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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-25-9957-2025</article-id><title-group><article-title>Tropical cirrus evolution in a kilometer-scale model with improved ice microphysics</article-title><alt-title>Tropical cirrus evolution in a kilometer-scale model with improved ice microphysics</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Gasparini</surname><given-names>Blaž</given-names></name>
          <email>blaz.gasparini@univie.ac.at</email>
        <ext-link>https://orcid.org/0000-0002-7177-0155</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Atlas</surname><given-names>Rachel</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4112-8735</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Voigt</surname><given-names>Aiko</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7394-8252</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4">
          <name><surname>Krämer</surname><given-names>Martina</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2888-1722</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Blossey</surname><given-names>Peter N.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0352-0840</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Meteorology and Geophysics, University of Vienna, Vienna, Austria</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>CNRS-Laboratoire de Météorologie Dynamique, LMD, Palaiseau, France</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Institute for Atmospheric Physics, University of Mainz, Mainz, Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>IEK-7, Forschungszentrum Jülich, Jülich, Germany</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Atmospheric and Climate Science, University of Washington, Seattle, WA, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Blaž Gasparini (blaz.gasparini@univie.ac.at)</corresp></author-notes><pub-date><day>8</day><month>September</month><year>2025</year></pub-date>
      
      <volume>25</volume>
      <issue>17</issue>
      <fpage>9957</fpage><lpage>9979</lpage>
      <history>
        <date date-type="received"><day>16</day><month>January</month><year>2025</year></date>
           <date date-type="rev-request"><day>5</day><month>February</month><year>2025</year></date>
           <date date-type="rev-recd"><day>1</day><month>July</month><year>2025</year></date>
           <date date-type="accepted"><day>2</day><month>July</month><year>2025</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2025 Blaž Gasparini et al.</copyright-statement>
        <copyright-year>2025</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/25/9957/2025/acp-25-9957-2025.html">This article is available from https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e145">Tropical cirrus clouds form through in situ ice nucleation below the homogeneous freezing temperature of water or through detrainment from deep convection. Despite their importance, limited understanding of their evolution and formation pathways contributes to large uncertainty in climate projections. To address these challenges, we implement novel passive tracers in the System for Atmospheric Modeling (SAM) cloud-resolving model to track the three-dimensional development of cirrus clouds. One tracer tracks air parcels exiting convective updrafts, revealing a rapid decline in ice crystal size and number as anvils age. Another tracer focuses on in situ cirrus, capturing their formation in the cold upper atmosphere and the subsequent reduction in their ice crystal number over time. We find that in situ cirrus dominate at colder temperatures and lower ice water contents, while anvil cirrus prevail at temperatures <inline-formula><mml:math id="M1" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M2" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>60 °C. Despite the frequent occurrence of in situ cirrus within the tropical tropopause layer, they account for only 6 %–7 % of the total tropical cirrus cloud top-of-the-atmosphere radiative effect. These findings improve our ability to assess the distinct roles of convective and in situ cirrus in shaping tropical cirrus properties and their impacts on climate.</p>

      <p id="d2e162">We also improve the model's representation of tropical cirrus through simple, computationally inexpensive microphysics modifications, improving agreement with tropical aircraft observations. We show that updrafts critical for tropical cirrus formation are only resolved in our simulations at a horizontal grid spacing of 250 m – much finer than those used in global storm-resolving models.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>H2020 Marie Skłodowska-Curie Actions</funding-source>
<award-id>101025473</award-id>
<award-id>101151941</award-id>
</award-group>
<award-group id="gs2">
<funding-source>National Science Foundation</funding-source>
<award-id>OISE-1743753</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e174">Tropical cirrus clouds, defined as ice clouds with tops at temperatures colder than <inline-formula><mml:math id="M3" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C, dominate regions of tropical ascent in both cloud fraction and radiative effects <xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx44" id="paren.1"/>. These clouds are diverse, with their origins and properties shaped by distinct formation mechanisms: convective cirrus originating from deep convective updrafts and in situ cirrus that are formed by ice nucleation in the cold tropical upper troposphere. Understanding the relative contributions and characteristics of these two cloud types is crucial for improving their representation in atmospheric models. The distinction between convective and in situ cirrus has practical implications for climate projections, as their formation mechanisms may respond differently to greenhouse gas forcing, potentially leading to different cloud feedbacks.</p>
      <p id="d2e187">Convective cirrus, or anvil clouds, are initially thick and optically dense but rapidly lose mass through precipitation as they spread horizontally over large areas <xref ref-type="bibr" rid="bib1.bibx38" id="paren.2"/>. Over time, they evolve into thinner clouds, often with optical depths of 1 to 2, which represent the most common form of tropical cirrus <xref ref-type="bibr" rid="bib1.bibx99" id="paren.3"/>. In contrast, in situ cirrus typically form in the tropical tropopause layer (TTL), above the mean detrainment level of convection. These clouds arise from ice nucleation triggered by small-scale dynamical processes, such as gravity-wave-induced temperature and wind fluctuations <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx67 bib1.bibx17 bib1.bibx13" id="paren.4"/>. Unlike anvils, in situ cirrus are optically thin and display distinct microphysical properties, such as ice crystals smaller than 20 <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m <xref ref-type="bibr" rid="bib1.bibx71" id="paren.5"/>.</p>
      <p id="d2e210">This study focuses on the life cycle and microphysical evolution of both anvil and in situ cirrus. Snapshots or long-term averages of cloud properties, typically provided by model output or observations, do not reveal enough information to fully understand the processes that shape tropical cirrus. Lagrangian methods, such as tracking cloud properties using trajectories, have been widely used in both models <xref ref-type="bibr" rid="bib1.bibx111 bib1.bibx38 bib1.bibx104" id="paren.6"/> and observations <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx57" id="paren.7"/>. Passive tracers, an alternative approach to disentangle the origin and evolution of cirrus clouds, are more flexible in their use compared to trajectories, easier to implement, and computationally more efficient.</p>
      <p id="d2e219">Tropical cirrus formation is shaped by processes spanning a wide range of spatial and temporal scales, from microphysical mechanisms such as ice nucleation, deposition, and sublimation to dynamical influences including gravity waves, turbulence, and mesoscale circulations <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx62 bib1.bibx39" id="paren.8"/>. However, even the most advanced models struggle to capture these complexities. Anvils originate in deep convective updrafts, which are unresolved in traditional general circulation models (GCMs). Although global storm-resolving models (GSRMs) with kilometer-scale grid spacings capture larger-scale convective dynamics, they fail to resolve the fine-scale dynamics critical to both anvil and in situ cirrus life cycles <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx68 bib1.bibx1" id="paren.9"/>.</p>
      <p id="d2e229">Moreover, GSRMs show large variability in simulating the microphysical properties of tropical cirrus <xref ref-type="bibr" rid="bib1.bibx4" id="paren.10"/> and their radiative effects <xref ref-type="bibr" rid="bib1.bibx106" id="paren.11"/>, sometimes performing worse than traditional GCMs. This reflects the trade-offs inherent in GSRMs, where the computational costs of high horizontal resolution are typically offset by simplified parameterizations of subgrid processes, particularly cloud microphysics.</p>
      <p id="d2e238">In this work, we demonstrate that simple and inexpensive modifications to cloud microphysics can largely improve the simulation of tropical cirrus. By tracking cloudy air parcels from detrainment or in situ nucleation, we identify key differences in their life cycle and microphysical properties, offering new insights into their respective contributions to tropical cirrus climatology and their radiative impacts. Furthermore, while kilometer-scale GSRMs can resolve updrafts near deep convection, we show that the dynamics critical for cirrus cloud formation in non-convective regions are only resolved at hectometer-scale grid spacings. These findings highlight some limitations of current modeling approaches and provide a pathway toward a more accurate representation of tropical cirrus in climate models.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Model</title>
      <p id="d2e256">We use the System for Atmospheric Modeling (SAM) cloud-resolving model <xref ref-type="bibr" rid="bib1.bibx65" id="paren.12"/> version 6.10.9. SAM uses a 1.5-order Smagorinsky-type closure scheme to represent subgrid-scale turbulence and subgrid-scale motions. The time step in SAM is adaptive and set based on the Courant–Friedrichs–Lewy criterion, which typically leads to a time step of about 4.5 s for simulations at the horizontal grid spacing of 1 km. Radiative fluxes and heating rates are computed with the  Rapid Radiative Transfer Model for GCMs <xref ref-type="bibr" rid="bib1.bibx83 bib1.bibx54" id="paren.13"><named-content content-type="pre">RRTMG;</named-content></xref>, which is called every 3 min. Cloud and precipitation processes use the Predicted Particle Property <xref ref-type="bibr" rid="bib1.bibx84" id="paren.14"><named-content content-type="pre">P3;</named-content></xref> microphysical scheme version 3.1.14.</p>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>Description and issues of ice nucleation in the standard P3 scheme</title>
      <p id="d2e279">In mixed-phase conditions, ice crystals are formed by the following processes (Fig. <xref ref-type="fig" rid="F1"/>a). <list list-type="bullet"><list-item>
      <p id="d2e286"><italic>Immersion freezing of cloud droplets and rain</italic>: a volume-dependent formulation from <xref ref-type="bibr" rid="bib1.bibx11" id="text.15"/> with parameters following <xref ref-type="bibr" rid="bib1.bibx9" id="text.16"/>.</p></list-item><list-item>
      <p id="d2e298"><italic>Deposition nucleation</italic>: a temperature-dependent formulation by <xref ref-type="bibr" rid="bib1.bibx18" id="text.17"/> that is limited to relative humidities with respect to ice (RH<sub>ice</sub>) of <inline-formula><mml:math id="M6" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 105 % and temperatures colder than <inline-formula><mml:math id="M7" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15 °C. Alternatively, a supersaturation-dependent <xref ref-type="bibr" rid="bib1.bibx81" id="text.18"/> parameterization can be used. The maximum number of newly nucleated ice crystals for both deposition freezing mechanisms is limited to 0.1 cm<sup>−3</sup> s<sup>−1</sup>.</p></list-item><list-item>
      <p id="d2e358"><italic>Homogeneous freezing of cloud droplets and rain</italic>: occurs instantaneously at a temperature of <inline-formula><mml:math id="M10" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C.</p></list-item></list></p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e372">A visualization of the number of nucleated ice crystals from ice-nucleating schemes in <bold>(a)</bold> the standard P3 freezing scheme and <bold>(b)</bold> its modified version. The solid line represents water saturation, and the dashed line represents the homogeneous nucleation limit following <xref ref-type="bibr" rid="bib1.bibx69" id="text.19"/>.</p></caption>
            <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f01.png"/>

          </fig>

      <p id="d2e390">Ice crystals continue to be nucleated at temperatures below <inline-formula><mml:math id="M11" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C using the <xref ref-type="bibr" rid="bib1.bibx18" id="text.20"/> or <xref ref-type="bibr" rid="bib1.bibx81" id="text.21"/> parameterizations, even though these schemes are not designed for such conditions. Moreover, nucleation events at such cold temperatures always lead to ice crystal concentrations of 0.1 cm<sup>−3</sup> s<sup>−1</sup>, as set by the ice nucleation limit. Such an approach therefore cannot lead to realistic cloud microphysical properties. Nevertheless, similar approaches to ice nucleation are used in a large number of microphysical schemes beyond the one used here <xref ref-type="bibr" rid="bib1.bibx85 bib1.bibx105" id="paren.22"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>Modifications to ice nucleation: mixed-phase freezing</title>
      <p id="d2e445">Due to issues with freezing parameterizations discussed above, we limit the deposition nucleation parameterizations to temperatures warmer than <inline-formula><mml:math id="M14" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C. Moreover, because deposition freezing is thought to be negligible in mixed-phase conditions <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx25 bib1.bibx48 bib1.bibx77" id="paren.23"><named-content content-type="pre">e.g.,</named-content></xref>, the ice crystals are allowed to form only in the presence of cloud droplets, effectively changing the deposition freezing parameterizations into a type of condensation freezing. The maximum number of nucleated ice crystals by the modified <xref ref-type="bibr" rid="bib1.bibx18" id="text.24"/> <xref ref-type="bibr" rid="bib1.bibx81" id="paren.25"><named-content content-type="pre">or, alternatively,</named-content></xref> scheme is increased to 0.15 cm<sup>−3</sup> s<sup>−1</sup>.  While these modifications aim to provide a more physically consistent representation of mixed-phase clouds, we did not explicitly evaluate the scheme's performance for this cloud type, as it lies outside the main scope of this study. A number of further refinements would be necessary to achieve a more accurate simulation of mixed-phase clouds, as discussed in Sect. <xref ref-type="sec" rid="Ch1.S6.SS1"/>.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS3">
  <label>2.1.3</label><title>Modifications to ice nucleation: cirrus ice nucleation</title>
      <p id="d2e503">As we limited the existing ice nucleation mechanisms to the mixed-phase regime (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS2"/>), we implement a new ice nucleation scheme for <inline-formula><mml:math id="M17" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M18" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M19" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C, which helps mitigate the bias in ice crystal number concentration (ICNC; see also Sect. 3.1 for more detail). The newly implemented approach follows <xref ref-type="bibr" rid="bib1.bibx97" id="text.26"/> (Fig. <xref ref-type="fig" rid="F1"/>b, labeled as cirrus nucleation) and represents the competition between homogeneous and heterogeneous nucleation in cirrus clouds <xref ref-type="bibr" rid="bib1.bibx76" id="paren.27"/> and the effect of pre-existing ice crystals. The scheme is fed by a predefined, temperature-dependent value of ice-nucleating particles (INPs). In this work, the INP number is set to 2 <inline-formula><mml:math id="M20" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> cm<sup>−3</sup> at temperatures colder than <inline-formula><mml:math id="M23" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>70 °C and increases linearly to 20 <inline-formula><mml:math id="M24" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> cm<sup>−3</sup> at temperatures of <inline-formula><mml:math id="M27" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C and warmer. While the INP number in the upper troposphere is subjected to large uncertainties, the suggested numbers are plausible for relatively clean, aerosol-free environments in the tropical Pacific and follow model-simulated INP concentrations <xref ref-type="bibr" rid="bib1.bibx35" id="paren.28"/>. The number of sulfate aerosols is set to 20 cm<sup>−3</sup> and is thus not a limiting factor in ice nucleation.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS4">
  <label>2.1.4</label><title>Modifications to ice nucleation: ice crystal number limit</title>
      <p id="d2e643">Very importantly, the maximum allowed ICNC is relaxed from a very limiting 0.5 to 20 cm<sup>−3</sup>. Such high concentrations were occasionally observed in aircraft measurements of fresh anvils <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx61" id="paren.29"/>. Increasing the ICNC limit alone was previously shown to change anvil cloud properties, leading to more thin cirrus <xref ref-type="bibr" rid="bib1.bibx37" id="paren.30"><named-content content-type="pre">e.g., Fig. 11a in</named-content></xref>.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS5">
  <label>2.1.5</label><title>Other changes impacting cirrus</title>
      <p id="d2e674">The cirrus nucleation scheme requires the input of an updraft velocity, and we choose to input the sum of the resolved vertical wind and an estimate of subgrid-scale updraft strength derived from the subgrid-scale turbulent kinetic energy (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TKE</mml:mi><mml:mi mathvariant="normal">SGS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) as <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">TKE</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">SGS</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">0.667</mml:mn><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">TKE</mml:mi><mml:mi mathvariant="normal">SGS</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, given that not all updrafts relevant for cloud formation are resolved at horizontal grid spacings of about 1 km (see more in Sect. 5.2). The <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">TKE</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">SGS</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> term is computed assuming that the <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TKE</mml:mi><mml:mi mathvariant="normal">SGS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TKE</mml:mi><mml:mi mathvariant="normal">SGS</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>v</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>)) is equally partitioned in the three directions (<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>v</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>), and therefore <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TKE</mml:mi><mml:mi mathvariant="normal">SGS</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">TKE</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">SGS</mml:mi></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e897">We use a more accurate formulation for the saturation vapor pressure of liquid water and ice <xref ref-type="bibr" rid="bib1.bibx86" id="paren.31"/>, replacing the <xref ref-type="bibr" rid="bib1.bibx30" id="text.32"/> formulation, which performs poorly at cold temperatures in the TTL. This change particularly affects in situ ice nucleation at temperatures below <inline-formula><mml:math id="M38" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>70 °C in the TTL <xref ref-type="bibr" rid="bib1.bibx86" id="paren.33"><named-content content-type="pre">see Fig. 11 in</named-content></xref>.</p>
      <p id="d2e918">Additionally, we adjust the homogeneous freezing threshold for cloud droplets from <inline-formula><mml:math id="M39" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 to <inline-formula><mml:math id="M40" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C. While droplets can freeze over a wide temperature range, larger droplets may freeze as warm as <inline-formula><mml:math id="M41" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>35 °C <xref ref-type="bibr" rid="bib1.bibx55 bib1.bibx95" id="paren.34"/>. Despite issues with using a fixed temperature freezing threshold <xref ref-type="bibr" rid="bib1.bibx47" id="paren.35"/>, <inline-formula><mml:math id="M42" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C is a more physically justified value than the <inline-formula><mml:math id="M43" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C used in the reference version of the P3 microphysical scheme.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS6">
  <label>2.1.6</label><title>Passive tracers</title>
      <p id="d2e971">We implemented two passive tracers to facilitate the analysis of the tropical cirrus life cycle. The “time after detrainment” or simply “detrainment” tracer, denoted <inline-formula><mml:math id="M44" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>, evolves as

              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M45" display="block"><mml:mrow><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi>w</mml:mi><mml:mo>|</mml:mo><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> m s<sup>−1</sup>, <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> kg kg<sup>−1</sup>, and <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and

              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M51" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>A</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace linebreak="nobreak" width="1em"/><mml:mi mathvariant="normal">elsewhere</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M52" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> is the vertical wind, <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the cloud liquid and ice mass mixing ratios, <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> the density temperature anomaly from the domain mean (which is proportional to buoyancy), and <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> min is an arbitrary decay timescale for <inline-formula><mml:math id="M57" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> that allows for analysis of processes on timescales of hours to days. Neglecting the effects of subgrid-scale mixing on the passive tracer, <inline-formula><mml:math id="M58" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>, the time since detrainment from active convection can be calculated as

              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M59" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">detr</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mi>log⁡</mml:mi><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e1231">The behavior of the tracer in the context of idealized tropical convection is described in the Appendix of <xref ref-type="bibr" rid="bib1.bibx39" id="text.36"/>.</p>
      <p id="d2e1237">Additionally, we implement an analogous tracer to determine the time after in situ ice nucleation. The tracer is set to 1 in all grid cells with active cirrus ice nucleation and decays elsewhere with the same decay timescale <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. We note that both implemented tracers follow air parcels and not ice crystals, which results in biases when ice crystals sediment out of air parcels.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Simulation setup</title>
      <p id="d2e1260">We use a tropical channel setup that is wide in the zonal direction (3888 km) and narrow in the meridional direction (36 km) with double-periodic boundary conditions. The prescribed sea surface temperatures vary sinusoidally in the zonal direction between 24 °C at the domain edge and 28 °C in the middle of the domain. Convection develops over the warmer sea surface temperatures (SSTs) and gives rise to a large-scale overturning circulation in the zonal direction reminiscent of the Walker circulation. Such a “mock-Walker” circulation setup is therefore appropriate for studying the interplay between convection, clouds, and radiation in the tropics <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx14 bib1.bibx114 bib1.bibx98" id="paren.37"/>. To accurately represent processes in the TTL, we impose a mean large-scale vertical wind based on observations by <xref ref-type="bibr" rid="bib1.bibx116" id="text.38"/>. Zonal winds increase linearly with altitude from 0 m s<sup>−1</sup> at the surface to 5 m s<sup>−1</sup> at altitudes above 14 km. Our “mock-Walker” setup follows the one described in more detail by <xref ref-type="bibr" rid="bib1.bibx12" id="text.39"/>. The simulations are performed for 30 d, the last 20 of which are used for analysis.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>In situ observations</title>
      <p id="d2e1304">For a fairer comparison with model data, which simulates a climate comparable to that of the tropical Pacific, we use airborne data from three campaigns in the tropical western Pacific: the Airborne Tropical TRopopause EXperiment <xref ref-type="bibr" rid="bib1.bibx60" id="paren.40"><named-content content-type="pre">ATTREX;</named-content></xref>; the Pacific Oxidants, Sulfur, Ice, Dehydration, and cONvection experiment <xref ref-type="bibr" rid="bib1.bibx61" id="paren.41"><named-content content-type="pre">POSIDON;</named-content></xref>; and the CONvective TRansport of Active Species in the Tropics (CONTRAST) experiment <xref ref-type="bibr" rid="bib1.bibx88" id="paren.42"/>.</p>
      <p id="d2e1320">Vertical wind data are only used from the tropical western Pacific flights of the ATTREX and POSIDON campaigns. The data are sampled using NASA's Meteorological Measurement System (MMS) instrument <xref ref-type="bibr" rid="bib1.bibx93" id="paren.43"/>, which has a time resolution of 20 Hz.  Vertical wind data are corrected by detrending and removing the mean of each flight leg. More details on the processing are described in <xref ref-type="bibr" rid="bib1.bibx3" id="text.44"/>.</p>
      <p id="d2e1329">In situ data for ice cloud properties for the three campaigns are taken from the <xref ref-type="bibr" rid="bib1.bibx71" id="text.45"/> dataset. The measurement resolution is 1 Hz, with an aircraft velocity of 170 m s<sup>−1</sup> in POSIDON and ATTREX and 200 m s<sup>−1</sup> in the CONTRAST campaign. The lower limit of detectable particle concentration in a given sampling time depends on the aircraft velocity and sampling area of the respective instrument <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx22" id="paren.46"/>. This limits the measurements for CONTRAST of ice crystals at ICNC <inline-formula><mml:math id="M65" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01 cm<sup>−3</sup> and mean mass ice radii smaller than 35 <inline-formula><mml:math id="M67" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m. For consistency, model output under such conditions is not included in the calculation of model performance. Due to the slower aircraft speed and different instrumentation, there is no such limitation for POSIDON and ATTREX. The dataset contains limited measurements within or very near active deep convection (see Fig. <xref ref-type="fig" rid="FA3"/>).</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Satellite retrievals</title>
      <p id="d2e1401">We use satellite retrievals from the years 2007–2010 for the tropical western Pacific (TWP) (20° S–20° N, 145–180° E), an almost exclusively ocean-covered area characterized by persistent deep convection throughout the year. In the selected years, all the satellite products used have complete data coverage.</p>
<sec id="Ch1.S2.SS4.SSS1">
  <label>2.4.1</label><title>DARDAR</title>
      <p id="d2e1411">This dataset is derived from combined retrievals from the CloudSat Cloud Profiling Radar <xref ref-type="bibr" rid="bib1.bibx102" id="paren.47"/> and the Cloud–Aerosol Lidar with Orthogonal Polarization <xref ref-type="bibr" rid="bib1.bibx115" id="paren.48"><named-content content-type="pre">CALIOP;</named-content></xref>. Merged CloudSat radar reflectivity and CALIOP lidar-attenuated backscatter signals were used to build the radar/lidar product <xref ref-type="bibr" rid="bib1.bibx24 bib1.bibx23" id="paren.49"><named-content content-type="pre">DARDAR;</named-content></xref> that estimates ice water content (IWC), effective ice crystal size, and the extinction coefficient. DARDAR has a horizontal footprint of 1.7 km and a vertical resolution of 60 m. We only use the vertically integrated IWC, which includes all frozen hydrometeors and is denoted here as ice water path (IWP). Since the lidar signal is noisier during daytime, resulting in the detection of fewer thin clouds <xref ref-type="bibr" rid="bib1.bibx5" id="paren.50"/>, we use nighttime-only data. While this may lead to a bias, the diurnal cycle of tropical oceanic convection is small and of second-order importance for the comparison with model results <xref ref-type="bibr" rid="bib1.bibx110 bib1.bibx39" id="paren.51"/>. As one measure of uncertainty in the retrievals, IWP comparisons are made with both the newest dataset (DARDARv3) and an older version of the retrieval algorithm (DARDARv2) <xref ref-type="bibr" rid="bib1.bibx16" id="paren.52"/>. IWP retrievals in DARDAR products are expected to reliably detect clouds down to an IWP of about 0.5 g m<sup>−2</sup> <xref ref-type="bibr" rid="bib1.bibx101" id="paren.53"/>.</p>
</sec>
<sec id="Ch1.S2.SS4.SSS2">
  <label>2.4.2</label><title>2C-ICE</title>
      <p id="d2e1460">We also use retrievals of IWP from the Cloudsat and CALIPSO Ice Cloud Property Product (2C-ICE) version RF05 <xref ref-type="bibr" rid="bib1.bibx26" id="paren.54"/>. Despite originating from the same input data as the DARDAR product, analyzing it along with DARDAR helps quantify the uncertainty in satellite-retrieved quantities.</p>
</sec>
<sec id="Ch1.S2.SS4.SSS3">
  <label>2.4.3</label><title>Cloudsat-Calipso-CERES-MODIS (CCCM)</title>
      <p id="d2e1474">The CALIPSO-CloudSat-CERES-MODIS (CCCM) dataset <xref ref-type="bibr" rid="bib1.bibx64" id="paren.55"/> merges cloud fraction data from the CALIPSO lidar <xref ref-type="bibr" rid="bib1.bibx115" id="paren.56"/> and CloudSat radar <xref ref-type="bibr" rid="bib1.bibx102" id="paren.57"/> with the Moderate Resolution Imaging Spectroradiometer (MODIS) IWP data and Clouds and the Earth's Radiant Energy System (CERES) radiative fluxes <xref ref-type="bibr" rid="bib1.bibx112" id="paren.58"/>. MODIS IWP retrievals are unreliable for detection of thin cirrus <xref ref-type="bibr" rid="bib1.bibx101" id="paren.59"><named-content content-type="pre">IWP smaller than about 4 g m<sup>−2</sup>;</named-content></xref>. CCCM's horizontal resolution is about 30 km, equivalent to CERES retrievals. Shortwave (SW) radiative fluxes from CERES used in this work are from the measured fluxes during the 13:30 LT satellite overpass, accounting for diurnally averaged insolation values. Data points with zenith angles greater than 70° are excluded to mitigate issues at high solar zenith angles. Albedo is computed based on incoming and outgoing SW fluxes at the top of the atmosphere (TOA). The average reflected SW flux during the day is calculated by multiplying the albedo by the daily and yearly average incoming radiation, set at 409.6 W m<sup>−2</sup>, the annual average insolation for the band between 20° S and 20° N <xref ref-type="bibr" rid="bib1.bibx113" id="paren.60"/>. This ensures that values of radiative fluxes are comparable to the climatological cloud radiative effects.</p>
      <p id="d2e1522">The TOA albedo (<inline-formula><mml:math id="M71" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>) and SW cloud radiative effect (CRE) are computed as

                  <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M72" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E4"><mml:mtd><mml:mtext>4</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mi mathvariant="normal">out</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mi mathvariant="normal">in</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mi mathvariant="normal">CRE</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>clear-sky</mml:mtext></mml:msub></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mn mathvariant="normal">409.6</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><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:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e1610">In addition, Fig. <xref ref-type="fig" rid="FB2"/> compares model-computed quantities with directly retrieved radiative fluxes to ensure better consistency with retrievals. SW CRE is thus computed as

              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M73" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mi mathvariant="normal">CRE</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mi mathvariant="normal">out</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">SW</mml:mi><mml:mtext>out,clear-sky</mml:mtext></mml:msub></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e1645">The LW CRE is computed as

              <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M74" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">LW</mml:mi><mml:mi mathvariant="normal">CRE</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="normal">OLR</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">OLR</mml:mi><mml:mtext>clear-sky</mml:mtext></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where OLR is outgoing LW radiation at the TOA.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Global storm-resolving models from DYAMOND-1</title>
      <p id="d2e1686">We compare the power spectral density of vertical wind between SAM and four global storm-resolving models (GSRMs) in Sect. <xref ref-type="sec" rid="Ch1.S5.SS2"/>. GSRM simulations were run with the Nonhydrostatic ICosahedral Atmospheric Model (NICAM), Global System for Atmospheric Modeling (gSAM), Finite Volume Cubed-Sphere Dynamical Core (FV3), and Icosahedral Nonhydrostatic Weather and Climate Model (ICON), as part of the DYAMOND-1 experiment <xref ref-type="bibr" rid="bib1.bibx103" id="paren.61"/>. The GSRM simulations have horizontal grid spacings of 2.5–5 km and vertical grid spacings of 400–500 m. Vertical winds are analyzed within a square swath in the tropical western Pacific (4° S–4° N, 144–152° E), a region overlapping the aircraft measurements with a climatology comparable to the SAM simulations. Vertical winds are analyzed for model levels closest to 14.2 km, the most common height for ATTREX level-leg sampling.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Cirrus properties</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Simulated tropical cirrus cloud properties and their comparison with aircraft observations and satellite retrievals</title>
      <p id="d2e1711">This section first outlines the step-by-step changes implemented in the ice microphysics scheme. We focus on changes under cirrus conditions, limiting the analysis to temperatures colder than <inline-formula><mml:math id="M75" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C and ice water contents larger than 10<sup>−5</sup> g m<sup>−3</sup>, which is close to the detectability threshold of the aircraft observations. The data are first presented in the ICNC–ice crystal mean mass radius (from now on: ice number–radius) space, which provides an intuitive aggregated perspective on ice cloud properties <xref ref-type="bibr" rid="bib1.bibx70 bib1.bibx36" id="paren.62"/>.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1750">Probability density function of ice properties for clouds at <inline-formula><mml:math id="M78" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M79" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M80" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C as a function of ICNC and ice mass radius <xref ref-type="bibr" rid="bib1.bibx71" id="paren.63"><named-content content-type="pre">computed as the radius of a solid ice sphere with mass IWC/ICNC, as in</named-content></xref> for <bold>(a)</bold> tropical Pacific aircraft observations and three versions of the SAM model: <bold>(b)</bold> the standard setup (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS1"/>), <bold>(c)</bold> the intermediate model version with a relaxed ICNC limit (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS4"/>), and <bold>(d)</bold> the final version with a modified ice nucleation scheme (also including improvements described in Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS2"/>, <xref ref-type="sec" rid="Ch1.S2.SS1.SSS3"/>, and <xref ref-type="sec" rid="Ch1.S2.SS1.SSS5"/>). The numbers in the upper left and right corner represent a 2D total variation distance of model data compared to aircraft observations (the smaller the number, the better the agreement), calculated separately for small (1–30 <inline-formula><mml:math id="M81" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m) and large particle sizes (30–120 <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m). Observations are limited or not available in the shaded area.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f02.png"/>

        </fig>

      <p id="d2e1825">Aircraft observations in Fig. <xref ref-type="fig" rid="F2"/>a show a peak ICNC between 1 and 10<sup>−2</sup> cm<sup>−3</sup> for particles with mean mass radii smaller than 30 <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m. For concentrations smaller than 10<sup>−1</sup> cm<sup>−3</sup>, the observed particle size often exceeds 50 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m. We note that due to retrieval limits, there are limited measurements available for ice radii smaller than 35 <inline-formula><mml:math id="M89" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m at number concentrations below about <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> cm<sup>−3</sup> (see the Methods section).</p>
      <p id="d2e1930">The standard version of the SAM model coupled with the P3 scheme (Fig. <xref ref-type="fig" rid="F2"/>b, Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS1"/>) is strongly biased compared to observations. Most notably, the model drastically underestimates ICNC as it lacks concentrations larger than 3 <inline-formula><mml:math id="M92" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<sup>−2</sup> cm<sup>−3</sup>. We resolve a large part of the bias by implementing three key changes to the ice microphysics.</p>
      <p id="d2e1968">We first relax the maximum ICNC limit from 5 <inline-formula><mml:math id="M95" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<sup>−2</sup> to 20 cm<sup>−3</sup> (Fig. <xref ref-type="fig" rid="F2"/>c, Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS4"/>). This particularly improves the representation of particles larger than 30 <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m, reducing the total variation distance metric <xref ref-type="bibr" rid="bib1.bibx42" id="paren.64"><named-content content-type="post">a 2D analog to the root mean square error</named-content></xref> from 0.52 to 0.35. However, the model still strongly underestimates the number densities of small ice crystals in the top left quadrant, indicating errors in parameterizing ice formation under cirrus conditions.</p>
      <p id="d2e2020">The second key modification addresses the deposition freezing parameterization, which was incorrectly active at temperatures both below and above the homogeneous freezing threshold. Originally calibrated for temperatures warmer than <inline-formula><mml:math id="M99" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>25 °C (Fig. <xref ref-type="fig" rid="F1"/>), this parameterization extended far beyond its intended range. We restrict it to <inline-formula><mml:math id="M100" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M101" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M102" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C and introduce a scheme to account for competition between homogeneous and heterogeneous nucleation at <inline-formula><mml:math id="M103" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M104" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M105" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>37 °C <xref ref-type="bibr" rid="bib1.bibx76 bib1.bibx97" id="paren.65"/> (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS2"/>, <xref ref-type="sec" rid="Ch1.S2.SS1.SSS3"/>). We also include a number of small changes to the microphysics, described in Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS5"/>.</p>
      <p id="d2e2085">All these changes combined cut the microphysical bias in half, improving the representation of both small and large particles (Fig. <xref ref-type="fig" rid="F2"/>d). Nevertheless, some biases remain. The model continues to underestimate ICNC for small ice crystals and overestimate ICNC for larger crystals. These remaining biases largely originate from persistent challenges in representing ice microphysics (see Sect. <xref ref-type="sec" rid="Ch1.S6.SS1"/>) and from vertical wind variance that is too low in the model (see Sect. <xref ref-type="sec" rid="Ch1.S5.SS2"/>).</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e2096">Cirrus cloud properties from tropical aircraft measurements <bold>(a, d, g)</bold> and SAM model simulations with improved microphysics at 1 km horizontal grid spacing <bold>(b, e, h)</bold>. Thick solid lines represent median values. Gray lines in the middle column represent median values of the standard model setup. Panels <bold>(c)</bold>, <bold>(f)</bold>, and <bold>(i)</bold> display the difference between improved SAM and aircraft data; lines are repeated from the first and second columns for reference. Blue lines in panels <bold>(a)</bold> and <bold>(b)</bold> show the theoretical maximum IWC formed locally by vapor deposition under ice-supersaturated conditions based on RH<sub>ice</sub> required to trigger homogeneous nucleation <xref ref-type="bibr" rid="bib1.bibx69" id="paren.66"/> (solid) and RH<sub>ice</sub> of 120 %, typical for efficient heterogeneous ice nucleation (dashed). All data are sorted into 4 °C temperature bins, with values normalized to add up to 100 % within each temperature bin.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f03.png"/>

        </fig>

      <p id="d2e2149">To provide an alternative perspective, we examine the model's performance by sorting results by temperature. The exponential decrease in IWC with decreasing temperature has improved compared to the standard model version and is well represented by the model (Fig. <xref ref-type="fig" rid="F3"/>a–c). Both observations and simulations indicate that a substantial portion of IWC must originate at warmer temperatures and be transported upward by convection. This is evident from IWC values that exceed the maximum expected from local ice nucleation and subsequent depositional growth constrained by the Clausius–Clapeyron relationship. The blue lines in Fig. <xref ref-type="fig" rid="F3"/>a and b illustrate these theoretical limits, derived in Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>. They represent the maximum IWC that can form locally through ice nucleation under supersaturated conditions with respect to ice, followed by vapor deposition until saturation is reached.</p>
      <p id="d2e2158">Observed ICNC shows large variability but only a weak dependence on temperature (Fig. <xref ref-type="fig" rid="F3"/>d). The model reproduces the observed median and spread, improving the agreement substantially compared to the standard model version (only the gray median is shown). Notably, the model still misses some of the (rather infrequent) high ICNC data points at cold temperatures.</p>
      <p id="d2e2163">Similarly to IWC, the mean mass radius decreases with temperature, with medians ranging from 80 <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m at <inline-formula><mml:math id="M109" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C to 15 <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m at <inline-formula><mml:math id="M111" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>80 °C. The model simulates particles that are too small at warmer temperatures (between <inline-formula><mml:math id="M112" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65 and <inline-formula><mml:math id="M113" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C) and comparable to observations for <inline-formula><mml:math id="M114" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M115" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M116" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65 °C. Notably, the spread in simulated particle size is narrower than observed, possibly due to the single-mode description of ice microphysics that is too simple (see Sect. <xref ref-type="sec" rid="Ch1.S6.SS1"/>).</p>
      <p id="d2e2234">In summary, the temperature-sorted model results offer a complementary perspective on cirrus cloud properties, showing generally  good agreement with observations, while also highlighting persistent biases in ICNC at colder temperatures and particle size at warmer temperatures. Nevertheless, this agreement represents a substantial improvement compared with the earlier model version (Fig. <xref ref-type="fig" rid="F2"/>b), emphasizing processes where further refinement is still needed. The addition of passive tracers discussed in Sect. <xref ref-type="sec" rid="Ch1.S4"/> helps pinpoint processes requiring further refinement, particularly the representation of in situ ice nucleation at cold temperatures.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>The relevance of tropical cirrus for top-of-the-atmosphere radiative fluxes</title>
      <p id="d2e2249">To link cirrus cloud properties to the TOA radiative budget, we take an integrated perspective and categorize cloud occurrence frequency and radiative effects based on IWP. We neglect infrequent scenes with low clouds underlying thin cirrus, where low clouds are expected to dominate the CRE signal. Figure <xref ref-type="fig" rid="F4"/>a compares the simulated IWP distribution with four satellite-derived datasets, showing that the improved model generally falls within or near the observed range, which also includes deep convective cores  <xref ref-type="bibr" rid="bib1.bibx99" id="paren.67"><named-content content-type="pre">typically associated with IWP <inline-formula><mml:math id="M117" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 10<sup>3</sup> g m<sup>−2</sup>, based on</named-content></xref>. We note that this association is statistical and that individual convective cores are unlikely to span a wide range of IWP values. The apparent overrepresentation of the thinnest cirrus in the model and the corresponding slight underestimation of other cloud types in the normalized PDF should not be interpreted as a bias, as satellite retrievals are known to underestimate the thinnest cirrus clouds <xref ref-type="bibr" rid="bib1.bibx7 bib1.bibx75" id="paren.68"/>. Thin cirrus with IWP <inline-formula><mml:math id="M120" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 g m<sup>−2</sup> make up 52 % of all simulated cirrus but contribute only 6 % to the LW CRE and 5 % to the SW CRE, indicating that their direct radiative impact at the TOA is modest despite their frequency. Focusing on clouds with IWP <inline-formula><mml:math id="M122" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 1 g m<sup>−2</sup>, which have a greater radiative influence, improves the model's agreement with satellite observations (Fig. <xref ref-type="fig" rid="FB1"/>).</p>

      <fig id="F4"><label>Figure 4</label><caption><p id="d2e2333"><bold>(a)</bold> Frequency of cloud occurrence in each ice water path (IWP) bin, <bold>(b)</bold> average CRE in each IWP bin, and <bold>(c)</bold> the contribution of each IWP bin to the CRE. The gray shading in panel <bold>(a)</bold> highlights the range of observations. Panels <bold>(b)</bold> and <bold>(c)</bold> show results only for the improved SAM model and the CCCM satellite product. Model results are presented for full resolution and regridded to 36 <inline-formula><mml:math id="M124" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 36 km grid, similar to the resolution of CERES satellite retrievals of CRE.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f04.png"/>

        </fig>

      <p id="d2e2367">Figure <xref ref-type="fig" rid="F4"/>b shows the averaged CRE for high clouds in each IWP bin. The most frequent anvils according to satellite datasets occur at an IWP of 3–30 g m<sup>−2</sup>, which corresponds to anvil clouds of intermediate optical depth (1–3) that yield a net positive, LW-dominated CRE <xref ref-type="bibr" rid="bib1.bibx99" id="paren.69"/>. For thicker clouds (IWP <inline-formula><mml:math id="M126" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 g m<sup>−2</sup>), both model and satellite data show a dominance of SW CRE, with net CRE exceeding <inline-formula><mml:math id="M128" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>100 W m<sup>−2</sup> for the thickest anvils. However, the model overestimates the SW CRE, a bias partially resolved by averaging the output onto coarser grid scales, similar to the CERES pixel data resolution (36 <inline-formula><mml:math id="M130" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 36 km grid boxes). Additionally, a recently identified bug in the ice optics parameterization likely increased the optical depth and radiative effects per unit IWP by <inline-formula><mml:math id="M131" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 %, but this issue could not be addressed in the current simulations. This SW bias becomes even more apparent when comparing CERES CRE retrieved during daytime satellite overpasses with model-simulated CRE between 13:00 and 14:00 LT (Fig. <xref ref-type="fig" rid="FB2"/>b).</p>
      <p id="d2e2443">Determining which type of tropical cirrus is radiatively most important is not straightforward. Are the less frequent but thick deep convective cores and fresh anvils, which have a strong influence on both SW and LW CRE, the most dominant, or do the more widespread anvil clouds of intermediate thickness dominate? Figure <xref ref-type="fig" rid="F4"/>c provides an answer by scaling the CRE in a given IWP bin by that bin's frequency of occurrence: the radiatively most dominant clouds have IWP between 1 and 3000 g m<sup>−2</sup>, similar to results by <xref ref-type="bibr" rid="bib1.bibx10" id="text.70"/>. These include anvil clouds with optical depths greater than approximately 1. Nonetheless, thinner cirrus (IWP 0.3–10 g m<sup>−2</sup>, Fig. <xref ref-type="fig" rid="F4"/>c) also contribute meaningfully to the net CRE, underscoring the importance of studying not only the thickest tropical cirrus but also their continued evolution until they reach an IWP of <inline-formula><mml:math id="M134" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1 g m<sup>−2</sup> (optical depth <inline-formula><mml:math id="M136" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.005). Additionally, the response of thin cirrus to global warming remains highly uncertain <xref ref-type="bibr" rid="bib1.bibx100" id="paren.71"/> and deserves further investigation.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Origin and evolution of cirrus</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Cirrus origin</title>
      <p id="d2e2523">We illustrate the utility of passive tracers in disentangling convective and in situ contributions to cirrus formation using a case study and statistical estimates of cirrus origin in the SAM model that includes all model improvements (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS2"/>–<xref ref-type="sec" rid="Ch1.S2.SS1.SSS5"/>) and the two passive tracers (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS6"/>). Our analysis begins with the model snapshot in Fig. <xref ref-type="fig" rid="F5"/>, while a Video Supplement shows the system's evolution over 2 d. The figure depicts a snapshot of a multicore mesoscale convective system with an anvil cloud shield extending approximately 500 km. This system includes a fresh, thick precipitating anvil cloud that evolves into a thinner, aged anvil cloud. Above this, a thin cirrus layer spans altitudes of 15–16 km. Identifying the origin of such thin cirrus from a single model output time step is challenging. Although thin TTL clouds are typically formed in situ <xref ref-type="bibr" rid="bib1.bibx70 bib1.bibx52" id="paren.72"/>, they might also be remnants of TTL-penetrating deep convection.</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e2539">A simulated mesoscale convective system with an extensive anvil cloud shield and overlying TTL cirrus. Panel <bold>(a)</bold> shows total condensed water,  with purple contours indicating rain. Panels <bold>(b)</bold> and <bold>(c)</bold> show values of detrainment and in situ nucleation tracers for the same cloud system, respectively. Panel <bold>(d)</bold> presents the outcome of a cirrus origin classification criterion. In situ cirrus (in orange) are defined as cloudy parcels that have not been in contact with detrained air for at least 24 h and where the time since in situ nucleation tracer is shorter compared to the time since detrainment. The remaining clouds are classified as anvil cirrus (blue). Portions of the anvil where the time since in situ nucleation tracer is shorter compared to the time since detrainment are classified as “dual-origin” (in brown). Gray contours in panels <bold>(b)</bold>, <bold>(c)</bold>, and <bold>(d)</bold> delineate vertical wind velocities of 1 m s<sup>−1</sup>. Red contours in panels <bold>(b)</bold> and <bold>(c)</bold> delineate total cloud condensate of <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> g kg<sup>−1</sup>.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f05.jpg"/>

        </fig>

      <p id="d2e2619">Passive tracers resolve this uncertainty. The detrainment tracer highlights regions of active deep convection and thick anvil clouds with times since detrainment typically less than 10 h and reveals that the overlying thin cirrus resides predominantly in air undisturbed by convection for at least 24 h (Fig. <xref ref-type="fig" rid="F5"/>b). The in situ nucleation tracer confirms this, showing that much of the thin cirrus originates from recent ice nucleation events (within the last 5 h; Fig. <xref ref-type="fig" rid="F5"/>c).</p>
      <p id="d2e2627">Interestingly, the nucleation tracer also indicates that some parts of the anvils experience ongoing ice nucleation. These events, driven by convective gravity waves or within-anvil updrafts, align with previous observational studies <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx45 bib1.bibx71 bib1.bibx99" id="paren.73"/>. However, their broader significance for tropical cirrus remains uncertain <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx40" id="paren.74"/>.</p>
      <p id="d2e2636">To better characterize the microphysical origin of cirrus, we classify them into three categories: in situ, anvil, and dual-origin. Anvil cirrus are defined as clouds where the time since detrainment is shorter than the time since in situ nucleation. In situ cirrus are those that have not experienced detrainment for at least 24 h and where the time since nucleation is shorter than the time since detrainment.</p>
      <p id="d2e2639">Dual-origin cirrus are clouds detrained within the last 24 h that have a shorter time since in situ nucleation compared to time after detrainment. These typically form within or near anvils or in cirrus clouds close to active convection (Fig. <xref ref-type="fig" rid="F5"/>d). To correct for classification biases due to ice crystal sedimentation impacting older anvils and in situ cirrus, clouds that were initially classified as in situ cirrus but located below dual-origin cirrus are reassigned to the dual-origin category. Although dual-origin cirrus are influenced by in situ nucleation, their total ice mass and number are still dominated by convective outflow (not shown).</p>
      <p id="d2e2644">Our tracer approach confirms previous findings highlighting IWC as a good predictor of cirrus origin <xref ref-type="bibr" rid="bib1.bibx70" id="paren.75"/>. High-IWC tropical cirrus are thought to be of convective origin, while low-IWC cirrus, particularly those at cold temperatures, are more likely of in situ origin <xref ref-type="bibr" rid="bib1.bibx78 bib1.bibx70" id="paren.76"/>. Using a two-dimensional IWC–temperature space, we find that in situ cirrus dominate only for the coldest low-IWC tropical cirrus (IWC <inline-formula><mml:math id="M140" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 10<sup>−3</sup> g m<sup>−3</sup>, <inline-formula><mml:math id="M143" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M144" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M145" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65 °C), while high-IWC cirrus and most cirrus at warmer temperatures are of convective origin (Fig. <xref ref-type="fig" rid="F6"/>a). In situ contributions range from 10 % (<inline-formula><mml:math id="M146" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M147" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M148" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>50 °C) to more than 70 % (<inline-formula><mml:math id="M149" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M150" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M151" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>70 °C). Additionally, we repeat the analysis using ICNC, which leads to less distinct patterns (Fig. <xref ref-type="fig" rid="F6"/>b). While the highest-ICNC bins are clearly associated with anvil cirrus, in situ cirrus fractions remain steady at <inline-formula><mml:math id="M152" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10–40 % for ICNC <inline-formula><mml:math id="M153" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.03 cm<sup>−3</sup>, increasing to over 60 % only at temperatures colder than <inline-formula><mml:math id="M155" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65 °C.</p>

      <fig id="F6"><label>Figure 6</label><caption><p id="d2e2789">Fraction of model-simulated in situ cirrus represented in the <bold>(a)</bold> temperature–IWC and <bold>(b)</bold> temperature–ICNC space for the cirrus classification criterion from Fig. <xref ref-type="fig" rid="F5"/>. The gray lines in the contour indicate the joint distribution of cloud occurrence in each two-dimensional phase space. Panel <bold>(c)</bold> shows the fraction of cirrus binned by IWP.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f06.png"/>

        </fig>

      <p id="d2e2810">Vertically integrated cirrus origin analysis in Fig. <xref ref-type="fig" rid="F6"/>c shows that in situ cirrus dominate at IWP <inline-formula><mml:math id="M156" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.4 g m<sup>−2</sup> and peak at IWP values between 0.1 and 0.5 g m<sup>−2</sup>. At IWP <inline-formula><mml:math id="M159" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 10 g m<sup>−2</sup>, in situ nucleation is highly unlikely due to limited vapor availability and slow depositional growth in the TTL. Clouds with IWPs of 1–50 g m<sup>−2</sup> often consist of contributions from both in situ and convective sources, suggesting that in situ nucleation plays a role in sustaining and prolonging the lifetime of aged anvil clouds. This analysis, together with our previous findings (Sect. 3.2), provides more information about the evolution of tropical cirrus. These can be split into two separate evolution pathways, as qualitatively depicted in Fig. <xref ref-type="fig" rid="F4"/>a. Thick anvils originating in high-IWP deep convective towers spread and thin towards IWP <inline-formula><mml:math id="M162" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 g m<sup>−2</sup>, while thinner cirrus (IWP <inline-formula><mml:math id="M164" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 g m<sup>−2</sup>) predominantly form via in situ ice nucleation. And while ice nucleation is very frequent and may play an important role in prolonging anvil lifetime <xref ref-type="bibr" rid="bib1.bibx45" id="paren.77"/>, dual-origin cirrus generally preserve convective-like properties and could, for simplicity, be merged with the anvil category.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Radiative importance of tropical cirrus based on their origin</title>
      <p id="d2e2930">Finally, by multiplying the cloud occurrence frequency in Fig. <xref ref-type="fig" rid="F6"/>c with the IWP-binned CRE in Fig. <xref ref-type="fig" rid="F4"/>b we estimate the radiative contribution of each of the three cirrus types, summarized in Table <xref ref-type="table" rid="T1"/>. Anvil clouds are radiatively most important, accounting for more than 50 % of both LW and SW CRE of all tropical cirrus. They dominate in the high IWP range, where SW CRE is stronger than LW CRE, leading to a net CRE of about <inline-formula><mml:math id="M166" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>8 W m<sup>−2</sup>. Dual-origin cirrus are aged anvils that dominate moderate IWP. They are still radiatively very important, leading to 40 % of the total LW and 30 % of the total SW CRE. Finally, in situ cirrus radiative contribution accounts only for 7 % of the total LW and SW CRE. The estimate of their SW CRE may be biased high due to the occurrence of lower-lying anvils or dual-origin clouds, likely leading to an overestimation of the SW CRE. A more detailed radiative analysis accounting for cloud overlap <xref ref-type="bibr" rid="bib1.bibx27" id="paren.78"><named-content content-type="pre">see, e.g.,</named-content></xref> is left for future work. We also note that the model-derived in situ cirrus CREs are comparable to satellite-derived CRE for TTL cirrus <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx74 bib1.bibx10" id="paren.79"/>.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e2970">Model-derived cloud radiative effects (CREs) for cirrus types and their respective relative importance (in parentheses).</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>
         <oasis:entry colname="col1">Type of cirrus</oasis:entry>
         <oasis:entry colname="col2">LW CRE</oasis:entry>
         <oasis:entry colname="col3">SW CRE</oasis:entry>
         <oasis:entry colname="col4">NET CRE</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(fraction of total)</oasis:entry>
         <oasis:entry colname="col3">(fraction of total)</oasis:entry>
         <oasis:entry colname="col4">(fraction of total)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Anvil cirrus</oasis:entry>
         <oasis:entry colname="col2">20.1 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M169" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>27.7 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M171" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7.6 W m<sup>−2</sup></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(53.0 %)</oasis:entry>
         <oasis:entry colname="col3">(62.2 %)</oasis:entry>
         <oasis:entry colname="col4">(115.2 %)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dual-origin cirrus</oasis:entry>
         <oasis:entry colname="col2">16.1 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M174" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>13.9 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col4">1.2 W m<sup>−2</sup></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(39.8 %)</oasis:entry>
         <oasis:entry colname="col3">(31.1 %)</oasis:entry>
         <oasis:entry colname="col4">(<inline-formula><mml:math id="M177" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>18.5 %)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">In situ cirrus</oasis:entry>
         <oasis:entry colname="col2">2.7 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M179" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.9 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M181" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.2 W m<sup>−2</sup></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(7.2 %)</oasis:entry>
         <oasis:entry colname="col3">(6.6 %)</oasis:entry>
         <oasis:entry colname="col4">(3.3 %)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">38.9 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M184" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>44.5 W m<sup>−2</sup></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M186" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.6 W m<sup>−2</sup></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Evolution of tropical cirrus</title>
      <p id="d2e3314">The two passive tracers provide new insights into the distinct microphysical evolution pathways of detrained anvils and in situ cirrus. This perspective helps differentiate and track the life cycle of numerous cirrus clouds formed in our simulation, offering a more comprehensive understanding of cirrus evolution compared to a snapshot perspective. For detrained anvils, deep convection initially injects high concentrations (ICNC <inline-formula><mml:math id="M188" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.1 cm<sup>−3</sup>) of ice crystals spanning a broad size range, including relatively large particles (Fig. <xref ref-type="fig" rid="F7"/>b). The tracers allow for the study of how these crystals evolve over time: within the first 1–3 h following detrainment, there is a rapid decrease in both number concentration and size due to sedimentation, marking the most dynamic phase of anvil evolution (compare Fig. <xref ref-type="fig" rid="F7"/>b and c). Beyond this period, the evolution slows, with ice mass and number decreasing gradually as sedimentation and sublimation deplete the ice crystals (compare Fig. <xref ref-type="fig" rid="F7"/>c and d). Figure <xref ref-type="fig" rid="F7"/>e shows properties of clouds classified as in situ cirrus in Figs. <xref ref-type="fig" rid="F5"/>d and <xref ref-type="fig" rid="F6"/>.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e3351">Evolution of microphysical properties tracked with passive tracers. Panels <bold>(a)</bold> and <bold>(f)</bold> represent the mean time of air parcels after detrainment and in situ nucleation. The other panels present the joint distribution of ICNC and mass radius for the stated time after detrainment <bold>(b–e)</bold> or time after in situ ice nucleation <bold>(g–i)</bold>. The two contour lines encircle the peak probability distribution of particles under the selected conditions (detrainment <inline-formula><mml:math id="M190" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> solid lines; nucleation <inline-formula><mml:math id="M191" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> dashed lines). Isolines of IWC are plotted in gray. Since there are very few grid boxes at times after in situ nucleation of more than 30 h, we omit that panel.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f07.png"/>

        </fig>

      <p id="d2e3387">In contrast, freshly nucleated in situ cirrus ice crystals form at smaller sizes and intermediate concentrations (ICNC: 0.02–0.2 cm<sup>−3</sup>). Homogeneous nucleation events occasionally spike these concentrations but remain transient and thus are barely visible in our frequency figure. Since most of the in situ crystals are smaller than the freshly detrained ones (Fig. <xref ref-type="fig" rid="F7"/>g–i), sublimation may be a more important ice crystal sink than sedimentation. This may imply a greater sensitivity to atmospheric thermodynamic conditions, such as temperature and supersaturation fluctuations. Over time, in situ cirrus tend to lose ice number and size, approaching microphysical properties that often overlap with those of aged anvil cirrus. In summary, while both in situ and detrained cirrus retain distinct properties in the first 3–5 h, they become harder to distinguish in the later stages of their evolution.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Horizontal grid spacing dependence</title>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Impact on cloud properties</title>
      <p id="d2e3421">All results presented so far are based on simulations with a horizontal grid spacing of 1 km, which is sufficient to represent anvil cloud evolution and their influence on mesoscale circulation <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx39" id="paren.80"/>. To assess the impact of model grid spacing, we include additional simulations at coarser (4 km) and finer (250 m) grid spacings. The 4 km grid spacing aligns with current GSRMs, while the 250 m grid spacing approaches the level of convergence for deep convective updraft strength in idealized and realistic tropical convection setups <xref ref-type="bibr" rid="bib1.bibx66 bib1.bibx56 bib1.bibx89" id="paren.81"/>.</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e3432">Grid spacing dependence of <bold>(a)</bold> ice water content (IWC), <bold>(b)</bold> ice crystal number concentration (ICNC), and <bold>(c)</bold> ice radius (<inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">ice</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) in SAM with improved microphysics compared to aircraft observations (in yellow). All data are regridded to a horizontal resolution of 4 km. Plotted are median values (solid lines) and 90th percentile values (dotted lines).</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f08.png"/>

        </fig>

      <p id="d2e3461">The sensitivity of simulated ice properties to horizontal grid spacing is most pronounced for ICNC, which increases by nearly an order of magnitude from the 4 km to the 250 m simulation, a trend also evident in the 90th percentiles (Fig. <xref ref-type="fig" rid="F8"/>b). IWC exhibits grid spacing dependence only at temperatures warmer than <inline-formula><mml:math id="M194" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>60 °C, with higher values at finer grid spacings (Fig. <xref ref-type="fig" rid="F8"/>a). In contrast, ice crystal radius shows little sensitivity to grid spacing (Fig. <xref ref-type="fig" rid="F8"/>c). Moreover, SAM underestimates the variability in ice crystal size across all grid spacings and fails to reproduce the 90th percentile of observed particle size.</p>
      <p id="d2e3478">Overall, simulated microphysical properties at all grid spacings fall within the range of observations. However, the 4 km simulations underestimate both IWC and ICNC across most temperatures, but these biases are gone in the 1 km simulation. The ice number–radius perspective provides a clearer view of these improvements, particularly for the low ICNC bias of ice crystals smaller than 30 <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m (Fig. <xref ref-type="fig" rid="FA1"/>). Increased model resolution helps identify and understand the sources of model bias. The following section explores vertical wind variability, a likely contributor to these biases and a key factor in the reduced model bias observed for finer horizontal grid spacing.</p>
</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>Vertical wind variability</title>
      <p id="d2e3499">Ice formation is strongly influenced by the availability of water vapor and  the supersaturation with respect to ice, which depends on the dynamical environment. Of particular significance are the high-frequency fluctuations, which are approximately 10 times larger than the slow synoptic-scale motions <xref ref-type="bibr" rid="bib1.bibx3" id="paren.82"/>. Accurately capturing vertical wind variability is thus critical for modeling cirrus cloud formation and properties <xref ref-type="bibr" rid="bib1.bibx8" id="paren.83"/>.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e3510">Standard deviation of vertical wind from simulations with the improved SAM model and aircraft observations for <bold>(a)</bold> all data, <bold>(b)</bold> locations near active deep convection (brightness temperatures <inline-formula><mml:math id="M196" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 240 K), and <bold>(c)</bold> areas far from active deep convection (brightness temperatures <inline-formula><mml:math id="M197" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 240 K).</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f09.png"/>

        </fig>

      <p id="d2e3542">The biases in extreme ICNC values align with the model's underestimate of strong updrafts. This results in a vertical wind distribution that is too narrow and an underestimated standard deviation (Fig. <xref ref-type="fig" rid="F9"/>). Including a subgrid-scale vertical wind term (Sect. <xref ref-type="sec" rid="Ch1.S2.SS1.SSS5"/>) slightly improves the issue by increasing the standard deviation in vertical wind by 1 %–10 % depending on the model grid spacing (2 %–4 % for 1 km grid spacing). Nevertheless, the model performs well in representing the vertical wind variability near regions of deep convection at all three horizontal grid spacings (4 km, 1 km, 250 m) (Fig. <xref ref-type="fig" rid="F9"/>b).</p>
      <p id="d2e3552">However, updraft variability is strongly underestimated in regions far from deep convection (defined as areas with brightness temperature <inline-formula><mml:math id="M198" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 240 K) for simulations at 4 and 1 km grid spacing. The 250 m simulation shows better agreement with the measured winds below 14 km, where anvil cloud coverage is the largest, but underestimates wind variability in the TTL, resulting in a persistent ICNC bias for small ice crystals (Fig. <xref ref-type="fig" rid="FA1"/>c and f). This also likely contributes to larger microphysical biases in clouds far from active convection compared to those near convection (Fig. <xref ref-type="fig" rid="FA2"/>).</p>
      <p id="d2e3566">Power spectra in Fig. <xref ref-type="fig" rid="F10"/>, calculated following <xref ref-type="bibr" rid="bib1.bibx3" id="text.84"/>, provide further insight into updraft variability across different wavelengths of atmospheric disturbances. Variability at wavelengths larger than <inline-formula><mml:math id="M199" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1000 km corresponds to synoptic-scale motion, while convectively generated gravity waves dominate at wavelengths between 1 and 1000 km. Turbulent processes of various sources dominate at wavelengths below <inline-formula><mml:math id="M200" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 200 m.</p>

      <fig id="F10"><label>Figure 10</label><caption><p id="d2e3590">Power spectrum of updrafts from ATTREX (red) and POSIDON (blue) aircraft measurements, improved SAM model simulations (in grayscale), and a selection of GSRMs (in green). The dashed pink line represents the <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> slope, where <inline-formula><mml:math id="M202" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> is the wavenumber.</p></caption>
          <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f10.png"/>

        </fig>

      <p id="d2e3624">As already shown by Fig. <xref ref-type="fig" rid="F9"/>, wind variance increases with finer horizontal grid spacing. While the 4 and 1 km simulations substantially underestimate wind variance and power, the 250 m simulation reproduces the observed wind variability for wavelengths between 1 and 10 km. Moreover, all SAM simulations under-represent variability at scales larger than <inline-formula><mml:math id="M203" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 km, which are better captured by GSRMs at horizontal grid spacings of about 4 km. Vertical wind spectra from models flatten out at the model effective resolution, which varies across the different GSRMs and SAM simulations shown in Fig. 10. Aircraft observations are most suitable for investigating vertical wind variability <inline-formula><mml:math id="M204" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 10 km and flatten out between 10 and 100 km, possibly due to a smaller signal-to-noise ratio, limited data, and/or changing atmospheric dynamics. Gravity waves, originating from deep convective updrafts, propagate hundreds to thousands of kilometers from their source. However, the narrow channel setup of the SAM simulation may restrict the generation and/or propagation of these waves compared to the real atmosphere or global GSRM simulations. While larger-scale updraft variability fosters favorable conditions for deep convection, its direct contribution to cloud formation is limited and of secondary importance for this study.</p>
</sec>
</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Discussion</title>
<sec id="Ch1.S6.SS1">
  <label>6.1</label><title>Ice microphysics</title>
      <p id="d2e3659">The representation of ice microphysics remains a limitation in this study, despite notable improvements achieved with the described computationally inexpensive changes. This reflects the broader challenge of accurately modeling ice microphysics in high-resolution models, where computational constraints and incomplete process understanding often impose trade-offs.</p>
      <p id="d2e3662">For example, the adopted <xref ref-type="bibr" rid="bib1.bibx97" id="text.85"/> scheme for ice nucleation, originally designed for coarse climate models, relies on empirical fits to parcel model simulations. While effective, this approach may not capture all the details of ice nucleation at cloud-resolving scales accurately. Future work could address this by implementing a physics-based nucleation scheme, such as the novel <xref ref-type="bibr" rid="bib1.bibx63" id="text.86"/> scheme, and incorporate a resolution-aware parameterization of wind variability to complement the model-resolved wind variability – similar to approaches being developed for liquid clouds <xref ref-type="bibr" rid="bib1.bibx92" id="paren.87"/>.</p>
      <p id="d2e3674">Secondary ice formation may be another area of interest, given that recent studies have shown that it plays a large role even at temperatures as cold as <inline-formula><mml:math id="M205" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>50 °C <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx53 bib1.bibx91" id="paren.88"/>. Incorporating secondary ice processes into SAM-P3 currently requires additional computationally expensive ice modes, but their inclusion could enhance the model’s ability to simulate anvil cloud evolution. Finally, increased model complexity brings additional challenges, often resulting in hindered process understanding, increased uncertainty, or the problem of equifinality <xref ref-type="bibr" rid="bib1.bibx90" id="paren.89"><named-content content-type="pre">refer to</named-content><named-content content-type="post">and references therein for a complete outline of these issues</named-content></xref>.</p>
      <p id="d2e3694">An alternative approach could involve introducing ice tracers for each ice nucleation process, similar to those used by <xref ref-type="bibr" rid="bib1.bibx79" id="text.90"/>. This would allow for a more accurate classification of cirrus cloud origins without relying on arbitrary thresholds. Although this would increase the model's computational costs, the expense is substantially lower than doubling the model's resolution, making it a viable path forward.</p>
</sec>
<sec id="Ch1.S6.SS2">
  <label>6.2</label><title>Resolution and Lagrangian approaches</title>
      <p id="d2e3708">Our findings confirm that increasing horizontal resolution improves the representation of atmospheric updrafts at scales crucial for cirrus cloud formation. However, this improvement comes at a large cost: a 4-fold increase in horizontal resolution results in a 16-fold increase in data output and a 20–25-fold increase in computational demand. This highlights the importance of exploring less computationally expensive alternatives to improve model performance. For instance, we achieved a large reduction in bias for ice cloud properties through straightforward modifications to the ice microphysics without appreciable increases in computational cost.</p>
      <p id="d2e3711">Encouragingly, the simulations at a typical GSRM grid spacing of 3–5 km show signs of convergence in updraft variability near active deep convection when compared to updraft observations averaged to same grid spacing, suggesting that the generation of convective gravity waves is reasonably well captured (note that model-simulated updraft variability still increases between simulations of 4 and 1 km grid spacing). However, these waves may not propagate far enough, as indicated by the underestimated updraft variance across all tested horizontal resolutions. Power spectral analyses indicate that grid spacings slightly finer than 250 m may sufficiently capture the scales of motion relevant for cirrus formation and maintenance. This is also the grid spacing at which convergence in cloud macroscopic variables and ice sources and sinks has been observed <xref ref-type="bibr" rid="bib1.bibx51" id="paren.91"/>.</p>
      <p id="d2e3717">Vertical resolution also plays a crucial role. Previous studies demonstrate its influence on tropical cirrus properties and their responses to global warming <xref ref-type="bibr" rid="bib1.bibx87" id="paren.92"/>, as well as convective self-aggregation <xref ref-type="bibr" rid="bib1.bibx58" id="paren.93"/>. We also perform a sensitivity test that halves the vertical grid spacing from 200 to 100 m, leading to the same model improvement as an increase in horizontal grid spacing from 1 km to 250 m (Fig. <xref ref-type="fig" rid="FA1"/>g). Doubling the vertical resolution in the upper troposphere increases the computational costs by only a factor of 2.5. This suggests that refining vertical resolution could be a more computationally efficient way to improve model updraft variability than increases in horizontal resolution, and it should be thoroughly investigated in future studies.</p>
      <p id="d2e3728">Nevertheless, higher resolution alone cannot address all challenges. Processes at microscopic scales, particularly the interactions between ice microphysics and radiation, remain poorly resolved. Efforts to improve ice microphysics in GSRMs are scarce <xref ref-type="bibr" rid="bib1.bibx94" id="paren.94"><named-content content-type="pre">e.g.,</named-content></xref> yet essential for advancing understanding of tropical cirrus evolution. Our study highlights the importance of accurately modeling cirrus evolution, a key factor in determining their microphysical properties and radiative effects.</p>
      <p id="d2e3737">Passive tracers, as demonstrated in this study, are a valuable tool for tracking the evolution of ice clouds in models. Although these tracers are purely computational, stable water isotopes, measurable in situ or via satellite, could serve as real-world tracer analogs, offering insights into the pathways of ice cloud evolution <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx28" id="paren.95"/>. Trajectory analysis, such as that in <xref ref-type="bibr" rid="bib1.bibx104" id="text.96"/>, can provide additional clarity on cirrus cloud evolution. Based on their analysis of cloud source and sink processes along trajectories, they proposed three cirrus cloud life cycles with distinct radiative signatures. In contrast, our analysis focused only on ice cloud properties. However, by enabling the 3D output of microphysical process rates, we could easily perform a similar process-rate analysis that would provide additional clarity on the two tropical cirrus formation pathways. Future work could explore a consistent integration of these approaches in models and observations, linking simulations with aircraft measurements as in <xref ref-type="bibr" rid="bib1.bibx31" id="text.97"/> and possibly satellite retrievals as well, in an effort to improve process understanding.</p>
</sec>
</sec>
<sec id="Ch1.S7" sec-type="conclusions">
  <label>7</label><title>Conclusions</title>
      <p id="d2e3758">The purpose of this work is twofold: first, we demonstrate the usefulness of passive tracers to track the evolution of cirrus microphysical properties. Second, we show that minor changes to cloud microphysics substantially improve the simulation of tropical cirrus at cloud-resolving scales with a minimal change in computational expense.</p>
      <p id="d2e3761">Our work reveals a simple, numerically inexpensive recipe that substantially improves simulations of tropical cirrus in the SAM cloud-resolving model. Although the recipe was tested only in this specific model, we believe that its elements can be applied to a wider range of models with little or no increase in computational load. The recipe is as follows. <list list-type="order"><list-item>
      <p id="d2e3766">Remove all nonphysical microphysical limits <xref ref-type="bibr" rid="bib1.bibx6" id="paren.98"><named-content content-type="pre">particularly the commonly used ICNC limits, see, e.g.,</named-content></xref>.</p></list-item><list-item>
      <p id="d2e3775">Ensure that freezing (or any other) parameterizations do not operate outside of their stated range of validity (e.g., limit mixed-phase freezing parameterizations to mixed-phase conditions).</p></list-item><list-item>
      <p id="d2e3779">If not present, add a nucleation scheme that is active under cirrus conditions, e.g., homogeneous nucleation of water solution droplets or a combination of homogeneous and heterogeneous nucleation.</p></list-item></list></p>
      <p id="d2e3782">We show that anvil clouds remain radiatively important hours after detrainment, despite substantial spreading, thinning, and advection by synoptic and/or mesoscale motion. Therefore, an evolutionary perspective on tropical cirrus is crucial for constraining their radiative impacts. To better capture this evolution, we implemented two passive tracers in the model: <list list-type="order"><list-item>
      <p id="d2e3787">A detrainment tracer, useful for tracking the evolution of anvil clouds.</p></list-item><list-item>
      <p id="d2e3791">An ice nucleation tracer, useful for tracking the evolution of in situ cirrus.</p></list-item></list></p>
      <p id="d2e3794">Tracers also provide important insights into the climatology of cirrus cloud formation. We find that in situ cirrus dominate under colder conditions (<inline-formula><mml:math id="M206" display="inline"><mml:mo lspace="0mm">&gt;</mml:mo></mml:math></inline-formula> 70 % of cirrus at temperatures below <inline-formula><mml:math id="M207" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>70 °C) and are prevalent at low ice water path values (IWP <inline-formula><mml:math id="M208" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 g m<sup>−2</sup>). Despite their low optical depth, in situ cirrus account for 7 % of the total tropical cirrus TOA CRE. However, our estimates are sensitive to the specific classification criteria used for cloud origin and lack considerations of cloud overlap, highlighting the need for more refined approaches.</p>
      <p id="d2e3831">Our results also suggest that simulations with horizontal grid spacing of 250 m can reproduce the observed power spectrum of vertical wind, capturing the scales of motion relevant for cirrus formation and maintenance, particularly below 14 km.</p>
      <p id="d2e3834">More broadly, our work highlights a significant limitation in existing global climate and cloud-resolving models, many of which fail to accurately simulate tropical cirrus evolution <xref ref-type="bibr" rid="bib1.bibx109 bib1.bibx106 bib1.bibx4" id="paren.99"/>. These biases pose difficulties for understanding the processes that occur between the formation of tropical cirrus and their dissipation <xref ref-type="bibr" rid="bib1.bibx40" id="paren.100"/>, leaving large uncertainties in the associated climate feedbacks <xref ref-type="bibr" rid="bib1.bibx96" id="paren.101"/>. Additionally, the interaction of ice crystals with radiation, which influences atmospheric temperatures, can alter cloud lifetimes <xref ref-type="bibr" rid="bib1.bibx39" id="paren.102"/>, regional climate <xref ref-type="bibr" rid="bib1.bibx107" id="paren.103"/>, and hydrological sensitivity <xref ref-type="bibr" rid="bib1.bibx80" id="paren.104"/>, with potentially important impacts as high clouds shift upward in a warming climate <xref ref-type="bibr" rid="bib1.bibx108 bib1.bibx41" id="paren.105"/>. By addressing these gaps, we have demonstrated that our improved SAM model is now equipped to explore these feedbacks with greater confidence.</p>
      <p id="d2e3859">Building on the advancements presented here, future studies should focus on reducing uncertainties in the fundamental understanding and modeling of cirrus properties and their evolution in the present and in a warmer climate. The combination of passive tracers, improved microphysics, and high-resolution modeling provides a promising pathway to achieve this goal.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>Additional model evaluation</title>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e3876">Model grid spacing dependence in the ICNC–<inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">ice</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> space. Probability density function of ice properties for clouds at <inline-formula><mml:math id="M211" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M212" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M213" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C. The upper row <bold>(a–c)</bold> shows aircraft observations averaged for consistency to 4 km, 1 km, and 250 m grids. Panels <bold>(d)</bold>–<bold>(f)</bold> show modeled properties at different horizontal grid spacings. Panel <bold>(g)</bold> shows modeled properties at 1 km horizontal grid spacing and doubled upper-tropospheric vertical grid spacing (to about 100 m). The number represents a two-dimensional total variation distance of model data compared to aircraft observations (the smaller, the better). Observations are limited or not available in the shaded area.</p></caption>
        
        <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f11.png"/>

      </fig>

      <fig id="FA2"><label>Figure A2</label><caption><p id="d2e3934">Probability density function of ice properties near (brightness temperature <inline-formula><mml:math id="M214" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 240 K) and far from active convection (brightness temperature <inline-formula><mml:math id="M215" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 240 K) at <inline-formula><mml:math id="M216" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40 °C <inline-formula><mml:math id="M217" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M218" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M219" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M220" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>60 °C. The number on the right is the dimensional total variation distance of model data compared to aircraft observations (the smaller, the better). Observations are limited or not available in the shaded area.</p></caption>
        
        <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f12.png"/>

      </fig>

<fig id="FA3"><label>Figure A3</label><caption><p id="d2e3999">Number of measurement hours for ICNC data. The measurement frequency is 1 Hz, so 1 h corresponds to 3600 measurements. The <inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">ice</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> data have the same number of flight hours, while there are slightly more IWC data.</p></caption>
        <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f13.png"/>

      </fig>

</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>Additional IWP-binned perspective on model output and satellite observations</title>

      <fig id="FB1"><label>Figure B1</label><caption><p id="d2e4029">Ice water path (IWP)-binned occurrence frequency. As in Fig. <xref ref-type="fig" rid="F4"/>a, but for IWP <inline-formula><mml:math id="M222" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.1 g m<sup>−2</sup>.</p></caption>
        <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f14.png"/>

      </fig>

<fig id="FB2"><label>Figure B2</label><caption><p id="d2e4062">Daytime-only ice water path (IWP)-binned cloud occurrence and radiative effect. The figure is similar to Fig. <xref ref-type="fig" rid="F4"/>, but with  model results for 13:00 and 14:00 LT only and  CCCM SW radiative fluxes computed as a difference between clear- and full-sky radiation.</p></caption>
        <graphic xlink:href="https://acp.copernicus.org/articles/25/9957/2025/acp-25-9957-2025-f15.png"/>

      </fig>

</app>

<app id="App1.Ch1.S3">
  <label>Appendix C</label><title>Computation of the maximum in situ nucleated ice water content in Fig. 3</title>
      <p id="d2e4081">The maximum ice water content from in situ homogeneous ice nucleation, <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IWC</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is derived following <xref ref-type="bibr" rid="bib1.bibx82" id="text.106"/>. The critical ice supersaturation ratio for homogeneous ice nucleation is defined as <inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the water vapor pressure at the homogeneous nucleation threshold and <inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the saturation vapor pressure over ice, computed from the temperature-dependent formulation of <xref ref-type="bibr" rid="bib1.bibx86" id="text.107"/>.</p>
      <p id="d2e4181">We approximate <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> using the expression from <xref ref-type="bibr" rid="bib1.bibx69" id="text.108"/> as reformulated by <xref ref-type="bibr" rid="bib1.bibx73" id="text.109"><named-content content-type="post">Eq. 7.33</named-content></xref>:

          <disp-formula id="App1.Ch1.S3.E8" content-type="numbered"><label>C1</label><mml:math id="M229" display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.305</mml:mn><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">sw</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">sw</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the saturation vapor pressure over liquid water based on <xref ref-type="bibr" rid="bib1.bibx86" id="text.110"/>. The density of water vapor <inline-formula><mml:math id="M231" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> is calculated from the ideal gas law <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M233" display="inline"><mml:mi>e</mml:mi></mml:math></inline-formula> is the water vapor pressure, <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the specific gas constant for water vapor, and <inline-formula><mml:math id="M235" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the temperature.</p>
      <p id="d2e4339">The maximum ice water content formed by homogeneous nucleation is then the excess vapor density above ice saturation:

          <disp-formula id="App1.Ch1.S3.E9" content-type="numbered"><label>C2</label><mml:math id="M236" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IWC</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e4424">Using <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, we obtain

          <disp-formula id="App1.Ch1.S3.E10" content-type="numbered"><label>C3</label><mml:math id="M238" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IWC</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">si</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e4534">This expression shows that the excess supersaturation (<inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) determines the amount of vapor available for depositional growth after a homogeneous nucleation event. The higher the supersaturation, the greater the potential for ice crystal growth and thus the higher the <inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IWC</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. A similar approach can be used to compute IWC at any fixed supersaturation threshold (e.g., <inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> or RH<sub>ice</sub> <inline-formula><mml:math id="M243" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 120 %, a threshold often associated with heterogeneous ice nucleation triggered by effective ice-nucleating particles) by substituting <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hom</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> with the desired value supersaturation threshold.</p>
</app>
  </app-group><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d2e4613">Data, plotting, and post-processing scripts, as well as key (modified) bits of the SAM model Fortran code, are available on Zenodo at <ext-link xlink:href="https://doi.org/10.5281/zenodo.15785518" ext-link-type="DOI">10.5281/zenodo.15785518</ext-link> <xref ref-type="bibr" rid="bib1.bibx32" id="paren.111"/>. The complete SAM model code is available for download at <uri>https://you.stonybrook.edu/somas/sam/</uri> (last access: 1 September 2025). Satellite data from the A-Train Integrated CALIPSO, CloudSat, CERES, and MODIS Merged Product Release B1 (CCCM) were obtained from <uri>https://search.earthdata.nasa.gov</uri> (last access: 20 February 2024). The DARDAR data are available at <uri>http://www.icare.univ-lille1.fr/</uri> (last access: 10 August 2024). The 2C-ICE data are available at <uri>https://www.cloudsat.cira.colostate.edu</uri> (last access: 9 November 2024). The POSIDON, ATTREX, and CONTRAST data used in this study are available at <uri>https://doi.org/10.34730/266CA2A41F4946FF97D874BFA458254C</uri> <xref ref-type="bibr" rid="bib1.bibx72" id="paren.112"/>. The original campaign data can be retrieved at <uri>https://espoarchive.nasa.gov/archive/browse/posidon/WB57</uri> (last access: 10 December 2024) (POSIDON), <uri>https://espo.nasa.gov/attrex/content/Welcome_to_the_ESPO_Data_Archive</uri> (last access: 10 December 2024) (ATTREX), and <uri>https://www2.acom.ucar.edu/contrast</uri> (last access: 10 December 2024) (CONTRAST). The complete model output is available for download at <uri>https://hdl.handle.net/11353/10.2150070</uri> <xref ref-type="bibr" rid="bib1.bibx34" id="paren.113"/>.</p>
  </notes><notes notes-type="videosupplement"><title>Video supplement</title>

      <p id="d2e4660">A Video Supplement showing the evolution of clouds in part of the model domain between days 22.75 and 27.75 is available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.15497521" ext-link-type="DOI">10.5281/zenodo.15497521</ext-link> <xref ref-type="bibr" rid="bib1.bibx33" id="paren.114"/>. The panels visualize quantities shown in Fig. <xref ref-type="fig" rid="F5"/>.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e4674">BG conceived the study, implemented code changes, conducted model simulations, processed the majority of the data, and contributed to writing and editing. RA processed part of the data and contributed to writing and editing. AV contributed to writing and editing. MK acquired and processed data and contributed to writing and editing. PNB implemented code changes, provided technical support, and contributed to writing and editing.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e4680">At least one of the (co-)authors is a member of the editorial board of <italic>Atmospheric Chemistry and Physics</italic>. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e4690">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e4696">This material is based upon work supported by the National Science Foundation under grant no. OISE-1743753 (Peter N. Blossey).  We would also like to acknowledge high-performance computing support from Cheyenne (<ext-link xlink:href="https://doi.org/10.5065/D6RX99HX" ext-link-type="DOI">10.5065/D6RX99HX</ext-link>, <xref ref-type="bibr" rid="bib1.bibx19" id="altparen.115"/>) and Derecho (<ext-link xlink:href="https://doi.org/10.5065/qx9a-pg09" ext-link-type="DOI">10.5065/qx9a-pg09</ext-link>, <xref ref-type="bibr" rid="bib1.bibx20" id="altparen.116"/>) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. The authors would like to thank Bernd Kärcher for useful comments on early work leading to this paper. We acknowledge the use of several AI tools to improve the language and clarity  of an earlier version of this paper. We thank the reviewers for their constructive comments that improved the paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e4713">This project has received funding from the European Union's Horizon 2020 research and innovation program under the   Marie Skłodowska-Curie Actions (grant agreement nos. 101025473 and  101151941) and the National Science Foundation (grant no. OISE-1743753).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e4719">This paper was edited by Shaocheng Xie and reviewed by four anonymous referees.</p>
  </notes><ref-list>
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