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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-15-1233-2022</article-id><title-group><article-title>Assessment of the quality of ACE-FTS stratospheric ozone data</article-title><alt-title>Assessment of the quality of ACE-FTS stratospheric ozone data</alt-title>
      </title-group><?xmltex \runningtitle{Assessment of the quality of ACE-FTS stratospheric ozone data}?><?xmltex \runningauthor{P. E. Sheese et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Sheese</surname><given-names>Patrick E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Walker</surname><given-names>Kaley A.</given-names></name>
          <email>kaley.walker@utoronto.ca</email>
        <ext-link>https://orcid.org/0000-0003-3420-9454</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Boone</surname><given-names>Chris D.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Bourassa</surname><given-names>Adam E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Degenstein</surname><given-names>Doug A.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Froidevaux</surname><given-names>Lucien</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>McElroy</surname><given-names>C. Thomas</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0184-6756</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Murtagh</surname><given-names>Donal</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1539-3559</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Russell III</surname><given-names>James M.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4835-7696</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zou</surname><given-names>Jiansheng</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Department of Physics, University of Toronto, Toronto, Canada</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Chemistry, University of Waterloo, Waterloo, Canada</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Physics and Engineering, University of Saskatchewan, ISAS, Saskatoon, Canada</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Earth and Space Science and Engineering, York University, Toronto, Canada</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Department of Space, Earth and Environment, Chalmers University of Technology, Gothenburg, Sweden</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>Center for Atmospheric Sciences, Hampton University, Hampton, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Kaley A. Walker (kaley.walker@utoronto.ca)</corresp></author-notes><pub-date><day>9</day><month>March</month><year>2022</year></pub-date>
      
      <volume>15</volume>
      <issue>5</issue>
      <fpage>1233</fpage><lpage>1249</lpage>
      <history>
        <date date-type="received"><day>19</day><month>August</month><year>2021</year></date>
           <date date-type="rev-request"><day>30</day><month>August</month><year>2021</year></date>
           <date date-type="rev-recd"><day>13</day><month>December</month><year>2021</year></date>
           <date date-type="accepted"><day>21</day><month>December</month><year>2021</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 </copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://amt.copernicus.org/articles/.html">This article is available from https://amt.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e205">For the past 17 years, the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) instrument on the Canadian SCISAT satellite
has been measuring profiles of atmospheric ozone. The latest operational
versions of the level 2 ozone data are versions 3.6 and 4.1. This study
characterizes how both products compare with correlative data from other
limb-sounding satellite instruments, namely MAESTRO, MLS, OSIRIS, SABER, and
SMR. In general, v3.6, with respect to the other instruments, exhibits a
smaller bias (which is on the order of <inline-formula><mml:math id="M1" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 %) in the middle
stratosphere than v4.1 (<inline-formula><mml:math id="M2" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 2 %–9 %); however, the bias exhibited
in the v4.1 data tends to be more stable, i.e. not changing significantly
over time in any altitude region. In the lower stratosphere, v3.6 has a
positive bias of about 3 %–5 % that is stable to within
<inline-formula><mml:math id="M3" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>1 % per decade, and v4.1 has a bias on the order of <inline-formula><mml:math id="M4" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 % to <inline-formula><mml:math id="M5" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>5 % and is also stable to within <inline-formula><mml:math id="M6" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>1 % per decade. In the middle stratosphere, v3.6 has a positive bias of <inline-formula><mml:math id="M7" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 % with a significant negative drift on the order of 0.5 %–2.5 % per decade, and v4.1 has a positive bias of 2 %–9 % that is stable to within <inline-formula><mml:math id="M8" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.5 % per decade. In the upper stratosphere, v3.6 has a positive bias that increases with altitude up to <inline-formula><mml:math id="M9" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 16 % and a significant negative drift on the order of 2 %–3 % per decade, and v4.1 has a positive bias that increases with altitude up to <inline-formula><mml:math id="M10" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 % and is stable to within <inline-formula><mml:math id="M11" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>1 % per decade. Estimates indicate that both versions 3.6 and 4.1 have precision values on the order of 0.1–0.2 ppmv below 20 km and above 45 km (<inline-formula><mml:math id="M12" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 %–10 %, depending on altitude). Between 20 and 45 km, the
