Nature 414, 60 - 62 (01 November 2001); doi:10.1038/35102044

W. S. B. PATERSON*† AND NIELS REEH*‡

† Paterson Geophysics Inc., Box 303, Heriot Bay, British Columbia VOP 1HO, Canada
‡ Ørsted-DTU, Electromagnetic Systems, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
* The authors contributed equally to this work

Correspondence and requests for materials should be addressed to N.R. (e-mail: nr@oersted.dtu.dk).

Thermal expansion of the oceans, as well as melting of glaciers, ice sheets and ice caps have been the main contributors to global sea level rise over the past century. The greatest uncertainty in predicting future sea level changes lies with our estimates of the mass balance of the ice sheets in Greenland and Antarctica¹. Satellite measurements have been used to determine changes in these ice sheets on short timescales, demonstrating that surface-elevation changes on timescales of decades or less result mainly from variations in snow accumulation². Here we present direct measurements of the changes in surface elevation between 1954 and 1995 on a traverse across the north Greenland ice sheet. Measurements over a time interval of this length should reflect changes in ice flow—the important quantity for predicting changes in sea level—relatively unperturbed by short-term fluctuations in snow accumulation. We find only small changes in the eastern part of the transect, except for some thickening of the north ice stream. On the west side, however, the thinning rates of the ice sheet are significantly higher and thinning extends to higher elevations than had been anticipated from previous studies³.

Because the Greenland ice sheet is still responding to climatic changes that occurred thousands of years ago⁴, a complicated pattern of thickening and thinning is expected. The earliest data of sufficient precision appear to be those of the British North Greenland Expedition (BNGE)⁵; we compare these with the latest digital elevation model⁶. The BNGE used trigonometric levelling to measure elevation at about 300 stations on a 1,200-km traverse in 1953–54 (Fig. 1)⁷. The survey started at Krebs Bjerg in Dronning Louise Land and ended at sea level on the west coast. The route crossed the north ice stream⁸. The work was spread over two summers; a tripod was left standing at the midpoint, station B73, throughout the winter.

Figure 1 Traverse route.   Full legend   High resolution image and legend (82k)

The closure error, found by calculating the elevation of B73 from each coast, was 13.8 m, elevations calculated from the east being the higher. It was subsequently reduced to 11.8 m when the elevation of Krebs Bjerg was redetermined. It was distributed as follows. East of B73, each height difference between adjacent stations was reduced by 5.9 m times the distance between them, expressed as a fraction of the total distance between Krebs Bjerg and B73. Height differences west of B73 were increased in a similar way. To set error limits, for stations east of B73 the elevation calculated from the east coast was taken as the upper limit and the lower limit was taken as that value minus twice the adjustment in elevation. Similarly, for stations west of B73, the elevation calculated from the west coast set a lower limit and twice the adjustment was added to obtain the upper limit. A second scheme, with the adjustment proportional to the elevation difference, rather than the distance, between adjacent stations was also used. Elevations calculated by the two schemes differed by up to 3 m. Their mean was taken as the true elevation; the maximum error is the root mean square of the adjustments calculated for the separate schemes. The latitude and longitude of each station were found from the measured distances and azimuths and checked by Sun sights at some stations. The precision is 0.1 minute of latitude and 0.5 minute of longitude, or about 200 m in each direction.

The digital elevation model (DEM) of the ice sheet, which has a grid spacing of 1 km, is based, in north Greenland, on radar altimetry from the ERS-1 satellite collected in 1994–95. The data were corrected for a slope-dependent bias that arises because the radar oversamples the crests of surface undulations relative to the troughs. The corrected radar data were compared with measurements of surface elevation made by laser altimeters in an aircraft. Because these have a precision of about 10 cm, the standard deviation of the difference between DEM and laser elevations, which is a function of surface slope, measures the precision of the DEM⁶. Although the laser elevations are more precise than the DEM, the data points are more scattered and some are several kilometres from the nearest BNGE station. We have therefore used the DEM.

DEM elevations are relative to the World Geodetic Systems 1984 (WGS 84) ellipsoid whereas BNGE elevations are relative to sea level. The conversion, made using the latest geoid model (Ohio State University 1991A; OSU 91A) improved with local gravity, introduces a maximum error of 1 m.

Figure 2 shows the measured changes in surface elevation. They can be interpreted as ice-thickness changes because bedrock beneath the ice is unlikely to be rising more than a few millimetres per year. To test the significance of the changes, we grouped the stations into longitude bands and calculated average values for each. We excluded the marginal regions, where the radar was probably measuring the elevations of nunataks off the traverse route. (A nunatak is an isolated peak of rock projecting above the surface of land ice.) The maximum error has four components: uncertainties in the BNGE elevations and in the DEM, both calculated as described above, the geoid–ellipsoid conversion, and the scatter of elevation changes within each band. The standard deviation of the DEM elevations and the standard error of the mean elevation change in each band were multiplied by two to make them comparable with the other errors, which are maximum errors. The components were combined by taking the square root of the sum of their squares.

Figure 2 Measured changes in surface elevation between 1954 and 1995.   Full legend   High resolution image and legend (36k)

We conclude that, between 1954 and 1995: (1) The ice stream (band A in Fig. 2) has thickened at a rate of 9.7 8.4 cm yr^-1; (2) ice thickness has not changed significantly in bands B–D; (3) the average thinning rate is 16.5 11.0 cm yr^-1 in band E and 31.0 10.7 cm yr^-1 in band F. These bands span elevations from 2,500 to 1,500 m. All limits quoted are maximum, not standard, errors.

We believe that the 41-year interval is long enough to ensure that we are measuring the dynamic response of the ice sheet rather than fluctuations in snow accumulation. Furthermore, annual accumulation data from a station on Humboldt Glacier⁹ and from near Camp Century (Fig. 1; E. Mosley-Thompson, personal communication) show no trend over this period.

The only other direct measurements of elevation changes in this area come from a study covering the whole ice sheet for the period 1994–99 (ref. 10). It shows slight thickening in bands E and F where we measured significant thinning. The thickening probably resulted from variations in snow accumulation.

An indirect method avoids the difficulties in interpreting short-term thickness changes³: the total snow accumulation over a drainage basin is compared with the ice flux out of it. This certainly measures the dynamic response of the ice sheet, but only a rough average over a large area¹¹. The Greenland study was restricted to elevations above 2,000 m by measuring fluxes at that contour. In north Greenland east of longitude 40° W an average thickening of 2 cm yr^-1 was obtained. This is consistent with our results except in the ice stream, a feature this method cannot resolve. Thinning was observed to the west but, even if the upper limits are used, at rates substantially less than those we measured.

Received 6 August 2001;accepted 18 September 2001

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Acknowledgements. We thank J. Bamber, S. Ekholm, W. Krabill and E. Mosley-Thompson for providing information and unpublished data.