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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0">
  <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-20-12795-2020</article-id><title-group><article-title>Improved inversion of aerosol components in the atmospheric column from remote sensing data</article-title><alt-title>Improved inversion of aerosol components in the atmospheric column</alt-title>
      </title-group><?xmltex \runningtitle{Improved inversion of aerosol components in the atmospheric column}?><?xmltex \runningauthor{Y. Zhang et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhang</surname><given-names>Ying</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Li</surname><given-names>Zhengqiang</given-names></name>
          <email>lizq@radi.ac.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Chen</surname><given-names>Yu</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff3">
          <name><surname>de Leeuw</surname><given-names>Gerrit</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1649-6333</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhang</surname><given-names>Chi</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Xie</surname><given-names>Yisong</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Li</surname><given-names>Kaitao</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2610-0064</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Aerospace Information Research Institute, Chinese Academy of Sciences,
Beijing 100101, China</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Public Meteorological Service Center, China Meteorological
Administration, Beijing 100081, China</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>R&amp;D Satellite
Observations, Royal Netherlands Meteorological Institute (KNMI), 3730AE De Bilt, the Netherlands</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Zhengqiang Li (lizq@radi.ac.cn)</corresp></author-notes><pub-date><day>4</day><month>November</month><year>2020</year></pub-date>
      
