ISMIP6 future projections for the Greenland ice sheet with the model SICOPOLIS

ISMIP6 future projections for the Greenland ice sheet with the model SICOPOLIS Ralf GREVE1,2, Christopher CHAMBERS1, Reinhard CALOV3 1Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan 2Arctic Research Center, Hokkaido University, Sapporo, Japan 3Potsdam Institute for Climate Impact Research, Potsdam, Germany Contact: R. Greve (grev[email protected]) September 17, 2020 Abstract Technical Report, Zenodo, doi: 10.5281/zenodo.3971251 (2020) The Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) brings together a consortium of international ice-sheet and climate modellers to simulate the contribution from the Greenland and Antarctic ice sheets to future sea-level rise. In this document (supplementary to Goelzer et al. 2020, doi: 10.5194/tc-14-3071-2020), we describe the ISMIP6 Greenland Tier-1 and Tier-2 experiments carried out with the ice-sheet model SICOPOLIS. First, we conduct a paleoclimatic spin-up over the last glacial-interglacial cycle until the year 1990. In this spin-up, we employ a nudging technique for the topography and aim at optimizing the match between simulated and observed surface velocities by adjusting the amount of basal sliding for individual drainage systems. Then, we carry out a historical run to bridge the gap between 1990 and 2015. The future climate projections run from the beginning of 2015 until the end of 2100. The simulated mass loss by 2100 is 133.0±40.7 mm SLE (mean ±1sigma uncertainty; SLE: sea-level equivalent) for the RCP8.5/SSP5-8.5 pathway that represents “business as usual”, and it is 48.6±6.2 mm SLE for the RCP2.6/SSP1-2.6 pathway that represents substantial emissions reductions. The large difference between the results for the two pathways highlights the importance of efficient climate change mitigation for limiting sea-level rise. Further, results obtained with forcings from the newer CMIP6 global climate models consistently produce larger mass losses than those obtained with the older CMIP5 global climate models. 1 1 Introduction The Coupled Model Intercomparison Project Phase 6 (CMIP6) is a major international climate modelling initiative (Eyring et al. 2016). As a part of this project, the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) was devised to assess the likely sealevel-rise contribution from the Greenland and Antarctic ice sheets until the end of this century (Nowicki et al. 2016, 2020). Goelzer et al. (2020) describe the set-up and results of the ISMIP6 projections for the Greenland ice sheet. The ensemble of simulations is based on 21 sets of ice-flow simulations from 14 modelling groups. The design of the experiments is sketched in Fig. 1. An initial state of the ice sheet is produced by either assimilation or spin-up techniques or a combination of both (Goelzer et al. 2018, Seroussi et al. 2019). The initialization date varies between the different models (here 1990 CE). A single historical run with a forcing that can be chosen freely bridges the gap between the initialization and the start date of the projections in January 2015. All projections run from this date until December 2100. The atmospheric forcing consists of anomalies for the surface mass balance (SMB) and surface temperature (ST), derived from selected CMIP5 and CMIP6 global climate models (Barthel et al. 2020) and then downscaled to the surface of the ice sheet by the regional climate model MAR (Mod`ele Atmosph´erique R´egional) v3.9.6 (Fettweis et al. 2017, Delhasse et al. 2020). The oceanic forcing is based on a retreat parameterization for tidewater glaciers, forced by MAR run-off and ocean temperature changes in seven drainage basins around Greenland (Slater et al. 2019, 2020). Figure 1: ISMIP6 experimental design. A model-specific initialization is followed by a historical simulation from 1990 until 2015. The several projections run from 2015 until the end of 2100. (Credit: Martin R¨uckamp, AWI Bremerhaven, Germany.) Here, we describe the ISMIP6 future projections for the Greenland ice sheet carried out with the ice-sheet model SICOPOLIS (SImulation COde for POLythermal Ice Sheets). The emphasis is on the model-specific features that are not covered in detail in the community papers (Goelzer et al. 2020, Payne et al. 2020). For the ISMIP6 future projections for the Antarctic ice sheet, see the companion document by Greve et al. (2020). 