Supplementary Materials for

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1 advances.sciencemag.org/cgi/content/full/2/9/e /dc1 Supplementary Materials for Geodetic measurements reveal similarities between post Last Glacial Maximum and present-day mass loss from the Greenland ice sheet Shfaqat A. Khan, Ingo Sasgen, Michael Bevis, Tonie van Dam, Jonathan L. Bamber, John Wahr, Michael Willis, Kurt H. Kjær, Bert Wouters, Veit Helm, Beata Csatho, Kevin Fleming, Anders A. Bjørk, Andy Aschwanden, Per Knudsen, Peter Kuipers Munneke This PDF file includes: Published 21 September 2016, Sci. Adv. 2, e (2016) DOI: /sciadv fig. S1. Locations of the permanent GPS stations in Greenland. fig. S2. Monthly mean values of vertical GPS solutions after removing the annual, semiannual, and elastic vertical displacement. fig. S3. Elevation change rate during fig. S4. Time series of GrIS mass loss rate. fig. S5. Ice thickness change since the LGM as represented by the Green1 VM- GPS. fig. S6. GIA rates. fig. S7. Landsat image of southeast Greenland. table S1. Location of GPS sites, data time span, observed uplift rates, predicted elastic uplift rates, and observed GIA uplift rate. table S2. 1D viscosity profiles for Greenland. table S3. 1D viscosity profiles assigned to each region in Greenland. table S4. Uncertainty of the scaling parameter caused by the load and Earth model parameters. table S5. Ratio of inferred scaling factor for the 3D viscosity profiles versus the 1D viscosity profile (VM-GPS). table S6. SLE mass change per basin since LGM. table S7. SLE mass change per basin during

2 fig. S1. Locations of the permanent GPS stations in Greenland.

3 fig. S2. Monthly mean values of vertical GPS solutions after removing the annual, semiannual, and elastic vertical displacement. The red line represents the best fitting linear term.

4 fig. S2 (continued). Monthly mean values of vertical GPS solutions after removing the annual, semiannual, and elastic vertical displacement. The red curve represents the best fitting linear term.

5 fig. S3. Elevation change rate during (A) , (B) , (C) , (D) , (E) , and (F) fig. S4. Time series of GrIS mass loss rate.

6 fig. S5. Ice thickness change since the LGM as represented by the Green1 VM-GPS.

7 fig. S6. GIA rates. (A) GIA vertical displacement rates from new model GNET-GIA, (B) Green1 GIA rates. (C) ICE-5G GIA rates.

8 fig. S7. Landsat image of southeast Greenland. The red circles denote the locations of GPS sites MIK2 and KUAQ. The numbers in Gt/yr denote the locations of areas of potential mass loss required to explain the observed uplift at KUAQ and MIK2 as an elastic signal.

9 table S1. Location of GPS sites, data time span, observed uplift rates, predicted elastic uplift rates, and observed GIA uplift rate. Site Latitude Longitude t_start t_end Up rate Elastic Up GIA Up Basin # rate rate Deg deg Year Year mm/yr mm/yr mm/yr BLAS N W ± ± ± LEFN N W ± ± ± JGBL N W ± ± ± KMJP N W ± ± ± JWLF N W ± ± ± HRDG N W ± ± ± KMOR N W ± ± ± SCBY N W ± ± ± KAGZ N W ± ± ± NORD N W ± ± ± DMHN N W ± ± ± LBIB N W ± ± ± YMER N W ± ± ± GMMA N W ± ± ± NRSK N W ± ± ± GROK N W ± ± ± SCOR N W ± ± ± 0.1 3A VFDG N W ± ± ± 0.5 3A DGJG N W ± ± ± 0.5 3A MSVG N W ± ± ± 0.2 3A HMBG N W ± ± ± 0.5 3A WTHG N W ± ± ± 0.4 3A DANE N W ± ± ± 0.2 3A MIK N W ± ± ± 0.2 3B KUAQ N W ± ± ± 1.3 3B KULU N W ± ± ± UTMG N W ± ± ± HJOR N W ± ± ± TREO N W ± ± ± TIMM N W ± ± ± LYNS N W ± ± ± KBUG N W ± ± ± HEL N W ± ± ± KSNB N W ± ± ± PLPK N W ± ± ± SENU N W ± ± ± NNVN N W ± ± ± QAQ N W ± ± ± KELY N W ± ± ± AASI N W ± ± ± QEQE N W ± ± ± ILUL N W ± ± ± KAGA N W ± ± ± NUUK N W ± ± ± KAPI N W ± ± ± THU N W ± ± ± 0.1 7A MARG N W ± ± ± 0.5 7A DKSG N W ± ± ± 0.6 7B ASKY N W ± ± ± 0.6 7B

10 KULL N W ± ± ± 0.3 7B SRMP N W ± ± ± 1.2 7B RINK N W ± ± ± 1.1 7B UPVK N W ± ± ± 0.1 7B QAAR N W ± ± ± 0.2 7B table S2. 1D viscosity profiles for Greenland. Parameter Unit Lower limit Upper limit Nominal VM-GPS Lithosphere thickness km Upper mantle viscosity x Pas Lower mantle viscosity x Pas table S3. 1D viscosity profiles assigned to each region in Greenland. Shading indicates the calibration regions (see text). Basin Viscosity profile LT (km) AV (10 20 Pas) UMV (10 20 Pas) A B A B Total table S4. Uncertainty of the scaling parameter caused by the load and Earth model parameters. The uncertainties represent relative uncertainties with respect to the unperturbed models. Rel. unc. (%) VM-GPS (1D) VM-GPS (3D) Basin Δt end Δh LT ΔAV Total Δt end Δh LT ΔAV Total A B A B

11 table S5. Ratio of inferred scaling factor for the 3D viscosity profiles versus the 1D viscosity profile (VM-GPS). Shading indicates the calibration regions (same viscosity profile; see text). Basin Scale factor 3D/1D A B A B 1.30 table S6. SLE mass change per basin since LGM. Site GPS rate Elastic rate GPS - elastic MIK ± KUAQ 23.8 ± table S7. SLE mass change per basin during Adopted from Kjeldsen el al, 2015 (14). Basin Green 1 SLE mm ± ± A 0.21 ± B 2.91 ± ± ± ± A 1.52 ± B* 5.23 ± 1.22 Total ± 6.42