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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-24-8703-2024</article-id><title-group><article-title>Elucidating the boundary layer turbulence dissipation rate using high-resolution measurements from a radar wind profiler network over the Tibetan Plateau</article-title><alt-title>Elucidating the boundary layer turbulence dissipation over the TP</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Meng</surname><given-names>Deli</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff3 aff4">
          <name><surname>Guo</surname><given-names>Jianping</given-names></name>
          <email>jpguocams@gmail.com</email>
        <ext-link>https://orcid.org/0000-0001-8530-8976</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Guo</surname><given-names>Xiaoran</given-names></name>
          <email>guoxiaoran2018@hotmail.com</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wang</surname><given-names>Yinjun</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3352-3815</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Li</surname><given-names>Ning</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Sun</surname><given-names>Yuping</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhang</surname><given-names>Zhen</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Tang</surname><given-names>Na</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Li</surname><given-names>Haoran</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3435-8698</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zhang</surname><given-names>Fan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Tong</surname><given-names>Bing</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Xu</surname><given-names>Hui</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Chen</surname><given-names>Tianmeng</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1564-7013</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>High Impact Weather Key Laboratory of China Meteorological Administration, Changsha 410073, China</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Fujian Key Laboratory of Severe Weather, Fujian Institute of Meteorological Sciences, Fuzhou 350028, China</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Xiong'an Atmospheric Boundary Layer Key Laboratory of China Meteorological Administration, Beijing 100085, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Jianping Guo (jpguocams@gmail.com) and Xiaoran Guo (guoxiaoran2018@hotmail.com)</corresp></author-notes><pub-date><day>7</day><month>August</month><year>2024</year></pub-date>
      
      <volume>24</volume>
      <issue>15</issue>
      <fpage>8703</fpage><lpage>8720</lpage>
      <history>
        <date date-type="received"><day>22</day><month>March</month><year>2024</year></date>
           <date date-type="accepted"><day>18</day><month>June</month><year>2024</year></date>
           <date date-type="rev-recd"><day>9</day><month>June</month><year>2024</year></date>
           <date date-type="rev-request"><day>11</day><month>April</month><year>2024</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2024 </copyright-statement>
        <copyright-year>2024</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/.html">This article is available from https://acp.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e219">The planetary boundary layer (PBL) over the Tibetan Plateau (TP) exerts a significant influence on regional and global climate, while its vertical structures of turbulence and evolution features remain poorly understood, largely due to the scarcity of observations. This study examines the vertical profile of and daytime variation in the turbulence dissipation rate (<inline-formula><mml:math id="M1" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>) in the PBL and free troposphere over the TP using the high-resolution (6 <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> and 120 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) measurements from a radar wind profiler (RWP) network, combined with hourly data from ERA5 during the period from 1 September 2022 to 31 October 2023. Observational analyses show that the magnitude of <inline-formula><mml:math id="M4" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> below 3 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> under all-sky conditions exhibits a large spatial discrepancy over the six RWP stations over the TP. Particularly, the values of <inline-formula><mml:math id="M6" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at Minfeng and Jiuquan over the northern TP and at Dingri (alternately Tingri) over the southern TP are roughly an order of magnitude greater than those at Lijiang, Ganzi (alternately Garzê), and Hongyuan over the eastern TP. This could be partially attributed to the difference in land cover across the six RWP stations. In terms of the diurnal variation, <inline-formula><mml:math id="M7" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> rapidly intensifies from 09:00 local standard time (LST) to 14:00 LST and then gradually levels off in the late afternoon. Under clear-sky conditions, both <inline-formula><mml:math id="M8" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and the planetary boundary layer height (<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are greater compared with cloudy-sky conditions, which could be due to the cooling effect of clouds, which reduces the solar irradiation reaching the surface. In the lower PBL (0.3 <inline-formula><mml:math id="M10" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M12" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), where <inline-formula><mml:math id="M13" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> is the height above ground level, the dominant influential factor in the development of turbulence is the surface–air temperature difference (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). By comparison, in the upper PBL (0.6 <inline-formula><mml:math id="M15" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M17" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0), both <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and vertical wind shear (VWS) affect the development of turbulence. Above the PBL (1.0 <inline-formula><mml:math id="M19" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M21" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0), the shear production resulting from VWS dominates the variation in turbulence. Under cloudy-sky conditions, the reduced <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and weakened surface sensible heat flux tend to inhibit the turbulent motion in the PBL. On the other hand, the strong VWS induced by clouds enhances the turbulence above the PBL. The findings obtained here underscore the importance of the RWP network in revealing the fine-scale structures of the PBL over the TP and gaining new insight into the PBL evolution.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>42325501</award-id>
</award-group>
<award-group id="gs2">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>U2142209</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="d1e452">Turbulence ranks among the most intricate phenomena within the atmosphere, ensuring that the planetary boundary layer (PBL) remains thoroughly mixed during daylight hours (Li et al., 2023). As a result, the structure of the PBL is, to a considerable extent, governed by the evolution of turbulence (Teixeira et al., 2021). The turbulence dissipation rate (<inline-formula><mml:math id="M23" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>) reflects the amount of turbulent kinetic energy (TKE) that is converted into heat at the Kolmogorov scale and is a measure of the turbulence intensity (McCaffrey et al., 2017; Muñoz-Esparza et al., 2018). Proper parameterizations of the turbulence dissipation term with the aid of observations have great impacts on the forecast skill of weather and climate models, as <inline-formula><mml:math id="M24" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> strongly affects vertical turbulent mixing through its influence on TKE (Yang et al., 2017). Accurate estimation of <inline-formula><mml:math id="M25" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is crucial for understanding the structure of turbulence in the PBL. To date, a variety of instruments have been used to observe or retrieve the vertical profiles of <inline-formula><mml:math id="M26" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, including sodar, radar wind profiler (RWP), radiosonde, Doppler wind lidar (DWL), and ultrasonic anemometer instruments (Jacoby-Koaly et al., 2002; Dodson and Griswold, 2021; Lv et al., 2021; Kotthaus et al., 2023). Compared with DWL, RWPs exhibit better capability in capturing turbulence structures in cloudy sky. Furthermore, it is hard for radiosondes and ultrasonic anemometers to perform temporally continuous measurements of atmospheric turbulence due to high costs.</p>
      <p id="d1e483">The Tibetan Plateau (TP), with an average elevation greater than 4000 <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> above sea level (<inline-formula><mml:math id="M28" display="inline"><mml:mrow class="unit"><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>) and an area of approximately <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, towers into the lower and middle troposphere (Huang et al., 2023). By receiving a greater amount of solar shortwave radiation, the surface layer of the TP can transfer more heat through the PBL to the free atmosphere (Wang et al., 2015; Ma et al., 2023). The PBL over the TP exhibits strong convective thermals of warm air and upward motions due to the lower air density and buoyancy effect, which results in significant turbulence motions and turbulence–convection interactions with “popcorn” cloud structures (Xu et al., 2002, 2023). Understanding the statistical behavior of <inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is key to revealing the vertical structure and evolution of PBL turbulence, which could improve the parameterization of PBL processes over the TP (Wang et al., 2015; Xu et al., 2019; Zhao et al., 2019; Ma et al., 2023). However, due to the limited observations of turbulence profiles, the daytime variation characteristics of <inline-formula><mml:math id="M32" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> over the TP and its main influencing mechanisms remain poorly understood.</p>
      <p id="d1e553">A vast range of previous studies have attempted to figure out the mechanisms behind the turbulence, but most of them have been based on radiosonde measurements, model simulation, or reanalysis data (e.g., Banerjee et al., 2018; Che and Zhao, 2021; C. X. Wang et al., 2023). A myriad of driving mechanisms have been proposed to account for the PBL development over the TP, such as surface thermal and dynamic forcing or atmospheric stability (Chen et al., 2016; Lai et al., 2021; Wang and Zhang, 2022; Chechin et al., 2023; C. X. Wang et al., 2023). It has been demonstrated that the buoyancy term contribution on the southern slope of the TP is significantly larger than that on the southeastern edge of the TP (Wang et al., 2015). A larger surface–air temperature difference (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and a larger sensible heat flux promote the rapid growth of a deep PBL in the western and southern TP (Chen et al., 2013, 2016; Wang et al., 2016; Z. G. Li et al., 2017; Zhang et al., 2022).</p>
      <p id="d1e574">Except for the abovementioned thermal and dynamic effects, the cloud radiative effect is found to be another significant factor that can dramatically modulate the evolution of daytime PBL turbulence (Bodenschatz et al., 2010; Davis et al., 2020). For instance, cloud radiative forcing accounts for the rapid morning transition from a stable to unstable PBL, thereby notably affecting the diurnal variation in the PBL (Su et al., 2023). Notably, longwave radiative cooling at the top of stratocumulus clouds can enhance turbulent diffusion within the stratocumulus-topped PBL (Sun et al., 2016). A recent observational study suggests that cloud radiative cooling contributed about 32 % to turbulent mixing even near the surface (Huang et al., 2020). In other words, cloud radiative processes, including entrainment and radiative cooling, can affect TKE in the atmosphere (Nicholls, 1986; Sedlar et al., 2022; Chechin et al., 2023).</p>
      <p id="d1e578">The TP is characterized by a high frequency of cumulus clouds that is about 5 times the regional mean over other areas of China (Wang et al., 2015), and the occurrence frequency of clouds over the TP shows large diurnal and spatial variability, with the maxima in the afternoon in the eastern TP (Wan et al., 2022). The clouds have been found to significantly suppress the development of the summer PBL in the early afternoon across China using fine-resolution radiosonde observations (Guo et al., 2019). Under continuous cloudy-sky conditions, the convective PBL develops slowly due to the smaller surface sensible heat compared to clear-sky conditions (Wang and Zhang, 2022). The turbulence motion in the PBL and its dynamic structure contribute to the formation and development of the popcorn-like convective clouds (Xu et al., 2002; Wang et al., 2020). Compared with eastern China, the higher occurrence of low cloud in the afternoon over the TP is found to facilitate the PBL development, mainly owing to the lower atmospheric density (Wang et al., 2020).</p>