2 Ice-sheet model SICOPOLIS v5.1 The three-dimensional, dynamic/thermodynamic model SICOPOLIS was originally created in a version for the Greenland ice sheet (Greve 1995, 1997a,b). Since then, the model has been developed continuously and applied to problems of past, present and future glaciation of Greenland, Antarctica, the entire northern hemisphere, the polar ice caps of 2 the planet Mars and others, resulting in more than 120 publications in the peer-reviewed literature (www.sicopolis.net, last accessed 2020-08-28). Here, we apply SICOPOLIS v5.1 (Greve and SICOPOLIS Developer Team 2019) to the Greenland ice sheet. The model domain covers the entire area of Greenland and the surrounding oceans. We use the EPSG:3413 grid, based on a polar stereographic projection with the WGS 84 reference ellipsoid, standard parallel 70◦N and central meridian 45◦W. The stereographic plane is spanned by the Cartesian coordinates xand y, and the coordinate zpoints upward. It is discretized by a regular (structured) grid with ∆x= 5 or 10 km resolution. In the vertical, we use terrain-following coordinates (sigma transformation) with 81 layers in the ice domain and 41 layers in the thermal lithosphere layer below. For the ice rheology, we use the regularized Glen flow law in the form of Greve and Blatter (2009, Sect. 4.3.2). The dynamics of grounded ice is modelled by either the shallow-ice approximation (SIA) or a hybrid SIA–SStA formulation (SStA: shelfy-stream approximation). The latter, abbreviated as ‘HYB’ in the following, is a modified form of Bernales et al.’s (2017) HS-1 scheme (hybrid scheme #1), which is described in detail in the companion document (Greve et al. 2020, Sect. 2). Floating ice is ignored. Ice thermodynamics is modelled by the one-layer melting-CTS enthalpy scheme (CTS: cold-temperate transition surface; Blatter and Greve 2015, Greve and Blatter 2016). The temperature-dependent rate factor for cold ice is by Cuffey and Paterson (2010, Sect. 3.4.6), and the water-contentdependent rate factor for temperate ice is by Lliboutry and Duval (1985). The ice surface is assumed to be traction-free. Basal sliding under grounded ice, vb, is described by a Weertman-Budd-type sliding law accounting for sub-melt sliding (Hindmarsh and Le Meur 2001) and the subglacial water-layer thickness (Kleiner and Humbert 2014, Calov et al. 2018): vb=−Cb τp b Nq b ,(1) with Cb=C0 bexp T0 b γ1 + c1−exp −Hw H0 w.(2) In Eq. (1), Cbis the sliding function, τbthe basal drag (shear stress), Nbthe basal normal stress (counted positive for compression; here assumed to be equal to the stress exerted by the overburden ice only, i.e., the counteracting water pressure is neglected), and pand q are the sliding exponents. In Eq. (2), C0 bis the sliding coefficient, T0 bthe basal temperature relative to pressure melting (in ◦C, always ≤0◦C), γthe sub-melt-sliding parameter, cthe coefficient for water-layer-enhanced basal sliding, Hwthe subglacial water-layer thickness and H0 wthe threshold water-layer thickness. Optionally, the simulated ice sheet can be divided into n= 1 . . . N regions, for which individual basal sliding coefficients (C0 b)nare set. We do this for N= 20 regions, the 19 basins by Zwally et al. (2012) plus a separate region for the North-East Greenland Ice Stream (NEGIS), defined by a surface velocity ≥50 m a−1 (Smith-Johnsen et al. 2020a,b); see Sects. 3.2.2 and 3.2.3. The water-layer thickness Hw is computed by a steady-state routing scheme for subglacial water that receives its input from the basal melting rate under grounded ice (Le Brocq et al. 2006, 2009). The bed topography is BedMachine v3 (Morlighem et al. 2017). Glacial isostatic adjustment (GIA) is included using a local-lithosphere–relaxing-asthenosphere (LLRA) model 3 Quantity Value Density of ice, ρ910 kg m−3 Density of sea water, ρsw 1028 kg m−3 Gravitational acceleration, g9.81 m s−2 Length of year, 1 a 31 556 926 s Power-law exponent, n3 Residual stress, σ010 kPa Flow enhancement factor, E1 / 3? Melting temperature at low pressure, T0273.16 K Clausius-Clapeyron gradient, β8.7×10−4K m−1 Universal gas constant, R8.314 J mol−1K−1 Heat conductivity of ice, κ9.828 e−0.0057 T[K] W m−1K−1 Specific heat of ice, c(146.3+7.253 T[K]) J kg−1K−1 Latent heat of ice, L3.35 ×105J kg−1 Sliding exponents, (p, q) (3,2) Sub-melt-sliding parameter, γ1◦C Coefficient for water-layer-enhanced basal sliding, c9 Threshold water-layer thickness, H0 w5 mm Density ×specific heat of the lithosphere, ρlcl2000 kJ m−3K−1 Heat conductivity of the lithosphere, κl3 W m−1K−1 Thickness of the thermal upper boundary layer of the lithosphere, Hlt 2 km Asthenosphere density, ρa3300 kg m−3 Time lag for the relaxing asthenosphere, τa3000 a Table 1: Physical parameters used for the simulations of this study. ?:E= 1 for Holocene or Eemian ice (deposited not earlier than 11 ka BP, or between 132 and 114 ka BP), E= 3 for Weichselian or pre-Eemian ice (deposited during other times). 