Spatial and temporal distribution of mass loss from the Greenland Ice Sheet since AD 1900

Journal name:
Nature
Volume:
528,
Pages:
396–400
Date published:
DOI:
doi:10.1038/nature16183
Received
Accepted
Published online

The response of the Greenland Ice Sheet (GIS) to changes in temperature during the twentieth century remains contentious1, largely owing to difficulties in estimating the spatial and temporal distribution of ice mass changes before 1992, when Greenland-wide observations first became available2. The only previous estimates of change during the twentieth century are based on empirical modelling3, 4, 5 and energy balance modelling6, 7. Consequently, no observation-based estimates of the contribution from the GIS to the global-mean sea level budget before 1990 are included in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change8. Here we calculate spatial ice mass loss around the entire GIS from 1900 to the present using aerial imagery from the 1980s. This allows accurate high-resolution mapping of geomorphic features related to the maximum extent of the GIS during the Little Ice Age9 at the end of the nineteenth century. We estimate the total ice mass loss and its spatial distribution for three periods: 1900–1983 (75.1 ± 29.4 gigatonnes per year), 1983–2003 (73.8 ± 40.5 gigatonnes per year), and 2003–2010 (186.4 ± 18.9 gigatonnes per year). Furthermore, using two surface mass balance models10, 11 we partition the mass balance into a term for surface mass balance (that is, total precipitation minus total sublimation minus runoff) and a dynamic term. We find that many areas currently undergoing change are identical to those that experienced considerable thinning throughout the twentieth century. We also reveal that the surface mass balance term shows a considerable decrease since 2003, whereas the dynamic term is constant over the past 110 years. Overall, our observation-based findings show that during the twentieth century the GIS contributed at least 25.0 ± 9.4 millimetres of global-mean sea level rise. Our result will help to close the twentieth-century sea level budget, which remains crucial for evaluating the reliability of models used to predict global sea level rise1, 8.

At a glance

Figures

  1. Three-dimensional models of Kangerlussuaq Glacier.
    Figure 1: Three-dimensional models of Kangerlussuaq Glacier.

    a, Reconstruction of the LIAmax ice surface at 1900. b, The 2013 ice surface. c, Close-up of the northern rim of the 2013 ice surface. The base map is Landsat 8 satellite imagery from 2013. The LIA marks a cold period during which the GIS expanded, often associated with the time interval from 1450–185029. A spectacular indication that the GIS has been shrinking over the last century are the fresh trimlines, that is, the pronounced boundaries between abraded and less abraded bedrock on valley sides and fresh non-vegetated moraines close to the present glacier fronts in many areas of Greenland. Both features are considered to mark the culmination of LIA-glacial advances and to have been mainly formed during the 1700s or at the end of the 1800s30.

  2. Surface elevation change rates in Greenland since the LIA maximum.
    Figure 2: Surface elevation change rates in Greenland since the LIA maximum.

    The colour scale applies to all panels. ac, Estimates of surface elevation change rates during LIAmax(1900)–1983 (a), 1983–2003 (b) and 2003–2010 (c). The numbers listed below each panel are the integrated Greenland-wide mass balance estimates expressed as gigatonnes per year and as millimetre per year GMSL equivalents. The associated uncertainties include an uncertainty related to the scaling approach, an error related to observed changes during 2003–2010, and an uncertainty related to the scaling of the point-based observations. df, Total estimates of surface elevation change rates due to SMB fluctuations, using revised SMB estimates from ref. 10 during LIAmax(1900)–1983 (d), 1983–2003 (e), and 2003–2010 (f). gi, The dynamically driven residual in elevation change rates during LIAmax(1900)–1983 (g), 1983–2003 (h), and 2003–2010 (i). Negative values indicate mass loss. Uncertainties are reported as 1σ. Labels in a refer to Jakobshavn Isbræ (JI), Kangiata Nunata Sermia (KNS), Frederikshåb Isblink (FIB), Qassimiut Lobe (QL), Kangerlussuaq Glacier (KG), Helheim Glacier (HG), Zachariae Isstrøm (ZI), and Nioghalvfjerdsfjorden Glacier (NG), respectively. Labels in c refer to north (N), northeast (NE), central east (CE), central west (CW), northwest (NW), southwest (SW) and southeast (SE), respectively.

