Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model...

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Title Simulations of the Greenland ice sheet 100 years into the futurewith the full Stokes model ElmerIce

Author(s) Seddik Hakime Greve Ralf Zwinger Thomas Gillet-Chaulet Fabien Gagliardini Olivier

Citation Journal of Glaciology 58(209) 427-440

Issue Date 2012-06

DOI

Doc URL httphdlhandlenet211550786

Right copy 2012 International Glaciological Society

Type article

AdditionalInformation

FileInformation JoG58-209_427-440pdf

Hokkaido University Collection of Scholarly and Academic Papers HUSCAP

Journal of Glaciology Vol 58 No 209 2012 doi 1031892012JoG11J177 427

Simulations of the Greenland ice sheet 100 years into the futurewith the full Stokes model ElmerIce

Hakime SEDDIK1 Ralf GREVE1 Thomas ZWINGER2 Fabien GILLET-CHAULET3

Olivier GAGLIARDINI34

1Institute of Low Temperature Science Hokkaido University Sapporo JapanE-mail hakimepoplowtemhokudaiacjp2CSC ndash IT Center for Science Espoo Finland

3Laboratoire de Glaciologie et Geophysique de lrsquoEnvironnement CNRSUniversite Joseph Fourier Grenoble France4Institut Universitaire de France Paris France

ABSTRACT It is likely that climate change will have a significant impact on the mass balance of theGreenland ice sheet contributing to future sea-level rise Here we present the implementation of thefull Stokes model ElmerIce for the Greenland ice sheet which includes a mesh refinement technique inorder to resolve fast-flowing ice streams and outlet glaciers We discuss simulations 100 years into thefuture forced by scenarios defined by the SeaRISE (Sea-level Response to Ice Sheet Evolution) communityeffort For comparison the same experiments are also run with the shallow-ice model SICOPOLIS(SImulation COde for POLythermal Ice Sheets) We find that ElmerIce issimsim43more sensitive (exhibitsa larger loss of ice-sheet volume relative to the control run) than SICOPOLIS for the ice-dynamic scenario(doubled basal sliding) butsimsim61 less sensitive for the direct global warming scenario (based on the A1Bmoderate-emission scenario for greenhouse gases) The scenario with combined A1B global warmingand doubled basal sliding forcing produces a Greenland contribution to sea-level rise of simsim15 cm forElmerIce and simsim12 cm for SICOPOLIS over the next 100 years

1 INTRODUCTIONThe Greenland ice sheet is the second largest land icemass on the present-day Earth and its volume amounts tosim73m sle (metres sea level equivalent) The current massbalance of the ice sheet is most likely negative with anaccelerating trend though the uncertainty is significant(Lemke and others 2007 Rignot and others 2011) Surfacemelting increases strongly with rising surface temperaturesmaking the ice sheet very susceptible to future global warm-ing In addition recent observations (Zwally and others2002 Rignot and Kanagaratnam 2006 Howat and others2007 Joughin and others 2008) have led to strong concernsthat ice-dynamical processes (basal sliding accelerated bysurface meltwater speed-up of ice streams and outletglaciers) may boost the decay and thus lead to an additionalcontribution to sea-level rise Therefore it is clearly neces-sary to comprehensively model the dynamics of the Green-land ice sheet including ice streams and outlet glaciersMany models have been developed to simulate the

dynamics and evolution of ice sheets and glaciers Theshallow-ice approximation (Hutter 1983 Morland 1984)has been widely used for ice-sheet models (eg Huybrechts1990 Calov and Hutter 1996 Ritz and others 2001Saito and Abe-Ouchi 2004 Rutt and others 2009) Thisapproximation neglects the normal deviatoric stress andhorizontal shear components thus implying a significantsimplification that works well for large-scale ice-sheetdynamics but is inappropriate in the vicinity of ice dividesand margins fast-flowing regions like ice streams and smallsteeply inclined glaciers in general (eg Greve and Blatter2009) This gave rise to the formulation of higher-ordermodels (Blatter 1995 Baral and others 2001 Hindmarsh2004) in which longitudinal stresses are taken into accountto various extents Many of these models have been

applied to two-dimensional (2-D) domains (Dahl-Jensen1989 Blatter 1995 Colinge and Blatter 1998 Pattyn2000) and Dahl-Jensen (1989) demonstrated the importanceof longitudinal deviatoric stresses for plane flow along aflowline Pattyn (1996 2000) and Pattyn and Decleir (1998)applied a 2-D higher-order model with thermomechanicalcoupling to Shirase drainage basin Dronning Maud LandAntarctica Pattyn (2003) developed a three-dimensional(3-D) higher-order thermomechanical sheet model carriedout the European Ice-Sheet Modelling Initiative (EISMINT) Iand II benchmark experiments (Huybrechts and others 1996Payne and others 2000) and provided a comparison with theSaitondashBlatter model that also includes higher-order dynamics(Saito and others 2003) More recent developments are themodels of Pollard and DeConto (2007 2009) and Buelerand Brown (2009) that employ heuristic combinations ofthe shallow-ice and shallow-shelf approximations (Morland1987 MacAyeal 1989) as well as the application of a first-order model to the Greenland ice sheet by Price and others(2011) However due to several shortcomings inherent inthose models none of their results contributed to the FourthAssessment Report (AR4) of the Intergovernmental Panelon Climate Change (Solomon and others 2007) whichrepresents a great opportunity for the development andapplication of full Stokes modelsModels that solve the full Stokes equations (in which

all stress components are accounted for) in two or threedimensions have been proposed and applied mainly toglacier systems or parts of an ice sheet (eg Gudmundsson1999 Sugiyama and others 2003 Martın and others2004 Price and others 2007 Jouvet and others 2009)Comparisons between various full Stokes and higher-ordermodels were carried out in the Higher-Order Model(HOM) intercomparison topic of the Ice-Sheet Model

428 Seddik and others Greenland simulations with ElmerIce

Table 1 Standard physical parameters used for the simulations with both ElmerIce and SICOPOLIS

Quantity Value

Density of ice ρ 910 kgmminus3Gravitational acceleration g 981m sminus2Length of year 31 556 926 sPower-law exponent n 3Flow-enhancement factor E 3Rate factor A(T prime ) A0 eminusQR(T0+T

prime)

Pre-exponential constant A0 3985times 10minus13 sminus1 Paminus3 (T prime le minus10C)1916times 103 sminus1 Paminus3 (T prime gt minus10C)

Activation energy Q 60 kJmolminus1 (T prime le minus10C)139 kJmolminus1 (T prime gt minus 10C)

Melting temperature at low pressure T0 27316KClausiusndashClapeyron constant β 98times 10minus8 K Paminus1Universal gas constant R 8314 Jmolminus1Kminus1Heat conductivity of ice κ 9828 eminus00057 T [K] Wmminus1 Kminus1Specific heat of ice c 1463 + 7253T [K] J kgminus1 Kminus1Latent heat of ice L 335times 105 J kgminus1