estimated v3.6 precision of <inline-formula><mml:math id="M13" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4 %–6 % is better than the
estimated v4.1 precision of <inline-formula><mml:math id="M14" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 6 %–10 %.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e317">It has been well established that prior to the implementation of the
Montreal Protocol, global stratospheric ozone (O<inline-formula><mml:math id="M15" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>) concentrations were
declining on the order of approximately 5 % per decade (WMO, 2018). Since
1997, after the implementation of the Montreal Protocol, stratospheric
O<inline-formula><mml:math id="M16" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations are no longer declining, and now the question
remains, <italic>are O</italic><inline-formula><mml:math id="M17" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> <italic>concentrations recovering</italic>? Multiple recent studies (e.g. Harris et al., 2015; Arosio
et al., 2019; Szelag et al., 2020) have shown that merged satellite O<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
data sets do exhibit positive stratospheric trends over the past decade or
so; however, the positive trends may or may not be considered significant
depending on how the uncertainties within the individual data sets are
treated (SPARC/IO3C/GAW, 2019). When calculating atmospheric trends, one type of
uncertainty that needs to be properly characterized is the stability of
systematic errors (drift) in the data. This is especially important when
merging O<inline-formula><mml:math id="M19" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data sets in order to produce a long-term data record on the
order of decades. The ACE-FTS (Atmospheric Chemistry Experiment Fourier
Transform Spectrometer) satellite instrument's O<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data set is
frequently used to help understand the state of stratospheric ozone. It is
important to note that this study in no way tries to answer the question of
whether O<inline-formula><mml:math id="M21" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations are recovering or not – it assesses the
quality of ACE-FTS O<inline-formula><mml:math id="M22" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data in the context of O<inline-formula><mml:math id="M23" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> recovery.</p>
      <p id="d1e407">As of yet, there have been no published studies focusing on characterizing
ACE-FTS O<inline-formula><mml:math id="M24" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> drift; however, Hubert et al. (2016) compared 14 different
O<inline-formula><mml:math id="M25" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data sets from satellite limb sounders to ground- and balloon-based
measurements in order to determine the long-term stability of the satellite
instruments. They did not find any significant drift in the version 3.0
ACE-FTS data, although the analysis only included ACE-FTS data from
2004–2010. Rahpoe et al. (2015) calculated relative drifts between six
different O<inline-formula><mml:math id="M26" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data sets from satellite limb sounders. Similarly, the
ACE-FTS version 3.0 data product used only spanned 2004–2010, and no
significant drift was identified. Although, as this study will show, it is
possible that significant drifts would have been identified had longer time
series been analyzed.</p>
      <p id="d1e437">In this study, ACE-FTS O<inline-formula><mml:math id="M27" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles have been compared to correlative
data sets from satellite-based limb sounders that overlap in time with
essentially the entire ACE-FTS mission, i.e. MAESTRO (Measurement of Aerosol
Extinction in the Stratosphere and Troposphere Retrieved by Occultation),
Aura MLS (Microwave Limb Sounder), OSIRIS (Optical Spectrograph and Infrared
Imaging System), SABER (Sounding of the Atmosphere using Broadband Emission
Radiometry), and SMR (Sub-Millimetre Radiometer). These five instruments
were all in orbit and measuring ozone in 2004, the year when ACE-FTS began
making measurements, and are still in operation.</p>
      <p id="d1e449">A description of the instrumentation can be found in Sect. 2, and the
methodology is described in Sect. 3. The global and regional results for
ACE-FTS O<inline-formula><mml:math id="M28" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> comparisons are discussed in Sect. 4, and all the results