  3. Mass balance and implication of GMSL.
    Figure 3: Mass balance and implication of GMSL.

    a, Revised estimates of SMB from ref. 10 (orange bars), the ice dynamic residual (DR, yellow bars), mass balance based on the geodetic method (MB, dark brown bars), and mass balance based on the temporal mass balance approach (grey bars) covering the three periods LIAmax(1900)–1983, 1983–2003 and 2003–2010. Black lines represent the associated 1σ uncertainty ranges. The results suggest that variability in SMB affects long-term mass loss more strongly than does dynamic variability, which on a centennial timescale is more constant. b, The orange trace shows the 5-year running mean of the revised SMB estimates from ref. 10, the blue line represents the ice discharge modelled as a function of runoff using a 6-year trailing mean, and the dotted grey and solid grey lines show the yearly and 5-year running mean mass balance, respectively. The shaded areas reflect the associated 1σ uncertainty range (Methods). c, Cumulative mass change since LIAmax(1900) from the geodetic approach (brown line) and from the temporal mass balance reconstruction (grey line), and the shading gives the 1σ uncertainty ranges. d, The bars show the contribution of mass loss of the GIS relative to different solutions of the twentieth century GMSL rise from ref. 26 (H15, light green), ref. 27 (J14, dark green), and ref. 28 (CW11, green). Our result shows the minimum relative input of the GIS to sea level rise, which ranges between 10% and 18% during LIAmax(1900)–2010, supporting a substantial contribution from Greenland during the twentieth century.

  4. The dh calculation scheme.
    Extended Data Fig. 1: The dh calculation scheme.

    a, Three simulated ice surface profiles based on Glen’s flow law, each representing time steps t1 (blue dots), t2 (red dots), and t3 (black dots). b, The same profiles as in a supplemented with the predicted profile hpre_t3 (grey line) derived using an S value of 2.2. The figure shows agreement between the profile ht3 and hpre_t3; hence, if we know the elevation change during one period (for example, t1 and t2), then it is possible to obtain the elevation change during another period (for example, t1 and t3) by multiplying with a constant S. c, The elevation changes between t1 and t2 (dht1t2, blue line) and between t1 and t3 (dht1t3, brown line). The black dots are the elevation changes between t1 and the predicted surface profile hpre_t3 derived using the elevation change between t1 and t2 and an S value of 2.2. The predicted difference (dht1t3_pre) between t1 and t3 is derived from dht1t2 and a constant, implying that the surface profile at t1 is part of both the input and of the output. d, dht1t2 (blue line), the elevation changes between t3 and t4 (dht3t4, dark green line), and the predicted dht3t4 (dht3t4_pre, black dots), which is derived using dht1t2 and an S value of 1.2; thus none of the ice surface profiles are part of both the input and output. If both dht1t2 and dht3t4 are known then S can be derived as the ratio between the observations. e, The uncertainty between the profile ht3 and hpre_t3 using a constant S. Generally the differences are small, though they increase near the margin. f, The elevation change between two time steps as a function of elevation. Changes are largest at lower elevation and become close to 0 at h > 2,500 m.

  5. Validation of the scaling approach.
    Extended Data Fig. 2: Validation of the scaling approach.

    a, Elevation profiles of Kangerlussuaq Glacier in southeast Greenland from the 1981 DEM (grey line), 2003 ATM data (red line), and the predicted surface profile (blue line) in 2003, derived using the scaling approach based on local scale values and the 2003–2010 elevation changes (dhsolid). (For a more complete description of the approach using observations see Methods section ‘LIAmax to 1978–87 mass balance’). b, The elevation change rate between the observed 2003 surface profile (red) and the predicted 2003 surface profile (blue) relative to the 1981 DEM. The blue vertical lines denote uncertainty estimates that include an uncertainty related to the scaling approach, an error related to observed changes during 2003–2010, and an uncertainty related to the scaling of point-based observations. The red vertical lines denote an uncertainty associated with the observed elevation changes during 1981–2003 and includes combined errors of the measured height derived from stereo photogrammetric DEM and 2003 ATM data. c, A 1981 orthophoto of Kangerlussuaq Glacier with 2003 ATM data (red dots) and the May 2003 glacier front (black line). df and gi illustrate the same as ac for Helheim Glacier and Jakobshavn Isbræ, respectively. However, for Jakobshavn Isbræ the DEM and orthophoto is from 1985. Note the different scales for each of the glaciers. Comparing the elevation change rates derived from the scaling approach and those directly from the observations, we find good agreement as the error bars overlap. Thus, we regard the illustrated comparison as a validation of our method of deriving ice-sheet-wide mass balance estimates.