<table-wrap id="Ch1.T1" specific-use="star"><label>Table 1</label><caption><p id="d1e584">Summary of the geographical conditions and land surface of the six radar wind profiler (RWP) stations over the Tibetan Plateau (TP).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">RWP station</oasis:entry>
         <oasis:entry colname="col2">Longitude (° E)</oasis:entry>
         <oasis:entry colname="col3">Latitude (° N)</oasis:entry>
         <oasis:entry colname="col4">Elevation (<inline-formula><mml:math id="M34" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Land cover types</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Minfeng</oasis:entry>
         <oasis:entry colname="col2">82.69</oasis:entry>
         <oasis:entry colname="col3">37.07</oasis:entry>
         <oasis:entry colname="col4">1408.9</oasis:entry>
         <oasis:entry colname="col5">Bare land</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Jiuquan</oasis:entry>
         <oasis:entry colname="col2">98.49</oasis:entry>
         <oasis:entry colname="col3">39.77</oasis:entry>
         <oasis:entry colname="col4">1477.2</oasis:entry>
         <oasis:entry colname="col5">Bare land</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dingri</oasis:entry>
         <oasis:entry colname="col2">87.07</oasis:entry>
         <oasis:entry colname="col3">28.39</oasis:entry>
         <oasis:entry colname="col4">4326.0</oasis:entry>
         <oasis:entry colname="col5">Grassland</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Ganzi</oasis:entry>
         <oasis:entry colname="col2">100.00</oasis:entry>
         <oasis:entry colname="col3">31.62</oasis:entry>
         <oasis:entry colname="col4">3353.0</oasis:entry>
         <oasis:entry colname="col5">Bare land, grassland</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Hongyuan</oasis:entry>
         <oasis:entry colname="col2">102.55</oasis:entry>
         <oasis:entry colname="col3">32.79</oasis:entry>
         <oasis:entry colname="col4">3465.0</oasis:entry>
         <oasis:entry colname="col5">Bare land, grassland</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Lijiang</oasis:entry>
         <oasis:entry colname="col2">100.22</oasis:entry>
         <oasis:entry colname="col3">26.85</oasis:entry>
         <oasis:entry colname="col4">2382.4</oasis:entry>
         <oasis:entry colname="col5">Bare land, grassland</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e744">However, the differences in turbulence vertical structures between clear-sky and cloudy-sky conditions are rarely explored, and the possible mechanism influencing the cloud-topped PBL turbulence evolution remains unclear. To the best of our knowledge, most of the abovementioned studies over the TP lack high-temporal-resolution turbulence profile observations. Coincidently, the RWP network in China provides us with a valuable opportunity to characterize the PBL turbulence structure over the TP (Guo et al., 2021a). Therefore, the main objective of this study is to resolve the above issues over the TP, using observations from the RWP network together with other ground-based meteorological measurements and the ERA5 data. We also analyze the joint effect of thermodynamics and dynamics on <inline-formula><mml:math id="M35" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> structure in the daytime (09:00–17:00 local standard time, LST) PBL through <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and vertical wind shear (VWS).</p>
      <p id="d1e772">The remainder of this paper proceeds as follows: Sect. <xref ref-type="sec" rid="Ch1.S2"/> describes the data and methods used in this study. In Sect. <xref ref-type="sec" rid="Ch1.S3"/>, we analyze the spatio-temporal characteristics and daytime pattern of <inline-formula><mml:math id="M37" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> over the TP and investigate the possible thermodynamic and dynamic effect on PBL turbulence under clear-sky and cloudy-sky conditions. The summary and conclusions are given in Sect. <xref ref-type="sec" rid="Ch1.S4"/>.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>The RWP network over the TP</title>
      <p id="d1e803">In this study, we use the vertical measurements of RWP data with a vertical resolution of 120 <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and a temporal resolution of 6 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> from the RWP network over the TP, which contains six operational stations (Minfeng, Jiuquan, Hongyuan, Ganzi (alternately Garzê), Lijiang, and Dingri (alternately Tingri)) operated by the China Meteorological Administration (CMA) during the period from 1 September 2022 to 31 October 2023. The spatial distribution of the RWP network over the TP is shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>, and detailed information for each RWP station, including longitude, latitude, elevation, and land cover type, is given in Table <xref ref-type="table" rid="Ch1.T1"/>. Among these six RWP stations, the Dingri station is located in the foothills of the Himalayas with an elevation of more than 4300 <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><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> and is dominated by the land cover of bare land and alpine grassland. The Lijiang station is located in the southeastern TP and is characterized by complex terrain with an elevation of about 2400 <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><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 Ganzi and Hongyuan stations are situated in the eastern TP, with elevations ranging from 3300 to 3500 <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><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> and whose underlying land cover is mainly alpine grassland. The Minfeng and Jiuquan stations are situated in arid and semiarid zones to the north of the TP, with elevations ranging from 1400 to 1500 <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, and their dominant underlying land cover is mainly bare land. Therefore, these two stations are good representatives of the northern TP.</p>

      <fig id="Ch1.F1"><label>Figure 1</label><caption><p id="d1e900">The spatial distribution of the radar wind profiler (RWP) network, which is comprised of six stations (in filled black circles) on the Tibetan Plateau (TP). The inset map surrounding the main frame denotes the RGB satellite image from ©Google Earth that is centered at each RWP station.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f01.jpg"/>