      <volume>20</volume>
      <issue>21</issue>
      <fpage>12795</fpage><lpage>12811</lpage>
      <history>
        <date date-type="received"><day>18</day><month>November</month><year>2019</year></date>
           <date date-type="rev-request"><day>22</day><month>January</month><year>2020</year></date>
           <date date-type="rev-recd"><day>10</day><month>August</month><year>2020</year></date>
           <date date-type="accepted"><day>23</day><month>September</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2020 </copyright-statement>
        <copyright-year>2020</copyright-year>
      <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><title>Abstract</title>
    <p id="d1e148">Knowledge of the composition of atmospheric aerosols is important
for reducing uncertainty in climate assessment. In this study, an
improved algorithm is developed for the retrieval of atmospheric columnar
aerosol components from optical remote sensing data. This is achieved by
using the complex refractive index (CRI) of a multicomponent liquid system
in the forward model and minimizing the differences with the observations.
The aerosol components in this algorithm comprise five species, combining
eight subcomponents including black carbon (BC), water-soluble organic matter (WSOM) and
water-insoluble organic matter (WIOM), ammonium nitrate (AN), sodium
chloride (SC), dust-like content (DU), and aerosol water content in the fine and
coarse modes (AW<inline-formula><mml:math id="M1" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> and AW<inline-formula><mml:math id="M2" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>). The calculation of the CRI in the
multicomponent liquid system allows for the separation of the water-soluble components
(AN, WSOM and AW<inline-formula><mml:math id="M3" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula>) in the fine mode and SC and AW<inline-formula><mml:math id="M4" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> in the
coarse mode. The uncertainty in the retrieval results is analyzed based on
the simulation of typical models, showing that the complex refractive index
obtained from instantaneous optical–physical inversion compares well with
that obtained from chemical estimation. The algorithm was used to retrieve
the columnar aerosol components over China using the ground-based remote
sensing measurements from the Sun–sky radiometer Observation NETwork (SONET)
in the period from 2010 to 2016. The results were used to analyze the
regional distribution and interannual variation. The analysis shows that the
atmospheric columnar DU component is dominant in the northern region of
China, whereas the AW is higher in the southern coastal region. The SC
component retrieved over the desert in northwest China originates from a
paleomarine source. The AN significantly decreased from 2011 to 2016, by
21.9 mg m<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, which is inseparable from China's environmental control
policies.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e208">Atmospheric aerosol consists of a suspension of solid and/or liquid
particles in the air. The chemical composition and mixing state of the
aerosol particles affect their optical characteristics, which in turn
influence the energy budget of the Earth–atmosphere system and thus climate
(Boucher et al., 2013).</p>
      <p id="d1e211">To measure aerosol composition, many methods are used including online
analysis in the field, sample analysis in the laboratory and remote sensing
estimation. Each technique provides information on the aerosol
composition which may differ in content and detail. Because of fast
observation and low cost, the application of remote sensing techniques to
estimate aerosol composition has developed rapidly since 2000. Satheesh and Srinivasan (2002), Satheesh et
al. (1999, 2002), and Satheesh and Krishna (2005) established an algorithm for the inversion of
aerosol components from remote sensing data based on the hypothesis of
external mixing and assuming fixed size distributions for each component.
But an external mixture usually cannot accurately describe the natural state
of aerosols. Even if the particles are individually pure when first
produced, numerous processes in the atmosphere will convert an external
mixture to an internal mixture (Lesins et al., 2002). Therefore, internal-mixing hypotheses are widely used and multiple approaches have been
developed (e.g., Schuster et al., 2005, 2009, 2016; Arola et al.,<?pagebreak page12796?> 2011; Z. Li et al., 2013; L. Li et al., 2019; Wang et al., 2013; van Beelen et al., 2014; Zhang et al.,
2018). Schuster et al. (2005) determined the volume fraction of black carbon
in an internal mixture with water and a soluble component by fitting the
calculated complex refractive index to retrieved AERONET values at all four
available wavelengths. In a follow-up study, Schuster et al. (2009) applied
a similar procedure to determine the aerosol water fraction by fitting the
real part of the refractive index of an internal mixture of water and soluble
and insoluble species to observations by minimizing the cost function at all
four wavelengths together. In this work the ratio of the dry volume fraction
of insoluble aerosols to that of soluble aerosols was constrained by using a
climatological value and the real refractive index which also prescribes the
aerosol hygroscopicity. This constraint also provides a maximum insoluble
fraction and the fraction of dust aerosol. Brown carbon was further
estimated by Arola et al. (2011) due to the large change in its absorbing
characteristics with wavelength for wavelengths smaller than 550 nm, but the
dust component was ignored in this study. Aerosol bimodal characteristics
were used by Schuster et al. (2016) to estimate the aerosol-absorbing
components including BC, brown carbon and hematite in the fine and coarse
modes. This method was also embedded in the GRASP (Generalized Retrieval of
Aerosol and Surface Properties; Dubovik et al., 2011) system by L. Li et al. (2019) for application to POLDER PARASOL observations. The above algorithms
are aimed at retrieving absorbing aerosol components, such as BC, brown
carbon and iron oxides, but have only simple treatment for scattering
components, especially the host of multicomponent liquids.</p>
      <p id="d1e214">Van Beelen et al. (2014) introduced water-soluble organic matter (WSOM) in
the inversion process based on the hygroscopicity of the organic matter (OM) mixture, but in
this study water-insoluble organic matter (WIOM) was not accounted for. Some
studies separated the OM based only on the spectral changes (Xie et al.,
2017; Choi and Ghim, 2016), leading to large uncertainty in the results.
Zhang et al. (2018) simultaneously retrieved the WSOM and WIOM components
but ignored the error in the refractive index introduced by the aerosol
volume averaging method applied to the multicomponent liquid system. For
other nonabsorbing components, the water content and inorganic components
in the fine mode are identified by the difference in hygroscopic growth
between organic and inorganic matter (Zhang et al., 2018; van Beelen et al.,
2014). In the coarse mode, sea salt is identified by the aerosol sphericity
in the study of Xie et al. (2017), but this parameter is difficult to
observe.</p>
      <p id="d1e217">Although the retrieval of aerosol components by using remote sensing methods
has been greatly developed, the application of hygroscopicity to identify
the weak and nonabsorbing components in a multicomponent liquid system
remains difficult. In the current study, hygroscopicity is introduced to
solve for the refractive index in a multicomponent liquid system. The
results are used in the algorithm to retrieve aerosol components from data
obtained from the ground-based remote sensing network SONET (Sun–sky radiometer Observation NETwork; Li et al., 2018). The data and method are described in Sects. 2 and 3, respectively.
The results for the aerosol components are presented and analyzed in Sect. 4, and we conclude this study in Sect. 5.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Measurements</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Sun–sky radiometer</title>
      <p id="d1e235">The multiwavelength polarized sun–sky radiometer CE318-DP manufactured by
Cimel Electronique in France, as an accurate instrument designed for
long-term continuous observations in the field, can automatically measure
solar and sky radiation. It consists of an optical head, a control box and a
biaxial stepping-motor system. The optical head has two views: one for
direct solar radiation with no focusing lens and the other for sky radiation
with a focusing lens. The internal optical system consists of a spectral and a
polarizing filter to measure radiation in different wavebands with
polarization directions. The nine wavebands vary from visible to near-infrared wavelengths (340, 380, 440, 500, 675, 870, 936, 1020, 1640 nm) with a full
width at half maximum of 10 nm. All bands provide both radiation and
polarization measurements, except the 936 nm band which only measures
radiation to determine the columnar water vapor. These radiation and
polarization measurements can provide sufficient information to calculate
the columnar aerosol optical depth (AOD) and further retrieve the aerosol
microphysical parameters.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>SONET</title>
      <p id="d1e246">The Sun–sky radiometer Observation NETwork (SONET) is a local observation
network in China for ground-based remote sensing measurements of aerosol
properties (Li et al., 2018). At present, there are 16 long-term observation
sites in China, which are evenly distributed over northern, southern and northwest China and the Tibetan Plateau (Fig. 1). The longest time series
is provided by the Beijing station, which was established in 2009. Five more
stations joined in 2011 and 2012, and the network has been gradually growing
to its current size. The geographical and topographical features of the
long-term sites, such as plateau, desert, hill, plain and
island, are diverse, including three megacities, three islands and one plateau site
(Table 1). SONET data provide sufficient variability, as regards length of
time series, spatial coverage, climatic and topographic features, and aerosol
properties, for the analysis of atmospheric aerosol characteristics across
China.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e252">SONET sites (name, location and geographical aspects) and
meteorological stations used in this study.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.92}[.92]?><oasis:tgroup cols="12">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right" colsep="1"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:colspec colnum="12" colname="col12" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col6" align="center" colsep="1">SONET site </oasis:entry>
         <oasis:entry namest="col7" nameend="col10" align="center">Meteorological station </oasis:entry>
         <oasis:entry colname="col11">Geographical feature</oasis:entry>
         <oasis:entry colname="col12">Geographical region</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Abbr</oasis:entry>
         <oasis:entry colname="col3">Long</oasis:entry>
         <oasis:entry colname="col4">Lat</oasis:entry>
         <oasis:entry colname="col5">Alt</oasis:entry>
         <oasis:entry colname="col6">Obs. period</oasis:entry>
         <oasis:entry colname="col7">No.<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">Long</oasis:entry>
         <oasis:entry colname="col9">Lat</oasis:entry>
         <oasis:entry colname="col10">Alt</oasis:entry>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">(<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">(<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">(m)</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8">(<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col9">(<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col10">(m)</oasis:entry>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Lhasa</oasis:entry>
         <oasis:entry colname="col2">LS</oasis:entry>
         <oasis:entry colname="col3">91.2</oasis:entry>
         <oasis:entry colname="col4">29.6</oasis:entry>
         <oasis:entry colname="col5">3678</oasis:entry>
         <oasis:entry colname="col6">Mar 2016–</oasis:entry>
         <oasis:entry colname="col7">55591</oasis:entry>
         <oasis:entry colname="col8">91.1</oasis:entry>
         <oasis:entry colname="col9">29.7</oasis:entry>
         <oasis:entry colname="col10">3649</oasis:entry>
         <oasis:entry colname="col11">Plateau</oasis:entry>
         <oasis:entry colname="col12">Qinghai–</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">May 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12">Tibet</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Kashgar</oasis:entry>
         <oasis:entry colname="col2">KS</oasis:entry>
         <oasis:entry colname="col3">75.9</oasis:entry>
         <oasis:entry colname="col4">39.5</oasis:entry>
         <oasis:entry colname="col5">1320</oasis:entry>
         <oasis:entry colname="col6">Sep 2013–</oasis:entry>
         <oasis:entry colname="col7">51709</oasis:entry>
         <oasis:entry colname="col8">76.0</oasis:entry>
         <oasis:entry colname="col9">39.5</oasis:entry>
         <oasis:entry colname="col10">1289</oasis:entry>
         <oasis:entry colname="col11">Desert</oasis:entry>
         <oasis:entry colname="col12">Northwest</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Zhangye</oasis:entry>
         <oasis:entry colname="col2">ZY</oasis:entry>
         <oasis:entry colname="col3">100.3</oasis:entry>
         <oasis:entry colname="col4">38.8</oasis:entry>
         <oasis:entry colname="col5">1364</oasis:entry>
         <oasis:entry colname="col6">Aug 2012–</oasis:entry>
         <oasis:entry colname="col7">52652</oasis:entry>
         <oasis:entry colname="col8">100.4</oasis:entry>
         <oasis:entry colname="col9">38.9</oasis:entry>
         <oasis:entry colname="col10">1483</oasis:entry>
         <oasis:entry colname="col11">Desert</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Oct 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Minqin</oasis:entry>
         <oasis:entry colname="col2">MQ</oasis:entry>
         <oasis:entry colname="col3">103.0</oasis:entry>
         <oasis:entry colname="col4">38.6</oasis:entry>
         <oasis:entry colname="col5">1589</oasis:entry>
         <oasis:entry colname="col6">Feb 2012–</oasis:entry>
         <oasis:entry colname="col7">52681</oasis:entry>
         <oasis:entry colname="col8">103.1</oasis:entry>
         <oasis:entry colname="col9">38.6</oasis:entry>
         <oasis:entry colname="col10">1368</oasis:entry>
         <oasis:entry colname="col11">Desert and hill</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Oct 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Xi'an</oasis:entry>
         <oasis:entry colname="col2">XA</oasis:entry>
         <oasis:entry colname="col3">108.9</oasis:entry>
         <oasis:entry colname="col4">34.2</oasis:entry>
         <oasis:entry colname="col5">389</oasis:entry>
         <oasis:entry colname="col6">May 2012–</oasis:entry>
         <oasis:entry colname="col7">57039</oasis:entry>
         <oasis:entry colname="col8">108.9</oasis:entry>
         <oasis:entry colname="col9">34.2</oasis:entry>
         <oasis:entry colname="col10">433</oasis:entry>
         <oasis:entry colname="col11">Half mountain,</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11">half plain</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Beijing</oasis:entry>
         <oasis:entry colname="col2">BJ</oasis:entry>
         <oasis:entry colname="col3">116.3</oasis:entry>
         <oasis:entry colname="col4">40.0</oasis:entry>
         <oasis:entry colname="col5">59</oasis:entry>
         <oasis:entry colname="col6">Dec 2009–</oasis:entry>
         <oasis:entry colname="col7">54399</oasis:entry>
         <oasis:entry colname="col8">116.3</oasis:entry>
         <oasis:entry colname="col9">40.0</oasis:entry>
         <oasis:entry colname="col10">46</oasis:entry>
         <oasis:entry colname="col11">Hill (megacity)</oasis:entry>
         <oasis:entry colname="col12">Northern</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Harbin</oasis:entry>
         <oasis:entry colname="col2">HrB</oasis:entry>
         <oasis:entry colname="col3">126.6</oasis:entry>
         <oasis:entry colname="col4">45.7</oasis:entry>
         <oasis:entry colname="col5">223</oasis:entry>
         <oasis:entry colname="col6">Dec 2013–</oasis:entry>
         <oasis:entry colname="col7">50953</oasis:entry>
         <oasis:entry colname="col8">126.8</oasis:entry>
         <oasis:entry colname="col9">45.8</oasis:entry>
         <oasis:entry colname="col10">118</oasis:entry>
         <oasis:entry colname="col11">Plain</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Songshan</oasis:entry>
         <oasis:entry colname="col2">SS</oasis:entry>
         <oasis:entry colname="col3">113.1</oasis:entry>
         <oasis:entry colname="col4">34.5</oasis:entry>
         <oasis:entry colname="col5">475</oasis:entry>
         <oasis:entry colname="col6">Dec 2013–</oasis:entry>
         <oasis:entry colname="col7">57084</oasis:entry>
         <oasis:entry colname="col8">113.1</oasis:entry>
         <oasis:entry colname="col9">34.5</oasis:entry>
         <oasis:entry colname="col10">1178</oasis:entry>
         <oasis:entry colname="col11">Mountain and hill</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Nanjing</oasis:entry>
         <oasis:entry colname="col2">NJ</oasis:entry>
         <oasis:entry colname="col3">119.0</oasis:entry>
         <oasis:entry colname="col4">32.1</oasis:entry>
         <oasis:entry colname="col5">52</oasis:entry>
         <oasis:entry colname="col6">Jan 2013–</oasis:entry>
         <oasis:entry colname="col7">58238</oasis:entry>
         <oasis:entry colname="col8">118.8</oasis:entry>
         <oasis:entry colname="col9">32.0</oasis:entry>
         <oasis:entry colname="col10">35</oasis:entry>
         <oasis:entry colname="col11">Plain and hill</oasis:entry>
         <oasis:entry colname="col12">Southern</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Jul 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Shanghai</oasis:entry>
         <oasis:entry colname="col2">SH</oasis:entry>
         <oasis:entry colname="col3">121.5</oasis:entry>
         <oasis:entry colname="col4">31.3</oasis:entry>
         <oasis:entry colname="col5">84</oasis:entry>
         <oasis:entry colname="col6">Mar 2013–</oasis:entry>
         <oasis:entry colname="col7">58362</oasis:entry>
         <oasis:entry colname="col8">121.5</oasis:entry>
         <oasis:entry colname="col9">31.4</oasis:entry>
         <oasis:entry colname="col10">6</oasis:entry>
         <oasis:entry colname="col11">Alluvial plain</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Apr 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11">(megacity)</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Hefei</oasis:entry>
         <oasis:entry colname="col2">HF</oasis:entry>
         <oasis:entry colname="col3">117.2</oasis:entry>
         <oasis:entry colname="col4">31.9</oasis:entry>
         <oasis:entry colname="col5">36</oasis:entry>
         <oasis:entry colname="col6">Nov 2013–</oasis:entry>
         <oasis:entry colname="col7">58321</oasis:entry>
         <oasis:entry colname="col8">117.2</oasis:entry>
         <oasis:entry colname="col9">31.9</oasis:entry>
         <oasis:entry colname="col10">27</oasis:entry>
         <oasis:entry colname="col11">Hill</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Zhoushan</oasis:entry>
         <oasis:entry colname="col2">ZS</oasis:entry>
         <oasis:entry colname="col3">122.1</oasis:entry>
         <oasis:entry colname="col4">29.9</oasis:entry>
         <oasis:entry colname="col5">29</oasis:entry>
         <oasis:entry colname="col6">Feb 2012–</oasis:entry>
         <oasis:entry colname="col7">58477</oasis:entry>
         <oasis:entry colname="col8">122.1</oasis:entry>
         <oasis:entry colname="col9">30.0</oasis:entry>
         <oasis:entry colname="col10">36</oasis:entry>
         <oasis:entry colname="col11">Islands</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Chengdu</oasis:entry>
         <oasis:entry colname="col2">CD</oasis:entry>
         <oasis:entry colname="col3">104.0</oasis:entry>
         <oasis:entry colname="col4">30.6</oasis:entry>
         <oasis:entry colname="col5">510</oasis:entry>
         <oasis:entry colname="col6">Jun 2013–</oasis:entry>
         <oasis:entry colname="col7">56276</oasis:entry>
         <oasis:entry colname="col8">103.8</oasis:entry>
         <oasis:entry colname="col9">30.4</oasis:entry>
         <oasis:entry colname="col10">461</oasis:entry>
         <oasis:entry colname="col11">Basin</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Jul 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Guangzhou</oasis:entry>
         <oasis:entry colname="col2">GZ</oasis:entry>
         <oasis:entry colname="col3">113.4</oasis:entry>
         <oasis:entry colname="col4">23.1</oasis:entry>
         <oasis:entry colname="col5">28</oasis:entry>
         <oasis:entry colname="col6">Oct 2011–</oasis:entry>
         <oasis:entry colname="col7">59287</oasis:entry>
         <oasis:entry colname="col8">113.3</oasis:entry>
         <oasis:entry colname="col9">23.2</oasis:entry>
         <oasis:entry colname="col10">41</oasis:entry>
         <oasis:entry colname="col11">Mountain, hill and</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11">plain (megacity)</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Haikou</oasis:entry>
         <oasis:entry colname="col2">HK</oasis:entry>
         <oasis:entry colname="col3">110.3</oasis:entry>
         <oasis:entry colname="col4">20.0</oasis:entry>
         <oasis:entry colname="col5">22</oasis:entry>
         <oasis:entry colname="col6">Mar 2014–</oasis:entry>
         <oasis:entry colname="col7">59758</oasis:entry>
         <oasis:entry colname="col8">110.3</oasis:entry>
         <oasis:entry colname="col9">20.0</oasis:entry>
         <oasis:entry colname="col10">64</oasis:entry>
         <oasis:entry colname="col11">Island</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Mar 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Sanya</oasis:entry>
         <oasis:entry colname="col2">SY</oasis:entry>
         <oasis:entry colname="col3">109.4</oasis:entry>
         <oasis:entry colname="col4">18.3</oasis:entry>
         <oasis:entry colname="col5">29</oasis:entry>
         <oasis:entry colname="col6">Sep 2014–</oasis:entry>
         <oasis:entry colname="col7">59948</oasis:entry>
         <oasis:entry colname="col8">109.5</oasis:entry>
         <oasis:entry colname="col9">18.2</oasis:entry>
         <oasis:entry colname="col10">419</oasis:entry>
         <oasis:entry colname="col11">Island</oasis:entry>
         <oasis:entry colname="col12"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">Nov 2016</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11"/>
         <oasis:entry colname="col12"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><table-wrap-foot><p id="d1e255"><inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> No. is the meteorological station number.</p></table-wrap-foot></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e1571">Locations of the 16 Sun–sky radiometer Observation NETwork (SONET)
sites projected onto an elevation map of China.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f01.png"/>

