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Johnsen, S.J.3
Rossi, A.4
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5
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3643077929
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note
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The deep borehole is located in a building, and the liquid surface in the borehole is found at a depth of 40 m. The temperatures measured in the top 40 m are very disturbed, so we used measurements from an air-filled shallow borehole (100 m) near the borehole.
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9
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0029530094
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Between 50 and 20 ka, the ice thickness was 50 m less than at present, even though the ice sheet covered a larger area. The maximum ice thickness of 3230 m is found at 10 ka, after which the ice thickness gradually has decreased to the present 3028.6 m. The depression and uplift of the bedrock influences the elevation of the surface [S. J. Johnsen, D. Dahl-Jensen, W. Dansgaard, N. S. Gundestrup, Tellus B 47, 624 (1995)].
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Tellus B
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Johnsen, S.J.1
Dahl-Jensen, D.2
Dansgaard, W.3
Gundestrup, N.S.4
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11
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3643055907
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note
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o is the present surface temperatures at the sites: -31.7°C at GRIP and -20.1°C at Dye 3, respectively (9).
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16
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3643120570
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note
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i}, evaluated in a near-optimal model, yields a set of eigenvectors in the model space whose orientations reveal efficient directions of perturbation for the random walk. The SVD method is included as a possible method of perturbing models especially in the start of the process as it speeds the Monte Carlo scheme significantly.
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3643134055
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note
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6 models tested during the random walk 30% have been accepted by the Monte Carlo scheme (16). Every 500 is chosen of those where the misfit function S (16) is less than the variance of the observations. The waiting time of 500 has been chosen to exceed the maximum correlation length of the output model parameters. This is a necessary condition for the 2000 models to be uncorrelated. To further ensure that the output models were uncorrelated, the random walk was frequently restarted at several random selected points in the model space.
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note
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The probabilistic formulation of the inverse problem leads to definition of a probability distribution in the model space, describing the likelihood of possible temperature histories and geothermal heat flow densities. The Monte Carlo scheme is constructed to sample according to this probability distribution. The histograms in Fig. 2 describe the probability distribution of the geothermal heat flow density and temperatures at times before present. The maxima in the histograms thus describe the most likely values. The method does not constrain the distributions to have a single maximum, indeed there could be histograms with several maxima, reflecting that more than one value of the temperature at this time would give a good fit to the observed temperature in the borehole. The histograms however, are all seen to have a well-defined zone with most likely past temperatures. A soft curve is fitted to the histograms and the maximum value is taken as the most likely value. The standard deviations shown in Fig. 3 are derived as deviations from the maximum value.
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19
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C. Clauser et al., ibid. 102, 18417 (1997); L. Guillou-Frottier, J.-C. Marescal, J. Musset, ibid. 103, 7385 (1998); H. N. Pollack, S. J. Hurter, J. R. Johnson, Rev. Geophys. 31, 267 (1993); W. G. Powell, D. S. Chapman, N. Balling, A. E. Beck, in Handbook of Terrestrial Heat-Flow Density Determination (Kluwer Academic, New York, 1988), pp. 167-222.
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C. Clauser et al., ibid. 102, 18417 (1997); L. Guillou-Frottier, J.-C. Marescal, J. Musset, ibid. 103, 7385 (1998); H. N. Pollack, S. J. Hurter, J. R. Johnson, Rev. Geophys. 31, 267 (1993); W. G. Powell, D. S. Chapman, N. Balling, A. E. Beck, in Handbook of Terrestrial Heat-Flow Density Determination (Kluwer Academic, New York, 1988), pp. 167-222.
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Powell, W.G.1
Chapman, D.S.2
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Beck, A.E.4
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3643145597
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note
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In order to produce a past temperature record from the calculated past surface temperatures, the temperatures have been corrected to the present elevation of the GRIP site (and Dye 3 site respectively) using the surface elevation changes described in (9) and a lapse rate of 0.006 K/m.
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25
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K. M. Cuffey et al., Science 270, 455 (1995).
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Copenhagen, 19 May 1993, K. Mosegaard, Ed. The Niels Bohr Institute for Astronomy, Physics and Geophysics, University of Copenhagen, Copenhagen
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C. U. Hammer et al., Report on the stratigraphic dating of the CRIP Ice Core. Special Report of the Geophysical Department (Niels Bohrs Institute for Astronomy, Physics and Geophysics, University of Copenhagen, Copenhagen, in press).
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Hammer, C.U.1
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3643061204
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The amplitude of the warming at 1930 A.D. must be considered to be more uncertain. The information leading to this result are the measured temperatures in an open shallow borehole, where air movements could influence the measurements.
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3643146643
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note
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To comply with this resolution the time steps have been chosen with increasing length back in time. The increasing length of the time steps can be considered as an efficient way of calculating the mean temperatures in the intervals so full available resolution is kept but the calculations are rationalized.
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2 is chosen as that found for our inversion, the mean glacial temperature is 19 K colder than the present, which is well in agreement with the results found for the GRIP reconstruction. Comparison of the Dye 3 temperature history presented in (7) and that presented here shows a general good agreement for the last 7 ky. The history presented in (7) is more intuitive and less detailed, and the history has not been corrected for elevation changes. The ice thickness was assumed constant in this reconstruction.
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Institute of Arctic and Alpine Research, University of Colorado, Boulder
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This is a contribution to the Greenland Ice Core Project (GRIP), a European Science Foundation program with eight nations and the European Economic Commission collaborating to drill through the central part of the Greenland Ice Sheet. G.D.C. thanks the USGS Climate History Program and NSF for support.
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