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<front>
<journal-meta>
<journal-id journal-id-type="publisher">ACP</journal-id>
<journal-title-group>
<journal-title>Atmospheric Chemistry and Physics</journal-title>
<abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1680-7324</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/acp-12-11465-2012</article-id>
<title-group>
<article-title>A new multi-gas constrained model of trace gas non-homogeneous transport in firn: evaluation and behaviour at eleven polar sites</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Witrant</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Martinerie</surname>
<given-names>P.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Hogan</surname>
<given-names>C.</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>Laube</surname>
<given-names>J. C.</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>Kawamura</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Capron</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Montzka</surname>
<given-names>S. A.</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Dlugokencky</surname>
<given-names>E. J.</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Etheridge</surname>
<given-names>D.</given-names>
</name>
<xref ref-type="aff" rid="aff9">
<sup>9</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Blunier</surname>
<given-names>T.</given-names>
</name>
<xref ref-type="aff" rid="aff10">
<sup>10</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Sturges</surname>
<given-names>W. T.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>UJF-Grenoble 1/CNRS, Grenoble Image Parole Signal Automatique (GIPSA-lab), UMR5216, B.P. 46, 38402 St Martin d&apos;Hères, France</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>UJF-Grenoble 1/CNRS, Laboratoire de Glaciologie et Géophysique de l&apos;Environnement (LGGE) UMR5183, Grenoble, 38041, France</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>National Institute of Polar Research, 10-3 Midorichou, Tachikawa, Tokyo 190-8518, Japan</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Institute of Biogeosciences, Japan Agency for Marine-Earth Science and Technology, 2-15 Natsushima-cho, Yokosuka 237-0061, Japan</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>Laboratoire des Sciences du Climat et de L&apos;Environnement, IPSL/CEA-CNRS-UVSQ, 91191 Gif-sur-Yvette, France</addr-line>
</aff>
<aff id="aff7">
<label>7</label>
<addr-line>British Antarctic Survey, Natural Environment Research Council, High Cross, Madingley Road, Cambridge CB3 0ET, UK</addr-line>
</aff>
<aff id="aff8">
<label>8</label>
<addr-line>NOAA Earth System Research Laboratory, Boulder, Colorado, USA</addr-line>
</aff>
<aff id="aff9">
<label>9</label>
<addr-line>Commonwealth Scientific and Industrial Research Organisation, Marine and Atmospheric Research, PMB 1, Aspendale, Vic. 3195, Australia</addr-line>
</aff>
<aff id="aff10">
<label>10</label>
<addr-line>Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Juliane Maries, VEJ 30, 2100 Copenhagen Ø, Denmark</addr-line>
</aff>
<pub-date pub-type="epub">
<day>04</day>
<month>12</month>
<year>2012</year>
</pub-date>
<volume>12</volume>
<issue>23</issue>
<fpage>11465</fpage>
<lpage>11483</lpage>
<permissions>
<license xlink:type="simple">
<license-p>This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
</license>
</permissions>
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<self-uri xlink:href="http://www.atmos-chem-phys.net/12/11465/2012/acp-12-11465-2012.pdf">The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/11465/2012/acp-12-11465-2012.pdf</self-uri>
<abstract>
<p>Insoluble trace gases are trapped in polar ice at the firn-ice transition, at
approximately 50 to 100 m below the surface, depending primarily on the site
temperature and snow accumulation. Models of trace gas transport in polar
firn are used to relate firn air and ice core records of trace gases to their
atmospheric history. We propose a new model based on the following
contributions. First, the firn air transport model is revised in a
poromechanics framework with emphasis on the non-homogeneous properties and
the treatment of gravitational settling. We then derive a nonlinear least
square multi-gas optimisation scheme to calculate the effective firn
