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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/acp-26-15333-2026</article-id><title-group><article-title>Source-dependent organic aerosol hygroscopicity in eastern China: observational evidence for conditional enhancement under biomass-burning influence</article-title><alt-title>Source-dependent organic aerosol hygroscopicity in eastern China</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Wu</surname><given-names>Yunfei</given-names></name>
          <email>wuyf@mail.iap.ac.cn</email>
        <ext-link>https://orcid.org/0000-0002-1251-0425</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Li</surname><given-names>Jiwei</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Zhang</surname><given-names>Zhisheng</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Tao</surname><given-names>Jun</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0936-4869</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Xia</surname><given-names>Yunjie</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ran</surname><given-names>Liang</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Deng</surname><given-names>Zhaoze</given-names></name>
          <email>dengzz@mail.iap.ac.cn</email>
        <ext-link>https://orcid.org/0000-0002-0955-6350</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>State Key Laboratory of Atmospheric Environment and Extreme Meteorology, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>School of Resources and Environmental Engineering, Shandong University of Technology, Zibo 255000, China</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>South China Institute of Environmental Sciences, Ministry of Ecology and Environmental, Guangzhou 510655, China</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Institute for Environmental and Climate Research, College of Environment and Climate, Jinan University, Guangzhou 511436, China</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Beijing Meteorological Observation Center, Beijing 100176, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Yunfei Wu (wuyf@mail.iap.ac.cn) and Zhaoze Deng (dengzz@mail.iap.ac.cn)</corresp></author-notes><pub-date><day>30</day><month>October</month><year>2026</year></pub-date>
      
      <volume>26</volume>
      <issue>21</issue>
      <fpage>15333</fpage><lpage>15347</lpage>
      <history>
        <date date-type="received"><day>13</day><month>July</month><year>2026</year></date>
           <date date-type="rev-request"><day>6</day><month>August</month><year>2026</year></date>
           <date date-type="rev-recd"><day>14</day><month>October</month><year>2026</year></date>
           <date date-type="accepted"><day>21</day><month>October</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Yunfei Wu et al.</copyright-statement>
        <copyright-year>2026</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/26/15333/2026/acp-26-15333-2026.html">This article is available from https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e171">Aerosol hygroscopicity is a key property governing aerosol water uptake and aerosol–cloud interactions, yet the hygroscopicity of organic aerosol (OA) remains poorly constrained because of its chemical complexity and diverse emission sources. Here, OA hygroscopicity (<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) was retrieved from comprehensive field observations at a rural site in eastern China using humidified light-scattering measurements and ZSR-based closure analysis. <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited pronounced temporal variability during winter, ranging from nearly zero to 0.49 with a mean value of 0.11 <inline-formula><mml:math id="M3" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.11. Although OA was generally highly oxidized, <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was only weakly correlated with the <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio, indicating that bulk oxidation state alone cannot explain its variability. Instead, <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> increased systematically with biomass-burning influence. Atmospheric aging substantially enhanced <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> under biomass-burning-dominated conditions, whereas highly oxidized OA under weak biomass-burning influence remained weakly hygroscopic. These findings demonstrate that the hygroscopic response of OA to atmospheric aging is fundamentally source dependent and indicate that source-dependent parameterizations provide a more physically realistic framework than conventional oxidation-based approaches for representing OA hygroscopicity in atmospheric models.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Chinese Academy of Sciences</funding-source>
<award-id>XDB0760200</award-id>
</award-group>
<award-group id="gs2">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>42275114</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e258">Aerosol hygroscopicity, which governs particle water uptake under ambient relative humidity (RH), is a fundamental property governing the environmental and climatic impacts of atmospheric aerosols (Wang and Chen, 2019). Hygroscopic growth modifies particle size and optical properties, thereby enhancing light extinction, reducing visibility, and altering aerosol radiative forcing. It also regulates cloud condensation nuclei (CCN) activation and cloud microphysical processes (Petters and Kreidenweis, 2007; Dusek et al., 2006). In hydrometeorologically active regions, even modest variations in aerosol hygroscopicity (<inline-formula><mml:math id="M8" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>) could alter CCN activation (Mallet et al., 2017) and thereby influence cloud microphysics, potentially modulating precipitation and extreme weather through aerosol–cloud–precipitation feedbacks (Fan et al., 2016; Rosenfeld et al., 2019). Furthermore, by increasing aerosol liquid water content, hygroscopic growth facilitates heterogeneous and multiphase chemical reactions that contribute to secondary aerosol formation (Ervens et al., 2011; Shi et al., 2024). Aerosol hygroscopicity is also a key parameter in satellite and lidar retrieval algorithms because aerosol optical and mass properties depend strongly on aerosol water uptake under ambient conditions (Zhao et al., 2017; Dawson et al., 2020). Despite its importance, however, aerosol hygroscopicity remains insufficiently constrained by observations, particularly for organic aerosol (OA).</p>
      <p id="d2e268">The hygroscopicity of internally mixed aerosols is commonly described using the <inline-formula><mml:math id="M9" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler framework (Petters and Kreidenweis, 2007), whereas bulk aerosol hygroscopicity can be predicted from individual chemical components through the Zdanovskii–Stokes–Robinson (ZSR) mixing rule (Stokes and Robinson, 1966). The hygroscopic behaviors of major inorganic species have been extensively characterized, allowing their contributions to bulk aerosol water uptake to be predicted with relatively high confidence. In contrast, OA remains much more difficult to constrain because of its extraordinary chemical complexity, diverse emission sources, and continuous atmospheric evolution (Jimenez et al., 2009). Direct measurements of ambient OA hygroscopicity (<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) are therefore challenging, and <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is generally inferred indirectly through closure analyses combining bulk hygroscopicity measurements with aerosol chemical composition within the ZSR framework (Kuang et al., 2021; Liu et al., 2021). Although a globally representative <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> value of approximately 0.12 has recently been suggested (Pöhlker et al., 2023), field observations reveal that <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> varies by more than one order of magnitude across different environments (Gunthe et al., 2009; Chang et al., 2010). Understanding the processes governing this variability remains a major challenge for accurately representing OA hygroscopicity in atmospheric models.</p>
      <p id="d2e322">Atmospheric oxidation has traditionally been regarded as the dominant process governing OA hygroscopicity. Laboratory studies have consistently shown that oxidation increases the abundance of oxygen-containing functional groups, thereby enhancing the water solubility and hygroscopicity of secondary organic aerosol (SOA; Zhao et al., 2016). Consequently, positive relationships between <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and oxidation metrics, particularly the elemental <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio, have been widely reported for laboratory-generated SOA systems (Lambe et al., 2011), motivating the development of empirical parameterizations that predict <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> directly from oxidation state. However, under real atmospheric conditions influenced by multiple emission sources and complex chemical processing, relationships between <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and oxidation metrics often become substantially weaker, highly nonlinear, or even inverse (Zhao et al., 2016; Kuang et al., 2021). For example, Cerully et al. (2015) found that biogenic isoprene-derived OA exhibited higher hygroscopicity than oxygenated OA despite its substantially lower oxidation level. These observations suggest that bulk oxidation state alone may not provide a universal predictor of OA hygroscopicity in the real atmosphere.</p>
      <p id="d2e370">Increasing evidence suggests that emission source may substantially influence OA hygroscopicity beyond bulk oxidation state. Ambient observations have shown that OA factors originating from different emission sources or formation pathways can exhibit markedly different hygroscopic properties despite having similar oxidation levels (Kuang et al., 2021; Liu et al., 2021). Furthermore, aerosols originating from different emission sources may undergo distinct chemical evolution during atmospheric aging, resulting in distinct hygroscopic responses to atmospheric oxidation. These findings imply that emission source influences OA hygroscopicity not only through source-specific chemical composition but also by modulating its evolution during atmospheric aging. Consequently, the relative importance of emission source and atmospheric oxidation in governing OA hygroscopicity under ambient conditions remains insufficiently understood. This knowledge gap is particularly relevant in regions experiencing rapid changes in emission structure, where the relative contributions of different OA sources continue to evolve.</p>
      <p id="d2e374">In eastern China, stringent emission controls over the past decade have led to substantial reductions in total aerosol loadings (Zheng et al., 2018). These changes have been associated with regional climate responses; for example, reduced aerosol loading has been shown to enhance Meiyu precipitation over the middle and lower reaches of the Yangtze River (Yang et al., 2022). Such findings highlight the sensitivity of regional climate to aerosol perturbations and underscore the importance of accurately constraining aerosol hygroscopicity. Meanwhile, the relative contribution of OA – characterized by diverse sources and complex chemical composition – has increased in fine particulate matter (Chen et al., 2024; Li et al., 2023). In addition to changes in aerosol abundance, ongoing transitions in emission structures have altered the relative importance of different OA sources and atmospheric processing pathways across eastern China, potentially leading to substantial changes in OA hygroscopic properties. Under these evolving emission scenarios, accurately representing OA hygroscopicity is becoming increasingly important for predicting aerosol radiative effects, aerosol–cloud interactions, and the associated regional climate responses.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e379"><bold>(a)</bold> The geographic location of the Huainan Climate and Environment Observatory marked by a triangle on the topographic map; <bold>(b)</bold> schematic diagram of the hygroscopicity observation system. Map data © 2025 Google.</p></caption>
        <graphic xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026-f01.jpg"/>