        </fig>

      <p id="d1e909">RWPs have the capability to obtain high-temporal-resolution atmospheric turbulence and wind profiles over the TP compared to the radiosonde and reanalysis, which makes it possible to analyze the fine PBL structures. The low-detection and medium-detection modes of RWPs can acquire the wind field and turbulence information below 5.0 <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> above ground level (<inline-formula><mml:math id="M45" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula>) (McCaffrey et al., 2017; Ruan et al., 2014). RWPs provide the radial observations (marked as the RAD subset), including profiles of the radial velocity, Doppler spectral width, and signal-to-noise ratio (SNR). Also provided by RWPs are real-time sampling data (marked as the ROBS subset), including the profiles of horizontal wind (direction and speed), vertical velocity, and refractive index structure constant (Liu et al., 2020). There exist large uncertainties in the profiling measurements from RWPs; thus the quality control for both RAD and ROBS subsets is indispensable before retrieving related dynamic variables over the TP (Liu et al., 2020; S. Q. Wang et al., 2023). For instance, the profiling measurements highly deviate from the truth below 0.5 <inline-formula><mml:math id="M46" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula> and above 5.0 <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula>, which is attributed to the near-surface clutter and significant beam attenuation, respectively (Guo et al., 2023). Thus, here only the RWP measurements at heights from 0.5 to 5.0 <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> are utilized for analysis.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Miscellaneous meteorological data</title>
      <p id="d1e997">In this study, hourly ground-based meteorological variables, including 2 <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> air temperature (<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), ground surface temperature (<inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), pressure, and cloud cover, are derived from the six automatic weather stations over the TP. Also, 1 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> rainfall observations from rain gauges are used to minimize the potential influence of rainfall on the profiling measurements from the RWP network. All these meteorological datasets are subjected to strict data quality control by the National Meteorological Information Center (NMIC) of the CMA (S. Q. Wang et al., 2023). In addition, the hourly temperature data at pressure levels from the ERA5 data are used in this study (Hersbach et al., 2020).</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Methods</title>
<sec id="Ch1.S2.SS3.SSS1">
  <label>2.3.1</label><title>Retrieval of the turbulence dissipation rate</title>
      <p id="d1e1053">As widely used ground-based equipment for detecting atmospheric wind profiles (Liu et al., 2020), RWPs have the advantage of estimating <inline-formula><mml:math id="M53" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, since they can measure the Doppler velocity spectrum in the radar volume where the turbulence parcel motion accounts for the spectral width broadening (Jacoby-Koaly et al., 2002; White et al., 1999). In this study, the spectral width method is applied to retrieve <inline-formula><mml:math id="M54" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> from the RAD subset based on the underlying assumption that turbulence is isotropic, and the contributions to the spectral width from turbulent and non-turbulent process are independent of each other (Solanki et al., 2022; White et al., 1999).</p>
      <p id="d1e1070">The major steps for <inline-formula><mml:math id="M55" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> retrieval can be summarized as follows: (1) the spectral width variance consisting of the turbulence and non-turbulence variance is obtained from the spectral width measurements. (2) The non-turbulent broadening variances are decomposed into beam-broadening variance due to the finite width of the beam, shear-broadening variance generated by the presence of a wind gradient, and broadening variance arising from data processing and other factors (Nastrom, 1997). (3) The turbulent broadening variance (<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>) is extracted from the spectral width variance by excluding the abovementioned non-turbulent broadening variances. (4) <inline-formula><mml:math id="M57" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is estimated from <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> (White et al., 1999). For more details about the spectral width method, refer to Jacoby-Koaly et al. (2002), McCaffrey et al. (2017), Nastrom (1997), and Solanki et al. (2021).</p>
      <p id="d1e1113">One caveat of the abovementioned methods used to estimate <inline-formula><mml:math id="M59" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> lies in its sensitivity to the uncertainty in measuring horizontal wind speed and the occurrence of negative values of <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, resulting in negative <inline-formula><mml:math id="M61" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> (i.e., an invalid retrieval that should be discarded), which has previously been documented (e.g., Chen et al., 2022; McCaffrey et al., 2017). It is noteworthy that <inline-formula><mml:math id="M62" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> estimates derived from the RWP network lack validation against in situ <inline-formula><mml:math id="M63" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> measurements from sonic anemometers in aircraft or towers. This is another factor causing uncertainties that needs to be addressed in the future.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <label>2.3.2</label><title>Estimation of planetary boundary layer height</title>
      <p id="d1e1166">The PBL height (hereafter referred to as <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is an important parameter for characterizing the fine vertical structure of the PBL, which has important implications for the air mass exchange between the Earth's surface and the atmosphere aloft and thus affects cloud development and air pollutant dispersion (Dai et al., 2014; Dodson and Griswold, 2021; Guo et al., 2021b; Z. Q. Li et al., 2017; Wang et al., 2022).</p>
      <p id="d1e1180">Here daytime <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at each RWP station is retrieved from the original SNR profiles from the RAD subset based on the improved threshold method (ITM), which was originally proposed by Liu et al. (2019). The steps are briefly outlined as follows. First of all, the original SNR profiles are normalized, leading to the profile of normalized SNR (NSNR), which is expected to avoid instrumental inconsistencies. Secondly, the NSNR threshold is set to 0.75 based on the <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> estimated by the radiosonde measurements at the same station. Thirdly, the profile of NSNR is scanned downward from the top to the ground surface. Finally, <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is determined as the height where the NSNR profile is greater than 0.75 for the first time. For more details about the ITM, refer to Liu et al. (2019).</p>
      <p id="d1e1216">It is not optimal to retrieve <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> directly from the RWP measurements during the nighttime, when the turbulence is weaker and SNR is stronger, leading to an overestimation of <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Duncan et al., 2022). The accuracy of the SNR data from RWPs directly affects the accuracy of <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> estimation for the ITM is particularly applicable in the daytime PBL (Bianco et al., 2008; Collaud Coen et al., 2014). The presence of clouds is proved to bring about uncertainty in <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> retrievals from the ITM due to the challenge in identifying the peak from the NSNR profile (Angel and Manoj, 2024). Notably, a convective cloud is accompanied by strong turbulence, which results in its boundary being misjudged as <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS3">
  <label>2.3.3</label><title>Vertical wind shear</title>
      <p id="d1e1294">The ROBS subset is used to calculate VWS, which is an important parameter that indicates the dynamical effect on the development of the PBL (Zhang et al., 2020). VWS is given as follows: 
              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M74" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">VWS</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="[" close="]"><mml:mrow><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfenced><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M75" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M76" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> denote the zonal and meridional wind component, respectively, and <inline-formula><mml:math id="M77" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> denotes the sample height in meters above ground level.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS4">
  <label>2.3.4</label><title>Classification of cloudy- and clear-sky conditions</title>
      <p id="d1e1386">Using RWPs combined with the ground-based cloud cover observations at each station, the effect of clouds on daytime variations in PBL turbulence and <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> over the TP is investigated. Firstly, the 1 <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> precipitation and 6 <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> RWP data are time-matched to remove the profile data 30 min before and after the precipitation and obtain non-precipitation data (Wu et al., 2024). Then, all-sky conditions are defined as non-precipitation hours. Finally, the clear-sky (cloudy-sky) conditions are identified as hours with the cloud fraction is less (greater) than 30 % (80 %) (Guo et al., 2016; Solanki et al., 2021).</p>
</sec>
<sec id="Ch1.S2.SS3.SSS5">
  <label>2.3.5</label><title>Calculation of the gradient Richardson number</title>
      <p id="d1e1425">The evolution of turbulence in the PBL has previously been recognized to be closely associated with atmospheric stability (Chechin et al., 2023; Chen et al., 2013; Lai et al., 2021; Muhsin et al., 2016). Therefore, we take the gradient Richardson number (<inline-formula><mml:math id="M81" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula>) as a variable to characterize atmospheric stability and the formation of turbulence over the TP. Following Stull (1988), <inline-formula><mml:math id="M82" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula> is formulated as follows:
              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M83" display="block"><mml:mrow><mml:mi mathvariant="italic">Ri</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>g</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>∂</mml:mo><mml:mi>v</mml:mi><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the virtual potential temperature from ERA5; <inline-formula><mml:math id="M85" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M86" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> are the hourly zonal and meridional wind components derived from RWPs, respectively; <inline-formula><mml:math id="M87" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the gravitational acceleration; and <inline-formula><mml:math id="M88" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> represents the sample height in meters above ground level.</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>Spatio-temporal distributions of the daytime PBL turbulence dissipation rate</title>
      <p id="d1e1570">Both the PBL turbulence dissipation rate and <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> have significant diurnal variations over mountain and urban areas (Adler and Kalthoff, 2014; Liu et al., 2019; Solanki et al., 2021; Yang et al., 2023). Since the longitude of the six stations over the TP ranges from 82.7 to 102.6° E, it is necessary to use the LST to accurately capture the daytime variations in the PBL and make a comparison between different stations.</p>

      <fig id="Ch1.F2" specific-use="star"><label>Figure 2</label><caption><p id="d1e1586">Spatial distribution of the diurnal evolution of the vertical profile of the logarithmic turbulence dissipation rate (<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in color shading; unit: <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>) at 120 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> vertical resolution and 6 <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> intervals and hourly mean planetary boundary layer height (<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, black line; unit: <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) during the daytime under all-sky conditions from 09:00 to 17:00 LST for the period September 2022 to October 2023 as retrieved from the profiling measurements at six RWP stations over the TP. The vertical bars indicate the 0.5 standard deviations for <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Also shown in the right-hand-side panels next to each colored panel is the temporally averaged vertical profile of <inline-formula><mml:math id="M97" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> (black line) and its corresponding 1 standard deviation (gray shading).</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f02.png"/>

