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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-24-3883-2024</article-id><title-group><article-title>Thermodynamic and cloud evolution in <?xmltex \hack{\break}?> a cold-air outbreak during HALO-(AC)<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>: <?xmltex \hack{\break}?> quasi-Lagrangian observations compared <?xmltex \hack{\break}?> to the ERA5 and CARRA reanalyses</article-title><alt-title>Thermodynamic and cloud evolution in a cold-air outbreak observed during HALO-(AC)<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></alt-title>
      </title-group><?xmltex \runningtitle{Thermodynamic and cloud evolution in a cold-air outbreak observed during HALO-(AC)${}^{{3}}$}?><?xmltex \runningauthor{B.~Kirbus et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Kirbus</surname><given-names>Benjamin</given-names></name>
          <email>benjamin.kirbus@uni-leipzig.de</email>
        <ext-link>https://orcid.org/0000-0002-8824-2244</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Schirmacher</surname><given-names>Imke</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4438-3077</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Klingebiel</surname><given-names>Marcus</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1544-6668</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Schäfer</surname><given-names>Michael</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1896-1574</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ehrlich</surname><given-names>André</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0860-8216</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Slättberg</surname><given-names>Nils</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1429-2561</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>Lucke</surname><given-names>Johannes</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6724-864X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Moser</surname><given-names>Manuel</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-8603-2756</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Müller</surname><given-names>Hanno</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5185-7384</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Wendisch</surname><given-names>Manfred</given-names></name>
          <email>m.wendisch@uni-leipzig.de</email>
        <ext-link>https://orcid.org/0000-0002-4652-5561</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Leipzig Institute for Meteorology, Leipzig University, Leipzig, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Institute of Geophysics and Meteorology, University of Cologne, Cologne, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Potsdam, Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Institute of Atmospheric Physics, German Aerospace Center (DLR), Weßling, Germany</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Faculty of Aerospace Engineering, Delft University of Technology, Delft, the Netherlands</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Benjamin Kirbus (benjamin.kirbus@uni-leipzig.de) and Manfred Wendisch (m.wendisch@uni-leipzig.de)</corresp></author-notes><pub-date><day>2</day><month>April</month><year>2024</year></pub-date>
      
      <volume>24</volume>
      <issue>6</issue>
      <fpage>3883</fpage><lpage>3904</lpage>
      <history>
        <date date-type="received"><day>11</day><month>December</month><year>2023</year></date>
           <date date-type="accepted"><day>18</day><month>February</month><year>2024</year></date>
           <date date-type="rev-recd"><day>16</day><month>February</month><year>2024</year></date>
           <date date-type="rev-request"><day>15</day><month>December</month><year>2023</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="d1e216">Arctic air masses undergo intense transformations when moving southward from closed sea ice to warmer open waters in marine cold-air outbreaks (CAOs). Due to the lack of measurements of diabatic heating and moisture uptake rates along CAO flows, studies often  depend on atmospheric reanalysis output.  However, the uncertainties connected to those datasets remain unclear.  Here, we present height-resolved airborne observations of diabatic heating, moisture uptake, and cloud evolution measured in a quasi-Lagrangian manner. The investigated  CAO was observed on 1 April 2022 during the HALO-(AC)<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>  campaign. Shortly after passing the sea-ice edge,  maximum diabatic heating rates  over 6 <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and moisture uptake over 0.3 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> were measured near the surface.  Clouds started forming and vertical mixing within the deepening boundary layer intensified. The quasi-Lagrangian observations are compared with the fifth-generation global reanalysis (ERA5) and the Copernicus Arctic Regional Reanalysis (CARRA). Compared to these observations, the mean absolute errors of ERA5 versus CARRA data are 14 % higher for air temperature over sea ice (1.14 K versus 1.00 K) and 62 % higher for specific humidity over ice-free ocean (0.112 <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> versus 0.069 <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). We relate these differences to issues with the representation of the marginal ice zone and corresponding surface fluxes in ERA5, as well as the cloud scheme producing excess liquid-bearing, precipitating clouds, which causes a too-dry marine boundary layer. CARRA's high spatial resolution and demonstrated higher fidelity towards  observations make it a promising candidate for further studies on Arctic air mass transformations.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Deutsche Forschungsgemeinschaft</funding-source>
<award-id>268020496</award-id>
<award-id>316646266</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <?pagebreak page3884?><p id="d1e314">Arctic air masses  over closed sea ice are subject to a sustained radiative cooling. Therefore, they are characterized both by low air temperatures and  low atmospheric moisture contents. Marine cold-air outbreaks (CAOs) manifest when such Arctic air masses depart the closed sea ice, traverse the marginal sea-ice zone (MIZ), and ultimately move southward onto considerably warmer ice-free oceans <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx15" id="paren.1"/>. In the early stages of CAOs, significant air mass transformations occur. They are driven by  strong surface energy fluxes of sensible and latent heat, as well as  by additional  entrainment fluxes through mixing with the overlying warmer air masses <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx102" id="paren.2"/>. The intense diabatic heating and moisture uptake initiates roll convection that leads to cloud evolution and a deepening of the atmospheric boundary layer <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx71 bib1.bibx75" id="paren.3"><named-content content-type="pre">ABL;</named-content></xref>.  As a result, the near-surface air temperature can increase by more than 20 K in a matter of hours  <xref ref-type="bibr" rid="bib1.bibx75 bib1.bibx113" id="paren.4"/>. Characteristic cloud streets of up to 1000 km length are formed, which later break up due to processes such as ABL decoupling and precipitation formation   <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx75 bib1.bibx48 bib1.bibx106 bib1.bibx15 bib1.bibx77 bib1.bibx66" id="paren.5"/>. This transition finally results in cellular cloud structures that have been reported to occur for boundary layer heights (BLHs) of over 1.4 km <xref ref-type="bibr" rid="bib1.bibx10" id="paren.6"/>. Then, the heat release from water vapor condensation into cloud droplets can even exceed the surface heat fluxes <xref ref-type="bibr" rid="bib1.bibx9" id="paren.7"/>. In the temperature range of <inline-formula><mml:math id="M8" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>25 to 0 °C, typical CAO clouds are of mixed-phase type, where the upper portions of the clouds are dominated by supercooled liquid water and the lower parts by ice particles  <xref ref-type="bibr" rid="bib1.bibx89 bib1.bibx63" id="paren.8"/>. The strongest CAO events occur in winter, when the  horizontal surface  temperature gradient between the cold sea ice and the adjacent ice-free ocean is the largest <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx71 bib1.bibx15" id="paren.9"/>. One of the primary gateways into and out of the central Arctic is the Fram Strait, located between Greenland and the Svalbard archipelago. CAOs are favored in this area because the North Atlantic Current transports significant heat northward, and consequently the MIZ and sea-ice edge are located far northward as well  <xref ref-type="bibr" rid="bib1.bibx15" id="paren.10"/>, which promotes intense CAOs in this region  <xref ref-type="bibr" rid="bib1.bibx71" id="paren.11"/>.</p>
      <p id="d1e361">Several factors have sparked scientific interest in studying CAOs.  The formation of cloud streets and their transition into open cells have important implications for the Arctic and the mid-latitude radiative energy budget, as the bright clouds over dark, ice-free ocean surfaces reflect a large fraction of incoming solar radiation, which causes a significant cooling at the surface <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx77 bib1.bibx66" id="paren.12"/>. Furthermore, large amounts of  heat are transferred from the ocean  into the atmosphere. Estimates show that about 60 %–80 % of oceanic heat loss in the Nordic Seas in winter is caused by CAOs, which has important implications for deep water formation  <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx99" id="paren.13"/>. CAOs have been linked to the evolution of short-lived polar lows and mesoscale cyclones  <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx97 bib1.bibx42 bib1.bibx60 bib1.bibx101" id="paren.14"/>. Either with or without such low-pressure systems being present, CAOs can trigger extreme weather conditions, such as freezing sea spray, intense snowfall, or high near-surface winds. These phenomena pose significant hazards at affected coastlines <xref ref-type="bibr" rid="bib1.bibx36 bib1.bibx42" id="paren.15"/>. The Arctic amplification observed in recent decades has caused a significant reduction in strong wintertime CAOs in the Fram Strait <xref ref-type="bibr" rid="bib1.bibx15" id="paren.16"/> and Barents Sea <xref ref-type="bibr" rid="bib1.bibx67" id="paren.17"/>. Also, in the future, strong wintertime CAOs are expected to decrease <xref ref-type="bibr" rid="bib1.bibx42" id="paren.18"/>. On the contrary, springtime CAOs are observed to intensify <xref ref-type="bibr" rid="bib1.bibx15" id="paren.19"/>. Not only are the CAO intensities expected to change, but the melting Arctic sea ice is also leading to a shift in spatial patterns <xref ref-type="bibr" rid="bib1.bibx42" id="paren.20"/>.</p>
      <p id="d1e392">CAOs have been studied intensively using satellite data <xref ref-type="bibr" rid="bib1.bibx78 bib1.bibx14 bib1.bibx118 bib1.bibx66 bib1.bibx54" id="paren.21"/>, atmospheric soundings <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx23 bib1.bibx61" id="paren.22"/>, and dedicated (mostly airborne) field campaigns <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx9 bib1.bibx23 bib1.bibx77 bib1.bibx57 bib1.bibx61 bib1.bibx93" id="paren.23"><named-content content-type="pre">such as reported by</named-content></xref>. The models applied to represent CAOs range from turbulence-resolving large eddy simulations <xref ref-type="bibr" rid="bib1.bibx104 bib1.bibx106 bib1.bibx44" id="paren.24"/> to mesoscale numerical weather prediction models <xref ref-type="bibr" rid="bib1.bibx109 bib1.bibx104 bib1.bibx20" id="paren.25"/> to global climate models <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx92" id="paren.26"/>.</p>
      <p id="d1e416">In addition, sophisticated atmospheric reanalyses have been developed. They assimilate a large amount of available measurements, such as atmospheric soundings and satellite data <xref ref-type="bibr" rid="bib1.bibx28" id="paren.27"/>. Reanalyses  deliver meteorological parameters on a continuous latitude–longitude–height grid, as well as at high temporal resolution  down to 1 h. The fifth-generation atmospheric reanalysis (ERA5) of the European Centre for Medium-Range Weather Forecasts (ECMWF) is frequently used for climatological studies <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx73 bib1.bibx15" id="paren.28"/>. Furthermore, dedicated Arctic reanalyses have been developed, such as the spatially much higher resolved  Copernicus Arctic Regional Reanalysis (CARRA). Investigations into characteristic properties and trends of Arctic CAOs based on reanalyses  have been created for classical Eulerian <xref ref-type="bibr" rid="bib1.bibx15" id="paren.29"/> and quasi-Lagrangian frameworks <xref ref-type="bibr" rid="bib1.bibx71" id="paren.30"/>. “Quasi-Lagrangian” highlights the fact that an air mass is not truly physically followed, as it may be possible by meteorological balloons <xref ref-type="bibr" rid="bib1.bibx12" id="paren.31"/>. Instead, wind fields  as available from reanalyses are used to model the flow of air masses <xref ref-type="bibr" rid="bib1.bibx95" id="paren.32"/>. Such kinematic trajectories are oblivious to sub-grid-scale turbulent motion leading to exchanges across neighboring air masses, which can be diagnosed as sources and sinks of, for example, moisture and heat. Yet they account for the mean drift along prevailing winds. Aircraft can be employed to trace the properties of specific air parcels along their trajectory <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx77" id="paren.33"/>. Finally, reanalysis output is  used to supply the boundary conditions and time-dependent forcings to much higher resolved models <xref ref-type="bibr" rid="bib1.bibx86 bib1.bibx44" id="paren.34"/>.</p>
      <?pagebreak page3885?><p id="d1e445">However, microphysical properties and the  processes governing the evolving clouds and their radiative properties remain notoriously difficult to model <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx75 bib1.bibx112" id="paren.35"/>. This is especially true over sea ice and the MIZ, where the widely employed satellite-based remote sensing faces serious challenges. As a result, many satellite studies investigating CAOs focus solely on the evolution over the fully ice-free open ocean <xref ref-type="bibr" rid="bib1.bibx118 bib1.bibx66 bib1.bibx54" id="paren.36"/>. Furthermore, the vertically non-uniform diabatic heating and moisture uptake by air masses along CAO trajectories are not sufficiently represented in models, which may cause issues in terms of  atmospheric stability and the lapse-rate feedback <xref ref-type="bibr" rid="bib1.bibx46" id="paren.37"/>. While the contributing processes are generally well understood, their relative importance and absolute magnitudes remain unspecified <xref ref-type="bibr" rid="bib1.bibx75 bib1.bibx112 bib1.bibx121 bib1.bibx120" id="paren.38"/>. As a result, the overall cloud effects on Arctic climate remain uncertain <xref ref-type="bibr" rid="bib1.bibx7 bib1.bibx112 bib1.bibx113" id="paren.39"/>.</p>
      <p id="d1e463">Here, we present airborne measurements of the height-dependent heating and moistening rates during a specific CAO event, based on quasi-Lagrangian  airborne observations. The investigated flight of  the <italic>High Altitude and LOng Range Aircraft</italic> (<italic>HALO</italic>) was conducted as part of the HALO-(AC)<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> airborne campaign, which took place in spring 2022. We compare the quasi-Lagrangian observations to the ERA5 and CARRA reanalyses. In our article, we address three specific research questions. (Q1) How do air temperature, specific humidity, and clouds evolve in the first 4 h of the developing CAO? (Q2) How do the ERA5 and CARRA reanalyses perform with respect to observations and compared to each other? (Q3) What are possible sources of errors which could explain deviations between reanalysis output and observations?</p>
      <p id="d1e481">The study is structured as follows. Section <xref ref-type="sec" rid="Ch1.S2"/> details the airborne observations which are the foundation of this study. The two ERA5 and CARRA reanalyses  are introduced, and the trajectory analysis is described. In Sect. <xref ref-type="sec" rid="Ch1.S3"/>, the airborne measurements  are  analyzed in a classical Eulerian framework. Subsequently, the  quasi-Lagrangian analysis will be used to present and discuss novel observation-derived heating and moistening rates along the CAO flow, as well as correlated cloud properties, and to compare them between the two reanalyses.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Airborne observations</title>
      <p id="d1e503">The CAO analyzed in this study was  observed on 1 April 2022 during the HALO-(AC)<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> campaign, which  was conducted in March and April 2022 as a dedicated quasi-Lagrangian Arctic airborne campaign <xref ref-type="bibr" rid="bib1.bibx112 bib1.bibx114" id="paren.40"/>. The meteorological conditions that prevailed during the campaign are described in <xref ref-type="bibr" rid="bib1.bibx110" id="text.41"/>.  HALO-(AC)<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> involved the  <italic>HALO</italic> research aircraft operated by the German Aerospace Center  <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx96" id="paren.42"/> for the long-range investigation of air mass transformations in combination with the lower-flying <italic>Polar 5</italic> and <italic>Polar 6</italic> research aircraft operated by the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research <xref ref-type="bibr" rid="bib1.bibx115" id="paren.43"/>. After taking off from the base in Kiruna (Sweden) at 07:30 UTC, <italic>HALO</italic> headed north. It then sampled the CAO cloud streets west of Svalbard; see Fig. <xref ref-type="fig" rid="Ch1.F1"/>. The speed of <italic>HALO</italic> at its typical flight altitude of 10–12 km is around 800 <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, which is much faster than the wind speed of 30–60 <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> measured by dropsondes on this day. Therefore, in order to facilitate a quasi-Lagrangian (i.e., air mass following) sampling of cloudy air masses, long horizontal cross-sections were flown across the off-ice flow. These flight legs not only covered the ice-free ocean, but also parts of the adjacent Arctic sea ice; see Fig. <xref ref-type="fig" rid="Ch1.F1"/>. Several such flight legs were conducted, where the legs were stepwise  shifted south roughly according to the forecast wind speed in the atmospheric boundary layer. Similar quasi-Lagrangian airborne sampling was performed previously, but taking place over the Atlantic <xref ref-type="bibr" rid="bib1.bibx59" id="paren.44"/> and   for a warm conveyor belt over Europe  <xref ref-type="bibr" rid="bib1.bibx6" id="paren.45"/>. Similar to our case, <xref ref-type="bibr" rid="bib1.bibx77" id="text.46"/> investigated the aerosol and cloud evolution in CAOs. From their quasi-Lagrangian observations, they contrast the evolving particle mode distributions between within and outside CAO flow. However,  they do not report, for example, on heating or moistening rates.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e603">Case overview. The gray line shows the flight track of <italic>HALO</italic>  on 1 April 2022. Diamond shapes show the locations where dropsondes were released. White-blueish contours represent 1 km high-resolution sea-ice concentration retrieved from a merged MODIS–AMSR2 satellite product <xref ref-type="bibr" rid="bib1.bibx51" id="paren.47"/>. Over the ice-free ocean, yellow-brownish contours indicate the ERA5-derived CAO index <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>; see Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>). Finally, the colored lines show  24 h backwards and 24 h forward trajectories initialized at the location of each dropsonde at 10 hPa above ground. The colors represent the evolving potential temperature (<inline-formula><mml:math id="M15" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>) of these air masses as traced from ERA5 data.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f01.png"/>