Intercomparison Project (ISMIP) (Pattyn and others 2008)It was found that all participating models produced resultsthat are in close agreement However the full Stokes modelswere most consistent with each other whereas the spreadamong the various higher-order models was larger thusclearly motivating the use of full Stokes modelsApart from the recent studies of Ren and Leslie (2011)

and Ren and others (2011ab) full Stokes models havenot yet been applied to an entire ice sheet because ofthe enormous computational demand Here the full Stokesthermomechanically coupled model ElmerIce (eg Zwingerand others 2007 Gagliardini and Zwinger 2008 Durandand others 2009 Zwinger and Moore 2009 Seddikand others 2011) is applied to the Greenland ice sheetElmerIce employs the finite-element method to solve thefull Stokes equations the temperature evolution equationand the evolution equation of the free surface The generalframework of this modelling effort is a contribution tothe Sea-level Response to Ice Sheet Evolution (SeaRISE)assessment project a community-organized effort to estimatethe likely range of ice-sheet contributions to sea-level riseover the next few hundred years (httptinyurlcomsrise-lanlhttptinyurlcomsrise-umt) We therefore carry out the fourSeaRISE experiments considered by Greve and others (2011)who defined climatic and dynamic future scenarios Resultsare also compared with the shallow-ice approximationmodel SICOPOLIS (SImulation COde for POLythermal IceSheets (eg Greve 1997 2000 Greve and others 2011))in order to assess the differences in the response of the twomodels

2 ELMERICE THERMOMECHANICALLY COUPLEDFULL STOKES FLOW MODEL21 Dynamicthermodynamic model equations211 Field equationsSince ice is an (almost) incompressible material conserva-tion of mass requires that the velocity field (vector v) issolenoidal

div v = 0 (1)

Further the acceleration (inertia force) is negligible so theequation of motion is given by the incompressible Stokesequation

minusgrad p+ηnabla2v+[grad v + (grad v)T

]middot grad η+ρg = 0 (2)

(eg Greve and Blatter 2009) where p is the pressure η theviscosity ρ the ice density and g = minusgez the gravitationalacceleration vector pointing downward The viscosity isdescribed by Glenrsquos flow law

η =12

(EA(T prime)

)minus1ndminus(1minus1n) (3)

where d =radic

12 tr (D

2) is the effective strain rate D =

sym L = 12 (L + LT) the strain-rate tensor (symmetric part of

the velocity gradient L = grad v) n the power-law exponentT prime = T minus Tm the temperature relative to pressure melting (Tis the absolute temperature Tm = T0 minus βp is the pressure-melting point T0 is the melting point at low pressure and βis the ClausiusndashClapeyron constant) A(T prime) the rate factor andE the flow-enhancement factor The rate factor is expressedby the Arrhenius law

A(T prime) = A0 eminusQR(T0+T prime) (4)

where A0 is the pre-exponential constant Q the activationenergy and R the universal gas constant All parameters aregiven in Table 1The temperature equation follows from the general

balance equation of internal energy and reads

ρc(T )(partTpartt+ v middot grad T

)= div

(κ(T ) grad T

)+ 4ηd2 (5)

(eg Greve and Blatter 2009) where κ and c are the heatconductivity and specific heat of ice respectively (Table 1)The free surface equation follows from the kinematic

boundary condition formulation and reads

parthpartt+ vx

parthpartx

+ vyparthparty

minus vz = as (6)

where h(x y t ) is the free surface and as(x y t ) is theaccumulationndashablation function or surface mass balance

Seddik and others Greenland simulations with ElmerIce 429

The ice base b(x y ) is assumed to be rigid (isostaticcompensation neglected) and thus at all times equal to theprescribed initial condition

212 Boundary conditionsWe extract the boundary conditions required to close thesystem of equations posed in Section 211 mainly from theSeaRISE specifications (see also Greve and others 2011)The ice surface is assumed to be stress-free (atmosphericpressure and wind stress neglected) The surface air tempera-ture is parameterized as a function of surface elevation hlatitude φ longitude λ and time t following Fausto andothers (2009)

Tma(λφ t ) = dma + γmah + cmaφ+ κmaλ+ΔT (t )

Tmj(λφ t ) = dmj + γmjh + cmjφ + κmjλ+ΔT (t ) (7)

where Tma and Tmj are the mean annual and mean July(summer) surface temperatures respectively the temperatureconstants are dma = 4183C and dmj = 1470C themean slope lapse rates are γma = minus6309Ckmminus1 andγmj = minus5426C kmminus1 the latitude coefficients are cma =minus07189C (N)minus1 and cmj = minus01585C (N)minus1 and thelongitude coefficients are κma = 00672C (W)minus1 andκmj = 00518C (W)minus1The purely time-dependent anomaly term ΔT (t ) de-

scribes the deviation from present-day conditions For thepast it is based on the oxygen isotope record (δ18O) fromthe Greenland Icecore Project (GRIP) ice core (Dansgaardand others 1993 Johnsen and others 1997) which wasconverted to a record of temperature variation from 125ka bpto the present (here the notation ka bp means thousandcalendar years before present) For the future Eqn (7) is onlyused for the experiments with constant present-day climateforcing (thus ΔT (t ) equiv 0) whereas the experiments with AR4climate forcing are driven directly by an ensemble averageof simulated surface temperatures (Section 32)For the present-day mean annual precipitation rate

Pmapresent(λφ) recent data of Ettema and others (2009)are used Past precipitation rates are not required in thisstudy because of the fixed-topography spin-up approach(Section 31) For the future runs with constant present-dayclimate forcing Pmapresent(λφ) is used unchanged while theAR4 climate experiments are driven directly by simulatedprecipitation rates analogous to the surface temperatureSurface melting is parameterized by Reehrsquos (1991) positive

degree-day (PDD) method supplemented by the semi-analytical solution for the PDD integral by Calov and Greve(2005) The PDD factors are βice = 8mm (ice) dminus1 Cminus1

for ice melt and βsnow = 3mm (ice) dminus1 Cminus1 for snowmelt(Huybrechts and deWolde 1999) Furthermore the standarddeviation of short-term statistical air-temperature fluctua-tions is σ = 5C (Huybrechts and de Wolde 1999) andthe saturation factor for the formation of superimposed iceis chosen as Pmax = 06 (Reeh 1991) Conversion from thepresent-day mean annual precipitation (Ettema and others2009) to the snowfall rate (solid precipitation) is done on amonthly basis using the empirical relation of Marsiat (1994)Mean monthly rainfall (liquid precipitation) is obtained asthe difference between precipitation and snowfallAt the base described by the function z = b(x y ) a

Weertman-type sliding law with sub-melt sliding is used

(Greve 2005)

vb(Tprimeb) = minusC

0b eT primebγ

ρgτpb

Nqb (8)

where τb is the basal drag (shear stress) Nb the basal normalstress T primeb the basal temperatures relative to pressure meltingC 0b = 105 aminus1 is the sliding coefficient p = 3 q = 2 arethe sliding exponents and γ = 1C is the sub-melt-slidingparameter (Hindmarsh and Le Meur 2001)If the base is cold (temperature below the pressure-melting

point) the energy jump condition yields a Neumann-typeboundary condition for the basal temperature

κ(T ) (grad T middot n)|z=b = qperpgeo minus vb middot t middot n (9)

(eg Greve and Blatter 2009) where the geothermal flux(qperpgeo) distribution over the bedrock is given by Shapiro andRitzwoller (2004) and t is the Cauchy stress tensor If the baseis temperate (temperature at the pressure-melting point) theenergy jump condition determines the basal melting rate

aperpb =qperpgeo minus κ(T ) (grad T middot n)|z=b minus vb middot t middot n

ρL (10)

where L is the latent heat of iceAt the lateral boundaries of the domain (vertical faces at

the ice margin) the stress-free condition is applied and thehorizontal temperature gradient is assumed to vanish (zero-flux condition)