  6. GIS calculation basin subdivision.
    Extended Data Fig. 3: GIS calculation basin subdivision.

    Calculation basins modified from ref. 44 to include slower-moving areas of the ice sheet. Note that three areas on the southeast coast have been omitted due to an insufficient number of LIA to 1978–87 data points caused by extensive snow cover on the vertical images. The total ice mask covers 1,647,907 km2. The additional areas included in the ice mask used by ref. 18 are shown in dark grey and in total the ice mask covers 1,739,564 km2.

  7. Mapping elevation changes during LIAmax to 1978–87.
    Extended Data Fig. 4: Mapping elevation changes during LIAmax to 1978–87.

    a, Type 1 points are placed at the trimline or lateral moraine marking the LIAmax position and at the 1978–87 ice surface perpendicular to the flow direction, and as we assume that the cross-section profile of the glacier is the same during the LIAmax and 1978–87 then the vertical difference dh is the thinning at this location. This approach is the same as used by ref. 9. b, For Type 2 points we assume that the longitudinal shape of the glacier is the same during the LIAmax as in 1978–87. Points are placed at the LIAmax margin and at the 1978–87 margin, and assuming a longitudinal profile that does not change over time, the distance dL is used to find the vertical difference between the 1978–87 point and a point on the glacier at a distance of dL following the same flowline. Points for glaciers receding on steep slopes have been discarded.

  8. Distribution and values of dhLIA points.
    Extended Data Fig. 5: Distribution and values of dhLIA points.

    a, Distribution of the two point types used to determine thinning between LIAmax and 1978–87. b, From the type 1 and type 2 points, net elevation change dhLIA is measured based on 3,003 point measurements from the LIAmax to 1978–87. Of the 3,003 pairs—that is, 6,006 point measurements—2,476 are measured as type 1 and 527 are type 2. The majority of the type 2 points are found along the land-terminating and slower-moving parts of the ice sheet, whereas type 1 points are found in valleys through which the ice flows and on nunataks. dhLIA values range between zero and −448 m (a negative value implies thinning). The largest dhLIA values are found along the major marine-outlet glaciers along the northwest and southeast coast and along the rim of the Qassimiut lobe (QL), while in contrast the lower dhLIA values are found along the slower-moving margins of the typically land-terminating ice sheet. In some areas around the ice sheet no trimlines are visible and/or the ice margin is in contact with the LIA moraines. Analysis of glacier front positions for outlet glaciers in the north, central west, southwest, and south using historical aerial photographs from the 1930s and onwards15, 57, 58 suggest that a few outlet glaciers, primarily land-terminating, have been stable or advanced since the LIA. In the northwest, central west, and southwest snow cover on the 1978–87 vertical aerial images is generally limited, which eases the distinction between freshly eroded bedrock, newly deposited glacial sediment, and non-eroded vegetated terrain surfaces. This supports the notion that if no trimline is visible on the photographs, then the ice margin is at an advanced and stable stage. Hence, the dhLIA and dLLIA values for points are zero. An example of a glacier that has advanced during the twentieth century is the Saqqap Sermia (SS)57 in the Nuup Kangerlua (Godthåbsfjord) complex in southwest Greenland. Here no trimlines are visible along the valley and the boundary between ice and vegetation cover is only interrupted by small meltwater channels, and at the glacier front no end moraines are visible on the meltwater plain. In the present setup we are not able to assign any post-LIA mass gain; however, as only a limited number of outlet glaciers have advanced and exceeded the LIA front position during the twentieth century we regard this mass gain as negligible relative to the ice-sheet-wide mass loss.

