<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<front>
<journal-meta>
<journal-id journal-id-type="publisher">GMDD</journal-id>
<journal-title-group>
<journal-title>Geoscientific Model Development Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">GMDD</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1991-962X</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/gmdd-6-685-2013</article-id>
<title-group>
<article-title>Numerical issues associated with compensating and competing processes in climate models: an example from ECHAM-HAM</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Wan</surname>
<given-names>H.</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>Rasch</surname>
<given-names>P. J.</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>Zhang</surname>
<given-names>K.</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>Kazil</surname>
<given-names>J.</given-names>
</name>
<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>Leung</surname>
<given-names>L. R.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Pacific Northwest National Laboratory, Richland, WA, USA</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Cooperative Institute for Research in Environmental Sciences (CIRES),          University of Colorado, Boulder, CO, USA</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>NOAA Earth System Research Laboratory (ESRL), Boulder, CO, USA</addr-line>
</aff>
<pub-date pub-type="epub">
<day>29</day>
<month>01</month>
<year>2013</year>
</pub-date>
<volume>6</volume>
<issue>1</issue>
<fpage>685</fpage>
<lpage>720</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>
<self-uri xlink:href="http://www.geosci-model-dev-discuss.net/6/685/2013/gmdd-6-685-2013.html">This article is available from http://www.geosci-model-dev-discuss.net/6/685/2013/gmdd-6-685-2013.html</self-uri>
<self-uri xlink:href="http://www.geosci-model-dev-discuss.net/6/685/2013/gmdd-6-685-2013.pdf">The full text article is available as a PDF file from http://www.geosci-model-dev-discuss.net/6/685/2013/gmdd-6-685-2013.pdf</self-uri>
<abstract>
<p>The purpose of this paper is to draw attention to the need for
      appropriate numerical techniques to represent process interactions in
      climate models.  In two versions of the ECHAM-HAM model, different
      time integration methods are used to solve the sulfuric acid (H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt;) gas
      evolution equation, which lead to substantially different results in
      the H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt; gas  concentration and the aerosol nucleation rate. Using
      convergence tests and sensitivity simulations performed with various
      time stepping schemes, it is confirmed that numerical errors in the
      second model version are significantly smaller than those in version
      one.  The use of sequential operator splitting in combination with
      long time step is identified as the main reason for the large
      systematic biases in the old model. The remaining errors of nucleation
      rate in version two, related to the competition between condensation
      and nucleation, have a clear impact on the simulated concentration of
      cloud condensation nuclei (CCN) in the lower troposphere.  These
      errors can be significantly reduced by employing an implicit solver
      that handles production, condensation and nucleation at the same time.
      Lessons learned in this work underline the need for more caution when
      treating multi-time-scale problems involving compensating and
      competing processes, a common occurrence in current climate models.</p>
</abstract>