22 Finite-element implementationThe model equations detailed in Section 21 are solvednumerically with the ElmerIce model It is based on theopen-source multi-physics package Elmer developed at theCSC ndash IT Center for Science in Espoo Finland (httpwwwcscfielmer) and uses the finite-element methodThe model domain covers the entire area of the present-

day Greenland ice sheet The domain is projected to apolar stereographic map with standard parallel 71N andcentral meridian 39W The present geometry (surface andbasal topographies) is derived from UC Herzfeld and others(unpublished information) where the basal topography wascreated so that the troughs at Jakobshavn Isbraelig and HelheimKangerdlugssuaq and Petermann glaciers are preserved Amesh of the computational domain is created using aninitial footprint that contains elements of 5 km horizontalresolution To limit the number of elements on the footprintwhile maximizing the spatial resolution in regions wherephysics demands higher accuracy an anisotropic meshadaptation scheme is employed Its metric is based on theHessian matrix of the observed surface velocities (distributedby SeaRISE based on work by Joughin and others (2010)with gaps filled by balance velocities of Bamber and others(2001b)) in order to equi-distribute the a priori error estimateusing an edge-based anisotropic mesh optimization Themetric tensor is computed following Frey and Alauzet(2005) and the adaptation is carried out with the automatictool YAMS (Frey 2001 Morlighem and others 2010)The resulting mesh in the central part of the Greenlandice sheet including the refinements at Jakobshavn Isbraeligand Kangerdlugssuaq Glacier is depicted in Figure 1The final footprint is vertically extruded to form a 3-Dmesh of 320 880 elements with 17 equidistant terrain-following layers


Fig 1 Observed surface velocities of the central part of the Greenland ice sheet (distributed by SeaRISE based on work by Joughin andothers (2010) with gaps filled by balance velocities of Bamber and others (2001b)) and anisotropic mesh with the clearly visible refinementsat Jakobshavn Isbraelig (JIS) and Kangerdlugssuaq Glacier (KL)

The nonlinearity of the model equations is dealt with by aPicard iteration scheme and stabilization methods (Francaand Frey 1992 Franca and others 1992) are applied tothe finite-element discretization The resulting system oflinear equations is solved with a direct method using theMUltifrontal Massively Parallel sparse direct Solver (MUMPSAmestoy and others 2001 2006)The current version of ElmerIce is not able to deal with

a changing domain in the map plane Thus the ice frontis fixed in time and a minimum ice thickness of 10mis applied everywhere and for all times This implies thatinitially glaciated points are not allowed to become ice-free

3 SeaRISE EXPERIMENTS31 Palaeoclimatic spin-upIn order to obtain a suitable present-day configuration of theGreenland ice sheet that can be used as an initial conditionfor future climate experiments it is desirable to carry outa palaeoclimatic spin-up over at least a full glacial cycleThe resulting present-day conditions of the Greenland icesheet can be particularly sensitive to the initialization method(Rogozhina and others 2011) Here similar to the spin-updescribed by Greve and others (2011) the forcing followsthat specified by SeaRISEWe have been unable to perform an entire spin-up with

ElmerIce due to the prohibitive computing time that wouldbe required for such a long simulation For this reasonwe conduct the palaeoclimatic spin-up from 125ka bp until200 years bp with the shallow-ice model SICOPOLIS Thehorizontal resolution is 10 km and the vertical directionis discretized by 81 equidistant terrain-following layersAfter an initial relaxation over 100 years (starting from thepresent-day topography and isothermal conditions at minus10Ceverywhere) in order to avoid spurious noise in the computedvelocity field (Calov 1994) we keep the topography fixedover time in order to preserve a good fit between thesimulated and observed present-day topographiesThe spin-up with SICOPOLIS is conducted only until

200 years bp because the initial conditions produced by ashallow-ice model then used in ElmerIce would produce

an initial shock that influences the results obtained with thefuture climate experiments In order to mitigate the effects ofthe initial conditions on the full Stokes model two successiveruns are conducted with ElmerIce to produce the present-day ice-sheet configuration The first run is conducted from200 to 100 years bp starting with the SICOPOLIS output thatis interpolated from the regularly spaced finite-differencegrid of SICOPOLIS to the finite-element mesh of ElmerIceusing a bilinear method This run keeps the topography fixedand is intended to relax the initial shock originating fromthe switch from the shallow-ice to the full Stokes dynamicsThe second run from 100 years bp until the present allowsthe ice-sheet surface to evolve forced by a constant present-day climate The obtained present-day configuration of theice sheet is used as the initial condition for the future climateexperiments with ElmerIce By contrast for the futureclimate experiments with SICOPOLIS a fixed-topographyspin-up with SICOPOLIS from 125ka bp until the presentis used

32 Future climate experimentsFor the future climate experiments we use the same set ofSeaRISE experiments as was employed by Greve and others(2011) This represents a subset of the suite defined in thelsquo2011 Sensitivity Experimentsrsquo Due to excessive computingtimes we run them only for 100 rather than 500 years

Experiment C1 Constant climate control run beginningat present (more precisely the epoch 1 January 2004000 corresponding to t = 0) and running for 100 yearsholding the climate steady to the present climate

Experiment S1 Constant climate forcing with increasedbasal lubrication This is implemented in ElmerIce byhalving the basal drag (essentially doubling the basalsliding) everywhere in the domain

Experiment C2 AR4 climate run starts with the samepresent-day condition but the climatic forcing (meanannual temperature mean July temperature precipita-tion) is derived from an ensemble average from 18 ofthe AR4 models run for the period 2004ndash98 under theA1B emission scenario beyond 2098 the climate persists


Fig 2 Present-day configuration computed by ElmerIce starting from the SICOPOLIS palaeoclimatic fixed-topography spin-up at200 years bp (a) Surface topography (b) surface velocity and (c) basal temperature relative to the pressure-melting point

to the end of the run 100 years into the future Inorder to avoid a sudden climate jump at the initial timethe forcing is applied by calculating precipitation andtemperature anomalies (relative to 2004) which are thenadded to the present-day climate specified by Eqn (7) andthe data by Ettema and others (2009)

Experiment T1 Combination of C2 and S1 ie AR4climate forcing with increased basal lubrication (halvedbasal drag)

In order to minimize the shock that arises from the transitionfrom the fixed-topography spin-up to the future climateexperiments with evolving topography in neither case is theice sheet allowed to extend beyond its present-day marginThe remaining experiments defined in the lsquo2011 Sensitivity

Experimentsrsquo of the SeaRISE group will be considered infuture work

4 RESULTS AND DISCUSSIONThe results of the initialization runs carried out with ElmerIce(Section 31) are shown in Figure 2 The surface topographyis in good agreement with that observed (Bamber and others2001a not shown) with differences of the order of tens ofmetres (see Table 2) as a consequence of the evolving free

surface during the last 100 years The surface velocity showsthe expected distribution with small velocities (lt10maminus1)around the major ice ridges and a general speed-uptowards the coast The pattern agrees well with Joughinand othersrsquo (2010) interferometrically measured velocitieswith the notable exception of the lsquoNortheast GreenlandIce Streamrsquo (NEGIS) and the northwestern outlet glacierswhere the velocities are relatively small Basal temperaturesare at pressure melting most notably in the southwestand southeast but also under the NEGIS For the ice-core locations GRIP NorthGRIP Camp Century and Dye 3where observations exist Table 2 shows the comparisonThe agreement is good for GRIP and Camp Century butpoor for NorthGRIP and Dye 3 This is probably due toshortcomings of the applied geothermal flux distribution byShapiro and Ritzwoller (2004) and could be improved bythe tuning method of Greve (2005) however in this studywe work with the Shapiro and Ritzwoller (2004) geothermalflux according to the SeaRISE recommendationStable results could be obtained with both the full Stokes

model ElmerIce and the shallow-ice model SICOPOLISfor all four future climate experiments described in Sec-tion 32 Simulated surface velocities for the control run C1(constant climate forcing) after 100 years are shown in Fig-ure 3 The results for ElmerIce (Fig 3a) show that major ice

