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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><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</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/acp-19-1357-2019</article-id><title-group><article-title>Possible heterogeneous chemistry of hydroxymethanesulfonate (HMS) in
northern China winter haze</article-title><alt-title>Heterogeneous HMS chemistry</alt-title>
      </title-group><?xmltex \runningtitle{Heterogeneous HMS chemistry}?><?xmltex \runningauthor{S.~Song et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Song</surname><given-names>Shaojie</given-names></name>
          <email>songs@seas.harvard.edu</email>
        <ext-link>https://orcid.org/0000-0001-6395-7422</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Gao</surname><given-names>Meng</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8657-3541</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>Xu</surname><given-names>Weiqi</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff2 aff3 aff4">
          <name><surname>Sun</surname><given-names>Yele</given-names></name>
          <email>sunyele@mail.iap.ac.cn</email>
        <ext-link>https://orcid.org/0000-0003-2354-0221</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Worsnop</surname><given-names>Douglas R.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Jayne</surname><given-names>John T.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhang</surname><given-names>Yuzhong</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5431-5022</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhu</surname><given-names>Lei</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3919-3095</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6 aff7">
          <name><surname>Li</surname><given-names>Mei</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6 aff7">
          <name><surname>Zhou</surname><given-names>Zhen</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6 aff7">
          <name><surname>Cheng</surname><given-names>Chunlei</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8">
          <name><surname>Lv</surname><given-names>Yibing</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Wang</surname><given-names>Ying</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-7903-151X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Peng</surname><given-names>Wei</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Xu</surname><given-names>Xiaobin</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4321-9267</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff10">
          <name><surname>Lin</surname><given-names>Nan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff11">
          <name><surname>Wang</surname><given-names>Yuxuan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1649-6974</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff12">
          <name><surname>Wang</surname><given-names>Shuxiao</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9727-1963</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Munger</surname><given-names>J. William</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1042-8452</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Jacob</surname><given-names>Daniel J.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>McElroy</surname><given-names>Michael B.</given-names></name>
          <email>mbm@seas.harvard.edu</email>
        </contrib>
        <aff id="aff1"><label>1</label><institution>School of Engineering and Applied Sciences, Harvard University,
Cambridge, MA 02138, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>State Key Laboratory of Atmospheric Boundary Physics and Atmospheric
Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences,
Beijing 100029, China</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>College of Earth Sciences, University of Chinese Academy of Sciences,
Beijing 100049, China</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Center for Excellence in Regional Atmospheric Environment, Institute
of Urban Environment, <?xmltex \hack{\break}?>Chinese Academy of Sciences, Xiamen 361021, China</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Aerodyne Research, Inc., Billerica, MA 01821, USA</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Institute of Mass Spectrometer and Atmospheric Environment, Jinan
University, Guangzhou 510632, China</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>Guangdong Provincial Engineering Research Center for Online Source
Apportionment <?xmltex \hack{\break}?>System of Air Pollution, Guangzhou 510632, China</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>China National Environmental Monitoring Center, Beijing 100012, China</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>State Key Laboratory of Severe Weather &amp; Key Laboratory for
Atmospheric Chemistry of CMA, <?xmltex \hack{\break}?>Chinese Academy of Meteorological Sciences,
Beijing 100081, China</institution>
        </aff>
        <aff id="aff10"><label>10</label><institution>Department of Earth System Science, Tsinghua University, Beijing
100084, China</institution>
        </aff>
        <aff id="aff11"><label>11</label><institution>Department of Earth and Atmospheric Sciences, University of Houston,
Houston, TX 77004, USA</institution>
        </aff>
        <aff id="aff12"><label>12</label><institution>School of Environment, Tsinghua University, Beijing 100084, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Shaojie Song (songs@seas.harvard.edu), Yele Sun (sunyele@mail.iap.ac.cn), <?xmltex \hack{\break}?>and Michael B. McElroy (mbm@seas.harvard.edu)</corresp></author-notes><pub-date><day>1</day><month>February</month><year>2019</year></pub-date>
      
      <volume>19</volume>
      <issue>2</issue>
      <fpage>1357</fpage><lpage>1371</lpage>
      <history>
        <date date-type="received"><day>26</day><month>September</month><year>2018</year></date>
           <date date-type="rev-request"><day>4</day><month>October</month><year>2018</year></date>
           <date date-type="rev-recd"><day>12</day><month>January</month><year>2019</year></date>
           <date date-type="accepted"><day>19</day><month>January</month><year>2019</year></date>
      </history>
      <permissions>
        
        
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/.html">This article is available from https://acp.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/.pdf</self-uri>
      <abstract>
    <p id="d1e352">The chemical mechanisms responsible for rapid sulfate production, an important
driver of winter haze formation in northern China, remain unclear. Here, we
propose a potentially important heterogeneous hydroxymethanesulfonate (HMS)
chemical mechanism. Through analyzing field measurements with aerosol mass
spectrometry, we show evidence for a possible significant existence in haze
aerosols of organosulfur primarily as HMS, misidentified as sulfate in
previous observations. We estimate that HMS can account for up to about
one-third of the sulfate concentrations unexplained by current air quality
models. Heterogeneous production of HMS by <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and formaldehyde is
favored under northern China winter haze conditions due to high aerosol water
content, moderately acidic pH values, high gaseous precursor levels, and low
temperature. These analyses identify an unappreciated importance of
formaldehyde in secondary aerosol formation and call for more research on
sources and on the chemistry of formaldehyde in northern China winter.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e373">Severe haze episodes occur frequently in Beijing and throughout the North
China Plain (NCP), especially in winter, posing substantial threats to
public health (Ding et al., 2016; Fu and Chen, 2017; Gao et al., 2017).
High concentrations of fine particles and reduced visibility are associated
with stagnant meteorological conditions, i.e., shallow boundary layers, weak
winds, and high relative humidity (RH)<?pagebreak page1358?> (Wang et al., 2014a; Cai et al.,
2017; Tie et al., 2017). The rapid formation of particulate sulfate is
considered one of the key drivers of haze pollution for several reasons:
sulfate is an important component of fine particles; it facilitates the
partitioning of gaseous ammonia into the particle phase; and it enhances
aerosol water uptake, changing the optical and chemical properties of
aerosols (Guo et al., 2014; Huang et al., 2014). Sulfate is also known to
impact climate and acid deposition (Charlson et al., 1992; Xie et al.,
2015).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p id="d1e378">Relationship between sulfate <inline-formula><mml:math id="M2" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molar ratio and RH.
The circles indicate hourly observations during the 2014 winter in urban Beijing and are colored according to the observed <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (particles with
diameter less than 1 <inline-formula><mml:math id="M5" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>M) concentrations. The solid and dashed
curves represent, respectively, the exponential fitting between the observed
and modeled sulfate <inline-formula><mml:math id="M6" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> ratios and the observed RH, i.e.,
<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn mathvariant="normal">0.06</mml:mn><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula>) and
<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn mathvariant="normal">0.07</mml:mn><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula>). Sulfate concentrations are
obtained from HR-AMS <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> measurements, and the corresponding model
results are from WRF-Chem simulations.</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/1357/2019/acp-19-1357-2019-f01.png"/>