      </fig>

      <p id="d2e393">In this study, we conducted comprehensive field observations of aerosol hygroscopicity at a rural site in eastern China by combining humidified light-scattering measurements, particle number size distributions, and real-time aerosol chemical composition measurements. Bulk aerosol hygroscopicity was first retrieved under subsaturated conditions and subsequently used to constrain OA hygroscopicity through ZSR-based closure analysis. We then investigated whether bulk oxidation state alone adequately explains the observed variability of <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, or whether emission source exerts a stronger control on OA hygroscopicity through its influence on atmospheric aging and chemical composition. Particular emphasis is placed on the influence of biomass-burning-related OA, whose contribution varies substantially during the observation period. Our results provide additional observational constraints on the mechanisms governing OA hygroscopicity and demonstrate that OA hygroscopicity parameterizations incorporating source-dependent information provide a more physically realistic framework than conventional oxidation-based approaches.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Experiment</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Observation Site</title>
      <p id="d2e422">Field campaigns were conducted at the Huainan Climate and Environment Observatory, a rural research facility operated by the Institute of Atmospheric Physics, Chinese Academy of Sciences, during winter (10 January–9 February 2021) and summer (30 June–27 July 2021) seasons. Situated in Anhui Province, East China (32.74° N, 117.14° E; 70 <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">s</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula>), the Huainan site occupies a forested hillside within a municipally maintained park located 20 <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> northeast of Huainan's urban core. The surrounding area exhibits mixed land-use patterns, with intensive agricultural activities dominating the northern and western sector and a residential community of approximately 7000 inhabitants bordering the southern foothills (Fig. 1a).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Measurements</title>
<sec id="Ch1.S2.SS2.SSS1">
  <label>2.2.1</label><title>Scattering hygroscopic growth</title>
      <p id="d2e469">A humidified scattering measurement system was employed to quantify the aerosol scattering hygroscopic growth factor, denoted as <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, across RH ranges of <inline-formula><mml:math id="M22" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40 %–90 %. The system comprises two integrating nephelometers operating in parallel: one measures dry aerosols under controlled conditions (e.g., <inline-formula><mml:math id="M23" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 40 <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula>), while the other monitors humidity-conditioned particles.</p>
      <p id="d2e511">For dry-condition measurements, <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> aerosols were dehydrated through a Nafion dryer (MD-700, Perma Pure LLC, USA) to residual humidity levels below 40 <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula> before entering the nephelometer. The humidified channel utilized a temperature-regulated water bath coupled with a Nafion membrane humidifier (MH-700, Perma Pure LLC, USA) to implement controlled RH ramping (Fig. 1b). Gradual humidity increases from <inline-formula><mml:math id="M27" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40 % to <inline-formula><mml:math id="M28" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 90 <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula> were achieved through heating at 0.8 <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">RH</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">min</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, followed by cooling phases at 1.2 <inline-formula><mml:math id="M31" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">min</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to reset baseline conditions.</p>
      <p id="d2e602">To enhance temporal resolution, two water baths operated alternately: one executing RH elevation while the concurrent bath underwent cooling. This reciprocating design enabled uninterrupted measurement of humidity ramping phases, reducing complete cycle durations from <inline-formula><mml:math id="M32" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 120 <inline-formula><mml:math id="M33" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> (single-bath mode) to <inline-formula><mml:math id="M34" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 60 <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula>. Each humidity ramp cycle (40 %–90 <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula>) provided synchronized dry and humidified scattering coefficients (<inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) for <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> computation.</p>
      <p id="d2e693">In this study, <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> were measured at 450, 525, and 635 <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> wavelengths using an Aurora 3000 multi-wavelength nephelometer (Ecotech, Australia), while <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> at 520 <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> were acquired through an Aurora 1000 single-wavelength nephelometer (Ecotech, Australia). To bridge this spectral discrepancy, <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values at 520 <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> were interpolated from tri-wavelength Aurora 3000 measurements using logarithmic-scale regression between <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and corresponding wavelength (<inline-formula><mml:math id="M47" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>):

              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M48" display="block"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where the coefficients <inline-formula><mml:math id="M49" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> (i.e., scattering Ångström exponent) and <inline-formula><mml:math id="M50" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> were determined through least-squares fitting of the 450, 525 and 635 <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> spectral data. This spectral alignment protocol ensured methodological consistency for calculating the hygroscopic enhancement factor of scattering coefficient at 520 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>:

              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M53" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow><mml:mn mathvariant="normal">520</mml:mn></mml:msubsup><mml:mo mathsize="1.1em">/</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow><mml:mn mathvariant="normal">520</mml:mn></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <label>2.2.2</label><title>Aerosol size distribution</title>
      <p id="d2e906">Particle number size distributions (PNSDs) were characterized using a scanning mobility particle sizer system (SMPS; TSI Inc., USA) covering dry mobility diameters (<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) of <inline-formula><mml:math id="M55" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15–750 <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>. During the winter campaign, the SMPS operated in standard scanning mode with 5 <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> temporal resolution, comprising a differential mobility analyzer (DMA 3081, TSI Inc., USA) and a condensation particle counter (CPC 3776, TSI Inc., USA).</p>
      <p id="d2e943">For summer measurements, the system was reconfigured with a stepwise voltage protocol. The DMA executed 27 discrete voltage steps corresponding to logarithmically spaced <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (18–750 <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>), with 6- or 10 <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula> dwell time per step (corresponding to 3- or 5 <inline-formula><mml:math id="M61" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> full cycle). At each <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, aerosol number concentrations were concurrently measured by the CPC for total particle counts and a cloud condensation nuclei counter (CCNC-100, Droplet Measurement Technologies) for CCN activation efficiency determination. This dual-detector configuration enabled simultaneous acquisition of size-resolved aerosol and CCN number concentration across the 18–750 <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> range. After aligning the time between DMA size selection and CPC/CCNC detection via the lag-time correction approach proposed by Wu et al. (2019), PNSD and corresponding CCN activation spectra (CCN/CN ratio vs. <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) were inverted using a custom algorithm based on Hagen and Alofs (1983).</p>
      <p id="d2e1023">A Grimm 11-C laser aerosol spectrometer (GRIMM Aerosol Technik, Germany) was deployed during both campaigns to extend PNSD measurements into the coarse-particle size range. The instrument determines single-particle optical diameters (<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) from 0.25 to 32 <inline-formula><mml:math id="M67" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> based on 90° light-scattering detection and operated at a flow rate of 1.2 <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">L</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">min</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> with a temporal resolution of 1 <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula>. Prior to deployment, the instrument was calibrated against a reference instrument maintained by the China Meteorological Administration. Owing to the <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> size-selective inlet used in this study, particles larger than approximately 2 <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> were largely excluded, resulting in measured <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> distributions spanning <inline-formula><mml:math id="M73" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.25–2 <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. The Grimm measurements were merged with the SMPS data to generate continuous PNSDs covering particle diameters from <inline-formula><mml:math id="M75" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> to 2 <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, and agreement between the two instruments was verified over their overlapping size range.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS3">
  <label>2.2.3</label><title>Chemical composition</title>
      <p id="d2e1156">Chemical characterization of non-refractory fine particulate matter with aerodynamic diameters smaller than 2.5 <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M79" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">nrPM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) was conducted in real-time using a Time-of-Flight Aerosol Chemical Speciation Monitor (ToF-ACSM; Aerodyne Research Inc., USA) configured with a <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> aerodynamic lens and a capture vaporizer. The instrument delivered continuous quantitative measurements of sulfate (<inline-formula><mml:math id="M81" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>), nitrate (<inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), ammonium (<inline-formula><mml:math id="M83" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), chloride (<inline-formula><mml:math id="M84" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Cl</mml:mi><mml:mo>-</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>), and OA mass concentrations in <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> at 10 <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> temporal resolution. Ambient aerosols were size-selected through a <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> cyclone inlet and subsequently thermally vaporized at 600 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> under high vacuum in the ToF-ACSM chamber. The resulting non-refractory components were quantitatively analyzed via time-of-flight aerosol mass spectrometry. Instrument calibrations were performed before and after each month-long campaign using ammonium nitrate (AN) and ammonium sulfate (AS) reference standards with <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 300 <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>. Wintertime OA mass spectra were resolved into four distinct components using positive matrix factorization (PMF) analysis implemented in the SoFi toolkit (Canonaco et al., 2013) using Igor Pro 6.37 (Wavemetrics Inc.). The identified factors included hydrocarbon-like OA (HOA), associated with traffic emissions; cooking-related OA (COA); biomass burning OA (BBOA); and oxygenated OA (OOA), representing secondary oxidized components. In contrast, summer OA mass spectra were adequately described by two factors, denoted as HOA and OOA (Sect. S1 in the Supplement). The spectrum of each OA factor is shown in Fig. S1 in the Supplement. Black carbon (BC) mass concentrations were continuously measured at a 1 <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> time resolution using an AE33 aethalometer (Aerosol d.o.o., Slovenia) equipped with a <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> size-selective inlet.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS4">
  <label>2.2.4</label><title>Aerosol absorption coefficient</title>
      <p id="d2e1332">The AE33 measurements were also used to determine the aerosol absorption coefficient, which is expressed as