diffusivity (automatic diffusivity tuning). The improvements gained by the
multi-gas approach are investigated (up to ten gases for a single site are
included in the optimisation process). We apply the model to four Arctic
(Devon Island, NEEM, North GRIP, Summit) and seven Antarctic (DE08, Berkner
Island, Siple Dome, Dronning Maud Land, South Pole, Dome C, Vostok) sites and
calculate their respective depth-dependent diffusivity profiles. Among these
different sites, a relationship is inferred between the snow accumulation
rate and an increasing thickness of the lock-in zone defined from the
isotopic composition of molecular nitrogen in firn air (denoted
&amp;delta;&lt;sup&gt;15&lt;/sup&gt;N). It is associated with a reduced diffusivity value and an
increased ratio of advective to diffusive flux in deep firn, which is
particularly important at high accumulation rate sites. This has implications
for the understanding of &amp;delta;&lt;sup&gt;15&lt;/sup&gt;N of N&lt;sub&gt;2&lt;/sub&gt; records in ice cores, in
relation with past variations of the snow accumulation rate. As the snow
accumulation rate is clearly a primary control on the thickness of the
lock-in zone, our new approach that allows for the estimation of the lock-in
zone width as a function of accumulation may lead to a better constraint on
the age difference between the ice and entrapped gases.</p>
</abstract>
<counts><page-count count="19"/></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"> Anderson, J.: Fundamentals of Aerodynamics, McGraw-Hill Companies, 1991. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple"> Battle, M., Bender, M., Sowers, T., Tans, P., Butler, J H., Elkins, J W., Ellis, J., Conway, T., Zhang, N., Lang, P., and Clarke, A.: Atmospheric gas concentrations over the past century measured in air from firn at the South Pole, Nature, 383, 231–235, 1996. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple"> Bender, M L., Sowers, T., Barnola, J.-M., and Chappellaz, J.: Changes in the O&lt;sub&gt;2&lt;/sub&gt;/N&lt;sub&gt;2&lt;/sub&gt; ratio of the atmosphere during recent decades reflected in the composition of air in the firn at Vostok Station, Antarctica, Geophys. Res. Lett., 21, 189–192, 1994. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple"> Bräunlich, M., Aballain, O., Marik, T., Jöckel, P., Brenninkmeijer, C., Chappellaz, J., Barnola, J.-M., Mulvaney, R., and Sturges, W.: Changes in the global atmospheric methane budget over the last decades inferred from $^13$C and D isotopic analysis of Antarctic firn air, J. Geophys. Res., 106, 20465–20481, 2001. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple"> Buizert, C., Martinerie, P., Petrenko, V. V., Severinghaus, J. P., Trudinger, C. M., Witrant, E., Rosen, J. L., Orsi, A. J., Rubino, M., Etheridge, D. M., Steele, L. P., Hogan, C., Laube, J. C., Sturges, W. T., Levchenko, V. A., Smith, A. M., Levin, I., Conway, T. J., Dlugokencky, E. J., Lang, P. M., Kawamura, K., Jenk, T. M., White, J. W. C., Sowers, T., Schwander, J., and Blunier, T.: Gas transport in firn: multiple-tracer characterisation and model intercomparison for NEEM, Northern Greenland, Atmos. Chem. Phys., 12, 4259–4277, http://dx.doi.org/10.5194/acp-12-4259-2012doi:10.5194/acp-12-4259-2012, 2012. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple"> Butler, J H., Battle, M., Bender, M L., Montzka, S A., Clarke, A D., Saltzman, E S., Sucher, C M., Severinghaus, J P., and Elkins, J W.: A record of atmospheric halocarbons during the twentieth century from polar firn air, Nature, 399, 749–755, 1999. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Byron Bird, R., Stewart, W., and Lightfoot, E.: Transport Phenomena, John Wiley &amp; Sons Ltd, 2nd edn., 2007. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple"> Coleman, T. and Li, Y.: On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds, Math. Program., 67, 189–224, 1994. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple"> Coleman, T. and Li, Y.: An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds, SIAM J. Optim., 6, 418–445, 1996. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple"> Coussy, O.: Poromechanics, John Wiley &amp; Sons Ltd, 2nd edn., 2003. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple"> CRYOSTAT: CRYOspheric STudies of Atmospheric Trends in stratospherically and radiatively important gases (CRYOSTAT), available at: http://badc.nerc.ac.uk/data/cryostat (last access: January 2011), 2007. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Fabre, A., Barnola, J.-M., Arnaud, L., and Chappellaz, J.: Determination of gas diffusivity in polar firn: Comparison between experimental measurements and inverse modelling, Geophys. Res. Lett., 27, 557–560, http://dx.doi.org/10.1029/1999GL010780doi:10.1029/1999GL010780, 2000. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Fa\&quot;in, X., Ferrari, C P., Dommergue, A., Albert, M C., Battle, M., Severinghaus, J., Arnaud, L., Barnola, J.-M., Cairns, W., Barbante, C., and Boutron, C.: Polar firn air reveals large-scale impact of anthropogenic mercury emissions during the 1970s, P. Natl. Acad. Sci., 106, 16114–16119, http://dx.doi.org/10.1073/pnas.0905117106doi:10.1073/pnas.0905117106, 2009. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple"> Firn Record of Trace Gases Relevant to Atmospheric Chemical Change over 100 yrs (FIRETRACC/100), available at: http://badc.nerc.ac.uk/data/firetracc (last access: January 2011), 2007. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> Freitag, J., Dobrindt, U., and Kipfstuhl, J.: A new method for predicting transport properties of polar firn with respect to gases on the pore-space scale, Ann. Glaciol., 35, 538–544, 2002. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> Goujon, C., Barnola, J.-M., and Ritz, C.: Modeling the densification of firn including heat diffusion: application to close-off, J. Geophys. Res., 108, ACL10.1–ACL10.18, http://dx.doi.org/10.1029/2002JD003319doi:10.1029/2002JD003319, 2003. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> Hörhold, M., Albert, M., and Freitag, J.: The impact of accumulation rate on anisotropy and air permeability of polar firn at a high-accumulation site, J. Glaciol., 55, 625–630, 2009. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple"> Landais, A., Barnola, J.-M., Kawamura, K., Caillon, N., Delmotte, M., Van Omnen, T., Dreyfus, G., Jouzel, J., Masson-Delmotte, V., Minster, B., Freitag, J., Leuenberger, M., Schwander, J., Etheridge, D., and Morgan, V.: Firn-air $\delta ^15$N in modern polar sites and glacial-interglacial ice: a model-data mismatch during glacial periods in Antarctica?, Quaternary Sci. Rev., 25, 49–62, http://dx.doi.org/10.1016/j.quascirev.2005.06.007doi:10.1016/j.quascirev.2005.06.007, 2006. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple"> Laube, J. C., Martinerie, P., Witrant, E., Blunier, T., Schwander, J., Brenninkmeijer, C. A. M., Schuck, T. J., Bolder, M., Röckmann, T., van der Veen, C., Bönisch, H., Engel, A., Mills, G. P., Newland, M. J., Oram, D. E., Reeves, C. E., and Sturges, W. T.: Accelerating growth of HFC-227ea (1,1,1,2,3,3,3-heptafluoropropane) in the atmosphere, Atmos. Chem. Phys., 10, 5903–5910, http://dx.doi.org/10.5194/acp-10-5903-2010doi:10.5194/acp-10-5903-2010, 2010. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple"> Ljung, L.: System Identification: Theory for the User, Information and System Sciences, PTR Prentice Hall, Upper Saddle River, NJ, 2nd edn., 1999. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Martinerie, P., Nourtier-Mazauric, E., Barnola, J.-M., Sturges, W. T., Worton, D. R., Atlas, E., Gohar, L. K., Shine, K. P., and Brasseur, G. P.: Long-lived halocarbon trends and budgets from atmospheric chemistry modelling constrained with measurements in polar firn, Atmos. Chem. Phys., 9, 3911–3934, http://dx.doi.org/10.5194/acp-9-3911-2009doi:10.5194/acp-9-3911-2009, 2009. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> Montzka, S., Reimann S. (Coordinating Lead Authors), Engel, A., Krüger, K., O&apos;Doherty, S., Sturges, W., Blake, D., Dorf, M., Fraser, P., Froidevaux, L., Jucks, K., Kreher, K., Kurylo, M., Mellouki, A., Miller, J., Nielsen, O., Orkin, V., Prinn, R., Rhew, R., Santee, M., Stohl, A., and Verdonik, D.: Scientific Assessment of Ozone Depletion: 2010, Global Ozone Research and Monitoring Project, Report No.52, 516 pp., chap. Ozone-Depleting Substances (ODSs) and Related Chemicals, Chapter 1, World Meteorological Organization, Geneva, Switzerland, 2011. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> Montzka, S A., Kuijpers, L., Battle, M O., Aydin, M., Verhulst, K R., Saltzman, E S., and Fahey, D W.: Recent increases in global HFC-23 emissions, Geophys. Res. Lett., 37, L02808, http://dx.doi.org/10.1029/2009GL041195doi:10.1029/2009GL041195, 2010. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple"> Rommelaere, V., Arnaud, L., and Barnola, J.-M.: Reconstructing recent atmospheric trace gas concentrations from polar firn and bubbly ice data by inverse methods, J. Geophys. Res., 102, 30069–30083, 1997. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Scanlon, B R., Nicot, J P., and Massmann, J W.: Soil Physics Companion, chap. Soil gas movement in unsaturated systems, 297–341, CRC Press Inc., Boca Raton, Florida, 2002. </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Schwander, J.: The transformation of snow to ice and the occlusion of gases, in: The Environmental Record in Glaciers and Ice Sheets, edited by Oeschger, H. and Langway Jr., C., 53–67, John Wiley, New York, 1989. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple"> Schwander, J., Barnola, J.-M., Andrié, C., Leuenberger, M., Ludin, A., Raynaud, D., and Stauffer, B.: The Age of the Air in the Firn and the Ice at Summit, Greenland, J. Geophys. Res., 98, 2831–2838, 1993.  </mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple"> Schwander, J., Sowers, T., Barnola, J.-M., Blunier, T., Malaiz, B., and Fuchs, A.: Age scale of the air in the summit ice: Implication for glacial-interglacial temperature change, J. Geophys. Res., 102, 19483–19494, 1997. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> Severinghaus, J. and Battle, M.: Fractionation of gases in polar ice during bubble close-off: New constraints from firn air Ne, Kr and Xe observations, Earth Planet. Sci. Lett., 244, 474–500, 2006. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> Severinghaus, J., Grachev, A., and Battle, M.: Thermal fractionation of air in polar firn by seasonal temperature gradients, Geochem. Geophys. Geosyst., 2, 1048, http://dx.doi.org/10.1029/2000GC000146doi:10.1029/2000GC000146, 2001. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> Severinghaus, J P., Albert, M R., Courville, Z R., Fahnestock, M A., Kawamura, K., Montzka, S A., Mühle, J., Scambos, T A., Shields, E., Shuman, C A., Suwa, M., Tans, P., and Weiss, R F.: Deep air convection in the firn at a zero-accumulation site, central Antarctica, Earth Planet. Sci. Lett., 293, 359–367, 2010. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> Sowers, T., Bernard, S., Aballain, O., Chappellaz, J., Barnola, J.-M., and Marik, T.: Records of the $\delta^13$C of atmospheric CH&lt;sub&gt;4&lt;/sub&gt; over the last 2 centuries as recorded in Antarctic snow and ice, Global Biogeochem. Cy., 19, GB2002, http://dx.doi.org/10.1029/2004GB002408doi:10.1029/2004GB002408, 2005. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Stauffer, B., Schwander, J., and Oeschger, H.: Enclosure of air during metamorphosis of dry firn to ice, Ann. Glaciol., 6, 108–112, 1985. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Trudinger, C., Enting, L., Etheridge, D., Francey, R., Levchenko, V., Steele, L., Raynaud, D., and Arnaud, L.: Modeling air movement and bubble trapping in firn, J. Geophys. Res., 102, 6747–6763, 1997. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple"> Trudinger, C M., Etheridge, D M., Rayner, P J., Enting, I G., Sturrock, G A., and Langensfelds, R L.: Reconstructing atmospheric histories from measurements of air composition in firn, J. Geophys. Res., 107, 4780, http://dx.doi.org/10.1029/2002JD002545doi:10.1029/2002JD002545, 2002. </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple"> Trudinger, C. M., Enting, I. G., Rayner, P. J., Etheridge, D. M., Buizert, C., Rubino, M., Krummel, P. B., and Blunier, T.: How well do different tracers constrain the firn diffusivity profile?, Atmos. Chem. Phys. Discuss., 12, 17773–17834, http://dx.doi.org/10.5194/acpd-12-17773-2012doi:10.5194/acpd-12-17773-2012, 2012. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple"> Webb, S. and Pruess, K.: The Use of Ficks Law for Modeling Trace Gas Diffusion in Porous Media, Transport in Porous Media, 51, 327–341, 2003. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> Witrant, E. and Martinerie, P.: A Variational Approach for Optimal Diffusivity Identification in Firns, in: Proc. of the 18th Med. Conf. on Control and Automation, 892–897, Marrakech, Morocco, 2010. </mixed-citation>
</ref>
</ref-list>
</back>
</article>