      </fig>

      <p id="d1e551">Most of the sulfate is of secondary origin, formed by the oxidation of
anthropogenic <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (He et al., 2018). The
exponential relationship between RH and the molar ratios of sulfate relative
to <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, as observed during the 2014 winter in Beijing (Fig. 1; see Sect. 2)
and in many previous studies (Sun et al., 2013; Zheng et al., 2015b; Wang
et al., 2016), imply that heterogeneous chemistry (processes involving
both gas and aerosol phases) plays an important role in the production of
sulfate. Indeed, air quality model simulations fail to capture the rapid
increase in sulfate from clean to hazy periods when considering only the
oxidation of <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the gas phase and in cloud/fog water, suggesting
missing heterogeneous sources of sulfate (Wang et al., 2014b; Zheng et
al., 2015a; Li et al., 2017a) (Fig. 1). Adding an apparent RH-dependent
heterogeneous uptake for <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> on aerosols greatly reduces the negative
bias in the modeled sulfate concentrations (see Sect. 2) (Wang et al.,
2014b; Zheng et al., 2015a).</p>
      <p id="d1e598">Several heterogeneous reaction pathways have been proposed (He et al.,
2014; Cheng et al., 2016; Wang et al., 2016; Li et al., 2017a; Hung et al.,
2018; Qin et al., 2018; Yu et al., 2018), including the oxidation of <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
aerosol water (by <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, transition-metal-catalyzed <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, or
<inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and on aerosol surfaces (by <inline-formula><mml:math id="M21" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and/or <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Their
relative importance for sulfate production in winter haze, however, is
unknown due to uncertainties in relevant reaction rates and estimates for
aerosol water pH values (most reaction pathways are pH-dependent) (Guo et
al., 2017b; Liu et al., 2017a; Li et al., 2018b; Wang et al., 2018; Zhao et
al., 2018). For example, Wang et al. (2016, 2018) found in laboratory
experiments that the rate for the oxidation of <inline-formula><mml:math id="M23" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> by <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> strongly
depended on the types of seed particles. In another example, Cheng et
al. (2016) suggested that reactions of <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> with <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in aerosol
water could be the source of missing sulfate given the neutralized feature
of haze aerosols (with a pH value of about 6 estimated with the ISORROPIA-II
thermodynamic equilibrium model). Guo et al. (2017b) argued that
the ISORROPIA-II calculation in Cheng et al. (2016) overestimated
aerosol water pH and that transition-metal-catalyzed <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> instead of
<inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> was the key oxidant of <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e752">Therefore, solution to the missing-sulfate problem (discrepancy between
observations and model results) in northern China winter haze remains
challenging and controversial. The term sulfate in the atmospheric chemistry
literature commonly refers to inorganic sulfate species. In addition to
inorganic sulfate, organosulfur compounds (OSs) have also been demonstrated
to be present in atmospheric aerosols, including organosulfates
(<inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">ROSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), sulfones
(<inline-formula><mml:math id="M31" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">RSO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msup><mml:mi mathvariant="normal">R</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>), and sulfonates
(<inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">RSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) such as methanesulfonate
(<inline-formula><mml:math id="M33" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
the deprotonated anion of methanesulfonic acid, MSA) and
hydroxyalkylsulfonates (<inline-formula><mml:math id="M34" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">RCH</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) (Eatough and
Hansen, 1984; Dixon and Aasen, 1999; Surratt et al., 2008; Tolocka and
Turpin, 2012; Sorooshian et al., 2015). OS may have been misidentified as
inorganic sulfate in previous ambient measurements, thus leading to a
positive observational bias (as described later). The formation of OS is
typically not included in air quality model simulations and thus can partly
explain the missing-sulfate problem if concentrations of these species are
appreciable. However, OS concentrations in northern China winter haze
aerosols have rarely been reported, and their formation mechanisms are also
unknown.</p>
      <p id="d1e836">In this study, we interpreted measurement data collected by a
high-resolution time-of-flight aerosol mass spectrometer (HR-AMS) and a
single-particle aerosol mass spectrometer (SPAMS) in Beijing winter. We
demonstrated the possible presence of OS in haze aerosols and discussed the
potential of different OS species. Hydroxymethanesulfonate (HMS,
<inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) was found to likely be the primary OS component. We found that heterogeneous production rate of
HMS through the reaction of formaldehyde (HCHO) and <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> was fast enough to
account for the identified OS by HR-AMS. Furthermore, we hypothesized that
HMS might lead to additional sulfate production through a mechanism
involving aqueous hydroxyl radicals (OH). Finally, we discussed the
implications of this heterogeneous HMS chemical<?pagebreak page1359?> mechanism for the missing-sulfate problem and also future research needs.</p>
</sec>
<sec id="Ch1.S2">
  <title>Methods</title>
<sec id="Ch1.S2.SS1">
  <title>Field measurements</title>
      <p id="d1e885">Aerosol and gaseous pollutants were measured in urban Beijing during winter
2014 (mid-November to mid-December) (Fig. S1 in the Supplement). Chemical
composition of non-refractory <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> was measured by a HR-AMS
(Aerodyne Research, Inc., USA). Individual particles (0.2–2 <inline-formula><mml:math id="M38" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m)
were detected by a SPAMS (Hexin Analytical Instrument Co., China). The gas
and aerosol collector ion chromatography (GAC-IC) system determined the
concentrations of semi-volatile gases (<inline-formula><mml:math id="M39" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and HCl),
and commercial analyzers were used to measure black carbon (AE33, Magee
Scientific, USA), gaseous HCHO (AL4021, Aero-Laser GmbH, Germany), and
<inline-formula><mml:math id="M41" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Thermo Fisher Scientific Inc., USA).
Meteorological data were also recorded. Details are provided below and in
Table S1 in the Supplement.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>HR-AMS measurements</title>
      <p id="d1e957">Particles were vaporized by impaction on a heated surface (600 <inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), and the resulting vapors were ionized by an electron impact ionization
source (70 eV) (DeCarlo et al., 2006; Sun et al., 2016). The positive
fragment ions generated were detected then using time-of-flight mass
spectrometry. The HR-AMS switched every 5 min between the mass-sensitive V mode (mass resolution of <inline-formula><mml:math id="M44" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2000) and the high-resolution W mode (mass resolution of <inline-formula><mml:math id="M45" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4500). A default
collection efficiency of 0.5 was assumed (Middlebrook et
al., 2012); because the mass fraction of ammonium nitrate was below 40 %,
the aerosol particles were moderately acidic (Song et
al., 2018), and a silica gel dryer was used to reduce RH in the sampling
line. The ionization efficiency calibrations were performed using pure
ammonium nitrate particles following Jayne et al. (2000),
and the default relative ionization efficiencies (RIEs), except for ammonium
that was calibrated by ammonium nitrate, were applied to all the chemical
species for mass quantifications. It is noted that the calibrated RIE values
of sulfate later in 2017 and 2018 ranged from 1.22 to 1.39 (unpublished
data), implying a possible overestimation of sulfate mass concentrations by
2 %–14 %. Mass concentrations of chemical components (ammonium,
sulfate, nitrate, chloride, and organics) and inorganic and organic
sulfur-containing fragment ions
(<inline-formula><mml:math id="M46" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) were
quantified with the standard data analysis software packages (Sueper
et al., 2018). These sulfur-containing ions were well separated
from adjacent peaks in the observed mass spectra and thus quantified with