  9. Horizontal and vertical displacements in aero-photogrammetric DEM.
    Extended Data Fig. 6: Horizontal and vertical displacements in aero-photogrammetric DEM.

    ac, Histograms of the horizontal (a) and vertical (b) co-registration displacements for each 50 km × 50 km grid cell show that the aero-photogrammetric DEM compilation is generally accurate to within 10 m horizontally and 6 m vertically with a precision greater than 4 m (1σ confidence level) (c). df, The horizontal (d) and vertical (e) components of the co-registration vectors between 50 km × 50 km sections of the aero-photogrammetric DEM compilation and ICESat laser altimetry are plotted with the root-mean-square error of stable terrain differences after adjusting for the three-dimensional mis-registration (f).

  10. Estimates of ice-sheet-wide iceberg discharge.
    Extended Data Fig. 7: Estimates of ice-sheet-wide iceberg discharge.

    Ice discharge estimates and associated errors (vertical bars) from ref. 24 (black), ref. 3 (blue), ref. 21 (red), and ref. 56 (grey). We note that the used discharge estimates of ref. 21 are 15 Gt yr−1 greater than those of ref. 56, 30 Gt yr−1 less than those of ref. 3, and 110 Gt yr−1 less than those of ref. 24. Such discrepancies are attributed to differences in data availability and assumptions used for filling gaps or the method used to correct for SMB between the inland flux gates and the grounding lines21.

  11. Temporal variability of the mass balance expressed as cumulative eustatic sea level rise.
    Extended Data Fig. 8: Temporal variability of the mass balance expressed as cumulative eustatic sea level rise.

    Reconstructed temporal mass balance during the period 1840–2012 derived using revised SMB estimates from ref. 10 and modelled ice discharge, calculated as a function of six-year average runoff. The uncertainty is assessed from a Monte Carlo simulation using 4,000 samples for each year.

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Author information

  1. These authors contributed equally to this work.

    • Kristian K. Kjeldsen &
    • Niels J. Korsgaard

Affiliations

  1. Centre for GeoGenetics, Natural History Museum, University of Copenhagen, Copenhagen 1350, Denmark

    • Kristian K. Kjeldsen,
    • Niels J. Korsgaard,
    • Anders A. Bjørk,
    • Svend Funder,
    • Nicolaj K. Larsen,
    • Marie-Louise Siggaard-Andersen,
    • Anders Schomacker,
    • Eske Willerslev &
    • Kurt H. Kjær
  2. Department of Earth Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

    • Kristian K. Kjeldsen
  3. DTU Space—National Space Institute, Technical University of Denmark, Department of Geodesy, Kongens Lyngby 2800, Denmark

    • Shfaqat A. Khan
  4. Geological Survey of Denmark and Greenland, Department of Marine Geology and Glaciology, Copenhagen 1350, Denmark

    • Jason E. Box,
    • William Colgan &
    • Camilla S. Andresen
  5. Department of Geoscience, Aarhus University, Aarhus 8000, Denmark

    • Nicolaj K. Larsen
  6. Bristol Glaciology Centre, University of Bristol, Bristol BS8 1SS, UK

    • Jonathan L. Bamber
  7. Department of Earth and Space Science and Engineering, York University, Toronto, Ontario M3J 1P3, Canada

    • William Colgan
  8. Institute for Marine and Atmospheric Research, Utrecht University, Utrecht 80005, The Netherlands

    • Michiel van den Broeke
  9. Department of Geosciences, University of Oslo, Oslo 0316, Norway

    • Christopher Nuth

Contributions

K.K.K. and K.H.K. designed and conducted the study. N.J.K. did photogrammetric modelling and aero-photogrammetric DEM processing, and quality control and validation with C.N. K.K.K. undertook the Geographical Information System analysis. A.A.B. conducted the manual photogrammetry measurements. S.A.K. carried out analysis of surface elevation data, developed the scaling method, and made the mass balance calculations. J.E.B., J.L.B., and M.v.d.B. provided SMB model and context. W.C., J.E.B., and K.K.K. performed temporal discharge and mass balance modelling. S.F. and N.K.L. provided the historical context of ice sheet extent. All authors contributed to discussion and writing of the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

