Disentangling the drivers of future Antarctic ice loss with a historically-calibrated ice-sheet model

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Disentangling the drivers of future Antarctic ice loss with a historically-calibrated ice-sheet model
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INTRODUCTION
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This dataset contains the data and scripts required to reproduce the figures and tables presented in the study:
"Disentangling the drivers of future Antarctic ice loss with a historically-calibrated ice-sheet model" in The Cryosphere.

We perform an ensemble of simulations of the Antarctic ice sheet between 1950 and 3014, forced by a panel of CMIP6 climate models, starting from present-day geometry with the Kori-ULB ice-sheet model v0.9. We calibrate our ensemble in a Bayesian framework to produce observationally-calibrated Antarctic projections used to investigate the future trajectory of the Antarctic ice sheet related to uncertainties in the future balance between sub-shelf melting and ice discharge on the one hand, and the surface mass balance on the other. All simulations are performed at a spatial resolution of 16 km.

Hindcasts of the behaviour of the AIS over the period 1950-2014 CE are reproduced using changes in oceanic and atmospheric boundary conditions derived from the CMIP5 climate model NorESM1-M. As of the year 2015 CE, climate projections derived from a subset of CMIP6 climate models (MRI-ESM2-0, IPSL-CM6A-LR, CESM2-WACCM and UKESM1-0-LL) are used as forcing until the year 2300 CE. Afterwards, no climate trend is applied. The forcing applied is derived from both the Shared Socioeconomic Pathways (SSP) 5-8.5 and 1-2.6 scenarios. 

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PROVIDED SCRIPTS: 
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 - 'KoriModelAll.m' and 'KoriInputParams.m': Kori-ULB ice flow model (more info at https://github.com/FrankPat/Kori-ULB)
 - 'Compute_Bayesian_Weight.m': calculation of the ensemble likelihood weights used in the Bayesian calibration.
 - 'Plot_parameter_space_distributions.m': calculation and plots of prior and posterior parameter  probability distributions.
 - 'Plot_sea_level_distributions.m': calculation and plots of prior and posterior sea-level distributions.
 - 'Plot_mass_balance_components_distributions.m': calculation and plots of mass balance components distributions.
 - 'Plot_mean_thickness_change.m': calculation and plots of calibrated mean thickness change.
 - 'Plot_ungrounded_probability.m': calculation and plots of the marginal probability of being ungrounded.
 - 'Plot_SMB_sensitivity.m': Calculation and plots of surface mass balance sensitivity.
 - 'run_MISMIPplus.m' and 'MISMIPplus.m': run and compare MISMIP+ experiment

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PROVIDED DATA: 
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• 'LHSensemble.mat': 100x9 matrices containing the values of the 100-member ensemble sampled (using maximin Latin Hypercube) within the parameter space in Table 1.
  • 1rst column ((:,1)) contains values of atmospheric present-day climatology (CLIMatm): MARv3.11 (1) - RACMOv2.3p2 (2)
  • 2nd column ((:,2)) contains values of oceanic present-day climatology (CLIMocn): Jourdain2020 (1) - Schmidtko2014 (2)
  • 3rd column ((:,3)) contains values of the atmospheric lapse rate (°C/km)
  • 4th column ((:,4)) contains values of the thickness of the thermally-active layer influencing surface refreezing (m)
  • 5th column ((:,5)) contains values of the contains values of the Degree day factor for the melting of ice (mm/PDD)
  • 6th column ((:,6)) contains values of the contains values of the Degree day factor for the melting of snow (mm/PDD)
  • 7th column ((:,7)) contains values of the applied Sub-shelf melt parameterisation: Quadratic-local Antarctic slope parameterisation (1) - PICO model (2) - Plume model (3) - ISMIP6 Nonlocal quadratic parameterisation (4) - ISMIP6 Nonlocal quadratic parameterisation including dependency on local slope (5)
  • 8th column ((:,8)) contains values of the effective ice-ocean heat flux: [0.1 x 10^-5 - 10 x 10^-5] m/s for gammaT* in PICO - [1 x 10^-4 - 10 x 10^-4] for Cd^1/2Gamma_TS in Plume -  [1 x 10^-4 - 10 x 10^-4] for K in Quadratic-local Antarctic slope parameterisation - [1 x 10^4 - 4 x 10^4] m/yr for gamma0 in ISMIP6 Nonlocal quadratic parameterisation - [1 x 10^6 - 4 x 10^6] m/yr for gamma0 in ISMIP6 Nonlocal quadratic parameterisation with slope dependency
  • 9th column ((:,9)) contains values of the CMIP6 climate model applied for climate forcing: MRI-ESM2-0 (1) - UKESM1-0-LL (2) - CESM2-WACCM (3) - IPSL-CM6A-LR (4)
    
    'LHval' and 'LHS' contain the absolute values and the values of the parameters scaled linearly between 0 and 1 (0: minimum value, 1:maximum value) of the nine parameters, respectively.
     