high confidence (examples in Fig. S2). The uncertainty quantification of
chemical species followed Bahreini et al. (2009)
(details in Sect. S1 in the Supplement).</p>
<sec id="Ch1.S2.SS2.SSS1">
  <title>SPAMS measurements</title>
      <p id="d1e1032">The SPAMS (Li et al., 2011) was based on the same principle
as the ATOFMS (aerosol time-of-flight mass spectrometer) designed by
Prather et al. (1994). Ambient aerosol particles were introduced
and focused into a narrow beam using an aerodynamic lens. Particles passed
through two continuous 532 nm Nd:YAG lasers with velocities determined on
the basis of observed traveling times. The individual particles were
ionized using a 266 nm Nd:YAG laser, and both positive and negative ions
were generated and detected by bipolar time-of-flight mass spectrometry. The
Computational Continuation Core software framework based on MATLAB (The
MathWorks, Inc., USA) was used to analyze these ions. The negative ion peak
at <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">111</mml:mn></mml:mrow></mml:math></inline-formula> has been assigned to HMS
(<inline-formula><mml:math id="M50" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) with no significant
interference from other species in previous laboratory and field studies
(Lee et al., 2003; Whiteaker and Prather, 2003; Dall'Osto et al., 2009;
Zhang et al., 2012). HMS-containing particles were identified by the
presence of a peak at <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">111</mml:mn></mml:mrow></mml:math></inline-formula> with the absolute and relative peak areas
greater than 50 % and 0.5 %, respectively. The negative ion peaks at
<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">155</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">187</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">199</mml:mn></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">215</mml:mn></mml:mrow></mml:math></inline-formula> were also analyzed in order to detect
individual organosulfate species. This technique has been employed to
measure individual organosulfates in different regions around the world
(Hatch et al., 2011a; Wang et al., 2017).</p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <title>HCHO measurements</title>
      <p id="d1e1162">The AL4021 analyzer is based on the Hantzsch reaction (HCHO reacts with
acetylacetone and ammonia in aqueous solution to form <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">α</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-dimethyl-<inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-diacetyl-pyridine which is excited at 400 nm and fluoresces at 510 nm). The
Hantzsch reagents were prepared every 3 days and were kept cool in a
refrigerator. A Teflon filter was installed at the sampling inlet to remove
particles from the air. This analyzer was calibrated with 1 <inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>M HCHO
standard solution every 2 to 3 days during the field measurements. The
measurement uncertainty is <inline-formula><mml:math id="M61" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 %, and the detection limit is
<inline-formula><mml:math id="M62" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.15 ppb (Hak et al., 2005).</p>
</sec>
<sec id="Ch1.S2.SS2.SSS3">
  <title>GAC-IC measurements</title>
      <p id="d1e1222">Three semi-volatile gases (<inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and HCl) were measured with
a time resolution of 30 min. The instrument was modified based on the Steam
Jet Aerosol Collector (Khlystov et al., 1995) in order to
better apply to the heavily polluted conditions in China
(Dong et al., 2012). Gases were absorbed in a wet
annular denuder and quantified by ion chromatography analyzers.
Intercomparison experiments with filter sampling and other online methods
showed that the relative uncertainties in GAC-IC were within <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> %
for major species (Song et al., 2018).</p>
</sec>
</sec>
<?pagebreak page1360?><sec id="Ch1.S2.SS3">
  <title>Approaches to estimating OS and methanesulfonate with HR-AMS</title>
      <p id="d1e1264">OSs are primarily fragmented into separate organic ions
(<inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mi>z</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) and inorganic
sulfur-containing ions
(<inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) with minimal
organic sulfur-containing ions
(<inline-formula><mml:math id="M68" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>), due to the low thermal
stability of OS and thermal vaporization and electron ionization of HR-AMS
(Farmer et al., 2010; Huang et al., 2015; Hu et al., 2017a). The sulfate
concentrations obtained by the standard HR-AMS data analysis are contributed
not only by inorganic sulfate but also by OS. <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is
considered the dominant inorganic sulfate species in northern China winter
haze aerosols due to the relatively high <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> levels and the resulting
moderate particle acidity (Song et al., 2018). The presence of OS and its
contribution to the HR-AMS sulfate (considered as the total sulfate) may be
detectable using ratios between different <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
due to different fragmentation patterns of <inline-formula><mml:math id="M72" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and OS (Hu
et al., 2017a). For example, the major <inline-formula><mml:math id="M73" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
from <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> includes <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M78" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, while some of
these (<inline-formula><mml:math id="M81" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) are not
generated by HMS (Ge et al., 2012; Gilardoni et al., 2016). We observed in
Beijing winter that the six ratios of <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
(<inline-formula><mml:math id="M86" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> refers to <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M88" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) were highly correlated with each
other (<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.9</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) and that all of these ratios significantly
increased with RH and <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations (Figs. 2a, b and S3). From
the clean and dry conditions (average
<inline-formula><mml:math id="M93" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M94" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 10 <inline-formula><mml:math id="M95" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and RH <inline-formula><mml:math id="M97" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 20 %) to the
haze (polluted and humid) conditions (average
<inline-formula><mml:math id="M98" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M99" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 160 <inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M101" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and RH <inline-formula><mml:math id="M102" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 70 %), these
ion ratios increased by approximately 25 %–41 %. During clean and
dry periods, the observed ratios agreed well with values from pure
<inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> calibrations (Ge et al., 2012; Gilardoni et al., 2016;
Hu et al., 2017a), supporting the dominance of <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> over
other sulfur-containing compounds. The variations in <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> were unlikely to be due to changes in the acidity of
haze aerosols (a pH of about 4 to about 5 in both clean and haze conditions)
(Song et al., 2018), and no clear relationship was found between these
fragment ratios and the fraction of ammonium nitrate in haze aerosols (Chen
et al., 2018). Examples are given in Fig. S4.</p>
      <p id="d1e1914">The enhancements of <inline-formula><mml:math id="M107" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
under haze conditions may suggest the presence of additional sulfur
compounds, which should either not generate <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M110" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M111" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> ions or have higher ratios of
<inline-formula><mml:math id="M112" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M113" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
relative to <inline-formula><mml:math id="M114" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Since several types of OS (e.g.,
organosulfates and HMS) satisfy this requirement, the observed HR-AMS mass
spectra of inorganic sulfur-containing ions cannot be used to quantify the
speciation of OS but may allow an estimate of sulfate-equivalent OS
concentration (<inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M116" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>):<?xmltex \hack{\newpage}?>

