 15 10 20 25 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 10.1029/2004JF000202 , 2007. study. study. Ice velocity from Rignot et f showntributaries, overlain on the intervals. -1 5498 5497 , 2011. intervals. 1 10.1029/2006JF000664 − , 2010. , 2012. 10.1029/2011GL047338

Bedmap2 Bedmap2 bed topography (colour scale) used in this 50 contours at isal. indicated (2011) grey ma by 1: Figure Catchments of the Filchner-Ronne Ice Shel Catchments of the Filchner-Ronne Ice Shelf tributaries, shown overlain on the Bedmap2 10.1093/qjmam/hbp025 10.1038/NGEO1468 J., and Wright, A.Antarctic P.: The Ice Ellsworth Sheet, Subglacial Geol. Soc. Highlands: Amer. inception Bull., and 10.1130/B30794.1, retreat 2013. phys. of Res., the 112, West F03S28, doi: analysis ofdoi: higher order glacier flowS.: models, Ice flux Q. divergenceL09501, anomalies doi: J. on 79north Mech. Glacier, Greenland, App. Geophys. Res. Math., Lett., 63, 38, 73–114, grounding line migration,2005. J. Geophys. Res., 110, F010003, doi: the grounding line ofdoi: the Weddell Sea sector in West Antarctica, Nat. Geosci., 5, 393–396, 432–438, 2008. Fig. 1. bed topography (colour scale) usedcated in by grey this contours study. at Ice 50 velocity ma from Rignot et al. (2011) is indi- Schoof, C.: Ice sheet grounding line dynamics: steady states,Schoof, stability, and hysteresis, C. J. Geo- and Hindmarsh, R.Seroussi, C. H., Morlighem, M., A.: Rignot, E., Larour, Thin-film E., Aubry, D., flows Ben Dhia, H., with and Kristensen, S. wall slip: AnVieli, asymptotic A. and Payne, A. J.: Assessing the ability of numerical ice sheet models to simulate Ross, N., Bingham, R., Corr, H. F. J., Ferracciolo, F., Jordan T. A., Rippin, D. M., Siegert, M. van den Broeke, M.: Depth and density of the Antarctic firn layer, Arct. Antarct. Alp. Res., 40, 5 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | C Ice Ice Shelf the basal traction parameter (a) asal mass balance fields for ed ice velocity, ice thickness and terations for (a) the basal traction . In each case the initial location of φ hown black. in

b b 5500 5499 . In each case the initial location of the grounding-line for ϕ = 0; (b) Basal mass balance of the Filchner-Ronne t and (b) the effective viscosity factor C Basal mass balance of the Filchner-Ronne Ice Shelf calculated by Joughin ective viscosity factor (b) ff Combined grounding-line and ambient basal mass balance fields for floating ice 0;

a a = the grounding-linethe for all s forward simulations is

Figure 2: Results of the control problem after 16 i parameter snow assuming and a steady-state. accumulation calculated calculated by Joughin and Padman (2003) from measur Figure 3: (a) Combined grounding-line and ambient b floating ice at time the e t Results of the control problem after 16 iterations for (b) Fig. 3. (a) at time and Padman (2003)assuming from a measured steady-state. ice velocity, ice thickness and snow accumulation and all forward simulations is shown in black. Fig. 2. and Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0 are = Carlson t Foundation (b) Plot of cumu- = (f) t (b) as solid 2000 yr). = t = 0 years; black, t Evans Ice Stream; (a) ) ) against time for each of the 3 f f Möller Ice Stream and c c within the model domain. iment with increasing levels of (e) te te the degree of grounding line 0 yr; black, -line -line in grey, ness (colour scale) and grounding- ice down to the margin of the ice e Stream. e ge ge (km ned volume change for all drainage b elf. elf. = Rutford Ice Stream; (d) Institute Ice t 5502 5501

e e b = 0) are shown as dashed lines and final positions t Institute Ice Stream; against time for each of the ice stream catchments, volumes 3 (d)

d a Grounding line locations are colour-coded to refinement, initial positions ( indica Figure 4: Results of the 200 grounding year convergence line exper resolution for the major ice streams

Stream; Ice (e) andMöller Stream; Stream (f) Foundation Ic lines. (a) Evans Ice Stream; (b) Carlson Inlet; (c) Map showing total change in ice thickness (colour scale) and grounding-line position a Rutford Ice Stream; shelf. The solid black line is the cumulative combi ice ice stream catchments, volumes include all floating basins Filchner-Ronne the Ice to contribute Sh that

line position over a 2000 year model run (grounding Figure 5: (a) Map showing total change in ice thick 2000 years). (b) Plot of cumulative net volume chan Results of the 200 year convergence experiment with increasing levels of grounding (c) Fig. 5. (a) over a 2000 yr model run (grounding-line in grey, line resolution forare the colour-coded major to ice indicate the streams degree within of the grounding line model refinement, domain. initial Grounding positions line locations Fig. 4. shown as dashed linesInlet; and final positionsIce Stream. as solid lines. lative net volume change km include all floating icetive down combined to volume the change for marginShelf. all of drainage the basins ice that shelf. contribute The to solid the Filchner-Ronne black Ice line is the cumula- Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (e, f) is the (g) 1.25; = and ψ (e) , (a), (a), (c), (c) (c, d) = 0. , t = 0.75; (c,d) (a) ψ is given in Fig. 5b. 0. 0.75; line at = = (h) t (a,b) ψ ψ and (f) end) over 2000 yr model runs. Right- (a, b) , = nt over the 2000 year model runs ψ (d) riment. In each experiment the sub- b ied by a factor ps showing changes in ice thickness , tive tive volume change against time for de for plot lines in (b), (d), (f) and (h) art, art, black=end) over 2000 year model h f f d b (b) 5504 5503 start, black =