• 'HIST_ENSEMBLE_DATA.mat' contains the following variables describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014).
  • H_ensemble: 4D matrix of dimension [X, Y, snap_time, ensemble member] with ice thickness field (in meters) for the 100 ensemble members at different years (snap_time). X and Y represent spatial coordinates on a grid.
  • MASK_ensemble: 4D matrix of dimension [X, Y, snap_time, ensemble member] with grounded mask field (in meters) for the 100 ensemble members at different years (snap_time). X and Y represent spatial coordinates on a grid. 
    It distinguishes grounded ice (1: grounded) from ocean or floating ice (0: ocean/floating).
  • mbcomp_ensemble: 3D matrix of dimension [time, mbcomp, ensemble member] with timeseries (yearly values at years time) of various mass balance components for the 100 ensemble members (in gigatons per year, Gt/yr). 
    The components mbcomp include the following ice-sheet aggregated and grounded ice sheet components:
                        (1) Ice-sheet aggregated surface mass balance
                        (2) Ice-sheet aggregated accumulation
                        (3) Ice-sheet aggregated surface melt
                        (4) Ice-sheet aggregated runoff
                        (5) Ice-sheet aggregated rain
                        (6) sub-shelf melt
                        (7) dynamic ice loss (calving)
                        (8) surface mass balance over the grounded ice sheet
                        (9) accumulation over the grounded ice sheet
                        (10) surface melt over the grounded ice sheet
                        (11) runoff over the grounded ice sheet
                        (12) rain over the grounded ice sheet            
                        (13) Net mass balance (rate of HAF change)
  • SLC_ensemble: 2D matrix of dimension [ensemble member, time] with timeseries (yearly values at years time) of the ice-sheet sea-level contribution (in m) 
     
• 'HIST_ENSEMBLE_DATA_NO_ELEVATION_FEEDBACK.mat': same as 'HIST_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014) when neglecting the melt-elevation feedback.
   
• 'HIST_ENSEMBLE_DATA_HYDROFRAC.mat': same as 'HIST_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014) when including surface melt-driven hydrofracturing of the ice shelves (estimated following Pollard et al., 2015).
   
• 'CONTROL_ENSEMBLE_DATA.mat': contains the variables H_ensemble, MASK_ensemble, mbcomp_ensemble and SLC_ensemble (as in 'HIST_ENSEMBLE_DATA') describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 when considering constant present-day conditions as of the year 2015.
   
• 'SSP126_ENSEMBLE_DATA.mat': contains the variables H_ensemble, MASK_ensemble, mbcomp_ensemble and SLC_ensemble (as in 'HIST_ENSEMBLE_DATA') describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under a SSP1-2.6 scenario.
   
• 'SSP585_ENSEMBLE_DATA.mat': contains the variables H_ensemble, MASK_ensemble, mbcomp_ensemble and SLC_ensemble (as in 'HIST_ENSEMBLE_DATA') describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under a SSP5-8.5 scenario. It also contains the variable Runoff_ensemble, a 4D matrix of dimension [X, Y, snap_time, ensemble member] with surface runoff field (in m/yr i.e.) for the 100 ensemble members at different years (snap_time). X and Y represent spatial coordinates on a grid, as used in Fig. 7.
   
• 'SSP585_ENSEMBLE_DATA_NO_ELEVATION_FEEDBACK.mat': same as 'SSP585_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when neglecting the melt-elevation feedback.
   
• 'SSP585_ENSEMBLE_DATA_HYDROFRAC.mat': same as 'SSP585_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when including surface melt-driven hydrofracturing of the ice shelves (estimated following Pollard et al., 2015).
   
• 'SSP585_ENSEMBLE_DATA_ATM_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when considering constant oceanic present-day conditions as of the year 2015.
   
• 'SSP585_ENSEMBLE_DATA_NO_ELEVATION_FEEDBACK_ATM_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when neglecting the melt-elevation feedback and considering constant oceanic present-day conditions as of the year 2015.
   
• 'SSP585_ENSEMBLE_DATA_OCEAN_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario considering constant atmospheric present-day conditions as of the year 2015.
   