Table 2 Simulated (ElmerIce) and observed present-day ice thicknesses and basal temperatures for the ice-core locations GRIP NorthGRIPCamp Century and Dye 3

GRIPlowast NorthGRIPdagger Camp CenturyDagger Dye 3sectH Tb H Tb H Tb H Tbkm C km C km C km C

Spin-up 2995 minus792 3067 minus697 1354 minus869 1913 minus045Observed 3029 minus856 3080 minus24 1387 minus130 2037 minus1322

lowastDansgaard and others (1993) Dahl-Jensen and others (1998) daggerDahl-Jensen and others (2003) NorthGRIP members (2004) DaggerDansgaard and others(1969) Gundestrup and others (1987 1993) sectGundestrup and Hansen (1984)


Fig 3 Surface velocities (a b) and basal temperatures relative to pressure melting (c d) computed with ElmerIce (a c) and SICOPOLIS(b d) for experiment C1 (constant climate control run) at t = 100 years (year 2104)

streams and outlet glaciers are active In particular Jakobs-havn Isbraelig and Petermann Kangerdlugssuaq Helheim andfurther southeast outlet glaciers show continued fast flowThe NEGIS however is characterized by lower velocitiesof 30ndash100maminus1 with no pronounced acceleration towardsthe margins The results for SICOPOLIS (Fig 3b) exhibitgenerally higher ice-surface velocities around the ice marginIn addition to Jacobshavn Isbraelig and Helheim and furthersoutheast outlet glaciers Kangerdlugssuaq Glacier the outletglaciers of the NEGIS and many further areas show fast flowwith velocities exceeding 1000maminus1This different dynamical behaviour of ElmerIce and

SICOPOLIS near the ice margin has several causes Therepresentation of fast-flowing ice streams and outlet glaciersin ElmerIce benefits from the much finer grid resolution andElmerIce solves the full Stokes equations so all componentsof the stress tensor are included The consequence withrespect to ice-stream dynamics is that ElmerIce accounts forthe lateral drag resulting from local fast flow embedded in

slower-flowing ice which limits the velocity contrast whilethe shallow-ice solver of SICOPOLIS does not exhibit lateraldrag and thus tends to over-predict fast ice flow Anotherreason for the generally lower surface velocities producedby ElmerIce lies in the different basal thermal conditions(Fig 3c and d) The temperatures computed with ElmerIceafter 100 years are generally lower and the temperate-based areas smaller while the temperatures computed withSICOPOLIS are higher The cooler conditions obtained withElmerIce originate from the initial conditions (Fig 2c)where the temperatures are generally lower than the initialconditions used by SICOPOLIS (not shown) However thecontrol run shows that the basal temperatures have generallyincreased in comparison to the initial conditions particularlyat Petermann and the northwestern outlet glaciers This couldindicate that the initial shock due to the sudden change of icedynamics from shallow ice to full Stokes has gradually beensmoothed out Of course the shallow-ice approximationused in SICOPOLIS applies also to Eqn (5) (neglect of the


Fig 4 Surface velocities (a b) and basal temperatures relative to pressure melting (c d) computed with ElmerIce (a c) and SICOPOLIS (bd) for experiment S1 (constant climate forcing doubled basal sliding) at t = 100 years (year 2104)

horizontal heat conduction) so the differences betweenthe two models also result from the different temperatureequationsFigure 4 shows the results obtained for experiment S1

(doubled basal sliding) The surface velocities computedwith both ElmerIce and SICOPOLIS show the expectedresponse an increase of the flow speed in all areas where thebase is at or near the pressure-melting point Consequentlyboth models produce faster-flowing ice streams and outletglaciers compared to the control run C1 The surfacevelocities computed with ElmerIce show higher sensitivitieswith higher flow speeds observed at Jakobshavn Isbraeligand the NEGIS and at the Petermann outlet glaciersElmerIce also produces more localized fast-flowing outletglaciers at the northwestern margins By contrast the surfacevelocities computed with SICOPOLIS are only larger thantheir ElmerIce counterparts at the eastern margins mainlyat Kangerdlugssuaq Glacier due to the larger area atthe pressure-melting point Here again the temperatures

produced by ElmerIce are lower but the increased basalheating related to the larger basal sliding allows the meltingpoint to be reached at larger areas for the NEGIS andJakobshavn Isbraelig as well as the major outlet glaciers It is alsoremarkable that although ElmerIce has smaller temperate-based areas than SICOPOLIS the model shows a majorspeed-up of the ice-sheet flow equal to or greater thanthat observed with SICOPOLIS At the same time for bothmodels the increased ice flow leads to increased advectionof cold interior surface ice downwards and outwards whichshould cool down the ice base compared to the controlrun This is more evident for ElmerIce than for SICOPOLISperhaps due to the lower vertical resolution that does notcapture so well the counteracting effect of increased strainheating near the baseThe surface velocities and basal temperatures computed

for experiments C2 (AR4 climate forcing) and T1 (AR4climate forcing plus doubled basal sliding) are shownin Figures 5 and 6 respectively For both ElmerIce and


Fig 5 Surface velocities (a b) and basal temperatures relative to pressure melting (c d) computed with ElmerIce (a c) and SICOPOLIS (bd) for experiment C2 (AR4 climate forcing) at t = 100 years (year 2104)

SICOPOLIS the results are very similar to those obtainedwith experiments C1 and S1 respectively Only a limitedspeed-up occurs because of the higher surface temperaturesthat penetrate slowly into the deeper ice This indicatesthat the impact of a warmer climate in the absence ofaccompanying dynamical forcings has only a small effecton the dynamics and thermodynamics of the ice sheet onthe considered timescale of 100 years and acts mainly bythe changed surface mass balanceLet us now focus on the detailed surface velocity evolution

in the vicinity of Jakobshavn Isbraelig This is particularlyinteresting because the Greenland topography data usedhere (Section 22) are based on a special algorithm thatpreserves the continuity and depth of the trough belowthe ice stream (and below Helheim Kangerdlussuaq andPetermann glaciers) in the gridded data (UC Herzfeld andothers unpublished information) Figures 7 and 8 showsnapshots at t = 1 10 and 100 years for experimentsC2 and T1 conducted with ElmerIce and SICOPOLIS

respectively On this zoomed spatial scale the two sets ofresults are immediately distinguishable due to the coarserresolution employed by SICOPOLIS Here the benefit ofthe mesh refinement manifests itself by a much smootherrepresentation of the fast-flowing ice stream within theslower-flowing environment In the ElmerIce results an areaof fast flow is visible and greatly expands out of the mainbed trough at t = 1 year for experiment T1 In the following(t = 10 and 100 years) and for experiment C2 the velocitiesdecrease and become more focused towards the margin Forexperiment T1 the fast-flowing area outside the bed troughpersists through time with only a conspicuous and localizeddrop in velocity at t = 100 years This local feature is due to alocalized drop in the basal temperature which translates intoa decrease in basal sliding This sudden drop in temperatureis probably not physical but rather related to some numericalissues The SICOPOLIS results do not exhibit the widenedareas of fast flow because of the local nature of the shallow-ice approximation whereas in ElmerIce the velocities are