        </fig>

      <p id="d1e1581">SONET provides continuous observations of direct sun and sky radiation
measured using the multiwavelength polarization sun–sky radiometer
(CE318-DP), following the AERONET protocol (Li et al., 2018). Based on<?pagebreak page12797?> the
inversion algorithm of Dubovik and King (2000) and Dubovik et al. (2000),
the 440, 675, 870 and 1020 nm wavebands are used to retrieve more than 20
parameters describing the optical, physical and chemical global properties
as column-integrated properties (Li et al., 2018), including the particle volume
size distribution (VSD), the complex refractive index (CRI) and aerosol
components. Using these data, VSD and CRI submodal parameters of
atmospheric aerosols are obtained using the modal decomposition method
proposed by Zhang et al. (2017). The real parts of the CRI of the fine and
coarse modes (<inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, respectively) are spectrally independent,
while the imaginary parts have spectral variation at 440 nm, so they are
written as (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Using these fine- and coarse-mode characteristics of the CRI, microphysical properties of
aerosols in each mode were analyzed (Z. Li et al., 2019), but the aerosol
chemical components were not determined.</p>
</sec>
<?pagebreak page12798?><sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Meteorological data</title>
      <p id="d1e1671">Meteorological data provide important supplementary information for the
analysis and interpretation of the SONET-retrieved aerosol information.
Hourly observations from surface meteorological stations were provided by
the China Meteorological Administration (CMA). Only data from manned weather
stations, which are maintained regularly, were used to ensure the best
possible data quality. The CMA stations closest to each SONET site were
selected, and the meteorological data were collocated in time with the SONET
observations by linear interpolation between the nearest observations.
Figure 2 shows the statistics of the relative humidity (RH) observations at
each of the 16 sites. The highest mean RH occurs at the Sanya site, and the
lowest value occurs at the Lhasa site. Generally, the mean RH is relatively low at
stations at northern latitudes and often also at high altitudes. The
standard deviations of wet (e.g., Sanya, Haikou) and dry (e.g., Lhasa,
Kashgar) sites are smaller than at other sites.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e1676">Boxplots of the relative humidities observed near each of the
SONET sites. The observation periods for each site are shown in Table 1. The
line and the diamond represent the median and mean values, respectively, and
the box shows the standard deviation (1<inline-formula><mml:math id="M18" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f02.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Methodology</title>
      <p id="d1e1701">The aerosol components are determined by comparison of the aerosol
microphysical properties calculated using a forward model with those
retrieved from the SONET observations (Zhang et al., 2017). This is achieved
by minimizing the iterative kernel function, i.e., the sum of the differences
between the calculated and observed properties at each of the four
wavelengths together, to find the optimum solution. The forward model
includes three modules: the Maxwell Garnett effective-medium approximation
(Schuster et al., 2005) module to calculate aerosol internal-mixing
characteristics, an aerosol hygroscopic growth module to solve the
hygroscopicity of water-soluble components in a multicomponent liquid
system and an organic component dynamic constraint module to keep a
reasonable ratio of organic matter.</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>The aerosol component classification</title>
      <p id="d1e1711">The aerosol component classification includes five principal species (black
carbon – BC, organic matter – OM, inorganic salt – IS, aerosol water content – AW, dust-like content – DU). Three of these components are further subdivided;
i.e., organic matter is subdivided into water-soluble organic matter (WSOM) and
water-insoluble organic matter (WIOM); inorganic salt consists of ammonium
nitrate (AN) in the fine mode and sodium chloride (SC) in the coarse mode,
and aerosol water content is the water content in the fine and in the coarse
mode. Thus there are eight subcomponents as illustrated in Fig. 3. All of
these eight aerosol components constitute a relatively complete system
comparable to those used in chemical transport models.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e1716">Aerosol component classification scheme.</p></caption>
          <?xmltex \igopts{width=469.470472pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f03.png"/>

        </fig>

      <p id="d1e1725">The aerosol components are identified following three steps. The first step
is the separation of the aerosol microphysical properties (VSD and CRI)
into those of the fine and coarse modes as summarized in Sect. S1 in the Supplement.
For the fine-mode fraction, the water-insoluble and water-soluble components
are identified using an empirical function (see Sect. 2.2.2 in Zhang et
al., 2018), which describes the ratio of the water-soluble to the
water-insoluble volume fractions determined by RH, together with the
parameterization of aerosol soluble volume fractions by Kandler and Schütz (2007). Then the subcomponents are separated into inclusion (BC and WIOM)
and their environment (AN, AW<inline-formula><mml:math id="M19" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> and WSOM) using their hygroscopic
and optical absorption properties. It should be noted that the water-soluble
property of aerosol components is not equivalent to hygroscopicity.
Dicarboxylic acids represented by oxalic acid are dominant in the WSOM
component, but their hygroscopicity is extremely low (Ma et al., 2013; Drozd
et al., 2014; Jing et al., 2016). Other organic compounds in aerosols
are also less hygroscopic as shown in Zhang et al. (2018, their Fig. 1).
Hence, the OM components (WSOM and WIOM) are treated as nonhygroscopic
components. For the coarse-mode fraction, the refractive index of the
mixture (AW<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> and SC) is determined by its hygroscopic growth factor.
Dust and hydrate in the aerosol mixture are separated by the effective-medium approximation.</p>
      <p id="d1e1747">In these processes, the hygroscopic growth is determined by the
hygroscopicity parameter <inline-formula><mml:math id="M21" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> and effective densities of the aerosol
subcomponents, and the aerosol mixture refractive index is calculated by
that of the subcomponents and the mixing state. Key parameters of the
forward model and references are listed in Table 2. We notice that the
effective densities for OC and DU reported from different studies cover a
wide range (Ganguly et al., 2009; McConnell et al., 2008; Wagner et al.,
2012; Bond and Bergstrom, 2006) because they depend on the mixing ratios. In
the current study the effective density of aerosol components is used from a
widely cited study by van Beelen et al. (2014).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1760">Growth-factor-derived hygroscopicity parameter (<inline-formula><mml:math id="M22" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>), complex
refractive indices (<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:math></inline-formula>) at four wavelengths and effective density
(<inline-formula><mml:math id="M24" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>) of model components. Real and imaginary parts at four standard
AERONET aerosol product wavelengths (440, 675, 870 and 1020 nm) are
considered.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right" colsep="1"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2">Component </oasis:entry>