        </fig>

      <p id="d1e1682">Figure <xref ref-type="fig" rid="Ch1.F2"/> presents a comprehensive overview of the <inline-formula><mml:math id="M98" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> profile at 6 <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> intervals and hourly averaged <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the lower troposphere at heights from 0.5 to 3.0 <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> for six RWP stations over the TP during the period from 1 September 2022 to 31 October 2023. As shown in the panels to the right of the colored panels in Fig. <xref ref-type="fig" rid="Ch1.F2"/>, <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> generally decreases with increased height at all six RWP stations. The magnitude of <inline-formula><mml:math id="M103" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and its vertical structures during the daytime at Minfeng and Jiuquan stations over the northern TP and at Dingri station over the southern TP stand in stark contrast to those at RWP stations (i.e., Lijiang, Ganzi, and Hongyuan) in the eastern TP. It is apparent that <inline-formula><mml:math id="M104" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> exhibits a large spatial discrepancy. In terms of the latitudinal variation, the 1-year-averaged <inline-formula><mml:math id="M105" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at the RWP stations in the eastern part of TP is smaller than in the western part of TP. In terms of the meridional variation, <inline-formula><mml:math id="M106" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> values at the two RWP stations in the northern TP have a significantly larger magnitude than at the other four stations. In particular, the maximum mean value of daytime <inline-formula><mml:math id="M107" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is found at Minfeng and Jiuquan in the northern TP, reaching values of up to 10<inline-formula><mml:math id="M108" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.59</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 10<inline-formula><mml:math id="M109" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.73</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>, respectively. By comparison, the lowest value of <inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is found in the eastern TP, with mean values of 10<inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.06</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, 10<inline-formula><mml:math id="M113" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.30</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and 10<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.22</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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> at Lijiang, Hongyuan, and Ganzi, respectively. Meanwhile, the mean magnitude of <inline-formula><mml:math id="M116" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at Dingri in the southern TP, which is 10<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.88</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M118" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>, lies between the magnitude of <inline-formula><mml:math id="M119" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> in the northern and eastern TP.</p>
      <p id="d1e1923">Overall, the spatial distribution of <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at all six RWP stations is clearly dependent on the geographical location (Fig. <xref ref-type="fig" rid="Ch1.F2"/>) and resembles that of the <inline-formula><mml:math id="M121" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>. The geographic pattern of <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from RWPs agrees well with those patterns from radiosonde measurements (Che and Zhao, 2021) and reanalysis (Slättberg et al., 2022). Of the six RWP stations, Dingri is located in the northern foothills of the Himalayas with an altitude of over 4300 <inline-formula><mml:math id="M123" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, where the bare-land type results in a large surface sensible heat flux. This, together with the lowest atmospheric density, leads to the highest daytime mean value of <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> up to 2.10 <inline-formula><mml:math id="M125" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (Wang et al., 2015). The land surfaces at the Minfeng and Jiuquan stations in the northern TP are dominated by barren and relatively homogenous terrain, in sharp contrast to the highly vegetated terrain at the Ganzi and Hongyuan stations in the eastern TP (Fig. <xref ref-type="fig" rid="Ch1.F1"/>). The sparse vegetation in the northern TP generally comes with large Bowen ratios during the daytime, which tends to produce larger sensible heat flux compared to that in the eastern TP. The increased turbulence intensity in the PBL is generally associated with larger sensible heat flux, which has been reported by previous studies (Wang et al., 2016; Zhang et al., 2022). Therefore, the spatial and temporal variations in daytime <inline-formula><mml:math id="M126" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> over the TP are affected by the underlying surface type and air density.</p>
      <p id="d1e1994">Regarding the daytime pattern of turbulence (all six panels with color shading in Fig. <xref ref-type="fig" rid="Ch1.F2"/>), the turbulence over the TP shows a pronounced signature of single-peak variability. During the period 09:00–11:00 LST, the magnitude of <inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at all six RWP stations is relatively weak. From 11:00 LST onward, with the increase in downward solar shortwave radiation, surface sensible heat flux gradually rises, which leads to the acceleration of turbulence mixing processes. Then, <inline-formula><mml:math id="M128" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> reaches peak in the early afternoon (13:00–15:00 LST). Afterwards, during the later afternoon (15:00–17:00 LST), <inline-formula><mml:math id="M129" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> diminishes gradually. Likewise, <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> almost follows the same daytime variation pattern as that of <inline-formula><mml:math id="M131" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e2039">On the seasonal scale, the turbulence at the six RWP stations is characterized by significant variability, which is shown in Fig. S1 in the Supplement. To be more specific, <inline-formula><mml:math id="M132" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> reaches a maximum in summer with the highest <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, while it reaches a minimum in winter at Minfeng and Jiuquan. At the remaining four stations, the strongest <inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is found in spring as opposed to the weakest <inline-formula><mml:math id="M135" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> in autumn.</p>

      <fig id="Ch1.F3" specific-use="star"><label>Figure 3</label><caption><p id="d1e2076"><bold>(a)</bold> The probability density function (PDF) of the surface–air temperature difference (<inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) for the northern and southern TP (red line) and eastern TP (blue line); <bold>(b)</bold> the same as <bold>(a)</bold> but for the PDF of <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> estimated from the measurements of radar wind profilers (RWPs) at heights ranging from 0.5 to 3.0 <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>; <bold>(c)</bold> scatterplot of <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> as a function of <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the northern and southern TP; <bold>(d)</bold> the same as <bold>(c)</bold> but for the eastern TP during the daytime under all-sky conditions from 09:00 to 17:00 LST (local standard time) for the period September 2022 to October 2023. The superscript <inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>∗</mml:mo><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> for <inline-formula><mml:math id="M142" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> indicates that the regression slope is statistically significant at the <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> level.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f03.png"/>

        </fig>

      <p id="d1e2205">The abovementioned findings imply that the turbulence intensity at the RWP stations over the northern and western TP is about 1 order of magnitude greater than that in the eastern TP. To further investigate the possible reasons for this significant difference in <inline-formula><mml:math id="M144" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, the relationships between <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M146" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> for different regions are presented in Fig. <xref ref-type="fig" rid="Ch1.F3"/>. The mean value of <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the northern and southern TP is 14.29 <inline-formula><mml:math id="M148" 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>, which is greater than that of the eastern TP with a value of 11.26 <inline-formula><mml:math id="M149" 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> (Fig. <xref ref-type="fig" rid="Ch1.F3"/>a). The mean daytime <inline-formula><mml:math id="M150" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> for the two regions reaches up to 10<inline-formula><mml:math id="M151" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.74</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 10<inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.20</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M153" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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>, respectively (Fig. <xref ref-type="fig" rid="Ch1.F3"/>b). Additionally, <inline-formula><mml:math id="M154" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is significantly and positively correlated with <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M156" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M157" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.35; <inline-formula><mml:math id="M158" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M159" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.005), which illustrates that the thermal forcing makes an important contribution to turbulence development in the TP (Fig. <xref ref-type="fig" rid="Ch1.F3"/>c and d). As shown in Fig. S2, there is a positive correlation between <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M161" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, indicating that the thermal effect of <inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can promote the development of turbulence at heights from 0.5 to 3.0 <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> under all-sky conditions. However, the relationship varies significantly between each RWP station. The slope values of the regression coefficients for the other five RWP stations, except for Hongyuan, are all greater than 0.015. The maximum slope values are observed at Lijiang (0.029) and Dingri (0.027) in the southern TP, as compared with the minimum slope of 0.007 at Hongyuan. This suggests that near-surface thermal properties have nothing to do with <inline-formula><mml:math id="M164" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at Hongyuan in the eastern TP.</p>
      <p id="d1e2453">The potential impact of VWS on <inline-formula><mml:math id="M165" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is also examined, which is shown Fig. S3. Overall, VWS is found to positively correlate with <inline-formula><mml:math id="M166" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at heights from 0.5 to 3.0 <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> under all-sky conditions, differing by RWP station. The maximum slope values are observed at Lijiang (79.34) and Hongyuan (68.56), as compared with the minimum slope of 1.15 at Minfeng. Therefore, it can be inferred that the atmospheric dynamic effect induced by VWS dominates the variability in <inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at regions with the same underlying terrain and land cover as Hongyuan.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Characteristics of the daytime PBL turbulence dissipation rate under clear- and cloudy-sky conditions</title>
      <p id="d1e2493">The influence of clouds on the PBL properties has been discussed and analyzed in previous studies (e.g., Guo et al., 2016; Huang et al., 2023; Ma et al., 2023; Schumann and Moeng, 1991; Yu et al., 2004). To reveal the potential impact of clouds on the PBL <inline-formula><mml:math id="M169" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> over the TP, the comparison analyses between clear- and cloudy-sky conditions are presented in this section. Figure <xref ref-type="fig" rid="Ch1.F4"/> shows the daytime cycle of mean <inline-formula><mml:math id="M170" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> profile and <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the six RWP stations under all-,clear-, and cloudy-sky conditions. Overall, the profiles of both <inline-formula><mml:math id="M172" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> under all-sky conditions over the TP present distinct single-peak variations, and their peaks approximately occur at 14:00 LST (Fig. <xref ref-type="fig" rid="Ch1.F4"/>a). The daytime-averaged <inline-formula><mml:math id="M174" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> below 3.0 <inline-formula><mml:math id="M175" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula> is 10<inline-formula><mml:math id="M176" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.95</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M177" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>, and the mean <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is 1.47 <inline-formula><mml:math id="M179" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. There is a significant positive correlation between <inline-formula><mml:math id="M180" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during the daytime (<inline-formula><mml:math id="M182" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M183" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.63; <inline-formula><mml:math id="M184" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M185" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01).</p>

      <fig id="Ch1.F4"><label>Figure 4</label><caption><p id="d1e2680">Diurnal evolution of the vertical profile of <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (color shading; unit: <inline-formula><mml:math id="M187" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>) and <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (solid line; unit: km) averaged over the six RWP stations over the TP during daytime from 09:00 to 17:00 LST for the period September 2022 to October 2023 for <bold>(a)</bold> all-sky conditions, <bold>(b)</bold> clear-sky conditions, and <bold>(c)</bold> cloudy-sky conditions. The vertical bars indicate the 0.5 standard deviations.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f04.png"/>

        </fig>

      <p id="d1e2743">Under clear-sky conditions, the daytime mean <inline-formula><mml:math id="M189" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is 10<inline-formula><mml:math id="M190" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.88</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M191" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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> (Fig. <xref ref-type="fig" rid="Ch1.F4"/>b). During the period 13:00–15:00 LST, <inline-formula><mml:math id="M192" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> ranges from 10<inline-formula><mml:math id="M193" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.43</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to 10<inline-formula><mml:math id="M194" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.82</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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> (10<inline-formula><mml:math id="M196" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.17</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to 10<inline-formula><mml:math id="M197" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.40</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M198" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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>) at heights from 0.5 <inline-formula><mml:math id="M199" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (1.0 <inline-formula><mml:math id="M200" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) to 1.0 <inline-formula><mml:math id="M201" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (2.0 <inline-formula><mml:math id="M202" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) in the lower (upper) PBL. Thus, the well-mixed turbulence maintains the development of the PBL in the early afternoon. By comparison, under cloudy-sky condition (Fig. <xref ref-type="fig" rid="Ch1.F4"/>c), the daytime mean value of <inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can reach up to 1.4 <inline-formula><mml:math id="M204" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, which is 0.12 <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> lower than that of clear-sky conditions. This means that clouds suppress the development of the PBL turbulence in the early afternoon, which has been observed by radiosonde observations described in Guo et al. (2016).</p>
      <p id="d1e2947">It is well known that there exists diurnal variation in the PBL. To better reveal the mechanism of how a myriad of geophysical parameters affect turbulence, the height-resolved <inline-formula><mml:math id="M206" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> retrievals are further normalized by the average PBL height. As noted above, the valid minimum altitude of the RWP data is 0.5 <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> at 120 <inline-formula><mml:math id="M208" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> vertical resolution, and the maximum <inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is approximately 2.0 <inline-formula><mml:math id="M210" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (Figs. <xref ref-type="fig" rid="Ch1.F2"/> and <xref ref-type="fig" rid="Ch1.F4"/>); <inline-formula><mml:math id="M211" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> is normalized by <inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to provide a nondimensional vertical coordinate for <inline-formula><mml:math id="M213" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>. It follows that <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is great than 0.25, and the range of <inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is set from 0.3 to 2.0 for the following analyses.</p>