4 (Le Meur and Huybrechts 1996). The geothermal heat flux is by Greve (2019), applied at the base of the thermal lithosphere layer (rather than directly at the ice base) to account for the thermal inertia of the lithosphere (Ritz 1987). The physical parameters are listed in Table 1. 3 Initialization via paleoclimatic spin-up A crucial prerequisite for future projections is a reasonable initial state of the ice sheet regarding ice geometry, surface velocities and englacial temperature (Goelzer et al. 2018, Seroussi et al. 2019). Here, we produce this initial state by carrying out a paleoclimatic spin-up over a full glacial cycle (134 ka) until the year 1990 CE (which corresponds to the time t= 0). It is similar to the spin-ups described by R¨uckamp et al. (2019) and Greve (2019). 3.1 Climate forcing The climatic forcing for the spin-up consists of time-dependent distributions of the surface temperature and precipitation. For the present-day mean annual and mean-July surface temperature, we employ the parameterizations by Fausto et al. (2009). These parameterizations express the temperature distributions as linear functions of surface elevation, latitude and longitude. However, the parameterizations are valid for 1996–2006, whereas our reference year (time t= 0) is 1990. In order to correct for this difference, we apply an offset of −1◦C to both parameterizations. This value was estimated based on the data shown by Kobashi et al. (2011, Fig. 1 therein). The main, time-dependent driver for the paleoclimatic spin-up is the surface temperature anomaly ∆T(t), assumed to be spatially uniform over the Greenland ice sheet. It is based on the δ18O record from the NGRIP ice core (North Greenland Ice Core Project members 2004) on the GICC05modelext time scale (Wolff et al. 2010), converted to temperature with the ∆T/δ18O transfer factor of 2.4◦Ch−1by Nielsen et al. (2018) (based on Huybrechts 2002). Warming during the Eemian is capped at ∆T= +4.5◦C (otherwise, the Eemian Greenland ice sheet becomes unrealistically small). The record is extended into the penultimate glacial by assuming ∆T=−20◦C at 140 ka b2k (before the year 2000) and a linear increase since then. For the most recent 4 ka, the surface temperature anomaly derived for the GISP2 site by Kobashi et al. (2011) is used instead of the NGRIP record. In addition, we prescribe the sea-level history, which is derived from the SPECMAP (Spectral Mapping Project) marine δ18O record (Imbrie et al. 1984). For the present-day precipitation, we use monthly means for the period 1958–2001, created with the regional energy and moisture balance model REMBO (Robinson et al. 2010). For any other time t, we assume a 7.3% change of the precipitation rate for every 1◦C of surface temperature (∆T) change (Huybrechts 2002). Conversion from precipitation to snowfall rate (solid precipitation) is done on a monthly-mean basis using the empirical fifth-order polynomial function by Bales et al. (2009). As in the study by Greve and Herzfeld (2013), surface melting is parameterized by Reeh’s (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 = 8 mm WE d−1◦C−1and 5 βsnow = 3 mm WE d−1◦C−1for ice and snow melt, respectively (where WE means water equivalent) (Huybrechts and de Wolde 1999). Furthermore, the standard deviation of short-term, statistical air temperature fluctuations is σ= 5◦C, and the saturation factor for the formation of superimposed ice is chosen as Pmax = 0.6 (Reeh 1991). We start the spin-up at t=−134 ka. At that time, ∆T=−11.13◦C, which is close to the mean anomaly over the whole period (R¨uckamp et al. 2019, Greve 2019). 3.2 Spin-up sequence 3.2.1 10 km resolution, SIA dynamics, t= –134. . . –9 ka (1) Simulation grl10 bm3 paleo17a Time t=−134 . . . −9 ka, starting from the observed present-day topography. The initial temperature field is computed by the Robin (1955) solution for grounded ice columns with positive SMB and a linear profile otherwise (SICOPOLIS parameter TEMP INIT = 4). Time steps: ∆t= 1 a (for dynamics and topography), ∆ttemp = 1 a (for thermodynamics). SIA dynamics, free evolution of the ice topography. Basal sliding with a constant sliding parameter C0 b= 2.5 m a−1Pa−1after −129 ka. During the first 5 ka (prior to −129 ka), basal sliding is ramped up according to R¨uckamp et al. (2019, Sect. 3.1, run (1)) (see also Greve et al. 2020, Sect. 3.2.1, run (2)). 