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M118" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E1"><mml:mtd/><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>C</mml:mi><mml:mtext>OS</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:msub><mml:mfenced open="[" close=""><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mtext>obs</mml:mtext><mml:mo>+</mml:mo></mml:msubsup></mml:mrow><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mfenced open="" close="]"><mml:mrow><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

            where SO<inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mtext>obs</mml:mtext><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, SO<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mtext>2,obs</mml:mtext><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and
<inline-formula><mml:math id="M121" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M122" display="inline"><mml:mo mathsize="1.1em">(</mml:mo></mml:math></inline-formula><inline-formula><mml:math id="M123" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M124" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M125" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M126" display="inline"><mml:mo mathsize="1.1em">)</mml:mo></mml:math></inline-formula> are
concentrations of the observed inorganic sulfur-containing ions,
<inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are
molar masses, and <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> indicate the average
ratios of the two corresponding ions observed during the clean and dry
periods. <inline-formula><mml:math id="M132" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> is considered to be the concentration of
<inline-formula><mml:math id="M133" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> attributable to inorganic sulfate, and its difference to SO<inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mtext>obs</mml:mtext><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> represents the contribution of OS. The same applies to
<inline-formula><mml:math id="M135" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">cd</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">obs</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula>. This approach results in a conservative
estimate of <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> because (1) it is assumed that OS do not generate
<inline-formula><mml:math id="M137" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M139" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> ions and
(2) several minor ions (e.g., <inline-formula><mml:math id="M140" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">33</mml:mn></mml:msup></mml:math></inline-formula><inline-formula><mml:math id="M142" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
generated by OS fragmentation are not taken into account (Hu et al., 2017b).
The uncertainty quantification of <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is provided in Sect. S1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p id="d1e2804">Possible presence of OS in Beijing winter haze aerosols.
<bold>(a)</bold> <inline-formula><mml:math id="M144" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations (left, gray-shaded area) and RH
(right, blue line). <bold>(b)</bold> Contributions of OS to TS (left,
green-shaded area) and ratios of <inline-formula><mml:math id="M145" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">SO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M146" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (right,
black line). The ratios between the other inorganic sulfur-containing ions
are given in Fig. S3. <bold>(c)</bold> Sulfate-equivalent OS concentrations
(left, black line) and AWC (right, red line). The gray-shaded area in
<bold>(c)</bold> indicates the 1<inline-formula><mml:math id="M147" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> uncertainty range of OS concentrations
(on average <inline-formula><mml:math id="M148" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40 % during haze periods).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/1357/2019/acp-19-1357-2019-f02.png"/>

        </fig>

      <p id="d1e2880">The organic sulfur-containing ions <inline-formula><mml:math id="M149" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M150" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> were used as the signature fragments of
methanesulfonate (Ge et al., 2012). In our field measurements, an excellent
linear correlation (<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.98</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) was observed between these two
ions, and the average ratio of <inline-formula><mml:math id="M153" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> to
<inline-formula><mml:math id="M154" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (2.9 <inline-formula><mml:math id="M155" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1) was consistent with the value of
2.9 <inline-formula><mml:math id="M156" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.3 from the HR-AMS mass spectrum of pure MSA particles found in
previous studies (Ge et al., 2012; Huang et al., 2015, 2017), confirming the
presence of methanesulfonate in haze aerosols (Fig. S5). We estimated the
levels of methanesulfonate using the observed <inline-formula><mml:math id="M157" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and its
fraction in the total signal intensity of MSA standards identified in Huang
et al. (2017).</p>
</sec>
<sec id="Ch1.S2.SS4">
  <title>WRF-Chem air quality model simulation</title>
      <p id="d1e3018">The Weather Research and Forecasting model coupled with Chemistry (WRF-Chem;
version 3.5.1) (Grell et al., 2005) was adopted to simulate concentrations of
particulate sulfate and gas-phase HCHO during the 2014 winter
(November–December). Two nested domains were configured to cover East Asia,
and model results from the inner domain focused on northern China with a
horizontal resolution of about 27 km were used for analysis. The
meteorological initial and boundary conditions were obtained from the NCEP
FNL (Final) Operational Global Analysis (NCEP, 2000), and temperature,
moisture, and wind fields were nudged to constrain the accuracy of the
simulated meteorology. The chemical initial and boundary conditions were
provided from MOZART-4 global model simulations of trace gases and aerosols
(Emmons et al., 2010). The Lin microphysics scheme (Lin et<?pagebreak page1361?> al., 1983), Rapid
Radiative Transfer Model (Mlawer et al., 1997), Goddard shortwave radiation
scheme (Kim and Wang, 2011), Noah Land Surface Model (Chen and Dudhia, 2001),
and YSU planetary boundary layer scheme (Hong et al., 2006) were used for the
calculations of cloud microphysics, longwave radiation, shortwave radiation,
land surface, and boundary layer processes, respectively. The Carbon Bond
Mechanism version Z (CBM-Z) (Zaveri and Peters, 1999) gas-phase chemical
mechanism coupled with the thermodynamic module MOSAIC (Model for Simulating
Aerosol Interactions and Chemistry) (Zaveri et al., 2008) was applied to
simulate gas-phase reactions and aerosol processes.</p>
      <p id="d1e3021">Anthropogenic emissions were obtained from the MIX inventory (Li et al.,
2017b) for five sectors, namely power generation, industry, residential,
transportation, and agriculture, including the emissions of <inline-formula><mml:math id="M158" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M159" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, CO, non-methane volatile organic compounds (NMVOCs),
<inline-formula><mml:math id="M160" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and primary inorganic and organic particulate matters. In
addition, biogenic emissions were estimated using the Model of Emissions of
Gases and Aerosols from Nature (MEGAN) (Guenther et al., 2006), and open
biomass burning emissions were taken from the Global Fire Emissions Database
version 4 (GFEDv4) (Randerson et al., 2017). In the WRF-Chem model, sulfate
was formed by the oxidation of <inline-formula><mml:math id="M161" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> both in the gas phase (initiated by
OH) and in cloud/fog water (by dissolved <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and
transition-metal-catalyzed <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) (Pandis and Seinfeld, 1989):