      <fig id="Ch1.F5" specific-use="star"><label>Figure 5</label><caption><p id="d1e3055">PDF of daytime <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(a)</bold> in the whole lower troposphere (0.3 <inline-formula><mml:math id="M217" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M219" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0), <bold>(b)</bold> in the PBL (0.3 <inline-formula><mml:math id="M220" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M222" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0), and <bold>(c)</bold> above the PBL (1.0 <inline-formula><mml:math id="M223" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M225" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0) over the TP under all-sky (black), clear-sky (red), and cloudy-sky (blue) conditions. <bold>(d)</bold> Normalized contoured frequency by altitude diagram (NCFAD) for the difference in <inline-formula><mml:math id="M226" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> between cloudy-sky and clear-sky conditions (<inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> over the TP. Note that <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes the depth of the PBL and the height (<inline-formula><mml:math id="M229" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>) and turbulence dissipation rate (<inline-formula><mml:math id="M230" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>) are normalized by <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in order to give a nondimensional vertical coordinate in the form of <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f05.png"/>

        </fig>

      <p id="d1e3249">The probability density function (PDF) of <inline-formula><mml:math id="M233" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> in the PBL (0.3 <inline-formula><mml:math id="M234" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M236" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0) and above the PBL (1.0 <inline-formula><mml:math id="M237" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M239" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0) under all-,clear-, and cloudy-sky conditions is given in Fig. <xref ref-type="fig" rid="Ch1.F5"/>. Overall, the mean <inline-formula><mml:math id="M240" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is 10<inline-formula><mml:math id="M241" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.82</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, 10<inline-formula><mml:math id="M242" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.79</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and 10<inline-formula><mml:math id="M243" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.85</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M244" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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> at the height range of 0.3 <inline-formula><mml:math id="M245" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M247" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0 under all-,clear-, and cloudy-sky conditions, respectively (Fig. <xref ref-type="fig" rid="Ch1.F5"/>a). Within the PBL (Fig. <xref ref-type="fig" rid="Ch1.F5"/>b), the mean <inline-formula><mml:math id="M248" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> under clear-sky conditions (10<inline-formula><mml:math id="M249" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.27</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M250" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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>) is greater than that under cloudy-sky conditions (10<inline-formula><mml:math id="M251" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.36</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M252" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>), and the standard deviation of <inline-formula><mml:math id="M253" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> under clear-sky conditions is slightly greater than that under cloudy-sky conditions. This illustrates that clouds can significantly inhibit the turbulence intensity in the PBL, with the value of <inline-formula><mml:math id="M254" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:math></inline-formula> between clear- and cloudy-sky conditions being <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M256" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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>. However, above the PBL (Fig. <xref ref-type="fig" rid="Ch1.F5"/>c), <inline-formula><mml:math id="M257" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> presents normal distribution characteristics, and there is no significant difference between the mean <inline-formula><mml:math id="M258" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> values under clear- and cloudy-sky conditions.</p>
      <p id="d1e3575">To examine the overall impact of clouds on the vertical structure of turbulence within and above the PBL, Fig. <xref ref-type="fig" rid="Ch1.F5"/>d shows the normalized contoured frequency by altitude diagram (NCFAD) of the <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:math></inline-formula> for normalized (<inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) profiles of <inline-formula><mml:math id="M261" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> between cloudy-sky and clear-sky conditions. Within the PBL, <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:math></inline-formula> is negative and <inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:mi mathvariant="normal">|</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">|</mml:mi></mml:mrow></mml:math></inline-formula> generally decreases with increased <inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:math></inline-formula> is <inline-formula><mml:math id="M266" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>10<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M268" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</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> at <inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M270" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.5 and <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M272" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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> at <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M274" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.0. This suggests that clouds may weaken turbulence within the PBL (Fig. <xref ref-type="fig" rid="Ch1.F4"/>b and c), especially in the lower PBL (<inline-formula><mml:math id="M275" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M276" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 820 <inline-formula><mml:math id="M277" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M279" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.5). Figure S4  further shows the distinct spatial variability in the cloud effect on <inline-formula><mml:math id="M280" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> across the six RWP stations. Particularly, the turbulence is weakened by clouds within the PBL at Minfeng and Jiuquan in the northern TP, as opposed to the enhanced <inline-formula><mml:math id="M281" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> within the PBL at Ganzi and Lijiang. This suggests that the cloud impact on <inline-formula><mml:math id="M282" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is much more complicated than expected. One of the reasons for this could concern the cloud life stage, which is not dealt with in this present study. On top of the life stage, the cloud impact on <inline-formula><mml:math id="M283" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, in combination with <inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS, exhibits a distinct altitude dependence, differing by RWP station (Fig. S5).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Potential factors influencing the daytime PBL turbulence dissipation rate</title>
<sec id="Ch1.S3.SS3.SSS1">
  <label>3.3.1</label><title>Surface–air temperature difference</title>
      <p id="d1e3891">The vertical structures of PBL <inline-formula><mml:math id="M285" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> over the TP show obvious spatial differences in the context of a complex subsurface. The diverse land cover types lead to differences in surface albedo and soil moisture, which in turn lead to distinctions in thermodynamic characteristics such as sensible heat flux (Ma et al., 2023). Buoyant production driven by solar heating from the surface is one of the dominant sources generating turbulence in the convective PBL. The surface sensible heat flux is an important thermodynamic factor that affects the buoyant convective processes (Stull, 1988). Meanwhile, previous studies (e.g., Wang et al., 2022; Yang et al., 2023) have suggested that <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can serve as a good proxy for the sensible heat flux. There are no sensible heat flux measurements at the six RWP stations in this study, and thus we directly take <inline-formula><mml:math id="M288" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as a proxy thermodynamic variable to analyze its potential connection to variation in PBL turbulence.</p>

      <fig id="Ch1.F6" specific-use="star"><label>Figure 6</label><caption><p id="d1e3950">Scatterplots (blue dots) of <inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> estimated from the measurements of RWPs in the whole lower troposphere (0.3 <inline-formula><mml:math id="M290" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M292" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0; <bold>a</bold>, <bold>d</bold>, <bold>g</bold>), in the PBL (0.3 <inline-formula><mml:math id="M293" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M295" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0; <bold>b</bold>, <bold>e</bold>, <bold>h</bold>), and above the PBL (1.0 <inline-formula><mml:math id="M296" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M298" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0; <bold>c</bold>, <bold>f</bold>, <bold>i</bold>) over the TP as a function of <inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> under all-sky <bold>(a–c)</bold>, clear-sky <bold>(d–f)</bold>, and cloudy-sky conditions <bold>(g–i)</bold>. Also overlaid are the corresponding box-and-whisker plots, regression linear equations, and correlation coefficients in each panel, where all <inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> samples are divided into 20 bins, each of which has the same sample size. Note that the median is shown as a line, whereas the outer boundaries of the boxes represent the 25th and 75th percentiles, and the dashed lines represent the interquartile range (IQR). The superscripts <inline-formula><mml:math id="M301" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>*</mml:mo><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> for <inline-formula><mml:math id="M302" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> indicate that the regression slopes are statistically significant (<inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>).</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f06.png"/>

          </fig>

      <fig id="Ch1.F7" specific-use="star"><label>Figure 7</label><caption><p id="d1e4168">Scatterplots of <inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> estimated from the measurements of RWPs in the whole lower troposphere (0.3 <inline-formula><mml:math id="M305" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M307" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0; <bold>a</bold>, <bold>d</bold>, <bold>g</bold>), in the PBL (0.3 <inline-formula><mml:math id="M308" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M310" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0; <bold>b</bold>, <bold>e</bold>, <bold>h</bold>), and above the PBL (1.0 <inline-formula><mml:math id="M311" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M313" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0; <bold>c</bold>, <bold>f</bold>, <bold>i</bold>) over the TP as a function of vertical wind shear (VWS) under all-sky <bold>(a–c)</bold>, clear-sky <bold>(d–f)</bold>, and cloudy-sky conditions <bold>(g–i)</bold>. Also overlaid are the corresponding box-and-whisker plots and fitting equations in each panel, where all VWS samples are divided into 20 bins, each of which has the same sample size. Note that the median is shown as a line, whereas the outer boundaries of the boxes represent the 25th and 75th percentiles, and the dashed lines represent the interquartile range (IQR).</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f07.png"/>