3.2.2 5 km resolution, SIA dynamics, t= –9. . . 0 ka (2) Simulation grl05 bm3 paleo17 init10a Short simulation over 10 a, starting from the observed present-day topography, no basal sliding, isothermal conditions (T=−10◦C everywhere). Time steps: ∆t= ∆ttemp = 0.1 a. SIA dynamics, free evolution of the ice topography. The purpose of this run is to produce a slightly smoothed present-day topography (surface htarget(x, y), bed btarget(x, y)) of the Greenland ice sheet that serves as a target for all subsequent runs that employ topography nudging. (3) Simulation grl05 bm3 paleo17b Time t=−9. . . 0 ka, starting from the resolution-doubled output of run (1) at t=−9 ka. Time steps: ∆t= ∆ttemp = 0.5 a. SIA dynamics. Basal sliding with a constant sliding parameter C0 b= 2.5 m a−1Pa−1. The computed topography is continuously nudged towards the output of run (2) by using the method by Rezvanbehbahani et al. (2019) and R¨uckamp et al. (2019) (see also Greve et al. (2020, Sect. 3.2.1, run (2)); SICOPOLIS parameter THK EVOL = 3). (4) Simulations grl05 bm3 paleo17b-{01,02,03,04,05,06,07} Each of these seven runs reads the output of run (3) at t=−1 ka and runs until t= 0. Time steps: ∆t= ∆ttemp = 0.5 a. The basal sliding coefficients (C0 b)k n (n= 1 . . . 20) are iteratively adjusted for the 20 regions described above (Sect. 2) to achieve optimum agreement between simulated and observed surface velocities in these regions. The index kcounts the iterations. The starting value (iteration 6 no. k= 0) is the value from run (3), (C0 b)0 n= 2.5 m a−1Pa−1. Except for the basal sliding, the set-up is the same as that of run (3). The k-th iteration of the run is called grl05 bm3 paleo17b-k. For each basin n, we compute a regression line for simulated vs. observed surface velocities (within the range [10 m a−1,10000 m a−1]) through the origin with the slope ak n, and update the sliding coefficient (C0 b)k n. This is described in detail in the companion document (Greve et al. 2020, Sect. 3.2.3, Eqs. (16)–(21)). The procedure is stopped after k= 7 iterations (grl05 bm3 paleo17b-07), when the overall slope (for the entire ice sheet) has reached the interval [0.95,1.05]: a7 all = 1.0472. Figure 2 demonstrates that the scheme has converged well; further iterations would not lead to a significant improvement of the fit. Figure 2: Slope ak all of the regression line for the entire ice sheet and RMSD (root mean square deviation) of the logarithmic surface velocity lg (v) (in m a−1) for the entire ice sheet after kiterations. (5a) Simulation grl05 bm3 paleo22b-07 Essentially a repetition of the final run (4) (grl05 bm3 paleo17b-07); however, with a modified set-up: All runs (1)–(4) use an over-implicit scheme for solving the diffusive SIA ice-thickness equation (OVI/w= 1.5 in the terminology by Greve and Calov (2002); SICOPOLIS parameter CALCTHK = 2). While this scheme has favourable stability properties, thus allowing large dynamics time steps ∆t, the way the diffusivity is treated (Type II in the terminology by Huybrechts et al. (1996), see their Eq. (19) and accompanying text) is not inherently mass-conserving. For the high resolution employed here and the correspondingly variable structure of the bed topography, this leads to a significant residual when trying to close the global mass balance for the ice sheet (change of volume with time equals total SMB, basal melting and discharge/calving). To avoid this, we switch to an explicit solver that discretizes the advection term of the general ice-thickness equation by a mass-conserving scheme in an upwind flux form (Calov et al. 2018, their Eq. (A1); SICOPOLIS parameter CALCTHK = 4). 