Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Three-dimensional models of Kangerlussuaq Glacier.
Figure 2: Surface elevation change rates in Greenland since the LIA maximum.
Figure 3: Mass balance and implication of GMSL.


  1. Gregory, J. M. et al. Twentieth-century global-mean sea level rise: is the whole greater than the sum of the parts? J. Clim. 26, 4476–4499 (2013)

    Article  ADS  Google Scholar 

  2. Khan, S. A. et al. Greenland ice sheet mass balance: a review. Rep. Prog. Phys. 78, 046801 (2015)

    Article  ADS  Google Scholar 

  3. Rignot, E., Box, J. E., Burgess, E. & Hanna, E. Mass balance of the Greenland ice sheet from 1958 to 2007. Geophys. Res. Lett. 35, L20502 (2008)

    Article  ADS  Google Scholar 

  4. Yanga, L. A southern Greenland ice sheet glacier discharge reconstruction: 1958–2007. Phys. Procedia 22, 292–298 (2011)

    Article  ADS  Google Scholar 

  5. Box, J. E. & Colgan, W. Greenland ice sheet mass balance reconstruction. Part III: marine ice loss and total mass balance (1840–2010). J. Clim. 26, 6990–7002 (2013)

    Article  ADS  Google Scholar 

  6. van de Wal, R. & Oerlemans, J. An energy balance model for the Greenland ice sheet. Global Planet. Change 9, 115–131 (1994)

    Article  ADS  Google Scholar 

  7. Zuo, Z. & Oerlemans, J. Contribution of glacier melt to sea-level rise since AD 1865: a regionally differentiated calculation. Clim. Dyn. 13, 835–845 (1997)

    Article  Google Scholar 

  8. Church, J. A. et al. in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al. .) 1137–1216 (Cambridge Univ. Press, 2013)

  9. Khan, S. A. et al. Glacier dynamics at Helheim and Kangerdlugssuaq glaciers, southeast Greenland, since the Little Ice Age. Cryosphere 8, 1497–1507 (2014)

    Article  ADS  Google Scholar 

  10. Box, J. E. Greenland ice sheet mass balance reconstruction. Part II: surface mass balance (1840–2010)*. J. Clim. 26, 6974–6989 (2013)

    Article  ADS  Google Scholar 

  11. van Angelen, J. H., van den Broeke, M. R. & van de Berg, W. J. Momentum budget of the atmospheric boundary layer over the Greenland ice sheet and its surrounding seas. J. Geophys. Res. 116, D10101 (2011)

    Article  ADS  Google Scholar 

  12. Csatho, B. M., Schenk, T., van der Veen, C. J. & Krabill, W. B. Intermittent thinning of Jakobshavn Isbræ, West Greenland, since the Little Ice Age. J. Glaciol. 54, 131–144 (2008)

    Article  ADS  Google Scholar 

  13. Lea, J. M. et al. Terminus-driven retreat of a major southwest Greenland tidewater glacier during the early 19th century: Insights from glacier reconstructions and numerical modelling. J. Glaciol. 60, 333–344 (2014)

    Article  ADS  Google Scholar 

  14. Bjørk, A. A. et al. An aerial view of 80 years of climate-related glacier fluctuations in southeast Greenland. Nat. Geosci. 5, 427–432 (2012)

    Article  ADS  Google Scholar 

  15. Higgins, A. K. North Greenland glacier velocities and calf ice production. Polarforschung 60, 1–23 (1990)

    Google Scholar 

  16. Colgan, W. et al. Greenland high-elevation mass balance: inference and implication of reference period (1961–90) imbalance. Ann. Glaciol. 56, 105–117 (2015)

    Article  ADS  Google Scholar 

  17. Shepherd, A. et al. A reconciled estimate of ice sheet mass balance. Science 338, 1183–1189 (2012)

    Article  CAS  ADS  Google Scholar 

  18. Khan, S. A. et al. Sustained mass loss of the northeast Greenland ice sheet triggered by regional warming. Nature Clim. Change 4, 292–299 (2014)

    Article  ADS  Google Scholar 

  19. Rignot, E., Velicogna, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. T. M. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys. Res. Lett. 38, L05503 (2011)

    Article  ADS  Google Scholar 

  20. van den Broeke, M. et al. Partitioning recent Greenland mass loss. Science 326, 984–986 (2009)

    Article  CAS  ADS  Google Scholar 

  21. Enderlin, E. M. et al. An improved mass budget for the Greenland ice sheet. Geophys. Res. Lett. 41, 866–872 (2014)

    Article  ADS  Google Scholar 

  22. Kjær, K. H. et al. Aerial photographs reveal late-20th-century dynamic ice loss in northwestern Greenland. Science 337, 569–573 (2012)