0.75 = 1.8. The colour scale for the volume changes in = = ψ ψ

are plan-view maps showing changes in ice thickness (colour = 1.8 = = 1.25 = 1.5 =

g c c ψ a e e g ψ ψ and (b) the melt-rate at the grounding melt-rate stream the (b) and ice ψ = 1.5; (g,h) Figure 6: Left hand side (a,c,e,g) are plan-view ma (colour (colour scale) and grounding-line position (grey=st runs. Right-hand side (b,d,f,h) are plots of cumula ψ are plots of cumulative volume change against time for each of the (a, c, e, g) 1.8. The colour scale for the volume changes in = = 1.25; (e,f) the melt-rate at the ice stream grounding line at

(e) (e) and (g) is the same as for Figure 5a and the co as a function of (a) is 5b. given in Figure Figure 7: Total volume change by ice stream catchme each each of the ice stream catchments for the same expe shelf accumulation/melt rate field has been multipl ψ ψ a (b) (b, d, f, h) (g, h) and Left hand side Total volume change by ice stream catchment over the 2000 yr model runs as a function ψ 1.5; (a) = Fig. 7. of hand side ice stream catchments forlation/melt the rate field same has experiment. been In multiplied each by experiment a the factor sub-shelf accumu- Fig. 6. scale) and grounding-line position (grey ψ same as for Fig. 5a and the code for plot lines in Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1.5 and in = ψ away from the

ψ (b)

= 0.05 m w.e. = 0.05 m ω 0.05 m w.e. = 1.5] am = ψ ω (f) , near near to the grounding line and (b) change over 2000 year model runs = 1.0; = 1.0; the the basal mass balance multiplier, locations along plots with time-series (e) gl

d f b ψ [ b = 0.025 m w.e. = and 0.025 m (e),(f) ω near to the grounding line and 5506 5505 (a) 0.025 m w.e. and = 0.01] 0.01] = = ω = 0.01 m w.e.; = 0.01 (c),(d) m ω ω

= 0.05] 0.05] = = 0.025] 0.025] = ω ω = 1.5, = (d) ψ [ , = 1.5, = = 1.5, = (c) = 1.0] ψ ψ e e [ [ c a a am ψ = 1.5 and in (a),(b)

of cumulative volume change by basin. In all plots Ice 8: Figure thickness changes and groundingline

= 1.5; = 1.5; gl 0.01 m w.e.; ψ a [ = Grounding line location and ice thickness change over 2000 yr model runs with en- ω Ice thickness changes and grounding line locations along with time-series plots of cu- (b) , Figure 9: Grounding line location and ice thickness with enhanced sub-shelf accumulation/melt only (a) groundingaway the from line. hanced sub-shelf accumulation/melt only Fig. 9. grounding line. Fig. 8. mulative volume change by basin. In all plots the basal mass balance multiplier, (a) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0.50 m w.e. in − (e, f) rived rived from the flux-divergence 0.25 m w.e. and duce an ice sheet that is in an − he grounding lines of ice rises ted ted and the ambient melt field (a,b) 0.0 m w.e.; (c,d) -0.25 m w.e. the the mass balance fluxes from surface

on the ice streams of the removal of the f. f. f d b (c, d) 5508 5507 0.0 m w.e.; = 0.0 m w.e. = 0.0 m am χ (a, b) = -0.25 m w.e. m = -0.25 = -0.50 m w.e. m = -0.50 am am χ e e a a c χ Figure 10: Results of modelling experiments within where the t Filchner-Ronne Ice Shelf have applied. The been ambient field has isola then been shifted by and (e,f) -0.50 m w.e. in order to test the effect rises shelbuttressing ice ice provide the these to ect on the ice streams of the removal of the buttressing these ice rises ff Appendix: Supplementary FiguresAppendix: Supplementary Figure S1: The additional mass balance component de after the 50 year relaxation run. This is added to accumulation and sub-shelf melt/accumulation to pro steady-stateapproximately for reference the run. The additional mass balance component derived from the flux-divergence after the Results of modelling experiments where the grounding lines of ice rises within the 50 yr relaxation run. Thissub-shelf is melt/accumulation added to to producefor the an the mass reference ice balance run. sheet fluxes that from surface is accumulation in and an approximately steady-state Fig. A1. Fig. 10. Filchner-Ronne Ice Shelf havefield been has isolated and then the been ambient shifted melt by field applied. The ambient provide to the ice shelf. order to test the e