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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article">
  <front>
    <journal-meta><journal-id journal-id-type="publisher">JECATS</journal-id><journal-title-group>
    <journal-title>Journal of Environmentally Compatible Air Transport System</journal-title>
    <abbrev-journal-title abbrev-type="publisher">JECATS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">J. Env. Com. Air Transp. Sys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">3053-9277</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/jecats-1-2-2026</article-id><title-group><article-title>Improving reanalysis weather for contrail validation by incorporating satellite observations</article-title><alt-title>Improving weather for contrail validation with satellite observations</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Geraedts</surname><given-names>Scott</given-names></name>
          <email>geraedts@google.com</email>
        <ext-link>https://orcid.org/0009-0001-6496-0153</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Sarna</surname><given-names>Aaron</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-8786-5581</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Rohs</surname><given-names>Susanne</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5473-2934</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Teoh</surname><given-names>Roger</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>McCloskey</surname><given-names>Kevin</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9967-4117</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Google Research, Mountain View, CA, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Institute of Energy and Climate Research 8 – Troposphere, Forschungszentrum Jülich GmbH, Jülich, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Civil and Environmental Engineering, Imperial College London, SW7 2A7, London, United Kingdom</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Scott Geraedts (geraedts@google.com)</corresp></author-notes><pub-date><day>10</day><month>July</month><year>2026</year></pub-date>
      
      <volume>1</volume>
      <elocation-id>2</elocation-id>
      <history>
        <date date-type="received"><day>2</day><month>April</month><year>2026</year></date>
           <date date-type="rev-request"><day>20</day><month>April</month><year>2026</year></date>
           <date date-type="rev-recd"><day>17</day><month>June</month><year>2026</year></date>
           <date date-type="accepted"><day>26</day><month>June</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Scott Geraedts et al.</copyright-statement>
        <copyright-year>2026</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026.html">This article is available from https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026.html</self-uri><self-uri xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026.pdf">The full text article is available as a PDF file from https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e132">Aviation-induced condensation trails (contrails) contribute significantly to anthropogenic radiative forcing. While navigational contrail avoidance has been proposed as a strategy to mitigate this climate impact, the operational viability of such maneuvers relies on the ability to verify their efficacy. Current verification methodologies often employ contrail models (such as CoCiP) driven by reanalysis weather data; however, these assessments are limited by the variable fidelity of the underlying meteorological datasets. In this work, we address this uncertainty by leveraging geostationary satellite observations to refine reanalysis estimates for specific contrail events. We demonstrate that this approach significantly improves the agreement between reanalysis data and in-situ measurements obtained from the IAGOS program, thereby offering a more robust framework for evaluating avoidance strategies.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e144">While the carbon dioxide emitted by aircraft is a well-known driver of global warming, recent research indicates that persistent contrails may have a comparable net impact on climate change. These “contrail-cirrus” clouds trap outgoing longwave radiation that would otherwise escape into space, potentially leading to a net warming effect <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx24" id="paren.1"/>.</p>
      <p id="d2e150">Navigational contrail avoidance has emerged as a high-potential climate solution because a vast majority of the warming is caused by a small fraction (roughly 2 % to 10 %) of flights that traverse specific atmospheric regions of high humidity <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx37 bib1.bibx38" id="paren.2"/>. By slightly altering the flight path or altitude of these specific flights to avoid ice-supersaturated regions, the aviation industry could potentially eliminate a large fraction of its non-CO<sub>2</sub> climate impact <xref ref-type="bibr" rid="bib1.bibx10" id="paren.3"/>.</p>
      <p id="d2e168">One challenge to navigational contrail avoidance is that current weather models do not always predict the exact location and depth of ice-supersaturated layers with the accuracy required for flight planning <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx1 bib1.bibx39" id="paren.4"/>. If navigational contrail avoidance is to be adopted, it must first be demonstrated that it actually leads to a reduction in persistent contrail formation. For this reason verification systems, which can answer the question “did this flight make a contrail”, are essential.</p>
      <p id="d2e174">There are two broad categories of methods which can be used to determine if a flight made a contrail. Observational methods try to visualize the contrail directly, for example using ground-based cameras or satellite imagery. Ground-based camera datasets such as <xref ref-type="bibr" rid="bib1.bibx19 bib1.bibx25" id="text.5"/> can struggle to identify contrails occluded by low-lying clouds and track persistent contrails beyond 30 min. They also are present only in some locations and so cannot see every flight. Low-earth-orbit satellites avoid some of these difficulties, but because they generally have revisit times longer than a contrail lifetime, they only see each contrail once. This makes them useful for determining whether a contrail has formed, but less useful for determining whether the contrail persists, which is a key problem since persistent contrails cause the bulk of the warming impact. Finally geostationary satellites such as GOES-ABI <xref ref-type="bibr" rid="bib1.bibx16" id="paren.6"/> or Meteosat Third Generation FCI <xref ref-type="bibr" rid="bib1.bibx8" id="paren.7"/> have excellent coverage and since they take images every few minutes can confirm that a contrail is persistent. But their relatively poor (2 km) spatial resolution makes it difficult to see freshly formed and optically thin contrails <xref ref-type="bibr" rid="bib1.bibx7 bib1.bibx9" id="paren.8"/>. It also means they can usually only see contrails 20–30 min after they are first formed, making attributing those contrails to a specific flight difficult <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx30" id="paren.9"/>.</p>
      <p id="d2e193">Alternatively, weather-based methods of determining whether a persistent contrail formed first determine what the weather was at the flight's location, and then apply a physical model to determine if the flight made a contrail. To a first approximation the physical model is a combination of the Schmidt-Appleman criterion <xref ref-type="bibr" rid="bib1.bibx31 bib1.bibx3 bib1.bibx32" id="paren.10"/> and ice supersaturation, though more complicated models are also possible such as the Contrail Cirrus Prediction Model (CoCiP) <xref ref-type="bibr" rid="bib1.bibx33" id="paren.11"/> and the  Aircraft Plume Chemistry, Emissions, and Microphysics Model (APCEMM) <xref ref-type="bibr" rid="bib1.bibx11" id="paren.12"/>. The main drawback of such approaches is the difficulty in getting accurate weather. In a small number of cases in-situ measurements (for example aircraft-based measurements or radiosondes) are available, but such measurements are too sparse for large-scale validation or to use as inputs to the above models. Furthermore such models must always be approximations to the physics of the system, in part because of the constraint of needing to be computed quickly enough to run on large numbers of points, and the simplified models can lead to inaccurate warming estimates <xref ref-type="bibr" rid="bib1.bibx2" id="paren.13"/>.</p>
      <p id="d2e208">In this work we combine the observational and weather-based approaches to create a method of contrail attribution which is better than either on their own. Our method weights weather ensemble members based on whether or not they agree with geostationary satellite observations. Our method produces a “contrail score” which can be used to assess whether persistent contrail forming conditions are present. We show that this contrail score agrees better with in-situ measurements than other methods of assessing contrail formation conditions based on weather data alone. We use our hybrid approach to produce a warming estimate for each flight which agrees in aggregate with warming estimates using weather data.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Summary of method</title>
      <p id="d2e226">Figure <xref ref-type="fig" rid="F1"/> is a summary of our method. Given multiple weather ensembles, we compare each ensemble member to contrail observations. The ensemble members which agree with the contrail observations are then given a higher weight than the ensembles which do not.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e233">An example of the method used in this work. The red dot is the location of an in-situ measurement which shows ice supersaturation, and the yellow region denotes the locations where the given ensemble member predicts ice supersaturation at the time and altitude of the measurement. The satellite image is a false color image taken 30 min after the in-situ measurement, using the infrared bands as described in <xref ref-type="bibr" rid="bib1.bibx26" id="paren.14"/>, with a detected contrail marked with the black line. Because our method applies a higher weight to “Ensemble 0”, the location of the contrail formation region it predicts better matches the observed contrail, and this leads to better agreement with the in-situ measurement.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f01.jpg"/>

        </fig>

      <p id="d2e245">For each in-situ measurement, we find all the flight waypoints within a threshold in distance, altitude difference and time difference. If the majority of those waypoints were found to match a contrail we label this in-situ measurement as observed <inline-formula><mml:math id="M2" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> True, otherwise we label it observed=False. We then linearly interpolate the weather ensemble data to the location of the in-situ measurement.</p>
      <p id="d2e256">We then compute the “contrail score” (<inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), a unitless number between <inline-formula><mml:math id="M4" display="inline"><mml:mn mathvariant="normal">0</mml:mn></mml:math></inline-formula> and <inline-formula><mml:math id="M5" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> where a higher score indicates a higher likelihood that a contrail formed, from this weather and observational data. This is similar to <xref ref-type="bibr" rid="bib1.bibx17" id="text.15"/>, who use a contrail score which is the fraction of ensemble members predicting persistent contrail formation conditions, here denoted <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. For our contrail score, we will combine the observations and ensemble weather forecasts using the following formula:

            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M7" display="block"><mml:mrow><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="{" close=""><mml:mtable class="cases" rowspacing="0.2ex" columnspacing="1em" columnalign="left left" framespacing="0em"><mml:mtr><mml:mtd><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">FPR</mml:mi><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant="normal">observed</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">True</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="normal">FPR</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant="normal">observed</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">False</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">FPR</mml:mi></mml:mrow></mml:math></inline-formula> are the true/false positive rate of the observation system. Equation (<xref ref-type="disp-formula" rid="Ch1.E1"/>) is just Bayes theorem where <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is “prior probability”, (the initial guess at the probability that a persistent contrail will form), and <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">FPR</mml:mi></mml:mrow></mml:math></inline-formula> are the probabilities of observing a contrail on a flight which did/did not actually create a contrail.  Another way to interpret the model scores is in the context of the weights in a weighted average over ensembles. The model score is the sum of the weights of all the ensemble members that predict a contrail. For <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> this is just the fraction of ensembles predicting contrails, but for <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> these ensembles get lower or higher weights depending on whether a contrail is observed.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Data</title>
      <p id="d2e524">Numerical weather data comes from the European Centre for Medium-Range Weather Forecasts (ECMWF). We studied both the forecast (IFS) and reanalysis (ERA5) <xref ref-type="bibr" rid="bib1.bibx18" id="paren.16"/> product, and both nominal and ensemble products. The nominal and ERA5 ensemble data use the “model-level” weather products which have a vertical resolution of <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> hPa while for the IFS ensembles due to bandwidth constraints when downloading the data we use the “pressure-level” data which has a resolution of <inline-formula><mml:math id="M14" display="inline"><mml:mn mathvariant="normal">25</mml:mn></mml:math></inline-formula> hPa. Resolutions are <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.25</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> for the ERA5 nominal weather, <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.5</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> for the ERA5 ensemble weather, and <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.1</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> for the IFS weather. The ERA5 ensemble weather is at a time resolution of 3 h while all other products have a 1 h resolution. In order to compensate for the well-known dry bias <xref ref-type="bibr" rid="bib1.bibx15" id="paren.17"/> of ECMWF high-altitude humidity data, we scale up the humidity field by dividing by <inline-formula><mml:math id="M18" display="inline"><mml:mn mathvariant="normal">0.97</mml:mn></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx20" id="paren.18"/>.</p>
      <p id="d2e591">In-situ weather measurements are from the In-Service Aircraft for a Global Observing System (IAGOS; <xref ref-type="bibr" rid="bib1.bibx5" id="altparen.19"/> <uri>https://www.iagos.org/</uri>, last access: 30 January 2026). IAGOS uses instruments mounted on commercial aircraft to collect a variety of atmospheric data, we used the temperature and specific humidity measurements. The time and spatial resolution of IAGOS measurements is far greater than that of our numerical weather data. We therefore grouped the measurements into bins based on the altitude (rounded to the nearest flight level), time (rounded to the nearest hour), latitude and longitude (rounded to the nearest 0.25°) and randomly selected one measurement from each bin.</p>
      <p id="d2e600">Contrail observations are obtained following the methods of <xref ref-type="bibr" rid="bib1.bibx12" id="text.20"/> and <xref ref-type="bibr" rid="bib1.bibx30" id="text.21"/>, summarized here. We first automatically detect contrails in GOES-ABI imagery <xref ref-type="bibr" rid="bib1.bibx26" id="paren.22"/>. We then obtain flight waypoints from ADS-B data licensed from <uri>https://flightaware.com</uri> (last access: January 2026). We advect the waypoints using ERA5 wind data with a Runge Kutta 3D method, and additionally sediment downwards using the terminal velocity of an estimated ice crystal size average. Finally we compare the locations of the advected flights to the locations of the detected contrails. If these are close enough over multiple frames (details in <xref ref-type="bibr" rid="bib1.bibx30" id="altparen.23"/>) we say that the flight waypoints are observed to be matching a contrail. Note that the advection is uncertain because the wind data used is imperfect and contains errors of around 12.4 km h<sup>−1</sup> <xref ref-type="bibr" rid="bib1.bibx36" id="paren.24"/>; the attribution algorithm accounts for this when it sets the tolerances of what flights can match an observed contrail.</p>
      <p id="d2e634">The data used in this work was in the region shown in Fig. <xref ref-type="fig" rid="F2"/>, covering the terrestrial Americas. We only have ADS-B data from terrestrial receivers so flight waypoints away from land are not included. The date range covered is 4 April to 31 December 2019 and 1 January to 31 December 2024. Our method has some tunable parameters, as defined below. We split our dataset by day of year and set aside every sixth day as the training set. The results in this work are evaluated on the remainder of the dataset. The complete dataset contains approximately 90 000 data points.</p>

      <fig id="F2"><label>Figure 2</label><caption><p id="d2e642">The region covered in this study is contained in the blue box.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f02.png"/>

        </fig>

      <p id="d2e651">Some of our results in this work come from simulating contrails using the pycontrails v0.60.3 <xref ref-type="bibr" rid="bib1.bibx35" id="paren.25"/> implementation of the CoCiP <xref ref-type="bibr" rid="bib1.bibx33" id="paren.26"/> contrails model. CoCiP is a parameterized physics model of contrail evolution which includes formation, initial downdraft, advection and sedimentation, continually reassessing whether the contrail persists or sublimates. We configured CoCiP using the Poll-Schumann model of aircraft performance data <xref ref-type="bibr" rid="bib1.bibx28" id="paren.27"/>, and we adapted the humidity inputs to CoCiP using the “histogram matching” method, which recalibrates the forecast humidity to better match in-situ observations <xref ref-type="bibr" rid="bib1.bibx27" id="paren.28"/>.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Metrics for comparing with in-situ measurements</title>
      <p id="d2e674">We will use the above contrail score to predict whether the in-situ measurements will show persistent contrail formation conditions. We define “persistent contrail formation conditions” as the Schmidt-Appleman criterion (SAC) being satisfied and ice supersaturation (ISS), i.e. the relative humidity over ice (RHi) <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula>.  The SAC requires aircraft information which is not in general defined for in-situ measurements, we used default values of 0.3 for overall efficiency and 1.25 for H<sub>2</sub>O emissions index. In Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/> we will also experiment with other contrail formation conditions.</p>
      <p id="d2e701">We assess the performance of different contrail verification systems by computing a contingency table like the one in Table <xref ref-type="table" rid="T1"/>. We then compute from the table “precision” <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:mo>≡</mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and “true positive rate” (TPR) <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mo>≡</mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. In the table <inline-formula><mml:math id="M24" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> can be any contrail score, such as <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. Since these contrail scores take continuous values we can create a curve on a precision/recall chart by varying the value of the threshold <inline-formula><mml:math id="M27" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>. We will also consider the contrail score <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">nominal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> which is simply whether the nominal weather predicts contrail formation conditions, and <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the score based purely on observations. These scores are either <inline-formula><mml:math id="M30" display="inline"><mml:mn mathvariant="normal">0</mml:mn></mml:math></inline-formula> or <inline-formula><mml:math id="M31" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> so <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> is the only contingency table that we compute.</p>

<table-wrap id="T1"><label>Table 1</label><caption><p id="d2e839">Example of a contingency table used in this work. Here <inline-formula><mml:math id="M33" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> is a contrail score and <inline-formula><mml:math id="M34" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> is a threshold above which we say that the contrail score predicts persistent contrail formation conditions.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry namest="col2" nameend="col3" align="center">In-situ contrail </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center">formation conditions </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M35" display="inline"><mml:mi>Y</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M36" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>≥</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M38" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M39" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M41" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M42" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Defining distance thresholds</title>
      <p id="d2e982">We say an in-situ measurement has observed contrails whenever nearby flights are observed making contrails. If there are multiple nearby points  the observed value is set to true if any of the points have observed contrails. We now define what “nearby” means, in terms of thresholds in distance, altitude and time. To do this we do a grid search over these thresholds. The search covered 5–50 km in distance, 10–300 m in altitude and 120–3600 s in time. For each set of thresholds, we compute <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the contrail score based solely on whether an in-situ point has observed contrails, on the training dataset defined in Sect. <xref ref-type="sec" rid="Ch1.S2.SS2"/>. Note that smaller distance thresholds naturally have a harder time finding nearby flight observations. The largest thresholds found <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:mn mathvariant="normal">17</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">005</mml:mn></mml:mrow></mml:math></inline-formula> matching observations, we limited our results to thresholds that found at least <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mn mathvariant="normal">15</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula>. The results are shown in Fig. <xref ref-type="fig" rid="F3"/>.  From these results we chose a set of thresholds which give high TPR and precision. We choose the following thresholds:

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M46" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="normal">distance</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">altitude</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">time</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          A sensitivity analysis with some other choices of distance parameters is given in Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/>.</p>

      <fig id="F3"><label>Figure 3</label><caption><p id="d2e1084">Precision<inline-formula><mml:math id="M47" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>TPR for <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for a number of different distance thresholds. The starred point is the one we chose, corresponding to the thresholds in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>).</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Estimating performance of observation system</title>
      <p id="d2e1122">Equation (<xref ref-type="disp-formula" rid="Ch1.E1"/>) includes the true positive rate (TPR) and false positive rate (FPR) of our observation system. We estimate these parameters using synthetic data, using methods described in detail in <xref ref-type="bibr" rid="bib1.bibx30" id="paren.29"/> and summarized here. In a contingency table like Table <xref ref-type="table" rid="T1"/>, <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>≡</mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mi mathvariant="normal">FPR</mml:mi><mml:mo>≡</mml:mo><mml:mi>C</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>+</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, but the contingency table compares to synthetic data rather than in-situ measurements. We start by simulating contrail evolution using CoCiP for all flights in a region covering most of North America, for 28 d spread out over the interval April 2019–April 2020. We use the simulated optical properties of these contrails to make synthetic contrail masks which are qualitatively similar to the masks produced by our contrail detector. Then we use our attribution system to attribute the flight paths to the synthetic contrails. In this simulated environment we know which flights actually made contrails, so we can assess how well the contrail attribution system worked. In <xref ref-type="bibr" rid="bib1.bibx30" id="text.30"/> a fraction of flight waypoints were dropped to simulate aircraft without ADS-B transponders. This reduced <inline-formula><mml:math id="M51" display="inline"><mml:mi mathvariant="normal">TPR</mml:mi></mml:math></inline-formula> since those flights could never be attributed. In this work we do not drop these flights, which assumes the user of the contrail score has access to location data for all the flights they are interested in. Note that the CoCiP simulations used in SynthOpenContrails make no attempt include interactions between different contrails which may lead to an overestimation of contrail impacts in high contrail density areas <xref ref-type="bibr" rid="bib1.bibx29" id="paren.31"/>. Also note that the synthetic data is generated using different wind data than that used during flight attributions, so measurements of the overall system performance include the effects of imperfect wind data.</p>
      <p id="d2e1194">To get the true/false positive rate, we need to define which contrails the observation system should be trying to find. We define this as all contrails with a total long-wave energy forcing <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> J. Such contrails are responsible for <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mn mathvariant="normal">96</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> of the total warming in our synthetic dataset, so this is a reasonable group to target. With this definition we find

            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M54" display="block"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">33</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi mathvariant="normal">FPR</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.7</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e1258">Figure <xref ref-type="fig" rid="F4"/> shows the results of putting these values into Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>). Because <inline-formula><mml:math id="M55" display="inline"><mml:mi mathvariant="normal">FPR</mml:mi></mml:math></inline-formula> is small, a contrail observation is taken as strong evidence that a contrail is in fact formed. Therefore <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">observed</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is much higher than <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. On the other hand <inline-formula><mml:math id="M58" display="inline"><mml:mi mathvariant="normal">TPR</mml:mi></mml:math></inline-formula> is not that close to one, so a lack of contrail observations is only weak evidence that no contrail is actually present. Therefore <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>hybrid(not observed)</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is only slightly reduced compared to <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. The TPR number is per-contrail, but because more warming contrails are larger and longer-lived, they are more likely to be observed. The observation system captures <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mn mathvariant="normal">33</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> of contrails but those contrails account for <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:mn mathvariant="normal">42</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> of the long-wave energy forcing.</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e1356">Scores computed using Eqs. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) and (<xref ref-type="disp-formula" rid="Ch1.E3"/>). We can see that observing a contrail leads to a large increase in score compared to <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, while not observing a contrail leads to a small decrease in score.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f04.png"/>

        </fig>

      <p id="d2e1380">The <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mi mathvariant="normal">TPR</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">FPR</mml:mi></mml:mrow></mml:math></inline-formula> values used here should be treated as estimates only. Their computation is based on the assumptions present in CoCiP, as well as the assumptions in <xref ref-type="bibr" rid="bib1.bibx30" id="text.32"/> about how contrail properties translate into contrail detections. For example, in order to better match observed results <xref ref-type="bibr" rid="bib1.bibx30" id="text.33"/> removes some simulated contrail detections in areas of high contrail density. This naturally lowers the <inline-formula><mml:math id="M65" display="inline"><mml:mi mathvariant="normal">TPR</mml:mi></mml:math></inline-formula>. But our simulations do not model contrail-contrail interactions, which means that they are likely overestimating the contrail impact in these regions <xref ref-type="bibr" rid="bib1.bibx29" id="paren.34"/>. The <inline-formula><mml:math id="M66" display="inline"><mml:mi mathvariant="normal">TPR</mml:mi></mml:math></inline-formula> reported here assumes that our contrail simulations are correct, but the truth may be partway between the simulations and our synthetic observations. The metrics are also dependent on how the contrails detections at high contrail density are removed. <xref ref-type="bibr" rid="bib1.bibx30" id="text.35"/> used a method which qualitatively matched real contrail detections but did not analyze if other methods could achieve as good or better agreement with real images. A sensitivity analysis to the TPR<inline-formula><mml:math id="M67" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values is given in Sect. <xref ref-type="sec" rid="Ch1.S3.SS2"/>.</p>
</sec>
<sec id="Ch1.S2.SS6">
  <label>2.6</label><title>Estimating the energy forcing of contrails</title>
      <p id="d2e1440">In this section we define a contrail energy forcing estimate which takes into account both observations and ensemble weather. Energy forcing is the total radiative impact of the contrail. It is obtained by integrating the contrail radiative forcing over the width and length of the contrail, and over the contrail lifetime <xref ref-type="bibr" rid="bib1.bibx34" id="paren.36"/>. A reasonable way to estimate contrail energy forcing in the absence of observations is to simply simulate contrails using CoCiP for each member of the ensemble, and average the results. Since ensembles that don't predict contrail formation also predict zero forcing, this is equivalent to averaging the energy forcings of only the ensemble members that predicted contrail formation, and multiplying by <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. To generalize this we write

            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M69" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mi>X</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>X</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">contrail</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>X</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is any contrail score (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, etc) and <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">contrail</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the mean warming over all ensemble members which predict a contrail.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Including observations increases agreement with in-situ measurements</title>
      <p id="d2e1543">Figure <xref ref-type="fig" rid="F5"/> shows the precision and <inline-formula><mml:math id="M74" display="inline"><mml:mi mathvariant="normal">TPR</mml:mi></mml:math></inline-formula> for <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">nominal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, compared to the in-situ measurements, for the ERA5 and IFS weather products. <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> has the best agreement with the in-situ measurements.</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e1602">Precision<inline-formula><mml:math id="M79" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>TPR plot for different contrail scores. We see that <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> has the highest values, implying the best agreement with in-situ observations. This pattern is true for both <bold>(a)</bold> reanalysis and <bold>(b)</bold> forecast data. For the forecast data the (10) curves use 10 ensemble members while the (50) curves use 50.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f05.png"/>

        </fig>

      <p id="d2e1635">We see that <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> does not perform better than <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">nominal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, a surprising result which is different to that found by <xref ref-type="bibr" rid="bib1.bibx17" id="text.37"/> (which uses a different numerical weather product). We expect that this is because the ensemble weather has a coarser spatiotemporal resolution than the nominal weather.</p>
      <p id="d2e1664">For the forecast product where 50 ensemble members are available, we see that <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> performs better with more ensemble members. This is especially true at the high-TPR (TPR <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>) part of the curve, likely because more ensemble members increases the resolution of <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, making it better able to estimate the steep slope of <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">observed</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="F4"/>.</p>
      <p id="d2e1720">One might expect the ERA5 reanalysis weather to always agree better with in-situ measurements than the forecast, since the reanalysis has assimilated weather data up to the time of the reanalysis observation. This is true of <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">nominal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, but <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are more mixed, with ERA5 performing better at the high recall parts of the curve while IFS performs better at high precision. However since the forecast and reanalysis weather have different resolutions we cannot clearly separate the effects of just changing from reanalysis to forecast data.</p>
      <p id="d2e1756">Computing the “hybrid” prediction requires satellite imagery, flight ADS-B data and weather data. The satellite imagery is available around 10 min after the image is taken, and the flight ADS-B data are available in near-real time. The good performance of the forecast weather in Fig. <xref ref-type="fig" rid="F5"/>b means that in principle the results of the hybrid method could be made available almost immediately after the flight time, allowing immediate feedback for aircraft operators on whether contrails were formed.</p>
      <p id="d2e1761">We can summarize Fig. <xref ref-type="fig" rid="F5"/> by computing the area under the curves (AUC) of the different forecasts. We define <inline-formula><mml:math id="M90" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> as the difference in the AUC between two curves, computed only in the TPR range where the curve is present, and divided by the size of the TPR region. Another interpretation of <inline-formula><mml:math id="M91" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> is the average precision difference between the curves. In Table <xref ref-type="table" rid="T2"/> we show <inline-formula><mml:math id="M92" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> for a few different cases. Error bars are 2 standard deviations obtained by bootstrap sampling the dataset 1000 times. Since points at similar locations and times may be correlated, during the bootstrapping we kept all data points on the same day together rather than sampling each data point individually.</p>

<table-wrap id="T2"><label>Table 2</label><caption><p id="d2e1810"><inline-formula><mml:math id="M93" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> for a few different cases.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Method</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M94" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">ERA5</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.021</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.006</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">IFS (10 ensemble members)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.040</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.012</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">IFS (50 ensemble members)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.049</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.009</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d2e1918">We also experimented using only ice supersaturation (ISS) rather than the combination of the Schmidt-Appleman criterion and ice supersaturation (SAC <inline-formula><mml:math id="M98" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> ISS) as the definition of “persistent contrail formation conditions”. The improvement of <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is smaller for ISS-only than for SAC <inline-formula><mml:math id="M101" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> ISS. (<inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">AUC</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.008</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.010</mml:mn></mml:mrow></mml:math></inline-formula> for ISS-only).</p>
      <p id="d2e1979">This is because in cases where ISS predicts a persistent contrail but SAC is not satisfied, no contrail actually forms. When our observations (correctly) observe no contrail, if we defined “persistent contrail formation conditions” as ISS-only, then this correct observation <italic>hurts</italic> the performance of <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in our metrics. The improved benefit for using observations when evaluating SAC <inline-formula><mml:math id="M104" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> ISS is therefore simply because SAC <inline-formula><mml:math id="M105" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> ISS is better at predicting the formation of persistent contrails than ISS alone.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Insensitivity of results to hybrid parameters</title>
      <p id="d2e2018">We now perform a sensitivity analysis of our results to the TPR<inline-formula><mml:math id="M106" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>). The other values tested are shown in Table <xref ref-type="table" rid="T3"/>. The “Warming contrails” case is defined in Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>) and used in the other results in this work. The “Linearized contrails” case is comparing the matched contrails from the SynthOpenContrails dataset only to the synthetic contrails that survived the rasterization and linearization process in <xref ref-type="bibr" rid="bib1.bibx30" id="text.38"/>. The biggest difference compared to the “Warming contrails” case is that SynthOpenContrails intentionally removes contrail detections in high contrail density areas to match the results on real images. The “Warming contrails” case assumes that these high contrail density detections are missing in real images because the contrail detector cannot resolve them, while the “Linearized contrails” case assumes that if CoCiP correctly simulated contrail-contrail interactions these contrails would not have formed. The “All contrails” case compares the observation system to all the contrails predicted by CoCiP with nonzero energy forcing. Figure <xref ref-type="fig" rid="F6"/>a shows how <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> changes in the different cases. All cases have low TPR, so in all cases the effect of observing a contrail is to dramatically increase <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> relative to <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. Relative to the “warming contrails” case the linearized (all) contrails case has higher (lower) TPR, which leads to larger (smaller) decrease in <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> when a contrail is not observed. In particular the very small TPR in the “all contrails” case means that a non-observation barely changes the contrail score. Figure <xref ref-type="fig" rid="F6"/>b shows the impact on <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>'s agreement with in-situ measurements. We see that the agreement is not very sensitive to the choice of TPR<inline-formula><mml:math id="M112" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR, and outperforms <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in all cases.</p>

<table-wrap id="T3"><label>Table 3</label><caption><p id="d2e2119">Alternate TPR<inline-formula><mml:math id="M114" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values (replacing those in Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/> evaluated in Fig. <xref ref-type="fig" rid="F6"/>).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Case</oasis:entry>
         <oasis:entry colname="col2">TPR</oasis:entry>
         <oasis:entry colname="col3">FPR</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Warming contrails</oasis:entry>
         <oasis:entry colname="col2">33 %</oasis:entry>
         <oasis:entry colname="col3">0.7 %</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Linearized contrails</oasis:entry>
         <oasis:entry colname="col2">62 %</oasis:entry>
         <oasis:entry colname="col3">1.4 %</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">All contrails</oasis:entry>
         <oasis:entry colname="col2">14 %</oasis:entry>
         <oasis:entry colname="col3">0.1 %</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e2200"><bold>(a)</bold> Same as Fig. <xref ref-type="fig" rid="F4"/> but including the different choices of TPR<inline-formula><mml:math id="M115" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR outlined in Table <xref ref-type="table" rid="T3"/>. For each case solid lines show <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">observed</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and dashed lines show <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>hybrid(not observed)</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. <bold>(b)</bold> Same as Fig. <xref ref-type="fig" rid="F5"/>a, but the dashed lines show  different <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for the different cases in Table <xref ref-type="table" rid="T3"/>.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f06.png"/>

        </fig>

      <p id="d2e2271">We also perform a sensitivity analysis of our results to the thresholds in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>). The other values tested are shown in Table <xref ref-type="table" rid="T4"/>. The base case is the one used elsewhere in this work, in this analysis we include points with increased time, distance and altitude threshold which still perform relatively well in TPR and precision. Figure <xref ref-type="fig" rid="F7"/>a shows the TPR and precision of these cases on our training dataset. Figure <xref ref-type="fig" rid="F7"/>b shows the effect of the different thresholds on the various contrail scores. Note that different thresholds include different points in the evaluation dataset, so each of the cases is evaluated on a slightly different dataset. In all cases the pattern of <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">nominal</mml:mi></mml:msub><mml:mo>⪅</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is present. Figure <xref ref-type="fig" rid="F7"/>a shows the largest sensitivity to altitude, potentially because the supersaturated layers that drive contrail formation are often vertically thin.</p>

<table-wrap id="T4"><label>Table 4</label><caption><p id="d2e2313">Alternate thresholds evaluated in Fig. <xref ref-type="fig" rid="F7"/>.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Case</oasis:entry>
         <oasis:entry colname="col2">Distance</oasis:entry>
         <oasis:entry colname="col3">Altitude</oasis:entry>
         <oasis:entry colname="col4">Time</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Base case</oasis:entry>
         <oasis:entry colname="col2">15 km</oasis:entry>
         <oasis:entry colname="col3">20 m</oasis:entry>
         <oasis:entry colname="col4">300 s</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Less Distance</oasis:entry>
         <oasis:entry colname="col2">10 km</oasis:entry>
         <oasis:entry colname="col3">20 m</oasis:entry>
         <oasis:entry colname="col4">300 s</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Time</oasis:entry>
         <oasis:entry colname="col2">15 km</oasis:entry>
         <oasis:entry colname="col3">20 m</oasis:entry>
         <oasis:entry colname="col4">600 s</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">More Distance</oasis:entry>
         <oasis:entry colname="col2">50 km</oasis:entry>
         <oasis:entry colname="col3">20 m</oasis:entry>
         <oasis:entry colname="col4">300 s</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Altitude</oasis:entry>
         <oasis:entry colname="col2">15 km</oasis:entry>
         <oasis:entry colname="col3">50 m</oasis:entry>
         <oasis:entry colname="col4">300 s</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e2430"><bold>(a)</bold> Same as Fig. <xref ref-type="fig" rid="F3"/> but including the different thresholds in Table <xref ref-type="table" rid="T4"/>. The orange star shows the base case while the crosses show the other cases. <bold>(b)</bold> Same as Fig. <xref ref-type="fig" rid="F5"/>a, but covering the different cases shown in Table <xref ref-type="table" rid="T4"/>.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f07.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Comparison of aggregate energy forcing values</title>
      <p id="d2e2460">We can also compare the warming values from Eq. (<xref ref-type="disp-formula" rid="Ch1.E4"/>). We chose one day per month in the span June 2024–May 2025 and computed <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for all the flights in Fig. <xref ref-type="fig" rid="F2"/>. The resulting dataset (which is different from the dataset used in the rest of this work) contains <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">430</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula> flights. We report energy forcing per meter (<inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>) by summing the energy forcings and flight distances over all flights in the dataset:

            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M124" display="block"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi>X</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mi>L</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          We find

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M125" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15.50</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.12</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">MJ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E7"><mml:mtd><mml:mtext>7</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15.55</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.12</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">MJ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          where the error bars are obtained by taking 2 standard deviations of 100 bootstrap samples. The fact that these values agree is partially by design as we chose the TPR<inline-formula><mml:math id="M126" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values in Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>) relative to synthetic CoCiP data. If we instead use the “Linearized contrails” TPR<inline-formula><mml:math id="M127" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values from Table <xref ref-type="table" rid="T3"/> then <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mn mathvariant="normal">13</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> lower than the <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, because (at least according to CoCiP) the contrails which form but do not create linear features in the SynthOpenContrails dataset do contribute some warming which those TPR<inline-formula><mml:math id="M131" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values would not capture. If we use the “All contrails” TPR<inline-formula><mml:math id="M132" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values we find that <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:mn mathvariant="normal">6</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> higher than <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, because in that case we are penalizing the TPR value to account for contrails which have only very small forcing. Figure <xref ref-type="fig" rid="F8"/> shows the aggregate forcing as a function of local hour. Both <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> show expected pattern of warming contrails at night and small forcing during the day.</p>

      <fig id="F8"><label>Figure 8</label><caption><p id="d2e2779">Energy forcing as a function of local time of day, for both <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mtext>ensemble mean</mml:mtext><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">EF</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi><mml:mi mathvariant="normal">pm</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>. We see that both have similar values and exhibit the expected diurnal pattern of warming at night and ambiguous results during the day.</p></caption>
          <graphic xlink:href="https://jecats.copernicus.org/articles/1/2/2026/jecats-1-2-2026-f08.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Discussion and Future Work</title>
      <p id="d2e2823">In this work we defined a “contrail score” <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">hybrid</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> which combines ensemble weather and contrail observations, and saw that it compared better to in-situ measurements than scores based entirely on weather data. We used this to define a method of estimating contrail warming which weights ensemble members by their agreement with observations, and showed that though the hybrid method is more correct on a per-contrail basis, it produces similar aggregate values to methods using only weather data.</p>
      <p id="d2e2837">In this work we used the aircraft-based IAGOS system as a source of in-situ measurements, but the method does not require the measurements to be on aircraft and future work could compare to other in-situ measurements such as from radiosondes.</p>
      <p id="d2e2840">This work shows that contrail observations can improve estimates of meteorological quantities related to contrails. We tested this approach using an 10-ensemble-member reanalysis product with low resolution and a 50-ensemble-member forecast product with higher resolution. We found that more ensemble members, and higher resolution improves performance, suggesting that the best possible estimates of whether a flight made a contrail could be obtained by a reanalysis product with higher resolution and more ensemble members. Another improvement might be to increase the number of ensemble members well beyond 50, for example by using an AI weather model <xref ref-type="bibr" rid="bib1.bibx23" id="paren.39"/>.</p>
      <p id="d2e2846">The approach taken in this work is a very basic method of combining observations and weather, and the fact that it leads to an improvement suggests that more sophisticated approaches, such as assimilating contrail observations directly into a weather model, may be worth pursuing. One could also try imposing spatial/temporal consistency on these ensemble weights, as opposed to this work where the weights are chosen independently for each measurement. Better agreement with in-situ measurements would be one way to assess the impact of such improvements, but there are others. It would be desirable if a future approach produced a more physically consistent set of weather fields. This would allow one to estimate warming by running a physical model once on the new weather data, which would be computationally cheaper than the approach in this work of running the physical model on each ensemble member and taking the weighted average of the results. The improvements in this work only apply to points near a flight path. This is not a problem for contrail avoidance applications since by definition we care most about points near flight paths, but extending the distance the improvements apply over could allow contrail observations to improve weather for non-contrail applications.</p>
      <p id="d2e2850">Another interesting direction could be to generalize the techniques in this work to other weather data. For example, one could try to improve wind data by weighting weather ensembles based on whether they agree with the observed motion of persistent contrails.</p>
      <p id="d2e2853">The contrail score and warming estimates produced in this work used CoCiP to determine the TPR<inline-formula><mml:math id="M141" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>FPR values in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) and to estimate warming. CoCiP is not the only method of estimating the evolution of contrails and other methods can give different contrail properties in case studies <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx22" id="paren.40"/>. Further research is needed to determine if these differences yield significant changes in agreement with in-situ measurements or aggregate contrail forcing. The methods used in this work can be straightforwardly adapted to use a different contrail model if desired.</p>
      <p id="d2e2868">In this work we showed that contrail observations can help to predict in-situ measurements of SAC and ISSR.  In-situ measurements of SAC and ISSR are a proxy of what we really want to observe, which is persistent contrail formation. These measurements must be a pretty good proxy, (otherwise contrail observations would not help to predict them), but they are likely not a perfect proxy due to both noise in the in-situ measurements and physical phenomena (e.g. wake-vortex interactions, advection, sedimentation) which are not modeled. In Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/> we saw how more accurate proxies of persistent contrail formation led observing a larger benefit of using observations. This is because in the results in this work every time the proxy incorrectly predicts a contrail and observations (correctly) do not observe one (and vice-versa), we count that as a mistake by the observations. Therefore we expect that the results in this work are understating the benefits of incorporating observations, a hypothesis which could be tested by comparing with improved “ground-truth” datasets, such as those being developed using ground cameras <xref ref-type="bibr" rid="bib1.bibx19" id="paren.41"/>.</p>
      <p id="d2e2876">For the purposes of determining whether an aircraft made a contrail, both weather models  and geostationary imagery have limitations <xref ref-type="bibr" rid="bib1.bibx1 bib1.bibx14 bib1.bibx7 bib1.bibx9" id="paren.42"/>. This work shows that despite their limitations, both approaches have complementary information and therefore taking them together leads to the best estimates of whether an aircraft made a persistent contrail.</p>
</sec>

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

      <p id="d2e2887">The dataset used for the analysis is available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.19440374" ext-link-type="DOI">10.5281/zenodo.19440374</ext-link> <xref ref-type="bibr" rid="bib1.bibx13" id="paren.43"/>. Per-flight data on whether a flight has been observed making a contrail, can be retrieved from the ContrailWatch API <uri>https://developers.google.com/contrails/v1/ContrailWatch-description</uri> (last access: 8 July 2026), as can per-flight estimates of the energy forcing described in Sect. <xref ref-type="sec" rid="Ch1.S2.SS6"/>.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e2904">SG designed and carried out the analysis. AS helped in accessing and understanding the SynthOpenContrails dataset. SR and RT provided the IAGOS data. KM provided scientific advising throughout the development of the study and the compiling of the results. SG prepared the manuscript with contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e2910">The authors declare the following competing interests: As denoted by their affiliations, some authors are employed by Google LLC. Google is a technology company that sells computing and machine learning services as part of its business.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e2916">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e2922">IAGOS data were created with support from the European Commission, national agencies in Germany (BMBF), France (MESR), and the UK (NERC), and the IAGOS member institutions (<uri>http://www.iagos.org/partners</uri>, last access: 8 July 2026). The participating airlines (Lufthansa, Air France, Austrian, China Airlines, Hawaiian Airlines, Air Canada, Iberia, Eurowings Discover, Cathay Pacific, Air Namibia, Sabena) supported IAGOS by carrying the measurement equipment free of charge since 1994. The data are available at <uri>http://www.iagos.fr</uri> (last access: 8 July 2026) thanks to additional support from AERIS. These results are based on data and products of the European Centre for Medium-Range Weather Forecasts (ECMWF). Google Gemini was used to help draft this manuscript.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e2933">This paper was edited by Radu Mirea and reviewed by two anonymous referees.</p>
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