    Article  ADS  Google Scholar 

  23. Howat, I. M., Joughin, I. R. & Scambos, T. A. Rapid changes in ice discharge from Greenland outlet glaciers. Science 315, 1559–1561 (2007)

    Article  CAS  ADS  Google Scholar 

  24. Bamber, J., van den Broeke, M. R., Ettema, J., Lenaerts, J. & Rignot, E. Recent large increases in freshwater fluxes from Greenland into the North Atlantic. Geophys. Res. Lett. 39, L19501 (2012)

    Article  ADS  Google Scholar 

  25. Box, J. E., Yang, L., Bromwich, D. H. & Bai, L.-S. Greenland Ice Sheet surface air temperature variability: 1840–2007*. J. Clim. 22, 4029–4049 (2009)

    Article  ADS  Google Scholar 

  26. Hay, C. C., Morrow, E., Kopp, R. E. & Mitrovica, J. X. Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517, 481–484 (2015)

    Article  CAS  ADS  Google Scholar 

  27. Jevrejeva, S., Moore, J. C., Grinsted, A., Matthews, P. & Spada, G. Trends and acceleration in global and regional sea levels since 1807. Global Planet. Change 113, 11–22 (2014)

    Article  ADS  Google Scholar 

  28. Church, J. A. & White, N. J. Sea-level rise from the late 19th to the early 21st century. Surv. Geophys. 32, 585–602 (2011)

    Article  ADS  Google Scholar 

  29. Kobashi, T. et al. On the origin of multidecadal to centennial Greenland temperature anomalies over the past 800 yr. Clim. Past 9, 583–596 (2013)

    Article  Google Scholar 

  30. Weidick, A., Bennike, O., Citterio, M. & Nørgaard-Pedersen, N. Neoglacial and historical glacier changes around Kangersuneq fjord in southern West Greenland. Geol. Surv. Denmark Greenland Bull. 27, 1–68, (2012)

    Google Scholar 

  31. Glasser, N. F., Harrison, S., Jansson, K. N., Anderson, K. & Cowley, A. Global sea-level contribution from the Patagonian Icefields since the Little Ice Age maximum. Nature Geosci . 4, 303–307 (2011)

    Article  CAS  ADS  Google Scholar 

  32. Carrivick, J. L., Davies, B. J., Glasser, N. F., Nývlt, D. & Hambrey, M. J. Late-Holocene changes in character and behaviour of land-terminating glaciers on James Ross Island, Antarctica. J. Glaciol. 58, 1176–1190 (2012)

    Article  ADS  Google Scholar 

  33. Cuffey, K. M. & Paterson, W. S. B. The Physics of Glaciers (Elsevier, 2010)

  34. Rignot, E. & Mouginot, J. Ice flow in Greenland for the International Polar Year 2008–2009. Geophys. Res. Lett. 39, L11501 (2012)

    Article  ADS  Google Scholar 

  35. Krabill, W. B . IceBridge ATM L2 Icessn Elevation, Slope, and Roughness, [2003-2010] data set (National Snow and Ice Data Center, 2014)

  36. Zwally, H. J. et al. GLAS/ICESat L2 Antarctic and Greenland Ice Sheet Altimetry Data V031 data set (National Snow and Ice Data Center, 2011)

  37. National Snow and Ice Data Center. ICESat: Description of Data Releases data set (2011)

  38. Howat, I. M., Smith, B. E., Joughin, I. R. & Scambos, T. A. Rates of southeast Greenland ice volume loss from combined ICESat and ASTER observations. Geophys. Res. Lett. 35, L17505 (2008)

    Article  ADS  Google Scholar 

  39. Pritchard, H. D., Arthern, R. J., Vaughan, D. G. & Edwards, L. A. Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets. Nature 461, 971–975 (2009)

    Article  CAS  ADS  Google Scholar 

  40. Blair, B. & Hofton, M. IceBridge LVIS L2 Geolocated Ground Elevation and Return Energy Quartiles, [2010] data set. (National Snow and Ice Data Center, 2010)

  41. Ewert, H., Groh, A. & Dietrich, R. Volume and mass changes of the Greenland ice sheet inferred from ICESat and GRACE. J. Geodyn. 59-60, 111–123 (2012)

    Article  Google Scholar 

  42. Kjeldsen, K. K. et al. Improved ice loss estimate of the northwestern Greenland ice sheet. J. Geophys. Res. Solid Earth 118, 698–708 (2013)

    Article  ADS  Google Scholar 

  43. Smith, B. E., Fricker, H. A., Joughin, I. R. & Tulaczyk, S. An inventory of active subglacial lakes in Antarctica detected by ICESat (2003–2008). J. Glaciol. 55, 573–595 (2009)

    Article  ADS  Google Scholar 

  44. Rignot, E. & Kanagaratnam, P. Changes in the velocity structure of the Greenland Ice Sheet. Science 311, 986–990 (2006)