        </fig>

      <p id="d1e643">We analyze a set of 40 dropsondes which were released from <italic>HALO</italic> northwest of Svalbard. These RD94 dropsondes recorded air pressure <inline-formula><mml:math id="M16" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> (accuracy 0.4 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:math></inline-formula>), air temperature <inline-formula><mml:math id="M18" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> (0.2 <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi></mml:mrow></mml:math></inline-formula>), relative humidity RH (2 %), derived potential temperature <inline-formula><mml:math id="M20" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>, and  specific humidity <inline-formula><mml:math id="M21" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>, as well as horizontal wind components <xref ref-type="bibr" rid="bib1.bibx108 bib1.bibx24" id="paren.48"><named-content content-type="pre">0.2 <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><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">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>;</named-content></xref>. The data were  assimilated by the ECMWF Integrated Forecasting System (IFS), also serving as input for the ERA5 and CARRA reanalyses. The profiles of <inline-formula><mml:math id="M23" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> are used to derive the atmospheric BLH from dropsonde measurements and  reanalyses. The BLH is  defined here as the altitude where the largest vertical gradient in <inline-formula><mml:math id="M24" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> is found <xref ref-type="bibr" rid="bib1.bibx87 bib1.bibx16 bib1.bibx1 bib1.bibx90" id="paren.49"><named-content content-type="pre">similar to</named-content></xref>.  For estimating the cloud top heights (CTHs), the 532 nm backscatter ratio from the water vapor differential absorption (WALES) lidar is used <xref ref-type="bibr" rid="bib1.bibx116" id="paren.50"/>. WALES has a vertical resolution of 15 m. We define the CTH as the maximum altitude above ground  where the backscatter ratio exceeds that of cloud-free sections. Cloud radar data from the HALO Microwave Package (HAMP) are  used to additionally evaluate cloud evolution <xref ref-type="bibr" rid="bib1.bibx56" id="paren.51"/>. The radar data have a vertical resolution of 30 m.  Furthermore, to better understand the heating and moistening rates, airborne observations from <italic>HALO</italic> are used to estimate the surface sensible and latent heat fluxes (SSHF, SLHF), similar to <xref ref-type="bibr" rid="bib1.bibx44" id="text.52"/>. SSHF and SLHF are calculated based on the Coupled Ocean–Atmosphere Response<?pagebreak page3886?> Experiment (COARE) bulk air–sea flux algorithms and aerodynamic formulas <xref ref-type="bibr" rid="bib1.bibx19" id="paren.53"/>. COARE is widely used for the calculation of air–sea turbulent heat fluxes <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx5 bib1.bibx45" id="paren.54"/> and has been found to perform the best among  12 examined bulk aerodynamic formulas <xref ref-type="bibr" rid="bib1.bibx11" id="paren.55"/>. The following basic equations were used to estimate SSHF and SLHF <xref ref-type="bibr" rid="bib1.bibx19" id="paren.56"/>:

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M25" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E1"><mml:mtd><mml:mtext>1</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>SSHF</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>air</mml:mtext></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>skin</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>SLHF</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>air</mml:mtext></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">Q</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.98</mml:mn><mml:msub><mml:mi>q</mml:mi><mml:mtext>sat,skin</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>air</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> denotes the air density (<inline-formula><mml:math id="M27" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">Q</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the transfer coefficients for heat and humidity (dimensionless), <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the specific heat capacity at constant pressure (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1004.7</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">J</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the latent heat of evaporation (<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.5008</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">J</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the wind speed at 10 m height (<inline-formula><mml:math id="M37" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><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">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>skin</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the temperature difference between the 10 m air temperature and skin temperature (K), and <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.98</mml:mn><mml:msub><mml:mi>q</mml:mi><mml:mtext>sat,skin</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the difference in specific humidity between the 10 m level and the specific saturation humidity taken at skin temperature ( <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). The factor of 0.98 accounts for the reduction in vapor pressure resulting from a typical seawater salinity of 3.4 % <xref ref-type="bibr" rid="bib1.bibx19" id="paren.57"/>. Dropsonde profiles are used to extract <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>air</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>  via interpolation to the 10 m height level. The  Video airbornE Longwave Observations within siX channels (VELOX) thermal infrared imager <xref ref-type="bibr" rid="bib1.bibx79" id="paren.58"/> is applied to obtain  <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>skin</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (accuracy 0.5 K) and  <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mtext>sat,skin</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for the cloud-free sections. The transfer coefficients of heat and humidity are directly calculated using the most recent COARE 3.5 bulk air–sea algorithm <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx2" id="paren.59"/>. At winds speeds up to 20 <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><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">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, COARE has a reported uncertainty of around 10 % <xref ref-type="bibr" rid="bib1.bibx19 bib1.bibx18" id="paren.60"/>. Together with  the measurement uncertainties, a combined uncertainty on the bulk fluxes (SSHF, SLHF) of at least 12 % is assumed. For the MIZ with its many open leads, the calculated fluxes were multiplied with the open sea fraction of a merged MODIS–AMSR2 satellite product <xref ref-type="bibr" rid="bib1.bibx51" id="paren.61"/>. However, it should be stressed that the real surface heat fluxes can be assumed to be highly heterogeneous in the MIZ and thus prone to much higher uncertainties <xref ref-type="bibr" rid="bib1.bibx102" id="paren.62"/>. Finally, to collect in situ cloud measurements, the <italic>Polar 6</italic> aircraft sampled concurrently with <italic>HALO</italic> (Fig. S2). <italic>Polar 6</italic> was based in Longyearbyen on Svalbard and was equipped with a wide range of in situ probes <xref ref-type="bibr" rid="bib1.bibx64" id="paren.63"/>, including a  Nevzorov sonde from which the liquid and frozen cloud water contents were obtained. For liquid water contents of around 0.05 <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> similar to that discussed here, the uncertainty on measurements is assumed to be at approximately 17 % of the observed values <xref ref-type="bibr" rid="bib1.bibx40 bib1.bibx49 bib1.bibx57" id="paren.64"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Reanalysis products</title>
      <p id="d1e1310">The ERA5 global reanalysis features a sophisticated four-dimensional variational  data assimilation scheme  and is based on ECMWF's IFS cycle 41r2 <xref ref-type="bibr" rid="bib1.bibx28" id="paren.65"/>. ERA5 data fields have a temporal resolution of 1 h, have a horizontal grid resolution of 31 km, and are available on 137  model levels. The model levels start 10 m above ground level (m a.g.l.) and are then situated approximately every 20 m, with an increasing spacing upwards. Several studies note the high performance of ERA5 in the Arctic region <xref ref-type="bibr" rid="bib1.bibx25 bib1.bibx117" id="paren.66"/>, specifically in the Fram Strait region <xref ref-type="bibr" rid="bib1.bibx26" id="paren.67"/>. Thus, numerous authors performing trajectory analysis in the Arctic rely on wind and meteorological data fields from ERA5 <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx70 bib1.bibx15 bib1.bibx120 bib1.bibx33 bib1.bibx34 bib1.bibx98" id="paren.68"><named-content content-type="pre">e.g., </named-content></xref>.</p>
      <?pagebreak page3887?><p id="d1e1327">The CARRA regional reanalysis was specifically tailored towards the unique conditions in the Arctic environment, such as the prevailing cold surfaces on Arctic sea ice and ice sheets. Notably, it explicitly simulates a snow layer on sea ice. CARRA is based on the HARMONIE-AROME non-hydrostatic regional numerical weather prediction model, which is operational in the Nordic countries and several other European countries <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx119" id="paren.69"/>. The reanalysis data can be retrieved for two distinct domains (CARRA-West covering Greenland and CARRA-East encompassing Svalbard and northern Scandinavia) that overlap in the vicinity of Svalbard  <xref ref-type="bibr" rid="bib1.bibx119" id="paren.70"/>. Boundary forcings are taken from ERA5.  CARRA analysis fields have a temporal resolution of 3 h, a horizontal grid resolution of 2.5 km, and 65 vertical model levels. The model levels start 15 m a.g.l. and are then situated approximately every 30 m, with an increasing spacing upwards.</p>
      <p id="d1e1336">In this study, ERA5 and CARRA wind fields are used for trajectory calculations, thermodynamic profiles are extracted at the dropsonde locations, and  several cloud-related parameters and turbulent energy fluxes are retrieved.  Compared to ERA5, a larger amount of local observations is assimilated into CARRA's three-dimensional variational  assimilation scheme, such as snow depths from satellite observations or actual measurements of glacier albedos. Satellite-borne sea-surface temperature and sea-ice data are assimilated at a higher spatial resolution compared to ERA5. Especially in areas with steep topography, the increased resolution of CARRA versus ERA5 is expected to better fit to observations <xref ref-type="bibr" rid="bib1.bibx119" id="paren.71"/>. <xref ref-type="bibr" rid="bib1.bibx32" id="text.72"/> show that both reanalyses reproduce the key features of the observed exceptional warming over the Barents Sea. However, CARRA shows more spatial details and larger regional surface air temperature trends. <xref ref-type="bibr" rid="bib1.bibx62" id="text.73"/> investigate winds in the 40–100 km narrow Nares Strait northwest of Greenland. They find a significant underestimation of local wind speeds in ERA5, which on average reach 40 % of the observed values versus 80 % in CARRA. <xref ref-type="bibr" rid="bib1.bibx8" id="text.74"/> evaluate five contemporary numerical prediction systems against in situ rainfall data from Greenland stations. CARRA shows the lowest average bias and the highest explained variance. <xref ref-type="bibr" rid="bib1.bibx39" id="text.75"/> systematically evaluate the representation of 10 m wind speed and  2 m air temperature against observations for the two CARRA domains.  The largest differences between CARRA and ERA5 are found in regions with complex terrain and coastlines, as well as over the Arctic sea ice for 2 m air temperature in winter. Over flat terrain, the added value is especially obvious for the air temperature. With these reported advantages in mind, CARRA focuses solely on the European Arctic sector and starts only in 1991. The 3-hourly analysis fields must be combined with short-range forecasts to match the same 1-hourly resolution of ERA5 <xref ref-type="bibr" rid="bib1.bibx119" id="paren.76"/>.</p>
      <p id="d1e1358">To classify the strength of the observed CAO, the marine cold-air-outbreak index <inline-formula><mml:math id="M49" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula>  <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx22" id="paren.77"/> is calculated based on ERA5 data and an 850 hPa reference level <xref ref-type="bibr" rid="bib1.bibx72 bib1.bibx71 bib1.bibx35 bib1.bibx15 bib1.bibx23 bib1.bibx54" id="paren.78"/>. Using the potential temperature <inline-formula><mml:math id="M50" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is computed as follows:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M52" display="block"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mtext>skin,ocean</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mtext>skin,ocean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> denotes the potential skin temperature over ice-free ocean. A positive <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> over a large area indicates the presence of a CAO event. The daily <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is averaged temporally from the hourly input data and spatially over a box surrounding Fram Strait. With an extent of 75–80° N and 10° W–10° E, this box is identical with previous studies <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx15" id="paren.79"/>. Consistent with the aforementioned works, CAO events can be  classified  as weak (<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>  below 4 K), moderate (<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>  between 4–8 K), or strong (<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>  above 8 K).</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Trajectory analysis</title>
      <p id="d1e1538">To evaluate whether the quasi-Lagrangian flight strategy on 1 April 2022 had been a success, both the ERA5 and CARRA three-dimensional wind fields are retrieved on  model levels. Note that all 40 released dropsondes   were assimilated by ECMWF, which  greatly improves the reliability of trajectory calculations. As will be shown, no significant differences in calculated trajectories are found when using ERA5 or CARRA data. A comparison of the very similar wind profiles is given in Figs. S3 and S4. <xref ref-type="bibr" rid="bib1.bibx39" id="text.80"/> also reported only small differences between ERA5 and CARRA wind fields in areas with flat terrain, such as over the Arctic Ocean.</p>
      <?pagebreak page3888?><p id="d1e1544">The Lagrangian Analysis Tool  <xref ref-type="bibr" rid="bib1.bibx95" id="paren.81"><named-content content-type="pre">LAGRANTO;</named-content></xref> is then used to identify quasi-Lagrangian matches, where the same air masses were sampled within a 20 km radius below <italic>HALO</italic> twice, first at times <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and then again at <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Air masses are initialized every 1 min along <italic>HALO</italic>'s flight track, vertically every 5 hPa between 250 hPa and the surface, and horizontally evenly spaced every 7 km in a 20 km radius. In total,   2.1 million trajectories are calculated 6 h forward in time. Caused by the vertical shear of wind direction and wind speed, the sampled air masses start moving in different directions. Only for a certain fraction, due to successful flight planning and/or some luck, are some of the same air masses sampled again in a different location and for a second time. A match is registered if the same air mass is seen again in the column below <italic>HALO</italic> within the same 20 km radius. In the final step, observations from dropsondes are included. Only those matches in the lowest 2 km are kept where the time difference between the matching air mass below the aircraft and the dropsonde in its time during descent is below 90 s. At a flight speed of around 800 <inline-formula><mml:math id="M61" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, this again corresponds to a maximum distance of 20 km. More details on the quasi-Lagrangian flight strategy during HALO-(AC)<inline-formula><mml:math id="M62" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> can be found in <xref ref-type="bibr" rid="bib1.bibx114" id="text.82"/>. As matches are altitude-dependent, from the closest dropsonde the vertically nearest  potential air temperature and specific humidity measurements are  retained. Potential temperature is chosen instead of regular air temperature to focus on diabatic processes  <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx15" id="paren.83"/>.  Applying all filters yields approx. 24 200 quasi-Lagrangian matches. The net diabatic heating and moistening rates are calculated as
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M63" display="block"><mml:mrow><mml:msub><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">θ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mtext>net</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          <?xmltex \hack{\newpage}?><?xmltex \hack{\vspace*{-6mm}}?>
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M64" display="block"><mml:mrow><mml:msub><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mtext>net</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1727">The air mass transformations occurring in CAOs are primarily forced by the transition from closed sea ice to ice-free ocean <xref ref-type="bibr" rid="bib1.bibx75 bib1.bibx113" id="paren.84"/>. Therefore, the quasi-Lagrangian matches are  grouped by the time each air mass has spent over ice-free ocean. For all dropsonde locations, 12 h backward trajectories are calculated using ERA5 and for the air masses in the lowest 10 hPa (approx. 100 m) above ground. The sea-ice concentration (SIC) is traced along each trajectory (Fig. S1 in the Supplement). For this purpose, the merged MODIS and ASI-AMSR2 data  at 1 km grid resolution generated by the University of Bremen <xref ref-type="bibr" rid="bib1.bibx51" id="paren.85"/> are interpolated to a <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.05</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>×</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> latitude–longitude grid. The duration over ocean is defined as the time the air mass spends over ice-free ocean (sea-ice concentration <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mtext>SIC</mml:mtext><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> %) until it first reaches a <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mtext>SIC</mml:mtext><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> %.</p>
      <p id="d1e1776">While the flight leg of <italic>Polar 6</italic> on 1 April 2022 was aligned in parallel with <italic>HALO</italic>'s center leg, it still covered different regions at different times than <italic>HALO</italic>, not least due to the much lower speed of <italic>Polar 6</italic> of around 300 <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. To make data comparable, the same approach is taken as for <italic>HALO</italic>: every 1 min along the flight track, air masses are initialized. However, due to the in situ sampling method, the air masses are started at the actual flight level of <italic>Polar 6</italic> and SIC traced (Fig. S2). As a result, the in situ observations are transformed into the same coordinate system of time over ice-free ocean as for <italic>HALO</italic>, which is the assumed primary driver of the observed air mass transformations. Due to its limited range, <italic>Polar 6</italic> only sampled the first 3 h of the CAO.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Case overview</title>
      <p id="d1e1837">Figure <xref ref-type="fig" rid="Ch1.F1"/> gives an overview of the conditions on 1 April 2022. The flight track of <italic>HALO</italic> and the dense grid of dropsondes released west of Svalbard are depicted. The daily averaged CAO index <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in the Fram Strait box is found to be 7.7 K. This qualifies the CAO investigated here between a moderate and strong  case, following the classification of   <xref ref-type="bibr" rid="bib1.bibx71" id="text.86"/> and <xref ref-type="bibr" rid="bib1.bibx15" id="text.87"/>. According to the ERA5-based CAO climatology 1979–2020 by <xref ref-type="bibr" rid="bib1.bibx15" id="text.88"/>, the median daily frequency of occurrence for CAOs in the Fram Strait is at around 50 %–70 % both in March and April. Furthermore, events of similar magnitude can be expected at around 40 % of all days <xref ref-type="bibr" rid="bib1.bibx15" id="paren.89"/>. This means that on 1 April 2022, <italic>HALO</italic> sampled a quite typical event for this region and time of the year. Figure <xref ref-type="fig" rid="Ch1.F1"/> also reveals a maximum <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mn mathvariant="normal">850</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">hPa</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of above 12 K close to the marginal sea-ice zone. This highlights the strong temperature contrasts that the cool Arctic air masses experience when departing the closed Arctic sea ice.</p>
      <p id="d1e1895"><?xmltex \hack{\newpage}?>To better comprehend the air mass flow, a set of 40 trajectories is initialized at the location of each dropsonde with 1 min temporal resolution. These trajectories are started at 10 hPa above ground and calculated both forwards and backwards in time over a 24 h period. The ERA5-derived potential temperature is then traced. As seen in Fig. <xref ref-type="fig" rid="Ch1.F1"/>, during their drift over closed Arctic sea ice, the near-surface air parcels do not undergo any significant diabatic temperature changes. However, once they cross the MIZ and reach the ice-free ocean, the air masses undergo a rapid diabatic heating of up to 20 K within 24 h.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Eulerian comparison of observations and reanalyses</title>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Sea-ice and cloud structures</title>
      <p id="d1e1916">Figure <xref ref-type="fig" rid="Ch1.F2"/> depicts a first  comparison between observations and the reanalyses. Figure <xref ref-type="fig" rid="Ch1.F2"/>a shows the Terra/MODIS corrected reflectance from NASA Worldview for 1 April 2022 <xref ref-type="bibr" rid="bib1.bibx68" id="paren.90"/>.  From the satellite imagery, it becomes clear that the Arctic sea ice northwest of Svalbard features many leads on different length scales. However, the MIZ is rather sharp, and the transition from closed sea ice to ice-free ocean water typically occurs within less than 1 km distance. Over the ice-free ocean, cloud streets due to roll convection are evident. The cloud streets form along the prevailing wind direction. Furthermore, a clear lee effect due to Svalbard's mountain ranges is seen to the west of the archipelago.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e1928">Sea-ice and cloud structures to the northwest of Svalbard on 1 April 2022 based on observations and reanalyses. In each subplot, the red line shows the flight path of <italic>HALO</italic>, and diamond shapes show the locations of released dropsondes. The shapes are colored by time near-surface air masses spent over ice-free ocean  (sea-ice concentration SIC below 20 %; <xref ref-type="bibr" rid="bib1.bibx51" id="altparen.91"/>). <bold>(a)</bold> The Terra/MODIS corrected reflectance  shows the formation of cloud streets shortly after the off-ice drift. The image is taken from <xref ref-type="bibr" rid="bib1.bibx68" id="text.92"/>. <bold>(b)</bold> ERA5 data at 12:00 UTC. The SIC (filled contours) and the total column cloud liquid and ice water (contour lines) are shown. <bold>(c)</bold> CARRA data at 12:00 UTC. SIC (filled contours) and the total combined column cloud liquid, ice, and graupel water (contour lines) are depicted.</p></caption>
            <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f02.png"/>