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Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: The dh calculation scheme. (197 KB)

    a, Three simulated ice surface profiles based on Glen’s flow law, each representing time steps t1 (blue dots), t2 (red dots), and t3 (black dots). b, The same profiles as in a supplemented with the predicted profile hpre_t3 (grey line) derived using an S value of 2.2. The figure shows agreement between the profile ht3 and hpre_t3; hence, if we know the elevation change during one period (for example, t1 and t2), then it is possible to obtain the elevation change during another period (for example, t1 and t3) by multiplying with a constant S. c, The elevation changes between t1 and t2 (dht1t2, blue line) and between t1 and t3 (dht1t3, brown line). The black dots are the elevation changes between t1 and the predicted surface profile hpre_t3 derived using the elevation change between t1 and t2 and an S value of 2.2. The predicted difference (dht1t3_pre) between t1 and t3 is derived from dht1t2 and a constant, implying that the surface profile at t1 is part of both the input and of the output. d, dht1t2 (blue line), the elevation changes between t3 and t4 (dht3t4, dark green line), and the predicted dht3t4 (dht3t4_pre, black dots), which is derived using dht1t2 and an S value of 1.2; thus none of the ice surface profiles are part of both the input and output. If both dht1t2 and dht3t4 are known then S can be derived as the ratio between the observations. e, The uncertainty between the profile ht3 and hpre_t3 using a constant S. Generally the differences are small, though they increase near the margin. f, The elevation change between two time steps as a function of elevation. Changes are largest at lower elevation and become close to 0 at h > 2,500 m.

  2. Extended Data Figure 2: Validation of the scaling approach. (391 KB)

    a, Elevation profiles of Kangerlussuaq Glacier in southeast Greenland from the 1981 DEM (grey line), 2003 ATM data (red line), and the predicted surface profile (blue line) in 2003, derived using the scaling approach based on local scale values and the 2003–2010 elevation changes (dhsolid). (For a more complete description of the approach using observations see Methods section ‘LIAmax to 1978–87 mass balance’). b, The elevation change rate between the observed 2003 surface profile (red) and the predicted 2003 surface profile (blue) relative to the 1981 DEM. The blue vertical lines denote uncertainty estimates that include an uncertainty related to the scaling approach, an error related to observed changes during 2003–2010, and an uncertainty related to the scaling of point-based observations. The red vertical lines denote an uncertainty associated with the observed elevation changes during 1981–2003 and includes combined errors of the measured height derived from stereo photogrammetric DEM and 2003 ATM data. c, A 1981 orthophoto of Kangerlussuaq Glacier with 2003 ATM data (red dots) and the May 2003 glacier front (black line). df and gi illustrate the same as ac for Helheim Glacier and Jakobshavn Isbræ, respectively. However, for Jakobshavn Isbræ the DEM and orthophoto is from 1985. Note the different scales for each of the glaciers. Comparing the elevation change rates derived from the scaling approach and those directly from the observations, we find good agreement as the error bars overlap. Thus, we regard the illustrated comparison as a validation of our method of deriving ice-sheet-wide mass balance estimates.

  3. Extended Data Figure 3: GIS calculation basin subdivision. (1,114 KB)

    Calculation basins modified from ref. 44 to include slower-moving areas of the ice sheet. Note that three areas on the southeast coast have been omitted due to an insufficient number of LIA to 1978–87 data points caused by extensive snow cover on the vertical images. The total ice mask covers 1,647,907 km2. The additional areas included in the ice mask used by ref. 18 are shown in dark grey and in total the ice mask covers 1,739,564 km2.

  4. Extended Data Figure 4: Mapping elevation changes during LIAmax to 1978–87. (157 KB)

    a, Type 1 points are placed at the trimline or lateral moraine marking the LIAmax position and at the 1978–87 ice surface perpendicular to the flow direction, and as we assume that the cross-section profile of the glacier is the same during the LIAmax and 1978–87 then the vertical difference dh is the thinning at this location. This approach is the same as used by ref. 9. b, For Type 2 points we assume that the longitudinal shape of the glacier is the same during the LIAmax as in 1978–87. Points are placed at the LIAmax margin and at the 1978–87 margin, and assuming a longitudinal profile that does not change over time, the distance dL is used to find the vertical difference between the 1978–87 point and a point on the glacier at a distance of dL following the same flowline. Points for glaciers receding on steep slopes have been discarded.