<counts><page-count count="36"/></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"> Beljaars,~A.: Numerical schemes for parameterizations, in: Numerical Methods in Atmospheric Models, ECMWF Seminar proceedings, European Centre for Medium-range Weather Forecast, Reading, UK, 1–42, 1991. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple"> Beljaars,~A., Bechtold,~P., Koehler,~M., Morcrette,~J.-J., Tompkins,~A., Viterbo,~P., and Wedi,~N.: The numerics of physical parameterization, in: ECMWF Seminar Proceedings, European Centre for Medium-range Weather Forecast, Reading, UK, 113–134, 2004. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple"> Benard,~P., Marki,~A., Neytchev,~P., and Prtenjak,~M.: Stabilization of nonlinear vertical diffusion schemes in the context of NWP models, Mon. Weather Rev., 128, 1937–1948, doi:http://dx.doi.org/10.1175/1520-0493(2000)128&lt;1937:SONVDS&gt;2.0.CO;210.1175/1520-0493(2000)128\textless1937:SONVDS\textgreater2.0.CO;2, 2000. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple"> Brinkop,~S. and Roeckner,~E.: Sensitivity of a general circulationmodel to parameterizations of cloud-turbulence interactions inthe atmospheric boundary layer, Tellus A, 47, 197–220, 1995. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Cheng,~T., Peng,~Y., Feichter,~J., and Tegen,~I.: An improvement on the dust emission scheme in the global aerosol-climate model ECHAM5-HAM, Atmos. Chem. Phys., 8, 1105–1117, doi:http://dx.doi.org/10.5194/acp-8-1105-200810.5194/acp-8-1105-2008, 2008. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Dentener,~F., Kinne,~S., Bond,~T., Boucher,~O., Cofala,~J., Generoso,~S., Ginoux,~P., Gong,~S., Hoelzemann,~J J., Ito,~A., Marelli,~L., Penner,~J E., Putaud,~J.-P., Textor,~C., Schulz,~M., van~der~Werf,~G R., and Wilson,~J.: Emissions of primary aerosol and precursor gases in the years 2000 and 1750 prescribed data-sets for AeroCom, Atmos. Chem. Phys., 6, 4321–4344, doi:http://dx.doi.org/10.5194/acp-6-4321-200610.5194/acp-6-4321-2006, 2006. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Fouquart,~Y. and Bonnel,~B.: Computations of solar heating of the earth&apos;s atmosphere: a new parameterization., Beitr. Phys. Atmos., 53, 35–62, 1980. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple"> Gettelman,~A., Morrison,~H., and Ghan,~S J.: A new two-moment bulk stratiform cloud microphysics scheme in the Community Atmospheric Model (CAM3), Part~II: Single-column and global results, J. Climate, 21, 3660–3679, 2008. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple"> Girard,~C. and Delage,~Y.: Stable schemes for nonlinear vertical diffusion in atmospheric circulation models, Mon. Weather Rev., 118, 737–745, doi:http://dx.doi.org/10.1175/1520-0493(1990)118&lt;0737:SSFNVD&gt;2.0.CO;210.1175/1520-0493(1990)118\textless0737:SSFNVD\textgreater2.0.CO;2, 1990. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple"> Herzog,~M., Weisenstein,~D K., and Penner,~J E.: A dynamic aerosol module for global chemical transport models: model description,~J. Geophys. Res., 109, D18202, doi:http://dx.doi.org/10.1029/2003JD00440510.1029/2003JD004405, 2004. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple"> Jacobson,~M Z.: Analysis of aerosol interactions with numerical techniques for solving coagulation, nucleation, condensation, dissolution, and reversible chemistry among multiple size distributions.,~J. Geophys. Res., 107, 4366, doi:http://dx.doi.org/10.1029/2001JD00204410.1029/2001JD002044, 2002. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Karypis,~G. and Kumar,~V.: Multilevel graph partitioning schemes, in: International Conference on Parallel Processing, 1995. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Karypis,~G. and Kumar,~V.: A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput., 20, 359–392, doi:http://dx.doi.org/10.1137/S106482759528799710.1137/S1064827595287997, 1998. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Kazil,~J. and Lovejoy,~E R.: A semi-analytical method for calculating rates of new sulfate aerosol formation from the gas phase, Atmos. Chem. Phys., 7, 3447–3459, doi:http://dx.doi.org/10.5194/acp-7-3447-200710.5194/acp-7-3447-2007, 2007. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Kazil,~J., Stier,~P., Zhang,~K., Quaas,~J., Kinne,~S., O&apos;Donnell,~D., Rast,~S., Esch,~M., Ferrachat,~S., Lohmann,~U., and Feichter,~J.: Aerosol nucleation and its role for clouds and Earth&apos;s radiative forcing in the aerosol-climate model ECHAM5-HAM, Atmos. Chem. Phys., 10, 10733–10752, doi:http://dx.doi.org/10.5194/acp-10-10733-201010.5194/acp-10-10733-2010, 2010. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Kerkweg,~A., Buchholz,~J., Ganzeveld,~L., Pozzer,~A., Tost,~H., and Jöckel,~P.: Technical Note: An implementation of the dry removal processes DRY DEPosition and SEDImentation in the Modular Earth Submodel System (MESSy), Atmos. Chem. Phys., 6, 4617–4632, doi:http://dx.doi.org/10.5194/acp-6-4617-200610.5194/acp-6-4617-2006, 2006. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Kokkola,~H., Hommel,~R., Kazil,~J., Niemeier,~U., Partanen,~A.-I., Feichter,~J., and Timmreck,~C.: Aerosol microphysics modules in the framework of the ECHAM5 climate model – intercomparison under stratospheric conditions, Geosci. Model Dev., 2, 97–112, doi:http://dx.doi.org/10.5194/gmd-2-97-200910.5194/gmd-2-97-2009, 2009. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple"> Kuang,~C., McMurry,~P H., McCormick,~A V., and Eisele,~F L.: Dependence of nucleation rates on sulfuric acid vapor concentration in diverse atmospheric locations, J. Geophys. Res., 113, D10209, doi:http://dx.doi.org/10.1029/2007JD00925310.1029/2007JD009253, 2008. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Kulmala,~M., Lehtinen,~K E J., and Laaksonen,~A.: Cluster activation theory as an explanation of the linear dependence between formation rate of 3nm particles and sulphuric acid concentration, Atmos. Chem. Phys., 6, 787–793, doi:http://dx.doi.org/10.5194/acp-6-787-200610.5194/acp-6-787-2006, 2006. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Laakso,~L., Petäjä,~T., Lehtinen,~K E J., Kulmala,~M., Paatero,~J., Hõrrak,~U., Tammet,~H., and Joutsensaari,~J.: Ion production rate in a boreal forest based on ion, particle and radiation measurements, Atmos. Chem. Phys., 4, 1933–1943, doi:http://dx.doi.org/10.5194/acp-4-1933-200410.5194/acp-4-1933-2004, 2004. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Lin,~S.-J. and Rood,~R B.: Multidimensional flux-form semi-Lagrangian transport schemes, Mon. Weather Rev., 124, 2046–2070, 1996. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Liu,~X., Easter,~R C., Ghan,~S J., Zaveri,~R., Rasch,~P., Shi,~X., Lamarque,~J.-F., Gettelman,~A., Morrison,~H., Vitt,~F., Conley,~A., Park,~S., Neale,~R., Hannay,~C., Ekman,~A M L., Hess,~P., Mahowald,~N., Collins,~W., Iacono,~M J., Bretherton,~C S., Flanner,~M G., and Mitchell,~D.: Toward a minimal representation of aerosols in climate models: description and evaluation in the Community Atmosphere Model CAM5, Geosci. Model Dev., 5, 709–739, doi:http://dx.doi.org/10.5194/gmd-5-709-201210.5194/gmd-5-709-2012, 2012. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Lohmann,~U. and Hoose,~C.: Sensitivity studies of different aerosol indirect effects in mixed-phase clouds, Atmos. Chem. Phys., 9, 8917–8934, doi:http://dx.doi.org/10.5194/acp-9-8917-200910.5194/acp-9-8917-2009, 2009. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Lohmann,~U., Stier,~P., Hoose,~C., Ferrachat,~S., Kloster,~S., Roeckner,~E., and Zhang,~J.: Cloud microphysics and aerosol indirect effects in the global climate model ECHAM5-HAM, Atmos. Chem. Phys., 7, 3425–3446, doi:http://dx.doi.org/10.5194/acp-7-3425-200710.5194/acp-7-3425-2007, 2007. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Mlawer,~E J., Taubman,~S J., Brown,~P D., Iacono,~M J., and Clough,~S A.: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave.,~J. Geophys. Res., 102, 16663–16682, 1997. </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Monahan,~E., Spiel,~D., and Davidson,~K.: A model of marine aerosol generation via whitecaps and wave disruption, in: Oceanic Whitecaps and their Role in Air-Sea Exchange, edited by: Reidel,~D., Norwell, Massachusetts, 167–174, 1986. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple"> Morrison,~H. and Gettelman,~A.: A new two-moment bulk stratiform cloud microphysics scheme in the Community Atmospheric Model (CAM3), Part~I: Description and numerical tests, J. Climate, 21, 3642–3659, 2008. </mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple"> Nordeng,~T E.: Extended versions of the convective parametrization scheme at ECMWF and their impact on the mean and transient activity of the model in the tropics, ECMWF Research Department, Technical Momorandum 206, European Centre for Medium-range Weather Forecast, Reading, UK, Reading, UK, 1994. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### O&apos;Donnell,~D., Tsigaridis,~K., and Feichter,~J.: Estimating the direct and indirect effects of secondary organic aerosols using ECHAM5-HAM, Atmos. Chem. Phys., 11, 8635–8659, doi:http://dx.doi.org/10.5194/acp-11-8635-201110.5194/acp-11-8635-2011, 2011. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Petters,~M D. and Kreidenweis,~S M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity, Atmos. Chem. Phys., 7, 1961–1971, doi:http://dx.doi.org/10.5194/acp-7-1961-200710.5194/acp-7-1961-2007, 2007. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Posselt,~R. and Lohmann,~U.: Introduction of prognostic rain in ECHAM5: design and single column model simulations, Atmos. Chem. Phys., 8, 2949–2963, doi:http://dx.doi.org/10.5194/acp-8-2949-200810.5194/acp-8-2949-2008, 2008. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Riipinen,~I., Sihto,~S.-L., Kulmala,~M., Arnold,~F., Dal~Maso,~M., Birmili,~W., Saarnio,~K., Teinilä,~K., Kerminen,~V.-M., Laaksonen,~A., and Lehtinen,~K E J.: Connections between atmospheric sulphuric acid and new particle formation during QUEST III–IV campaigns in Heidelberg and Hyytiälä, Atmos. Chem. Phys., 7, 1899–1914, doi:http://dx.doi.org/10.5194/acp-7-1899-200710.5194/acp-7-1899-2007, 2007. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Roeckner,~E., Bäuml,~G., Bonaventura,~L., Brokopf,~R., Esch,~M., Giorgetta,~M., Hagemann,~S., Kirchner,~I., Kornblueh,~L., Manzini,~E., Rhodin,~A., Schlese,~U., Schulzweida,~U., and Tompkins,~A.: The atmospheric general circulation model ECHAM5. PART I: model description, Technical Report 349, Max Planck Institute for Meteorology, 2003. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Roeckner,~E., Brokopf,~R., Esch,~M., Giorgetta,~M., Hagemann,~S., Kornblueh,~L., Manzini,~E., Schlese,~U., and Schulzweida,~U.: Sensitivity of simulated climate to horizontal and vertical resolution in the ECHAM5 atmosphere model,~J. Climate, 19, 3771–3791, 2006. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Schlegel,~M., Knoth,~O., Arnold,~M., and Wolke,~R.: Implementation of multirate time integration methods for air pollution modelling, Geosci. Model Dev., 5, 1395–1405, doi:http://dx.doi.org/10.5194/gmd-5-1395-201210.5194/gmd-5-1395-2012, 2012. </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple"> Simmons,~A J. and Burridge,~D M.: An energy and angular-momentum conserving vertical finite difference scheme and hybrid vertical coordinates, Mon. Weather Rev., 109, 758–766, 1981. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple"> Smith,~M. and Harrison,~N.: The sea spray generation function.,~J. Aerosol Sci., 29, 189–190, doi:http://dx.doi.org/10.1016/S0021-8502(98)00280-810.1016/S0021-8502(98)00280-8, 1998. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Stier,~P., Feichter,~J., Kinne,~S., Kloster,~S., Vignati,~E., Wilson,~J., Ganzeveld,~L., Tegen,~I., Werner,~M., Balkanski,~Y., Schulz,~M., Boucher,~O., Minikin,~A., and Petzold,~A.: The aerosol-climate model ECHAM5-HAM, Atmos. Chem. Phys., 5, 1125–1156, doi:http://dx.doi.org/10.5194/acp-5-1125-200510.5194/acp-5-1125-2005, 2005. </mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple"> Tegen,~I., Harrison,~S P., Kohfeld,~K., Prentice,~I C., Coe,~M., and Heimann,~M.: Impact of vegetation and preferential source areas on global dust aerosol: results from a model study.,~J. Geophys. Res., 107, 4576–4597, doi:http://dx.doi.org/10.1029/2001JD00096310.1029/2001JD000963, 2002. </mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple"> Teixeira,~J.: Boundary layer clouds in large scale atmospheric models: cloud schemes and numerical aspects, Phd thesis, European Centre for Medium-range Weather Forecast, Reading, UK, 2000. </mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple"> Tiedtke,~M.: A comprehensive mass flux scheme for cumulus parameterization in large scale models, Mon. Weather Rev., 117, 1779–1800, 1989. </mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Tudor,~M.: A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models, Geosci. Model Dev. Discuss., 5, 4233–4268, doi:http://dx.doi.org/10.5194/gmdd-5-4233-201210.5194/gmdd-5-4233-2012, 2012. </mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple"> Uppala,~S M., Kallberg,~P W., Simmons,~A J., Andrae,~U., Bechtold,~V D C., Fiorino,~M., Gibson,~J K., Haseler,~J., Hernandez,~A., Kelly,~G A., Li,~X., Onogi,~K., Saarinen,~S., Sokka,~N., Allan,~R P., Andersson,~E., Arpe,~K., Balmaseda,~M A., Beljaars,~A C M., Berg,~L V D., Bidlot,~J., Bormann,~N., Caires,~S., Chevallier,~F., Dethof,~A., Dragosavac,~M., Fisher,~M., Fuentes,~M., Hagemann,~S., Holm,~E., Hoskins,~B J., Isaksen,~L., Janssen,~P A E M., Jenne,~R., Mcnally,~A P., Mahfouf,~J.-F., Morcrette,~J.-J., Rayner,~N A., Saunders,~R W., Simon,~P., Sterl,~A., Trenberth,~K E., Untch,~A., Vasiljevic,~D., Viterbo,~P., and Woollen,~J.: The ERA-40 re-analysis, Q. J. Roy. Meteor. Soc., 131, 2961–3012, doi:http://dx.doi.org/10.1256/qj.04.17610.1256/qj.04.176, 2005. </mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple"> Vignati,~E., Wilson,~J., and Stier,~P.: M7: An efficient size-resolved aerosol microphysics module for large-scale aerosol transport models.,~J. Geophys. Res., 109, D22202, doi:http://dx.doi.org/10.1029/2003JD00448510.1029/2003JD004485, 2004. </mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple"> Wood,~N., Diamantakis,~M., and Staniforth,~A.: A monotonically-damping second-order-accurate unconditionally-stable numerical scheme for diffusion, Q. J. Roy. Meteor. Soc., 133, 1559–1573, doi:http://dx.doi.org/10.1002/qj.11610.1002/qj.116, 2007. </mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple"> Zaveri,~R A., Easter,~R C., Fast,~J D., and Peters,~L K.: Model for Simulating Aerosol Interactions and Chemistry (MOSAIC), J. Geophys. Res.-Atmos., 113, D13204, doi:http://dx.doi.org/10.1029/2007JD00878210.1029/2007JD008782, 2008. </mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Zhang,~K., Wan,~H., Wang,~B., Zhang,~M., Feichter,~J., and Liu,~X.: Tropospheric aerosol size distributions simulated by three online global aerosol models using the M7 microphysics module, Atmos. Chem. Phys., 10, 6409–6434, doi:http://dx.doi.org/10.5194/acp-10-6409-201010.5194/acp-10-6409-2010, 2010. </mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple"> % ### SELF-REFERENCE ### Zhang,~K., O&apos;Donnell,~D., Kazil,~J., Stier,~P., Kinne,~S., Lohmann,~U., Ferrachat,~S., Croft,~B., Quaas,~J., Wan,~H., Rast,~S., and Feichter,~J.: The global aerosol-climate model ECHAM-HAM, version 2: sensitivity to improvements in process representations, Atmos. Chem. Phys., 12, 8911–8949, doi:http://dx.doi.org/10.5194/acp-12-8911-201210.5194/acp-12-8911-2012, 2012. </mixed-citation>
</ref>
</ref-list>
</back>
</article>