         <oasis:entry colname="col3">Growth-factor-</oasis:entry>

         <oasis:entry rowsep="1" namest="col4" nameend="col7" align="center" colsep="1">Real part </oasis:entry>

         <oasis:entry rowsep="1" namest="col8" nameend="col9" align="center">Imaginary part </oasis:entry>

         <oasis:entry colname="col10"><inline-formula><mml:math id="M34" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">derived <inline-formula><mml:math id="M35" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col4"><inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">440</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">675</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6"><inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">870</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col7"><inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">1020</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col8"><inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">440</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9"><inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn mathvariant="normal">675</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1020</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col10">(g cm<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="1">OM</oasis:entry>

         <oasis:entry colname="col2">WIOM</oasis:entry>

         <oasis:entry colname="col3">0.000</oasis:entry>

         <oasis:entry colname="col4">1.530<inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.530</oasis:entry>

         <oasis:entry colname="col6">1.530</oasis:entry>

         <oasis:entry colname="col7">1.530</oasis:entry>

         <oasis:entry colname="col8">0.035<inline-formula><mml:math id="M44" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">d</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.001</oasis:entry>

         <oasis:entry rowsep="1" colname="col10" morerows="1">1.547<inline-formula><mml:math id="M45" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">WSOM</oasis:entry>

         <oasis:entry colname="col3">0.000<inline-formula><mml:math id="M46" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col4">1.530<inline-formula><mml:math id="M47" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.530</oasis:entry>

         <oasis:entry colname="col6">1.530</oasis:entry>

         <oasis:entry colname="col7">1.530</oasis:entry>

         <oasis:entry colname="col8">0.006<inline-formula><mml:math id="M48" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">d</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.000</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">AN</oasis:entry>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">0.547<inline-formula><mml:math id="M49" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col4">1.559<inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.553</oasis:entry>

         <oasis:entry colname="col6">1.550</oasis:entry>

         <oasis:entry colname="col7">1.548</oasis:entry>

         <oasis:entry colname="col8">0.000<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.000</oasis:entry>

         <oasis:entry colname="col10">1.760<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">BC</oasis:entry>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">0.000</oasis:entry>

         <oasis:entry colname="col4">1.950<inline-formula><mml:math id="M53" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.950</oasis:entry>

         <oasis:entry colname="col6">1.950</oasis:entry>

         <oasis:entry colname="col7">1.950</oasis:entry>

         <oasis:entry colname="col8">0.790<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.790</oasis:entry>

         <oasis:entry colname="col10">1.800<inline-formula><mml:math id="M55" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">AW</oasis:entry>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">0.000</oasis:entry>

         <oasis:entry colname="col4">1.337<inline-formula><mml:math id="M56" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.332</oasis:entry>

         <oasis:entry colname="col6">1.330</oasis:entry>

         <oasis:entry colname="col7">1.328</oasis:entry>

         <oasis:entry colname="col8">0.000<inline-formula><mml:math id="M57" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">g</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.000</oasis:entry>

         <oasis:entry colname="col10">1.000<inline-formula><mml:math id="M58" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">DU</oasis:entry>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">0.000</oasis:entry>

         <oasis:entry colname="col4">1.534<inline-formula><mml:math id="M59" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">g</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.534</oasis:entry>

         <oasis:entry colname="col6">1.534</oasis:entry>

         <oasis:entry colname="col7">1.534</oasis:entry>

         <oasis:entry colname="col8">0.002<inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">h</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.001</oasis:entry>

         <oasis:entry colname="col10">2.650<inline-formula><mml:math id="M61" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">SC</oasis:entry>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">1.120<inline-formula><mml:math id="M62" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col4">1.562<inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">h</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">1.541</oasis:entry>

         <oasis:entry colname="col6">1.534</oasis:entry>

         <oasis:entry colname="col7">1.530</oasis:entry>

         <oasis:entry colname="col8">0.000<inline-formula><mml:math id="M64" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9">0.000</oasis:entry>

         <oasis:entry colname="col10">2.165<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e1795"><inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Petters and Kreidenweis (2007). <inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> Kreidenweis et al. (2008).
<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msup></mml:math></inline-formula> Sun et al. (2007). <inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">d</mml:mi></mml:msup></mml:math></inline-formula> Chen and Bond (2010). <inline-formula><mml:math id="M29" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msup></mml:math></inline-formula> Schuster et al. (2005). <inline-formula><mml:math id="M30" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msup></mml:math></inline-formula> Bond and Bergstrom (2006). <inline-formula><mml:math id="M31" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">g</mml:mi></mml:msup></mml:math></inline-formula> Koven and Fung (2006). <inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">h</mml:mi></mml:msup></mml:math></inline-formula> Toon et al. (1976). <inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msup></mml:math></inline-formula> Van Beelen et al. (2014).</p></table-wrap-foot></table-wrap>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Complex refractive index in a multicomponent liquid system</title>
      <p id="d1e2466">The multiple water-soluble aerosol components together with the aerosol
water content make up a liquid system, with increased complexity of the
calculation of hygroscopic growth and complex refractive index. The
<inline-formula><mml:math id="M66" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler theory proposed by Petters and Kreidenweis (2007) can
cope with the hygroscopicity of the multicomponent liquid system. In this
theory, the water activity of aqueous atmospheric particulate matter can be
represented by the functional form
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M67" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="italic">κ</mml:mi><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume of the dry particulate matter and <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
volume of the aerosol water content. The activity of water in solution
(<inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is close to the relative humidity (RH) due to a lower curvature
effect and can therefore be replaced with RH (Tang, 1996). The
hygroscopicity parameter <inline-formula><mml:math id="M71" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> is<?pagebreak page12799?> defined through its effect on the
water activity of the solution. In Eq. (1), the ratio of <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to
<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be further applied to the calculation of the volume fraction
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M74" display="block"><mml:mrow><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">κ</mml:mi></mml:mrow></mml:mfenced><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume fraction of the <inline-formula><mml:math id="M76" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th component
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M77" display="block"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume of the <inline-formula><mml:math id="M79" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th component.</p>
      <?pagebreak page12800?><p id="d1e2725">In the multicomponent liquid system, the hygroscopicity parameter <inline-formula><mml:math id="M80" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>
is given by the simple mixing rule
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M81" display="block"><mml:mrow><mml:mi mathvariant="italic">κ</mml:mi><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi mathvariant="normal">dry</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the hygroscopicity parameter of the <inline-formula><mml:math id="M83" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th component
obtained from the literature (Table 2) and <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi mathvariant="normal">dry</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the dry
component volume fraction defined as
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M85" display="block"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi mathvariant="normal">dry</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Using Eq. (2) for the relationship between the volume fraction and the
hygroscopicity parameter, the complex refractive index of the
multicomponent aerosol system can be derived using the Lorentz–Lorenz
relation (Heller, 1965). Firstly, the molar refractivity (<inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) at
wavelength <inline-formula><mml:math id="M87" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> can be calculated from the real part of the complex
refractive index (<inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the volume fraction of the individual
components:
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M89" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Here <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the molar refractivity of the <inline-formula><mml:math id="M91" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th component represented by
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M92" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msubsup><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msubsup><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Then, the real and imaginary parts of the complex refractive index at
wavelength <inline-formula><mml:math id="M93" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> of the multicomponent liquid system,
<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, are obtained by using
the molar refractivity and the imaginary part of the complex refractive
index of the <inline-formula><mml:math id="M96" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th component (<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, respectively.