7 This solver requires a greatly reduced dynamics time step of ∆t= 0.02 a, while the thermodynamics time step ∆ttemp = 0.5 a can be retained. Topography nudging is changed from the method described above (see run (3)) to the implied SMB by Calov et al. (2018) (their Eq. (10) with a relaxation time τrelax = 100 a) (SICOPOLIS parameters THK EVOL = 1, ACCSURFACE = 7, ABLSURFACE= 7 ). Further, marine-ice formation is enabled (SICOPOLIS parameter MARGIN = 2) with a minimum sea-bed elevation of −300 m. (6a) Simulations grl05 bm3 paleo22b-{08,09} Two further iteration steps for the regional basal sliding coefficients with the modified set-up of run (5a), reading the output of run (5) at t=−100 a and running until t= 0. Time steps: ∆t= 0.02 a, ∆ttemp = 0.5 a. The resulting basal sliding coefficients (Fig. 3) show a great variability. By far the largest value occurs in region No. 6, which is the NEGIS region, followed by Nos. 17 and 16, which are the Jakobshavn drainage basin and the adjacent basin to the south, respectively. Figure 3: (a) Basal sliding coefficients (C0 b)nfor the 20 regions (19 basins by Zwally et al. (2012) plus a separate NEGIS region) obtained for SIA dynamics. (b) Location of the regions, marked by circled numbers that correspond to the region number nin panel (a). (7a) Simulation grl05 bm3 paleo22c-09 Time t=−1. . . 0 ka, starting from the output of run (3) at t=−1 ka. Otherwise, same set-up as the final run (6a). (8a) Simulation grl05 bm3 paleo22d-09 Time t=−120 . . . 0 a, re-run of the last 120 a of run (7a) with annual output of scalar and 2D fields as requested by the ISMIP6 protocol. The final state of this run is our initial ice sheet for the year 1990 CE with SIA dynamics. 8 3.2.3 5 km resolution, HYB dynamics, t= –1. . . 0 ka (5b) Simulation grl05 bm3 paleo23b-07 Like run (5a), but with HYB dynamics (modified HS-1 scheme, see Sect. 2). Time t=−1. . . 0 ka. Time steps ∆t= 0.02 a, ∆ttemp = 0.5 a. (6b) Simulation grl05 bm3 paleo23c-{08,09} Two further iteration steps for the regional basal sliding coefficients with the set-up of run (5b). Time t=−1. . . 0 ka. Time steps ∆t= 0.02 a, ∆ttemp = 0.5 a. Note that this differs from the SIA runs (6a), where the two iterations were carried out only for 100 a. Figure 4 shows the resulting basal sliding coefficients. The distribution has not changed significantly compared to the SIA case (Fig. 3). However, the value for the NEGIS region (No. 6) has become even larger, and region No. 16 (south of Jakobshavn) features now a slightly larger sliding coefficient than No. 17 (Jakobshavn). Figure 4: Basal sliding coefficients (C0 b)nfor the 20 regions (19 basins by Zwally et al. (2012) plus a separate NEGIS region, see Fig. 3b) obtained for HYB dynamics. (7b) Simulation grl05 bm3 paleo23d-09 Time t=−120 . . . 0 a, re-run of the last 120 a of the final run (6b) with annual output of scalar and 2D fields as requested by the ISMIP6 protocol. The final state of this run is our initial ice sheet for the year 1990 CE with HYB dynamics. 3.3 Simulated initial (1990 CE) ice sheet For the HYB case, the spin-up sequence produces an initial ice sheet with a total volume of V= 2.940 ×106km3, a volume above flotation of Vaf = 7.279 m SLE (sea-level equivalent) and an ice area of A= 1.781 ×106km2. For SIA, the values are very similar, V= 2.934 ×106km3,Vaf = 7.264 m SLE and A= 1.781 ×106km2. In the following, we will focus on the HYB case (more sophisticated ice dynamics) and report the SIA results only briefly for comparison. Due to the topography nudging 9 Acknowledgements We thank the Climate and Cryosphere (CliC) effort, which provided support for ISMIP6 through sponsoring of workshops, hosting the ISMIP6 website and wiki, and promoting ISMIP6. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP5 and CMIP6. We thank the climate modelling groups for producing their model output and making it available; the Earth System Grid Federation (ESGF) for archiving the CMIP data and providing access to it; the University at Buffalo for ISMIP6 data distribution and upload; and the multiple funding agencies who support CMIP5, CMIP6, and ESGF. We thank the ISMIP6 steering committee, the ISMIP6 model selection group and ISMIP6 dataset preparation group for their continuous engagement in defining ISMIP6. This is ISMIP6 contribution No. 22. Ralf Greve and Chris Chambers were supported by Japan Society for the Promotion of Science (JSPS) KAKENHI grant No. JP16H02224. Ralf Greve was supported by JSPS KAKENHI grant No. JP17H06104, by a Leadership Research Grant of Hokkaido University’s Institute of Low Temperature Science (ILTS), and by the Arctic Challenge for Sustainability (ArCS) project of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) (program grant number JPMXD1300000000). Reinhard Calov was funded by the PalMod project (PalMod 1.1 and 1.3 with grants 01LP1502C and 01LP1504D) of the German Federal Ministry of Education and Research (BMBF). References Bales, R. C., Guo, Q., Shen, D., McConnell, J. R., Du, G., Burkhart, J. F., Spikes, V. 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