              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M93" display="block"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:mtext>eBC</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the aerosol absorption coefficient at wavelength <inline-formula><mml:math id="M95" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>; <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mtext>eBC</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the equivalent BC mass concentration reported by the AE33 at its seven operating wavelengths (370, 470, 520, 590, 660, 880 and 950 <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>); and <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the mass absorption cross-section provided by the manufacture. The factor <inline-formula><mml:math id="M99" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> accounts for multiple scattering by the filter membrane as well as the influence of aerosol scattering on absorption measurement. In this study, a wavelength-independent value of <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.9</mml:mn></mml:mrow></mml:math></inline-formula> was adopted, based on intercomparison between the AE33 and two photoacoustic extinctiometers (PAX, DMT, USA) with operating wavelengths of 375 and 870 <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>, respectively (Fig. S2), which provides reference measurement of <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>ap</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> using the photoacoustic technique and is not affected by filter-based scattering artifacts.</p>
      <p id="d2e1471">In regions far from major dust sources, such as Huainan in East China, <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is expected to be dominated by emissions from fossil fuel combustion and biomass burning. Accordingly, <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> can be expressed as the sum of contributions from fossil fuel combustion (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>ff</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and biomass burning (<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>bb</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>):

              <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M107" display="block"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>ff</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>bb</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e1595">The spectral dependence of both <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>ff</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mtext>bb</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is commonly described by a power–law relationship. Therefore, Eq. (4) can be rewritten as:

              <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M110" display="block"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>ff</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>bb</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the absorption Ångström exponents (AAE) for fossil fuel combustion and biomass burning, respectively, while <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are fitting coefficients derived from absorption measurements of the AE33 operating wavelengths between 470 and 950 <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>. Following Sandradewi et al. (2008), <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> were fixed at 1.0 and 2.0, respectively. The relative contribution of biomass burning to BC (<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) was then estimated as the fraction of biomass-burning-derived absorption to total aerosol absorption at 950 <inline-formula><mml:math id="M119" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>, where aerosol light absorption is assumed to be dominated by BC.</p>
      <p id="d2e1783"><inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> can also be decomposed into contributions from BC and non-BC components, thus can be expressed as:

              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M121" display="block"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>BC</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>BC</mml:mtext></mml:msub></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>nonBC</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>nonBC</mml:mtext></mml:msub></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>BC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>nonBC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the AAE for BC and non-BC components, respectively, while <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>BC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>nonBC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are fitting coefficients derived from measurements at the seven operating wavelengths of the AE33. Following common practice, <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>BC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was fixed at 1.0 in this study. <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>nonBC</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was constrained to the range of 2–8, and the optimal value was selected by minimizing the residuals between the measured and fitted <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>ap</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (Chen et al., 2015; Ran et al., 2016). Absorption by non-BC components is expected to mainly arises from light-absorbing OA (i.e., brown carbon; BrC) in this study, because the observation site is far from major dust sources.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS5">
  <label>2.2.5</label><title>Auxiliary measurements</title>
      <p id="d2e1951">Auxiliary measurements included meteorological parameters and trace gases. Air temperature, RH, atmospheric pressure, wind speed, and wind direction at 2 <inline-formula><mml:math id="M129" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> above ground level were continuously monitored using a meteorological sensor (WXT530, Vaisala, Finland). Mixing ratios of <inline-formula><mml:math id="M130" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M131" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">CO</mml:mi></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M132" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were measured using Model 43i, 48i, and 49i analyzers (Thermo Scientific, USA), respectively, whereas <inline-formula><mml:math id="M133" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">NO</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M134" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were measured using a Model 42i analyzer (Thermo Scientific, USA). In addition, daily filter samples were collected for offline chemical analyses, including water-soluble inorganic ions, organic carbon (OC), elemental carbon (EC), and selected water-soluble organic compounds such as levoglucosan and mannosan. Detailed information on the filter sampling and chemical analyses is beyond the scope of this study and will be reported separately.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e2014">The workflow for PNSD merging and <inline-formula><mml:math id="M135" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> inversion.</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026-f02.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Data processing</title>
<sec id="Ch1.S2.SS3.SSS1">
  <label>2.3.1</label><title>Merging of aerosol size distribution</title>
      <p id="d2e2046">Data integration between SMPS (<inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and Grimm 11-C (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) measurements required reconciling their distinct sizing principles. As the Grimm spectrometer was factory-calibrated using polystyrene latex (PSL) spheres with a refractive index (RI) of 1.59, raw <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values exhibited systematic underestimation for ambient aerosols with divergent RIs, evidenced by discrepancies in particle PNSD within the overlapping size range (360–720 <inline-formula><mml:math id="M139" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>; Fig. S3). To resolve this, we developed a RI correction protocol grounded in Mie theory-derived scattering cross-section (<inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>sp</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) calculations. First, the <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>sp</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> value for each Grimm-reported <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was computed under PSL-calibrated conditions (RI <inline-formula><mml:math id="M143" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.59), incorporating the instrument's angular detection geometry (60–120° scattering angles). Next, we gradually adjusted the RI from 1.35 to 1.60 (<inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>RI</mml:mtext></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M145" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.005) to calculate <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>sp</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>-equivalent <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values and correspondingly Grimm-derived PNSD. The optimal RI was identified by minimizing the root-mean-square error (RMSE) between adjusted Grimm-derived and SMPS-measured particle volume size distributions (PVSD) over the 360–720 <inline-formula><mml:math id="M148" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> overlap range, considering the reference measurement of SMPS (Fig. 2). This procedure generated unified PNSD data spanning from <inline-formula><mml:math id="M149" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 <inline-formula><mml:math id="M150" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M151" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 <inline-formula><mml:math id="M152" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. S3). For the merged PNSD, the particle diameter is denoted as <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, instead of either <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <label>2.3.2</label><title>Inversion of hygroscopic parameter</title>
      <p id="d2e2253">Following the determination of optimal RI and merged dry-aerosol PNSD, the theoretical <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> was computed via Mie theory under spherical particle assumptions, incorporating Müller et al. (2011) angular response corrections for the Aurora 3000 nephelometer's non-ideal illumination geometry (e.g., 10–171° scattering angles). To distinguish model outputs from observations, calculated and measured <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values are denoted as <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext><mml:mo>,</mml:mo><mml:mtext>calc</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext><mml:mo>,</mml:mo><mml:mtext>meas</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, respectively. <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext><mml:mo>,</mml:mo><mml:mtext>calc</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext><mml:mo>,</mml:mo><mml:mtext>meas</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values showed strong agreement across 450, 525, and 635 <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> wavelengths (<inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M164" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.99; Fig. S4), validating the RI correction and Mie computation framework.</p>
      <p id="d2e2395">To calculate the humidified PNSD, the <inline-formula><mml:math id="M165" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler equation (Petters and Kreidenweis, 2007) is used. For a given <inline-formula><mml:math id="M166" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>, we calculated the diameter growth factor at arbitrary RH, denoted as <inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, by solving the <inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler equation:

              <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M169" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mtext>RH</mml:mtext><mml:mn mathvariant="normal">100</mml:mn></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">κ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>exp</mml:mtext><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mtext>water</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mo>⋅</mml:mo><mml:mi>T</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the surface tension of solution/air interface, <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>water</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the molecular weight of water, <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>water</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the density of water, <inline-formula><mml:math id="M173" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the universal gas constant, <inline-formula><mml:math id="M174" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is kelvin temperature, and <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the dry particle diameter. Then the diameter of humidified particle diameter (<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) at arbitrary RH can be calculated as <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e2675">In practice, because the dry PNSD is measured under low RH conditions (e.g., RH <inline-formula><mml:math id="M178" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 40 %) rather than the absolutely dry condition with RH <inline-formula><mml:math id="M179" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0, we derived the absolutely dry PNSD (RH <inline-formula><mml:math id="M180" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0) from the measured PNSD under low RH conditions using the <inline-formula><mml:math id="M181" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler equation first, and then calculated the humidified PNSD across the RH levels of <inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> measurement. The RH of dry aerosols was recorded by the dry Aurora 3000 nephelometer. The RI of humidified particles was estimated from PNSD-merging derived RI of dry particles and RI of pure water using the Maxwell–Garnett mixing rule (Garnett, 1904). Combination the humidified PNSD and RI, the theoretical scattering coefficient of wet particles (<inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext><mml:mo>,</mml:mo><mml:mtext>calc</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) was determined via Mie theory. Notably, the angular response correction was also applied in calculating <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext><mml:mo>,</mml:mo><mml:mtext>calc</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, assuming that the Aurora 1000 shares the same angular sensitivity function as the Aurora 3000, as reported by Müller et al. (2011), owing to their similar instrument designs. Then, the theoretical <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, denoted as <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, was obtained using Eq. (2) by replacing measured <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>dry</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext><mml:mo>,</mml:mo><mml:mtext>wet</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> by theoretical ones. A range of <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values corresponding to different aerosol hygroscopic ability were acquired by changing <inline-formula><mml:math id="M190" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> in a range of 0.1–0.6 (<inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">κ</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M192" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.01). The optimal <inline-formula><mml:math id="M193" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> (hereafter denoted as <inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) was identified by minimizing the RMSE between <inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>meas</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> over selected RH ranges (Fig. S3). The overall workflow – from PNSD merging to <inline-formula><mml:math id="M197" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> inversion – is schematized in Fig. 2. The <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values were derived for different RH intervals (e.g., 50 %–60 %, 60 %–70 %, 70 %–80 %, 80 %–90 %) as well as for the entire 40 %–90 <inline-formula><mml:math id="M199" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula> range. Unless otherwise specified, <inline-formula><mml:math id="M200" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula><sub>inv</sub> values retrieved over the 80 %–90 <inline-formula><mml:math id="M202" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula> range are used to represent bulk aerosol hygroscopicity, as the results are directly comparable with previous studies that report <inline-formula><mml:math id="M203" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula><sub>inv</sub> within this RH range (Kuang et al., 2020, 2021) and are consistent with the RH conditions corresponding to the <inline-formula><mml:math id="M205" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values adopted for well-characterized inorganic species when estimating OA hygroscopicity, as discussed below.</p>
      <p id="d2e2999">We also applied a single-parameter fitting to <inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>meas</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, expressed as

              <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M207" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>RH</mml:mtext><mml:msub><mml:mo>)</mml:mo><mml:mtext>meas</mml:mtext></mml:msub><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 mathvariant="italic">κ</mml:mi><mml:mtext>fit</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:mo>-</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>fit</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mtext>RH</mml:mtext><mml:mtext>dry</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mtext>RH</mml:mtext><mml:mtext>dry</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>fit</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the fitting parameter and <inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:msub><mml:mtext>RH</mml:mtext><mml:mtext>dry</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the RH of dry aerosols. <inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>fit</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can be used as a simple proxy for aerosol hygroscopic ability, with higher values indicating stronger water uptake; however, compared to <inline-formula><mml:math id="M211" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula><sub>inv</sub>, it is also influenced by the PNSD in addition to aerosol chemical composition.</p>

<table-wrap id="T1"><label>Table 1</label><caption><p id="d2e3153">Densities (<inline-formula><mml:math id="M213" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>) and hygroscopicity parameters (<inline-formula><mml:math id="M214" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>) of different species.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <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"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">AN</oasis:entry>
         <oasis:entry colname="col3">AS</oasis:entry>
         <oasis:entry colname="col4">ABS</oasis:entry>
         <oasis:entry colname="col5">PC</oasis:entry>
         <oasis:entry colname="col6">BC</oasis:entry>
         <oasis:entry colname="col7">rPM</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(<inline-formula><mml:math id="M215" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3">(<inline-formula><mml:math id="M216" display="inline"><mml:mrow class="chem"><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">(<inline-formula><mml:math id="M217" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">HSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">(<inline-formula><mml:math id="M218" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">KCl</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M219" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">1.72</oasis:entry>
         <oasis:entry colname="col3">1.77</oasis:entry>
         <oasis:entry colname="col4">1.78</oasis:entry>
         <oasis:entry colname="col5">1.98</oasis:entry>
         <oasis:entry colname="col6">1.70</oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M220" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.58</oasis:entry>
         <oasis:entry colname="col3">0.48</oasis:entry>
         <oasis:entry colname="col4">0.56</oasis:entry>
         <oasis:entry colname="col5">0.89</oasis:entry>
         <oasis:entry colname="col6">0</oasis:entry>
         <oasis:entry colname="col7">0.05</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S2.SS3.SSS3">
  <label>2.3.3</label><title>Hygroscopicity of OA</title>
      <p id="d2e3373">The bulk aerosol <inline-formula><mml:math id="M221" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> is usually chemically estimated using the ZSR volume-weighted mixing rule by assuming an internal mixture (Stokes and Robinson, 1966; Wu et al., 2016; Kuang et al., 2021):

              <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M222" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>chem</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mo>∑</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</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="M223" 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> and <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represent the hygroscopicity parameter and volume fraction of species <inline-formula><mml:math id="M225" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>, respectively. Chemical composition derived from the ToF-ACSM and AE33 measurements included AN, AS, ammonium bisulfate (ABS), potassium chloride (PC), OA, and BC. A simplified ion-pairing scheme following Gysel et al. (2007) was applied to convert the ion mass concentrations reported by the ToF-ACSM into the corresponding inorganic salt mass concentrations. Chloride was assumed to be entirely associated with potassium, forming PC, in consideration of the influence of biomass burning in the study region. The densities of the identified species, including AN, AS, ABS, PC and BC, were adopted from Gysel et al. (2007) and Kuang et al. (2021) and are summarized in Table 1. The density of OA was estimated using the governing equation developed by Kuwata et al. (2012), with the elemental ratios <inline-formula><mml:math id="M226" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M227" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> as input parameters. The <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratios were calculated from <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">44</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (the fractional ion intensity at <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M232" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 44 from unit-mass-resolution data) and <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">43</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (analogous to <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">44</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> but at <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M236" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 43) using the fitted relationships established for an aerosol mass spectrometer equipped with a capture vaporizer (Fig. 5 in the Supporting Information of Hu et al., 2018). Other refractory species (rPM) were accounted for by residual volume calculation:

              <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M237" display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>PM</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>AN</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>AS</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>ABS</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>PC</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>OA</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>BC</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where total <inline-formula><mml:math id="M238" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> volume (<inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>PM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) was integrated from merged PVSD (<inline-formula><mml:math id="M240" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula>  15 <inline-formula><mml:math id="M241" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>–2.0 <inline-formula><mml:math id="M242" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). The upper integration limit aligns with the volume-equivalent diameter (<inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) to aerodynamic diameter (<inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) relationship: <inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>≈</mml:mo></mml:mrow></mml:math></inline-formula> (1.1–1.3) <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for typical aerosol densities (1.2–1.7 <inline-formula><mml:math id="M247" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). These remaining refractory species were assumed to exhibit weak hygroscopicity and were assigned a hygroscopicity parameter of <inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M249" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.05 following Kuang et al. (2021). The <inline-formula><mml:math id="M250" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values adopted for individual aerosol components are taken from Kuang et al. (2020, 2021) and are summarized in Table 1. Since <inline-formula><mml:math id="M251" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> is RH dependent under sub-saturation conditions (Zhao et al., 2022), the selected values are assumed to represent aerosol hygroscopicity at an RH of <inline-formula><mml:math id="M252" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 85 %, consistent with the <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values retrieved over the 80 %–90 <inline-formula><mml:math id="M254" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">RH</mml:mi></mml:mrow></mml:math></inline-formula> range. The consistency between <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>chem</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> has been theoretically demonstrated by Kuang et al. (2020), thus OA hygroscopicity (<inline-formula><mml:math id="M257" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) was subsequently derived as:

              <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M258" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mtable class="array" columnalign="center"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>AN</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>AN</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>AS</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>AS</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>ABS</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>ABS</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>PC</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>PC</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>BC</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>BC</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e3945">The derived <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> may be subject to uncertainties in the input parameters used in the inversion, thus, we performed a Monte Carlo uncertainty propagation analysis, with 10 ,000 realizations for each data point in the <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> time series. In each realization, the input variables in Eqs. (10) and (11) were randomly perturbed according to their prescribed uncertainties. Given the similarities in the measurement and inversion methods, the uncertainties assigned to the input variables, including the mass concentrations of non-refractory aerosol species measured by the ToF-ACSM, <inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>PM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, were based on the estimates reported in Table 2 of Kuang et al. (2021). It should be noted that the derived <inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> does not account for the potential contribution of OA components lost during the drying process before the aerosol enters the measurement instruments. In addition, the potential contribution of co-condensation to aerosol hygroscopic growth (Gunthe et al., 2021) is not explicitly considered because gas-phase precursor measurements (e.g., <inline-formula><mml:math id="M265" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">HCl</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M266" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and a dedicated thermodynamic analysis are not available in this study. These factors may introduce additional uncertainties that are not captured by the Monte Carlo analysis.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and Discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Overview of Meteorology and Aerosol</title>
      <p id="d2e4051">The study site is located in the temperate monsoon region of eastern China, which is characterized by relatively cold and dry winters and hot and humid summers. During the winter campaign, the mean air temperature was 6.6 <inline-formula><mml:math id="M267" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4.1 <inline-formula><mml:math id="M268" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and the ambient RH averaged 54.0 <inline-formula><mml:math id="M269" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 20.5 % (Fig. S5). In contrast, the summer campaign was considerably warmer and more humid, with a mean temperature of 27.3 <inline-formula><mml:math id="M270" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.0 <inline-formula><mml:math id="M271" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and an RH of 75.0 <inline-formula><mml:math id="M272" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 11.2 % (Fig. S6). Prevailing winds during both campaigns were predominantly from the south, with intermittent northwesterly air masses (Fig. S7).</p>
      <p id="d2e4103">Pronounced seasonal differences were observed in aerosol loading and chemical composition. The mean <inline-formula><mml:math id="M273" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">nrPM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration reached 58.1 <inline-formula><mml:math id="M274" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 39.8 <inline-formula><mml:math id="M275" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> during winter, nearly three times higher than the summer average (20.8 <inline-formula><mml:math id="M276" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 12.0 <inline-formula><mml:math id="M277" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). Wintertime aerosol loadings were comparable to those reported for heavily polluted urban areas in eastern China (e.g., Nanjing; Zhang et al., 2017), indicating that the rural Huainan site was frequently influenced by severe regional pollution. High-pollution episodes generally coincided with elevated RH (Fig. S5), suggesting favourable conditions for secondary aerosol formation through multiphase processes and potential deterioration of air quality by hygroscopic growth.</p>
      <p id="d2e4169">OA was the dominant constituent of <inline-formula><mml:math id="M278" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">nrPM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> during both campaigns, accounting for 44.3 % of the aerosol mass in winter and increasing to 55.2 % in summer. OOA represented the largest OA fraction, contributing 84.0 % of total OA in winter and 94.0 % in summer, indicating that ambient OA was predominantly aged throughout both observation periods. BBOA accounted for 4.3 % of OA mass during winter but was not resolved during summer, reflecting enhanced biomass-burning emissions associated with wintertime heating. In addition, wintertime BBOA showed a strong positive correlation with COA (<inline-formula><mml:math id="M279" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M280" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.69, <inline-formula><mml:math id="M281" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M282" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001), implying that local biomass-burning emissions were closely associated with residential activities.</p>
      <p id="d2e4211">Overall, the observations reveal a polluted atmosphere characterized by persistently aged OA and frequent high-RH conditions, particularly during winter pollution episodes. Such conditions provide an ideal opportunity to investigate aerosol hygroscopicity and to evaluate the respective contributions of inorganic and organic aerosol components to bulk aerosol water uptake.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Bulk Aerosol Hygroscopicity</title>
      <p id="d2e4222">Bulk aerosol hygroscopicity exhibited pronounced seasonal variability. The mean <inline-formula><mml:math id="M283" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>fit</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was 0.18 <inline-formula><mml:math id="M284" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03 during winter and 0.26 <inline-formula><mml:math id="M285" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.06 during summer, whereas the corresponding <inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> were systematically higher, averaging 0.25 <inline-formula><mml:math id="M287" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04 and 0.31 <inline-formula><mml:math id="M288" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.08, respectively (Figs. S5 and S6). It should be noted that <inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was available for only six days (2–7 July 2021) during the summer campaign because of CPC instrument failure. Consequently, the following analyses focus primarily on the winter observations.</p>
      <p id="d2e4287">The wintertime <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> measured at Huainan was generally higher than that reported at the rural Heshan site in the Pearl River Delta (Kuang et al., 2021). This difference is consistent with the substantially higher inorganic-to-organic mass ratio observed at Huainan (1.27 compared with 0.72 at Heshan), highlighting the dominant contribution of hygroscopic inorganic salts to bulk aerosol water uptake. Nevertheless, the winter mean <inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (0.25 <inline-formula><mml:math id="M292" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04) remained lower than the continental aerosol value of 0.3 that is commonly adopted in atmospheric models (e.g., Andreae and Rosenfeld, 2008). Using <inline-formula><mml:math id="M293" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M294" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.3 instead of the measurement-constrained value resulted in an overestimation of CCN number concentration (<inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>CCN</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) by as much as 10 % at a supersaturation of 0.1 %, although the bias decreased to approximately 3 % at 0.8 % supersaturation (Fig. S8). These results demonstrate that regionally constrained hygroscopicity parameters can substantially improve CCN predictions, particularly under low-supersaturation conditions where aerosol activation is highly sensitive to <inline-formula><mml:math id="M296" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>.</p>
      <p id="d2e4352">Interestingly, <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited a systematic decrease with increasing RH (Fig. S9a). The RH dependence became more pronounced for aerosol populations with larger <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>yvalues (Fig. S9b), indicating that aerosol hygroscopicity cannot always be represented by a constant <inline-formula><mml:math id="M299" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> under ambient conditions. Possible explanations include non-ideal solution effects, RH-dependent solute mass fractions and liquid–liquid phase separation at elevated RH (Liu et al., 2018; Li et al., 2021; Zhao et al., 2022), whereas uncertainties associated with surface tension assumptions (Figs. S10 and S11) and particle equilibration time (Liu et al., 2018) are unlikely to fully account for the observed trend. A similar decrease in <inline-formula><mml:math id="M300" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> with increasing RH was reported by Zhao et al. (2022) for both individual inorganic aerosols (e.g., AS) and ambient aerosols, which was attributed, at least in part, to variations in solute mass fraction within the aerosol–water system. A higher inorganic fraction generally leads to larger <inline-formula><mml:math id="M301" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> values and greater RH-induced variability in <inline-formula><mml:math id="M302" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>. Therefore, aerosol populations with higher <inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values, which are likely associated with larger inorganic fractions, may exhibit stronger RH dependence. Because elucidating the underlying mechanisms is beyond the scope of the present study, this RH dependence is not discussed further.</p>
      <p id="d2e4417">Distinct diurnal and pollution-dependent variations in <inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> were closely associated with changes in aerosol chemical composition (Figs. S12–S14). Higher <inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values generally coincided with larger fractions of hygroscopic inorganic salts, whereas increased contributions from OA and BC were associated with lower bulk hygroscopicity. As pollution intensified, <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>inv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> first increased and then decreased, reflecting a compositional transition from inorganic-dominated aerosol growth at moderate pollution levels to increasingly OA-rich aerosol populations under heavily polluted conditions (Fig. S14).</p>
      <p id="d2e4454">These observations indicate that although inorganic salts dominate bulk aerosol hygroscopicity, the increasing contribution of OA during polluted periods may substantially modify aerosol water uptake. Quantifying the hygroscopicity of OA is therefore essential for understanding the observed variability in bulk aerosol hygroscopicity and is the focus of the following sections.</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e4459">Time series of <bold>(a)</bold> volume concentrations, <bold>(b)</bold> volume fractions of different chemical species in <inline-formula><mml:math id="M307" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>(c)</bold> mass fractions of different OA factors and <inline-formula><mml:math id="M308" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio, <bold>(d)</bold> <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and relative contribution of biomass burning to BC (<inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) at the Huainan site during the winter campaign. The shaded area denotes a persistent pollution episode from 20 to 25 January 2021, with different colors indicating distinct stages of the episode.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Variability and Controls of OA Hygroscopicity</title>
      <p id="d2e4534">Wintertime <inline-formula><mml:math id="M311" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited substantial temporal variability, ranging from nearly zero to 0.49 and averaging 0.11 <inline-formula><mml:math id="M312" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.11 (mean <inline-formula><mml:math id="M313" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> standard deviation, Fig. 3d). This mean <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was slightly higher than those reported at the Gucheng site in the North China Plain (0.08 <inline-formula><mml:math id="M315" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.06; Kuang et al., 2020) and the Heshan site in the Pearl River Delta (0.085; Kuang et al., 2021), suggesting that OA at Huainan was, on average, relatively more hygroscopic. Such pronounced variability indicates that OA hygroscopicity cannot be represented by a single characteristic value and highlights the need to identify the controlling factors governing <inline-formula><mml:math id="M316" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. Monte Carlo uncertainty analysis showed that he standard deviations of the simulated <inline-formula><mml:math id="M317" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> distributions at individual measurement points ranged from 0.01 to 0.18 (Fig. S15). Larger uncertainties generally occurred at higher <inline-formula><mml:math id="M318" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values and lower OA volume fractions, indicating greater sensitivity of the ZSR-based retrieval under these conditions (Fig. S16). Despite the substantial point-by-point uncertainties, the Monte Carlo mean values agreed well with the baseline estimates (Fig. S15a), yielding the same campaign-average <inline-formula><mml:math id="M319" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 0.11 and a correlation coefficient of 0.99 between the two sets of estimates. Additional Monte Carlo sensitivity tests, in which each input parameter was perturbed individually while the others were held constant, showed that uncertainties in <inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>PM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>rPM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> contributed most strongly to the uncertainty in the retrieved <inline-formula><mml:math id="M322" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. S15c).Previous studies have commonly related <inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> to bulk oxidation metrics, particularly the <inline-formula><mml:math id="M324" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio and <inline-formula><mml:math id="M325" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">44</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, leading to several widely adopted empirical parameterizations (Chang et al., 2010; Lambe et al., 2011; Wu et al., 2016). Consistent with this framework, the relatively high average oxidation level observed at Huainan (mean <inline-formula><mml:math id="M326" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M327" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.80 <inline-formula><mml:math id="M328" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.06) may partly explain why the mean <inline-formula><mml:math id="M329" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exceeded values reported at several other field sites. However, oxidation state alone explained little of the observed temporal variability. Throughout the campaign, <inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited only a weak negative correlation with <inline-formula><mml:math id="M331" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M332" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M333" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M334" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.13, <inline-formula><mml:math id="M335" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M336" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.004), despite the relatively narrow range of <inline-formula><mml:math id="M337" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> (0.6–0.9). This result indicates that although oxidation may contribute to the overall hygroscopicity level of ambient OA, it cannot account for the pronounced fluctuations observed on shorter temporal scales. Similar weak relationships between <inline-formula><mml:math id="M338" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and bulk oxidation metrics have also been reported in previous ambient studies (e.g., Kuang et al., 2021; Liu et al., 2021). These observations indicate that bulk oxidation state may determine the overall hygroscopicity level of ambient OA but provides limited explanatory power for its pronounced temporal variability.</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e4815">Diurnal variations of <inline-formula><mml:math id="M339" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, mass fraction of four OA factors, and <inline-formula><mml:math id="M340" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio during the winter campaign. The upper and lower bounds of each box represent the 75th and 25th percentiles, and the upper and lower whiskers represent the 95th and 5th percentiles. The line in each box is the median value and the square represents the mean.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026-f04.png"/>