Fig 6 Same as Figure 5 but for experiment T1 (AR4 climate forcing doubled basal sliding)

more influenced by the topography in the vicinity of the maintrough due to the non-local full Stokes force balanceThe simulated ice volumes as functions of time are shown

in Figure 9 The ice sheet reacts distinctly to all appliedforcings The control run C1 with ElmerIce produces an icevolume gain of sim6 cm sle during the 100 years of modeltime while the same run with SICOPOLIS produces an icevolume loss of sim3 cm sle This difference and in particularthe stronger reaction of the ElmerIce run is presumably dueto the thermodynamically different initial conditions used bythe two models In order to largely remove this effect wediscuss the results of the three other experiments (S1 C2T1) relative to the control run C1 After 100 years of modeltime the ice volume losses ΔV are as follows

S1 (2times sliding) ndash C1 (control)ΔVElmerIce sim 13 cm sle ΔVSICOPOLIS sim 8 cm sle

C2 (AR4 climate) ndash C1 (control)ΔVElmerIce sim 2 cm sle ΔVSICOPOLIS sim 4 cm sle

T1 (AR4 climate 2times sliding) ndash C1 (control)ΔVElmerIce sim 15 cm sle ΔVSICOPOLIS sim 12 cm sle

The results from ElmerIce for the 2times basal sliding runS1 show a sim43 higher sensitivity for ice volume lossthan those from SICOPOLIS (computed as (ΔVElmerIce minusΔVSICOPOLIS)[ 12 (ΔVElmerIce + ΔVSICOPOLIS)]) This is par-ticularly remarkable because as was discussed abovesimulated flow velocities of ElmerIce are generally similarto SICOPOLIS with only a few areas with faster velocitiesso the higher sensitivity of ElmerIce is a consequence ofthe higher resolution of the fast-flowing areas MoreoverElmerIce seems to show that the full Stokes model hasa higher sensitivity to dynamical changes a crucial resultfor the implication of the Greenland destabilization due toincreased basal lubricationFor the direct global warming (AR4 climate) run C2

ElmerIce is sim61 less sensitive than SICOPOLIS The largedifference is mainly explained by the initial conditions usedby ElmerIce where the present-day conditions computed


Fig 7 Surface velocities in the area of Jakobshavn Isbraelig computed with ElmerIce for experiments C2 (AR4 climate forcing) and T1 (AR4climate forcing doubled basal sliding) at t = 1 year (year 2005) 10 years (year 2014) and 100 years (year 2104)

Fig 8 Same as Figure 7 but computed with SICOPOLIS


by the spin-up run have higher surface elevations aroundthe margins that built up during the last 100 spin-up yearswith freely evolving topography This has an importantconsequence for the surface temperatures computed for theconstant climate (Section 32) because the mean annual andmean July (summer) surface temperatures are dependent onthe surface elevation (Eqn (7)) so the atmospheric lapserate is effective Because of the higher surface elevationsat the margins for the initial conditions used by ElmerIcesurface temperatures are colder and surface melting islower implying that the evolution of the ice sheet from theimposed global warming driven by the change of the surfacemass balance is more effective in the case of SICOPOLISThe different sensitivities of ElmerIce and SICOPOLIS forexperiment C2 are therefore not due to the differencesbetween the two models (the representation of the surfacemass balance is the same in both models) but mainly dueto the different initial conditionsFor the combined (AR4 climate)(2times sliding) forcing of run

T1 the sensitivities of both ElmerIce and SICOPOLIS areessentially equal to the sums of the sensitivities to the 2timessliding forcing (S1) and the AR4 climate forcing (C2) whichin relative terms makes ElmerIce sim21 more sensitivethan SICOPOLIS This near-linear behaviour results from theshort model time of 100 years during which the absolutechanges in ice volume are limited to a few per cent sothe mutual influence between surface melting and ice flowremains small

5 CONCLUSIONThe full Stokes finite-element model ElmerIce was appliedto the entire Greenland ice sheet We carried out a setof SeaRISE experiments with it and compared results withthe SICOPOLIS shallow-ice model This work marks animportant step in ice-sheet modelling as it is the first attemptto assess the likely range of the contribution of an ice sheetto sea-level rise in the future with a prognostic full Stokesmodel that captures ice dynamics most adequatelyConsidering the computed surface velocities the differ-

ences between the two force balances (full Stokes vs shallowice) became evident The surface velocities computed withElmerIce are lower than those computed with SICOPOLISfor the control run and the AR4 climate run For the fast-flowing ice streams and outlet glaciers this is mainly dueto the lateral drag taken into account in the full Stokesmodel The improved representation of fast-flow areas alsobenefited from the mesh refinement technique applied inElmerIce that allows us to resolve them properly whilethe regular 10 km grid of SICOPOLIS smears them outsignificantly Further disparities were observed for the basaltemperatures The temperatures computed with ElmerIceare generally lower and the temperate-based areas smallerThis is possibly a shortcoming of the ElmerIce simulationsthat is due to the different initial conditions used by themodels and the rather low vertical resolution of 17 layers(while SICOPOLIS employs 81 layers) So far we have notsucceeded in increasing the vertical resolution because thisleads to finite elements with a very small aspect ratio and thusnumerical instabilities For the experiments with dynamicalforcing (S1 and T1) ElmerIce showed a higher sensitivitythan SICOPOLIS with a greater acceleration of the ice flowat major ice streams and outlet glaciers This greater speed-up in the case of ElmerIce produces surface velocities that

Fig 9 Ice volume (V ) changes simulated with (a) ElmerIce and(b) SICOPOLIS for experiments C1 (constant climate control run)S1 (constant climate forcing doubled basal sliding) C2 (AR4 climateforcing) and T1 (AR4 climate forcing doubled basal sliding) Notethat t = 0 corresponds to the year 2004

are equal to or greater than the velocities obtained withSICOPOLISThe computed ice volume evolutions for the experiment

with dynamical forcing (doubled basal sliding) showed asim43 greater sensitivity for ElmerIce than for SICOPOLIS(relative to the constant climate control runs) The fullStokes approach of ElmerIce along with the higher meshresolution that leads to greatly improved representationsof the fast-flowing zones means that the model is moresensitive to dynamical destabilization processes which isof great importance when investigating such phenomena tobetter estimate the resulting sea-level rise Under the AR4climate forcing ElmerIce was sim61 less sensitive thanSICOPOLIS and under the combined forcing ElmerIce wassim21 more sensitive in absolute terms essentially the sumof the two individual contributions The higher sensitivity ofSICOPOLIS for the AR4 climate forcing is mainly due to thedifferent initial conditions used by the models in the caseof ElmerIce the higher surface elevations near the ice-sheetmargins limit surface meltingSome important limitations of the results of this study

must be noted Although the full Stokes approach and themesh refinement allow for an adequate representation ofice-stream dynamics the appliedWeertman-type sliding lawEqn (8) is a severe simplification It works reasonably wellfor the ice sheet as a whole (Greve and others 1998 Greve2005) but its validity for fast-flowing ice with particular


basal conditions is questionable In addition we have notattempted to account for the particular marine ice dynamicsthat play a role in changes of Jakobshavn Isbraelig Thiscalls for improvements to be tackled in future work Mostimportantly inverse methods will be applied in order todetermine more suitable sliding laws for the ice streamsand outlet glaciers to be constrained by interferometricallymeasured present-day surface velocities (Joughin and others2010) This will also require improving the initial conditionsand running ElmerIce in full Stokes for a larger part oreven the duration of the spin-up Further desirable changesconcern treatment of the ice margins (implementation ofmoving margins temperature boundary conditions) anda higher vertical resolution (which requires overcomingnumerical stability issues due to extremely shallow finiteelements) These improvements are partly underway and willhopefully lead to more accurate and reliable simulations ofice volume variations under changing climates