• 'HIST_ENSEMBLE_DATA_BASIN.mat' contains the following variables describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014) integrated over 27 drainage basins (http://imbie.org/imbie-2016/drainage-basins/).
  • SLC_ensemble_basin: 3D matrix of dimension [basin, ensemble member, time] with timeseries (yearly values at years time) of the ice-sheet sea-level contribution (in m) by basin
  • mbcomp_ensemble_basin: 4D matrix of dimension [basin, time, mbcomp, ensemble member] with timeseries (yearly values at years time) of various mass balance components for the 100 ensemble members (in gigatons per year, Gt/yr) by basin. The components mbcomp include the same ice-sheet aggregated and grounded ice-sheet components as in 'HIST_ENSEMBLE_DATA.mat'.
     
• 'HIST_ENSEMBLE_DATA_BASIN_NO_ELEVATION_DATA.mat': same as 'HIST_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014) when neglecting the melt-elevation feedback.
   
• 'HIST_ENSEMBLE_DATA_BASIN_HYDROFRAC.mat': same as 'HIST_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the historical period (1950-2014) when including surface melt-driven hydrofracturing of the ice shelves (estimated following Pollard et al., 2015).
   
• 'SSP126_ENSEMBLE_DATA_BASIN.mat': contains the variables SLC_ensemble_basin and mbcomp_ensemble_basin (as in 'HIST_ENSEMBLE_DATA°BASIN') describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under a SSP1-2.6 scenario.
   
• 'SSP585_ENSEMBLE_DATA_BASIN.mat': contains the variables SLC_ensemble_basin and mbcomp_ensemble_basin (as in 'HIST_ENSEMBLE_DATA') describing the evolution of the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under a SSP5-8.5 scenario.
   
• 'SSP585_ENSEMBLE_DATA_BASIN_NO_ELEVATION_FEEDBACK.mat': same as 'SSP585_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under a SSP5-8.5 scenario when neglecting the melt-elevation feedback.
   
• 'SSP585_ENSEMBLE_DATA_BASIN_HYDROFRAC.mat': same as 'SSP585_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when including surface melt-driven hydrofracturing of the ice shelves (estimated following Pollard et al., 2015).
   
• 'SSP585_ENSEMBLE_DATA_BASIN_ATM_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when considering constant oceanic present-day conditions as of the year 2015.
   
• 'SSP585_ENSEMBLE_DATA_BASIN_NO_ELEVATION_FEEDBACK_ATM_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario when neglecting the melt-elevation feedback and considering constant oceanic present-day conditions as of the year 2015.
   
• 'SSP585_ENSEMBLE_DATA_BASIN_OCEAN_ONLY.mat': same as 'SSP585_ENSEMBLE_DATA_BASIN.mat' for the 100-member ensemble of simulations of the Antarctic ice sheet over the period 2015-3014 under an SSP5-8.5 scenario considering constant atmospheric present-day conditions as of the year 2015.
   
• 'GCM_SSPXXX_mean_aTs.mat': Timeseries of the regionally-averaged (between 90–60°S) annual near-surface (2-m) air temperature anomaly (°C) projected by the climate model 'GCM' from the sixth phase of the Coupled Model Intercomparison Project (CMIP6) between 2015 and 2300 under the SSPXXX emission scenario, compared to the 1995-2014 reference period. SSPXXX may be 'SSP126' and 'SSP585' and GCM may be 'MRI-ESM2-0', 'CESM2-WACCM', 'IPSL-CM6A-LR', or 'UKESM1-0-LL'.
   
• 'CALIBRATION DATA.mat': values ('val'), uncertainty ('sigma'), beginning ('year1') and end ('year2') of the average time period of the 12 regionally and temporally aggregated IMBIE data used in the Bayesian calibration (Table 2 in this study, coming from Table 2 from Otosaka et al., 2023)
   
• 'INIT_MAR_aNorESM1-M_1950.mat' and 'INIT_RACMO_aNorESM1-M_1950.mat': Ice-sheet initial states at year 1950 obtained with the 1995-2014 atmospheric climatology from MARv3.11(Kittel eta l.,2021) or RACMOv2.3p2 (van Wessem et al., 2018), respectively, adjusted with a 1945-1955 anomaly from NorESM1-M. H is the ice thickness (in meters), B is the bedrock topography (in meters), and u is the surface velocity (in m/yr). These files were provided as input files to Kori-ULB to produce the projections. More info on the input files and their variables can be found here: https://github.com/FrankPat/Kori-ULB.