        </fig>

      <p id="d2e4847">To further evaluate whether OA composition could explain the variability of <inline-formula><mml:math id="M341" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, relationships between <inline-formula><mml:math id="M342" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and PMF-derived OA factors were examined. Previous studies have generally reported higher hygroscopicity for oxygenated OA than for primary OA (Kuang et al., 2021), implying that source apportionment may provide additional information beyond bulk oxidation metrics. At Huainan, however, <inline-formula><mml:math id="M343" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remained only weakly correlated with all resolved OA factors, with correlation coefficients of 0.24, 0.03, 0.07, and <inline-formula><mml:math id="M344" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.26 for the mass fraction of HOA, COA, BBOA, and OOA, respectively. One possible explanation is that OOA could not be further resolved into less-oxidized and more-oxidized components because of the relatively simple OA mass spectra during winter. Consequently, variations associated with atmospheric aging remained embedded within a single OOA factor, weakening the apparent relationship between <inline-formula><mml:math id="M345" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and OA source apportionment. These results suggest that the variability of <inline-formula><mml:math id="M346" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> cannot be adequately explained by either bulk oxidation metrics or the resolved OA factors alone, implying that the processes governing OA hygroscopicity extend beyond conventional bulk descriptors of OA composition.</p>
      <p id="d2e4914">Further insight can be gained from the diurnal evolution of <inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. 4). <inline-formula><mml:math id="M348" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited a pronounced daytime maximum and lower values during the morning and evening. This temporal variation closely resembled that of the OOA fraction while opposing the evolution of primary OA. The morning decrease in <inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> coincided with enhanced HOA contributions associated with traffic emissions, as indicated by concurrent peaks in <inline-formula><mml:math id="M350" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">NO</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M351" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">CO</mml:mi></mml:mrow></mml:math></inline-formula> concentrations (Fig. S13). During the evening, increased contributions from cooking and residential biomass-burning emissions enhanced the fractions of COA and BBOA, leading to another reduction in <inline-formula><mml:math id="M352" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. These observations indicate that freshly emitted primary OA generally suppresses OA hygroscopicity, whereas secondary processing tends to increase it. However, these diurnal patterns are not reflected in the weak point-by-point correlations between <inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the individual OA factors. This discrepancy suggests that the influence of atmospheric aging depends strongly on the chemical nature of the emitted OA rather than simply on its bulk oxidation state.</p>
      <p id="d2e4989">Collectively, the analyses above demonstrate that bulk oxidation metrics explain the average hygroscopicity of OA only to a limited extent and fail to capture its large temporal variability. Likewise, conventional PMF source apportionment alone provides insufficient explanatory power in this study. These findings indicate that the hygroscopic response of OA is likely governed by source-dependent chemical composition and atmospheric processing acting together. We therefore next examine biomass-burning emissions, which exhibit the strongest association with <inline-formula><mml:math id="M354" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> throughout the observation period, to further elucidate the source dependence of OA hygroscopicity.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Source-dependent Controls on OA Hygroscopicity</title>
      <p id="d2e5011">The analyses presented above suggest that bulk oxidation metrics alone cannot adequately explain the observed variability in <inline-formula><mml:math id="M355" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. We therefore further investigated whether source-dependent composition exerts a stronger control on <inline-formula><mml:math id="M356" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> by examining the relationship between <inline-formula><mml:math id="M357" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the relative contribution of biomass burning (<inline-formula><mml:math id="M358" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). As shown in Fig. 3d, temporal variations in <inline-formula><mml:math id="M359" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> closely tracked those of <inline-formula><mml:math id="M360" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> throughout the campaign, with periods of enhanced biomass-burning influence generally accompanied by elevated <inline-formula><mml:math id="M361" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values. This relationship is further supported by the point-by-point comparison (Fig. 5), which reveals a statistically significant positive correlation between <inline-formula><mml:math id="M362" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M363" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M364" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M365" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.48, <inline-formula><mml:math id="M366" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M367" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001). Consistently, binned averages show a systematic increase in <inline-formula><mml:math id="M368" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> with increasing biomass-burning contribution, with mean <inline-formula><mml:math id="M369" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> rising from approximately 0.03 at <inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M371" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 19 % to about 0.17 when <inline-formula><mml:math id="M372" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exceeded 40 % (Fig. 5). Compared with the weak relationship between <inline-formula><mml:math id="M373" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and bulk oxidation metrics, these observations indicate that biomass-burning influence explains substantially more of the temporal variability in OA hygroscopicity. The robustness of the <inline-formula><mml:math id="M374" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M375" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> relationship was examined through sensitivity tests by varying <inline-formula><mml:math id="M376" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from 2.0 to 1.8 and 2.2 while keeping <inline-formula><mml:math id="M377" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> fixed at 1.0, and by varying <inline-formula><mml:math id="M378" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>ff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from 1.0 to 0.9 and 1.1 while keeping <inline-formula><mml:math id="M379" display="inline"><mml:mrow><mml:msub><mml:mtext>AAE</mml:mtext><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> fixed at 2.0. Although the estimated <inline-formula><mml:math id="M380" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values varied with the assumed AAE parameters, the increasing trend of <inline-formula><mml:math id="M381" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> with <inline-formula><mml:math id="M382" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remained qualitatively consistent (Fig. S17).</p>