          </fig>

<table-wrap id="Ch1.T2" specific-use="star"><label>Table 2</label><caption><p id="d1e4320">A summary of the correlation of <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> at different altitude ranges under all-,clear-, and cloudy-sky conditions with <inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and vertical wind shear (VWS) for all six RWP stations. The superscript <inline-formula><mml:math id="M316" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula> for <inline-formula><mml:math id="M317" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> indicates that the regression slope is statistically significant at <inline-formula><mml:math id="M318" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Conditions</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M319" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> vs. <inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> vs. VWS</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">All-sky, 0.3 <inline-formula><mml:math id="M322" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M324" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M325" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M326" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.010<inline-formula><mml:math id="M327" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M328" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.05; <inline-formula><mml:math id="M329" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M330" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.21<inline-formula><mml:math id="M331" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M332" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M333" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 13.6<inline-formula><mml:math id="M334" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M335" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.19; <inline-formula><mml:math id="M336" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M337" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.29<inline-formula><mml:math id="M338" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">All-sky, 0.3 <inline-formula><mml:math id="M339" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M341" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M342" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M343" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.018<inline-formula><mml:math id="M344" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M345" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.70; <inline-formula><mml:math id="M346" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M347" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.29<inline-formula><mml:math id="M348" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M349" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M350" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 13.2<inline-formula><mml:math id="M351" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M352" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.77; <inline-formula><mml:math id="M353" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M354" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.20<inline-formula><mml:math id="M355" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">All-sky, 1.0 <inline-formula><mml:math id="M356" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M357" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M358" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M359" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M360" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M361" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.004<inline-formula><mml:math id="M362" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M363" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.20; <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> <inline-formula><mml:math id="M366" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.09<inline-formula><mml:math id="M367" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M368" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M369" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 17.6<inline-formula><mml:math id="M370" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M371" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.57; <inline-formula><mml:math id="M372" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M373" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.36<inline-formula><mml:math id="M374" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Clear-sky, 0.3 <inline-formula><mml:math id="M375" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M376" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M377" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M378" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M379" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.011<inline-formula><mml:math id="M380" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M381" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.04; <inline-formula><mml:math id="M382" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M383" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.23<inline-formula><mml:math id="M384" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M385" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M386" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 10.7<inline-formula><mml:math id="M387" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M388" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.13; <inline-formula><mml:math id="M389" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M390" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.26<inline-formula><mml:math id="M391" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Clear-sky, 0.3 <inline-formula><mml:math id="M392" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M393" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M394" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M395" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M396" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.018<inline-formula><mml:math id="M397" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M398" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.67; <inline-formula><mml:math id="M399" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M400" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.30<inline-formula><mml:math id="M401" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M402" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M403" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 11.1<inline-formula><mml:math id="M404" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M405" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.70; <inline-formula><mml:math id="M406" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M407" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.17<inline-formula><mml:math id="M408" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Clear-sky, 1.0 <inline-formula><mml:math id="M409" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M411" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M412" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M413" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M414" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.005<inline-formula><mml:math id="M415" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M416" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.17; <inline-formula><mml:math id="M417" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M418" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M419" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.11<inline-formula><mml:math id="M420" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M421" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M422" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 13.8<inline-formula><mml:math id="M423" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M424" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.52; <inline-formula><mml:math id="M425" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M426" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.34<inline-formula><mml:math id="M427" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Cloudy-sky, 0.3 <inline-formula><mml:math id="M428" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M429" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M430" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M431" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M432" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.009<inline-formula><mml:math id="M433" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M434" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.06; <inline-formula><mml:math id="M435" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M436" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.16<inline-formula><mml:math id="M437" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M438" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M439" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 18.5<inline-formula><mml:math id="M440" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M441" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.29; <inline-formula><mml:math id="M442" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M443" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.33<inline-formula><mml:math id="M444" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Cloudy-sky, 0.3 <inline-formula><mml:math id="M445" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M446" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M447" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M448" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M449" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.018<inline-formula><mml:math id="M450" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M451" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.71; <inline-formula><mml:math id="M452" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M453" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.26<inline-formula><mml:math id="M454" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M455" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M456" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 15.5<inline-formula><mml:math id="M457" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M458" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 3.84; <inline-formula><mml:math id="M459" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M460" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.23<inline-formula><mml:math id="M461" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Cloudy-sky, 1.0 <inline-formula><mml:math id="M462" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M463" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M464" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M465" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M466" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M467" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.004<inline-formula><mml:math id="M468" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M469" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.22; <inline-formula><mml:math id="M470" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M471" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M472" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.08<inline-formula><mml:math id="M473" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M474" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M475" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 26.2<inline-formula><mml:math id="M476" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M477" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> 4.67; <inline-formula><mml:math id="M478" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M479" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.42<inline-formula><mml:math id="M480" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e5772">Figure <xref ref-type="fig" rid="Ch1.F6"/> shows that the magnitude of <inline-formula><mml:math id="M481" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> varies as a function of <inline-formula><mml:math id="M482" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for all six stations, within (0.3 <inline-formula><mml:math id="M483" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M484" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M485" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0) and above (1.0 <inline-formula><mml:math id="M486" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M487" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M488" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0) the PBL, under all-,clear-, and cloudy-sky conditions, respectively. <inline-formula><mml:math id="M489" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values are first classified into five bins, which are then statistically analyzed against the corresponding <inline-formula><mml:math id="M490" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> averaged for <inline-formula><mml:math id="M491" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values between 0.3 and 2.0 to obtain regression equations incorporating slopes. Further, Table <xref ref-type="table" rid="Ch1.T2"/> shows details of the scatterplots between <inline-formula><mml:math id="M492" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F6"/>) and <inline-formula><mml:math id="M493" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (and VWS, Fig. <xref ref-type="fig" rid="Ch1.F7"/>) at different altitude ranges under all-,clear-, and cloudy-sky conditions. <inline-formula><mml:math id="M494" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is found to be linearly correlated with <inline-formula><mml:math id="M495" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (and VWS) (<inline-formula><mml:math id="M496" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M497" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.05). The surface sensible heat flux generally increases with increased <inline-formula><mml:math id="M498" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>; thus the increased <inline-formula><mml:math id="M499" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> intensifies the turbulence in the PBL (0.3 <inline-formula><mml:math id="M500" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M501" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M502" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0), which is shown in Fig. <xref ref-type="fig" rid="Ch1.F6"/>b, e, and h. Within the PBL, <inline-formula><mml:math id="M503" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is also positively correlated with <inline-formula><mml:math id="M504" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, whose slope values are larger than those at 0.3 <inline-formula><mml:math id="M505" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M506" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M507" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0. As <inline-formula><mml:math id="M508" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> rises, the larger surface sensible heat flux would lead to enhanced buoyancy process and turbulent motion within the PBL. On the other hand, <inline-formula><mml:math id="M509" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> above the PBL is negatively correlated with <inline-formula><mml:math id="M510" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F6"/>c, f, and i). This suggests that <inline-formula><mml:math id="M511" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dramatically affects the development of turbulence within the PBL, whereas it has little effect on the turbulence above the PBL.</p>
      <p id="d1e6187">Within the PBL, the magnitude of the slope (slope <inline-formula><mml:math id="M512" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.019) under clear-sky conditions is larger than that under cloudy conditions (slope <inline-formula><mml:math id="M513" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.015) as shown in Fig. <xref ref-type="fig" rid="Ch1.F6"/>e and h. This implies that <inline-formula><mml:math id="M514" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> rather than cloud cover is the governing parameter affecting the PBL turbulence, particularly under the clear-sky conditions. Given that turbulence in the mixed PBL over the TP is usually driven by convection (Xu et al., 2023), as <inline-formula><mml:math id="M515" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> decreases when clouds are present, less heat is transferred from the surface to the atmosphere, reducing the buoyancy flux and leading to weaker turbulence in the PBL, especially for the lower PBL (0.3 <inline-formula><mml:math id="M516" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M517" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M518" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), as shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/>b and c. Consequently, the clouds tend to suppress the development of the PBL (Fig. <xref ref-type="fig" rid="Ch1.F5"/>a) and reduce <inline-formula><mml:math id="M519" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S3.SS3.SSS2">
  <label>3.3.2</label><title>Vertical wind shear</title>
      <p id="d1e6295">Besides <inline-formula><mml:math id="M520" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, VWS is another crucial dynamic parameter that is related to the mechanical turbulence within the PBL. Similarly to Fig. <xref ref-type="fig" rid="Ch1.F6"/>, Fig. <xref ref-type="fig" rid="Ch1.F7"/> presents the relationship between <inline-formula><mml:math id="M521" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and VWS (both normalized by <inline-formula><mml:math id="M522" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) within and above the PBL under all-,clear-, and cloudy-sky conditions. The near-surface clutter significantly increases the uncertainty in RWP data, which leads to an inability to analyze the effect of wind shear on <inline-formula><mml:math id="M523" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> below 0.5 <inline-formula><mml:math id="M524" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">a</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M525" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula>) in the following sections.</p>
      <p id="d1e6393">Regardless of whether it is within or above the PBL, <inline-formula><mml:math id="M526" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is positively correlated with VWS, as shown in Fig. <xref ref-type="fig" rid="Ch1.F7"/>a, d, and g and Table <xref ref-type="table" rid="Ch1.T2"/>, which indicates that larger VWS leads to stronger turbulence. This suggests that the dynamic effect of VWS promotes the development of turbulence. Within the PBL (Fig. <xref ref-type="fig" rid="Ch1.F7"/>b, e, and h), the slope of <inline-formula><mml:math id="M527" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> against VWS is smaller than at 0.3 <inline-formula><mml:math id="M528" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M529" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M530" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0, with values ranging from 9.5 to 10.3. Above the PBL (Fig. <xref ref-type="fig" rid="Ch1.F7"/>c, f, and i), the values of the slope are larger, with values ranging from 10.7 to 18.1, which demonstrates that the dynamical effects of VWS influence the development of turbulence both within the upper PBL and above the PBL.</p>
      <p id="d1e6448">Under cloudy-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F7"/>h and i), the effect of VWS on turbulence within the upper PBL (slope <inline-formula><mml:math id="M531" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 10.3) is significantly weaker than above the PBL (slope <inline-formula><mml:math id="M532" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 18.1). Compared to the clear-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F7"/>e and f), the values of the slopes are larger under cloudy-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F7"/>h and i) both within and above the PBL. Remarkably, above the PBL, the effect of clouds on turbulence is more dramatic, as the slope value under cloudy-sky conditions is nearly twice as large as that under clear-sky conditions. These results indicate that the significant mechanical processes driven by VWS are important in the development of turbulence. Larger VWS in the PBL corresponds to stronger turbulence. Besides, above the PBL, the mechanical process of VWS is enhanced under cloudy-sky conditions.</p>
</sec>
<sec id="Ch1.S3.SS3.SSS3">
  <label>3.3.3</label><title>Joint influence of <inline-formula><mml:math id="M533" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, VWS, and atmospheric stability on <inline-formula><mml:math id="M534" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula></title>
      <p id="d1e6504">It has been stated that turbulence can be produced by buoyant convective processes (i.e., thermals of warm air rising) and by mechanical processes (i.e., wind shear). From the previous section, it is known that <inline-formula><mml:math id="M535" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS both affect the development of PBL turbulence. Figure <xref ref-type="fig" rid="Ch1.F8"/> gives the slope profiles of <inline-formula><mml:math id="M536" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> against <inline-formula><mml:math id="M537" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS at normalized heights (<inline-formula><mml:math id="M538" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) under all-,clear-, and cloudy-sky conditions.</p>