ACKNOWLEDGEMENTSWe thank RA Bindschadler S Nowicki and others fortheir efforts in the management of the SeaRISE projectand JV Johnson UC Herzfeld and others for compilingand maintaining the SeaRISE datasets We also thankJ Ruokolainen and P Raback for continuous support andvaluable help with the Elmer software Comments byA Aschwanden and an anonymous reviewer helped toconsiderably improve the manuscript HS was supportedby a Postdoctoral Fellowship for Foreign Researchers anda Grant-in-Aid for Postdoctoral Research Fellows (No2008821) from the Japan Society for the Promotion ofScience (JSPS) Since expiry of these funds in October 2010HS and RG have been supported by a JSPS Grant-in-Aidfor Scientific Research A (No 22244058)

REFERENCES

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Amestoy PR Guermouche A LrsquoExcellent J-Y and Pralet S (2006) Hy-brid scheduling for the parallel solution of linear systems ParallelComput 32(2) 136ndash156 (doi 101016jparco200507004)

Bamber JL Ekholm S and Krabill WB (2001a) A new high-resolution digital elevation model of Greenland fully validatedwith airborne laser altimeter data J Geophys Res 106(B4)6733ndash6745 (doi 1010292000JB900365)

Bamber JL Layberry RL and Gogineni SP (2001b) A new icethickness and bed data set for the Greenland ice sheet 1Measurement data reduction and errors J Geophys Res106(D24) 33 773ndash33 780

Baral D Hutter K and Greve R (2001) Asymptotic theoriesof large-scale motion temperature and moisture distributionin land-based polythermal ice sheets a critical review andnew developments Appl Mech Rev 54(3) 215ndash256 (doi10111513097296)

Blatter H (1995) Velocity and stress fields in grounded glaciersa simple algorithm for including deviatoric stress gradientsJ Glaciol 41(138) 333ndash344

Bueler E and Brown J (2009) Shallow shelf approximation as alsquosliding lawrsquo in a thermomechanically coupled ice sheet modelJ Geophys Res 114(F3) F03008 (doi 1010292008JF001179)

Calov R (1994) Das thermomechanische Verhalten desGronlandischen Eisschildes unter der Wirkung verschiedener

Klimaszenarien ndash Antworten eines theoretisch-numerischenModells (PhD thesis Technische Hochschule Darmstadt)

Calov R and Greve R (2005) Correspondence A semi-analyticalsolution for the positive degree-day model with stochastictemperature variations J Glaciol 51(172) 173ndash175

Calov R and Hutter K (1996) The thermomechanical response of theGreenland ice sheet to various climate scenarios Climate Dyn12(4) 243ndash260

Colinge J and Blatter H (1998) Stress and velocity fields in glaciersPart I Finite-difference schemes for higher-order glacier modelsJ Glaciol 44(148) 448ndash456

Dahl-Jensen D (1989) Steady thermomechanical flow along two-dimensional flow lines in large grounded ice sheets J GeophysRes 94(B8) 10 355ndash10 362

Dahl-Jensen D and 6 others (1998) Past temperatures directly fromthe Greenland ice sheet Science 282(5387) 268ndash271

Dahl-Jensen D Gundestrup N Gogineni SP and Miller H (2003)Basal melt at NorthGRIP modeled from borehole ice-core andradio-echo sounder observations Ann Glaciol 37 207ndash212(doi 103189172756403781815492)

Dansgaard W Johnsen SJ Moslashller J and Langway CC Jr (1969) Onethousand centuries of climatic record from Camp Century on theGreenland ice sheet Science 166(3903) 377ndash381

Dansgaard W and 10 others (1993) Evidence for general instabilityof past climate from a 250-kyr ice-core record Nature364(6434) 218ndash220

Durand G Gagliardini O Zwinger T Le Meur E and Hind-marsh RCA (2009) Full Stokes modeling of marine ice sheetsinfluence of the grid size Ann Glaciol 50(52) 109ndash114 (doi103189172756409789624283)

Ettema J and 6 others (2009) Higher surface mass balanceof the Greenland ice sheet revealed by high-resolution cli-mate modelling Geophys Res Lett 36(12) L12501 (doi1010292009GL038110)

Fausto RS Ahlstroslashm AP Van As D Boslashggild CE and Johnsen SJ(2009) A new present-day temperature parameterization forGreenland J Glaciol 55(189) 95ndash105 (doi 103189002214309788608985)

Franca LP and Frey SL (1992) Stabilized finite element methodsII The incompressible NavierndashStokes equations Comput MethAppl Mech Eng 99(2ndash3) 209ndash233

Franca LP Frey SL and Hughes TJR (1992) Stabilized finite elementmethods I Comput Meth Appl Mech Eng 95(2) 253ndash276(doi 1010160045-7825(92)90143-8)

Frey PJ (2001) YAMS a fully automatic adaptive isotropic surfaceremeshing procedure Institut National de Recherche en Informa-tique et Automatique Rocquencourt (INRIA Tech Note RT-0252)

Frey PJ and Alauzet F (2005) Anisotropic mesh adaptation for CFDcomputations Comput Meth Appl Mech Eng 194(48ndash49)5068ndash5082 (doi 101016jcma200411025)

Gagliardini O and Zwinger T (2008) The ISMIP-HOM benchmarkexperiments performed using the Finite-Element code ElmerCryosphere 2(1) 67ndash76

Greve R (1997) Application of a polythermal three-dimensional icesheet model to the Greenland ice sheet response to steady-stateand transient climate scenarios J Climate 10(5) 901ndash918

Greve R (2000) On the response of the Greenland ice sheet togreenhouse climate change Climatic Change 46(3) 289ndash303

Greve R (2005) Relation of measured basal temperatures andthe spatial distribution of the geothermal heat flux for theGreenland ice sheet Ann Glaciol 42(1) 424ndash432 (doi103189172756405781812510)

Greve R and Blatter H (2009) Dynamics of ice sheets and glaciersSpringer-Verlag Dordrecht

Greve R Weis M and Hutter K (1998) Palaeoclimatic evolution andpresent conditions of the Greenland ice sheet in the vicinity ofSummit an approach by large-scale modelling Palaeoclimates2(2ndash3) 133ndash161

Greve R Saito F and Abe-Ouchi A (2011) Initial results of theSeaRISE numerical experiments with the models SICOPOLIS and


IcIES for the Greenland ice sheet Ann Glaciol 52(58) 23ndash30(doi 103189172756411797252068)

Gudmundsson GH (1999) A three-dimensional numerical modelof the confluence area of Unteraargletscher Bernese AlpsSwitzerland J Glaciol 45(150) 219ndash230

Gundestrup NS and Hansen BL (1984) Bore-hole survey at Dye 3south Greenland J Glaciol 30(106) 282ndash288

Gundestrup NS Clausen HB Hansen BL and Rand J (1987) CampCentury survey 1986 Cold Reg Sci Technol 14(3) 281ndash288

Gundestrup N Dahl-Jensen D Hansen BL and Kelty J (1993) Bore-hole survey at Camp Century 1989 Cold Reg Sci Technol21(2) 187ndash193

Hindmarsh RCA (2004) A numerical comparison of approximationsto the Stokes equations used in ice sheet and glacier modelingJ Geophys Res 109(F1) F01012 (doi 1010292003JF000065)

Hindmarsh RCA and Le Meur E (2001) Dynamical processesinvolved in the retreat of marine ice sheets J Glaciol 47(157)271ndash282 (doi 103189172756501781832269)

Howat IM Joughin IR and Scambos TA (2007) Rapid changes in icedischarge from Greenland outlet glaciers Science 315(5818)1559ndash1561

Hutter K (1983) Theoretical glaciology material science of iceand the mechanics of glaciers and ice sheets D ReidelDordrechtTerra Scientific Tokyo