      <fig id="F5"><label>Figure 5</label><caption><p id="d2e5308">Variation of <inline-formula><mml:math id="M383" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> as a function of relative contribution of biomass burning to BC (<inline-formula><mml:math id="M384" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), with colors indicating the corresponding <inline-formula><mml:math id="M385" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratios. Black open squares represent binned mean <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values based on <inline-formula><mml:math id="M387" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> bins defined by 20-percentile intervals, with error bars indicating one standard deviation. The dashed line shows a linear regression fitted to the binned means.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/26/15333/2026/acp-26-15333-2026-f05.png"/>

        </fig>

      <p id="d2e5373">Although <inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited a clear positive relationship with biomass-burning influence, this relationship could still arise indirectly because biomass-burning aerosol also experiences continuous atmospheric aging after emission. To disentangle the respective influence of emission source and atmospheric oxidation, <inline-formula><mml:math id="M389" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was further examined under contrasting biomass-burning conditions. When biomass-burning influence was weak (<inline-formula><mml:math id="M390" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M391" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 24 %, corresponding to the 20th percentile), <inline-formula><mml:math id="M392" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remained consistently low despite relatively high bulk oxidation levels (mean <inline-formula><mml:math id="M393" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M394" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.82), indicating that highly oxidized OA associated primarily with fossil-fuel-related emissions does not necessarily exhibit strong hygroscopicity (Fig. 5). In contrast, under strong biomass-burning influence (<inline-formula><mml:math id="M395" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M396" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 36 %, corresponding to the 80th percentile), <inline-formula><mml:math id="M397" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> became strongly dependent on oxidation state. Samples with <inline-formula><mml:math id="M398" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratios above 0.8 exhibited substantially higher hygroscopicity (mean <inline-formula><mml:math id="M399" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M400" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.21) than those with <inline-formula><mml:math id="M401" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratios below 0.7 (mean <inline-formula><mml:math id="M402" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M403" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.10). These contrasting behaviours indicate that atmospheric oxidation enhances OA hygroscopicity primarily when biomass-burning-derived OA constitutes a substantial fraction of ambient organic aerosol. In other words, the influence of oxidation on OA hygroscopicity is fundamentally source dependent rather than universal. This interpretation is also consistent with previous laboratory and field studies showing that freshly emitted biomass-burning OA generally exhibits low hygroscopicity, whereas atmospheric aging substantially enhances <inline-formula><mml:math id="M404" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> through oxidative processing (Carrico et al., 2010; Martin et al., 2013; Mallet et al., 2017). Additional interaction analysis further supports this interpretation by demonstrating a statistically significant coupling between biomass-burning contribution and oxidation state (Sect. S2 in the Supplement), indicating that the sensitivity of <inline-formula><mml:math id="M405" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> to oxidation increases progressively with increasing biomass-burning influence.</p>
      <p id="d2e5561">The statistical relationships described above are further evaluated using a persistent pollution episode from 20 to 25 January 2021 (Fig. 3), which provides an independent case study validating the statistical relationships described above. During the first stage of the episode (red shaded area in Fig. 3), <inline-formula><mml:math id="M406" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">PM</mml:mi><mml:mn mathvariant="normal">2.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> increased progressively and was accompanied by continuous particle growth (Fig. S5), indicating sustained aerosol accumulation and aging. Biomass-burning influence remained relatively strong throughout this period, with <inline-formula><mml:math id="M407" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaging approximately 30 %. Elevated levoglucosan concentrations independently confirmed the substantial contribution of biomass-burning emissions (Fig. S18). Although the bulk <inline-formula><mml:math id="M408" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio first decreased from approximately 0.8 to 0.5 before gradually recovering to around 0.8, <inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> increased continuously from nearly zero to approximately 0.2. Considering that OOA remained the dominant OA component (<inline-formula><mml:math id="M410" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 80 %) throughout this stage, the increase in <inline-formula><mml:math id="M411" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is unlikely to be explained solely by changes in bulk oxidation level. Instead, it most likely reflects the progressive atmospheric aging of biomass-burning-derived OA under sustained biomass-burning influence, which gradually enhances its hygroscopicity. This interpretation is consistent with the field observations of Kuang et al. (2021), who reported substantially higher hygroscopicity for aged biomass-burning OA than for freshly emitted biomass-burning aerosol.</p>
      <p id="d2e5628">A striking contrast occurred during the second stage of the episode (blue shaded area in Fig. 3). Following a rapid transition in air masses, backward trajectory analysis indicates that transport shifted from eastern China to northern China (Fig. S19), accompanied by increased sulfate contribution and a marked reduction in biomass-burning influence. The average <inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>bb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> decreased to approximately 15 %, whereas OOA accounted for nearly 94 % of total OA mass. Despite the predominance of highly oxidized OA and the continued increase in <inline-formula><mml:math id="M413" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio, <inline-formula><mml:math id="M414" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> decreased abruptly from approximately 0.2 to nearly zero and remained extremely low throughout this stage. Such behaviour would not be expected if oxidation state were the primary control on OA hygroscopicity. Instead, the coexistence of high oxidation levels with negligible hygroscopicity indicates that these transported aerosols, likely associated with coal-combustion-related emissions from North China, as supported by the enhanced sulfate fraction and lower <inline-formula><mml:math id="M415" display="inline"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> ratios during this stage, remained weakly hygroscopic despite extensive atmospheric aging. This contrasting evolution between the two stages provides compelling observational validation that the hygroscopic response to atmospheric oxidation depends strongly on emission source.</p>
      <p id="d2e5685">To examine whether the source-dependent behaviour identified above is representative beyond this individual episode, we further examined the relationship between <inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the molar ratio of <inline-formula><mml:math id="M417" display="inline"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>/</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>, which is commonly used as an indicator of the relative importance of mobile and coal-combustion-related emissions. <inline-formula><mml:math id="M418" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited a moderate positive correlation with <inline-formula><mml:math id="M419" display="inline"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>/</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M420" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M421" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.34, <inline-formula><mml:math id="M422" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M423" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001; Fig. S20), indicating systematically lower OA hygroscopicity under sulfate-rich conditions associated with stronger coal-combustion influence. This independent statistical relationship corroborates the conclusions drawn from the pollution episode and further demonstrates that emission source exerts a stronger influence on <inline-formula><mml:math id="M424" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> than oxidation state alone.</p>