      <fig id="Ch1.F8"><label>Figure 8</label><caption><p id="d1e6576">The vertical profiles of the least-squares regression slope between <inline-formula><mml:math id="M539" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M540" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <bold>(a)</bold> and between <inline-formula><mml:math id="M541" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and VWS <bold>(b)</bold> over the TP under all-sky (black), clear-sky (red), and cloudy-sky (blue) conditions.</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f08.png"/>

          </fig>

      <p id="d1e6635">As inferred from the previous findings, <inline-formula><mml:math id="M542" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> primarily influences turbulence development within the PBL, irrespective of clear-sky and cloudy-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). Figure <xref ref-type="fig" rid="Ch1.F8"/>a shows that the slope values within the PBL are predominantly positive, and the slope value decreases rapidly with height, which indicates that the influence of <inline-formula><mml:math id="M543" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> on PBL turbulence decreases with height. Interestingly, there is a nearly linear variation in the slope from the lower PBL to the top of the PBL. Within the PBL, the slope is positive; above the PBL, the slope becomes negative. This may be due to the linear decrease in heat flux transport and the buoyancy term in the convective PBL (Stull, 1988). Therefore, these findings highlight the predominant thermal forcing of <inline-formula><mml:math id="M544" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> acting on turbulence development within the lower PBL. Figure <xref ref-type="fig" rid="Ch1.F8"/> clearly shows the influence of cloud cover on <inline-formula><mml:math id="M545" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the effect of the surface heating on the turbulence in the lower half of the PBL (0.3 <inline-formula><mml:math id="M546" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M547" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M548" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), while there is little difference for the clear-sky and cloudy-sky conditions when <inline-formula><mml:math id="M549" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M550" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.5. Hence, under clear-sky conditions, the thermodynamic effect of <inline-formula><mml:math id="M551" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is more pronounced within the lower PBL.</p>

      <fig id="Ch1.F9" specific-use="star"><label>Figure 9</label><caption><p id="d1e6790">Joint dependence of <inline-formula><mml:math id="M552" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (color shading) on the VWS and <inline-formula><mml:math id="M553" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> within and above the PBL (<bold>a</bold>, <bold>d</bold>, <bold>g</bold>), in the PBL (<bold>b</bold>, <bold>e</bold>, <bold>h</bold>), and above the PBL <bold>(c, f, i)</bold> over the TP under all-sky <bold>(a–c)</bold>, clear-sky <bold>(d–f)</bold>, and cloudy-sky <bold>(g–i)</bold> conditions. The number given in each cell is the total number of samples used.</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f09.png"/>

          </fig>

      <p id="d1e6862">As shown in Fig. <xref ref-type="fig" rid="Ch1.F7"/>, it is evident that VWS influences turbulence development within and above the PBL. Figure <xref ref-type="fig" rid="Ch1.F8"/>b shows that when 0.3 <inline-formula><mml:math id="M554" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M555" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M556" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0, the slope values are consistently positive, indicating that VWS predominantly affects turbulence development within the middle and upper PBL and above the PBL. Moreover, when 0.3 <inline-formula><mml:math id="M557" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M558" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M559" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.2, the slope values increase with height. However, when 1.4 <inline-formula><mml:math id="M560" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M561" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M562" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0, the slope decreases with height, which suggests a diminishing influence of VWS. Additionally, within the PBL (0.3 <inline-formula><mml:math id="M563" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M564" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M565" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.7), the slope values under clear-sky conditions are close to those under cloudy-sky conditions, while the slope values under cloudy-sky conditions are even greater when 0.7 <inline-formula><mml:math id="M566" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M567" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M568" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0. For instance, when <inline-formula><mml:math id="M569" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M570" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.4, <inline-formula><mml:math id="M571" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">Slope</mml:mi><mml:mrow><mml:mi mathvariant="normal">Clear</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">sky</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M572" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 14.6, while <inline-formula><mml:math id="M573" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">Slope</mml:mi><mml:mrow><mml:mi mathvariant="normal">Cloudy</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">sky</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M574" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 27.0, indicating that the latter is 1.8 times larger than the former. These results suggest that clouds are primarily responsible for enhancing mechanical processes from VWS acting on turbulence within the upper PBL and above the PBL.</p>
      <p id="d1e7085">Furthermore, it can be concluded that <inline-formula><mml:math id="M575" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a thermodynamic factor influencing turbulence development within the lower PBL (0.3 <inline-formula><mml:math id="M576" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M577" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M578" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), both <inline-formula><mml:math id="M579" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS jointly strengthen turbulence development in the upper PBL (0.6 <inline-formula><mml:math id="M580" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M581" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M582" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0), and VWS emerges as the predominant factor affecting turbulence development above the PBL (1.0 <inline-formula><mml:math id="M583" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M584" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M585" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0) (Fig. <xref ref-type="fig" rid="Ch1.F8"/>a and b).</p>

      <fig id="Ch1.F10" specific-use="star"><label>Figure 10</label><caption><p id="d1e7217">Joint dependence of <inline-formula><mml:math id="M586" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:msub><mml:mtext>Log</mml:mtext><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (color shading) on the gradient Richardson number (<inline-formula><mml:math id="M587" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula>) and <inline-formula><mml:math id="M588" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in and above the PBL <bold>(a, d, g)</bold>, in the PBL <bold>(b, e, h)</bold>, and above the PBL (<bold>c</bold>, <bold>f</bold>, <bold>i</bold>) over the TP under all-sky <bold>(a–c)</bold>, clear-sky <bold>(d–f)</bold>, and cloudy-sky <bold>(g–i)</bold> conditions. The number given in each cell is the total number of samples used.</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/24/8703/2024/acp-24-8703-2024-f10.png"/>

          </fig>

      <p id="d1e7289">The previous sections have revealed that hours of both high <inline-formula><mml:math id="M589" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and strong wind shear would strengthen the turbulence within the PBL. Therefore, it is necessary to analyze the combined influence of thermodynamic and dynamic factors on the development of turbulence. Figure <xref ref-type="fig" rid="Ch1.F9"/> presents the joint distribution of <inline-formula><mml:math id="M590" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> with <inline-formula><mml:math id="M591" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS within and above the PBL under all-,clear-, and cloudy-sky conditions. Within the PBL (Fig. <xref ref-type="fig" rid="Ch1.F9"/>b, e, and h), higher <inline-formula><mml:math id="M592" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS correspond to stronger turbulence (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). In contrast, the thermodynamic effect of <inline-formula><mml:math id="M593" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> on turbulence has diminished and is no longer a dominant factor above the PBL, while the dynamical effect of VWS has become the dominant factor (Fig. <xref ref-type="fig" rid="Ch1.F9"/>c, f, and i). Compared to clear-sky conditions, both <inline-formula><mml:math id="M594" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS decrease under cloudy-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F9"/>h). This means that the weakening of both thermodynamic and dynamic effects leads to a decrease in turbulence, thereby inhibiting the development of turbulence within the PBL. Therefore, under cloudy-sky conditions, although the VWS is reduced, the dynamical effect of VWS on turbulence is strengthened (Figs. <xref ref-type="fig" rid="Ch1.F7"/>i and <xref ref-type="fig" rid="Ch1.F8"/>b), which in turn strengthens turbulence.</p>
      <p id="d1e7413">Since buoyant forcing and mechanic forcing jointly influence the turbulence within the PBL and VWS only represents the dynamic driving effect, VWS cannot accurately portray the effect of thermodynamic and dynamic effects on the PBL turbulence. The gradient Richardson number (<inline-formula><mml:math id="M595" display="inline"><mml:mrow><mml:mi mathvariant="italic">Ri</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, on the other hand, is one of the important parameters characterizing atmospheric stability and can be used to compare the buoyant turbulence production term and the shear production term in the form of a dimensionless ratio.</p>
      <p id="d1e7426">Similarly to Fig. <xref ref-type="fig" rid="Ch1.F9"/>, the joint distribution of <inline-formula><mml:math id="M596" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> with <inline-formula><mml:math id="M597" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M598" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula> within and above the PBL under all-sky, clear-sky, and cloudy-sky conditions is given in Fig. <xref ref-type="fig" rid="Ch1.F10"/>. As shown in Fig. <xref ref-type="fig" rid="Ch1.F10"/>b, e, and h, it is evident that the turbulence in the PBL tends to be enhanced for unstable conditions. Furthermore, under clear-sky conditions (Fig. <xref ref-type="fig" rid="Ch1.F10"/>e), the maximum number of samples is found when <inline-formula><mml:math id="M599" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M600" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1.0 and <inline-formula><mml:math id="M601" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M602" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 21.1 in strongly unstable conditions, which may be caused by the buoyancy forcing driven by the larger <inline-formula><mml:math id="M603" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. By comparison, the effect of <inline-formula><mml:math id="M604" display="inline"><mml:mi mathvariant="italic">Ri</mml:mi></mml:math></inline-formula> on turbulence is relatively weakened above the PBL (Fig. <xref ref-type="fig" rid="Ch1.F10"/>c, f, and i).</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Summary and concluding remarks</title>
      <p id="d1e7547">This study investigates the characteristics of the spatio-temporal distribution of the daytime PBL turbulence dissipation rate (<inline-formula><mml:math id="M605" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>) based on a record spanning more than 1 year (September 2022–October 2023) of profiling measurements from a radar wind profiler (RWP) network on the Tibetan Plateau (TP). Also analyzed are the evolution of <inline-formula><mml:math id="M606" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> in the PBL and possible influential mechanisms.</p>
      <p id="d1e7564">First of all, <inline-formula><mml:math id="M607" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is retrieved from the vertical wind measurements from RWPs using the spectral width method. Afterwards, the spatial pattern of <inline-formula><mml:math id="M608" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is examined. Results shows that the values of <inline-formula><mml:math id="M609" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> at the Minfeng and Jiuquan stations in the northern TP and at Dingri over the southern TP are about 1 order of magnitude greater than those at the RWP stations of Lijiang, Ganzi, and Hongyuan over the eastern TP. Coincidently, Minfeng and Jiuquan are dominated by bare or semiarid land, as opposed to the land surface of high vegetation cover at Lijiang, Ganzi, and Hongyuan. This suggests the spatial discrepancy of <inline-formula><mml:math id="M610" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> over the TP is highly relevant to the types of underlying land cover.</p>
      <p id="d1e7595">Although <inline-formula><mml:math id="M611" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> exhibits a variety of magnitudes among the six RWPs, the daytime pattern and vertical structure of <inline-formula><mml:math id="M612" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> are similar. Turbulence reaches a peak in the early afternoon (13:00–15:00 LST), coinciding with the highest PBL top. Under cloudy-sky conditions, the daytime mean value of <inline-formula><mml:math id="M613" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> is 10<inline-formula><mml:math id="M614" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.02</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M615" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</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>, and the daytime mean value of the PBL height (<inline-formula><mml:math id="M616" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) can reach up to 1.40 <inline-formula><mml:math id="M617" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, which is 0.12 <inline-formula><mml:math id="M618" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> lower than that of clear-sky conditions, indicating that clouds suppress the development of PBL turbulence.</p>
      <p id="d1e7679">As far as both the thermodynamic and the dynamic forcings are concerned, surface–air temperature difference (<inline-formula><mml:math id="M619" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and vertical wind shear (VWS) variables are examined by performing correlation analysis with <inline-formula><mml:math id="M620" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>. The slope values of <inline-formula><mml:math id="M621" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> against <inline-formula><mml:math id="M622" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> under clear-sky conditions are larger (slope <inline-formula><mml:math id="M623" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.019) than under cloudy conditions (slope <inline-formula><mml:math id="M624" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.013) within the PBL, while those values are negative above the PBL. The slope values of <inline-formula><mml:math id="M625" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> against VWS are positive regardless of whether they are within or above the PBL, where the largest value of 18.1 is observed above the PBL under cloudy-sky conditions and the smallest value of 9.5 is observed in the PBL under clear-sky conditions.</p>
      <p id="d1e7755">Both the thermodynamic effect of <inline-formula><mml:math id="M626" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the dynamic effect of VWS enhance the development of turbulence under clear-sky or cloudy-sky conditions in the PBL. In the lower PBL (0.3 <inline-formula><mml:math id="M627" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M628" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M629" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), <inline-formula><mml:math id="M630" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> has a larger positive slope with <inline-formula><mml:math id="M631" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, which suggests that thermal forcing emerges as the dominant factor influencing development of the turbulence and PBL. By comparison, in the upper PBL (0.6 <inline-formula><mml:math id="M632" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M633" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M634" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 1.0), <inline-formula><mml:math id="M635" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and VWS jointly influence the development of turbulence, with larger <inline-formula><mml:math id="M636" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values, leading to unstable atmospheric stability and stronger turbulence. Above the PBL (1.0 <inline-formula><mml:math id="M637" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M638" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M639" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2.0), VWS becomes the dominant factor influencing the development of turbulence. Compared to clear-sky conditions, on one hand, clouds diminish <inline-formula><mml:math id="M640" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, resulting in decreased heat transfer from the surface to the PBL top, thereby weakening turbulence within the lower PBL (0.3 <inline-formula><mml:math id="M641" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M642" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M643" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 0.5), inhibiting PBL development, and decreasing <inline-formula><mml:math id="M644" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. On the other hand, the stronger wind shear process enhances the turbulence above the PBL under cloudy-sky conditions.</p>
      <p id="d1e7985">Although the abovementioned findings of the PBL turbulence over the TP are the first results from profiling network observations to the best of our knowledge, the fine-resolution spatial distribution remains unclear, largely due to the sparse distribution of the RWP network on the TP. On top of this, the role of roughness length, vertical velocity, and entrainment remains unknown in terms of the variation in and evolution of atmospheric turbulence, warranting further in-depth studies based on intensive field campaigns in combination with theoretical analysis and numerical simulation experiments in the future.</p>
</sec>

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

      <p id="d1e7993">The meteorological dataset from weather stations and the measurements from radar wind profiler were obtained from the National Meteorological Information Center of the China Meteorological Administration (Guo et al., 2021a), and the hourly ERA5 reanalysis data (<ext-link xlink:href="https://doi.org/10.24381/cds.bd0915c6" ext-link-type="DOI">10.24381/cds.bd0915c6</ext-link>, Hersbach et al., 2023) used here are available from the ECMWF in Hersbach et al. (2020).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e7999">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-24-8703-2024-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-24-8703-2024-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e8008">The study was completed with close cooperation between all authors. JG and XG conceived of the idea for this work. DM performed the analysis. DM and JG drafted the original manuscript with contributions from XG, NL, YS, ZZ, and NT. YW, HL, FZ, BT, HX, and TC provided useful suggestions and comments for the study and helped revise the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e8015">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="d1e8021">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. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e8027">This work was jointly supported by the National Natural Science Foundation of China under grant nos. 42325501, U2142209, and 42105090; the High Impact Weather Key Laboratory of China Meteorological Administration; the CMA Xiong'an Atmospheric Boundary Layer Key Laboratory under grant no. 2023LABL-B06; and the Chinese Academy of Meteorological Sciences under grant nos. 2021KJ008 and 2024Z003. Last but not least, we appreciated tremendously the constructive comments and suggestions made by Gerrit de Leeuw and the anonymous reviewer, which significantly improved the quality of our paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e8032">This research has been supported by the National Natural Science Foundation of China (grant nos. 42325501 and U2142209).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e8038">This paper was edited by Dantong Liu and reviewed by Gerrit de Leeuw and one anonymous referee.</p>
  </notes><ref-list>
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