Huybrechts P (1990) A 3-D model for the Antarctic ice sheeta sensitivity study on the glacialndashinterglacial contrast ClimateDyn 5(2) 79ndash92

Huybrechts P and de Wolde J (1999) The dynamic response of theGreenland and Antarctic ice sheets to multiple-century climaticwarming J Climate 12(8) 2169ndash2188

Huybrechts P Payne T and the EISMINT Intercomparison Group(1996) The EISMINT benchmarks for testing ice-sheet modelsAnn Glaciol 23 1ndash12

Johnsen SJ and 14 others (1997) The δ18O record along theGreenland Ice Core Project deep ice core and the problem ofpossible Eemian climatic instability J Geophys Res 102(C12)26 397ndash26 410

Joughin I and 8 others (2008) Ice-front variation and tidewaterbehavior on Helheim and Kangerdlugssuaq Glaciers GreenlandJ Geophys Res 113(F1) F01004 (doi 1010292007JF000837)

Joughin I Smith BE Howat IM Scambos T and Moon T(2010) Greenland flow variability from ice-sheet-widevelocity mapping J Glaciol 56(197) 415ndash430 (doi 103189002214310792447734)

Jouvet G Huss M Blatter H Picasso M and Rappaz J (2009) Numer-ical simulation of Rhonegletscher from 1874 to 2100 J ComputPhys 228(17) 6426ndash6439 (doi 101016jjcp200905033)

Lemke P and 10 others (2007) Observations changes in snowice and frozen ground In Solomon S and 7 others edsClimate change 2007 the physical science basis Contributionof Working Group I to the Fourth Assessment Report ofthe Intergovernmental Panel on Climate Change CambridgeUniversity Press Cambridge 339ndash383

MacAyeal DR (1989) Large-scale ice flow over a viscous basalsediment theory and application to Ice Stream B AntarcticaJ Geophys Res 94(B4) 4071ndash4087 (doi 10102988JB03848)

Marsiat I (1994) Simulation of the Northern Hemisphere continentalice sheets over the last glacialndashinterglacial cycle experimentswith a latitudendashlongitude vertically integrated ice sheet modelcoupled to a zonally averaged climate model Palaeoclimates1(1) 59ndash98

Martın C Navarro FJ Otero J Cuadrado ML and Corcuera MI(2004) Three-dimensional modelling of the dynamics of JohnsonsGlacier Livingston Island Antarctica Ann Glaciol 39 1ndash8(doi 103189172756404781814537)

Morland LW (1984) Thermomechanical balances of ice sheetflows Geophys Astrophys Fluid Dyn 29(1ndash4) 237ndash266 (doi10108003091928408248191)

Morland LW (1987) Unconfined ice-shelf flow In Van der Veen CJand Oerlemans J eds Dynamics of the West Antarctic ice sheetD Reidel Dordrecht 99ndash116

Morlighem M Rignot E Seroussi H Larour E Ben Dhia H andAubry D (2010) Spatial patterns of basal drag inferred usingcontrol methods from a full-Stokes and simpler models for PineIsland Glacier West Antarctica Geophys Res Lett 37(14)L14502 (doi 1010292010GL043853)

North Greenland Ice Core Project (NorthGRIP) members (2004)High-resolution record of Northern Hemisphere climate extend-ing into the last interglacial period Nature 431(7005) 111ndash228(doi 101038nature02805)

Pattyn F (1996) Numerical modelling of a fast-flowing outlet glacierexperiments with different basal conditions Ann Glaciol 23237ndash246

Pattyn F (2000) Ice-sheet modelling at different spatial resolutionsfocus on the grounding zone Ann Glaciol 31 211ndash216 (doi103189172756400781820435)

Pattyn F (2003) A new three-dimensional higher-order thermo-mechanical ice-sheet model basic sensitivity ice stream devel-opment and ice flow across subglacial lakes J Geophys Res108(B8) 2382 (doi 1010292002JB002329)

Pattyn F and Decleir H (1998) The Shirase flow-line model anadditional tool for interpreting the Dome-Fuji signal PolarMeteorol Glaciol 12 104ndash111

Pattyn F and 20 others (2008) Benchmark experiments forhigher-order and full-Stokes ice sheet models (ISMIP-HOM)Cryosphere 2(2) 95ndash108 (doi 105194tc-2-95-2008)

Payne AJ and 10 others (2000) Results from the EISMINTmodel intercomparison the effects of thermomechanicalcoupling J Glaciol 46(153) 227ndash238 (doi 103189172756500781832891)

Pollard D and DeConto RM (2007) A coupled ice-sheetice-shelfsediment model applied to a marine margin flowlineforced and unforced variations In Hambrey MJ Christoffersen PGlasser NF and Hubbard B eds Glacial sedimentary processesand products Blackwell Malden MA 37ndash52

Pollard D and DeConto RM (2009) Modelling West Antarctic icesheet growth and collapse through the past five million yearsNature 458(7236) 329ndash332 (doi 101038nature07809)

Price SF Waddington ED and Conway H (2007) A full-stress thermomechanical flow band model using the finitevolume method J Geophys Res 112(F3) F03020 (doi1010292006JF000724)

Price SF Payne AJ Howat IM and Smith BE (2011) Committedsea-level rise for the next century from Greenland ice sheetdynamics during the past decade Proc Natl Acad Sci USA(PNAS) 108(22) 8978ndash8983 (doi 101073pnas1017313108)

ReehN (1991) Parameterization of melt rate and surface temperatureon the Greenland ice sheet Polarforschung 59(3) 113ndash128

Ren D and Leslie LM (2011) Three positive feedback mechanismsfor ice-sheet melting in a warming climate J Glaciol 57(206)1057ndash1066

Ren D Fu R Leslie LM Chen J Wilson C and Karoly DJ (2011a)The Greenland ice sheet response to transient climate changeJ Climate 24 3469ndash3483

Ren D Fu R Leslie LM Karoly DJ Chen J and Wilson C (2011b)A multirheology ice model formulation and application to theGreenland ice sheet J Geophys Res 116(D5) D05112 (doi1010292010JD014855)

Rignot E and Kanagaratnam P (2006) Changes in the velocitystructure of the Greenland Ice Sheet Science 311(5673) 986ndash990 (doi 101126science1121381)

Rignot E Velicogna I Van den Broeke MR Monaghan A andLenaerts J (2011) Acceleration of the contribution of theGreenland and Antarctic ice sheets to sea level rise GeophysRes Lett 38(5) L05503 (doi 1010292011GL046583)

Ritz C Rommelaere V and Dumas C (2001) Modeling the evolutionof Antarctic ice sheet over the last 420 000 years implications


for altitude changes in the Vostok region J Geophys Res106(D23) 31 943ndash31 964

Rogozhina I Martinec Z Hagedoorn JM Thomas M and Fleming K(2011) On the long-term memory of the Greenland Ice SheetJ Geophys Res 116(F1) F01011 (doi 1010292010JF001787)

Rutt IC Hagdorn M Hulton NRJ and Payne AJ (2009) The Glimmercommunity ice sheet model J Geophys Res 114(F2) F02004(doi 1010292008JF001015)

Saito F and Abe-Ouchi A (2004) Thermal structure of Dome Fujiand east Dronning Maud Land Antarctica simulated by a three-dimensional ice-sheet model Ann Glaciol 39 433ndash438 (doi103189172756404781814258)

Saito F Abe-Ouchi A and Blatter H (2003) Effects of first-orderstress gradients in an ice sheet evaluated by a three-dimensionalthermomechanical coupled model Ann Glaciol 37 166ndash172(doi 103189172756403781815645)

