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  <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-11-473-2018</article-id><title-group><article-title>Retrieval of <inline-formula><mml:math id="M1" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M2" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> volume
emission rates in the mesosphere and lower thermosphere using SCIAMACHY
<?xmltex \hack{\break}?>MLT limb scans</article-title>
      </title-group><?xmltex \runningtitle{SCIAMACHY {$\chem{O_{2}(^{1}\Sigma)}$} and {$\chem{O_{2}(^{1}\Delta)}$} MLT volume emission rates}?><?xmltex \runningauthor{A. Zarboo et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Zarboo</surname><given-names>Amirmahdi</given-names></name>
          <email>amirmahdi.zarboo@kit.edu</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff3">
          <name><surname>Bender</surname><given-names>Stefan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8728-053X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Burrows</surname><given-names>John P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1547-8130</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Orphal</surname><given-names>Johannes</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Sinnhuber</surname><given-names>Miriam</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3527-9051</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Institute of Meteorolgy and Climate Research (IMK-ASF), Karlsruhe Institute of Technology, Karlsruhe, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Institute of Environmental Physics, University of Bremen, Bremen, Germany</institution>
        </aff>
        <aff id="aff3"><label>a</label><institution>now at: Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Amirmahdi Zarboo (amirmahdi.zarboo@kit.edu)</corresp></author-notes><pub-date><day>23</day><month>January</month><year>2018</year></pub-date>
      
      <volume>11</volume>
      <issue>1</issue>
      <fpage>473</fpage><lpage>487</lpage>
      <history>
        <date date-type="received"><day>27</day><month>July</month><year>2017</year></date>
           <date date-type="rev-request"><day>14</day><month>August</month><year>2017</year></date>
           <date date-type="rev-recd"><day>16</day><month>November</month><year>2017</year></date>
           <date date-type="accepted"><day>9</day><month>December</month><year>2017</year></date>
      </history>
      <permissions>
        
        
      <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/11/473/2018/amt-11-473-2018.html">This article is available from https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018.pdf</self-uri>
      <abstract>
    <p id="d1e170">We present the retrieved volume emission rates (VERs) from the
airglow of both the daytime and twilight <inline-formula><mml:math id="M3" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band and
<inline-formula><mml:math id="M4" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band emissions in the mesosphere and lower thermosphere
(MLT). The SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY)
onboard the European Space Agency Envisat satellite
observes upwelling radiances in limb-viewing geometry during its special MLT
mode over the range 50–150 km. In this study we use the limb observations
in the visible (595–811 nm) and near-infrared (1200–1360 nm) bands.</p>
    <p id="d1e215">We have investigated the daily mean latitudinal distributions and the time
series of the retrieved VER in the altitude range from 53 to 149 km. The
maximal observed VERs of <inline-formula><mml:math id="M5" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> during daytime are typically 1
to 2 orders of magnitude larger than those of <inline-formula><mml:math id="M6" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The
latter peaks at around 90 km, whereas the <inline-formula><mml:math id="M7" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emissivity
decreases with altitude, with the largest values at the lower edge of the
observations (about 53 km). The VER values in the upper mesosphere (above
80 km) are found to depend on the position of the sun, with pronounced high
values occurring during summer for <inline-formula><mml:math id="M8" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M9" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
emissions show additional high values at polar latitudes during winter and
spring. These additional high values are presumably related to the
downwelling of atomic oxygen after large sudden stratospheric warmings (SSWs).
Accurate measurements of the <inline-formula><mml:math id="M10" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M11" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
airglow, provided that the mechanism of their production is understood, yield
valuable information about both the chemistry and dynamics in the MLT. For
example, they can be used to infer the amounts and distribution of ozone,
solar heating rates, and temperature in the MLT.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p id="d1e368">Schematic overview depicting processes that contribute to the
production of Oxygen emission bands in the middle atmosphere. The black solid
arrows are the most important gas phase reactions (<inline-formula><mml:math id="M12" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>) and quenching
reactions (<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The blue and green solid arrows are photodissociation and
photoexcitation processes respectively (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). Dashed arrows correspond
to spontaneous radiative emissions (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), and the red dashed arrows show
the radiative emissions that are the subject of this study. (<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>) in
<inline-formula><mml:math id="M17" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> denotes several excited states (see text for explanation).</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f01.pdf"/>

      </fig>

      <p id="d1e440">The atmospheric airglow in the mesosphere and thermosphere above
<inline-formula><mml:math id="M18" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 60 km is formed by fluorescent emission from excited states of
atoms and molecules. Atoms and molecules in the mesosphere and lower
thermosphere (MLT) can be excited by absorption of solar radiation
(photoluminescence) or by exothermic chemical reactions (chemiluminescence; see, e.g., <xref ref-type="bibr" rid="bib1.bibx7" id="altparen.1"/>).</p>
      <p id="d1e453">The processes that contribute to the airglow of atomic and molecular oxygen
in the mesosphere and lower thermosphere are shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>.
The recombination of atomic oxygen <xref ref-type="bibr" rid="bib1.bibx1" id="paren.2"/>, denoted as
Reaction (<xref ref-type="disp-formula" rid="R1"/>) and (<inline-formula><mml:math id="M19" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>) in Fig. <xref ref-type="fig" rid="Ch1.F1"/>, produces
<inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> excited molecules:
          <disp-formula id="R1" content-type="numbered reaction"><mml:math id="M21" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>⟶</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        Here, <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> represents any of the seven states below the first dissociation
limit. Bates and others argue that the population distribution between these
states can best be approximated statistically, in which the
<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Π</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> state is produced in almost 40 % of the collisions
<xref ref-type="bibr" rid="bib1.bibx45 bib1.bibx5 bib1.bibx51" id="paren.3"/>. Most of the <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> derived
from recombination is found in the <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> state
<xref ref-type="bibr" rid="bib1.bibx43" id="paren.4"/>, and in a recent review Huestis concludes that all of the
recombining atoms pass through the Herzberg states <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msup><mml:msup><mml:mi>A</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx19" id="paren.5"/>.
<xref ref-type="bibr" rid="bib1.bibx46" id="text.6"/> provide the quenching parameters resulted from
analyzing the measurements of the near-ultraviolet portion of the nightglow
to fit the synthetic spectra of the Herzberg bands of <inline-formula><mml:math id="M29" 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>. These
parameters set an upper limit of 10 % production efficiency on the
generation of <inline-formula><mml:math id="M30" 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>(<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) in the atomic oxygen
association reaction . Admittedly, proper accounting of the correct products
of Reaction (<xref ref-type="disp-formula" rid="R1"/>) can be complex. Recent research has
investigated this issue (e.g., <xref ref-type="bibr" rid="bib1.bibx23 bib1.bibx22" id="altparen.7"/>). Therefore
we assume the production of a surrogate “hybrid” state <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> in the
photochemical model.</p>
      <p id="d1e727">The photolysis of ozone (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>,
Reaction <xref ref-type="disp-formula" rid="R2"/>) in the Hartley band (<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">310</mml:mn></mml:mrow></mml:math></inline-formula> nm) leads to the
first electronically excited state of atomic oxygen <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
molecular oxygen <inline-formula><mml:math id="M36" display="inline"><mml:mrow><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:mo>(</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx12" id="paren.8"/>:
          <disp-formula id="R2" content-type="numbered reaction"><mml:math id="M37" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">310</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        The photolysis of molecular oxygen in the Schumann–Runge continuum
(<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">SRC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>, Reaction <xref ref-type="disp-formula" rid="Ch1.E1"/>) and at
Lyman <inline-formula><mml:math id="M39" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>,
Reaction <xref ref-type="disp-formula" rid="Ch1.E2"/>) leads to electronically excited oxygen atoms
<inline-formula><mml:math id="M41" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx34" id="paren.9"/>:

              <disp-formula specific-use="align" content-type="numbered reaction"><mml:math id="M42" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E1"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">130</mml:mn><mml:mo>≤</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">175</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">121.6</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e1112">Quenching (collisional de-excitation) processes are represented by black
solid arrows and denoted by (<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) in Fig. <xref ref-type="fig" rid="Ch1.F1"/>. The <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
produced by Reaction (<xref ref-type="disp-formula" rid="R1"/>), can be quenched by atomic oxygen
to produce <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> via Reaction (<xref ref-type="disp-formula" rid="Ch1.E3"/>) (<inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
Fig. <xref ref-type="fig" rid="Ch1.F1"/>) <xref ref-type="bibr" rid="bib1.bibx2" id="paren.10"/> or quenched by molecular oxygen to
produce <inline-formula><mml:math id="M47" 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>(<inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) via
Reaction (<xref ref-type="disp-formula" rid="Ch1.E4"/>) (<inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>)
<xref ref-type="bibr" rid="bib1.bibx16" id="paren.11"/>:

              <disp-formula specific-use="align" content-type="numbered reaction"><mml:math id="M50" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E4"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>.</mml:mo><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, by quenching with <inline-formula><mml:math id="M52" 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>(<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>),
produces <inline-formula><mml:math id="M54" 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>(<inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) via Reaction (<xref ref-type="disp-formula" rid="R3"/>),
which combines <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>q</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.F1"/> <xref ref-type="bibr" rid="bib1.bibx30" id="paren.12"/>:
          <disp-formula id="R3" content-type="numbered reaction"><mml:math id="M58" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        Photoabsorption of the solar radiation at 761.9 nm produces
<inline-formula><mml:math id="M59" 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>(<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) directly via
          <disp-formula id="R4" content-type="numbered reaction"><mml:math id="M61" display="block"><mml:mrow><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">761.9</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
        in the sunlit mesosphere <xref ref-type="bibr" rid="bib1.bibx32" id="paren.13"/>, shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>
as the radiative excitation <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e1725">Then, according to Reaction (<xref ref-type="disp-formula" rid="R5"/>), <inline-formula><mml:math id="M63" 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>(<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
can be reduced in energy to <inline-formula><mml:math id="M65" 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>(<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) by collisions
with any of the abundant species such as <inline-formula><mml:math id="M67" 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>, <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M69" 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>,
or <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> (denoted by “M”), shown as <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>
<xref ref-type="bibr" rid="bib1.bibx30" id="paren.14"/>:
          <disp-formula id="R5" content-type="numbered reaction"><mml:math id="M72" display="block"><mml:mrow><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:mo>(</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        Note that the above is a fast process (spin-conserved).</p>
      <p id="d1e1908"><inline-formula><mml:math id="M73" 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>(<inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) can in turn be quenched via
Reaction (<xref ref-type="disp-formula" rid="R6"/>) (<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>) to produce
<inline-formula><mml:math id="M76" 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>(<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>):
          <disp-formula id="R6" content-type="numbered reaction"><mml:math id="M78" display="block"><mml:mrow><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:mo>(</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        which is a slow process (spin forbidden because the ground state is
<inline-formula><mml:math id="M79" 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>(<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)).</p>
      <p id="d1e2074">Spontaneous radiative emissions are represented by dashed arrows and denoted
by (<inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) in Fig. <xref ref-type="fig" rid="Ch1.F1"/>. <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> decays to <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by
emitting 557.7 nm photons (the oxygen green line, Reaction <xref ref-type="disp-formula" rid="R7"/>, <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>A</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.F1"/>), which is fast (because it conserves the spin)
<xref ref-type="bibr" rid="bib1.bibx2" id="paren.15"/>:
          <disp-formula id="R7" content-type="numbered reaction"><mml:math id="M85" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>→</mml:mo><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">557.7</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e2197">Reactions (<xref ref-type="disp-formula" rid="R1"/>), (<xref ref-type="disp-formula" rid="Ch1.E3"/>), and (<xref ref-type="disp-formula" rid="R7"/>) are commonly
referred to as the Barth mechanism (<xref ref-type="bibr" rid="bib1.bibx2" id="altparen.16"/>; see, e.g., the
review by <xref ref-type="bibr" rid="bib1.bibx3" id="altparen.17"/>). The green line emission allows the deduction of the
atomic oxygen densities near 100 km, as shown for example by
<xref ref-type="bibr" rid="bib1.bibx25" id="text.18"/>. The oxygen 297.2 nm line is one of the prominent
components of the ultraviolet nightglow <xref ref-type="bibr" rid="bib1.bibx42" id="paren.19"/>, and it is
produced by <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> via Reaction (<xref ref-type="disp-formula" rid="R8"/>) <xref ref-type="bibr" rid="bib1.bibx20" id="paren.20"/>:
          <disp-formula id="R8" content-type="numbered reaction"><mml:math id="M87" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">297.2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        which is indicated by <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>.</p>
      <p id="d1e2309"><inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> – produced from Reactions (<xref ref-type="disp-formula" rid="R2"/>, <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>),
(<xref ref-type="disp-formula" rid="Ch1.E1"/>, <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">SRC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), (<xref ref-type="disp-formula" rid="Ch1.E2"/>, <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), or
(<xref ref-type="disp-formula" rid="R7"/>, <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) – can be deactivated to the ground state <inline-formula><mml:math id="M94" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by
the slow (spin-forbidden) emission:
          <disp-formula id="R9" content-type="numbered reaction"><mml:math id="M95" display="block"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">630.0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where the 630.0 nm red line <xref ref-type="bibr" rid="bib1.bibx20" id="paren.21"/> is represented by <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
Fig. <xref ref-type="fig" rid="Ch1.F1"/>.</p>
      <p id="d1e2470">Among the strongest features of the day and night airglow are the infrared
atmospheric band (<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
and the atmospheric band (<inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>→</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) of molecular oxygen <xref ref-type="bibr" rid="bib1.bibx49" id="paren.22"/>. These two
spontaneous radiative emissions, which we deal with in this work, are
represented by the thick red dashed arrows in Fig. <xref ref-type="fig" rid="Ch1.F1"/>. They are
emitted by the deactivation of the two excited states of the molecular oxygen
<inline-formula><mml:math id="M99" 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>(<inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) at 761.9 nm via
Reaction (<xref ref-type="disp-formula" rid="Ch1.E5"/>) (<inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>) and
<inline-formula><mml:math id="M102" 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>(<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) at 1.27 <inline-formula><mml:math id="M104" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m via
Reaction (<xref ref-type="disp-formula" rid="Ch1.E6"/>) (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
Fig. <xref ref-type="fig" rid="Ch1.F1"/>) <xref ref-type="bibr" rid="bib1.bibx32" id="paren.23"/>:

              <disp-formula specific-use="align" content-type="numbered reaction"><mml:math id="M106" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E5"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><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:mo>(</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">761.9</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>nm</mml:mtext><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><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:mo>(</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>→</mml:mo><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:mo>(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi mathvariant="italic">ν</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.27</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e2795">Assuming that the processes in Fig. <xref ref-type="fig" rid="Ch1.F1"/> describe the
photochemistry and chemistry, one can deduce ozone densities from
measurements of the infrared atmospheric volume emission rates (VERs) in the
<inline-formula><mml:math id="M107" 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>(<inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M109" 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>(<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
bands (hereafter <inline-formula><mml:math id="M111" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M112" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> bands
respectively). For this, the rates of all of these processes such as <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>q</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.F1"/> and in the Reactions (<xref ref-type="disp-formula" rid="R3"/>)
and (<xref ref-type="disp-formula" rid="R5"/>) should be known
<xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx47 bib1.bibx30 bib1.bibx29" id="paren.24"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
<sec id="Ch1.S1.SS1">
  <title>Previous measurements</title>
      <p id="d1e2938">The oxygen airglow was measured from spaceborne platforms and rocket
experiments in several previous studies. Measurements of the
<inline-formula><mml:math id="M115" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band include the Fabry–Pérot interferometer on the
Dynamics Explorer 2 (DE-2) satellite <xref ref-type="bibr" rid="bib1.bibx41" id="paren.25"/>, which were used to
study the overall brightness of the emission. The high-resolution Doppler
imager (HRDI) on the Upper Atmosphere Research Satellite (UARS)
<xref ref-type="bibr" rid="bib1.bibx18" id="paren.26"/> measured the Doppler shifts of rotational lines of the
<inline-formula><mml:math id="M116" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> atmospheric band to determine the winds in the
stratosphere, mesosphere, and lower thermosphere. The Wind Imaging
Interferometer (WINDII) on the same satellite <xref ref-type="bibr" rid="bib1.bibx38" id="paren.27"/> measured
wind, temperature, and emission rates. The TIMED Doppler Interferometer
(TIDI) on the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics
(TIMED) satellite <xref ref-type="bibr" rid="bib1.bibx21" id="paren.28"/> performed remote sensing measurements
of upper atmosphere winds and temperatures based on <inline-formula><mml:math id="M117" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
emission. The Remote Atmospheric and Ionospheric Detection System (RAIDS) on
the International Space Station's Kibo module <xref ref-type="bibr" rid="bib1.bibx11" id="paren.29"/>
measured the limb brightness of the <inline-formula><mml:math id="M118" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (0,0), (0,1), and
(1,1) vibrational band emissions from 80 to 180 km. The Optical Spectrograph
and InfraRed Imaging System (OSIRIS), onboard the Odin satellite
<xref ref-type="bibr" rid="bib1.bibx37" id="paren.30"/>, was used to derive temperatures in the mesosphere and lower
thermosphere region (MLT) from <inline-formula><mml:math id="M119" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e3060">Previous measurements of the <inline-formula><mml:math id="M120" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band include observations
from the near-infrared spectrometer experiment on the Solar Mesosphere
Explorer satellite (SME). SME measured emission from <inline-formula><mml:math id="M121" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
produced by photolysis of <inline-formula><mml:math id="M122" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx48" id="paren.31"/>. The infrared
atmospheric-band airglow radiometer (IRA) aboard the satellite OHZORA
measured the mesospheric ozone profile derived from <inline-formula><mml:math id="M123" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
emission <xref ref-type="bibr" rid="bib1.bibx52" id="paren.32"/>. One part of the Optical Spectrograph
and InfraRed Imager System instrument onboard the Odin satellite is a
three-channel infrared imager (IRI)
that observes the scattered sunlight and the airglow from the oxygen infrared
atmospheric band at 1.27 <inline-formula><mml:math id="M124" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m <xref ref-type="bibr" rid="bib1.bibx26" id="paren.33"/>. The TIMED–SABER
(Sounding of the Atmosphere using Broadband Emission Radiometry) data were
used to measure the <inline-formula><mml:math id="M125" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> airglow emission by a channel with
central wavelength of 1.27 <inline-formula><mml:math id="M126" display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m <xref ref-type="bibr" rid="bib1.bibx14" id="paren.34"/>.</p>
      <p id="d1e3181">All of the abovementioned studies include satellite observations of only one
of the <inline-formula><mml:math id="M127" 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> bands, either <inline-formula><mml:math id="M128" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M129" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
Simultaneous measurements of both <inline-formula><mml:math id="M130" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M131" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> airglow were part of the Mesosphere–Thermosphere
Emissions for Ozone Remote Sensing (METEORS) sounding rocket experiment. It
was launched from White Sands Missile Range, New Mexico
<xref ref-type="bibr" rid="bib1.bibx29" id="paren.35"/>, and was used to derive ozone concentrations
separately from each of the <inline-formula><mml:math id="M132" 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> bands.</p>
</sec>
<sec id="Ch1.S1.SS2">
  <title>Present work</title>
      <p id="d1e3296">In this work, we retrieve volume emission rates from the airglow of
the <inline-formula><mml:math id="M133" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M134" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> bands in the
mesosphere and lower thermosphere from the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY
(SCIAMACHY <xref ref-type="bibr" rid="bib1.bibx10" id="altparen.36"/>, <xref ref-type="bibr" rid="bib1.bibx6" id="altparen.37"/> and references therein)
onboard the European Space Agency Envisat satellite. We present the
retrieval algorithm and <inline-formula><mml:math id="M135" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M136" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band
volume emission rates. We analyze daily mean latitudinal distributions of
VERs in the altitude range of approximately 50–150 km.</p>
      <p id="d1e3386">In Sect. <xref ref-type="sec" rid="Ch1.S2"/> we describe the SCIAMACHY dataset and our
method to retrieve both the <inline-formula><mml:math id="M137" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math id="M138" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
volume emission rates. Results are presented in Sect. <xref ref-type="sec" rid="Ch1.S3"/>,
including the retrieved volume emission rates and first results on the
temporal and spatial variations of the volume emission rates. We also include
one example study of the relation between the temporal variations and the
sudden stratospheric warming (SSW) in 2009. In Sect. <xref ref-type="sec" rid="Ch1.S4"/> we summarize
the findings of our study and give conclusions.</p>
</sec>
</sec>
<sec id="Ch1.S2">
  <title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <title>Data</title>
      <p id="d1e3447">The SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY
is a passive remote sensing spectrometer that observes back-scattered, reflected, transmitted, or emitted radiation from the atmosphere
and the Earth's surface in the 240–2380 nm wavelength range. The instrument
is part of the atmospheric chemistry payload onboard the Envisat satellite,
which was operational from March 2002 until April 2012. SCIAMACHY has three
different viewing geometries: nadir, limb, and moon–sun occultations. From
July 2008 until April 2012, SCIAMACHY observed the mesosphere and lower
thermosphere region (50–150 km) regularly twice a month. This special
MLT limb mode scans the mesosphere and lower thermosphere in 30 limb points
from 50 to 150 km altitude with a vertical spacing of about 3 km. These
scans were scheduled in place of the nominal mode scans and there were
20 limb scans along one semi-orbit. Overall 84 days of mesosphere and lower
thermosphere limb measurements were carried out. In this work, we use the
visible and near-infrared spectra from channel 4 (595–811 nm) and channel 6
(1200–1360 nm) in the MLT limb-viewing geometry to retrieve volume emission
rates (VERs) from the airglow of the <inline-formula><mml:math id="M139" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M140" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> bands. Use of the additional channels covering the green
line or UV is beyond our current work, and we refer to
<xref ref-type="bibr" rid="bib1.bibx25" id="text.38"/>.</p>
      <p id="d1e3493">To generate data for our study, we used the SCIAMACHY dataset level 1b
version 8.02 and the SCIAMACHY command line tool
<monospace>SciaL1c</monospace><fn id="Ch1.Footn1"><p id="d1e3498"><uri>https://earth.esa.int/web/guest/software-tools/content/-/article/scial1c-command-line-tool-4073</uri></p></fn>
from the SCIAMACHY calibration tools. We selected two windows for each of the
two bands: 750–780 nm for the O<inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band (759–767 nm) and
1200–1360 nm for the O<inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band (1255–1285 nm). We subtract the
spectrum measured at <inline-formula><mml:math id="M143" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 360 km tangent height as a dark spectrum
from the measured spectra at all of the other tangent heights. This spectrum
contains some residual spectral (readout) patterns left from the calibration
step, and subtracting it from other spectra which have almost the same
patterns cancels out that. For the <inline-formula><mml:math id="M144" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band, there are two
masked points that appear in every scan located around 1262 and 1282 nm.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>Daytime spectra</title>
      <p id="d1e3574">A typical orbit starts with a limb measurement of the twilit atmosphere,
followed by the solar occultation measurement during sunrise over the North
Pole and an optimized limb-nadir sequence <xref ref-type="bibr" rid="bib1.bibx6" id="paren.39"/>. Our
criterion to select daytime observations out of twilight measurements is that
we require the tangent point solar zenith angle to be less than or equal to
88<inline-formula><mml:math id="M145" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Using this approach we avoid twilight measurements and all of
the measurement points are located on the dayside.</p>
      <p id="d1e3589">Examples of the daytime-calibrated spectra for orbit number 41 455, measured
on 3 February 2010 at a mean latitude of 17.3<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and a mean
longitude of 94.3<inline-formula><mml:math id="M147" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E, are shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>a for the
<inline-formula><mml:math id="M148" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band and in Fig. <xref ref-type="fig" rid="Ch1.F2"/>b for the
<inline-formula><mml:math id="M149" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.</p>
      <p id="d1e3655">The spectral region used to observe the daytime <inline-formula><mml:math id="M150" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> spectrum
includes a Rayleigh-scattering background which perturbs the retrieval.
Consequently it is necessary to estimate the Rayleigh scattering and subtract
it from the observational spectrum to yield the <inline-formula><mml:math id="M151" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission spectra. This
background scattering is attributed in part to the upwelling radiation,
multiple scattering in the lower atmosphere, and the terrestrial albedo. This
results in an absorption signature for <inline-formula><mml:math id="M152" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx37" id="paren.40"/>. To account for the multiple scattering and absorption
from the ground state <inline-formula><mml:math id="M153" 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>(<inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) to the
<inline-formula><mml:math id="M155" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, a background signal comprising the <inline-formula><mml:math id="M156" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
spectrum at the highest altitude (<inline-formula><mml:math id="M157" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 148 km) scaled to the ratio of
the mean of the out-of-band radiances is subtracted from the limb spectra at
each tangent height. We consider the spectra in the 750–759 and 767–780 nm
as out of band.</p>
      <p id="d1e3795">After this correction, we subtract a linear background from the whole signal
in each level. An example of the background-subtracted spectrum containing
the <inline-formula><mml:math id="M158" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission is shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>c.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p id="d1e3823">Examples of the daytime-calibrated spectra and the
background-corrected spectra. <bold>(a)</bold> <inline-formula><mml:math id="M159" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> on
3 February 2010; orbit 41 455; mean latitude 17.3<inline-formula><mml:math id="M160" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, mean
longitude 94.3<inline-formula><mml:math id="M161" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E. <bold>(b)</bold> as <bold>(a)</bold> but for
the <inline-formula><mml:math id="M162" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. <bold>(c)</bold> as <bold>(a)</bold> but with background
correction applied. <bold>(d)</bold> as <bold>(b)</bold> but with background
correction applied. </p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f02.pdf"/>

        </fig>

      <p id="d1e3912">For the <inline-formula><mml:math id="M163" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band, the absorption signature in the spectral
background is negligible compared to the daytime <inline-formula><mml:math id="M164" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band
spectra; therefore, we only subtract a linear background from the observation.
An example for the daytime <inline-formula><mml:math id="M165" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band spectra with background
subtracted is shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>d.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Twilight spectra</title>
      <p id="d1e3983">Because the tangent point solar zenith angle for the sun being below the
horizon varies with tangent altitude, we use Eq. (<xref ref-type="disp-formula" rid="Ch1.E7"/>) to calculate
the horizon angle for each tangent point (<inline-formula><mml:math id="M166" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the radius of the Earth and
<inline-formula><mml:math id="M167" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> is the tangent point height):
            <disp-formula id="Ch1.E7" content-type="numbered"><mml:math id="M168" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>horizon</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:msup><mml:mi>cos⁡</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>R</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          As a criterion to select twilight data, we remove every limb scan in which at
least one point measurement has a solar zenith angle less than given by
Eq. (<xref ref-type="disp-formula" rid="Ch1.E7"/>). Based on this, we obtain the <inline-formula><mml:math id="M169" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the
<inline-formula><mml:math id="M170" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> background-subtracted twilight spectra shown in
Fig. <xref ref-type="fig" rid="Ch1.F3"/>a and c for the example orbit (41 455). For the twilight
<inline-formula><mml:math id="M171" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band, we apply the same background subtraction as for
daylight. Figure <xref ref-type="fig" rid="Ch1.F3"/>b shows the twilight <inline-formula><mml:math id="M172" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
spectra, and panel (d) shows the background-corrected twilight
<inline-formula><mml:math id="M173" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> spectra for the same example orbit (41 455). It is
apparent that the background signal is negligible for both of the
<inline-formula><mml:math id="M174" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M175" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> twilight spectra.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><caption><p id="d1e4197">Examples of the twilight-calibrated spectra and the spectra from
which the background <inline-formula><mml:math id="M176" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M177" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
absorption has been subtracted. <bold>(a)</bold> for the <inline-formula><mml:math id="M178" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band on 3 February 2010; orbit
number 41 455; mean latitude of 78.0<inline-formula><mml:math id="M179" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, mean longitude of
226.5<inline-formula><mml:math id="M180" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E.
<bold>(b)</bold> as <bold>(a)</bold> but for the <inline-formula><mml:math id="M181" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.
<bold>(c)</bold> as <bold>(a)</bold> but with background subtracted.
<bold>(d)</bold> as <bold>(b)</bold> but with background subtracted.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f03.pdf"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS4">
  <title>Retrieval</title>
      <p id="d1e4336">To invert the observed radiation to spectral emission rates, we set up
30 layers around the Earth, such that each layer is centered at one tangent
height. We denote the observed spectral radiances by <inline-formula><mml:math id="M182" display="inline"><mml:mi mathvariant="bold">Y</mml:mi></mml:math></inline-formula>, the path
length of each of the observed lines of sight through each of the atmospheric
layers by <inline-formula><mml:math id="M183" display="inline"><mml:mi mathvariant="bold">L</mml:mi></mml:math></inline-formula>, and the emission rate from the layer by <inline-formula><mml:math id="M184" display="inline"><mml:mi mathvariant="bold">X</mml:mi></mml:math></inline-formula>.
Assuming no self-absorption, this yields the linear relation
            <disp-formula id="Ch1.E8" content-type="numbered"><mml:math id="M185" display="block"><mml:mrow><mml:mi mathvariant="bold">Y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="bold">LX</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          In Eq. (<xref ref-type="disp-formula" rid="Ch1.E8"/>), dim(<inline-formula><mml:math id="M186" display="inline"><mml:mi mathvariant="bold">Y</mml:mi></mml:math></inline-formula>) <inline-formula><mml:math id="M187" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> number of atmospheric
layers <inline-formula><mml:math id="M188" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> number of spectral points <inline-formula><mml:math id="M189" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">144</mml:mn></mml:mrow></mml:math></inline-formula> for the
<inline-formula><mml:math id="M191" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band and <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">210</mml:mn></mml:mrow></mml:math></inline-formula> for the <inline-formula><mml:math id="M193" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
band. Dim(<inline-formula><mml:math id="M194" display="inline"><mml:mi mathvariant="bold">L</mml:mi></mml:math></inline-formula>) <inline-formula><mml:math id="M195" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> number of the atmospheric
layers <inline-formula><mml:math id="M196" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> number of tangent heights in each scan <inline-formula><mml:math id="M197" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula>. Dim(<inline-formula><mml:math id="M199" display="inline"><mml:mi mathvariant="bold">X</mml:mi></mml:math></inline-formula>) <inline-formula><mml:math id="M200" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> number of atmospheric layers <inline-formula><mml:math id="M201" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> number
of spectral points in the corresponding wavelength interval <inline-formula><mml:math id="M202" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">144</mml:mn></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M204" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M205" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">210</mml:mn></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M206" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e4605">We solve Eq. (<xref ref-type="disp-formula" rid="Ch1.E8"/>) by minimizing
<inline-formula><mml:math id="M207" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mo>|</mml:mo><mml:mi mathvariant="bold">Y</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="bold">LX</mml:mi><mml:mo>|</mml:mo><mml:msup><mml:mo>|</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> using standard least squares and
normalization with the error covariance matrix <inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and obtain the
inverted spectral emission intensity <inline-formula><mml:math id="M209" display="inline"><mml:mi mathvariant="bold">X</mml:mi></mml:math></inline-formula>:
            <disp-formula id="Ch1.E9" content-type="numbered"><mml:math id="M210" display="block"><mml:mrow><mml:mi mathvariant="bold">X</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="bold">L</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msup><mml:msubsup><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:mi mathvariant="bold">L</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi mathvariant="bold">L</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msup><mml:msubsup><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:mi mathvariant="bold">Y</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The error covariance matrix <inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> has diagonal elements of the
out-of-band variances of the background-corrected spectra in each altitude.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
<sec id="Ch1.S3.SS1">
  <title>Inverted spectra</title>
      <p id="d1e4733">Using our method in Sect. <xref ref-type="sec" rid="Ch1.S2.SS4"/>, the emission intensities
are calculated for the spectra described in
Sect. <xref ref-type="sec" rid="Ch1.S2.SS2"/> and <xref ref-type="sec" rid="Ch1.S2.SS3"/>. Examples of
the emission intensity for daytime <inline-formula><mml:math id="M212" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are shown in
Fig. <xref ref-type="fig" rid="Ch1.F4"/>a and for daytime <inline-formula><mml:math id="M213" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in
Fig. <xref ref-type="fig" rid="Ch1.F4"/>b.</p>
      <p id="d1e4788">The spectral shapes of the <inline-formula><mml:math id="M214" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band in the daytime
<inline-formula><mml:math id="M215" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> spectra and of the <inline-formula><mml:math id="M216" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band in the
daytime <inline-formula><mml:math id="M217" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> spectra are clearly visible. We find that the
largest values for the daytime <inline-formula><mml:math id="M218" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band are located at about
90 km altitude, and for the <inline-formula><mml:math id="M219" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band at 54 km, noting that
the SCIAMACHY MLT scan range is 50 to 150 km. We also note that the maximum
<inline-formula><mml:math id="M220" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission intensities in each limb scan are about 2 orders of magnitude larger than the maximum values of the
<inline-formula><mml:math id="M221" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band in the corresponding limb scan.</p>
      <p id="d1e4952">Figure <xref ref-type="fig" rid="Ch1.F4"/>c shows the twilight <inline-formula><mml:math id="M222" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission
intensity, and Fig. <xref ref-type="fig" rid="Ch1.F4"/>d shows the twilight <inline-formula><mml:math id="M223" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
emission intensity for the same orbit but retrieved from one of the three
twilight MLT scans (see Sect. <xref ref-type="sec" rid="Ch1.S2.SS3"/>). The
<inline-formula><mml:math id="M224" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band is about 1 order of magnitude smaller than during
daylight. The twilight <inline-formula><mml:math id="M225" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band signal is more pronounced
but about 2 orders of magnitude smaller than during the day. The error bars
in the panels of Fig. <xref ref-type="fig" rid="Ch1.F4"/> represent the square root of each of the
diagonal elements of the retrieval error covariance matrix
<inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold">S</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for each altitude:
            <disp-formula id="Ch1.E10" content-type="numbered"><mml:math id="M227" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="bold">S</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold">GS</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msup><mml:mi mathvariant="bold">G</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          in which the contribution function matrix <inline-formula><mml:math id="M228" display="inline"><mml:mi mathvariant="bold">G</mml:mi></mml:math></inline-formula> is defined as
            <disp-formula id="Ch1.E11" content-type="numbered"><mml:math id="M229" display="block"><mml:mrow><mml:mi mathvariant="bold">G</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:msup><mml:mi mathvariant="bold">L</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msup><mml:msubsup><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:mi mathvariant="bold">L</mml:mi></mml:mfenced><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi mathvariant="bold">L</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msup><mml:msubsup><mml:mi mathvariant="bold">S</mml:mi><mml:mi>y</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e5138">Evaluating all altitudes, not shown here but indicated in
Fig. <xref ref-type="fig" rid="Ch1.F4"/>a, we observe the strongest signal of daytime
<inline-formula><mml:math id="M230" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> around 83–99 km. Hereafter, we use the term
“significant” for data with a signal-to-noise ratio (SNR) greater than 1.</p>
      <p id="d1e5164">Figure <xref ref-type="fig" rid="Ch1.F4"/>c shows that the twilight <inline-formula><mml:math id="M231" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band
emission intensities have large noise masking the signal. The daytime
<inline-formula><mml:math id="M232" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission intensities are in general of higher SNR than
the twilight <inline-formula><mml:math id="M233" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission intensities. The daytime
<inline-formula><mml:math id="M234" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission intensities are strongest at the lowest
observable altitudes, i.e., 54 km (Fig. <xref ref-type="fig" rid="Ch1.F4"/>b). The strongest
twilight <inline-formula><mml:math id="M235" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emissions are located in the 83–96 km
altitude range (Fig. <xref ref-type="fig" rid="Ch1.F4"/>d shows only a selection of altitudes).</p>

      <fig id="Ch1.F4" specific-use="star"><caption><p id="d1e5275">Examples of the emission intensities that are obtained by solving
Eq. (<xref ref-type="disp-formula" rid="Ch1.E9"/>). <bold>(a)</bold> For the daytime
<inline-formula><mml:math id="M236" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band on the date 3 February 2010; orbit number
41 455; mean latitude of 17.3<inline-formula><mml:math id="M237" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, mean longitude of
94.3<inline-formula><mml:math id="M238" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E. <bold>(b)</bold> as <bold>(a)</bold> but for the <inline-formula><mml:math id="M239" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
band. <bold>(c)</bold> For the twilight <inline-formula><mml:math id="M240" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band on the date
3 February 2010; orbit number 41 455; mean latitude 78.0<inline-formula><mml:math id="M241" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, mean
longitude 226.5<inline-formula><mml:math id="M242" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E. <bold>(d)</bold> as <bold>(c)</bold> but for
the <inline-formula><mml:math id="M243" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. Error bars represent the retrieval errors.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f04.pdf"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p id="d1e5424">Typical profiles of the VER for different latitudes.
<bold>(a)</bold> For the daytime <inline-formula><mml:math id="M244" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER on the date
3 February 2010; orbit number 41 455. <bold>(b)</bold> as <bold>(a)</bold> for
the daytime <inline-formula><mml:math id="M245" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. Error bars represent the retrieval
errors.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f05.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <title>Volume emission rates</title>
      <p id="d1e5489">We integrate the spectral emission intensity from 759 to 767 nm to obtain
the <inline-formula><mml:math id="M246" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band integrated volume emission rate. Volume
emission rate profiles for one sample satellite orbit (41 455 on
3 February 2010) for daytime <inline-formula><mml:math id="M247" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M248" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
are shown in Fig. <xref ref-type="fig" rid="Ch1.F5"/>a and b respectively. Examples of the volume
emission rate latitude–altitude distributions for the same orbit for daytime
<inline-formula><mml:math id="M249" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are shown in Fig. <xref ref-type="fig" rid="Ch1.F6"/>a and for daytime
<inline-formula><mml:math id="M250" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F6"/>b. The blank regions represent
areas with signal-to-noise ratios of less than 1.</p>

      <fig id="Ch1.F6" specific-use="star"><caption><p id="d1e5603">Latitude–altitude contours of the daytime VER. <bold>(a)</bold> for the
<inline-formula><mml:math id="M251" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band and for one satellite orbit on the date 3
February 2010; orbit number 41 455. <bold>(b)</bold> as <bold>(a)</bold> for
<inline-formula><mml:math id="M252" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Signal-to-noise ratios less than 1 and large noisy
values are excluded. <bold>(c)</bold> and <bold>(d)</bold> as
<bold>(a)</bold> and <bold>(b)</bold> respectively, averaged on all of the orbits on
the whole day of 3 February 2010, with the same logarithmic scale. Negative
values are excluded. <bold>(e)</bold> Signal-to-noise ratios of the daily mean of
<inline-formula><mml:math id="M253" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs. Areas where the signal-to-noise ratio is less
than 1 are plotted in white. <bold>(f)</bold> as <bold>(e)</bold> for the
<inline-formula><mml:math id="M254" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f06.png"/>

        </fig>

      <p id="d1e5725">The <inline-formula><mml:math id="M255" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER has its maximum in the 90–98 km altitude
range, which is 2 orders of magnitude smaller than the <inline-formula><mml:math id="M256" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
maximum VER, as shown in Fig. <xref ref-type="fig" rid="Ch1.F5"/>a. The volume emission rate
profile of dayglow <inline-formula><mml:math id="M257" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> observed by TIMED–SABER often has
its maximum around 50 km altitude, as shown for example in Fig. 1 of
<xref ref-type="bibr" rid="bib1.bibx33" id="text.41"/>. Figure <xref ref-type="fig" rid="Ch1.F5"/>b shows that the SCIAMACHY
MLT volume emission rate profiles are largest at the bottom of the observed
altitude range, around 54 km. These VER profiles sometimes show secondary
maxima in the range 80–90 km, which are at least 1 order of magnitude
smaller than the largest SCIAMACHY VER. This secondary maximum occurs
especially around equinox times. The measurement errors of the volume
emission rates (not shown here) for different orbits show that the
<inline-formula><mml:math id="M258" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> volume emission rates are significant from 65 to
140 km and do not depend on latitude. Inspecting the volume emission rate
altitude profiles (not shown here), we see that the <inline-formula><mml:math id="M259" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
volume emission rates have the largest SNR below 125 km and above 85 km.The
best signal of the <inline-formula><mml:math id="M260" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER is below 95 km.</p>
      <p id="d1e5856">In a region above the South Atlantic and off the Brazilian coast, the Earth's
magnetic field is anomalously low and the ionizing radiation can be increased
by several orders of magnitude. This region is called the South Atlantic
Anomaly (SAA, see for example <xref ref-type="bibr" rid="bib1.bibx24" id="altparen.42"/>) and any spacecraft
which crosses this region can give false instrument readings. In our
retrievals, the SNRs of the volume emission rates in the orbits that cross
this region are affected by the SAA. The most dramatic influence of the SAA
on our dataset is on the <inline-formula><mml:math id="M261" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> volume emission rates SNR,
although the values are still significant in the 80–100 km altitude range.
The SAA influences the <inline-formula><mml:math id="M262" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> measurements more than the
<inline-formula><mml:math id="M263" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> measurements.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p id="d1e5925">Time series of the daily mean VER. <bold>(a)</bold> for the daytime
<inline-formula><mml:math id="M264" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER; 30<inline-formula><mml:math id="M265" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N; July 2008 to March 2012.
<bold>(b)</bold> as <bold>(a)</bold> for the daytime <inline-formula><mml:math id="M266" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f07.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <title>Daily mean VER latitude–altitude distributions</title>
      <p id="d1e6000">We calculate the daily mean VERs as follows. We bin the measurements into
5<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> latitude bins. In each bin, the measurements located within
<inline-formula><mml:math id="M268" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>2.5<inline-formula><mml:math id="M269" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> are attributed to that latitude and averaged to the daily mean
VER. An example of the daily mean daytime <inline-formula><mml:math id="M270" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER
latitude–altitude distribution (on 3 February 2010) is shown in
Fig. <xref ref-type="fig" rid="Ch1.F6"/>c and of the daily mean daytime <inline-formula><mml:math id="M271" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER
in Fig. <xref ref-type="fig" rid="Ch1.F6"/>d (VERs with low signal-to-noise ratios and with large
measurement errors are excluded). The daily mean <inline-formula><mml:math id="M272" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs
have maximum values of about 1–2 orders of magnitude smaller than
<inline-formula><mml:math id="M273" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Similar to our results for a single orbit
(Sect. <xref ref-type="sec" rid="Ch1.S3.SS2"/>), we observe the largest
<inline-formula><mml:math id="M274" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER below 60 km and the largest <inline-formula><mml:math id="M275" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
VER at 90 km.</p>
      <p id="d1e6158">To assess the signal-to-noise ratio for the daytime VERs,
Fig. <xref ref-type="fig" rid="Ch1.F6"/>e shows the daily mean <inline-formula><mml:math id="M276" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER signal-to-noise ratios. We observe the strongest signal of daytime <inline-formula><mml:math id="M277" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
in the 70–130 km altitude range. The strongest signal of the twilight
<inline-formula><mml:math id="M278" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is observed between 84 and 95 km (not shown here).
Figure <xref ref-type="fig" rid="Ch1.F6"/>f shows that the stronger signal of daytime
<inline-formula><mml:math id="M279" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is observed below 105 km, with the strongest around
70 km. The largest signal of twilight <inline-formula><mml:math id="M280" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is observed in
the altitude range of 83–97 km (not shown).</p>
</sec>
<sec id="Ch1.S3.SS4">
  <title>Time series</title>
      <p id="d1e6272">In the following, we discuss the variation of the daily mean VERs versus
latitude and time. First we will discuss the temporal variation in the
mesosphere and lower thermosphere (70–140 km) at 30<inline-formula><mml:math id="M281" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. Thereafter
we will discuss the variation of the peak values, peak altitudes, and
centroid altitudes as a function of time and latitude.</p>
<sec id="Ch1.S3.SS4.SSS1">
  <?xmltex \opttitle{Time series at 30{${}^{{\circ}}$}\,N}?><title>Time series at 30<inline-formula><mml:math id="M282" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</title>
      <p id="d1e6299">By calculating the daily mean VERs for all of the days on which SCIAMACHY MLT
limb scans are available, we obtain time series of the daily mean VERs from
July 2008 to March 2012. An example of these time series of the daily mean
daytime <inline-formula><mml:math id="M283" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER, chosen for 30<inline-formula><mml:math id="M284" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N from all
altitude combinations, is shown in Fig. <xref ref-type="fig" rid="Ch1.F7"/>a and for the daytime
<inline-formula><mml:math id="M285" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER of the same location in Fig. <xref ref-type="fig" rid="Ch1.F7"/>b.</p>
      <p id="d1e6357">We found a semi-annual variation with the strongest <inline-formula><mml:math id="M286" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
signal in the 90–95 km range during May–June and September–November and
the lowest signal in December–March, with a secondary minimum in August. The
highest values of the <inline-formula><mml:math id="M287" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER are located at the lowest
altitude of observations, formed mostly by ozone photodissociation
<xref ref-type="bibr" rid="bib1.bibx48" id="paren.43"/>. We observe secondary maximum values which mostly
occur in May–June and September–November (approximately spring and autumn)
in the 75–95 km altitude range. The secondary maximum of
<inline-formula><mml:math id="M288" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> occurs in the same altitude range and with the same
temporal variation as the <inline-formula><mml:math id="M289" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signal. This will be
investigated in more detail in the following section.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS2">
  <title>Variation of peak values</title>
      <p id="d1e6449">Next we evaluate the variations of the maximal daily mean VERs in the
mesosphere and lower thermosphere with respect to latitude and time. For
this, we derive the maximal values from the daily mean VERs for
<inline-formula><mml:math id="M290" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and between 85 and 100 km altitude for
<inline-formula><mml:math id="M291" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, which are shown in Fig. <xref ref-type="fig" rid="Ch1.F8"/>a and b
respectively. Only those regions are shown in Fig. <xref ref-type="fig" rid="Ch1.F8"/>b, d, and f
where the secondary maxima of <inline-formula><mml:math id="M292" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> exist. The peak altitudes
are also obtained at the same time and will be discussed in
Sect. <xref ref-type="sec" rid="Ch1.S3.SS4.SSS3"/>. The maxima of the
<inline-formula><mml:math id="M293" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER at middle to low latitudes
(60<inline-formula><mml:math id="M294" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M295" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) appear to be correlated with the maximum
intensity of solar radiance. Additionally, we sometimes observe attenuations
in the maximum values in the late northern winters, mostly from late January
until early March of each year. Also there are some high values at northern
polar latitudes: in spring 2009, from autumn to spring 2009–2010, from
autumn to winter 2010, and from autumn to spring 2011–2012.</p>
      <p id="d1e6557">The secondary maxima of the <inline-formula><mml:math id="M296" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER are confined to winter
at mid-to-high latitudes.</p>
      <p id="d1e6580">The correlation of the <inline-formula><mml:math id="M297" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs with the solar radiance
suggests formation caused by solar light, either by ozone photolysis
(Reactions <xref ref-type="disp-formula" rid="R2"/> and <xref ref-type="disp-formula" rid="R3"/>) or by larger
abundances of atomic oxygen owing to stronger O<inline-formula><mml:math id="M298" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> photolysis. In the second
case, the formation of the excited states could also be due to the
recombination of atomic oxygen
(Reactions <xref ref-type="disp-formula" rid="R1"/> and <xref ref-type="disp-formula" rid="Ch1.E4"/>). The maximal
values at high latitudes, where the solar flux is low, in general suggest
other sources such as recombination of atomic oxygen <xref ref-type="bibr" rid="bib1.bibx48" id="paren.44"/>.
This is true in particular for <inline-formula><mml:math id="M299" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, where high values occur
at high latitudes in winter and spring; these are probably caused by downward
transport of thermospheric atomic oxygen into the mesosphere and lower
thermosphere.</p>
      <p id="d1e6644">There are two possibilities for secondary maxima of <inline-formula><mml:math id="M300" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
They happen in the region where the secondary ozone maximum is strongest.
Also, atomic oxygen densities might be strongest due to enhanced mixing with
the lower thermosphere. Detailed study of the processes which result in the
formation of the secondary maxima of <inline-formula><mml:math id="M301" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is beyond our work.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS3">
  <title>Variation of peak altitudes</title>
      <p id="d1e6693">The altitudes of the peak values of <inline-formula><mml:math id="M302" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M303" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are shown in Fig. <xref ref-type="fig" rid="Ch1.F8"/>c and d. The altitudes
of the peak values of <inline-formula><mml:math id="M304" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> roughly follow the maximum
intensity of solar radiance but show highest values at low-to-middle
latitudes. We refer to the maximum intensity of solar radiance as the
latitudes and times in which solar zenith angles have their lowest values.
The low values of the maximum VERs and the high altitudes of the maximal VERs
at the outermost high latitudes in the northern winters correspond to low
signal-to-noise ratios and are below our significance level.<?xmltex \hack{\newpage}?></p>
      <p id="d1e6759">In the regions where the secondary maxima of <inline-formula><mml:math id="M305" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> happen, the
peak altitudes occur in the <inline-formula><mml:math id="M306" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 84–89 km altitude range.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><caption><p id="d1e6791"><bold>(a)</bold> Time series of the maximal daily mean
<inline-formula><mml:math id="M307" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER. <bold>(b)</bold> as <bold>(a)</bold> for
the <inline-formula><mml:math id="M308" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. <bold>(c)</bold> Time series of the altitudes of the
maximum daily mean <inline-formula><mml:math id="M309" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER. <bold>(d)</bold> as <bold>(c)</bold>
for the <inline-formula><mml:math id="M310" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. <bold>(e)</bold> Time series of the centroid
altitudes of the daytime <inline-formula><mml:math id="M311" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> daily mean VER (km).
<bold>(f)</bold> as <bold>(e)</bold> for the <inline-formula><mml:math id="M312" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f08.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS4.SSS4">
  <title>Centroid altitudes</title>
      <p id="d1e6961">The estimation of the peak altitude is affected by instrument noise and
vertical resolution. A more stable measure is the centroid altitude
<inline-formula><mml:math id="M313" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:
              <disp-formula id="Ch1.E12" content-type="numbered"><mml:math id="M314" display="block"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume emission rate at altitude <inline-formula><mml:math id="M316" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which ranges
from <inline-formula><mml:math id="M317" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 50 to <inline-formula><mml:math id="M318" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 150 km for <inline-formula><mml:math id="M319" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and from
<inline-formula><mml:math id="M320" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 85 to <inline-formula><mml:math id="M321" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 km for <inline-formula><mml:math id="M322" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
Figure <xref ref-type="fig" rid="Ch1.F8"/>e shows the centroid altitude for daytime
<inline-formula><mml:math id="M323" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and Fig. <xref ref-type="fig" rid="Ch1.F8"/>f for daytime
<inline-formula><mml:math id="M324" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e7157">The maximum <inline-formula><mml:math id="M325" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values of the <inline-formula><mml:math id="M326" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band are correlated
with the (maximum intensity) of solar radiance. We also observe maximal
values of <inline-formula><mml:math id="M327" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in a narrow band at northern polar latitudes, where
the solar flux generally is low. This also suggests recombination of atomic
oxygen as a source, as discussed in the Sect. <xref ref-type="sec" rid="Ch1.S3.SS4.SSS2"/>.
The very low values of the <inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>s, at the highest latitudes, mostly
in the hemispheric wintertimes, correspond to low signal-to-noise ratios of
the corresponding VERs (not shown here) and are below our significance level.</p>
      <p id="d1e7215">The <inline-formula><mml:math id="M329" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> secondary maximums occur in winter at high
latitudes. The values of the <inline-formula><mml:math id="M330" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M331" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> range
between <inline-formula><mml:math id="M332" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 88 and <inline-formula><mml:math id="M333" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 89 km altitude.</p>
      <p id="d1e7283">Figure <xref ref-type="fig" rid="Ch1.F8"/>c, d, and f show a decrease in the altitude of the
maximum <inline-formula><mml:math id="M334" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, altitude of the maximum <inline-formula><mml:math id="M335" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
and <inline-formula><mml:math id="M336" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">CA</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> respectively between November 2010
and February 2011. This is due to a change in the limb sequence so that
tangent altitudes were shifted, as seen for example at lower altitudes in
these days. However, this does not have any notable effect on the VER time
series in Figs. <xref ref-type="fig" rid="Ch1.F7"/>a, b, <xref ref-type="fig" rid="Ch1.F8"/>a, and b.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS5">
  <title>Discussion of temporal–spatial variation</title>
      <p id="d1e7370">The temporal–latitudinal variation in peak values and altitudes suggests that
<inline-formula><mml:math id="M338" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> at 85–100 km altitude is formed by a combination of
ozone photolysis and atomic oxygen recombination. At high latitudes during
winter and spring, atomic oxygen recombination dominates, but, in the
subsolar region, ozone photolysis is more important. In contrast, the
secondary peak of <inline-formula><mml:math id="M339" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> stems mainly from atomic oxygen
recombination, in particular at high latitudes during winter.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><caption><p id="d1e7415">Modeled VERs of <inline-formula><mml:math id="M340" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <bold>(a)</bold> and
<inline-formula><mml:math id="M341" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <bold>(b)</bold>. Solid lines are the mean of all model
results for solar zenith angles 0, 10, 20, 30, 40, 50, 60, 70, 80, and
88<inline-formula><mml:math id="M342" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> considering all formation processes; dotted lines show the
variability due to photolysis reactions (<inline-formula><mml:math id="M343" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> standard deviation). The
dashed, dash-dotted, and dash–dot–dot lines show the contributions of
individual formation processes: <inline-formula><mml:math id="M344" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M345" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> quenching, and
resonant excitation for <inline-formula><mml:math id="M346" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M347" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M348" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and ozone photolysis for <inline-formula><mml:math id="M349" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Black
lines with symbols are SCIAMACHY profiles at five latitudes observed on
3 February 2010 (see Fig. <xref ref-type="fig" rid="Ch1.F5"/>).</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f09.pdf"/>

          </fig>

      <p id="d1e7591">The temporal–latitudinal variation in peak values and altitudes suggests that
the daytime VERs of <inline-formula><mml:math id="M350" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M351" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in the
altitude range of 80–100 km are formed by a combination of ozone and
<inline-formula><mml:math id="M352" 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> photolysis and atomic oxygen recombination. At high latitudes
during winter and spring, atomic oxygen recombination dominates, but, in the
subpolar region, photolysis of ozone and <inline-formula><mml:math id="M353" 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> is more important.</p>
      <p id="d1e7656">To test whether these conclusions are generally consistent with our
understanding of the photochemical production and loss of
<inline-formula><mml:math id="M354" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M355" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, a simple photochemical model
covering the production and loss reactions summarized in
Sect. <xref ref-type="sec" rid="Ch1.S1"/>
(Reactions <xref ref-type="disp-formula" rid="R1"/>–<xref ref-type="disp-formula" rid="Ch1.E6"/>)
was set up. Photochemical equilibrium was considered for
<inline-formula><mml:math id="M356" 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>(<inline-formula><mml:math id="M357" display="inline"><mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M358" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M359" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M360" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M361" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Reaction rates were taken
from the JPL recommendation <xref ref-type="bibr" rid="bib1.bibx9" id="paren.45"/> with the exception
of the quenching of the intermediate <inline-formula><mml:math id="M362" 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>(<inline-formula><mml:math id="M363" display="inline"><mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
state (the <inline-formula><mml:math id="M364" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">6</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M365" display="inline"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> rates shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>), which was
taken from <xref ref-type="bibr" rid="bib1.bibx46" id="text.46"/> with <inline-formula><mml:math id="M366" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> coefficients from
<xref ref-type="bibr" rid="bib1.bibx4" id="text.47"/>. Einstein coefficients for the
<inline-formula><mml:math id="M367" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M368" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M369" 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>(<inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
transition (<inline-formula><mml:math id="M371" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="Ch1.F1"/>) were taken from
<xref ref-type="bibr" rid="bib1.bibx31" id="text.48"/>, for the
<inline-formula><mml:math id="M372" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M373" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M374" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> transition (<inline-formula><mml:math id="M375" display="inline"><mml:mrow><mml:msub><mml:mi>A</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.F1"/>) from the NIST atomic spectra database
<fn id="Ch1.Footn2"><p id="d1e8008"><uri>www.nist.gov</uri></p></fn>, for the
<inline-formula><mml:math id="M376" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M377" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M378" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> transition (<inline-formula><mml:math id="M379" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
Fig. <xref ref-type="fig" rid="Ch1.F1"/>) from the NIST atomic spectra database, and for the
<inline-formula><mml:math id="M380" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> products (not given in Fig. <xref ref-type="fig" rid="Ch1.F1"/>) from
<xref ref-type="bibr" rid="bib1.bibx46" id="text.49"/>. Photolysis rates for solar zenith angles 0, 10,
20, 30, 40, 50, 60, 70, 80, and 88<inline-formula><mml:math id="M381" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> were calculated using a fixed
ozone profile using the 3dCTM model <xref ref-type="bibr" rid="bib1.bibx39" id="paren.50"/>. The rate
of photoexcitation of the ground state <inline-formula><mml:math id="M382" 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>(<inline-formula><mml:math id="M383" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>)
to the second excited state <inline-formula><mml:math id="M384" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was calculated following
<xref ref-type="bibr" rid="bib1.bibx8" id="paren.51"/> but using recent line-strength data provided by the
HITRAN database at <uri>http://hitran.org</uri> <xref ref-type="bibr" rid="bib1.bibx36" id="paren.52"/>,
yielding a rate of <inline-formula><mml:math id="M385" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.04</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> photons cm<inline-formula><mml:math id="M386" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M387" 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> above
70 km. Temperature, total air density, and the densities of <inline-formula><mml:math id="M388" 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> and
<inline-formula><mml:math id="M389" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were taken from the NRLMSISE-00 model <xref ref-type="bibr" rid="bib1.bibx35" id="paren.53"/>
at 10:00 local time at the equator. The production of <inline-formula><mml:math id="M390" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by
photolysis of <inline-formula><mml:math id="M391" 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="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> in the Ly-<inline-formula><mml:math id="M393" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> range was also
considered, and <inline-formula><mml:math id="M394" 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="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> were assumed to have constant
mixing ratios of 1 ppm (<inline-formula><mml:math id="M396" 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 380 ppm (<inline-formula><mml:math id="M397" 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>). Ozone
density was adapted from a multi-year global average of SABER data
in the altitude region 70–104 km (see <xref ref-type="bibr" rid="bib1.bibx44" id="altparen.54"/>,
Fig. 3). Atomic oxygen was calculated from photochemical equilibrium of ozone
considering only ozone photolysis and production by <inline-formula><mml:math id="M398" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The
resulting VERs of <inline-formula><mml:math id="M399" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M400" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are shown in
Fig. <xref ref-type="fig" rid="Ch1.F9"/>, compared to the SCIAMACHY daytime data of
3 February 2010 (shown in Fig. <xref ref-type="fig" rid="Ch1.F5"/>). Considering that the ozone
profile, <inline-formula><mml:math id="M401" 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>, <inline-formula><mml:math id="M402" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and temperature are not chosen to fit those
specific observations, the agreement is very good for both emissions,
indicating that the main processes of <inline-formula><mml:math id="M403" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M404" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> formation and loss are reproduced well by this simple
model. Also shown are the contributions of the individual production
reactions: O <inline-formula><mml:math id="M405" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> O, quenching of <inline-formula><mml:math id="M406" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and resonance excitation of
<inline-formula><mml:math id="M407" 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>(<inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) for <inline-formula><mml:math id="M409" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M410" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>,
quenching of <inline-formula><mml:math id="M411" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and ozone photolysis for
<inline-formula><mml:math id="M412" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e8573">Below about 82 km, <inline-formula><mml:math id="M413" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is formed in about equal amounts by
quenching of <inline-formula><mml:math id="M414" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, while above quenching of <inline-formula><mml:math id="M415" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
dominates. The reaction of <inline-formula><mml:math id="M416" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> contributes about 1 order of
magnitude less <inline-formula><mml:math id="M417" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> than the other two branches even in the
region where it has the largest contribution (around 90 km). This is
consistent with the ratio of emission intensities during twilight and during
daytime of about a factor of 10 as discussed in
Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/>, considering that, during nighttime and
twilight, <inline-formula><mml:math id="M418" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is formed solely by the O <inline-formula><mml:math id="M419" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> O reaction.
The formation of <inline-formula><mml:math id="M420" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is dominated by ozone photolysis at all
altitudes, though below 90 km <inline-formula><mml:math id="M421" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> quenching contributes
about 10–25 %.</p>
      <p id="d1e8732"><inline-formula><mml:math id="M422" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is formed mainly by photolysis of <inline-formula><mml:math id="M423" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> below 90 km and
by photolysis of <inline-formula><mml:math id="M424" 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> above that altitude. During daytime, both
the <inline-formula><mml:math id="M425" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M426" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> states
are formed by photolysis in agreement with
our observation that the peak maxima correlate with the maximum intensity of
solar radiance. The contribution of the <inline-formula><mml:math id="M427" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> reaction generally is
smaller by 1 to 3 orders of magnitude than the contribution of photolysis, in
agreement with the lower VERs observed during twilight when photolysis is not
a significant production process. However, it should be pointed out that the
relation between the <inline-formula><mml:math id="M428" 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> airglow and atomic oxygen by the <inline-formula><mml:math id="M429" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
reaction and de-excitation of the excited intermediate states such as
<inline-formula><mml:math id="M430" 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>(<inline-formula><mml:math id="M431" display="inline"><mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) is probably quadratic to cubic;
increased amounts of atomic oxygen, e.g., at high latitudes during winter
when large amounts of atomic oxygen can be transported or mixed down from the
lower thermosphere, can therefore increase the contribution of the <inline-formula><mml:math id="M432" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
reaction to the overall airglow considerably. This explains the observed
enhancements of the airglow at high northern latitudes in winter and spring,
in particular as the centroid altitudes in these occasions range around
90 km, the altitude where the <inline-formula><mml:math id="M433" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> reaction has the strongest
influence.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><caption><p id="d1e8904"><bold>(a)</bold> Daily mean of the daytime <inline-formula><mml:math id="M434" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER
from December 2008 to April 2009 averaged between 60 and 70<inline-formula><mml:math id="M435" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N
latitude. <bold>(b)</bold> as <bold>(a)</bold> for the <inline-formula><mml:math id="M436" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band.
<bold>(c)</bold> Daily mean of the signal-to-noise ratios of the daytime
<inline-formula><mml:math id="M437" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER from December 2008 to April 2009 averaged between
60 and 70<inline-formula><mml:math id="M438" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N latitude. <bold>(d)</bold> as <bold>(c)</bold> for
<inline-formula><mml:math id="M439" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER signal-to-noise ratios.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/473/2018/amt-11-473-2018-f10.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS5">
  <title>Relationship between the VER time series variations and sudden stratospheric warmings – example</title>
      <p id="d1e9041">Sudden stratospheric warmings are dynamical phenomena in the winter
polar stratosphere caused by upward propagating planetary waves interacting
with the mean flow <xref ref-type="bibr" rid="bib1.bibx28" id="paren.55"/>. During the so-called recovery phase
of SSWs, the reformation of the jet changes gravity wave propagation to the
mesosphere.The induced change in the residual circulation results in an
enhanced descent of air. This causes adiabatic warming and the stratopause
reforms at altitudes as high as 75–80 km <xref ref-type="bibr" rid="bib1.bibx40" id="paren.56"/>. The unusual
brightening of the <inline-formula><mml:math id="M440" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">OH</mml:mi></mml:mrow></mml:math></inline-formula> airglow <xref ref-type="bibr" rid="bib1.bibx50" id="paren.57"/> is presumably caused
by enhanced downwelling of atomic oxygen. According to <xref ref-type="bibr" rid="bib1.bibx17" id="text.58"/>, a
major SSW event happened around 21 January 2009 (Fig. 1 of that paper). We
therefore expect to observe enhanced airglow at the end of January 2009.</p>
      <p id="d1e9064">Based on the temporal evolution of mesospheric temperature during the SSW
event, <xref ref-type="bibr" rid="bib1.bibx15" id="text.59"/> divided the response in the mesosphere into
three stages: the period prior to day 15 is considered the normal stage, days 15–22
correspond to the cooling stage, and days post-22 correspond to the recovery
stage. According to this, they reported that the <inline-formula><mml:math id="M441" 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> nightglow
brightness decreased by about a factor of 10 during the cooling stage and
then increased by about a factor of 3 during the recovery stage relative to
the normal stage. Figure <xref ref-type="fig" rid="Ch1.F10"/>a and b show the time series from
December 2008 to April 2009 of the daytime <inline-formula><mml:math id="M442" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M443" display="inline"><mml:mrow><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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> daily mean VER, averaged from 60 to 70<inline-formula><mml:math id="M444" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. We
observe that on the last day of the cooling stage, i.e., 22 January 2009, the
daily zonal mean <inline-formula><mml:math id="M445" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M446" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs show a
reduced maximum intensity in the 82–87 km altitude range. We observe larger
intensities on the next measurement day of SCIAMACHY about 3 weeks later,
i.e., on 10 February 2009. This is expected from a decrease of atomic oxygen
due to horizontal mixing and upwelling during the cooling stage and then
downward extension of the MLT region with large mixing ratio of <inline-formula><mml:math id="M447" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
during the recovery stage of the SSW <xref ref-type="bibr" rid="bib1.bibx15" id="paren.60"/>. On the
measurement day of SCIAMACHY after the recovery phase, i.e., 23 March 2009,
the relative difference in the <inline-formula><mml:math id="M448" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signal is less prominent
compared to the relative difference in <inline-formula><mml:math id="M449" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. A detailed
analysis of this relationship is beyond the scope of this paper.</p>
      <p id="d1e9227">We also note that the signal-to-noise ratios of the VERs for
<inline-formula><mml:math id="M450" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> shown in Fig. <xref ref-type="fig" rid="Ch1.F10"/>c are statistically
significant. It is shown in Fig. <xref ref-type="fig" rid="Ch1.F10"/>d that, during and after the
initial stage of the SSW event, the <inline-formula><mml:math id="M451" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signal becomes
weaker and stronger respectively, and the signal-to-noise ratio of the data
are such that this behavior is statistically significant.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Discussion and conclusions</title>
      <p id="d1e9281">We present the retrieval of daytime and twilight <inline-formula><mml:math id="M452" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M453" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> spectral emissions from MLT measurements of the airglow
in limb-viewing geometry from the SCIAMACHY instrument onboard Envisat. From
the retrieved spectra, we calculate the band integrated VERs for both bands.
The maxima of the <inline-formula><mml:math id="M454" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER and the centroid altitude of the
<inline-formula><mml:math id="M455" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are correlated with the maximum intensity of solar
radiance. High values of maximum VER and centroid altitude are additionally
seen at northern polar latitudes. The (30<inline-formula><mml:math id="M456" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) time series of
<inline-formula><mml:math id="M457" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER shows a maximum in the 90–98 km altitude range.
The maximum values correspond to high centroid altitudes for
<inline-formula><mml:math id="M458" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The daily zonal (60–70<inline-formula><mml:math id="M459" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) mean
<inline-formula><mml:math id="M460" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs show a reduced maximum intensity in the 82–87 km
range and in the initiation of the sudden stratospheric warming 2009 event as
well as an increase in intensity about 3 weeks later.</p>
      <p id="d1e9443">The maxima of the <inline-formula><mml:math id="M461" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs are also correlated with the
maximum intensity of solar radiance. They are most prominent in summer, while
the altitudes of the maximal values have their highest values in winter, and
both occur at high latitudes. The time series of <inline-formula><mml:math id="M462" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER is
2 orders of magnitude larger than <inline-formula><mml:math id="M463" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER at its maximal
values which are located below the observation altitude (<inline-formula><mml:math id="M464" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 60 km), but it
shows some secondary maxima about 1 order of magnitude smaller than the
primary maxima at 84–89 km. This happens in winter at high latitudes. The
maximum VERs correspond to the low centroid altitudes for the
<inline-formula><mml:math id="M465" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band. The daily zonal (60–70<inline-formula><mml:math id="M466" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) mean
<inline-formula><mml:math id="M467" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VERs show a reduced maximum intensity in the 82–87 km
range and in the initiation of the sudden stratospheric warming 2009 event as
well as an increase in intensity about 3 weeks later, although the relative
difference in the <inline-formula><mml:math id="M468" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band signal is less prominent compared
to the relative difference in <inline-formula><mml:math id="M469" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e9603">The intensification of the VER during the sudden stratospheric warming in
early 2009 presumably corresponds to the downwelling of the atomic oxygen
following the warming, while the decrease is probably due to upwelling as
well as horizontal mixing during the warming event.</p>
      <p id="d1e9606">Our results suggest that at low and middle latitudes <inline-formula><mml:math id="M470" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M471" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> abundances during daytime are dominated by photolysis of
ozone below 90 km and by photolysis of ozone and <inline-formula><mml:math id="M472" 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> above 90 km as
supported by our observed correlation with solar illumination, and they are consistent
with the processes depicted in Fig. <xref ref-type="fig" rid="Ch1.F1"/>. At high latitudes,
however, in particular during winter, atomic oxygen abundances might be a
more important driver due to the recombination of <inline-formula><mml:math id="M473" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> and subsequent
de-excitation via <inline-formula><mml:math id="M474" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M475" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e9713">As the formation of the <inline-formula><mml:math id="M476" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band is dominated by ozone
photolysis, this band can be used to derive ozone densities directly.
However, as quenching of <inline-formula><mml:math id="M477" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> contributes about 10–25 %
to the overall production in 70–90 km, the accuracy of this retrieval can
be improved considerably when both lines are available. The
<inline-formula><mml:math id="M478" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> band is dominated by quenching of <inline-formula><mml:math id="M479" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and
daytime <inline-formula><mml:math id="M480" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> can be derived from observations of the
<inline-formula><mml:math id="M481" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> VER. However, below <inline-formula><mml:math id="M482" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 90 km, the resonant
excitation from the ground state has to be taken into account as well. The
rate used here based on new line-strength data from HITRAN is lower by about
a factor of 2 compared to a similar estimate used for HRDI data as
described in <xref ref-type="bibr" rid="bib1.bibx27" id="text.61"/> and lower by about a factor of 4
compared to the original estimate by <xref ref-type="bibr" rid="bib1.bibx8" id="text.62"/>. We conclude
that the retrieval of <inline-formula><mml:math id="M483" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and ozone as the main source of
<inline-formula><mml:math id="M484" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> below 90 km from <inline-formula><mml:math id="M485" 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:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is possible but needs a
careful estimation of the rate of resonant excitation.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p id="d1e9904">The data are available on request to the authors
(amirmahdi.zarboo@kit.edu or miriam.sinnhuber@kit.edu).</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e9910">The authors declare that they have no conflict of
interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e9916">Amirmahdi Zarboo and Miriam Sinnhuber gratefully acknowledge funding by BMBF
grant 01LG1208A (ROMIC-MesoEnergy). The support of the BMBF ROMIC project for the
University of Bremen is also gratefully acknowledged. The SCIAMACHY project
was funded by Germany with support from the Netherlands and Belgium as a
national contribution to ESA Envisat. The authors also acknowledge the
reviewers for the very constructive comments on the paper.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?> The article processing charges for this open-access
<?xmltex \hack{\newline}?> publication were covered by a Research <?xmltex \hack{\newline}?> Centre
of the Helmholtz Association.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>Edited by:
William Ward<?xmltex \hack{\newline}?> Reviewed by: two anonymous referees</p></ack><ref-list>
    <title>References</title>

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    <!--<article-title-html>Retrieval of O<sub>2</sub>(<sup>1</sup>Σ) and O<sub>2</sub>(<sup>1</sup>Δ) volume emission rates in the mesosphere and lower thermosphere using SCIAMACHY MLT limb scans</article-title-html>
<abstract-html><p class="p">We present the retrieved volume emission rates (VERs) from the
airglow of both the daytime and twilight O<sub>2</sub>(<sup>1</sup>Σ) band and
O<sub>2</sub>(<sup>1</sup>Δ) band emissions in the mesosphere and lower thermosphere
(MLT). The SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY)
onboard the European Space Agency Envisat satellite
observes upwelling radiances in limb-viewing geometry during its special MLT
mode over the range 50–150 km. In this study we use the limb observations
in the visible (595–811 nm) and near-infrared (1200–1360 nm) bands.</p><p class="p">We have investigated the daily mean latitudinal distributions and the time
series of the retrieved VER in the altitude range from 53 to 149 km. The
maximal observed VERs of O<sub>2</sub>(<sup>1</sup>Δ) during daytime are typically 1
to 2 orders of magnitude larger than those of O<sub>2</sub>(<sup>1</sup>Σ). The
latter peaks at around 90 km, whereas the O<sub>2</sub>(<sup>1</sup>Δ) emissivity
decreases with altitude, with the largest values at the lower edge of the
observations (about 53 km). The VER values in the upper mesosphere (above
80 km) are found to depend on the position of the sun, with pronounced high
values occurring during summer for O<sub>2</sub>(<sup>1</sup>Δ). O<sub>2</sub>(<sup>1</sup>Σ)
emissions show additional high values at polar latitudes during winter and
spring. These additional high values are presumably related to the
downwelling of atomic oxygen after large sudden stratospheric warmings (SSWs).
Accurate measurements of the O<sub>2</sub>(<sup>1</sup>Σ) and O<sub>2</sub>(<sup>1</sup>Δ)
airglow, provided that the mechanism of their production is understood, yield
valuable information about both the chemistry and dynamics in the MLT. For
example, they can be used to infer the amounts and distribution of ozone,
solar heating rates, and temperature in the MLT.</p></abstract-html>
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