          </fig>

      <?pagebreak page3889?><p id="d1e1956">Figure <xref ref-type="fig" rid="Ch1.F2"/>b shows the corresponding fields as represented by  ERA5 at 12:00 UTC noon. Due to its coarse spatial resolution, no leads are modeled in the SIC data fields, and the MIZ width is on a length scale of approximately 80 km. This is a typical MIZ width for ERA5 <xref ref-type="bibr" rid="bib1.bibx76" id="paren.93"/>. Instead of cloud streets, a stratiform liquid and ice containing cloud deck is simulated, which thickens in off-ice direction. Clouds are partly also already formed over closed sea ice.  In contrast, clouds in CARRA are exclusively formed over the ice-free ocean; see Fig. <xref ref-type="fig" rid="Ch1.F2"/>c. The high spatial resolution allows convection to be modeled. As a result, several distinct cloud streets are reproduced. In addition, CARRA better reproduces the sharp MIZ, which here is on the scale of around 10 km. The sharper MIZ of CARRA  in comparison to ERA5 is not only a matter of spatial resolution (2.5 km for CARRA versus 30 km for ERA5). The sea-ice concentrations in ERA5 are derived from the Operational Sea Surface Temperature and Ice Analysis dataset, produced by the UK Met Office <xref ref-type="bibr" rid="bib1.bibx17" id="paren.94"><named-content content-type="pre">OSTIA; </named-content></xref>. OSTIA outputs daily sea-surface temperature and sea-ice concentration fields based on satellite observations, with a native resolution of <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.05</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>×</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> (roughly 6 km). Yet the sea-ice data are based on the   EUMETSAT OSI-SAF 401 dataset utilizing 19 GHz and 37 GHz microwave channels at along-track resolutions of coarse 69 and 37 km <xref ref-type="bibr" rid="bib1.bibx105 bib1.bibx76" id="paren.95"/>.  On the contrary, CARRA strongly relies on the European Space Agency's Sea Ice Climate Change Initiative product <xref ref-type="bibr" rid="bib1.bibx107" id="paren.96"><named-content content-type="pre">SICCI;</named-content></xref> with a native resolution of 15–25 km. These data are additionally filtered based on the high-resolution sea-surface temperature fields and then regridded to the CARRA grid <xref ref-type="bibr" rid="bib1.bibx119" id="paren.97"/>.  Several authors noted that improved sea-ice and MIZ representation crucially improve the performance of models in the lower-tropospheric layers <xref ref-type="bibr" rid="bib1.bibx47 bib1.bibx27 bib1.bibx13 bib1.bibx65 bib1.bibx94" id="paren.98"/>. As will be shown later, the magnitude of turbulent heat fluxes is directly correlated to the distribution of sea-ice versus ice-free ocean, which is the primary driver of CAO transformations. Errors in MIZ width can have significant downstream effects over several hundreds of kilometers <xref ref-type="bibr" rid="bib1.bibx104 bib1.bibx94" id="paren.99"/>.</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Vertical thermodynamic profiles</title>
      <p id="d1e2013">Figure <xref ref-type="fig" rid="Ch1.F3"/>a shows the profiles of air temperature from observations. Over sea ice, clear temperature inversions are found. The coldest near-surface temperatures reach <inline-formula><mml:math id="M72" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>27 °C, and the thickness of the inversions is around 0.6–0.9 km. As air masses spend more time over ice-free waters, they become warmer near the surface, leading to stronger coupled ABLs and the development of a typical marine stratification. This is accompanied by a steady, linear increase in the calculated BLHs and closely correlated CTHs.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2027">Vertical profiles of air temperature (<inline-formula><mml:math id="M73" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>) in the lowest 2 km above ground taken from observations and reanalyses. In all panels, profiles are colored by the time air masses spent over open ocean. <bold>(a)</bold> Observed profiles of air temperature. Measurement-derived atmospheric BLHs and lidar-derived CTHs are indicated on the left-hand side. <bold>(b)</bold> Deviation of the ERA5 profiles from the observed profiles, and <bold>(c)</bold> deviation of the  CARRA profiles from the observed profiles. </p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f03.png"/>