Seddik H Greve R Zwinger T and Placidi L (2011) A full Stokesice flow model for the vicinity of Dome Fuji Antarcticawith induced anisotropy and fabric evolution Cryosphere 5(2)495ndash508 (doi 105194tc-5-495-2011)

Shapiro NM and Ritzwoller MH (2004) Inferring surface heatflux distribution guided by a global seismic model particular

application to Antarctica Earth Planet Sci Lett 233(1ndash2)213ndash224

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Sugiyama S Gudmundsson GH and Helbing J (2003) Numericalinvestigation of the effects of temporal variations in basallubrication on englacial strain-rate distribution Ann Glaciol37 49ndash54 (doi 103189172756403781815618)

Zwally HJ Abdalati W Herring T Larson K Saba J and Steffen K(2002) Surface melt-induced acceleration of Greenland ice-sheet flow Science 297(5579) 218ndash222 (doi 101126sci-ence1072708)

Zwinger T and Moore JC (2009) Diagnostic and prognosticsimulations with a full Stokes model accounting for super-imposed ice of Midtre Lovenbreen Svalbard Cryosphere 3(2)217ndash229

Zwinger T Greve R Gagliardini O Shiraiwa T and Lyly M (2007)A full Stokes-flow thermo-mechanical model for firn and iceapplied to the Gorshkov crater glacier Kamchatka Ann Glaciol45 29ndash37 (doi 103189172756407782282543)

MS received 18 August 2011 and accepted in revised form 31 January 2012

Journal of Glaciology Vol 58 No 209 2012 doi 1031892012JoG11J177 427

Simulations of the Greenland ice sheet 100 years into the futurewith the full Stokes model ElmerIce

Hakime SEDDIK1 Ralf GREVE1 Thomas ZWINGER2 Fabien GILLET-CHAULET3

Olivier GAGLIARDINI34

1Institute of Low Temperature Science Hokkaido University Sapporo JapanE-mail hakimepoplowtemhokudaiacjp2CSC ndash IT Center for Science Espoo Finland

3Laboratoire de Glaciologie et Geophysique de lrsquoEnvironnement CNRSUniversite Joseph Fourier Grenoble France4Institut Universitaire de France Paris France

ABSTRACT It is likely that climate change will have a significant impact on the mass balance of theGreenland ice sheet contributing to future sea-level rise Here we present the implementation of thefull Stokes model ElmerIce for the Greenland ice sheet which includes a mesh refinement technique inorder to resolve fast-flowing ice streams and outlet glaciers We discuss simulations 100 years into thefuture forced by scenarios defined by the SeaRISE (Sea-level Response to Ice Sheet Evolution) communityeffort For comparison the same experiments are also run with the shallow-ice model SICOPOLIS(SImulation COde for POLythermal Ice Sheets) We find that ElmerIce issimsim43more sensitive (exhibitsa larger loss of ice-sheet volume relative to the control run) than SICOPOLIS for the ice-dynamic scenario(doubled basal sliding) butsimsim61 less sensitive for the direct global warming scenario (based on the A1Bmoderate-emission scenario for greenhouse gases) The scenario with combined A1B global warmingand doubled basal sliding forcing produces a Greenland contribution to sea-level rise of simsim15 cm forElmerIce and simsim12 cm for SICOPOLIS over the next 100 years

1 INTRODUCTIONThe Greenland ice sheet is the second largest land icemass on the present-day Earth and its volume amounts tosim73m sle (metres sea level equivalent) The current massbalance of the ice sheet is most likely negative with anaccelerating trend though the uncertainty is significant(Lemke and others 2007 Rignot and others 2011) Surfacemelting increases strongly with rising surface temperaturesmaking the ice sheet very susceptible to future global warm-ing In addition recent observations (Zwally and others2002 Rignot and Kanagaratnam 2006 Howat and others2007 Joughin and others 2008) have led to strong concernsthat ice-dynamical processes (basal sliding accelerated bysurface meltwater speed-up of ice streams and outletglaciers) may boost the decay and thus lead to an additionalcontribution to sea-level rise Therefore it is clearly neces-sary to comprehensively model the dynamics of the Green-land ice sheet including ice streams and outlet glaciersMany models have been developed to simulate the

dynamics and evolution of ice sheets and glaciers Theshallow-ice approximation (Hutter 1983 Morland 1984)has been widely used for ice-sheet models (eg Huybrechts1990 Calov and Hutter 1996 Ritz and others 2001Saito and Abe-Ouchi 2004 Rutt and others 2009) Thisapproximation neglects the normal deviatoric stress andhorizontal shear components thus implying a significantsimplification that works well for large-scale ice-sheetdynamics but is inappropriate in the vicinity of ice dividesand margins fast-flowing regions like ice streams and smallsteeply inclined glaciers in general (eg Greve and Blatter2009) This gave rise to the formulation of higher-ordermodels (Blatter 1995 Baral and others 2001 Hindmarsh2004) in which longitudinal stresses are taken into accountto various extents Many of these models have been

applied to two-dimensional (2-D) domains (Dahl-Jensen1989 Blatter 1995 Colinge and Blatter 1998 Pattyn2000) and Dahl-Jensen (1989) demonstrated the importanceof longitudinal deviatoric stresses for plane flow along aflowline Pattyn (1996 2000) and Pattyn and Decleir (1998)applied a 2-D higher-order model with thermomechanicalcoupling to Shirase drainage basin Dronning Maud LandAntarctica Pattyn (2003) developed a three-dimensional(3-D) higher-order thermomechanical sheet model carriedout the European Ice-Sheet Modelling Initiative (EISMINT) Iand II benchmark experiments (Huybrechts and others 1996Payne and others 2000) and provided a comparison with theSaitondashBlatter model that also includes higher-order dynamics(Saito and others 2003) More recent developments are themodels of Pollard and DeConto (2007 2009) and Buelerand Brown (2009) that employ heuristic combinations ofthe shallow-ice and shallow-shelf approximations (Morland1987 MacAyeal 1989) as well as the application of a first-order model to the Greenland ice sheet by Price and others(2011) However due to several shortcomings inherent inthose models none of their results contributed to the FourthAssessment Report (AR4) of the Intergovernmental Panelon Climate Change (Solomon and others 2007) whichrepresents a great opportunity for the development andapplication of full Stokes modelsModels that solve the full Stokes equations (in which

all stress components are accounted for) in two or threedimensions have been proposed and applied mainly toglacier systems or parts of an ice sheet (eg Gudmundsson1999 Sugiyama and others 2003 Martın and others2004 Price and others 2007 Jouvet and others 2009)Comparisons between various full Stokes and higher-ordermodels were carried out in the Higher-Order Model(HOM) intercomparison topic of the Ice-Sheet Model



Quantity Value


prime)







div v = 0 (1)





η =12

(EA(T prime)


where d =radic

12 tr (D








)= div

(κ(T ) grad T

)+ 4ηd2 (5)



parthpartt+ vx

parthpartx

+ vyparthparty

minus vz = as (6)













(Greve 2005)


0b eT primebγ

ρgτpb

Nqb (8)






ρL (10)






































































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div v = 0 (1)





η =12

(EA(T prime)


where d =radic

12 tr (D








)= div

(κ(T ) grad T

)+ 4ηd2 (5)



parthpartt+ vx

parthpartx

+ vyparthparty

minus vz = as (6)













(Greve 2005)


0b eT primebγ

ρgτpb

Nqb (8)






ρL (10)






































































REFERENCES




































































































(Greve 2005)


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ρgτpb

Nqb (8)






ρL (10)






































































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Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model...

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