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M165" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">HO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E4"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mover><mml:mo movablelimits="false">⟶</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Mn</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">Fe</mml:mi><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mover><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M166" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the sum of <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M168" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M169" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>.
We conducted two model
simulations: (1) a BASE scenario with normal settings and (2) a
5 <inline-formula><mml:math id="M170" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> EMIS scenario in which primary HCHO emissions from the
transportation sector were elevated by a factor of 5. This is because, as
described in Sect. 3, the BASE scenario
significantly underestimated ambient HCHO concentrations. It remains unclear
whether primary or secondary sources of HCHO are responsible for its high
wintertime levels. Jobson and colleagues have recently suggested that HCHO
emissions during motor vehicle cold starts, especially in cold winter, are
significantly underestimated in current inventories (Jobson et al., 2017).
Accordingly, a 5 <inline-formula><mml:math id="M171" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> EMIS scenario with increasing primary HCHO
emissions from transportation was conducted, which greatly reduces the
negative biases in the modeled HCHO and thus was used to calculate the
formation rate of HMS.</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page1362?><sec id="Ch1.S2.SS5">
  <title>Apparent heterogeneous sulfate production rate</title>
      <p id="d1e3425">An apparent heterogeneous uptake of <inline-formula><mml:math id="M172" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> on aerosols has been shown to
be able to compensate for the missing sulfate (<inline-formula><mml:math id="M173" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>) in
current air quality models during northern China winter haze episodes (Wang
et al., 2014b; Zheng et al., 2015a; Li et al., 2018b). The heterogeneous
sulfate production rate, <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, was parameterized with an uptake
coefficient <inline-formula><mml:math id="M175" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> (the fraction of gas–aerosol collisions resulting in
chemical reaction) (Jacob, 2000):
            <disp-formula id="Ch1.E6" content-type="numbered"><mml:math id="M176" display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mtext>g</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mo>/</mml:mo><mml:mi>v</mml:mi><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mtext>g</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the average aerosol droplet radius taken as
0.15 <inline-formula><mml:math id="M178" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m following Cheng et al. (2016), <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>g</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the
gas-phase diffusion coefficient of <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M181" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> is the average molecular
speed of <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the aerosol surface area per unit
volume of air, and <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mfenced close="]" open="["><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> is the gas-phase
concentration. <inline-formula><mml:math id="M185" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> is 2 <inline-formula><mml:math id="M186" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> when RH <inline-formula><mml:math id="M188" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 50 %
and increases linearly from 2 <inline-formula><mml:math id="M189" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M190" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to 5 <inline-formula><mml:math id="M191" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M192" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
when 50 % <inline-formula><mml:math id="M193" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> RH <inline-formula><mml:math id="M194" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 100 % (Zheng et al., 2015a), consistent
with other laboratory and model studies (Wang et al., 2016; Li et al.,
2017a). The heterogeneous reaction rate required to produce the identified OS
(<inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) can be expressed as
            <disp-formula id="Ch1.E7" content-type="numbered"><mml:math id="M196" display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>OS</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S2.SS6">
  <title>ISORROPIA-II thermodynamic equilibrium model calculation</title>
      <p id="d1e3791">We estimated aerosol water content (AWC), aerosol water pH, and ionic strength with the ISORROPIA-II
inorganic model (Fountoukis and Nenes, 2007) and also considered the
contribution of carbonaceous species. Detailed calculations were given in our
recent study (Song et al., 2018). Briefly, ISORROPIA-II predicts the phase
partitioning of an
<inline-formula><mml:math id="M197" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M198" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M199" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M200" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M201" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M202" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M203" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M204" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Cl</mml:mi><mml:mo>-</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-<inline-formula><mml:math id="M205" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
aerosol and semi-volatile gases (<inline-formula><mml:math id="M206" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M208" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">HCl</mml:mi></mml:mrow></mml:math></inline-formula>), and
can be used in either forward mode (the total (gas <inline-formula><mml:math id="M209" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> aerosol) concentration
of each species is fixed) or reverse mode (the aerosol concentration of each
species is fixed). The forward-mode results were adopted in this study, since
the reverse-mode calculations of pH are sensitive to aerosol composition
measurement errors and should be avoided. The model inputs were taken from
the HR-AMS (bulk <inline-formula><mml:math id="M210" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> composition) and GAC-IC (semi-volatile gas)
measurements except for crustal species that were estimated based on their
levels in <inline-formula><mml:math id="M211" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and typical size distributions (Song et al., 2018). The
inorganic aerosol phase state was assumed to be metastable, meaning that the
aqueous solution does not crystallize but remains supersaturated when the RH
is below the deliquescence RH, although aerosols may reside in a stable
state, meaning that the aqueous solution crystallizes once saturation is
exceeded (Rood et al., 1989). The assumed phase state led to a small
difference in pH (<inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> units on average) and an average
<inline-formula><mml:math id="M213" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 % difference in AWC (Song et al., 2018) and thus did not
affect the major conclusions of this study. The AWC modeled by ISORROPIA-II
has been shown to be in good agreement with those based on ambient
measurements in northern China (Wu et al., 2018). The validity of pH
calculations was supported by the reasonable agreement between the predicted
and observed gas-particle partitioning of semi-volatile species (Song et al.,
2018).</p>
      <p id="d1e3988">The aerosol water associated with carbonaceous species was estimated with
the hygroscopicity parameter <inline-formula><mml:math id="M214" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> (Cheng et al., 2016).
<inline-formula><mml:math id="M215" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values of 0.06 and 0.04 were used for organics and black carbon,
respectively (Song et al., 2018). The contribution of
carbonaceous species to AWC was found to be small (<inline-formula><mml:math id="M216" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 10 %),
leading to a minor effect on pH (<inline-formula><mml:math id="M217" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 0.05 unit). The ionic
strength of aerosol water was estimated using the predicted aerosol
composition and AWC (Herrmann, 2003). The uncertainty in pH was
estimated with a Monte Carlo approach accounting for measurement errors in
the model inputs including gas and aerosol species and meteorological
parameters. The 95 % confidence interval for calculated pH values was 4.1
to 5.5, very similar to the pH range found in previous northern China winter
haze studies (Song et al., 2018).</p>
</sec>
<sec id="Ch1.S2.SS7">
  <title>Kinetics and thermodynamics of HMS heterogeneous production</title>
      <p id="d1e4025">The chemical mechanism for HMS production can be expressed as
(Boyce and Hoffmann, 1984)

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M218" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E8"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>↔</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E9"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>↔</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M219" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E10"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mover><mml:mo movablelimits="false">⟷</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mover><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E11"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mrow><mml:mover><mml:mo movablelimits="false">⟷</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mover><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E12"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>↔</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E13"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mo>↔</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            <inline-formula><mml:math id="M220" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mi mathvariant="normal">H</mml:mi></mml:mrow></mml:math></inline-formula> (hydroxymethanesulfonic acid, HMSA) dissociates
twice to form <inline-formula><mml:math id="M221" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> with
the dissociation constants <inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula>,
respectively, and thus, in the pH range of this study, the adduct existed as
<inline-formula><mml:math id="M225" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. The acid catalysis of HMS production was
significant only at pH <inline-formula><mml:math id="M226" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 and thus irrelevant in the present context
(Olson and Hoffmann, 1989). It is noted that <inline-formula><mml:math id="M227" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> may
form salts by the neutralization reaction with ammonium or other cations
(e.g., <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M230" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and undergo precipitation when the
ambient RH becomes lower than the efflorescence RH value.</p>
      <?pagebreak page1363?><p id="d1e4548">The production of HMS in aerosol water was not found to be limited by the mass transfer
processes and hydration of HCHO (Sect. S2). The rate for the heterogeneous
production of HMS, <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (in sulfate-equivalent
<inline-formula><mml:math id="M232" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M233" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> h<inline-formula><mml:math id="M234" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), was calculated as