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MATLAB FUNCTIONS USED IN SCRIPTS: 
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- imagescn: imagesc with transparent NaNs, by Chad Greene (2023), downloaded from MATLAB Central File Exchange (https://www.mathworks.com/matlabcentral/fileexchange/61293-imagescn), 
- brewermap: provides all ColorBrewer colorschemes for MATLAB, by Stephen23. Downloaded from https://github.com/DrosteEffect/BrewerMap.
- crameri: returns perceptually-uniform scientific colormaps created by Fabio Crameri (requires CrameriColourMaps8.0.mat)

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EXTERNAL DATA NOT CONTAINED IN THIS REPOSITORY:
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- BedMachine data used for the present-day grounding lines in Figures 2 and 7: It is BedMachine v2 (Morlighem et al., 2020) and can be found here: https://nsidc.org/data/nsidc-0756/versions/2.
- The delineation of the 27 Zwally Basins used to identify and separate the West and East Antarctic ice sheets and the Antarctic Peninsula can be found at http://imbie.org/imbie-2016/drainage-basins/
- Outputs from MAR(CNRM-CM6-1) and MAR(CESM2) used in Figures 7 and S10. The data can be downloaded at 10.5281/zenodo.4529004 and 10.5281/zenodo.4529002, respectively. It was then interpolated to the 16-km grid used by Kori-ULB.
- CESM2-WACCM outputs used in Figure 7 were downloaded from the CMIP6 search interface (https://esgf-node.llnl.gov/search/cmip6/) and interpolated to the 16-km grid used by Kori-ULB.
- The CMIP6 forcing data used in this study (and plotted in Figures S6 and S7) are accessible through the CMIP6 search interface (https://esgf-node.llnl.gov/search/cmip6/). They have been interpolated to the interpolated to the 16-km grid used by Kori-ULB.

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REFERENCES: 
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Kittel, C., Amory, C., Agosta, C., Jourdain, N. C., Hofer, S., Delhasse, A., Doutreloup, S., Huot, P.-V., Lang, C., Fichefet, T., and Fettweis, X.: Diverging future surface mass balance between the Antarctic ice shelves and grounded ice sheet, The Cryosphere, 15, 1215–1236, https://doi.org/10.5194/tc-15-1215-2021, 2021.

Morlighem, M., Rignot, E., Binder, T. et al. Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nat. Geosci. 13, 132–137 (2020). https://doi.org/10.1038/s41561-019-0510-8

Otosaka, I. N., Shepherd, A., Ivins, E. R., Schlegel, N.-J., Amory, C., van den Broeke, M. R., Horwath, M., Joughin, I., King, M. D., Krinner, G., Nowicki, S., Payne, A. J., Rignot, E., Scambos, T., Simon, K. M., Smith, B. E., Sørensen, L. S., Velicogna, I., Whitehouse, P. L., A, G., Agosta, C., Ahlstrøm, A. P., Blazquez, A., Colgan, W., Engdahl, M. E., Fettweis, X., Forsberg, R., Gallée, H., Gardner, A., Gilbert, L., Gourmelen, N., Groh, A., Gunter, B. C., Harig, C., Helm, V., Khan, S. A., Kittel, C., Konrad, H., Langen, P. L., Lecavalier, B. S., Liang, C.-C., Loomis, B. D., McMillan, M., Melini, D., Mernild, S. H., Mottram, R., Mouginot, J., Nilsson, J., Noël, B., Pattle, M. E., Peltier, W. R., Pie, N., Roca, M., Sasgen, I., Save, H. V., Seo, K.-W., Scheuchl, B., Schrama, E. J. O., Schröder, L., Simonsen, S. B., Slater, T., Spada, G., Sutterley, T. C., Vishwakarma, B. D., van Wessem, J. M., Wiese, D., van der Wal, W., and Wouters, B.: Mass balance of the Greenland and Antarctic ice sheets from 1992 to 2020, Earth Syst. Sci. Data, 15, 1597–1616, https://doi.org/10.5194/essd-15-1597-2023, 2023.

Pollard, D., DeConto, R. M., and Alley, R. B.: Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure, Earth and Planetary Science Letters, 412, 112–121, https://doi.org/10.1016/j.epsl.2014.12.035, 2015.
 
van Wessem, J. M., van de Berg, W. J., Noël, B. P. Y., van Meijgaard, E., Amory, C., Birnbaum, G., Jakobs, C. L., Krüger, K., Lenaerts, J. T. M., Lhermitte, S., Ligtenberg, S. R. M., Medley, B., Reijmer, C. H., van Tricht, K., Trusel, L. D., van Ulft, L. H., Wouters, B., Wuite, J., and van den Broeke, M. R.: Modelling the climate and surface mass balance of polar ice sheets using RACMO2 – Part 2: Antarctica (1979–2016), The Cryosphere, 12, 1479–1498, https://doi.org/10.5194/tc-12-1479-2018, 2018.