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M98" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E8"><mml:mtd><mml:mtext>8</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>n</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msqrt><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>A</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:msqrt></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E9"><mml:mtd><mml:mtext>9</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>k</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            Equations (8) and (9) apply to the estimation of the complex refractive
index of a multicomponent liquid system with hygroscopic growth.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Effective-medium approximation</title>
      <p id="d1e3132">To determine the complex refractive index of a particle, i.e., including both
the multicomponent liquid system and water-insoluble matter, the complex
refractive index (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:math></inline-formula>) at wavelength <inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> is expressed in terms of
the permittivity, <inline-formula><mml:math id="M101" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>):
            <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M103" display="block"><mml:mrow><mml:mi>m</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msqrt><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="|" open="|"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:msqrt><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:msqrt><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="|" close="|"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:msqrt><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The permittivity of the multicomponent liquid system can then be calculated
using Eqs. (8)–(10). Considering the water-insoluble matter in a
particle as inclusion and the water-soluble matter as the environment, the
permittivity of the entire aerosol particle can be obtained by the Maxwell
Garnett effective-medium approximation (Schuster et al., 2005):
            <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M104" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">eff</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced close="]" open="["><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>j</mml:mi></mml:msub><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:msub><mml:mi>f</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi>j</mml:mi></mml:munder><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:msub><mml:mi>f</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M105" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula> is the number of water-insoluble components and <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are the
permittivities of the inclusion and its environment. The complex refractive
index of the entire aerosol is estimated by the aerosol component fraction using
Eq. (10).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e3434">Flowchart of the aerosol component classification inversion
algorithm.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Inversion procedure</title>
      <p id="d1e3452">The flowchart for the inversion of the aerosol components is shown in
Fig. 4. In the fine mode, the ratio of WS and WI matter is estimated using
RH as described in Sect. 2.2.2 in Zhang et al. (2018). The initial value
of the host refractive index and the extreme value for the BC component are
set by the calculation modules of the complex refractive index in the
multicomponent liquid system (see Sect. 3.2) and the effective-medium
approximation (see Sect. 3.3), respectively. In the loop to determine the
BC component, two constraints are applied to separate BC from other
components. The WSOM <inline-formula><mml:math id="M108" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> WIOM ratio constraint was developed by Zhang et al. (2018) based on considerations published in the literature (Chalbot et al.,
2016; Bougiatioti et al., 2013; Wozniak et al., 2013; Mayol-Bracero et al.,
2002; Krivácsy et al., 2001; Zappoli et al., 1999):
            <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M109" display="block"><mml:mrow><mml:mfenced open="{" close=""><mml:mrow><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">WSOM</mml:mi></mml:msub><mml:mo>≅</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">WIOM</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:msubsup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">WSOM</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:msubsup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">WSOM</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">β</mml:mi><mml:mo>∈</mml:mo><mml:mfenced close="]" open="["><mml:mrow><mml:mn mathvariant="normal">44</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">77</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          For more detail, see Sect. 2.3.1 in Zhang et al. (2018). The volume
normalization of the aerosol components in both the<?pagebreak page12801?> fine and coarse modes is
used to constrain the volume fraction of the aerosol components to a
reasonable range (similar to in Sect. 2.3.2 in Zhang et al., 2018):
            <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M110" display="block"><mml:mrow><mml:mfenced open="{" close=""><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">fine</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">coarse</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">fine</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">BC</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">AN</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">WSOM</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">WIOM</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">AW</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">coarse</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">DU</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">SC</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">AW</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
          Then the inner loop of WSOM computes the CRIs of the fine mode at different
BC levels and outputs the aerosol components of minimum <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">χ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. The
inversion procedure for the coarse mode is simpler than that for the fine
mode. There is only a loop for DU, and the complex refractive index of the
host can be directly calculated by Eqs. (2)–(8) with only the input of
RH. The function chi-squared (<inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">χ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as an iterative kernel function
is expressed in the sum of the differences between the complex refractive
index estimated from the forward model (<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the retrievals (<inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">rtrl</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), at
multiple wavelengths:
            <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M115" display="block"><mml:mtable columnspacing="1em" class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msup><mml:mi mathvariant="italic">χ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:munder><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">rtrl</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>m</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">rtrl</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">440</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">675</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">870</mml:mn><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>and</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mn mathvariant="normal">1020</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">nm</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          The retrieval is completed when the value of <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">χ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> reaches a
minimum. The volume fractions of the aerosol components can be obtained by
solving the above Eqs. (10)–(12). The aerosol mass concentration in the
atmospheric column is calculated using the volume and effective density of
the aerosol components.</p>
      <p id="d1e3817">The retrieval algorithm described here is an improvement over that described
in Zhang et al. (2018). In the previous algorithm, the WSOM component was
added to the host, but it could only be considered as a nonhygroscopic
component. The proportions of solute and solution in the host mixture at
different relative humidities should be measured in the laboratory, which
limits the choice of aerosol components in the inversion process. Also, the
real part of the CRI of the host was calculated by volume averaging, which
can introduce a small error. The improved algorithm described here is more
suitable for the calculation of the properties of a mixture of multiple
water-soluble components as long as the hygroscopicity parameter is known,
which is not only convenient to measure but also independent of particle
size. The hygroscopicity parameter of WSOM can be varied according to the
choice of mixing components instead of by changing the algorithm itself.
Similarly, some other water-soluble<?pagebreak page12802?> components (e.g., sulfate) can be
introduced into the inversion algorithm without laboratory measurements.</p>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Uncertainty analysis</title>
      <p id="d1e3828">The uncertainty in the retrieval results was evaluated using synthetic data,
both without and with input errors added. For the first case (without input
errors), a set of complex refractive indices has been obtained by
calculating a set of volume fractions of the aerosol components using the
forward chemical model, which was used as input for the retrieval of the
aerosol components without any noise added. For the aerosol components, the
volume fraction of BC was constrained between 0.0 % to 3.0 % with an
interval of 0.5 % and corresponding dynamic ranges for the other
components with intervals of 10 %, in three ambient relative humidity
conditions (40 %, 60 % and 80 %). Figure 5 shows the comparison of the
aerosol component volume fractions from forward modeling used as input and
their retrieved values. The volume fractions of the retrieved aerosol
components reproduce the input values reasonably well. For the fine-mode
fraction, most data pairs are located close to the <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line, with a
mean absolute error (MAE) of the aerosol component volume fractions of
3.0 %. In five samples the difference in the AW<inline-formula><mml:math id="M118" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> is more than
20.0 %, though the overall MAE for AW<inline-formula><mml:math id="M119" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> is only 5.5 %. In these five
samples, the BC component is low and organic matter contributes
substantially to the aerosol light absorption, resulting in underestimation
of the AW<inline-formula><mml:math id="M120" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> volume fraction at high RH and overestimation for moderate
RH. WSOM is overall slightly overestimated, and AN is underestimated by only
a few percent. The correlation between the input and retrieved aerosol
volume fractions in the coarse mode is even better than that in fine mode.
The regression coefficient for all samples is 0.99, and the MAE is only
2.0 %. These results show the very small uncertainty in the retrieved
aerosol component volume fractions.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e3872">Scatterplots of volume fractions of aerosol components in the
fine <bold>(a)</bold> and coarse <bold>(b)</bold> modes retrieved using the algorithm described
in Sect. 3  versus those used as input calculated with the forward model.
The solid line is the <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line, and the dashed line is the fitting line.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f05.png"/>

        </fig>

      <p id="d1e3899">To further evaluate the inversion results, errors were added to the
synthetic data. To this end, three typical pollution cases were chosen in
which the main pollutants are water-soluble aerosols, biomass burning aerosols and dust
aerosols, respectively, hereafter referred to as WS, BB and DU pollution
types. Each type is described by the different aerosol size distribution and
refractive index parameters derived from Zhang et al. (2017). These
parameters are listed in Table S1. Note that although the
acronyms of the three pollution types are the same as the aerosol component
names above, it does not mean that each type includes only one single
aerosol component, as illustrated below.</p>
      <p id="d1e3903">Figure 6 shows the aerosol volume size distribution, complex refractive
index and eight aerosol components in the WS, BB and DU types used in this
exercise. For the size distribution, the highest volume concentrations occur
in the fine mode of the WS and BB types, whereas for the DU type the coarse
mode dominates. For the complex refractive index, significant absorption
occurs in the fine-mode fraction of the BB type, while relatively low
absorption occurs in the other models. In the WS type, the mass fraction of
AW<inline-formula><mml:math id="M122" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> is close to 20 % and for AN it is about 18 %, significantly
larger than for the other types. By comparison, the BC mass fraction in the
BB type is close to 3 %, and organic carbon is also high, with WSOM and
WIOM mass fractions of 23 % and 11 %. In the DU type, the dust component
is completely dominant, as expected, and the mass fractions of other
components are less than 2 %.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e3917">The fine- and coarse-mode volume size distribution, complex
refractive index, and aerosol components describing the aerosol models used
in the synthetic case study (WS: water soluble, BB: biomass burning, DU:
dust).</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f06.png"/>

        </fig>

      <p id="d1e3926">The three main sources of error in the model input parameters are the RH and
the complex refractive index in the fine and coarse modes. The uncertainties
due to inversion errors in the modal refractive index were discussed in
detail in Zhang et al. (2017) and are directly used here to estimate their
effects on aerosol components. For RH, the observation error is about 5 %
(WMO, 2008); in this exercise a larger error (10 %) is introduced to more
rigorously assess the uncertainty in the estimated aerosol components. These
typical uncertainties are listed in Table S2. The total relative error
(TRE), which is the propagated relative error calculated by the mean aerosol
component error induced by the errors in sub-CRIs and RH in three pollution
types, is used to assess the uncertainty in the aerosol composition
inversion. As shown in Table 3, the TRE of BC is 32.21 %, less than other
components in the fine mode, and the largest source of TRE is the imaginary
part of the complex refractive index (<inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), with 25.68 %. Compared
with BC, the TRE of OM is larger (about 75 %), primarily contributed to by
RH, followed by <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The uncertainty in the imaginary part impacts very
little due to the low absorption of OM. The uncertainty in AN due to the
imaginary part is low, but a very high uncertainty is caused by RH. Another
component of IS is SC which usually occurs in the coarse mode. The large TRE
of SC is contributed to by the real part of the complex refractive index in the
coarse mode (<inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, with 912.87 %, leading to the largest TRE of IS.
Affected by SC, the TRE of AW<inline-formula><mml:math id="M126" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> is also large due to <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, but the TRE
of AW<inline-formula><mml:math id="M128" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> is much smaller (50.05 %). In the coarse mode, the TRE of DU
is smallest in all of the aerosol components, only 15.79 %, mainly caused
by <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Overall, most of the uncertainties in the fine mode are from RH,
and those in the coarse mode are from <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Fortunately, the RH observed by
ground-based stations is accurate, with an error which is usually less than
about 5 % (WMO, 2008), which can significantly reduce the uncertainty in
the retrieved aerosol scattering components. It should be noted that the
uncertainties in Table 3 are for single measurements. One important
advantage of remote sensing is that multiple measurements can be made during
a short period of time. Thus, the average uncertainty in the aerosol
components can be effectively reduced by taking into account independent
errors in each observation. In addition, the accuracy of the retrieved
<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> needs to be improved in order to deal with the aerosol component
inversion.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e4036">Estimated total relative errors (TREs) of aerosol component mass
fractions in the three aerosol models used to evaluate the aerosol component
classification inversion algorithm.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="11">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right" colsep="1"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right" colsep="1"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2">Aerosol </oasis:entry>