  5. Extended Data Figure 5: Distribution and values of dhLIA points. (654 KB)

    a, Distribution of the two point types used to determine thinning between LIAmax and 1978–87. b, From the type 1 and type 2 points, net elevation change dhLIA is measured based on 3,003 point measurements from the LIAmax to 1978–87. Of the 3,003 pairs—that is, 6,006 point measurements—2,476 are measured as type 1 and 527 are type 2. The majority of the type 2 points are found along the land-terminating and slower-moving parts of the ice sheet, whereas type 1 points are found in valleys through which the ice flows and on nunataks. dhLIA values range between zero and −448 m (a negative value implies thinning). The largest dhLIA values are found along the major marine-outlet glaciers along the northwest and southeast coast and along the rim of the Qassimiut lobe (QL), while in contrast the lower dhLIA values are found along the slower-moving margins of the typically land-terminating ice sheet. In some areas around the ice sheet no trimlines are visible and/or the ice margin is in contact with the LIA moraines. Analysis of glacier front positions for outlet glaciers in the north, central west, southwest, and south using historical aerial photographs from the 1930s and onwards15, 57, 58 suggest that a few outlet glaciers, primarily land-terminating, have been stable or advanced since the LIA. In the northwest, central west, and southwest snow cover on the 1978–87 vertical aerial images is generally limited, which eases the distinction between freshly eroded bedrock, newly deposited glacial sediment, and non-eroded vegetated terrain surfaces. This supports the notion that if no trimline is visible on the photographs, then the ice margin is at an advanced and stable stage. Hence, the dhLIA and dLLIA values for points are zero. An example of a glacier that has advanced during the twentieth century is the Saqqap Sermia (SS)57 in the Nuup Kangerlua (Godthåbsfjord) complex in southwest Greenland. Here no trimlines are visible along the valley and the boundary between ice and vegetation cover is only interrupted by small meltwater channels, and at the glacier front no end moraines are visible on the meltwater plain. In the present setup we are not able to assign any post-LIA mass gain; however, as only a limited number of outlet glaciers have advanced and exceeded the LIA front position during the twentieth century we regard this mass gain as negligible relative to the ice-sheet-wide mass loss.

  6. Extended Data Figure 6: Horizontal and vertical displacements in aero-photogrammetric DEM. (365 KB)

    ac, Histograms of the horizontal (a) and vertical (b) co-registration displacements for each 50 km × 50 km grid cell show that the aero-photogrammetric DEM compilation is generally accurate to within 10 m horizontally and 6 m vertically with a precision greater than 4 m (1σ confidence level) (c). df, The horizontal (d) and vertical (e) components of the co-registration vectors between 50 km × 50 km sections of the aero-photogrammetric DEM compilation and ICESat laser altimetry are plotted with the root-mean-square error of stable terrain differences after adjusting for the three-dimensional mis-registration (f).

  7. Extended Data Figure 7: Estimates of ice-sheet-wide iceberg discharge. (129 KB)

    Ice discharge estimates and associated errors (vertical bars) from ref. 24 (black), ref. 3 (blue), ref. 21 (red), and ref. 56 (grey). We note that the used discharge estimates of ref. 21 are 15 Gt yr−1 greater than those of ref. 56, 30 Gt yr−1 less than those of ref. 3, and 110 Gt yr−1 less than those of ref. 24. Such discrepancies are attributed to differences in data availability and assumptions used for filling gaps or the method used to correct for SMB between the inland flux gates and the grounding lines21.

  8. Extended Data Figure 8: Temporal variability of the mass balance expressed as cumulative eustatic sea level rise. (282 KB)

    Reconstructed temporal mass balance during the period 1840–2012 derived using revised SMB estimates from ref. 10 and modelled ice discharge, calculated as a function of six-year average runoff. The uncertainty is assessed from a Monte Carlo simulation using 4,000 samples for each year.

Additional data