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M235" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E14"><mml:mtd/><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:mfenced open="[" close="]"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>⋅</mml:mo><mml:mfenced open="[" close="]"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">AWC</mml:mi></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were, respectively, the forward rate constants for
Eqs. (10) and (11), <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mfenced open="[" close="]"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> (defined as the sum
of <inline-formula><mml:math id="M239" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M240" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M241" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>) and
<inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:mfenced open="[" close="]"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> was aqueous-phase concentrations estimated
with their gas-phase levels and Henry's law constants. <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> represented the fractions of <inline-formula><mml:math id="M245" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M246" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> in <inline-formula><mml:math id="M247" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, respectively, and both were
functions of pH. The production of HMS was reversible and the equilibrium
constant <inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>eq</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> could be expressed as
            <disp-formula id="Ch1.E15" content-type="numbered"><mml:math id="M249" display="block"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>eq</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HMS</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>/</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mfenced close="]" open="["><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HMS</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mfenced close="]" open="["><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:mfenced close="]" open="["><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HMS</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> was the
aqueous-phase concentration of HMS. Because the time to reach the
equilibrium under winter haze conditions was typically greater than that for
haze formation, the precursors and HMS were usually not equilibrated
(Sect. S3). The relevant physical and chemical properties of <inline-formula><mml:math id="M251" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, HCHO, and
HMS are summarized in Tables S2 and S3.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results and discussion</title>
<sec id="Ch1.S3.SS1">
  <title>The presence of OS in Beijing winter haze aerosols</title>
      <p id="d1e4987">The standard HR-AMS data analysis usually does not distinguish OS from
inorganic sulfate, since OSs are fragmented primarily into separate organic
ions and inorganic sulfur-containing ions (Hu et al., 2017a). Using the
distinct fragmentation patterns of inorganic sulfur-containing ions in the
observed HR-AMS mass spectra, we derived a conservative estimate of total OS
concentrations (expressed in sulfate-equivalent <inline-formula><mml:math id="M252" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M253" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) in
<inline-formula><mml:math id="M254" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (particles with an aerodynamic diameter below 1 <inline-formula><mml:math id="M255" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>M),
as described in Sect. 2. During several winter haze periods (defined as
<inline-formula><mml:math id="M256" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M257" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 <inline-formula><mml:math id="M258" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M259" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), OSs were estimated to
contribute significantly to the total sulfate (TS) identified by the standard
HR-AMS data analysis, with an average <inline-formula><mml:math id="M260" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">OS</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">TS</mml:mi></mml:mrow></mml:math></inline-formula> ratio of 17 % <inline-formula><mml:math id="M261" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 7 %
and a maximum ratio of 31 % (Fig. 2a–b). Thus, previously reported
sulfate concentrations in Beijing winter haze aerosols from HR-AMS
measurements may have been biased high due to the presence of OS.</p>
      <p id="d1e5084">A good positive correlation (<inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.82</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) was found between
OS and the AWC (Fig. 2c) estimated on the basis of the ISORROPIA-II
thermodynamic equilibrium model constrained using in situ gas and aerosol
compositional and meteorological measurements (see Sect. 2), suggesting that
aerosol water serves as a medium enabling the production of OS. It has been
shown that <inline-formula><mml:math id="M264" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is in the liquid phase state during Beijing winter haze
periods (Liu et al., 2017b). In contrast, OSs were
unrelated to the presence or absence of cloud/fog events (Fig. S6),
indicating that the identified OSs were less likely formed by local cloud/fog
processing (Moch et al., 2018). Although our
interpretation of the HR-AMS fragmentation of inorganic sulfur-containing
ions cannot directly determine the speciation of OS (organosulfates,
sulfones, methanesulfonate, and hydroxyalkylsulfonates), we suggest, through
the following analyses, that HMS may be the major OS species in Beijing
winter haze aerosols.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Methanesulfonate, sulfones, and organosulfates are likely minor OS
species</title>
      <p id="d1e5128">The contribution of methanesulfonate to OS was only 2 %–8 % estimated
using <inline-formula><mml:math id="M265" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> as the characteristic fragment in the HR-AMS
mass spectra (see Sect. 2 and Fig. S5) (Huang et al., 2017). Its estimated
concentrations were comparable to those from a previous study (Yuan et al.,
2004). The methanesulfonate in Beijing winter is likely formed by the oxidation of dimethyl sulfite or dimethyl sulfoxide emitted from waste disposal (Yuan
et al., 2004). Aerosol water has been suggested to play important roles in
the formation of methanesulfonate and its condensation onto particles (Barnes
et al., 2006; Gaston et al., 2010).</p>
      <p id="d1e5149">The formation of bis-hydroxymethyl sulfone (<inline-formula><mml:math id="M266" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the only sulfone
that has been identified in ambient aerosols, is inhibited by atmospheric
water and is thus unlikely to be important in winter haze (Eatough and
Hansen, 1984). Organosulfates, formed through reactions of gaseous organics
(e.g., epoxides and aldehydes) and particulate inorganic sulfate, also seem
to represent minor contributions to OS based on the following evidence. The
most common organosulfates identified previously in ambient aerosols, such as
glycolic acid sulfate (<inline-formula><mml:math id="M267" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">6</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), 2-methylglyceric acid sulfate
(<inline-formula><mml:math id="M268" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">7</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), isoprene epoxydiols sulfate
(<inline-formula><mml:math id="M269" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">11</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">7</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), and benzyl (or methyl phenyl) sulfate
(<inline-formula><mml:math id="M270" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) (Froyd et al., 2010; Hatch et al., 2011a; Ma et al.,
2014), were not detected by SPAMS measurements taken in Beijing winter.
The production of organosulfates is enhanced by increased aerosol acidity
(Surratt et al., 2010; Hatch et al., 2011b; Riva et al., 2016), whereas the
relatively high pH values of about 4 to about 5 for winter haze aerosols in
northern China may represent a limiting factor (Song et al., 2018).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><caption><p id="d1e5267">Production and existence of HMS in Beijing winter haze aerosols.
<bold>(a)</bold> Schematic of heterogeneous HMS chemistry in northern China
winter haze. <bold>(b)</bold> <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (left, red line) and OS
concentrations (right, black line). <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was only available for a
haze episode in December 2014 due to instrumentation constraints.
<bold>(c)</bold> Gas-phase concentrations of observed <inline-formula><mml:math id="M273" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (left, black
line) and modeled HCHO (right, blue line). <bold>(d)</bold> <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
(left, pink-shaded area) and <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (right, black line). The
pink-shaded area shows the uncertainty in <inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> due to the
estimated range of pH (4.1–5.5). The inserted figure indicates the linear
correlation of <inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> at a pH of 5.5.</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/1357/2019/acp-19-1357-2019-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <title>HMS is likely the major OS species</title>
      <p id="d1e5384">Since the only known source of HMS (<inline-formula><mml:math id="M279" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) is the
nucleophilic addition of <inline-formula><mml:math id="M280" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M281" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> to HCHO in aqueous
solutions (Boyce and Hoffmann, 1984) (Fig. 3a; see Sect. 2), the
dominance of HMS in OS can explain the excellent correlation found between OS
and AWC (Fig. 2c). The other hydroxyalkylsulfonate species are estimated to
be less important than HMS, according to the laboratory experimental data
from Hoffmann and colleagues (Olson and<?pagebreak page1364?> Hoffmann, 1989) and the
abundance of different aldehydes in the atmosphere (Sect. S3).</p>
      <p id="d1e5440">Mass concentrations of HMS have been observed to be low, on the order of
0.01 <inline-formula><mml:math id="M282" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M283" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, during several field campaigns in the United
States, Germany, and Japan (Dixon and Aasen, 1999; Suzuki et al., 2001;
Scheinhardt et al., 2014). However, the heterogeneous production of HMS can be
fast during winter haze periods in northern China because of a moderately
acidic pH of aerosol water, high AWC, high precursor (<inline-formula><mml:math id="M284" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and HCHO)
concentrations, and low temperature. First, laboratory experiments have
indicated that HMS production rates increase rapidly with pH, responding
mainly to the dependence of <inline-formula><mml:math id="M285" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> (a more efficient nucleophile than
<inline-formula><mml:math id="M286" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) on pH (Boyce and Hoffmann, 1984; Kok et al., 1986). Values of
aerosol water pH of about 4 to 5 obtained during the NCP winter haze events
(Song et al., 2018) are 2 to 3 units higher than typically found in North
America and Europe (Guo et al., 2017a), implying a factor of <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> enhancement in HMS production rates. Second, the AWC during winter
haze periods (on the order of 100 <inline-formula><mml:math id="M288" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math id="M289" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) is among the highest
in the world (Nguyen et al., 2016), providing a reactor to facilitate aqueous reactions. Third, concentrations of both precursor gases are
relatively high. Gaseous HCHO has been measured to be about 6 ppb on average
in Beijing winter and increases on haze days (Rao et al., 2016). Although
emissions of <inline-formula><mml:math id="M290" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> have rapidly declined, especially since the implementation of the National Air Pollution Prevention and Control Action
Plan in 2013, its concentrations in the NCP remain much higher than in many
other parts of the world (Shao et al., 2018). Last, low temperature in winter
increases the solubility of precursor gases in water (Sander, 2015) and thus
enhances HMS production rates. The reaction rate constants for HMS production
decrease at low temperature but to a lesser extent (Boyce and Hoffmann, 1984).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p id="d1e5548">Comparison of modeled and observed HCHO concentrations.
<bold>(a)</bold> BASE scenario. <bold>(b)</bold> 5 <inline-formula><mml:math id="M291" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> EMIS scenario. The dots
are colored according to <inline-formula><mml:math id="M292" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations. Model results from
WRF-Chem are shown.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/19/1357/2019/acp-19-1357-2019-f04.png"/>

