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<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<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"><?xmltex \hack{\allowdisplaybreaks}?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">AMT</journal-id><journal-title-group>
    <journal-title>Atmospheric Measurement Techniques</journal-title>
    <abbrev-journal-title abbrev-type="publisher">AMT</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Meas. Tech.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1867-8548</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/amt-13-2887-2020</article-id><title-group><article-title>Towards spaceborne monitoring of localized <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions: an instrument concept and first performance assessment</article-title><alt-title>Spaceborne monitoring of localized <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions</alt-title>
      </title-group><?xmltex \runningtitle{Spaceborne monitoring of localized {$\chem{CO_{2}}$} emissions}?><?xmltex \runningauthor{J.~Strandgren et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Strandgren</surname><given-names>Johan</given-names></name>
          <email>johan.strandgren@dlr.de</email>
        <ext-link>https://orcid.org/0000-0001-7876-5845</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Krutz</surname><given-names>David</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff3">
          <name><surname>Wilzewski</surname><given-names>Jonas</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1392-2966</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Paproth</surname><given-names>Carsten</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Sebastian</surname><given-names>Ilse</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Gurney</surname><given-names>Kevin R.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Liang</surname><given-names>Jianming</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Roiger</surname><given-names>Anke</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Butz</surname><given-names>André</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0593-1608</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Deutsches Zentrum für Luft- und Raumfahrt, Institut für
Physik der Atmosphäre, Oberpfaffenhofen, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Deutsches Zentrum für Luft- und Raumfahrt, Institut für
Optische Sensorsysteme, Berlin-Adlershof, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Meteorological Institute Munich, Ludwig-Maximilians-Universität, Munich, Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>School of Informatics, Computing and Cyber Systems, Northern Arizona University, Flagstaff, AZ, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>School of Life Sciences, Arizona State University, Tempe, AZ, USA</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Institut für Umweltphysik, Universität Heidelberg, Heidelberg, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Johan Strandgren (johan.strandgren@dlr.de)</corresp></author-notes><pub-date><day>3</day><month>June</month><year>2020</year></pub-date>
      
      <volume>13</volume>
      <issue>6</issue>
      <fpage>2887</fpage><lpage>2904</lpage>
      <history>
        <date date-type="received"><day>31</day><month>October</month><year>2019</year></date>
           <date date-type="rev-request"><day>16</day><month>January</month><year>2020</year></date>
           <date date-type="rev-recd"><day>6</day><month>April</month><year>2020</year></date>
           <date date-type="accepted"><day>17</day><month>April</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2020 Johan Strandgren et al.</copyright-statement>
        <copyright-year>2020</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://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020.html">This article is available from https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e211">The UNFCCC (United Nations Framework Convention on Climate Change) requires the nations of the world to report their carbon dioxide (<inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) emissions. The independent verification of these reported emissions is a cornerstone for advancing towards the emission accounting and reduction measures agreed upon in the Paris Agreement. In this paper, we present the concept and first performance assessment of a compact spaceborne imaging spectrometer with a spatial resolution of <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> that could contribute to the “monitoring, verification and reporting” (MVR) of <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions worldwide. <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from medium-sized power plants (1–10 <inline-formula><mml:math id="M8" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), currently not targeted by other spaceborne missions, represent a significant part of the global <inline-formula><mml:math id="M9" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission budget. In this paper we show that the proposed instrument concept is able to resolve emission plumes from such localized sources as a first step towards corresponding <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux estimates.</p>
    <p id="d1e316">Through radiative transfer simulations, including a realistic instrument noise model and a global trial ensemble covering various geophysical scenarios, it is shown that an instrument noise error of 1.1 ppm (<inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>) can be achieved for the retrieval of the column-averaged dry-air mole fraction of <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (X<inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Despite a limited amount of information from a single spectral window and a relatively coarse spectral resolution, scattering by atmospheric aerosol and cirrus can be partly accounted for in the X<inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval, with deviations of at most 4.0 ppm from the true abundance for two-thirds of the scenes in the global trial ensemble.</p>
    <p id="d1e362">We further simulate the ability of the proposed instrument concept to observe <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plumes from single power plants in an urban area using high-resolution <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission and surface albedo data for the city of Indianapolis. Given the preliminary instrument design and the corresponding instrument noise error, emission plumes from point sources with an emission rate down to the order of 0.3 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> can be resolved, i.e., well below the target source strength of 1 <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. This leaves a significant margin for additional error sources, like scattering particles and complex meteorology, and shows the potential for subsequent <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux estimates with the proposed instrument concept.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e448"><bold>(a)</bold> Geographical distribution of reported and estimated annual <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from power plants worldwide for the year 2009, as provided by the CARMA v3.0 database. <bold>(b)</bold> Corresponding cumulative distribution showing the fraction of the power plant emission total (9.9 <inline-formula><mml:math id="M21" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) that power plants with a source strength greater than X <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> make up. This should be understood as the fraction of the power plant <inline-formula><mml:math id="M23" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission total that can theoretically be observed by an instrument with a given sensitivity. For visualization purposes, the marker sizes in <bold>(a)</bold> are scaled according to the respective emission rates.</p></caption>
      <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f01.png"/>

    </fig>

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <?pagebreak page2888?><p id="d1e541">Despite the broad consensus on the negative long-term effects of carbon dioxide (<inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) emissions and the efforts to reduce these emissions, the atmospheric <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations continue to rise. During the course of 2018, the average <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration increased from 407 to 410 ppm at the Mauna Loa observatory, representing the fourth-highest annual growth ever recorded at that observatory <xref ref-type="bibr" rid="bib1.bibx43" id="paren.1"/>. <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from localized point sources represent a large fraction of the <inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emitted into the atmosphere. The International Energy Agency (IEA) recently reported that emissions from coal-fired power plants exceeded 10 <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for the first time in 2018, hence accounting for approximately 30 % of the global <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions <xref ref-type="bibr" rid="bib1.bibx27" id="paren.2"/>, mainly due to the continued growth of coal use in Asia and other emerging economies. Figure <xref ref-type="fig" rid="Ch1.F1"/> depicts the global distribution of reported and estimated annual <inline-formula><mml:math id="M31" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from power plants for the year 2009, as provided by the CARMA (Carbon Monitoring for Action) v3.0 database <xref ref-type="bibr" rid="bib1.bibx64 bib1.bibx61" id="paren.3"/>, together with the corresponding cumulative distribution of the power plant emissions. The emission total from 16 898 individual power plants, where exact or approximate coordinates are available, adds up to 9.9 <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. A large fraction of power plant emissions originates from a relatively small number of large to medium-sized power plants. The CARMA data show that 153 large power plants (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) accounted for 24 % of the total annual power plant <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions, whereas 2111 large and medium-sized power plants (<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) accounted for as much as 88 % of the power plant <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission budget, clearly demonstrating the significant contribution from medium-sized power plants (1–10 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) to the global <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission budget.</p>
      <p id="d1e803">To advance towards emission accounting and reduction measures, agreed upon in the Paris Agreement in force since 2016, the independent verification of reported emissions is of high importance. To this end, spaceborne instruments provide a suitable platform with which continuous long-term measurements can potentially be combined with near-global coverage with no geopolitical boundaries.</p>
      <?pagebreak page2889?><p id="d1e806">Most of the currently operating, planned and proposed instruments for passive <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> observations from space measure the reflected shortwave infrared (SWIR) solar radiation in several spectral windows covering the oxygen A (<inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> A) band near 750 nm as well as the weak and strong <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands near 1600 and 2000 nm, respectively, e.g., GOSAT <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx34" id="paren.4"><named-content content-type="pre">Greenhouse Gases Observing Satellite;</named-content></xref>, OCO-2 <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx13" id="paren.5"><named-content content-type="pre">Orbiting Carbon Observatory-2;</named-content></xref>, TanSat <xref ref-type="bibr" rid="bib1.bibx36" id="paren.6"/>, GOSAT-2 <xref ref-type="bibr" rid="bib1.bibx41" id="paren.7"/>, OCO-3 <xref ref-type="bibr" rid="bib1.bibx16" id="paren.8"/>, MicroCarb <xref ref-type="bibr" rid="bib1.bibx5" id="paren.9"/>, GeoCarb <xref ref-type="bibr" rid="bib1.bibx40" id="paren.10"/>, CarbonSat <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx4" id="paren.11"/> and G3E <xref ref-type="bibr" rid="bib1.bibx10" id="paren.12"><named-content content-type="pre">Geostationary Emission Explorer for Europe;</named-content></xref>. These instruments and instrument concepts further rely on a comparatively high spectral resolution on the order of approximately 0.05–0.3 nm, representing resolving powers (ratio of wavelength over the full-width half-maximum of the instrument spectral response function) ranging from approximately 3600 for the strong <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands near 2000 nm for CarbonSat <xref ref-type="bibr" rid="bib1.bibx4" id="paren.13"/> up to <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula> for the OCO and GOSAT instruments. Such advanced instruments, like GOSAT and OCO-2 that have been operating since 2009 and 2014, respectively, generally target an accuracy and coverage sufficient to study the natural <inline-formula><mml:math id="M46" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> cycle on a regional to continental scale <xref ref-type="bibr" rid="bib1.bibx19 bib1.bibx37 bib1.bibx44 bib1.bibx15 bib1.bibx11 bib1.bibx35" id="paren.14"><named-content content-type="pre">e.g.,</named-content></xref> but have also been used to observe and quantify <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> gradients on the regional scale caused by anthropogenic <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions in urban areas <xref ref-type="bibr" rid="bib1.bibx30 bib1.bibx23 bib1.bibx52 bib1.bibx47" id="paren.15"/>. OCO-2 data have further been used to observe strong <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plumes from localized natural and anthropogenic <inline-formula><mml:math id="M50" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sources like volcanoes and coal-fired power plants <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx52 bib1.bibx47" id="paren.16"/>, demonstrating the capabilities of imaging spectrometers to monitor <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from space. The spatial resolution of OCO-2 and similar instruments like OCO-3, TanSat and the planned Copernicus <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> Monitoring mission CO2M (on the order of 2–4 <inline-formula><mml:math id="M53" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) does, however, pose a difficulty for the routine monitoring of localized power plant <inline-formula><mml:math id="M54" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions, since the plume is usually only sampled by a handful of pixels in which <inline-formula><mml:math id="M55" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume enhancements cannot be fully separated from the background, making quantitative <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rate estimates difficult and vulnerable to cloud contamination and instrument noise propagating into <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors. For this reason CO2M will target isolated large power plants (<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mi mathvariant="italic">≳</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and large urban agglomerations (<inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="italic">≳</mml:mi></mml:math></inline-formula> Berlin) <xref ref-type="bibr" rid="bib1.bibx32" id="paren.17"/>, and thus a large fraction of the emission total will be missed.</p>
      <p id="d1e1093">To contribute to closing this gap and expanding on future <inline-formula><mml:math id="M61" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring from space, we present the concept and a first performance assessment of a spaceborne imaging spectrometer that could be deployed for the dedicated monitoring of localized <inline-formula><mml:math id="M62" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions. By targeting power plants with an annual emission rate down to approximately 1 <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, a substantial fraction of the <inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from power plants and hence a significant part of the global man-made <inline-formula><mml:math id="M65" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission budget in total could be resolved (given global coverage through a fleet of instruments). As shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>, it is of key importance to also cover medium-sized power plants (1–10 <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) as they alone contributed to approximately 64 % of the <inline-formula><mml:math id="M67" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from power plants in 2009 according to the CARMA v3.0 data. To achieve this, the proposed instrument has an envisaged spatial resolution of <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. With such a high spatial resolution and large amount of ground pixels per unit area, averaging plume enhancements and background concentration fields is avoided. This leads to an enhanced contrast compared to a coarser spatial resolution. To increase the number of collected photons and hence the signal-to-noise ratio (SNR) and relative precision of the <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration retrievals, such a high spatial resolution has to be compensated for with a rather coarse spectral resolution. To further compensate for the limited spatial coverage of a single instrument, a comparatively compact and low-cost instrument design is an important aspect, as it would allow for a fleet of instruments to be deployed, increasing the spatial coverage.</p>
      <p id="d1e1235"><xref ref-type="bibr" rid="bib1.bibx65" id="text.18"/> recently demonstrated that atmospheric <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations can be retrieved with an accuracy <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> % using such a comparatively simple spectral setup with one single spectral window and a relatively coarse spectral resolution of approximately 1.3–1.4 nm (resolving power of 1400–1600). <xref ref-type="bibr" rid="bib1.bibx55" id="text.19"/> demonstrated the ability to resolve and quantify methane (<inline-formula><mml:math id="M73" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) plumes, which pose a similar remote sensing challenge as <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, using data from the spaceborne Hyperion imaging spectrometer with a spectral and spatial resolution of 10 nm (resolving power around 230) and 30 m, respectively. The observation of emission plumes, from plume detection to enhancement quantification and flux estimation, using imaging spectroscopy with a single narrow spectral window and a spectral resolution as coarse as 5 to 10 nm (resolving power around 200–500) has further been repeatedly demonstrated using airborne imaging spectroscopy data for both <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx14 bib1.bibx59" id="paren.20"/> and <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx57 bib1.bibx54 bib1.bibx56 bib1.bibx59 bib1.bibx28" id="paren.21"/>. For an airborne instrument primarily dedicated to the quantitative imaging of <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, but also <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plumes, <xref ref-type="bibr" rid="bib1.bibx58" id="text.22"/> proposed a single spectral window and a spectral resolution of 1.0 nm (resolving power around 2000–2400), again coarse enough to reach a spatial resolution on the order of 10–100 m. The commercial instrument GHGSat-D operated by the Canadian company GHGSat Inc. was launched in 2016 as a demonstrator for a satellite constellation concept targeting the detection of <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plumes from individual point sources within selected <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> km<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> target regions at a spectral and spatial resolution of 0.1 nm (resolving power around 16 000) and 50 m, respectively <xref ref-type="bibr" rid="bib1.bibx62" id="paren.23"/>. <xref ref-type="bibr" rid="bib1.bibx63" id="text.24"/> recently showed how anomalously large <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> point sources can be discovered with GHGSat-D observations.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e1395">Ray-tracing diagram of the preliminary optical design assuming a three-mirror anastigmat (TMA) telescope combined with an Offner-type spectrometer.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f02.png"/>

      </fig>

      <p id="d1e1404">Given the results from previous studies and the technology at hand, we are confident that the proposed instrument concept presented here could be realized and that it would be an important complement to the fleet of current and planned spaceborne <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> instruments, allowing for the routine quantitative monitoring of <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from large and medium-sized power plants. The proposed instrument concept would also serve as a good complement and companion to CO2M<?pagebreak page2890?> by also targeting medium-sized power plants and providing high-resolution images with finer <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume structures. The added value of such an instrument would be of interest both in terms of advancing science and providing independent emission estimates that could be used to verify reported <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rates at the facility level and inform policy makers on the progress of reducing man-made <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions. The proposed instrument concept is described in Sect. <xref ref-type="sec" rid="Ch1.S2"/>, followed by a description of the instrument noise model in Sect. <xref ref-type="sec" rid="Ch1.S3"/>. A global performance assessment addressing instrument noise and the errors introduced by atmospheric aerosol is presented in Sect. <xref ref-type="sec" rid="Ch1.S4"/>. The ability to resolve single <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes at an urban scale is further simulated in Sect. <xref ref-type="sec" rid="Ch1.S5"/>. A short summary and our concluding remarks are finally presented in Sect. <xref ref-type="sec" rid="Ch1.S6"/>.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Mission and instrument concept </title>
      <p id="d1e1492">The instrument concept presented in this paper is based on a spaceborne push-broom imaging grating spectrometer measuring spectra of reflected solar radiation in one single SWIR spectral window, from which the column-averaged dry-air mole fraction of <inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (X<inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) can be retrieved. With an expected instrument mass of approximately 90 kg, it is suitable for  deployment on small satellite buses. Since the proposed instrument targets the quantification of localized <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from, e.g., coal-fired power plants, a high spatial resolution of <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> is envisaged. The instrument is designed to fly in a sun-synchronous orbit at an altitude of 600 km and a local equatorial crossing time at 13:00 LT. This orbit is chosen in order to have a well-developed boundary layer at overpass together with good radiometric performance (high SNR).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e1553">Simulated synthetic measurements of spectral radiances for the two spectral setups near 1600 nm (SWIR-1) <bold>(a)</bold> and 2000 nm (SWIR-2) <bold>(b)</bold> for our reference scene with surface albedo 0.1 and an SZA of 70<inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Thin grey lines show corresponding spectral radiances at 0.003 nm spectral resolution.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f03.png"/>

      </fig>

      <p id="d1e1577">The preliminary optical design assumes a circular aperture (15 cm in diameter) and is based on a three-mirror anastigmat (TMA) telescope, combined with an Offner-type spectrometer, as shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>. The optic system relies on metal-based mirrors and is designed as an athermal configuration for a wide temperature range onboard the satellite. The three mirrors of the TMA are standard aspheres aligned on a single optical axis. The efficiency of the optical bench (throughput), including transmittance and grating efficiency, is estimated to 0.48, and the <inline-formula><mml:math id="M95" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> number (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">num</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), equal to the ratio of focal length to aperture diameter, amounts to 2.4. The dispersed electromagnetic radiation is focused onto a two-dimensional array detector that captures the spatial across-track dimension and the spectral dimension of the incoming radiation. A detector with a pixel area of 900 <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and a quantum efficiency of 0.8 is assumed for this study. The quantum efficiency depends on the wavelength but is for now assumed constant for both spectral windows. These values are in line with typical values for a state-of-the-art detector.</p>
      <?pagebreak page2891?><p id="d1e1614">In order to reach a sufficient SNR, the proposed spatial resolution only allows for a relatively coarse spectral resolution. <xref ref-type="bibr" rid="bib1.bibx65" id="text.25"/> used spectrally degraded GOSAT soundings to demonstrate the capability of retrieving X<inline-formula><mml:math id="M98" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from a single spectral window at such a coarse spectral resolution using a spectral setup (in terms of spectral range, resolution and oversampling ratio) compact enough to fit onto 256 detector pixels. They evaluate two alternative spectral setups covering the spectral ranges 1559–1672 nm (hereafter also referred to as SWIR-1) and 1982–2092 nm (hereafter also referred to as SWIR-2) with a spectral resolution (full-width half-maximum –  FWHM – of the instrument spectral response function) of 1.37 and 1.29 nm, respectively, and an oversampling ratio of 3. The resolving power of the SWIR-1 and SWIR-2 setups amounts to approximately 1200 and 1600, respectively. For optics design reasons, we use a spectral oversampling ratio of 2.5 in this study, resulting in a spectral sampling distance of 0.55 and 0.52 nm for SWIR-1 and SWIR-2, respectively. Simulated synthetic measurements of spectral radiances for the two prospective spectral setups are shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>, assuming a Gaussian instrument response function with an FWHM of 1.37 and 1.29 nm, respectively, as proposed by <xref ref-type="bibr" rid="bib1.bibx65" id="text.26"/>. The SWIR-1 window (Fig. <xref ref-type="fig" rid="Ch1.F3"/>a) exhibits two weak <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands around 1568–1585 nm and 1598–1615 nm and has the advantage of a stronger top-of-atmosphere (TOA) signal due to higher solar irradiance and surface albedo at these wavelengths. It also allows for the simultaneous retrieval of <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> using the <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption band near 1666 nm. The SWIR-2 window, on the other hand, exhibits two stronger <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands around 1995–2035 and 2045–2080 nm and has higher sensitivity to atmospheric aerosol that can potentially be exploited during the X<inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval <xref ref-type="bibr" rid="bib1.bibx65" id="paren.27"/>. <xref ref-type="bibr" rid="bib1.bibx65" id="text.28"/> showed similar performance for SWIR-1 and SWIR-2 but suspect SWIR-2 to be the favorable spectral setup given the stronger <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands, the ability to account for particle scattering and the lower radiance SNR required to reach sufficiently small X<inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors. In this paper, we further investigate the performance of the two spectral setups in order to finally conclude which is the more suitable one given the preliminary instrument design and realistic instrument SNR assumed here.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1726">Mission and instrument design parameters of the proposed spaceborne <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring instrument concept.</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="left"/>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Orbit</oasis:entry>
         <oasis:entry colname="col2">600 km, sun-synchronous</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mass</oasis:entry>
         <oasis:entry colname="col2">90 kg</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Swath</oasis:entry>
         <oasis:entry colname="col2">50 km</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Spatial resolution</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Spectral range</oasis:entry>
         <oasis:entry colname="col2">1559–1672 or 1982–2092 nm</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FWHM (2.5 pix)</oasis:entry>
         <oasis:entry colname="col2">1.37 or 1.29 nm</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Resolving power</oasis:entry>
         <oasis:entry colname="col2">1200 or 1600 (–)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Aperture diameter</oasis:entry>
         <oasis:entry colname="col2">15.0 cm</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M109" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> number (<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">num</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">2.4 (–)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Optical efficiency (<inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">0.48 (–)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Integration time (<inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">70 ms</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Detector pixel area (<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">det</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">900 <inline-formula><mml:math id="M114" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Quantum efficiency (<inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">0.8 e<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula> photon<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dark current (<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">1.6 fA pix<inline-formula><mml:math id="M119" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M120" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Readout noise</oasis:entry>
         <oasis:entry colname="col2">100 e<inline-formula><mml:math id="M121" display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Quantization noise</oasis:entry>
         <oasis:entry colname="col2">40 e<inline-formula><mml:math id="M122" display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e2058">The instrument is designed to have a radiance SNR of 100 at the continuum for a reference scene with a Lambertian surface albedo of 0.1 and solar zenith angle (SZA) of 70<inline-formula><mml:math id="M123" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Given the altitude of 600 km and the corresponding orbital velocity of 7562 <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, the instrument traverses along one 50 m ground pixel in 7.2 ms. The number of photons collected over the course of 7.2 ms is, however, not enough to reach an SNR of 100. To increase the SNR, we suggest increasing the integration time to 70 ms. This would normally lead to elongated ground pixels (approx. <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M126" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>), but by using forward motion compensation (FMC), the instrument can be periodically altered in the along-track direction such that each ground pixel is sampled for a time period longer than the actual satellite overpass time <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx1" id="paren.29"><named-content content-type="pre">see, e.g.,</named-content></xref>. FMC has the evident drawback that the coverage along the satellite track is discontinuous, since no data are sampled when the instrument returns to the starting forward position. A second disadvantage is the geometrical distortion of the ground pixels that increases with the maximum off-nadir angle. The baseline design assumes 1000 measurements to be made in the along-track dimension for each FMC repetition, leading to off-nadir angles up to approximately 20<inline-formula><mml:math id="M127" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Further assuming 1000 detector pixels in the spatial dimension would consequently result in observed tiles on the order of <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M129" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e2148">Table <xref ref-type="table" rid="Ch1.T1"/> summarizes the preliminary mission concept and instrument design parameters assumed for this study. It should be clear that this is a preliminary baseline design used to demonstrate the <inline-formula><mml:math id="M130" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring abilities and added value of the proposed instrument concept. Alternative instrument designs will be further investigated, and the exact instrument design will most likely be subject to change before the instrument is realized. The continuum SNR for our reference scene should nevertheless remain at roughly 100, ensuring a similar performance as presented in this paper.</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Instrument noise model </title>
      <p id="d1e2173">To assess the performance of the proposed instrument concept with respect to retrieving X<inline-formula><mml:math id="M131" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and resolving localized <inline-formula><mml:math id="M132" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions, the expected instrument noise levels that accompany the measurements have to be quantified. To this end a numerical instrument noise model that calculates the instrument's SNR is developed, following a similar approach as, e.g., <xref ref-type="bibr" rid="bib1.bibx3" id="text.30"/> and <xref ref-type="bibr" rid="bib1.bibx10" id="text.31"/>. The SNR is given by
          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M133" display="block"><mml:mrow><mml:mtext>SNR</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M134" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> is the signal, i.e., the number of photons emerging from a <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M136" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> ground pixel that generate a charge in the detector, and <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the corresponding instrument noise. The signal <inline-formula><mml:math id="M138" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> is calculated as
          <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M139" display="block"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">det</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>⋅</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mi mathvariant="normal">num</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:mi mathvariant="italic">η</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the simulated reflected solar spectral radiance at the telescope, <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">det</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the detector pixel area, <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">num</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the instrument's <inline-formula><mml:math id="M143" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> number, <inline-formula><mml:math id="M144" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula> the efficiency of the optical bench, <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the detector's quantum efficiency, <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:math></inline-formula> the wavelength range covered by a single detector pixel and <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the integration time between the detector pixel readouts. Following the thin lens equation (for large distances between a lens and an object) and the magnification formula, the term <inline-formula><mml:math id="M148" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">det</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>⋅</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mi mathvariant="normal">num</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle></mml:math></inline-formula> can also be expressed as <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">ap</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">ap</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the area of the aperture (<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> with <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn></mml:mrow></mml:math></inline-formula> cm) and <inline-formula><mml:math id="M153" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula> the instrument's solid angle, i.e., the squared ratio of the ground sampling distance (50 m) over the orbit altitude (600 km). Apart from <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that is calculated for each scene using a forward radiative transfer model, all quantities in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>) and their corresponding values were introduced in Sect. <xref ref-type="sec" rid="Ch1.S2"/>.</p>
      <?pagebreak page2892?><p id="d1e2531">The total noise <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) accounts for the noise contribution from five separate instrument noise sources:
          <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M156" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ss</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">bg</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">dc</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ro</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">qz</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ss</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mi>S</mml:mi></mml:msqrt></mml:mrow></mml:math></inline-formula> is the signal shot noise, <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the noise due to thermal background radiation incident on the detector, <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the noise due to dark current in the detector, <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ro</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the noise upon detector readout and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">qz</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the quantization noise that arises when the analog signal is digitized. The thermal background signal per detector pixel is approximated as
          <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M162" display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">det</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">BB</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">BB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the thermal black-body irradiance incident on the detector. <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">BB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is determined by integrating the black-body spectral radiance <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mtext>BB</mml:mtext></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emitted by the background over the detector's cutoff wavelengths <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and hemispheric opening angle,
          <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M168" display="block"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">BB</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mtext>BB</mml:mtext></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mi>d</mml:mi><mml:mi mathvariant="italic">λ</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        For this study, detector cutoff wavelengths of 900 and 2500 nm are assumed, and the background temperature <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is estimated to 200 K. The thermal background noise is then calculated as <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">bg</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>. Similarly, the dark current noise is given by <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> is the per-pixel detector signal due to dark current. While <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">6.242</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> electrons C<inline-formula><mml:math id="M174" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is constant, the dark current <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> strongly depends on the detector's operating temperature and is estimated to 1.6 fA pix<inline-formula><mml:math id="M176" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M177" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (assuming 150 K detector temperature), yielding a dark current signal of approximately <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula> electrons (e<inline-formula><mml:math id="M179" display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula>) per detector pixel and second. Finally, the readout noise (<inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ro</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and quantization noise (<inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">qz</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are estimated to 100 and 40 e<inline-formula><mml:math id="M182" display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula>, respectively. These noise levels are preliminary estimates used to test and evaluate the instrument concept but are comparable to those of state-of-the-art detectors for space applications.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e3039"><bold>(a)</bold> Continuum SNR as a function of scene brightness (<inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:mtext>Albedo</mml:mtext><mml:mo>⋅</mml:mo><mml:mi>cos⁡</mml:mi><mml:mo>(</mml:mo><mml:mtext>SZA</mml:mtext><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi mathvariant="italic">π</mml:mi></mml:mrow></mml:math></inline-formula>) for the SWIR-1 and SWIR-2 spectral setups, with the dotted line indicating the brightness of our reference scene. The highest scene brightness (approx. 0.22) represents a bright scene with an albedo of 0.7 and an SZA of 0<inline-formula><mml:math id="M184" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. <bold>(b)</bold> Instrument noise contributions for a simulated SWIR-2 spectrum.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f04.png"/>

      </fig>

      <p id="d1e3085">Figure <xref ref-type="fig" rid="Ch1.F4"/>a shows the continuum SNR (calculated with Eqs. <xref ref-type="disp-formula" rid="Ch1.E1"/>–<xref ref-type="disp-formula" rid="Ch1.E5"/>) as a function of the scene brightness for the two prospective spectral setups SWIR-1 and SWIR-2. The scene brightness describes the conversion from incident solar irradiance to reflected solar radiance and is calculated as the product of the surface albedo and the cosine of the SZA divided by <inline-formula><mml:math id="M185" display="inline"><mml:mi mathvariant="italic">π</mml:mi></mml:math></inline-formula>, hence assuming a Lambertian surface. For the reference scene (albedo 0.1, SZA 70<inline-formula><mml:math id="M186" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>), the continuum SNR is approximately 180 and 100 for SWIR-1 and SWIR-2, respectively. The consistently higher SNR for SWIR-1 compared to SWIR-2 is mainly the result of higher solar radiance (see Fig. <xref ref-type="fig" rid="Ch1.F3"/>) and generally higher surface albedo (see, e.g., Fig. 7 in <xref ref-type="bibr" rid="bib1.bibx6" id="altparen.32"/>) in SWIR-1. Looking at the individual contributions from the different instrument noise sources in Fig. <xref ref-type="fig" rid="Ch1.F4"/>b, it is clear that the readout noise and signal shot noise are the major contributors, whereas the noise arising from quantization errors, dark current and thermal background radiation has a small or even negligible contribution in comparison. The signal shot noise is, however, smaller than the dark current, readout noise and quantization noise inside the <inline-formula><mml:math id="M187" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands, in which the signal, and hence the signal shot noise, decreases. Note that all noise terms except for the signal shot noise, <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, are constant.</p>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Generic performance evaluation </title>
      <p id="d1e3148">In this section we conduct a first performance evaluation of the proposed instrument concept by assessing the X<inline-formula><mml:math id="M189" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors expected on a global scale. Such errors arise due to instrument noise and because of inadequate knowledge about the light path through the atmosphere due to scattering aerosol and cirrus particles. For this purpose we use a global trial ensemble with a large  collection of geophysical scenarios with varying atmospheric gas concentrations, meteorological conditions, surface albedo, SZA, and aerosol and cirrus compositions that can be expected to be observed by a polar-orbiting instrument. The same methodology and dataset have been used in several previous studies to assess the greenhouse gas retrieval performance of different satellite instruments <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx7 bib1.bibx9 bib1.bibx10" id="paren.33"/>.</p>
      <?pagebreak page2893?><p id="d1e3165">The global trial ensemble contains geophysical data representative for the months of January, April, July and October. Atmospheric gas concentrations stem from the CarbonTracker model <xref ref-type="bibr" rid="bib1.bibx45" id="paren.34"><named-content content-type="pre"><inline-formula><mml:math id="M190" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> for the year 2010;</named-content></xref>, the Tracer Model 4 <xref ref-type="bibr" rid="bib1.bibx39" id="paren.35"><named-content content-type="pre"><inline-formula><mml:math id="M191" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> for the year 2006;</named-content></xref> and the ECHAM5-HAM model <xref ref-type="bibr" rid="bib1.bibx53" id="paren.36"><named-content content-type="pre"><inline-formula><mml:math id="M192" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>;</named-content></xref>. Surface albedo data representative for the SWIR-1 and SWIR-2 windows stem from the MODIS (Moderate Resolution Imaging Spectroradiometer) MCD43A4 product <xref ref-type="bibr" rid="bib1.bibx50" id="paren.37"/>. Aerosol optical properties are calculated (assuming Mie scattering) for an aerosol size distribution superimposed from seven lognormal
size distributions and five chemical types at 19 vertical layers, as provided by the ECHAM5-HAM model <xref ref-type="bibr" rid="bib1.bibx53" id="paren.38"/>. Cirrus optical properties are calculated for randomly oriented hexagonal columns and plates following the ray-tracing model of <xref ref-type="bibr" rid="bib1.bibx25" id="text.39"/> and <xref ref-type="bibr" rid="bib1.bibx26" id="text.40"/>. In total the global trial ensemble consists of approximately 10 000 scenes with X<inline-formula><mml:math id="M193" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> ranging from 340 to 400 ppm with an average of 382 ppm, albedo ranging from 0 to 0.7 with an average of 0.13 (SWIR-2 window), aerosol optical thickness (AOT) ranging from 0 to 1.0 with an average of 0.05 (SWIR-2 window) and cirrus optical thickness (COT) ranging from 0 to 0.8 with an average of 0.13 (SWIR-2 window). Thus, the global trial ensemble contains challenging scenes with scattering loads that would be filtered out by current satellite retrievals, such as those applied to OCO-2 and GOSAT data, which typically screen scenes with scattering optical thickness greater than 0.3 (at the <inline-formula><mml:math id="M194" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> A band around 760 <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nm</mml:mi></mml:mrow></mml:math></inline-formula>). All data in the global trial ensemble are re-gridded to a spatial resolution of approximately 2.8<inline-formula><mml:math id="M196" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M197" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 2.8<inline-formula><mml:math id="M198" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. This is, of course, much coarser than the envisaged <inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M200" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, but for investigating the propagation of instrument noise into the target quantity X<inline-formula><mml:math id="M201" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> on a  global scale, this dataset serves its purpose. See previous studies <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx7" id="paren.41"><named-content content-type="pre">e.g.,</named-content></xref> for further details on the content of the global trial ensemble.</p>
      <p id="d1e3323">The geophysical data for each scene are fed to the radiative transfer software RemoTeC <xref ref-type="bibr" rid="bib1.bibx8 bib1.bibx51" id="paren.42"/> in order to simulate corresponding synthetic measurements. The measurement noise is calculated by propagating the instrument's SNR (Sect. <xref ref-type="sec" rid="Ch1.S3"/>) into a statistical error estimate according to the rules of Gaussian error propagation <xref ref-type="bibr" rid="bib1.bibx48" id="paren.43"/>. Simulations are conducted globally for the 16th day of each of the four months January, April, July and October, hence covering SZA conditions ranging from 0 to 86<inline-formula><mml:math id="M202" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e3343">By retrieving X<inline-formula><mml:math id="M203" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the simulated synthetic spectra, the range of X<inline-formula><mml:math id="M204" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors that can be expected with the proposed instrument concept can be estimated, as can the ability to account for atmospheric aerosol. The RemoTeC retrieval algorithm <xref ref-type="bibr" rid="bib1.bibx8" id="paren.44"><named-content content-type="pre">e.g.,</named-content></xref> is based on a Philipps–Tikhonov regularization scheme <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx60" id="paren.45"/> that uses the first-order difference operator as a side constraint to retrieve the <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> partial column profiles, from which X<inline-formula><mml:math id="M206" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> can be determined. Additional retrieval parameters are the total column concentrations of <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M208" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (only for SWIR-1), surface albedo (as a second-order polynomial), spectral shift, solar shift, and possibly information on scattering aerosol. Here we assume knowledge about the air mass (needed to calculate X<inline-formula><mml:math id="M209" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), but in reality meteorological and topography data would be required to estimate the air mass.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e3437"><bold>(a)</bold> Cumulative distribution of the estimated X<inline-formula><mml:math id="M210" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors arising from instrument noise for all scenes in the global ensemble. <bold>(b)</bold> X<inline-formula><mml:math id="M211" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors as a function of surface brightness, with the dotted line indicating our reference scene and the dashed lines indicating the 68th and 95th percentiles of the X<inline-formula><mml:math id="M212" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors for the different spectral setups. Note that the red and grey lines for the 95th percentile overlap at 2.03 ppm. Marker colors in <bold>(b)</bold> correspond to those in <bold>(a)</bold>. Both panels show the results for the SWIR-1 (blue) and SWIR-2 (red) setups as well as for an alternative SWIR-1 (grey) setup for comparison (see the text for details).</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f05.png"/>

      </fig>

<sec id="Ch1.S4.SS1">
  <label>4.1</label><?xmltex \opttitle{Instrument-noise-induced X{$\protect\chem{CO_{2}}$} errors }?><title>Instrument-noise-induced X<inline-formula><mml:math id="M213" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors </title>
      <p id="d1e3510">In a first step, we assess X<inline-formula><mml:math id="M214" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors that are induced by instrument noise. To this end, for now, we neglect scattering by aerosol and cirrus. These so-called non-scattering simulations assume no scattering particles to be present in the atmosphere and simply compute the transmittance along the geometric light path (Rayleigh scattering is included).</p>
      <p id="d1e3524">Figure <xref ref-type="fig" rid="Ch1.F5"/>a shows the cumulative distribution of the random X<inline-formula><mml:math id="M215" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise error, i.e., the instrument noise propagated into X<inline-formula><mml:math id="M216" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uncertainties via Gaussian error propagation. Furthermore, Fig. <xref ref-type="fig" rid="Ch1.F5"/>b shows the X<inline-formula><mml:math id="M217" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise error for each simulated scene as a function of the corresponding scene brightness. The noise errors are significantly smaller for the SWIR-2 setup (red) when using the proposed integration time <inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">int</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 70 ms. The red dashed lines in Fig. <xref ref-type="fig" rid="Ch1.F5"/>b show that on average 68 % and 95 % (<inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>, respectively) of the retrievals have noise errors of less than approximately 1.1 and 2.0 ppm, respectively. For the SWIR-1 setup (blue), the corresponding numbers are 2.9 and 5.0 ppm. For the SWIR-2 setup, only retrievals over scenes that are darker than our reference scene (albedo 0.1, SZA 70<inline-formula><mml:math id="M221" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) are expected to have instrument-noise-induced errors larger than approximately 2 ppm. For comparison and as a reference, we also investigate how much the integration time has to be increased for the SWIR-1 setup in order to reach an SNR sufficient to yield X<inline-formula><mml:math id="M222" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors comparable to those obtained with the SWIR-2 setup. We find that with the preliminary instrument design assumed here, the integration time has to be increased to at least 350 ms (i.e., by a factor of 5) for SWIR-1 (grey) in order to reach a similar performance.</p>
      <p id="d1e3618">Despite the advantage of being able to retrieve X<inline-formula><mml:math id="M223" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> alongside X<inline-formula><mml:math id="M224" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> using the SWIR-1 setup, the much longer integration time required to reach sufficiently low <inline-formula><mml:math id="M225" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> noise errors is not feasible for the purpose of the proposed instrument concept. Hence, we conclude that the SWIR-2 setup is superior for the passive satellite-based <inline-formula><mml:math id="M226" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring instrument proposed in this paper. Consequently, the remainder of this paper is limited to the SWIR-2 setup, covering the spectral range 1982–2092 nm with a spectral resolution (FWHM) of 1.29 nm, resolving power around 1600 and a spectral sampling distance of 0.52 nm.</p>
</sec>
<?pagebreak page2894?><sec id="Ch1.S4.SS2">
  <label>4.2</label><?xmltex \opttitle{Aerosol-induced X{$\protect\chem{CO_{2}}$} errors }?><title>Aerosol-induced X<inline-formula><mml:math id="M227" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors </title>
      <p id="d1e3685">Atmospheric aerosol and cirrus particles modify the light path of the reflected solar radiation to a certain degree, depending on the particle abundance, optical properties, height and surface albedo. Consequently, this can cause large errors in the retrieved X<inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> if the effect of <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption and particle scattering on the measured reflected solar radiation cannot be adequately separated during the retrieval process. In this section the ability to account for atmospheric aerosol and cirrus during the retrieval is investigated by including scattering by atmospheric particles in the simulation of the synthetic measurements and in the corresponding X<inline-formula><mml:math id="M230" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrievals. This is done by using a more complex forward model and representation of the aerosol and cirrus particles when simulating the spectra, as well as a comparatively simple representation and forward model for the corresponding retrievals. More precisely, the full physical representation of the vertical profiles of hexagonal cirrus particles and spherical aerosol particles of the five chemical types characterized by the seven lognormal size distributions with known microphysical properties for each aerosol and cirrus particle type is used when simulating the synthetic measurement for each scene in the global trial ensemble. In contrast, only three aerosol parameters are fitted during the corresponding retrieval: the total column number density, the size parameter of a single-mode power-law size distribution and the center height of a Gaussian height distribution. Such differences in the aerosol and cirrus representation lead to forward model errors that, alongside the instrument-noise-induced errors, propagate into the retrieved quantity X<inline-formula><mml:math id="M231" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Previous studies have shown that this approach gives a good approximation of how well a satellite sensor can account for scattering by atmospheric aerosol while retrieving target gas concentrations <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx7" id="paren.46"><named-content content-type="pre">e.g.,</named-content></xref>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e3739"><bold>(a, b)</bold> X<inline-formula><mml:math id="M232" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors as a function of the total particulate optical thickness <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:mtext>AOT</mml:mtext><mml:mo>+</mml:mo><mml:mtext>COT</mml:mtext></mml:mrow></mml:math></inline-formula> for scattering <bold>(a)</bold> and non-scattering <bold>(b)</bold> RemoTeC retrievals. <bold>(c, d)</bold> X<inline-formula><mml:math id="M234" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval errors as a function of SWIR-2 surface albedo for scattering <bold>(c)</bold> and non-scattering <bold>(d)</bold> RemoTeC retrievals. <inline-formula><mml:math id="M235" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> denotes the number of retrievals. Note the different ranges of the <inline-formula><mml:math id="M236" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axes in the upper and lower panels.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f06.png"/>

        </fig>

      <p id="d1e3814">Figure <xref ref-type="fig" rid="Ch1.F6"/>a shows the difference between the X<inline-formula><mml:math id="M237" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieved (“retr”) from the synthetic measurements and the corresponding “true” X<inline-formula><mml:math id="M238" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> used as input to simulate these synthetic measurements. This deviation from the truth contains information on both random instrument noise error (Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>) and systematic errors arising from insufficient modeling of the aerosol and cirrus properties. For comparison, Fig. <xref ref-type="fig" rid="Ch1.F6"/>b shows the corresponding results achieved when using a non-scattering retrieval, i.e., when the scattering by atmospheric aerosol and cirrus, now present in the atmosphere and the simulated synthetic spectra, is neglected (similar to Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>). The retrieval errors are strongly reduced when the RemoTeC retrieval algorithm accounts for the scattering by atmospheric aerosol. When scattering is considered, half of the X<inline-formula><mml:math id="M239" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrievals deviate from the true abundance by less than 2.5 ppm, while two-thirds of the retrievals deviate by less than 4 ppm (approx. 1 %), with no clear error correlation with the optical thickness of the scattering particles. For the non-scattering retrieval, the corresponding numbers are 16 and 28 ppm, with a mean bias of <inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> ppm that increases with optical thickness, exposing the necessity of accounting for atmospheric aerosol and cirrus when retrieving the X<inline-formula><mml:math id="M241" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e3881">Scattering particles can modify the light path and hence the X<inline-formula><mml:math id="M242" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval in primarily two ways. Firstly, an elevated layer of aerosol or cirrus will scatter parts of the incoming solar radiation towards the observing sensor at a higher altitude compared to the Earth's surface, leading to a reduced light path. Secondly, aerosol and cirrus will extend the light<?pagebreak page2895?> path to some degree as a result of multiple scattering between scattering particles and the surface. Such modifications of the light path will be understood as <inline-formula><mml:math id="M243" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations in the atmosphere that are either too low (overall reduced light path) or too high (overall extended light path) if scattering cannot be accounted for in the retrieval. Which effect dominates is primarily driven by the surface albedo. This is visualized in Fig. <xref ref-type="fig" rid="Ch1.F6"/>d that shows the difference between retrieved and true X<inline-formula><mml:math id="M244" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> as a function of the surface albedo when scattering by aerosol and cirrus is neglected in the retrieval. Over darker surfaces for which the effect of multiple scattering between aerosol and the surface is limited, aerosol and cirrus particles scattering the incoming solar radiation towards the sensor higher up in the atmosphere become the dominating effect, leading to a reduced light path and underestimation of the X<inline-formula><mml:math id="M245" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Over brighter surfaces for which the effect of multiple scattering becomes dominant, the non-scattering retrieval is more likely to overestimate the <inline-formula><mml:math id="M246" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> abundance because the loss of radiation due to an extended light path, resulting from the multiple scattering, is assumed to be caused by more absorbing <inline-formula><mml:math id="M247" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molecules in the atmosphere. Figure <xref ref-type="fig" rid="Ch1.F6"/>c shows the difference between retrieved and true X<inline-formula><mml:math id="M248" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> as a function of the surface albedo when scattering by aerosol and cirrus is accounted for when retrieving X<inline-formula><mml:math id="M249" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the synthetic measurements of the proposed satellite concept. It is clear that when aerosol properties are retrieved alongside the <inline-formula><mml:math id="M250" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> abundance, the curve-shaped relationship between the X<inline-formula><mml:math id="M251" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> error and surface albedo vanishes with no clear error correlation other than X<inline-formula><mml:math id="M252" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors increasing with decreasing albedo (and thus SNR). Note that errors arising from the Lambertian albedo assumption (BRDF – bidirectional reflectance distribution function – effects) are neglected in the scattering simulations.</p>
      <p id="d1e4011">Although layers of aerosol and cirrus can be partly accounted for in the retrieval, scenes with thicker clouds and aerosol layers will have to be identified and filtered out in the data processing chain. Such a cloud filter could exploit the different optical depths of the two <inline-formula><mml:math id="M253" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> bands in the SWIR-2 window by retrieving X<inline-formula><mml:math id="M254" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the two <inline-formula><mml:math id="M255" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> bands independently (assuming a non-scattering atmosphere) and filtering for discrepancies.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Performance evaluation for an urban case study </title>
      <?pagebreak page2896?><p id="d1e4056">While the previous section assessed X<inline-formula><mml:math id="M256" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors for the range of geophysical conditions expected to be encountered on a global scale, this section evaluates the <inline-formula><mml:math id="M257" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring capabilities at an urban scale using high-resolution <inline-formula><mml:math id="M258" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration and surface albedo data. Similar to Sect. <xref ref-type="sec" rid="Ch1.S4"/>, the high-resolution data are used to simulate synthetic measurements, from which synthetic X<inline-formula><mml:math id="M259" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> abundances can be retrieved in order to make a first assessment of the <inline-formula><mml:math id="M260" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring ability of the proposed instrument concept in terms of resolving <inline-formula><mml:math id="M261" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes.</p>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Datasets</title>
<sec id="Ch1.S5.SS1.SSS1">
  <label>5.1.1</label><?xmltex \opttitle{{$\protect\chem{CO_{2}}$} concentration field from the Hestia dataset}?><title><inline-formula><mml:math id="M262" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration field from the Hestia dataset</title>
      <p id="d1e4153">To compute a high-resolution three-dimensional field of <inline-formula><mml:math id="M263" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations to be used as input for the radiative transfer simulations, annual estimates of fossil fuel <inline-formula><mml:math id="M264" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions for the city of Indianapolis in the year 2015 are used. These data are generated by the Hestia Project <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx22" id="paren.47"/> for which the fossil fuel <inline-formula><mml:math id="M265" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions are quantified in urban areas down to the scale of individual buildings and streets using a bottom-up approach. The results for the city of Indianapolis are gridded and archived at a spatial resolution of <inline-formula><mml:math id="M266" display="inline"><mml:mrow><mml:mn mathvariant="normal">200</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">200</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M267" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. For this study, however, the Hestia Project dataset was gridded to <inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M269" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> via request to the Hestia research team in order to match the envisaged spatial resolution of the proposed instrument concept. The fossil fuel <inline-formula><mml:math id="M270" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rates for Indianapolis at <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M272" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> resolution can be seen in Fig. <xref ref-type="fig" rid="Ch1.F7"/>a. <inline-formula><mml:math id="M273" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from different sources and sectors like road traffic and point sources (single yellow pixels) can be seen. There is also an apparent emission gradient, with stronger emissions in the city center and weaker emissions towards the suburbs. Hence, the Hestia <inline-formula><mml:math id="M274" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data for Indianapolis provide a realistic emission scenario for evaluating the <inline-formula><mml:math id="M275" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring capabilities of the proposed instrument concept. Moreover, the area of the Hestia domain (approx. <inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:mn mathvariant="normal">34</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">33</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M277" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) is comparable to what the prospective tile size of each observation target area could be.</p>
      <p id="d1e4332">The Hestia <inline-formula><mml:math id="M278" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data are used as input to a Gaussian dispersion model in order to compute a three-dimensional <inline-formula><mml:math id="M279" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration field. For a given <inline-formula><mml:math id="M280" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rate <inline-formula><mml:math id="M281" display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M282" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), the <inline-formula><mml:math id="M283" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration <inline-formula><mml:math id="M284" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M285" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) at a given position (<inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula>) downwind of the emitter is calculated as
              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M287" display="block"><mml:mtable rowspacing="0.2ex" columnspacing="1em" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>Q</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>u</mml:mi><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>exp⁡</mml:mi><mml:mo mathsize="2.0em">(</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo mathsize="2.0em">)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo mathsize="2.0em">[</mml:mo><mml:mi>exp⁡</mml:mi><mml:mo mathsize="2.0em">(</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>-</mml:mo><mml:mi>h</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo mathsize="2.0em">)</mml:mo><mml:mo>+</mml:mo><mml:mi>exp⁡</mml:mi><mml:mo mathsize="2.0em">(</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo mathsize="2.0em">)</mml:mo><mml:mo mathsize="2.0em">]</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
            where <inline-formula><mml:math id="M288" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> is the horizontal wind speed in the <inline-formula><mml:math id="M289" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> direction (along-wind), <inline-formula><mml:math id="M290" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> is the height of the emitting source (in meters above ground level), and <inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the standard deviations of the concentration distribution (in meters) in the horizontal across-wind and vertical dimension, respectively; <inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and hence the spread of the emission plume, depend on the atmospheric instability, i.e., the degree of atmospheric turbulence and the downwind distance <inline-formula><mml:math id="M295" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> from the emitting source. Here, we calculate <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> assuming the Pasquill–Gifford stability class C (slightly unstable atmosphere). Furthermore, a constant wind speed <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M299" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and an emitting source height <inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> m (for all sources) are assumed. This model setup is comparable to similar studies <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx14" id="paren.48"><named-content content-type="pre">e.g.,</named-content></xref>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e4747"><bold>(a)</bold> Hestia fossil fuel <inline-formula><mml:math id="M301" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data for Indianapolis in 2015 at <inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M303" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution. <bold>(b)</bold> Corresponding field of vertically integrated X<inline-formula><mml:math id="M304" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements at <inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M306" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution with respect to a constant background, computed using the Hestia <inline-formula><mml:math id="M307" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data and a Gaussian dispersion model. Panel <bold>(c)</bold> is the same as <bold>(b)</bold>, but at <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M309" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution. <bold>(d)</bold> Per-pixel X<inline-formula><mml:math id="M310" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements for three along-track excerpts centered at 400, 1500 and 4000 m downwind of the emitter at <inline-formula><mml:math id="M311" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M312" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M313" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M314" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution. The respective positions of the along-track excerpts are indicated by the small grey lines in <bold>(b)</bold> and <bold>(c)</bold>. The <inline-formula><mml:math id="M315" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M316" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> dimensions of the Hestia Indianapolis domain are illustrated as hypothetical satellite across-track and along-track dimensions, respectively.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f07.png"/>

          </fig>

      <p id="d1e4953">Downwind <inline-formula><mml:math id="M317" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations from each emitting source (pixel) in the Hestia dataset are calculated across an equidistant grid at 50 m resolution in all dimensions, and the contributions from all individual emitting sources (pixels) are subsequently combined to form a three-dimensional <inline-formula><mml:math id="M318" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration field over Indianapolis. Figure <xref ref-type="fig" rid="Ch1.F7"/>b shows the resulting (vertically integrated) two-dimensional field of (noiseless) X<inline-formula><mml:math id="M319" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements at <inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M321" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution over a constant background with a surface pressure of 1013 hPa. While weaker diffuse sources like streets cannot be identified, the plumes from stronger point sources are clearly pronounced given the high spatial resolution that allows for a detailed mapping of the plumes. For comparison, Fig. <xref ref-type="fig" rid="Ch1.F7"/>c shows the corresponding X<inline-formula><mml:math id="M322" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements assuming a coarser spatial resolution of <inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M324" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. Although the stronger plumes can still be identified at the coarser resolution, the X<inline-formula><mml:math id="M325" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements are significantly lower and each plume is only sampled by a few pixels. Figure <xref ref-type="fig" rid="Ch1.F7"/>d further shows these X<inline-formula><mml:math id="M326" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements in more detail for three along-track excerpts centered at 400, 1500 and 4000 m downwind of the strongest emitter in Indianapolis, with an annual emission rate of 3.24 <inline-formula><mml:math id="M327" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in 2015. The positions of the three along-track excerpts are indicated with grey lines in Fig. <xref ref-type="fig" rid="Ch1.F7"/>b and c. With a spatial resolution of <inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, the along-track plume excerpts are only sampled by one pixel each, with a maximum X<inline-formula><mml:math id="M330" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancement of 1.2 ppm. With the envisaged  <inline-formula><mml:math id="M331" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M332" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution, however, the plume is sampled by 7, 15 and 29 pixels in the along-track dimension 400, 1500 and 4000 m downwind of the emitter, respectively, with maximum X<inline-formula><mml:math id="M333" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements reaching approximately 18, 6 and 3 ppm, respectively. This clearly demonstrates the benefit of an instrument with a high spatial resolution when resolving <inline-formula><mml:math id="M334" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes from space.</p>
</sec>
<sec id="Ch1.S5.SS1.SSS2">
  <label>5.1.2</label><title>Surface albedo data from Sentinel-2</title>
      <?pagebreak page2897?><p id="d1e5189">To accurately simulate the instrument SNR and hence the measurement noise, it is important to know how large a fraction of the solar radiation incident on the Earth's surface is reflected back towards space. To get realistic estimates of the surface albedo within the Hestia Indianapolis domain, data from the European Sentinel-2 satellites are used. The multispectral instrument aboard Sentinel-2 measures the TOA radiance in 13 spectral bands with a spatial resolution ranging from  <inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M336" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:mn mathvariant="normal">60</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M338" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. For this study, we use the Sentinel-2 L1C radiances measured in spectral band 12 (centered at approx. 2200 nm) at a spatial resolution of <inline-formula><mml:math id="M339" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M340" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. The software Sen2Cor <xref ref-type="bibr" rid="bib1.bibx17" id="paren.49"/> is employed to compute the corresponding L2 surface reflectances from the L1C TOA radiances through a so-called atmospheric correction.</p>
      <p id="d1e5265">Surface reflectance data for the month of July 2018 are computed and re-gridded (using nearest neighbor) to the envisaged spatial resolution of <inline-formula><mml:math id="M341" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M342" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. The surface reflectance for Sentinel-2 pixels classified as vegetation is scaled by a factor of 0.82 in order to account for the generally lower reflectance by vegetation in the SWIR-2 window compared to Sentinel-2's band 12. The scaling factor has been derived using spectral reflectance data from the ECOSTRESS spectral library <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx38" id="paren.50"/>. Figure <xref ref-type="fig" rid="Ch1.F8"/>b shows the gridded surface reflectance data for Indianapolis together with a corresponding red–green–blue (RGB) composite (Fig. <xref ref-type="fig" rid="Ch1.F8"/>a) using Sentinel-2 data from the bands centered at red, green and blue wavelengths as a reference. The scaled and gridded Sentinel-2 surface reflectance data are taken as representative for a constant Lambertian surface albedo within the entire SWIR-2 window. Figure S1 in the Supplement shows spectral reflectances in the SWIR spectral region for various urban materials using data from the Spectral Library of impervious Urban Materials <xref ref-type="bibr" rid="bib1.bibx31" id="paren.51"><named-content content-type="pre">SLUM;</named-content></xref>. The small spectral variations within the SWIR-2 spectral window used in this study indicate that the true spectral signatures of the surface albedo could be fitted with sufficient precision using the second-order polynomial during the retrieval, and hence the assumption of a constant albedo is reasonable for this study.</p>
      <p id="d1e5304">The average surface reflectance within the Hestia domain is 0.13. Despite annual variability in surface reflectance, mainly due to changes in vegetation and/or crops, this is a value representative throughout most of the year. For comparison, average surface reflectances from the same source for January (snow-free days), April and October 2018 amount to 0.11, 0.17 and 0.11, respectively.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e5310"><bold>(a)</bold> Sentinel-2 true-color RGB image of Indianapolis (Hestia domain) at <inline-formula><mml:math id="M343" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M344" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution derived from Sentinel-2 measurements in July 2018. <bold>(b)</bold> Corresponding surface reflectance data using data from Sentinel-2's spectral band 12 centered at approximately 2200 nm, scaled to the SWIR-2 spectral window. Again, the <inline-formula><mml:math id="M345" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M346" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> dimensions of the Hestia Indianapolis domain are illustrated as hypothetical satellite across-track and along-track dimensions, respectively.</p></caption>
            <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f08.png"/>

          </fig>

</sec>
<sec id="Ch1.S5.SS1.SSS3">
  <label>5.1.3</label><title>Background data from CarbonTracker</title>
      <p id="d1e5369">Background data, including vertical profiles of <inline-formula><mml:math id="M347" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M348" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>, temperature and pressure, are taken for 15 July 2016 from the CarbonTracker CT2017 dataset <xref ref-type="bibr" rid="bib1.bibx45" id="paren.52"><named-content content-type="post">with updates documented at <uri>http://carbontracker.noaa.gov</uri>, last access: 18 March 2019</named-content></xref>. The CarbonTracker CT2017 data over Indianapolis are provided at a spatial resolution of 1<inline-formula><mml:math id="M349" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M350" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1<inline-formula><mml:math id="M351" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, meaning that the entire Hestia Indianapolis domain is covered by one single CarbonTracker pixel, leading to a constant background data field.</p>
</sec>
</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><?xmltex \opttitle{Simulated {$\protect\chem{CO_{2}}$} plume observations}?><title>Simulated <inline-formula><mml:math id="M352" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume observations</title>
      <p id="d1e5451">As in Sect. <xref ref-type="sec" rid="Ch1.S4"/>, the above sets of input data are used to simulate synthetic measurements (spectral radiances) and the corresponding instrument noise of the proposed instrument concept using the forward model and the instrument noise model (Sect. <xref ref-type="sec" rid="Ch1.S3"/>). The SZA is calculated for the given coordinates in the Hestia domain assuming the sun-synchronous orbit described in Sect. <xref ref-type="sec" rid="Ch1.S2"/> and an observation date of 15 July 2018, which translates to an SZA of about 18<inline-formula><mml:math id="M353" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Corresponding X<inline-formula><mml:math id="M354" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> abundances are then retrieved from the simulated spectral radiances such that the ability to observe the <inline-formula><mml:math id="M355" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes from the Hestia Indianapolis data can be evaluated. In this first assessment we focus solely on the instrument performance in terms of its <inline-formula><mml:math id="M356" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume quantification capabilities, and hence we perform the high-resolution simulations with the expected instrument-noise-induced errors only, i.e., by assuming a non-scattering atmosphere.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e5505"><bold>(a)</bold> X<inline-formula><mml:math id="M357" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements with respect to the background retrieved from the simulated synthetic measurements over the Hestia Indianapolis domain under non-scattering conditions. Locations of the four strongest point sources are labeled with <inline-formula><mml:math id="M358" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. <bold>(b)</bold> Corresponding deviations between retrieved (“retr”) and true X<inline-formula><mml:math id="M359" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Dark scenes with albedo <inline-formula><mml:math id="M360" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> have been filtered out due to unreliable X<inline-formula><mml:math id="M361" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrievals.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f09.png"/>

        </fig>

      <?pagebreak page2898?><p id="d1e5579">Figure <xref ref-type="fig" rid="Ch1.F9"/>a shows the retrieved field of X<inline-formula><mml:math id="M362" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements with respect to the retrieved background X<inline-formula><mml:math id="M363" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> over the Hestia domain. The <inline-formula><mml:math id="M364" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume from the strongest point source, <inline-formula><mml:math id="M365" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, with an annual <inline-formula><mml:math id="M366" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rate of <inline-formula><mml:math id="M367" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.24</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M368" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, is clearly resolved with local X<inline-formula><mml:math id="M369" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements well above 100 ppm close to the emitting source. Although they emit considerably less <inline-formula><mml:math id="M370" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the plumes from the second- and third-strongest point sources, <inline-formula><mml:math id="M371" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M372" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, with annual <inline-formula><mml:math id="M373" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rates of <inline-formula><mml:math id="M374" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.55</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M375" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M376" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.48</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M377" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, respectively, can be clearly separated from the background as well. The plume from the fourth-strongest point source, <inline-formula><mml:math id="M378" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, with an annual <inline-formula><mml:math id="M379" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rate of <inline-formula><mml:math id="M380" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.32</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M381" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, can also be observed but is partly obscured by filtered-out dark surface areas for which retrieval errors are too high. Plumes from weaker point sources (<inline-formula><mml:math id="M382" display="inline"><mml:mrow><mml:mi mathvariant="italic">≲</mml:mi><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M383" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and other sources like streets and highways cannot be identified given the spatial resolution and instrument noise errors of the proposed instrument.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><label>Figure 10</label><caption><p id="d1e5907">Upper panels: retrieved two-dimensional fields of X<inline-formula><mml:math id="M384" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements in the vicinity of the four strongest <inline-formula><mml:math id="M385" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emitters <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M387" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M389" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> within the Hestia Indianapolis dataset. Lower panels: corresponding per-pixel (circles) and average (solid lines) along-track X<inline-formula><mml:math id="M390" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements within the area 200 to 2200 m downwind and <inline-formula><mml:math id="M391" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula> to 1000 across-wind of the respective emitters. The blue rectangles in the upper panels show the areas from which the corresponding per-pixel and average along-track X<inline-formula><mml:math id="M392" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements, depicted in the respective lower panels, are extracted and calculated. The color of the circles follows the color bars in the respective upper panels.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://amt.copernicus.org/articles/13/2887/2020/amt-13-2887-2020-f10.png"/>

        </fig>

      <p id="d1e6015">One concern with high-resolution <inline-formula><mml:math id="M393" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> remote sensing is the impact of albedo heterogeneity at an urban scale at such a high spatial resolution. For the non-scattering scenario simulated here, the albedo fitted by the retrieval algorithm matches the reference input albedo with an average (absolute) deviation of 0.14 %, and there is consequently no spatial variability in the accuracy of the albedo retrieval that in turn affects the X<inline-formula><mml:math id="M394" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrieval accuracy. There is, however, the evident effect that a higher albedo leads to a higher SNR and hence a generally lower noise error. This is evident from Fig. <xref ref-type="fig" rid="Ch1.F9"/>b, showing the difference between the retrieved and true X<inline-formula><mml:math id="M395" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, thus illustrating an instantaneous noise error field that would be expected for a single satellite overpass. Generally, the deviations from the true X<inline-formula><mml:math id="M396" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are smaller over areas of brighter surfaces like concrete, whereas the deviations are larger over dark surfaces like forests (see also Fig. <xref ref-type="fig" rid="Ch1.F8"/>). The effect of albedo heterogeneity in combination with scattering<?pagebreak page2899?> particles is not addressed in this paper and will have to be analyzed in future studies.</p>
      <p id="d1e6067">Across the entire Hestia domain (but excluding dark scenes with albedo <inline-formula><mml:math id="M397" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>) 68 % and 95 % of the X<inline-formula><mml:math id="M398" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrievals deviate from the true X<inline-formula><mml:math id="M399" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> by less than 1.1 and 2.3 ppm, respectively. This is comparable to the noise error obtained for the global trial ensemble in Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/> (1.1 and 2.0 ppm, respectively).</p>
      <p id="d1e6104">Figure <xref ref-type="fig" rid="Ch1.F10"/> shows close-ups of the simulated X<inline-formula><mml:math id="M400" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancement field (upper panels) in the vicinity of the four strongest emitters in the Hestia Indianapolis dataset (<inline-formula><mml:math id="M401" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M402" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F9"/>a), along with the corresponding per-pixel and average along-track X<inline-formula><mml:math id="M403" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements (lower panels) for the range 200–2200 m downwind of the respective emitting sources. Enhancements from the 200 m closest to each emitting source are excluded as those scenes could likely be obscured by condensate in a real situation.</p>
      <?pagebreak page2900?><p id="d1e6156">The plume of the strongest emitter <inline-formula><mml:math id="M404" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Indianapolis with an annual emission rate of <inline-formula><mml:math id="M405" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.24</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M406" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is clearly resolved. Within the area 200–2200 m downwind of the emitting source (blue square), maximum enhancements exceed 25 ppm, and in total, approximately 200 (60) pixels have enhancements above 4 ppm (8 ppm), representing enhancements of approximately 1 % (2 %) with respect to the background. The average along-track X<inline-formula><mml:math id="M407" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancement 200–2200 m downwind of the emitting source (blue and white line) reaches 12 ppm. The plumes from the second- and third-strongest emitters, <inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, which are approximately 6 times weaker than <inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> with annual emission rates of <inline-formula><mml:math id="M411" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.55</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.48</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M413" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, respectively, have considerably lower X<inline-formula><mml:math id="M414" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements but can nevertheless clearly be separated from the background with distinct increments in both per-pixel and average X<inline-formula><mml:math id="M415" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements within the area 200–2200 m downwind of the emitters (blue squares). While the background fields vary from approximately <inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> to 1 ppm due to instrument noise, the per-pixel plume enhancements vary from approximately 0.5 to 3 ppm, with single enhancements exceeding 4 ppm close to the emitting source. The average along-track X<inline-formula><mml:math id="M417" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements 200–2200 m downwind of the emitting sources (blue and white lines) reach 1.9 and 1.5 ppm for <inline-formula><mml:math id="M418" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M419" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, respectively. Despite being partly obscured by filtered-out dark surfaces (water), the plume from the fourth-strongest emitter <inline-formula><mml:math id="M420" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, with an annual emission rate of <inline-formula><mml:math id="M421" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.32</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M422" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, can also be separated from the background both when looking at the two-dimensional field and the per-pixel enhancements within the area 200–2200 m downwind of the emitter. With maximum average X<inline-formula><mml:math id="M423" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements of at most approximately 1.3 ppm, the proposed instrument concept is, however, approaching the limit of what it could achieve in terms of <inline-formula><mml:math id="M424" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume observations under favorable conditions, i.e., when the effect of aerosol-induced errors is neglected and the SZA is relatively low. A second peak in the average along-track X<inline-formula><mml:math id="M425" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements is observed approximately 850 m above (north of) the fourth-strongest emitter <inline-formula><mml:math id="M426" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. This enhancement stems from the <inline-formula><mml:math id="M427" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume from the seventh-strongest emitter in Indianapolis (labeled <inline-formula><mml:math id="M428" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the top right panel of Fig. <xref ref-type="fig" rid="Ch1.F10"/>), with an annual emission rate of <inline-formula><mml:math id="M429" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M430" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Quantifying the <inline-formula><mml:math id="M431" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rate from such a weak source is, however, not realistic given the low sampling density (especially further downwind) in combination with the weak per-pixel enhancements.</p>
</sec>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e6549">To follow the progress on reducing anthropogenic <inline-formula><mml:math id="M432" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions worldwide, independent monitoring systems are of key importance. In this paper, we present the concept of a compact spaceborne imaging spectrometer with a high spatial resolution of <inline-formula><mml:math id="M433" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M434" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> targeting the monitoring of localized <inline-formula><mml:math id="M435" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions. We further demonstrate how the instrument concept could resolve <inline-formula><mml:math id="M436" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes from localized point sources like medium-sized power plants, thus having the potential to contribute to the independent large-scale verification of reported <inline-formula><mml:math id="M437" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions at the facility level.</p>
      <p id="d1e6620">Through radiative transfer simulations using a global trial ensemble, a preliminary yet realistic instrument design and an instrument noise model, we show that the expected instrument-noise-induced X<inline-formula><mml:math id="M438" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors are smaller than 1.1 and 2.0 ppm for 68 % and 95 % of the retrievals, respectively, using the SWIR-2 spectral setup covering the <inline-formula><mml:math id="M439" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands near 2000 nm. For the SWIR-1 spectral setup covering the weaker <inline-formula><mml:math id="M440" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> absorption bands near 1600 nm, the instrument-noise-induced X<inline-formula><mml:math id="M441" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors are significantly higher, making it inadequate for the proposed instrument concept. Although the main focus in this paper is on the performance of the proposed <inline-formula><mml:math id="M442" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring instrument concept, we could also show that despite the usage of a single spectral window and a relatively coarse spectral resolution of <inline-formula><mml:math id="M443" display="inline"><mml:mn mathvariant="normal">1.29</mml:mn></mml:math></inline-formula> nm, scattering by highly complex atmospheric aerosol compositions can be partly accounted for during X<inline-formula><mml:math id="M444" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> retrievals on the global scale, limiting the deviation from the true X<inline-formula><mml:math id="M445" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to at most 4.0 ppm for two-thirds of the retrievals. This gives us confidence that accurate two-dimensional fields of X<inline-formula><mml:math id="M446" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements could be retrieved from real spectra measured by the proposed instrument concept. A reasonable a priori state vector with respect to the aerosol properties (e.g., provided through models or a companion aerosol instrument; <xref ref-type="bibr" rid="bib1.bibx24" id="altparen.53"/>) would, however, still be important. As an example, a multi-angle polarimeter instrument is planned to fly together with the <inline-formula><mml:math id="M447" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> instrument onboard the CO2M mission in order to minimize systematic X<inline-formula><mml:math id="M448" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> errors <xref ref-type="bibr" rid="bib1.bibx18" id="paren.54"/>.</p>
      <p id="d1e6748">Using high-resolution <inline-formula><mml:math id="M449" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data for the city of Indianapolis together with a Gaussian dispersion model, corresponding high-resolution albedo data and additional radiative transfer simulations, we have clearly demonstrated that the instrument is well suited for the task of the spaceborne <inline-formula><mml:math id="M450" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring of large and medium-sized power plants and can (only limited by its own instrument noise) resolve emission plumes from point sources with an emission source strength down to the order of 0.3 <inline-formula><mml:math id="M451" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. This is well below the target emission source strength of 1 <inline-formula><mml:math id="M452" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, hence leaving a significant margin for additional error sources and aspects not yet addressed here.</p>
      <p id="d1e6819">Given the results from this first performance assessment, the proposed instrument concept demonstrates clear potential for the independent quantification of <inline-formula><mml:math id="M453" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from medium-sized power plants (1–10 <inline-formula><mml:math id="M454" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Mt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), which are currently not targeted by other planned spaceborne <inline-formula><mml:math id="M455" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> monitoring missions. On the local scale (Indianapolis), we have constrained the present analysis to a day in July using a rather simplistic Gaussian dispersion model that assumes constant atmospheric stability and (unidirectional) horizontal wind speed. It might be that the ability to resolve <inline-formula><mml:math id="M456" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes will become more, perhaps even too, challenging under certain more realistic conditions. Nevertheless, these first results are certainly promising and encourage further studies.</p>
      <p id="d1e6879">The high spatial resolution needed to resolve emission plumes from localized sources like medium-sized power plant does, however, imply limitations in terms of spatial coverage arising from the narrow swath (50 km assuming 1000 detector pixels in the spatial dimension) and the forward motion compensation. Hence, a single satellite with the proposed instrument concept could not quantify <inline-formula><mml:math id="M457" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions at the local to regional scale with dense global coverage and high temporal resolution but would have to be restricted to some predefined targets. The relatively compact design with a single spectral window could, however, allow for the deployment of a fleet of instruments and hence the independent monitoring of localized <inline-formula><mml:math id="M458" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions on a larger scale with high temporal resolution. As an alternative to a fleet of satellites, the proposed instrument concept could also prove useful in synergy with a spaceborne <inline-formula><mml:math id="M459" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> lidar <xref ref-type="bibr" rid="bib1.bibx29" id="paren.55"><named-content content-type="pre">e.g.,</named-content></xref>; the passive spectrometer would benefit from the lidar's accuracy and knowledge of the light path, and the lidar would benefit from the spectrometer's imaging capability.</p>
      <p id="d1e6920">With the successful demonstration in this paper, i.e., that <inline-formula><mml:math id="M460" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission plumes from medium-sized power plants can be resolved from space with a compact yet realistic instrument design, the next step will be to analyze the ability to quantify the corresponding <inline-formula><mml:math id="M461" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission rates from the two-dimensional fields of synthetically retrieved X<inline-formula><mml:math id="M462" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> enhancements. This follow-up study will be conducted for different seasons (with varying surface albedo<?pagebreak page2901?> and solar zenith angles), meteorological conditions and emission source strengths using large eddy, rather than Gaussian, modeling of the <inline-formula><mml:math id="M463" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plume dispersion. Although the effect of aerosols has partly been assessed on the global scale in this study, information on the properties and distribution of aerosols should also be included in the local-scale simulations in order to better understand the instrument's ability to resolve and quantify localized <inline-formula><mml:math id="M464" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions under more realistic conditions. Such an in-depth aerosol analysis is, however, the task of further future studies.</p>
</sec>

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

      <p id="d1e6982">Hestia Project data at <inline-formula><mml:math id="M465" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M466" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution are available from KG upon request (Hestia Project data at original <inline-formula><mml:math id="M467" display="inline"><mml:mrow><mml:mn mathvariant="normal">200</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">200</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M468" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> spatial resolution are available at <ext-link xlink:href="https://doi.org/10.18434/T4/1503341" ext-link-type="DOI">10.18434/T4/1503341</ext-link>; <xref ref-type="bibr" rid="bib1.bibx21" id="altparen.56"/>). Sentinel-2 data are available at <uri>https://scihub.copernicus.eu/dhus/#/home</uri> (last access: 9 July 2019). ECOSTRESS Spectral Library data are available at <uri>https://speclib.jpl.nasa.gov</uri> (last access: 12 February 2019). CarbonTracker CT2017 data are available at <uri>http://carbontracker.noaa.gov</uri> (last access: 18 March 2019). SLUM data are available at <uri>http://www.met.reading.ac.uk/micromet/LUMA/SLUM.html</uri> (last access: 18 March 2020).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e7050">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/amt-13-2887-2020-supplement" xlink:title="pdf">https://doi.org/10.5194/amt-13-2887-2020-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e7059">JS developed the instrument noise model, performed the simulations and wrote most of the paper. DK led the instrument design work. JW performed the spectral sizing. CP assisted in developing the instrument noise model and performed the FMC analysis. IS did the optical design. KRG and JL developed and provided the Hestia Project <inline-formula><mml:math id="M469" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data. JS, DK, JW, CP, IS, AR and AB defined the mission concept and instrument design. AR and AB led the study.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e7077">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e7083">We kindly acknowledge all persons and institutions that made their data available to us for this study. CARMA v3.0 <inline-formula><mml:math id="M470" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission data for power plants worldwide were provided by Kevin Ummel. Sentinel-2 data used to derive high-resolution surface reflectance data were provided by the ESA trough the Copernicus Open Acess Hub. Spectral reflectance data used to scale the Sentinel-2 surface reflectance data were reproduced from the ECOSTRESS Spectral Library through the courtesy of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. CarbonTracker CT2017 data were provided by NOAA ESRL, Boulder, Colorado, USA. Spectral reflectance data for urban materials (see the Supplement) were reproduced from the Spectral Library of impervious Urban Materials (SLUM) through the courtesy of the University of Reading, UK.  We also thank Peter Haschberger, Claas Köhler, Günter Lichtenberg, Andreas Baumgartner, Christoph Kiemle, Luca Bugliaro, Julian Kostinek and Andreas Luther for valuable input on the mission concept, instrument design and/or a previous version of this paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e7099">The article processing charges for this open-access publication  were covered by a Research  Centre of the Helmholtz Association.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e7105">This paper was edited by Andreas Richter and reviewed by Luis Guanter and one anonymous referee.</p>
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<abstract-html><p>The UNFCCC (United Nations Framework Convention on Climate Change) requires the nations of the world to report their carbon dioxide (CO<sub>2</sub>) emissions. The independent verification of these reported emissions is a cornerstone for advancing towards the emission accounting and reduction measures agreed upon in the Paris Agreement. In this paper, we present the concept and first performance assessment of a compact spaceborne imaging spectrometer with a spatial resolution of 50×50&thinsp;m<sup>2</sup> that could contribute to the <q>monitoring, verification and reporting</q> (MVR) of CO<sub>2</sub> emissions worldwide. CO<sub>2</sub> emissions from medium-sized power plants (1–10&thinsp;Mt CO<sub>2</sub> yr<sup>−1</sup>), currently not targeted by other spaceborne missions, represent a significant part of the global CO<sub>2</sub> emission budget. In this paper we show that the proposed instrument concept is able to resolve emission plumes from such localized sources as a first step towards corresponding CO<sub>2</sub> flux estimates.</p><p>Through radiative transfer simulations, including a realistic instrument noise model and a global trial ensemble covering various geophysical scenarios, it is shown that an instrument noise error of 1.1&thinsp;ppm (1<i>σ</i>) can be achieved for the retrieval of the column-averaged dry-air mole fraction of CO<sub>2</sub> (XCO<sub>2</sub>). Despite a limited amount of information from a single spectral window and a relatively coarse spectral resolution, scattering by atmospheric aerosol and cirrus can be partly accounted for in the XCO<sub>2</sub> retrieval, with deviations of at most 4.0&thinsp;ppm from the true abundance for two-thirds of the scenes in the global trial ensemble.</p><p>We further simulate the ability of the proposed instrument concept to observe CO<sub>2</sub> plumes from single power plants in an urban area using high-resolution CO<sub>2</sub> emission and surface albedo data for the city of Indianapolis. Given the preliminary instrument design and the corresponding instrument noise error, emission plumes from point sources with an emission rate down to the order of 0.3&thinsp;Mt CO<sub>2</sub> yr<sup>−1</sup> can be resolved, i.e., well below the target source strength of 1&thinsp;Mt CO<sub>2</sub> yr<sup>−1</sup>. This leaves a significant margin for additional error sources, like scattering particles and complex meteorology, and shows the potential for subsequent CO<sub>2</sub> flux estimates with the proposed instrument concept.</p></abstract-html>
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