         <oasis:entry colname="col3">RH</oasis:entry>

         <oasis:entry rowsep="1" namest="col4" nameend="col6" align="center" colsep="1">Fine mode </oasis:entry>

         <oasis:entry rowsep="1" namest="col7" nameend="col9" align="center" colsep="1">Coarse mode </oasis:entry>

         <oasis:entry namest="col10" nameend="col11" align="center">TRE<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">components </oasis:entry>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4"><inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5"><inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6"><inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col7"><inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col8"><inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col9"><inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col10"/>

         <oasis:entry colname="col11"/>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">

         <oasis:entry namest="col1" nameend="col2">BC </oasis:entry>

         <oasis:entry colname="col3">5.74 %</oasis:entry>

         <oasis:entry colname="col4">0.59 %</oasis:entry>

         <oasis:entry colname="col5">25.68 %</oasis:entry>

         <oasis:entry colname="col6">18.57 %</oasis:entry>

         <oasis:entry colname="col7">0.00 %</oasis:entry>

         <oasis:entry colname="col8">0.00 %</oasis:entry>

         <oasis:entry colname="col9">0.00 %</oasis:entry>

         <oasis:entry namest="col10" nameend="col11" align="center">32.21 % </oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="1">OM</oasis:entry>

         <oasis:entry colname="col2">WIOM</oasis:entry>

         <oasis:entry colname="col3">75.82 %</oasis:entry>

         <oasis:entry colname="col4">4.55 %</oasis:entry>

         <oasis:entry colname="col5">5.28 %</oasis:entry>

         <oasis:entry colname="col6">1.08 %</oasis:entry>

         <oasis:entry colname="col7">0.00 %</oasis:entry>

         <oasis:entry colname="col8">0.00 %</oasis:entry>

         <oasis:entry colname="col9">0.00 %</oasis:entry>

         <oasis:entry colname="col10">76.15 %</oasis:entry>

         <oasis:entry rowsep="1" colname="col11" morerows="1" align="right">74.73 %</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">WSOM</oasis:entry>

         <oasis:entry colname="col3">51.60 %</oasis:entry>

         <oasis:entry colname="col4">51.92 %</oasis:entry>

         <oasis:entry colname="col5">3.44 %</oasis:entry>

         <oasis:entry colname="col6">2.11 %</oasis:entry>

         <oasis:entry colname="col7">0.00 %</oasis:entry>

         <oasis:entry colname="col8">0.00 %</oasis:entry>

         <oasis:entry colname="col9">0.00 %</oasis:entry>

         <oasis:entry colname="col10">73.31 %</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="1">IS</oasis:entry>

         <oasis:entry colname="col2">AN</oasis:entry>

         <oasis:entry colname="col3">207.00 %</oasis:entry>

         <oasis:entry colname="col4">60.86 %</oasis:entry>

         <oasis:entry colname="col5">7.07 %</oasis:entry>

         <oasis:entry colname="col6">6.04 %</oasis:entry>

         <oasis:entry colname="col7">0.00 %</oasis:entry>

         <oasis:entry colname="col8">0.00 %</oasis:entry>

         <oasis:entry colname="col9">0.00 %</oasis:entry>

         <oasis:entry colname="col10">215.96 %</oasis:entry>

         <oasis:entry rowsep="1" colname="col11" morerows="1" align="right">564.42 %</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">SC</oasis:entry>

         <oasis:entry colname="col3">25.71 %</oasis:entry>

         <oasis:entry colname="col4">0.00 %</oasis:entry>

         <oasis:entry colname="col5">0.00 %</oasis:entry>

         <oasis:entry colname="col6">0.00 %</oasis:entry>

         <oasis:entry colname="col7">912.51 %</oasis:entry>

         <oasis:entry colname="col8">2.16 %</oasis:entry>

         <oasis:entry colname="col9">1.23 %</oasis:entry>

         <oasis:entry colname="col10">912.87 %</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="1">AW</oasis:entry>

         <oasis:entry colname="col2">AW<inline-formula><mml:math id="M143" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">49.77 %</oasis:entry>

         <oasis:entry colname="col4">3.80 %</oasis:entry>

         <oasis:entry colname="col5">3.71 %</oasis:entry>

         <oasis:entry colname="col6">0.00 %</oasis:entry>

         <oasis:entry colname="col7">0.00 %</oasis:entry>

         <oasis:entry colname="col8">0.00 %</oasis:entry>

         <oasis:entry colname="col9">0.00 %</oasis:entry>

         <oasis:entry colname="col10">50.05 %</oasis:entry>

         <oasis:entry rowsep="1" colname="col11" morerows="1" align="right">481.32 %</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">AW<inline-formula><mml:math id="M144" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col3">8.95 %</oasis:entry>

         <oasis:entry colname="col4">0.00 %</oasis:entry>

         <oasis:entry colname="col5">0.00 %</oasis:entry>

         <oasis:entry colname="col6">0.00 %</oasis:entry>

         <oasis:entry colname="col7">912.55 %</oasis:entry>

         <oasis:entry colname="col8">2.10 %</oasis:entry>

         <oasis:entry colname="col9">1.17 %</oasis:entry>

         <oasis:entry colname="col10">912.60 %</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry namest="col1" nameend="col2">DU </oasis:entry>

         <oasis:entry colname="col3">0.34 %</oasis:entry>

         <oasis:entry colname="col4">0.00 %</oasis:entry>

         <oasis:entry colname="col5">0.00 %</oasis:entry>

         <oasis:entry colname="col6">0.00 %</oasis:entry>

         <oasis:entry colname="col7">15.78 %</oasis:entry>

         <oasis:entry colname="col8">0.04 %</oasis:entry>

         <oasis:entry colname="col9">0.02 %</oasis:entry>

         <oasis:entry namest="col10" nameend="col11" align="center">15.79 % </oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e4039"><inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> TRE <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">7</mml:mn></mml:msubsup><mml:msubsup><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi>i</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M134" display="inline"><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover></mml:math></inline-formula> represents
the mean error in aerosol components from three aerosol types. The RH is
given input error of <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> %, and the inversion errors in sub-CRIs are
from Zhang et al. (2017) listed in Table S2.</p></table-wrap-foot></table-wrap>

</sec>
</sec>
<?pagebreak page12803?><sec id="Ch1.S4">
  <label>4</label><title>Results</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Aerosol component retrievals</title>
      <p id="d1e4554">The averaged mass fractions of the aerosol components measured at 16 SONET
sites are presented in Fig. 7. Each pie chart is marked with the site
name, coordinates, observation period and BC fraction. The mass fractions
are also listed in Table S3. The pie charts show that the coarse-mode mass
fraction usually dominates at the northern and northwestern sites. The mass
fraction of the dust component is significantly higher than that of others,
with a fraction of more than 50 % at the western sites (Lhasa, Zhangye, Kashgar,
Minqin and Xi'an) and the Beijing, Harbin and Songshan sites, which is different
from surface observations of chemical components (Zhang et al., 2012; Liu et
al., 2014). This is because sun photometers provide data integrated over the
whole atmospheric column and thus include the dust transport layer near 4 km
(Proestakis et al., 2018), where dust concentrations may be substantial,
whereas surface observations are<?pagebreak page12804?> local point measurements. The lowest dust
fractions are observed at southern sites, especially at the Guangzhou site,
with a mass fraction of 31.5 %. In contrast, the water content is dominant
at southern sites in both the fine and coarse modes. The maximum AW (AW<inline-formula><mml:math id="M145" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula>
and AW<inline-formula><mml:math id="M146" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>) fraction occurs at the Guangzhou site (28.7 %), and the
lowest mass fractions of 2.0 % and 7.5 % are observed at the Lhasa and
Kashgar sites, respectively. High AW<inline-formula><mml:math id="M147" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> occurs in the cities of
east central China due to the higher occurrence of inorganic salts with
larger hygroscopicity in the fine mode at these sites, whereas the dominant
AW<inline-formula><mml:math id="M148" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> in the western sites can be explained by the inorganic salt coating
of larger particles in the dust source region (Rosenfeld et al., 2001). The
IS fraction (AN and SC) gradually increases from north to south, which is
consistent with the trend of the water content. The fraction of the AN
subcomponent is less than 7.0 % at Lhasa, Zhangye, Kashgar and Minqin,
whereas it is more than 20 % at Chengdu, Guangzhou, Haikou and Sanya. At
the Zhoushan site a high AN fraction is also observed, up to 17.1 %. For
the SC component, the maximum value occurs at the Kashgar (17.1 %) site.
The high SC fraction at the southeast coastal sites is readily ascribed to
the influence of the ocean; the high SC fraction at the Kashgar site is due
to the paleomarine source of dust over the Taklamakan Desert (Huang et al.,
2010). The WIOM component fraction is high in the central sites but
relatively low in the southern coastal and northwest sites. For the WSOM
component, the low value of less than 3 % appears only at northwestern
sites (Zhangye, Kashgar and Minqin). In the atmospheric column, the mass
fraction of the BC component averaged over 16 sites is only 0.59 %, lower
than from near-surface in situ observations (usually 1 %–5 %), which implies that the BC fraction may be reduced by the suspended
layer with other components such as dust aerosols. Nevertheless, the
unusually high mass fraction of BC in Shanghai could be due to observation
uncertainty, also accompanied by the large error for aerosol component
inversion.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e4595">The averaged mass fraction of aerosol components at SONET sites.
The site name, location, observation period and BC fraction are marked in
each subgraph. The mass fractions of other components are listed in Table S3.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f07.png"/>

        </fig>

      <?pagebreak page12805?><p id="d1e4604">The closure of the CRI between instantaneous optical–physical inversion and
chemical estimation is examined by the data pair frequency. Figure 8 shows
scatter density plots of the chemically estimated and
sun-photometer-retrieved imaginary parts of the fine mode at 675 nm
(<inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and 440 nm (<inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the real parts of the fine mode at 440 nm (<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The points are colored by the number of data pairs (retrieved,
estimated), which are sorted according to ordered pairs in 0.0005 intervals
for the imaginary parts of the CRI and 0.001 intervals for the real parts. The
data pairs of <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are closely concentrated around the <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line, although
a slight underestimation is observed with 94.3 % of the estimated values
lower than the retrieved values; only 5.3 % of the data pairs have a
relatively large absolute error (AE <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>). The mean bias is not
large (<inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.003</mml:mn></mml:mrow></mml:math></inline-formula>), and the mean absolute value is equal to the mean absolute
error (MAE <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.003</mml:mn></mml:mrow></mml:math></inline-formula>). There are two reasons for this slight underestimation
in chemical estimation. On the one hand, the imaginary part of the
refractive index of BC is much larger than for the other components due to
its strong absorption. Thus, the inversion of the BC concentration is very
sensitive to the estimation of the refractive index. As shown in Table 3,
although the TRE of BC is the lowest, the errors caused by <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are larger than for any other component. On the other hand,
<inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is not only affected by BC in the inversion process but also
affected by organic components (WSOM and WIOM) with spectral absorption
characteristics. Therefore, in most cases, <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is underestimated in
chemical estimation and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is overestimated (bias <inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.007</mml:mn></mml:mrow></mml:math></inline-formula>). The
mean relative error (RE) is 27.1 %, and 62.8 % of the data points are
below the average relative error line. This indicates that most inversion
results have good optical closure. For the closure of the real part of the
fine mode, the data pairs of <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are also concentrated around the identity
line, although 76.5 % of the <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is above the identity line.
Underestimation occurs mainly when <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is larger than 1.56, because the
only component with the real part of the CRI larger than 1.56 is BC, but its
concentration is mainly determined by the imaginary part. The bias of the
estimated <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (bias <inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.009</mml:mn></mml:mrow></mml:math></inline-formula>) is larger than that of <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> due to the
fact that the value and the range of <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are larger than those of
<inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e4867">In addition, the comparison of aerosol components with those from Zhang et
al. (2018) is given in Sect. S3. Figures S1 and S2 demonstrate that the
algorithm in this study shows a positive effect on AN and AW<inline-formula><mml:math id="M171" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula>, although
there are few validation points.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e4881">Data pair frequency of instantaneous imaginary parts of the
complex refractive index at 675 nm (<inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and 440 nm (<inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">440</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the real
part at 440 nm (<inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) which are sorted according to ordered pairs
(retrieved, estimated) in 0.0005 and 0.001 intervals for imaginary and real
parts, respectively. “Retrieved” represents the subcomponent of the CRI from the
optical–physical retrievals, and “estimated” is estimated by retrieved
chemical components. The color represents the number of cases (color bar),
and the solid black line shows the <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Seasonal variation</title>
      <?pagebreak page12806?><p id="d1e4949">The seasonal variation in the aerosol component mass concentrations,
averaged over 15 stations (Lhasa is not used due to lack of adequate
seasonal data) and all available years, is shown as box-and-whisker plots in
Fig. 9. The top and bottom edges of each box represent the top and bottom
quartiles (Q3 and Q1), and the corresponding whiskers are the outliers
(Q3 <inline-formula><mml:math id="M176" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 1.5IQR and Q1 <inline-formula><mml:math id="M177" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 1.5IQR; IQR is interquartile range). The mean value is
indicated by a plus sign (<inline-formula><mml:math id="M178" display="inline"><mml:mo lspace="0mm">+</mml:mo></mml:math></inline-formula>), and the median value is indicated by a short line inside
the box (<inline-formula><mml:math id="M179" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>). Figure 9 shows that the DU component exhibits an obvious
seasonality. The DU mass concentration is very high in the spring, and the
mean value reaches up to 332.9 mg m<inline-formula><mml:math id="M180" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> due to dust transport from the
northwest of China. With the weakening of dust transport and the increase in
moisture, the DU fraction decreases in other seasons, with a mean value of
around 240.0 mg m<inline-formula><mml:math id="M181" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Although the DU concentration is lower in the
summer than in other seasons, it is still relatively high near the dust
source area, which results in a large difference between the upper and lower
quartiles. In contrast, the AN mass concentration mean value peaks in the
summer (76.8 mg m<inline-formula><mml:math id="M182" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), whereas a minimum occurs in the spring (47.7 mg m<inline-formula><mml:math id="M183" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). It is worth noting that although the mean value in the winter is
not high (51.1 mg m<inline-formula><mml:math id="M184" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), the interval between the upper and lower
quartiles of AN is the smallest in the winter. The minimum value of AN (17.9 mg m<inline-formula><mml:math id="M185" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) is higher than in other seasons (4.1 mg m<inline-formula><mml:math id="M186" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in spring, 9.5 mg m<inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in summer and 11.1 mg m<inline-formula><mml:math id="M188" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in autumn). The seasonal
variation in the water content is slightly different from that of inorganic
salts. The low values of mean AW<inline-formula><mml:math id="M189" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> occur in the spring, while AW<inline-formula><mml:math id="M190" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>
is significantly lower in the winter (21.0 mg m<inline-formula><mml:math id="M191" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) than in other
seasons. The difference between the upper and lower quartiles of AW<inline-formula><mml:math id="M192" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> in
the summer is larger than in other seasons, indicating that in the summer the
aerosol at some sites has a low hygroscopicity. The OM mass concentration is
slightly higher in the winter than that in other seasons probably due to the
occurrence of haze pollution in the winter, with mean concentrations of the
WIOM and WSOM fractions of 22.3 and 38.8 mg m<inline-formula><mml:math id="M193" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively. In the
summer, the OM concentration is only about two-thirds of that in the winter.
The median value of the BC mass concentration is higher in the winter (3.0 mg m<inline-formula><mml:math id="M194" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), which can be related to heating in northern China. Low
concentrations of BC in the other seasons are mainly due to the influence of
frequent dust events in the spring and high aerosol hygroscopic growth in
the summer. Similarly to AN, the SC concentration peaks in the summer and has
a minimum in the winter, due to the influence of the Asian monsoon. The
median values in these two seasons are 41.6 and 19.6 mg m<inline-formula><mml:math id="M195" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e5168">The mass concentrations of aerosol components in four seasons
(winter, spring, summer and autumn). For the box-and-whisker plot, the mean
value is indicated by a plus sign (<inline-formula><mml:math id="M196" display="inline"><mml:mo lspace="0mm">+</mml:mo></mml:math></inline-formula>), and the median value is indicated by a short
line inside the box (<inline-formula><mml:math id="M197" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>). The top and bottom edges of each box represent the
top and bottom quartiles (Q3 and Q1), and the corresponding whiskers are the
outliers (Q3 <inline-formula><mml:math id="M198" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 1.5IQR and Q1 <inline-formula><mml:math id="M199" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 1.5IQR; IQR is interquartile range).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f09.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><?xmltex \currentcnt{10}?><label>Figure 10</label><caption><p id="d1e5207">Comparison of aerosol component mass concentrations in northern
(Xi'an, Beijing, Harbin, Hefei and Songshan) and southern (Nanjing,
Shanghai, Zhoushan, Guangzhou, Haikou and Sanya) China.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f10.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><label>Figure 11</label><caption><p id="d1e5219">The interannual variations in mean aerosol component mass
concentrations integrated over the whole atmospheric column with SONET sites
from 2010 to 2016. The gray line represents the mean mass concentration of
aerosol components averaged over the 16 sites; the points in each graph show
the yearly value at each site. The abbreviations for the site names are from
Table 1.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/20/12795/2020/acp-20-12795-2020-f11.png"/>

        </fig>

      <p id="d1e5228"><?xmltex \hack{\newpage}?>The seasonal variation in the main aerosol components in the fine mode is
discussed on a regional basis (Fig. 10). BC concentrations in typical
northern regions are higher than in southern regions, because of emissions
due to winter heating only in the north. Other BC sources are vehicle
emissions and biomass burning. Adverse meteorological conditions in winter
result in the accumulation of BC in the atmosphere resulting in high BC
values in both the north and the south. The highest BC mass concentration
in the northern region in the winter is 4.3 mg m<inline-formula><mml:math id="M200" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. OM is one of the
dominant components in the fine mode, with sources similar to those of BC.
The impact of biomass burning in the winter and spring over southern China
(Chen et al., 2017) is significant, leading to OM concentrations of more
than 50.0 mg m<inline-formula><mml:math id="M201" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. In the northern region, much biomass burning occurs
in the autumn (Wang et al., 2020). With the influence of heating, the OM
level in the north can reach up to 80.1 mg m<inline-formula><mml:math id="M202" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Therefore, the OM mass
concentration in the northern region is only low in the summer (50.8 mg m<inline-formula><mml:math id="M203" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). AN is us<?pagebreak page12807?>ually formed by secondary reactions of gaseous precursors
in complex air pollution areas. In both the northern and the southern
region, AN mass concentration is larger in the summer than in other seasons,
and the seasonal variation in the southern region is significantly smaller
than that in the north. The mean AN mass concentration in the southern
region is 8.7 mg m<inline-formula><mml:math id="M204" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> higher than that in the northern region. This
suggests that more AN is produced by secondary reactions in the humid
climate in the south than in the northern region.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Interannual variation</title>
      <p id="d1e5300">Figure 11 shows the interannual variations in the aerosol component mass
concentrations in the atmospheric column from 2010 to 2016. The 16 SONET sites
have been established in succession, so the number of available observations
increased year by year with the longest time series from the Beijing site
(see also Table 1). The annual mean mass concentrations shown in Fig. 11
are averages over all sites; i.e., the number of sites was not accounted for,
and, in particular in the earlier years (2010–2011), the annual mean may
thus be representative of one (Beijing) or a few sites. Therefore, the
annual means for each site available have been plotted as well. Figure 11
shows that the annual mean mass concentrations of most of the aerosol
components in the fine mode increased in most of the first years and then
decreased. Influenced by China's environmental control policies, the mean AN
decreased significantly from 72.4 mg m<inline-formula><mml:math id="M205" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2011 to 50.5 mg m<inline-formula><mml:math id="M206" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in
2016, i.e., a reduction by 21.9 mg m<inline-formula><mml:math id="M207" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The yearly mass concentrations
of AN at most sites also follow a downward trend, and AN in the southeastern
coastal sites is significantly higher than that in the northwestern sites.
In contrast, the mean BC mass concentration shows a peak (3.9 mg m<inline-formula><mml:math id="M208" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
in 2011, drops in 2012 to the lowest value during the whole period (2.3 mg m<inline-formula><mml:math id="M209" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and then increases somewhat to a second peak (2.7 mg m<inline-formula><mml:math id="M210" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) in
2013. After a decrease in 2014, BC climbed to 2.8 mg m<inline-formula><mml:math id="M211" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2016. In
the southeastern coastal and northwestern sites, BC concentrations were
relatively low. The unusually high values at Shanghai in 2016 may be due to
observational errors. Similarly to BC, AW<inline-formula><mml:math id="M212" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> also experienced a small
fluctuation after a significant decline in 2012. The AW<inline-formula><mml:math id="M213" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> in aerosol
measured at the southern sites is higher than that at other sites. The fine-mode WIOM and WSOM components show different behavior. WIOM reached a peak
in 2013, with the peak value of 32.3 mg m<inline-formula><mml:math id="M214" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and then showed a
significant decline after 2013. WSOM also reached a peak concentration of
35.8 mg m<inline-formula><mml:math id="M215" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2013, which is 2 mg m<inline-formula><mml:math id="M216" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> lower than the peak in
2016, and overall the concentrations increased. These results suggest that
the policy of air pollution control in China is effective in controlling
inorganic salts and WIOM aerosols, while WSOM still needs to be further
controlled. The concentrations of the coarse-mode aerosol components
fluctuate somewhat during the observation period, with a slight peak in
2013. The concentration of each component in the coarse mode at the
northwestern sites is higher than those at other<?pagebreak page12808?> sites, which can be related
to the high fraction of large particles. Due to the large influence of
geographical factors on the coarse-mode aerosol components, DU in 2010 (only
Beijing site) was significantly larger than in other years. Since 2014, the
mean DU mass concentration has increased, while a downward tendency has been
observed in the AW<inline-formula><mml:math id="M217" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> and SC concentrations since 2013. Coarse-mode
aerosols usually derive from natural sources, and their variations can be
associated with changes in the meteorological conditions.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions and discussions</title>
      <p id="d1e5462">The accurate measurement of atmospheric aerosol components plays an
important role in reducing uncertainty in climate assessment. In the
current study, we updated the refractive index calculation in a
multicomponent liquid system and improved the component inversion algorithm
of Zhang et al. (2018) to retrieve atmospheric columnar aerosol components
including black carbon (BC), organic matter (WSOM and WIOM), inorganic salt (AN
and SC), dust-like content (DU), and water content in the fine and coarse modes
(AW<inline-formula><mml:math id="M218" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> and AW<inline-formula><mml:math id="M219" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>). This algorithm was applied to data from the SONET
sun photometer network, and the regional distribution and interannual
variation in atmospheric aerosol components in China were analyzed for the
period from 2010 to 2016. The results show that the dust-like component is
dominant in northern China but the aerosol water content (AW<inline-formula><mml:math id="M220" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:math></inline-formula> and AW<inline-formula><mml:math id="M221" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>) is dominant in the southern coastal region. The inorganic salt
(AN) in the fine mode has a significant seasonal variation, with a mass
concentration of 76.8 mg m<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in the summer which is significantly
higher than that in other seasons. Meanwhile, the AN concentrations have
significantly decreased from 2011 to 2016, which is inseparable from China's
environmental control policies. However, the slight increase in WSOM and BC
is still noteworthy.</p>
      <p id="d1e5513">As the aerosol concentrations in the atmospheric column obtained from the
inversion of remote sensing data are different from those measured by in
situ measurements near the surface, such as with on-line aerosol mass
spectrometers, the validation of the retrieval results is difficult.
Proestakis et al. (2018) used data from the Cloud-Aerosol Lidar with
Orthogonal Polarization (CALIOP) on the CALIPSO satellite to analyze the
distribution of mineral dust over China, and the results show a higher
concentration of the DU component in the atmospheric column over northern
China. Similarly, Huang et al. (2010) provided a basis for the high SC
content at the Kashgar station due to the paleomarine source. However, for
the direct comparison of our retrievals with independent data, airborne
measurements of the vertical distribution of atmospheric aerosol components
are needed (Kahn et al., 2017). In future research, we will design a
verification experiment to comprehensively evaluate the results from our
inversion method.</p>
      <p id="d1e5516"><?xmltex \hack{\newpage}?>The method presented can be used not only for ground-based sun–sky
photometer measurements but also for other remote sensing instruments (e.g.
lidar) and even for satellite remote sensing in the future. Meanwhile, as
long as measurements of multiwavelength extinction coefficients and aerosol
particle size distributions are available, the inversion of atmospheric
particulate matter composition can also be performed using comprehensive
observations with multiple instruments near the surface. Therefore, this
method can be widely used in low-cost and wide-area measurements in the
future, providing a possibility for obtaining the global distribution of
aerosol composition.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e5524">The aerosol component data used in this study can be requested from the corresponding author (lizq@radi.ac.cn).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e5527">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-20-12795-2020-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-20-12795-2020-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e5536">ZL conceived and designed the study. YC collected and processed the
meteorological data. KL and YX collected the remote sensing data. CZ
collected the DEM data and drew the map. YZ improved the aerosol component
method and performed the inversions. YZ analyzed the spatiotemporal trends
of aerosol component concentrations. YZ and GL prepared the paper with
contributions from all coauthors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e5542">The authors declare that they have no conflict of interest.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e5548">This article is part of the special issue “Satellite and ground-based remote sensing of aerosol optical, physical, and chemical properties over China”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5554">This work was supported by the National Natural Science Foundation of China
(41925019, 41601386) and the National Key R&amp;D Program of China
(2016YFE0201400).</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e5559">This work was supported by the National Natural Science Foundation of China (grant nos. 41925019 and 41601386) and the National Key R&amp;D Program of China (grant no. 2016YFE0201400).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e5565">This paper was edited by Stelios Kazadzis and reviewed by three anonymous referees.</p>
  </notes><?xmltex \hack{\newpage}?><ref-list>
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    <!--<article-title-html>Improved inversion of aerosol components in the atmospheric column from remote sensing data</article-title-html>
<abstract-html><p>Knowledge of the composition of atmospheric aerosols is important
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chloride (SC), dust-like content (DU), and aerosol water content in the fine and
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China, whereas the AW is higher in the southern coastal region. The SC
component retrieved over the desert in northwest China originates from a
paleomarine source. The AN significantly decreased from 2011 to 2016, by
21.9&thinsp;mg&thinsp;m<sup>−2</sup>, which is inseparable from China's environmental control
policies.</p></abstract-html>
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