        </fig>

      <?pagebreak page1365?><p id="d1e5581">In order to evaluate whether HMS production was fast enough to account for
the identified OS, we calculated the rate for HMS production in aerosol water
(<inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and compared this with the apparent heterogeneous reaction
rate that would be required to produce the identified OS (<inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). As
described in Sect. 2, <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculations involved concentrations
of gaseous <inline-formula><mml:math id="M296" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and HCHO (Fig. 3c), Henry's law constants, AWC and pH
(95 % confidence interval: 4.1–5.5), and reaction rate constants from
laboratory experiments. HCHO concentrations simulated by the WRF-Chem air
quality model (5 <inline-formula><mml:math id="M297" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> EMIS scenario; see Sect. 2) were used because its
measurements were available only in December. The modeled HCHO was well
correlated with its measured values (<inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) but was biased
low by <inline-formula><mml:math id="M300" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 % (Fig. 4). <inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was most sensitive to
particle acidity and increased rapidly with pH, becoming comparable to
<inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> when using the upper limit of pH (5.5) (Fig. 3d).
<inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculated here was expected to be conservative. Henry's law
constants and kinetic data were obtained in relatively dilute solutions,
while aerosol water constitutes a concentrated electrolyte solution. The high
ionic strength of aerosol water (<inline-formula><mml:math id="M304" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 11 M during haze periods) may
strongly increase formaldehyde solubility (Toda et al., 2014) and may further
enhance kinetic rates for HMS production (Sect. S4). Gaseous HCHO
concentrations used in the calculations were also biased low. It is very
likely that the actual <inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was comparable to <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>OS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> at a
pH below 5.5, within the uncertainty range of the calculated aerosol water
pH. Note that the production of HMS was a minor sink of HCHO because the
corresponding lifetime of <inline-formula><mml:math id="M307" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4 days was greater than that
of photolysis and oxidation by OH (<inline-formula><mml:math id="M308" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 1 day in Beijing winter).</p>
      <p id="d1e5745">Our field measurements with SPAMS confirmed the existence of HMS in winter
haze aerosols (Fig. 3b). Individual particles containing HMS were identified
by the characteristic mass-to-charge ratio <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">111</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M311" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
in the SPAMS mass spectra (Whiteaker and Prather, 2003). The
observed number concentration of HMS-containing particles (<inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was
closely correlated with AWC (<inline-formula><mml:math id="M313" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.86</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>), supporting the
production of HMS in aerosol droplets. A good relationship was also found
between <inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the identified OS from HR-AMS (Fig. 3b). Although the
SPAMS data showed a significant percentage (<inline-formula><mml:math id="M316" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 10 % during haze
periods) of HMS-containing particles in the total particle counts, a
quantitative estimate of HMS mass concentration is not available here because
HMS may be fragmented into smaller ions, such as <inline-formula><mml:math id="M317" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M318" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
depending on the countercations in particles (i.e., matrix effects) (Neubauer
et al., 1997; Whiteaker and Prather, 2003). These ions coexist with the HMS
peak in the SPAMS mass spectra (Fig. S7).</p>
</sec>
<sec id="Ch1.S3.SS4">
  <title>Implications of heterogeneous HMS chemistry</title>
      <p id="d1e5880">We have shown above in Beijing winter haze aerosols that a significant
fraction of the missing sulfate based on HR-AMS measurements may be
attributed to OSs, which likely exist primarily as HMS and are misidentified
as inorganic sulfate by the standard HR-AMS data analysis. If HMS is assumed
to represent the only OS compound, we estimated that it may account for about
one-third of the missing sulfate in Beijing winter haze aerosols (Fig. S8).
Interestingly, HMS would also likely be misidentified as inorganic sulfate
(<inline-formula><mml:math id="M319" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>) with typical ion chromatography (IC) analysis, another
common method used to determine aerosol chemical compositions. In fact,
nearly all of the particulate sulfate measurements in northern China winter
haze have been made using these two techniques (He et al., 2014, 2018; Cheng
et al., 2016; Wang et al., 2016; Li et al., 2017a). For anion detection in
IC, the pH of the carrier fluid (known as eluent, a solution of KOH, NaOH,
NaHC<inline-formula><mml:math id="M320" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, etc.) is usually greater than 9 (Wang et al., 2005; Cao et
al., 2012; Liu et al., 2016; Han et al., 2017). HMS is unstable under such an
alkaline environment and dissociates rapidly into <inline-formula><mml:math id="M321" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> and HCHO
(Seinfeld and Pandis, 2016):
            <disp-formula id="Ch1.E16" content-type="numbered"><mml:math id="M322" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The characteristic time for HMS dissociation at pH <inline-formula><mml:math id="M323" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 9 is less
than 1 min (Seinfeld and Pandis, 2016), much less than the retention
time of <inline-formula><mml:math id="M324" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>. The product <inline-formula><mml:math id="M325" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> can be rapidly oxidized to
<inline-formula><mml:math id="M326" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> by oxidants (e.g., <inline-formula><mml:math id="M327" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M328" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) either
generated or dissolved in aqueous extracts.</p>
      <p id="d1e6070">As described in Sect. 2.6, HMS should exist as the <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>
anion in wet aerosols and may form salts with ammonium or other cations when
aerosol particles dry out. A possible fate of HMS is to be oxidized by
aqueous OH radicals producing peroxysulfate radicals
(<inline-formula><mml:math id="M330" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">5</mml:mn><mml:mrow><mml:mi class="Radical" mathvariant="normal">⚫</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>)
(HMS is resistant to <inline-formula><mml:math id="M331" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M332" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) (Olson and
Fessenden, 1992):
            <disp-formula id="Ch1.E17" content-type="numbered"><mml:math id="M333" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mi mathvariant="normal">HCHO</mml:mi><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">5</mml:mn><mml:mrow><mml:mi class="Radical" mathvariant="normal">⚫</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          <inline-formula><mml:math id="M334" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">5</mml:mn><mml:mrow><mml:mi class="Radical" mathvariant="normal">⚫</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> is an intermediate in the free-radical chain
reactions oxidizing <inline-formula><mml:math id="M335" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M336" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>, and for each attack of
OH on HMS, multiple <inline-formula><mml:math id="M337" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> ions are produced (Fig. S9).
Importantly, an HCHO molecule is released by Eq. (17), suggesting that this
reaction pathway does not result in net consumption of HCHO and that HMS
serves as a temporary reservoir of tetravalent sulfur. We speculate from the
diurnal patterns of HMS production rates (<inline-formula><mml:math id="M338" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">HMS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the
identified OS concentrations that the oxidation of HMS by OH is likely to
occur during daytime (Tan et al., 2018) (Fig. S9). But the rate of Eq. (17)
should be relatively slow when compared with that of Eqs. (10)–(11) because
a significant level of HMS is expected to reside in the haze aerosol
particles. A quantitative rate estimation for this pathway, however, is
difficult because aqueous OH is short-lived and it can be derived as a result
of uptake from the gas phase or be generated or scavenged in the condensed
phase (Jacob, 1986; Ervens et al., 2014).</p>
</sec>
<?pagebreak page1366?><sec id="Ch1.S3.SS5">
  <title>Future research needs</title>
      <p id="d1e6285">This study points to a potentially important role of heterogeneous HMS
chemistry in explaining the missing-sulfate problem during Beijing winter
haze episodes. HMS has also been suggested to promote new particle formation
by stabilizing sulfuric acid clusters (Li et al., 2018a). Although our field
measurements and data interpretation focus on Beijing, this chemical
mechanism should be important throughout the NCP because winter haze
pollution is regional, as indicated by the distribution of <inline-formula><mml:math id="M339" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
HCHO (Fig. S10). Different from many other proposed pathways for sulfate
production, HMS chemistry has a characteristic reaction product. More
accurate quantification of HMS (e.g., using capillary electrophoresis and ion
pairing chromatography; Munger et al., 1986; Scheinhardt et al., 2014) in
future field studies is essential to improve our understanding of this
mechanism. In addition, three-dimensional chemical transport model studies
should be conducted to further explore the HMS formation pathways and the
associated uncertainties (e.g., pH values). The modeling simulations may also
demonstrate whether significant amounts of HMS can be formed in cloud
droplets before being transported to the ground level (Eck et al., 2012; Li
et al., 2014). This study reveals the unappreciated role of HCHO in Chinese
haze through forming the complex HMS with <inline-formula><mml:math id="M340" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and it should be noted
that HCHO also serves as a critical source of <inline-formula><mml:math id="M341" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HO</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
(OH <inline-formula><mml:math id="M342" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M343" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) radicals by photolysis (Rao et al., 2016) and as a
carcinogen (Zhu et al., 2017). In spite of its importance, our knowledge of
the sources and chemical processes of HCHO during northern China winter haze
events remains limited. Further research should be conducted to elucidate
HCHO sources in the northern China winter and to design targeted mitigation
measures.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Summary</title>
      <p id="d1e6346">Combining field measurements and model calculations, we propose a potentially
important chemical mechanism, heterogeneous HMS chemistry, for secondary
aerosol formation during northern China winter haze episodes. This mechanism
involves the production of HMS by HCHO and <inline-formula><mml:math id="M344" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in aerosol water,
which is favored under northern China winter haze conditions due to several
factors, including high aerosol water content, a moderately acidic pH, high
gaseous precursor levels, and low temperature. More field, laboratory, and
modeling studies are needed in order to elucidate this chemical mechanism and
to better understand the emission sources and atmospheric chemical processes
impacting HCHO under winter haze conditions.</p><?xmltex \hack{\newpage}?>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p id="d1e6366">All data supporting this study are available in this
article and its Supplement or from the corresponding authors upon
request.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e6369">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-19-1357-2019-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-19-1357-2019-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution">

      <p id="d1e6378">SS, YS, and MBM designed and led the study. YS, WX,
DRW, and JTJ contributed to HR-AMS measurement and data analysis. ML, ZZ, CC,
YB, and YL collected and analyzed SPAMS measurement data. YW, WP, and XX performed
HCHO measurements. MG, NL, YW, and SW provided air quality model results. YZ, LZ,
JWM, and DJ contributed to data interpretation. SS wrote the paper with input from all
co-authors.</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e6384">The authors declare that they have no conflict of
interest.</p>
  </notes><notes notes-type="sistatement">

      <p id="d1e6390">This article is part of the special issue “Multiphase chemistry
of secondary aerosol formation under severe haze”. It is not associated with
a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e6396">This work was supported by the Harvard Global Institute and the National
Natural Science Foundation of China (91744207, 21607056, 41175114, and
21625701). SPAMS measurements were also funded by the Guangdong Province
Public Interest Research and Capacity Building Special Fund
(2014B020216005). We thank Jing Cai, Xing Chang, Yunle Chen, Michael Hoffmann,
Lyatt Jaeglé, Lijie Li, Chris P. Nielsen, Viral Shah, Jingyuan Shao, Yu Song, Jay Turner, and Mei Zheng for helpful discussions.
<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: Aijun Ding<?xmltex \hack{\newline}?>
Reviewed by: Jeffrey Collett and one anonymous referee</p></ack><ref-list>
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    <!--<article-title-html>Possible heterogeneous chemistry of hydroxymethanesulfonate (HMS) in northern China winter haze</article-title-html>
<abstract-html><p>The chemical mechanisms responsible for rapid sulfate production, an important
driver of winter haze formation in northern China, remain unclear. Here, we
propose a potentially important heterogeneous hydroxymethanesulfonate (HMS)
chemical mechanism. Through analyzing field measurements with aerosol mass
spectrometry, we show evidence for a possible significant existence in haze
aerosols of organosulfur primarily as HMS, misidentified as sulfate in
previous observations. We estimate that HMS can account for up to about
one-third of the sulfate concentrations unexplained by current air quality
models. Heterogeneous production of HMS by SO<sub>2</sub> and formaldehyde is
favored under northern China winter haze conditions due to high aerosol water
content, moderately acidic pH values, high gaseous precursor levels, and low
temperature. These analyses identify an unappreciated importance of
formaldehyde in secondary aerosol formation and call for more research on
sources and on the chemistry of formaldehyde in northern China winter.</p></abstract-html>
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