      <p id="d2e5794">The enhanced hygroscopicity associated with biomass-burning influence is most likely attributable to the distinct chemical composition of biomass-burning-derived OA and its evolution during atmospheric aging. Fresh biomass-burning emissions contain a complex mixture of organic compounds, including weakly hygroscopic primary organics together with abundant brown carbon (BrC). Consequently, freshly emitted biomass-burning OA generally exhibits relatively low hygroscopicity despite containing substantial amounts of BrC (Carrico et al., 2010). During atmospheric aging, oxidative processing and secondary organic aerosol formation progressively transform this complex organic mixture, increasing the relative abundance of water-soluble oxygenated compounds while simultaneously modifying the optical and chemical properties of BrC. Consequently, aged biomass-burning OA becomes substantially more hygroscopic than freshly emitted biomass-burning aerosol, consistent with previous laboratory and field observations (Martin et al., 2013; Mallet et al., 2017). Supporting this interpretation, <inline-formula><mml:math id="M425" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited a significant positive correlation with the OA mass absorption efficiency at 370 <inline-formula><mml:math id="M426" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M427" display="inline"><mml:mrow><mml:msub><mml:mtext>MAE</mml:mtext><mml:mrow><mml:mtext>OA</mml:mtext><mml:mo>,</mml:mo><mml:mn mathvariant="normal">370</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M428" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M429" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.59, <inline-formula><mml:math id="M430" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M431" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001; Fig. S21), which serves as an indicator for the abundance of biomass-burning-derived chromophoric organic matter. Rather than suggesting that BrC itself directly controls OA hygroscopicity, this relationship indicates that BrC co-varies with a broader suite of biomass-burning-derived water-soluble organic compounds that collectively enhance the hygroscopicity of aged biomass-burning aerosol. This interpretation is fully consistent with the source-dependent framework proposed in this study, in which biomass-burning influence enhances OA hygroscopicity not because BrC alone is highly hygroscopic. Instead, BrC should be regarded as an indicator of a chemically evolving biomass-burning OA mixture enriched in water-soluble organic compounds, whose collective compositional evolution enhances OA hygroscopicity during atmospheric aging.</p>
      <p id="d2e5865">Overall, the statistical relationships, interaction analysis, pollution episode, and optical evidence consistently demonstrate that the influence of atmospheric oxidation on OA hygroscopicity is fundamentally source dependent rather than universal. Atmospheric aging substantially enhances <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> when biomass-burning-derived OA constitutes a significant fraction of ambient organic aerosol. Consequently, parameterizations representing <inline-formula><mml:math id="M433" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> solely as a function of oxidation state are unlikely to capture the large temporal variability observed in polluted continental atmospheres. Incorporating source-dependent constraints into <inline-formula><mml:math id="M434" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> parameterizations therefore provides a more physically realistic framework for predicting aerosol water uptake, aerosol–cloud interactions, and the climatic impacts of biomass-burning emissions.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d2e5910">By combining humidified light-scattering measurements with ZSR-based component separation, this study provides observational constraints on the variability and controlling mechanisms of OA hygroscopicity at a polluted rural site in eastern China. Although OA generally reduced bulk aerosol hygroscopicity, with a mean <inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 0.11 during the winter campaign, <inline-formula><mml:math id="M436" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited pronounced temporal variability, ranging from nearly zero to 0.49. Such large variability highlights the importance of accurately representing OA hygroscopicity for predicting bulk aerosol hygroscopicity under ambient conditions.</p>
      <p id="d2e5935">Our results demonstrate that this variability cannot be satisfactorily explained by bulk oxidation state alone. Although OA at the study site was generally highly oxidized, <inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exhibited only weak relationships with conventional oxidation metrics, including the <inline-formula><mml:math id="M438" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> ratio and PMF-derived OA factors. In contrast, <inline-formula><mml:math id="M439" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> showed a substantially stronger dependence on source-related composition, particularly the relative contribution of biomass-burning-derived OA. Multiple lines of evidence – including statistical relationships, interaction analysis, pollution episode evolution, air-mass transport, and BrC optical properties – consistently demonstrate that the hygroscopic response of OA to atmospheric oxidation is fundamentally source dependent rather than universal. Atmospheric aging substantially enhanced <inline-formula><mml:math id="M440" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> when biomass-burning-derived OA constituted a significant fraction of ambient organic aerosol, whereas highly oxidized OA associated with coal-combustion-dominated air masses remained weakly hygroscopic. These observations indicate that emission source fundamentally modulates the influence of atmospheric aging on OA hygroscopicity.</p>
      <p id="d2e5983">The source-dependent behaviour identified in this study most likely originates from differences in the chemical evolution of OA from different emission sources during atmospheric aging. In particular, biomass-burning-derived OA undergoes progressive oxidative processing that enriches water-soluble oxygenated compounds and substantially enhances its hygroscopicity. The observed positive relationship between <inline-formula><mml:math id="M441" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and BrC-related optical properties further suggests that BrC serves primarily as an indicator of a chemically evolving biomass-burning OA mixture rather than acting as the direct cause of enhanced hygroscopicity. Together, these findings highlight the coupled roles of emission source, atmospheric aging, and chemical evolution in governing OA hygroscopic behaviour under complex ambient conditions.</p>
      <p id="d2e5997">Given the increasing relative importance of OA under ongoing emission-control policies in eastern China, these findings have important implications for improving OA hygroscopicity parameterizations in atmospheric models. Representing <inline-formula><mml:math id="M442" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">κ</mml:mi><mml:mtext>OA</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> solely as a function of oxidation state is unlikely to capture the pronounced temporal variability observed in polluted continental atmospheres. Instead, incorporating source-dependent information provides a more physically realistic framework for simulating aerosol water uptake, aerosol–cloud interactions, and regional climate effects under evolving emission scenarios. Future field observations spanning a wider range of atmospheric environments, together with laboratory investigations of the hygroscopic evolution of OA from representative emission sources, are needed to further evaluate and generalize the source-dependent framework proposed in this study. More broadly, our results suggest that the climatic impacts of biomass-burning emissions may arise not only from the direct radiative effects of BrC, but also from indirect effects associated with enhanced aerosol hygroscopicity and its influence on aerosol water uptake and aerosol–cloud interactions.</p>
</sec>

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

      <p id="d2e6016">Data supporting this study were obtained through direct measurements by the authors. Processed datasets are publicly available at <ext-link xlink:href="https://doi.org/10.57760/sciencedb.42983" ext-link-type="DOI">10.57760/sciencedb.42983</ext-link> (Wu, 2026).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d2e6022">The supplement related to this article is available online at <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-26-15333-2026-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-26-15333-2026-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e6031">YW and ZD conceptualized the study, designed the methodology, and developed the inversion procedure. The investigation was performed by YW, JL, YX, ZZ, and JT. YW and JL curated the data and conducted the formal analysis. YW performed the validation, prepared the visualizations, and wrote the original draft. The manuscript was reviewed and edited by ZD, JL, LR, and JT.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e6037">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e6043">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e6049">We gratefully acknowledge the staff of the Huainan Observation Station, Institute of Atmospheric Physics, Chinese Academy of Sciences, for their support and assistance during the observational experiments. We also extend our appreciation to all individuals who contributed to the experiments but are not listed as authors.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e6054">This research was funded by the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB0760200), and also supported by the National Natural Science Foundation of China (grant no. 42275114), the Fundamental Research Funds of Institute of Atmospheric Physics, Chinese Academy of Sciences and State Key Laboratory of Atmospheric Environment and Extreme Meteorology (grant no. 2024ZD04).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e6060">This paper was edited by Manabu Shiraiwa and reviewed by two anonymous referees.</p>
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