    Article  CAS  ADS  Google Scholar 

  45. Arendt, A. et al. Randolph Glacier Inventory—A Dataset of Global Glacier Outlines Version 3.2, (Global Land Ice Measurements from Space, 2013)

  46. Danish Geodata Agency. Ground control for 1:150,000 scale aerials, Greenland (GST, 2013)

  47. Nuth, C. & Kääb, A. Co-registration and bias corrections of satellite elevation data sets for quantifying glacier thickness change. Cryosphere 5, 271–290 (2011)

    Article  ADS  Google Scholar 

  48. Kääb, A. Remote Sensing of Mountain Glaciers and Permafrost Creep. Schriftenreihe Physische Geographie (Univ. Zürich, Department of Geography, 2005)

  49. Wang, W., Li, J. & Zwally, H. J. Dynamic inland propagation of thinning due to ice loss at the margins of the Greenland ice sheet. J. Glaciol. 58, 734–740 (2012)

    Article  ADS  Google Scholar 

  50. Krabill, W. B. et al. Greenland Ice Sheet: increased coastal thinning. Geophys. Res. Lett. 31, L24402 (2004)

    Article  ADS  Google Scholar 

  51. Sasgen, I. et al. Timing and origin of recent regional ice-mass loss in Greenland. Earth Planet. Sci. Lett. 333–334, 293–303 (2012)

    Article  ADS  Google Scholar 

  52. Hurkmans, R. T. W. L. et al. Time-evolving mass loss of the Greenland Ice Sheet from satellite altimetry. Cryosphere 8, 1725–1740 (2014)

    Article  ADS  Google Scholar 

  53. Lecavalier, B. S. et al. Revised estimates of Greenland ice sheet thinning histories based on ice-core records Greenland. Quat. Sci. Rev. 63, 73–82 (2013)

    Article  ADS  Google Scholar 

  54. Pfeffer, W. T., Meier, M. F. & Illangasekare, T. H. Retention of Greenland runoff by refreezing: implications for projected future sea level change. J. Geophys. Res. 96, 22117–22124 (1991)

    Article  ADS  Google Scholar 

  55. Box, J. E. et al. Greenland ice sheet mass balance reconstruction. Part I: Net snow accumulation (1600-2009). J. Clim. 26, 3919–3934 (2013)

    Article  ADS  Google Scholar 

  56. Andersen, M. L. et al. Basin-scale partitioning of Greenland ice sheet mass balance components (2007–2011). Earth Planet. Sci. Lett. 409, 89–95 (2015)

    Article  CAS  ADS  Google Scholar 

  57. Weidick, A. Historical fluctuations of calving glaciers in South and West Greenland. Rapp. Grønlands Geol. Unders . 161, 73–79 (1994)

    Google Scholar 

  58. Weidick, B. A. Neoglacial glaciations around Hans Tausen Iskappe, Peary Land, North Greenland. Medd. Gronl. Geosci . 39, 5–26 (2001)

    Google Scholar 

Download references


This study would not have been possible without the aid of The Danish Geodata Agency (GST), who gave us access to their historical aerial photographs. This work is a part of the X_Centuries project funded by the Danish Council for Independent Research (FNU) (grant number DFF-0602-02526B) and the Centre for GeoGenetics supported by the Danish National Research Foundation (DNRF94). K.K.K. acknowledges support from the Danish Council for Independent Research (FNU) and the Sapere Aude: DFF-Research Talent programme (grant number DFF-4090-00151). J.E.B., K.H.K. and N.K.L. acknowledge support by the GeoCenter Denmark (“Multi-millennial ice volume changes of the Greenland ice sheet”). S.A.K. acknowledges supports from the Carlsberg Foundation (grant number CF14-0145) and the Danish Council for Independent Research (FNU) (grant number DFF-4181-00126). M.v.d.B. acknowledges support from the Netherlands Polar Program of the Netherlands Organization of Scientific Research (NWO). C.N. acknowledges support by the European Research Council (EUFP7/ERC grant number 320816). We thank A. J. Long, S. A. Woodroffe, B. M. Vinther, and R. Hurkmans for contribution during the early phase of this study.

Author information

Authors and Affiliations



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.

Corresponding author

Correspondence to Kurt H. Kjær.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 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.

Extended Data Figure 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.

Extended Data Figure 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.

Extended Data Figure 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.

Extended Data Figure 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.

Extended Data Figure 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).

Extended Data Figure 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.

Extended Data Figure 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.

PowerPoint slides

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kjeldsen, K., Korsgaard, N., Bjørk, A. et al. Spatial and temporal distribution of mass loss from the Greenland Ice Sheet since AD 1900. Nature 528, 396–400 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing