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<front>
<journal-meta>
<journal-id journal-id-type="publisher">GMD</journal-id>
<journal-title-group>
<journal-title>Geoscientific Model Development</journal-title>
<abbrev-journal-title abbrev-type="publisher">GMD</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Geosci. Model Dev.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1991-9603</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/gmd-7-1395-2014</article-id>
<title-group>
<article-title>Semi-Lagrangian transport of oxygen isotopes in polythermal ice sheets: implementation and first results</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Goelles</surname>
<given-names>T.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Grosfeld</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Lohmann</surname>
<given-names>G.</given-names>
<ext-link>https://orcid.org/0000-0003-2089-733X</ext-link>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>The University Centre in Svalbard (UNIS), Longyearbyen, Norway</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Norwegian University of Life Sciences (NMBU), Aas, Norway</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Alfred Wegener Institute Helmholtz Center for Polar and Marine Research (AWI), Bremerhaven, Germany</addr-line>
</aff>
<pub-date pub-type="epub">
<day>11</day>
<month>07</month>
<year>2014</year>
</pub-date>
<volume>7</volume>
<issue>4</issue>
<fpage>1395</fpage>
<lpage>1408</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 T. Goelles et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
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<self-uri xlink:href="https://gmd.copernicus.org/articles/7/1395/2014/gmd-7-1395-2014.pdf">The full text article is available as a PDF file from https://gmd.copernicus.org/articles/7/1395/2014/gmd-7-1395-2014.pdf</self-uri>
<abstract>
<p>Modelling the evolution of the Earth system on long timescales
  requires the knowledge and understanding of driving mechanisms, such
  as the hydrological cycle. This is dominant in all components of the
  Earth&apos;s system, such as atmosphere, ocean, land surfaces/vegetation
  and the cryosphere. Observations and measurements of stable water
  isotopes in climate archives can help to decipher and reconstruct
  climate change and its regional variations. For the cryosphere, the
  δ&lt;sup&gt;18&lt;/sup&gt;O cycle in the current generation of
  Earth system models is missing and an efficient and accurate tracer
  transport scheme is required.  We describe ISOPOLIS 1.0, a modular
  semi-Lagrangian transport scheme of second-order accuracy, which is
  coupled to the polythermal and thermomechanical ice sheet model
  SICOPOLIS (version 2.9).  Model skill is demonstrated by experiments
  with a simplified ice sheet geometry and by comparisons of simulated
  ice cores with data from Greenland (GRIP) and Antarctica (Vostok).
  The presented method is a valuable tool to investigate the transport
  of any kind of passive tracer inside the cold ice part of a polythermal ice sheet and is
  an important step to model the whole δ&lt;sup&gt;18&lt;/sup&gt;O cycle.</p>
</abstract>
<counts><page-count count="14"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow, Part I, J. Comput. Phys., 135, 103–114, 1997.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Behrens, J.: Adaptive semi-Lagrangian finite element method for the solution of the shallow water equations: implementation and parallelization, Berichte zur Polarforschung, 217, 167, &lt;a href=&quot;http://dx.doi.org/10013/epic.10218&quot;&gt;https://doi.org/10013/epic.10218&lt;/a&gt;, 1996.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Clarke, G. and Marshall, S. J.: Isotopic balance of the Greenland Ice Sheet: modelled concentrations of water isotopes from 30 000 BP to present, Quaternary Sci. Rev., 21, 419–430, 2002.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Clarke, G., Lhomme, N., and Marshall, S. J.: Tracer transport in the Greenland ice sheet: three-dimensional isotopic stratigraphy, Quaternary Sci. Rev., 24, 155–171, 2005.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Cuffey, K. M.: Methodology for use of isotopic climate forcings in ice sheet models, Geophys. Res. Lett., 27, 3065–3068, 2000.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Cuffey, K. M. and Clow, G. D.: Temperature, accumulation, and ice sheet elevation in central Greenland through the last deglacial transition, J. Geophys. Res.-Oceans, 102, 26383–26396, 1997.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Dansgaard, W.: Stable isotopes in precipitation, Tellus, 16, 436–468, &lt;a href=&quot;http://dx.doi.org/10.1111/j.2153-3490.1964.tb00181.x&quot;&gt;https://doi.org/10.1111/j.2153-3490.1964.tb00181.x&lt;/a&gt;, 1964.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Dansgaard, W., Johnsen, S. J., Clausen, H. B., Dahl, D., Gundestrup, N. S., Hammer, C. U., Hvidberg, C. S., Steffensen, J. P., Sveinbjörnsdottir, A. E., Jouzel, J. and Bond, G.: Evidence for general instability of past climate from a 250-kyr ice-core record, Nature, 364, 218–220, &lt;a href=&quot;http://dx.doi.org/10.1038/364218a0&quot;&gt;https://doi.org/10.1038/364218a0&lt;/a&gt;, 1993.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">de Almeida, R. C., Costa, G. A. S., Da Fonseca, L. C. M., and Alves, J. L. D.: Particle trajectory calculations with a two-step three-time level semi-Lagrangian scheme well suited for curved flows, Int. J. Numer. Meth. Fl., 61, 995–1028, &lt;a href=&quot;http://dx.doi.org/10.1002/fld.1993&quot;&gt;https://doi.org/10.1002/fld.1993&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Forsstrom, P.-L., Sallasmaa, O., Greve, R., and Zwinger, T.: Simulation of fast-flow features of the Fennoscandian ice sheet during the Last Glacial Maximum, Ann. Glaciol., 37, 383–389, 2003.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Gat, J. R.: Oxygen and hydrogen isotopes in the hydrologic cycle, Ann. Rev. Earth Planet. Sci., 24, 225–262, &lt;a href=&quot;http://dx.doi.org/10.1146/annurev.earth.24.1.225&quot;&gt;https://doi.org/10.1146/annurev.earth.24.1.225&lt;/a&gt;, 1996.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Gornitz, V. (Ed.): Encyclopedia of Paleoclimatology and Ancient Environments (Encyclopedia of Earth Sciences Series), 1st Edn., Springer, New York, 2009.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Greve, R.: A continuum-mechanical formulation for shallow polythermal ice sheets, Philos. T. R. Soc. Lond., 355, 921–974, 1997a.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Greve, R.: Application of a polythermal three-dimensional ice sheet model to the Greenland Ice Sheet: response to steady-state and transient climate scenarios, J. Climate, 10, 901–918, 1997b.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Greve, R.: Relation of measured basal temperatures and the spatial distribution of the geothermal heat flux for the Greenland ice sheet, Ann. Glaciol., 42, 424–432, 2005.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Hoffmann, G., Werner, M., and Heimann, M.: Water isotope module of the ECHAM atmospheric general circulation model: a study on timescales from days to several years, J. Geophys. Res., 103, 16871–16896, 1998.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Hortal, M.: The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ECMWF forecast modeld, Q. J. Roy. Meteor. Soc., 128, 1671–1687, 2002.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Jean-Baptiste, P., Jouzel, J., Stievenard, M., and Ciais, P.: Experimental determination of the diffusion rate of deuterated water vapor in ice and application to the stable isotopes smoothing of ice cores, Earth Planet. Sc. Lett., 158, 81–90, 1998.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Johnsen, S. J., Dahl-Jensen, D., Dansgaard, W., and Gundestrup, N.: Greenland paleotemperatures derived from GRIP bore hole temperature and ice core isotope profiles, Tellus B, 47, 624–629, 1995.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Johnsen, S. J., Clausen, H. B., Dansgaard, W., Gundestrup, N., Hammer, C., Andersen, U., Andersen, K. K., Hvidberg, C., Dahl-Jensen, D., Steffensen, J. P., Shoji, H., Sveinbjörnsdóttir, A., White, J., Jouzel, J., and Fisher, D.: The δ18O record along the Greenland Ice Core Project deep ice core and the problem of possible Eemian climatic instability, J. Geophys. Res.-Oceans, 102, 26397–26410, 1997.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Jouzel, J., Russell, G. L., Suozzo, R. J., Koster, R. D., White, J. W. C., and Broecker, W. S.: Simulations of the HDO and \chemH_2^{18O atmospheric cycles using the NASA GISS General Circulation Model: the seasonal cycle for present-day conditions}, J. Geophys. Res., 92, 14739–14760, 1987.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Jouzel, J., Alley, R. B., Cuffey, K. M., Dansgaard, W., Grootes, P., Hoffmann, G., Johnsen, S. J., Koster, R. D., Peel, D., Shuman, C. A., Stievenard, M., Stuiver, M., and White, J.: Validity of the temperature reconstruction from water isotopes in ice cores, J. Geophys. Res.-Oceans, 102, 26471–26487, &lt;a href=&quot;http://dx.doi.org/10.1029/97JC01283&quot;&gt;https://doi.org/10.1029/97JC01283&lt;/a&gt;,1997.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Langebroek, P. M., Paul, A., and Schulz, M.: Simulating the sea level imprint on marine oxygen isotope records during the middle Miocene using an ice sheet–climate model, Paleoceanography, 25, PA4203, &lt;a href=&quot;http://dx.doi.org/10.1029/2008PA001704&quot;&gt;https://doi.org/10.1029/2008PA001704&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Lhomme, N.: Modelling water isotopes in polar ice sheets, Ph. D. thesis, The University of British Columbia, 2004.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Lhomme, N., Clarke, G., and Marshall, S. J.: Tracer transport in the Greenland Ice Sheet: constraints on ice cores and glacial history, Quaternary Sci. Rev., 24, 173–194, 2005a.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Lhomme, N., Clarke, G., and Ritz, C.: Global budget of water isotopes inferred from polar ice sheets, Geophys. Res. Lett., 32, 173–194, &lt;a href=&quot;http://dx.doi.org/10.1029/2005GL023774&quot;&gt;https://doi.org/10.1029/2005GL023774&lt;/a&gt;, 2005b.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Lliboutry, L. and Duval, P.: Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies, Ann. Geophys., 3, 207–224, 1985.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Masson-Delmotte, V., Hou, S., Ekaykin, A., Jouzel, J., Aristarain, A., Bernardo, R. T., Bromwich, D., Cattani, O., Delmotte, M., Falourd, S., Frezzotti, M., Gallee, H., Genoni, L., Isaksson, E., Landais, A., Helsen, M. M., Hoffmann, G., Lopez, J., Morgan, V., Motoyama, H., Noone, D., Oerter, H., Petit, J. R., Royer, A., Uemura, R., Schmidt, G. A., Schlosser, E., Simoes, J. C., Steig, E. J., Stenni, B., Stievenard, M., van den Broeke, M. R., van de Wal, R. S. W., van de Berg, W. J., Vimeux, F. and White, J. W. C.: A review of Antarctic surface snow isotopic composition: observations, atmospheric circulation, and isotopic modeling, J. Climate, 21, 3359–3387, 2008.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">McGregor, J. L.: Economical determination of departure points for semi-Lagrangian models, Mon. Weather Rev., 121, 221–230, 1993.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Nair, R. D., Scroggs, J., and Semazzi, F.: A forward-trajectory global semi-Lagrangian transport scheme, J. Comput. Phys., 190, 275–294, 2003.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Parrenin, F., Remy, F., Ritz, C., Siegert, M. J., and Jouzel, J.: New modeling of the Vostok ice flow line and implication for the glaciological chronology of the Vostok ice core, J. Geophys. Res., 109, D20102, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JD004561&quot;&gt;https://doi.org/10.1029/2004JD004561&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Payne, A., Huybrechts, P., Abe-Ouchi, A., Calov, R., Fastook, J., Greve, R., Marshall, S. J., Marsiat, I., Ritz, C., Tarasov, L., and Thomassen, M.: Results from the EISMINT model intercomparison: the effects of thermomechanical coupling, J. Glaciol., 46, 227–238, 2000.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Petit, J. R., Jouzel, J., Raynaud, D., Barkov, N., Barnola, J. M., Basile, I., Bender, M., Chappellaz, J., Davis, M., Delaygue, G., Delmotte, M., Kotlyakov, V., Legrand, M., Lipenkov, V., Lorius, C., Pepin, L., Ritz, C., Saltzman, E., and Stievenard, M.: Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica, Nature, 399, 429–436, 1999.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in Fortran 90: the Art of Parallel Scientific Computing, 2nd Edn., Cambridge University Press, New York, NY, USA, 1996.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Purser, R. and Leslie, L.: An efficient semi-Lagrangian scheme using third-order semi-implicit time integration and forward trajectories, Mon. Weather Rev., 122, 745–756, 1994.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Rew, R. K. and Davis, G. P.: NetCDF: An interface for scientific data access, IEEE Comput. Grap. Appl., 10, 76–82, &lt;a href=&quot;http://dx.doi.org/10.1109/38.56302&quot;&gt;https://doi.org/10.1109/38.56302&lt;/a&gt;, 1990.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Rybak, O. and Huybrechts, P.: A comparison of Eulerian and Lagrangian methods for dating in numerical ice-sheet models, Ann. Glaciol., 37, 150–158, 2003.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Staniforth, A. and Côté, J.: Semi-Lagrangian integration schemes for atmospheric models – a review, Mon. Weather Rev., 119, 2206–2223, 1991.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Staniforth, A. and Pudykiewicz, J.: Reply to comments on and addenda to &quot;some properties and comparative performance of the semi-lagrangian method of Robert in the solution of the advection-diffusion equation&quot;, Atmos.-Ocean, 23, 195–200, &lt;a href=&quot;http://dx.doi.org/10.1080/07055900.1985.9649224&quot;&gt;https://doi.org/10.1080/07055900.1985.9649224&lt;/a&gt;, 1985.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Staniforth, A., White, A., and Wood, N.: Analysis of semi-Lagrangian trajectory computations, Q. J. Roy. Meteor. Soc., 129, 2065–2085, 2003.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Sturm, C., Zhang, Q., and Noone, D.: An introduction to stable water isotopes in climate models: benefits of forward proxy modelling for paleoclimatology, Clim. Past, 6, 115–129, &lt;a href=&quot;http://dx.doi.org/10.5194/cp-6-115-2010&quot;&gt;https://doi.org/10.5194/cp-6-115-2010&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Tarasov, L. and Peltier, W.: Greenland glacial history, borehole constraints, and Eemian extent, J. Geophys. Res.-Solid Earth, 108, 2143, &lt;a href=&quot;http://dx.doi.org/10.1029/2001JB001731&quot;&gt;https://doi.org/10.1029/2001JB001731&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Werner, M., Langebroek, P. M., Carlsen, T., Herold, M., and Lohmann, G.: Stable water isotopes in the ECHAM5 general circulation model: toward high-resolution isotope modeling on a global scale, J. Geophys. Res.-Atmos., 116, D15109, &lt;a href=&quot;http://dx.doi.org/10.1029/2011JD015681&quot;&gt;https://doi.org/10.1029/2011JD015681&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Wessel, P. and Smith, W. H. F.: New, improved version of Generic Mapping Tools released, EOS Transactions, American Geophysical Union, 79, 579, &lt;a href=&quot;http://dx.doi.org/10.1029/98EO00426&quot;&gt;https://doi.org/10.1029/98EO00426&lt;/a&gt;, 1998.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Xu, X., Werner, M., Butzin, M., and Lohmann, G.: Water isotope variations in the global ocean model MPI-OM, Geosci. Model Dev., 5, 809–818, &lt;a href=&quot;http://dx.doi.org/10.5194/gmd-5-809-2012&quot;&gt;https://doi.org/10.5194/gmd-5-809-2012&lt;/a&gt;, 2012.</mixed-citation>
</ref>
</ref-list>
</back>
</article>