          </fig>

      <p id="d1e2052">By linearly interpolating all data to 100 m vertical resolution, the temperature  differences <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> between ERA5/CARRA and the observations are computed. The results are shown in  Fig. <xref ref-type="fig" rid="Ch1.F3"/>b and c. Despite the reanalysis assimilating all the employed dropsondes,  the ERA5 profiles show a distinct warm bias in near-surface air temperatures of mean 2 K over Arctic sea ice. Many authors reported on similar warm biases of skin and near-surface air temperatures in ERA5 <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx111 bib1.bibx103 bib1.bibx55" id="paren.100"/>. The skin temperatures are generally considered too warm as an insulating layer of snow is missing atop the floating ice, which can introduce surplus heat into the lower atmosphere <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx111" id="paren.101"/>.  The surface warm bias turns to a mean cold bias of <inline-formula><mml:math id="M75" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 K at altitudes of 0.25–0.50 km. Over the ocean, the mean temperature bias is much lower and reaches <inline-formula><mml:math id="M76" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.5 K at around 1 km altitude. In the CARRA data, the near-surface temperature bias is reduced to an average of 1 K. Similar improvements over ERA5 have been reported by others <xref ref-type="bibr" rid="bib1.bibx39" id="paren.102"/>. However, CARRA also faces challenges in accurately representing temperature inversions. This is reflected in the cold bias of around <inline-formula><mml:math id="M77" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.5 K at altitudes of 0.20–0.40 km.</p>
      <p id="d1e2099">The mean absolute errors (MAEs) of ERA5 and CARRA with regards to measurements are computed. Output from both reanalyses as well as dropsondes is interpolated to a common vertical coordinate of altitude above ground in 10 m steps. To evaluate especially the crucial ABL representation, MAEs are averaged vertically from  the surface up to the observation-derived BLHs, plus an additional 200 m margin to capture the dipole pattern of errors. Table <xref ref-type="table" rid="Ch1.T1"/> summarizes the results separately for dropsondes released over sea ice and ice-free ocean. For air temperature over ice, CARRA shows a slightly smaller MAE of 1.00 K versus 1.14 K for ERA5. Over the ice-free waters of Fram Strait, these errors are significantly reduced in both products, yielding a  MAE of 0.39 K in CARRA and 0.44 K in ERA5.</p>

<table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e2106">Mean absolute errors (MAEs) of ERA5 and CARRA profiles compared to observations. The MAEs are averaged vertically up to the observed boundary-layer heights, plus an additional 200 m margin. Results are shown for the variables air temperature (<inline-formula><mml:math id="M78" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>) and specific humidity (<inline-formula><mml:math id="M79" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>), grouped by surface type. Profiles are classed as sea ice (open ocean) if the AMSR2 sea-ice concentrations is above (below) 50 %.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <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:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Variable</oasis:entry>
         <oasis:entry colname="col2">Surface</oasis:entry>
         <oasis:entry colname="col3">MAE of ERA5</oasis:entry>
         <oasis:entry colname="col4">MAE of CARRA</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M80" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">sea ice</oasis:entry>
         <oasis:entry colname="col3">1.14 K</oasis:entry>
         <oasis:entry colname="col4">1.00 K</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">open ocean</oasis:entry>
         <oasis:entry colname="col3">0.44 K</oasis:entry>
         <oasis:entry colname="col4">0.39 K</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M81" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">sea ice</oasis:entry>
         <oasis:entry colname="col3">0.037 <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.037 <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">open ocean</oasis:entry>
         <oasis:entry colname="col3">0.112 <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.069 <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{1}?></table-wrap>

      <p id="d1e2290">Next, the vertical profiles of specific humidity are examined. Figure <xref ref-type="fig" rid="Ch1.F4"/>a depicts the observed profiles, as extracted from the dropsonde measurements. Over sea ice, a uniform and dry ABL  is found, where maximum values of around 0.6 <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are measured. Near-surface layers are the driest, at around 0.4 <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The longer the air masses reside over<?pagebreak page3890?> the sea, the more water vapor is picked up by the lower air mass layers  through evaporation from the ocean surface.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2331">Same as Fig. <xref ref-type="fig" rid="Ch1.F3"/> but for specific humidity in the lowest 2 km above ground. <bold>(a)</bold> Observed profiles of specific humidity. <bold>(b)</bold> Deviation of the  ERA5 profiles from the observed profiles, and <bold>(c)</bold> deviation of the CARRA profiles from the observed profiles.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f04.png"/>

          </fig>

      <p id="d1e2351">Over sea ice, ERA5 shows a mean near-surface moist bias of 0.05 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F4"/>b), as well as a slight dry bias close to the BLHs. Once air masses drift over the sea, a strong dry bias is found throughout the ABL. It increases over time and reaches down to <inline-formula><mml:math id="M89" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.5 <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, which corresponds to about 30 % of the observed values. CARRA shows different patterns (Fig. <xref ref-type="fig" rid="Ch1.F4"/>c). Over the closed ice pack, the lowest 0.2 km shows a negligible humidity bias.  However, in higher layers above 0.5 km, a slight moist bias is seen. During the off-ice drift, at first a slight moist and later dry bias becomes obvious; however, this is much smaller compared to the ERA5 reanalysis. The same patterns are found in the quantified MAEs within the ABLs; see again Table <xref ref-type="table" rid="Ch1.T1"/>. Notably, over the ice-free ocean, CARRA's MAE of  0.069 <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is significantly lower than ERA5's MAE of 0.112 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p>
</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Quasi-Lagrangian comparison of observations and reanalyses</title>
<sec id="Ch1.S3.SS3.SSS1">
  <label>3.3.1</label><title>Quasi-Lagrangian matches</title>
      <p id="d1e2452">Figure <xref ref-type="fig" rid="Ch1.F5"/> gives an overview of the  quasi-Lagrangian matches calculated with reference to  the dropsondes. All matches are colored by the time air masses spent over ice-free ocean. As described in the Methods (Sect. <xref ref-type="sec" rid="Ch1.S2"/>), these approximately 24 200 matches are a function of height above ground  because not only are the zonal and meridional winds height-dependent, but also the vertical velocity is used for the three-dimensional trajectory calculations. This allows air masses to ascend or descend along their horizontal flow. The matches cover 150 km along the prevailing wind direction over the Arctic sea ice and  about 200 km along the CAO evolution over ice-free ocean.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2461">Spatial overview of the location of matching ERA5 trajectories, which were calculated with respect to a 20 km circle around the dropsondes. Matching lines are colored by the time air masses spent over ocean. The background Terra/MODIS satellite image is taken from <xref ref-type="bibr" rid="bib1.bibx68" id="text.103"/>.</p></caption>
            <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f05.png"/>

          </fig>

      <p id="d1e2473">Naturally, the question arises of how reliable the trajectory calculations presented here are. In previous studies, sometimes additional criteria were applied to prove the reliability of trajectories. These are similar hydrocarbon fingerprints between matches   <xref ref-type="bibr" rid="bib1.bibx59" id="paren.104"/> or an inert perfluoromethylcyclopentane  tracer being deployed <xref ref-type="bibr" rid="bib1.bibx6" id="paren.105"/>. However, such a use of tracers is only<?pagebreak page3891?> possible in case of in situ sampling. In the CAO presented here, the assimilation of the high-density grid of dropsondes serves as crucial input for ERA5 and CARRA. This can also be seen in the comparison of wind profiles as shown in Figs. S3 and S4. With the exception of the nearest-surface layers, a close match is seen between dropsondes and both reanalyses. Also, as trajectories are only calculated over short spatiotemporal scales (on the order of 1–4 h, 50–200 km), small errors can not add up as much. For some research questions, it might be more valuable to investigate transformations over larger spatiotemporal scales, such as was done, for example, for aerosol and hydrocarbon species <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx77" id="paren.106"/>. However, as will be demonstrated, the highly important thermodynamic evolution occurs on timescales of a few hours and below. If too much time passes between two matching observations, the “net” rates, e.g. of <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mtext>net</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>q</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mtext>net</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> introduced in Eqs. (<xref ref-type="disp-formula" rid="Ch1.E4"/>) and (<xref ref-type="disp-formula" rid="Ch1.E5"/>), would smooth out  short-lived effects even more; models would be increasingly needed to disentangle the net rates calculated over longer time frames into sections of more or less intense transformations. Finally, the  approach presented here of initializing and then registering matches for a large number of  trajectories within a radius of 20 km around <italic>HALO</italic>'s location is also essential to better assess the statistical significance of matches. Notably, all deviations seen between the aforementioned observed and modeled wind profiles result in an error of less than this 20 km radius over 1–3 h of drift.</p>
</sec>
<sec id="Ch1.S3.SS3.SSS2">
  <label>3.3.2</label><title>Diabatic heating and moistening rates</title>
      <p id="d1e2547">The evolution of thermodynamic properties in the form of heating and moistening rates is analyzed in a quasi-Lagrangian framework, grouped by time air masses spent over ice-free ocean.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e2552">Diabatic heating rates grouped by  time air masses spent over the ice-free ocean. On the left side of each panel, the mean BLH in each class is plotted as a square. Lines depict the mean values and shading the 25th–75th percentiles. <bold>(a)</bold> Heating rates based on the quasi-Lagrangian dropsonde observations. Solid lines are from ERA5 trajectories, and the dashes lines are from CARRA trajectories. <bold>(b)</bold> Corresponding heating rates extracted from ERA5. <bold>(c)</bold> Corresponding heating rates extracted from CARRA.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f06.png"/>

          </fig>

      <p id="d1e2570">First, the evolution of diabatic heating rates is analyzed. Figure <xref ref-type="fig" rid="Ch1.F6"/>a shows the vertically resolved diabatic heating rates based on the quasi-Lagrangian dropsonde observations. No significant differences exist between using ERA5 or CARRA<?pagebreak page3892?> winds as input. The MAE between ERA5 and CARRA heating rates in the lowest 1.5 km above ground and averaged for all times over ice-free ocean amounts to only 0.13 <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Note that air parcels of the first category  (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>–1 h) are drifting almost exclusively over sea ice and leads (Fig. <xref ref-type="fig" rid="Ch1.F5"/>). For these air masses, a maximum near-surface warming of around 1.8 <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is found. This possibly stems from some of the leads crossed  by the trajectories. However, the heat is contained within the very shallow ABL, and all heating rates above the BLHs of around 0.30 km are around 0 <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. After crossing the MIZ and reaching the ice-free ocean (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–2 h), a very intense surface warming is seen, where values larger than 6 <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are found. This heating is starting to be mixed upwards into the increasingly deep ABL, which reaches BLHs of around 0.70 km. After the initial rapid exposure of the cold and dry Arctic air masses to the much warmer ocean surface, the heating in the lowest layers declines rapidly and stays around 2 <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The vertical mixing is now dominating and leads to almost homogeneous mixing within the lowest 0.75 km of the troposphere. Interestingly, some layers above show regions with negative heating rates, i.e., a net cooling of air masses at altitudes around the BLHs. An analysis of ERA5 temperature tendencies indicates that this is not a sign of a net cloud-top radiative cooling effect but instead of the mixing of colder near-surface air with the original, overlying warmer air (Fig. S5). Previous airborne studies have shown that in the early stages of CAOs, the heat budget has several sources. Notably, the  strong surface heat fluxes are reinforced by entrainment fluxes with the warmer inversion aloft. The relative contributions of the heat sources change with distance from the sea-ice edge. Over leads in the MIZ, entrainment heat fluxes exceeding 30 % of the surface heat fluxes have been observed in single cases <xref ref-type="bibr" rid="bib1.bibx102" id="paren.107"/>. Shortly after passing the sea-ice edge, this ratio can initially increase to 80 %, which then again decreases to 30 % for fetches over 150 km <xref ref-type="bibr" rid="bib1.bibx9" id="paren.108"/>. In the region of deep, cellular convection, condensation can even become the dominating contributor to air-mass heating <xref ref-type="bibr" rid="bib1.bibx9" id="paren.109"/>.  Overall, these previous studies indicate that the diabatic cooling near cloud tops corresponds to a  warming below cloud tops, caused by the entrainment fluxes.</p>
      <p id="d1e2704">The ERA5-derived heating rates reflect the general features of the observations (Fig. <xref ref-type="fig" rid="Ch1.F6"/>b). This can be attributed to the assimilation of  all 40 dropsondes into ERA5. However, some important  differences are found. Over the Arctic sea ice, ERA5 shows BLHs almost twice as high as that seen in observations. While the slight surface warming of around 1.6–1.8 <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is also seen in ERA5, it shows excess heat that it mixes upwards towards the BLH. The intense surface warming at <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–2 h is not represented  in ERA5. This is  in agreement with the sea-ice distribution shown on the overview map in Fig. <xref ref-type="fig" rid="Ch1.F2"/>b, which revealed a wide MIZ on the order of 80 km – much wider than that shown in the observations. As a result, the initial stage of the CAO is delayed in ERA5. The later stages (<inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> h) of the CAO, however, are represented rather well, yet again with an<?pagebreak page3893?> exaggerated vertical mixing. The essential feature of negative heating rates in higher altitudes is captured.</p>
      <p id="d1e2758">Figure <xref ref-type="fig" rid="Ch1.F6"/>c shows the heating rates extracted from the CARRA product. Generally, these  settle in between the observations and ERA5. All BLHs are lower than in ERA5 and significantly closer to the observed values. For <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–2 h, the observed intense  warming rate higher than 6 <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is also not represented fully, yet it is much better  than in ERA5. A maximum value for the near-surface heating of around 4 <inline-formula><mml:math id="M107" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is found, which is homogeneously mixed upwards  up to 0.40 km altitude. This might in part be caused by the much sharper MIZ, which is closer to reality (Fig. <xref ref-type="fig" rid="Ch1.F2"/>c).</p>
      <p id="d1e2814">In the early stage of CAOs, the primary source for turbulent heat fluxes is the warm ocean surface  <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx75" id="paren.110"/>. To study the evolution of the heating profiles along the CAO, it is thus essential to investigate  the surface sensible heat fluxes (SSHFs). A comparison between the observation-derived and reanalysis-based SSHFs is given in Fig. <xref ref-type="fig" rid="Ch1.F7"/>a. All data are grouped by time spent over ice-free ocean.  Over the Arctic sea ice and MIZ, the observation-derived SSHFs show a mean of below 50 <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, with the 95th percentile peaking above 150 <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. However, as was outlined in Sect. <xref ref-type="sec" rid="Ch1.S2"/>, the computation of turbulent heat fluxes over the sea ice and MIZ based on dropsondes is prone to high uncertainty. Both reanalyses show higher values, especially ERA5. For <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>–1 h, this corresponds to heating rates in both reanalyses being slightly too large and a mixing that is exaggerated.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e2876"><bold>(a)</bold> Surface sensible heat fluxes (SSHFs) and <bold>(b)</bold> surface latent heat fluxes (SLHFs) as derived from observations, ERA5, and CARRA. Box plots show the median as thick lines, the 25th–75th percentiles as boxes, and the 5th–95th percentiles indicated as whiskers. Data are grouped by time over ice-free ocean. </p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f07.png"/>

          </fig>

      <p id="d1e2890">After the air masses cross the MIZ, large values of SSHF of around 520 <inline-formula><mml:math id="M111" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are observed. Such values are typical in CAOs  <xref ref-type="bibr" rid="bib1.bibx88" id="paren.111"/>.  ERA5 significantly underestimates the observed SSHFs by at least 130 <inline-formula><mml:math id="M112" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, while CARRA slightly exaggerates it. Later into the CAO, the observed SSHFs drop slightly yet are again best captured by CARRA. In general, the reduction of SSHFs over time is expected, as the temperature difference between the sea surface and the overlying air is reducing. This can potentially be counterbalanced, for example, by increasing underlying sea-surface temperatures, increased winds, or decreased surface roughness <xref ref-type="bibr" rid="bib1.bibx71" id="paren.112"/>.</p>
      <p id="d1e2934">The different parameters that are required for the calculations of SSHF as shown in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) are investigated in Fig. S6. Notably, over ocean both reanalyses significantly underestimate <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, with CARRA being always closer to the observations. The horizontal thermal gradient between sea ice and the ice-free water surface causes a marked off-ice breeze, an analogue to sea–land breezes. Similar to that reported by <xref ref-type="bibr" rid="bib1.bibx9" id="text.113"/>, in our case, <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> reached its maximum near the sea-ice edge, and the off-ice  acceleration due to thermal contrasts is estimated to be around  2.6 <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><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">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>  (calculations can be found in the Appendix). Therefore, the <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in CARRA might be closer to observations than ERA5 as (i) the MIZ is narrower in CARRA and (ii) the discussed near-surface warm bias over sea ice is weaker in CARRA. Previous studies have also found ERA5 underestimates the highest near-surface winds over the ocean next to the MIZ, as well as SSHFs and SLHFs over the MIZ   <xref ref-type="bibr" rid="bib1.bibx76" id="paren.114"/>. Feeding coarse-resolution sea-ice data (with a MIZ of around 80 km, such as in ERA5) into higher-resolution models was also found to smear out the rapid increases in air temperature, wind speed, and surface fluxes <xref ref-type="bibr" rid="bib1.bibx76" id="paren.115"/>.</p>
      <p id="d1e3023">In order to evaluate whether the differences between CARRA and ERA5 discovered for 1 April 2022 are of a systematic nature, a climatological comparison of SSHFs from both reanalyses for  1991–2022 can be found in Fig. S8. It shows that during CAO conditions, CARRA SSHFs are systematically larger than ERA5 SSHFs, and this is consistent over several decades. It is especially pronounced over ocean and corroborates our results for the case study of 1 April 2022. Similar systematic differences  in the output surface turbulent  heat fluxes have been reported also for comparisons of other reanalyses <xref ref-type="bibr" rid="bib1.bibx122 bib1.bibx100" id="paren.116"/>.  Underestimated fluxes  result in too-low uptake rates for heat and moisture, particularly close to the ice edge <xref ref-type="bibr" rid="bib1.bibx104 bib1.bibx94" id="paren.117"/>. However, similar studies like <xref ref-type="bibr" rid="bib1.bibx91" id="text.118"/> are required for a deeper systematic evaluation  of ERA5 versus CARRA, for example, to disentangle the combined effects on <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> as caused by MIZ width, parameterized surface roughness, or synoptic patterns.</p>
      <p id="d1e3051">Figure <xref ref-type="fig" rid="Ch1.F8"/>a shows the vertically resolved moistening  rates based on the quasi-Lagrangian dropsonde observations. The MAE on the observed moisture uptake rates based on  ERA5 versus CARRA trajectories as input is very low at 0.01 <inline-formula><mml:math id="M118" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. For the air masses mostly sampled over  sea ice, only minimal moisture uptake is found. The highest uptake at <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–2 h reaches around 0.4 <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at the surface. For longer times over the ice-free ocean, this moisture is then quickly mixed upwards. The magnitude of upward mixing partly exceeds the moisture uptake near the surface at later stages.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e3116">Moistening rates expressed as the change of specific humidity <inline-formula><mml:math id="M121" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula> per hour as a function of the time air masses spent over the ice-free ocean.  Lines depict the mean values and shading the 25th–75th percentiles. <bold>(a)</bold> Moistening rates based on the quasi-Lagrangian dropsonde observations. Solid lines are from ERA5 trajectories, and the dashes lines are from CARRA trajectories. <bold>(b)</bold> Corresponding moistening rates extracted from ERA5. <bold>(c)</bold> Corresponding moistening rates extracted from CARRA.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f08.png"/>

          </fig>

      <p id="d1e3141">Figure <xref ref-type="fig" rid="Ch1.F8"/>b shows the corresponding rates as extracted from ERA5. ERA5 underestimates  the near-surface moistening rates significantly; also layers further up show rates which are 2–3 times too low. CARRA  performs better than ERA5 (Fig. <xref ref-type="fig" rid="Ch1.F8"/>c). Not only are the near-surface moistening rates closer to observations, but also the upward mixing is more realistic. An insufficient moistening rate within the lower troposphere during a CAO can be caused by (i) an insufficient supply of moisture from the surface, i.e., too-low SLHF, and/or (ii) an exaggerated removal of water vapor from the atmospheric column. Here, we check both factors separately.</p>
      <p id="d1e3149">Figure <xref ref-type="fig" rid="Ch1.F7"/>b compares the SLHFs between observations and the two reanalyses. Over sea ice, very low SLHFs with a median below 25 <inline-formula><mml:math id="M122" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are found. Over the ocean, both ERA5 and CARRA underestimate the SLHF, and they are close to each other. Surprisingly, ERA5 always predicts slightly higher SLHFs than CARRA, which at first seems not to agree with the much lower moistening rates. Also the climatological comparison under CAO conditions shows that ERA5<?pagebreak page3894?> SLHFs exhibit a constant bias towards larger values than in CARRA (Fig. S8).  Overall, these findings hint towards mechanisms in ERA5 leading to an exaggerated removal of water vapor, namely cloud processes and precipitation. This is investigated in the next section.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e3173">Vertical profiles of cloud structures, sorted by time air masses spent over ice-free ocean. <bold>(a)</bold> Profiles of the HAMP radar reflectivities measured aboard <italic>HALO</italic>. <bold>(b)</bold> Profiles of cloud liquid water content <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mtext>liq.</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, based on a Nevzorov sonde aboard  <italic>Polar 6</italic>, <bold>(c)</bold> <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mtext>liq.</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> taken from ERA5, with the observed values as dashed lines, and <bold>(d)</bold> <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mtext>liq.</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> taken from CARRA, with the observed values as dashed lines.</p></caption>
            <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f09.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS3.SSS3">
  <label>3.3.3</label><title>Cloud properties</title>
      <p id="d1e3242">To help understand possible errors in the reanalyses connected to cloud physics,  HAMP radar reflectivities from aboard <italic>HALO</italic> <xref ref-type="bibr" rid="bib1.bibx56" id="paren.119"/>  as well as  in situ Nevzorov measurements of cloud liquid water and ice contents by the <italic>Polar 6</italic> aircraft are utilized <xref ref-type="bibr" rid="bib1.bibx49" id="paren.120"/>. A deeper investigation of cloud microphysical processes, such as riming, precipitation formation, or cloud street aspect ratios, is outside the scope of this article. However, details on these<?pagebreak page3895?> processes specifically including the CAO on 1 April 2022 are reported by  <xref ref-type="bibr" rid="bib1.bibx82" id="text.121"/> and <xref ref-type="bibr" rid="bib1.bibx53" id="text.122"/>.</p>
      <p id="d1e3264">Figure <xref ref-type="fig" rid="Ch1.F9"/>a shows the measured HAMP radar reflectivity profiles averaged for 2 min around the time of each dropsonde release and up to 6 h into the CAO. The profiles are plotted as  function of time air masses spent over ice-free ocean. For the locations over sea ice, either very low (radar reflectivity below <inline-formula><mml:math id="M126" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>25 dBz) or no radar signals were recorded. As the air moves onto open waters, the radar reflectivities increase, and cloud tops are seen to rise linearly. Radar reflectivities for the first time cross the threshold of <inline-formula><mml:math id="M127" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5 dBz only for <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> h. This indicates the presence of precipitation <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx52" id="paren.123"/>.</p>
      <p id="d1e3301">As <italic>Polar 6</italic> has a range much lower than <italic>HALO</italic>, it was able to only sample the first 3 h of the CAO. Figure <xref ref-type="fig" rid="Ch1.F9"/>b–d shows the height-resolved measured specific  cloud liquid water contents <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mtext>liq</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. Over the closed sea ice (Fig. <xref ref-type="fig" rid="Ch1.F9"/>b), in the sampled lowest 0.6 km above ground, no cloud liquid water was found, yet with low amounts at the top of the ABLs. After the drift across the MIZ, noticeable amounts of cloud water of up to 0.07 <inline-formula><mml:math id="M130" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are seen up to around 1  km altitude, which corresponds to the altitude of moisture uptake. Surprisingly, the liquid water content decreases in the next time step. This might be correlated with an increase of the frozen hydrometeors (i.e., cloud ice and snow) depicted in Fig. S7a. Several in situ probes confirm the occurrence of riming during the flight of <italic>Polar 6</italic> <xref ref-type="bibr" rid="bib1.bibx53" id="paren.124"/>. With the air temperatures always in the range of  <inline-formula><mml:math id="M131" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>25 to 0 °C (see Fig. <xref ref-type="fig" rid="Ch1.F3"/>), mixed-phase clouds are possible, and also the typical pattern of a supercooled layer above the ice layer is reproduced.</p>
      <p id="d1e3358">Figure <xref ref-type="fig" rid="Ch1.F9"/>c shows the cloud structures as reproduced by ERA5. ERA5 tends to overestimate the amount of liquid water present in the clouds. A similar enhanced abundance of liquid-bearing clouds especially over sea ice has been reported for the IFS, the model behind ERA5 <xref ref-type="bibr" rid="bib1.bibx103 bib1.bibx55" id="paren.125"/>. In the CAO case here, this is in  contrast to CARRA (Fig. <xref ref-type="fig" rid="Ch1.F9"/>d). With the exception of missing the strong increase in liquid clouds at <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–2 h, CARRA matches the observations well. The overabundance of liquid-bearing clouds in ERA5 might explain the exaggerated vertical mixing of heat in ERA5. Even though ERA5 featured lower SSHFs compared to CARRA, the more pronounced cloud tops might lead to stronger entrainment fluxes. Also, the condensation into cloud droplets releases additional heat to the surrounding air masses.</p>
      <?pagebreak page3896?><p id="d1e3384">Furthermore, total precipitation at the surface is much higher in ERA5 than in CARRA, which creates an additional sink for atmospheric moisture already over sea ice (Fig. <xref ref-type="fig" rid="Ch1.F10"/>). Precipitation over sea ice is unlikely based on the presented HAMP radar reflectivities. The <inline-formula><mml:math id="M133" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5 dBz threshold is only exceeded at <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>ocean</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> h. This threshold translates to a precipitation rate of around 0.02–0.09 <inline-formula><mml:math id="M135" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mm</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx81" id="paren.126"/>.  The statistical comparison between ERA5 and CARRA presented in Fig. S8 substantiates the finding of this case study.  ERA5 has a strong bias to form liquid-bearing clouds already over sea ice and the MIZ. Over the ocean, there also is a strong bias towards higher cloud liquid hydrometeor contents. The ERA5 clouds systematically precipitate more strongly over the MIZ and ocean than clouds in CARRA. The significance of our findings is reinforced by <xref ref-type="bibr" rid="bib1.bibx55" id="text.127"/>, who showed that issues such as an overabundance of low, liquid-bearing clouds can propagate into higher-resolution models  through large-scale forcings.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e3437">Total precipitation reaching surface level for ERA5 and CARRA. Box plots show the median as thick lines, the 25th–75th percentiles as boxes, and the 5th–95th percentiles as whiskers. Data are grouped by time over ice-free ocean.</p></caption>
            <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://acp.copernicus.org/articles/24/3883/2024/acp-24-3883-2024-f10.png"/>

          </fig>

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<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Summary and conclusions</title>
      <p id="d1e3456">We have presented a combined Eulerian and quasi-Lagrangian analysis of an Arctic marine cold-air outbreak (CAO). The CAO was closely sampled as part of the HALO-(AC)<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> airborne campaign on 1 April 2022 in the Fram Strait, west of Svalbard. It was a representative CAO, which can be considered typical for this location and time of year as well as in its intensity. The performance of two state-of-the-art atmospheric reanalyses, ERA5 and CARRA, was evaluated against the measurements, with a focus on thermodynamic (air temperature, humidity)  and cloud  (cloud liquid water content) properties.  We furthermore apply the quasi-Lagrangian approach to convert observations from both <italic>HALO</italic> and <italic>Polar 6</italic> into a common coordinate system (time over ocean). The spatiotemporally highly resolved airborne measurements allow for a thorough characterization of the state of the lower troposphere over Arctic sea ice, the marginal sea-ice zone (MIZ), and the ice-free ocean.  To the best of our knowledge, this is the first report on height-resolved diabatic heating and moistening rates in a developing CAO directly derived from quasi-Lagrangian observations. Going back to the research questions posed at the beginning of this article, we can answer them as follows. <list list-type="custom"><list-item><label>Q1.</label>
      <p id="d1e3476">How do air temperature, specific humidity, and clouds evolve in the first 4 h of the developing CAO? Still over sea ice, some leads cause a weak heating and moisture uptake into the shallow atmospheric boundary layer of around 0.2 km height. Within the first hour of departing the closed sea ice, the strong contrast between the cold and dry Arctic air masses and the much warmer ocean causes a diabatic heating larger than 6 <inline-formula><mml:math id="M137" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at the surface, a moisture uptake of more than 0.3 <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, and the formation of mixed-phase clouds.  As time progresses and clouds start forming, heat and moisture mix  upwards vertically in the developing marine boundary layer. After 4 h, the atmospheric boundary-layer height exceeds 1.5 km. At around the boundary-layer heights, a slight net diabatic cooling and moisture loss are registered, which can be attributed to the upward mixing of air masses into the original, overlying warmer air.</p></list-item><list-item><label>Q2.</label>
      <p id="d1e3523">How do the ERA5 and CARRA reanalyses perform with respect to observations and compared to each other? In the Eulerian (i.e., fixed in space) framework, the coarse-resolution  ERA5 reproduces some well-known issues. The skin and near-surface air temperatures are exaggerated, atmospheric boundary-layer heights are too large, and too many clouds are present.  CARRA  significantly improves all of these issues:  for air temperature over sea ice, ERA5 features a mean absolute error (MAE)   14 % higher than CARRA (1.14 K versus 1.00 K), while for specific humidity over ice-free ocean the MAE is found to be 62 % higher in ERA5 compared to CARRA (0.112 <inline-formula><mml:math id="M139" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> versus 0.069 <inline-formula><mml:math id="M140" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). Taking the quasi-Lagrangian perspective, the heating rates are reasonably  reproduced  both in ERA5 and CARRA. However,  the strong initial surface-based heating is not captured by ERA5. Even more pronounced are the differences in the moistening rates, where ERA5 estimates are up to 3 times too low and much better captured by CARRA. Overall, our height-resolved diabatic heating and moistening rates extend the quasi-Lagrangian, ERA5-based climatological CAO investigation of <xref ref-type="bibr" rid="bib1.bibx71" id="text.128"/> to the vertical dimension. However, as the intense fluxes and transformations in the MIZ are not represented well by ERA5, the heating and especially moistening rates reported by them are likely biased towards lower values.</p></list-item><list-item><label>Q3.</label>
      <p id="d1e3564">What are some possible sources of errors which could explain deviations between reanalysis output and observations? Generally, uncertainties in reanalyses  can stem from insufficient spatiotemporal resolution, different measurement sets being assimilated, and also the underlying model physics. The observed discrepancies between the two reanalyses  and the observations result from the complex interplay of several processes. Over sea ice, the missing snow on ice layer leads to skin and near-surface air temperatures being too high in ERA5, which might explain the exaggerated boundary-layer heights. Moreover, it is well established that the MIZ is too wide in ERA5. Thus, turbulent fluxes are underestimated significantly in the first 2 to 3 h of the CAO. The reduced 10 m wind speeds might be related<?pagebreak page3897?> to the too-wide MIZ as well. Especially for the surface sensible heat flux, CARRA greatly improves on this. ERA5 forms liquid-bearing clouds too early and too thick. This  can be due to too-warm initial temperatures or due to issues with the parameterization of  the mixed-phase clouds, as well as a combination of both. In all stages investigated, ERA5 clouds thus precipitate considerably more than in CARRA, and too much water vapor is lost to this sink. A similar propagation of errors in initial conditions has been previously reported to affect the atmospheric state hundreds of kilometers downstream.</p></list-item></list></p>
      <p id="d1e3567">Overall, we find CARRA fulfilling its intended goal of improving on the global ERA5 reanalysis with regard to the thermodynamic and cloud evolution, based on the parameters investigated  in the critical first 4 h of the CAO. CARRA might thus be better suited for driving higher-resolution models, such as large eddy simulations. While some climatological comparisons of differences between ERA5 and CARRA were supplied, deeper investigations  are required to further support the statistical significance of our findings  and to determine which components of CARRA are primarily responsible for the improvements. Ideally, these analyses should include extended data rows of observations, such as from regular radiosonde launches. Finally, the unprecedented quasi-Lagrangian observations collected during HALO-(AC)<inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> pose a rich database for future studies.  For example, sensitivity studies could reveal the influence that initial aerosol concentrations (cloud-condensation nuclei, ice-nucleating particles) and different cloud schemes (one-moment or two-moment) have on the vertical mixing of heat and moisture, especially considering the intense surface forcings and additional entrainment fluxes.</p>
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    <back><app-group>

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Estimating the off-ice acceleration</title>
      <p id="d1e3591">One key parameter determining SSHF and SLHF is the 10 m wind speed <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. As was already noted by <xref ref-type="bibr" rid="bib1.bibx9" id="text.129"/>, the horizontal thermal gradient between sea ice and the ice-free water surface causes a marked off-ice breeze, an analogue to sea–land breezes.  In our case, <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> reached its maximum near the sea-ice edge, which has also been observed before by <xref ref-type="bibr" rid="bib1.bibx9" id="text.130"/>. The off-ice breeze can be estimated by starting with the static pressure equation:
          <disp-formula id="App1.Ch1.S1.E6" content-type="numbered"><label>A1</label><mml:math id="M144" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>g</mml:mi><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math></inline-formula> denotes the difference in pressure over a <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> deep ABL, <inline-formula><mml:math id="M147" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the gravitational acceleration, <inline-formula><mml:math id="M148" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is the mean pressure, <inline-formula><mml:math id="M149" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the gas constant for dry air, and <inline-formula><mml:math id="M150" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the air temperature. By differentiating this equation with regard to <inline-formula><mml:math id="M151" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, we get
          <disp-formula id="App1.Ch1.S1.E7" content-type="numbered"><label>A2</label><mml:math id="M152" display="block"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>g</mml:mi><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>z</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">d</mml:mi><mml:mi>T</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        In our case, a BLH of about 200 m thickness is found over sea ice. <inline-formula><mml:math id="M153" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> shows an increase of 9 K over 100 km. A mean pressure of 1010 hPa and  mean temperature of 255 K in the ABL are found. From this, a horizontal pressure gradient of around 1 hPa over 100 km results near the surface.  While this appears small, the resulting pressure gradient force accelerates air masses in the off-ice direction:
          <disp-formula id="App1.Ch1.S1.E8" content-type="numbered"><label>A3</label><mml:math id="M154" display="block"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">ρ</mml:mi></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        On 1 April 2022, this  corresponds to an acceleration <inline-formula><mml:math id="M155" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> of about 2.6 <inline-formula><mml:math id="M156" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><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">1</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. <?xmltex \hack{\\}?></p>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e3843">Most airborne observational data used in this study were accessed through the ac3airborne module (<ext-link xlink:href="https://doi.org/10.5281/zenodo.7305585" ext-link-type="DOI">10.5281/zenodo.7305585</ext-link>, <xref ref-type="bibr" rid="bib1.bibx58" id="altparen.131"/>), with the following exceptions. The Nevzorov liquid and total water contents are available from <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.963628" ext-link-type="DOI">10.1594/PANGAEA.963628</ext-link> <xref ref-type="bibr" rid="bib1.bibx50" id="paren.132"/>. VELOX-derived skin temperature measurements can be obtained from <ext-link xlink:href="https://doi.org/10.1594/PANGAEA.963401" ext-link-type="DOI">10.1594/PANGAEA.963401</ext-link> <xref ref-type="bibr" rid="bib1.bibx80" id="paren.133"/>. A Python implementation of the COARE 3.5 bulk air–sea flux algorithm is available from <ext-link xlink:href="https://doi.org/10.5281/zenodo.5110991" ext-link-type="DOI">10.5281/zenodo.5110991</ext-link> <xref ref-type="bibr" rid="bib1.bibx2" id="paren.134"/>. For CARRA, data are available on model levels (<ext-link xlink:href="https://doi.org/10.24381/cds.d29ad2c6" ext-link-type="DOI">10.24381/cds.d29ad2c6</ext-link>, <xref ref-type="bibr" rid="bib1.bibx83" id="altparen.135"/>), pressure levels (<ext-link xlink:href="https://doi.org/10.24381/cds.e3c841ad" ext-link-type="DOI">10.24381/cds.e3c841ad</ext-link>, <xref ref-type="bibr" rid="bib1.bibx84" id="altparen.136"/>), and single levels (<ext-link xlink:href="https://doi.org/10.24381/cds.713858f6" ext-link-type="DOI">10.24381/cds.713858f6</ext-link>, <xref ref-type="bibr" rid="bib1.bibx85" id="altparen.137"/>). Further information can be found in CARRA's documentation <xref ref-type="bibr" rid="bib1.bibx119" id="paren.138"/> and  user guide <xref ref-type="bibr" rid="bib1.bibx69" id="paren.139"/>. ERA5 is also available on model levels <xref ref-type="bibr" rid="bib1.bibx29" id="paren.140"/>, pressure levels (<ext-link xlink:href="https://doi.org/10.24381/cds.bd0915c6" ext-link-type="DOI">10.24381/cds.bd0915c6</ext-link>, <xref ref-type="bibr" rid="bib1.bibx30" id="altparen.141"/>), and single levels (<ext-link xlink:href="https://doi.org/10.24381/cds.adbb2d47" ext-link-type="DOI">10.24381/cds.adbb2d47</ext-link>, <xref ref-type="bibr" rid="bib1.bibx31" id="altparen.142"/>); see <xref ref-type="bibr" rid="bib1.bibx28" id="text.143"/>.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e3915">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-24-3883-2024-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-24-3883-2024-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e3924">BK, IS, MK, AE, and MW contributed to conception and design of the study. BK elaborated the methods, performed the analyses, created the figures, and prepared the original draft. IS and MK supported the development of analysis methods. MS provided the VELOX-derived skin temperature measurements. NS supported the processing and analysis of CARRA data. MM and JL provided and discussed the Nevzorov data. HM supported the processing of ERA5 data. All authors discussed the results, contributed to manuscript revision and approved the final submitted version.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e3930">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><?xmltex \hack{\newpage}?><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e3937">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. <?xmltex \hack{\newline}?><?xmltex \hack{\newline}?><?xmltex \hack{\noindent}?>The results presented here contain modified C3S information. Neither the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus information or data it contains.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e3947">This article is part of the special issue “HALO-(AC)<inline-formula><mml:math id="M157" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> – an airborne campaign to study air mass transformations during warm-air intrusions and cold-air outbreaks”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e3962">We gratefully acknowledge the funding and support of TRR 172 by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), within the Transregional Collaborative Research Center's Arctic Amplification: Climate Relevant Atmospheric and Surface Processes, and Feedback Mechanisms (AC)<inline-formula><mml:math id="M158" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>. We are furthermore grateful for funding and support by DFG within the framework of the priority program SPP 1294 to promote research with <italic>HALO</italic>. The publication of this article was supported by the Open Access Publication Funding program of the Publishing Fund of Leipzig University. We cordially thank the Alfred Wegener Institute, German Aerospace Center (DLR), as well as all aircraft crew and participants which made the HALO-(AC)<inline-formula><mml:math id="M159" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> campaign possible. We also thank the Institute of Environmental Physics at the University of Bremen for providing the merged MODIS–AMSR2 sea-ice concentration data (<uri>https://data.seaice.uni-bremen.de/modis_amsr2</uri>, last access: 20 October 2023). We acknowledge the use of imagery from the NASA Worldview application (<uri>https://worldview.earthdata.nasa.gov/</uri>, last access: 14 November 2023), part of the NASA Earth Observing System Data and Information System (EOSDIS).</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e3994">This research has been supported by the Deutsche Forschungsgemeinschaft (grants nos. 268020496 and 316646266).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4000">This paper was edited by Franziska Aemisegger and reviewed by two anonymous referees.</p>
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