are summarized in Sect. 5.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Instrumentation</title>
      <p id="d1e469">Table 1 gives an overview of some of the key details related to the
satellite instruments used in this study.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e475">Selected details of the instruments and the O<inline-formula><mml:math id="M29" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data sets used
in the comparisons.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Instrument</oasis:entry>
         <oasis:entry colname="col2">Satellite</oasis:entry>
         <oasis:entry colname="col3">Observation</oasis:entry>
         <oasis:entry colname="col4">O<inline-formula><mml:math id="M30" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> version</oasis:entry>
         <oasis:entry colname="col5">Comparison</oasis:entry>
         <oasis:entry colname="col6">Vertical</oasis:entry>
         <oasis:entry colname="col7">Max no. of</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">method</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">coverage</oasis:entry>
         <oasis:entry colname="col6">resolution</oasis:entry>
         <oasis:entry colname="col7">coincidences</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">(km)</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">ACE-FTS</oasis:entry>
         <oasis:entry colname="col2">SCISAT</oasis:entry>
         <oasis:entry colname="col3">Solar occultation</oasis:entry>
         <oasis:entry colname="col4">3.6 and 4.1</oasis:entry>
         <oasis:entry colname="col5">85<inline-formula><mml:math id="M31" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–87<inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">3–6</oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAESTRO</oasis:entry>
         <oasis:entry colname="col2">SCISAT</oasis:entry>
         <oasis:entry colname="col3">Solar occultation</oasis:entry>
         <oasis:entry colname="col4">3.13</oasis:entry>
         <oasis:entry colname="col5">85<inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–87<inline-formula><mml:math id="M34" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">1</oasis:entry>
         <oasis:entry colname="col7">55 254</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MLS</oasis:entry>
         <oasis:entry colname="col2">Aura</oasis:entry>
         <oasis:entry colname="col3">Limb emission</oasis:entry>
         <oasis:entry colname="col4">5.1</oasis:entry>
         <oasis:entry colname="col5">82<inline-formula><mml:math id="M35" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–82<inline-formula><mml:math id="M36" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">2.5-4</oasis:entry>
         <oasis:entry colname="col7">26 408</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">OSIRIS</oasis:entry>
         <oasis:entry colname="col2">Odin</oasis:entry>
         <oasis:entry colname="col3">Limb scatter</oasis:entry>
         <oasis:entry colname="col4">5.10</oasis:entry>
         <oasis:entry colname="col5">83<inline-formula><mml:math id="M37" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–82<inline-formula><mml:math id="M38" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">2</oasis:entry>
         <oasis:entry colname="col7">4329</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SABER</oasis:entry>
         <oasis:entry colname="col2">TIMED</oasis:entry>
         <oasis:entry colname="col3">Limb emission</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5">82<inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–82<inline-formula><mml:math id="M40" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">2</oasis:entry>
         <oasis:entry colname="col7">19 079</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMR</oasis:entry>
         <oasis:entry colname="col2">Odin</oasis:entry>
         <oasis:entry colname="col3">Limb emission</oasis:entry>
         <oasis:entry colname="col4">3.0</oasis:entry>
         <oasis:entry colname="col5">83<inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–82<inline-formula><mml:math id="M42" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N</oasis:entry>
         <oasis:entry colname="col6">2–3</oasis:entry>
         <oasis:entry colname="col7">8672</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Instruments on SCISAT</title>
      <p id="d1e854">The Canadian SCISAT satellite was launched into a non-sun synchronous,
high-inclination orbit in 2003 at an altitude of <inline-formula><mml:math id="M43" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 650 km. On
board are two instruments, ACE-FTS and MAESTRO, both of which use solar
occultation viewing geometry to measure profiles of atmospheric state
parameters. Both instruments began making regular measurements in February
2004 and are still in operation as of 2021.</p>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>ACE-FTS</title>
      <p id="d1e871">The ACE-FTS instrument (Bernath et al., 2005) is a high-spectral-resolution
(0.02 cm<inline-formula><mml:math id="M44" 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>) spectrometer viewing the Earth's limb in the infrared
between 750 and 4400 cm<inline-formula><mml:math id="M45" 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>, measuring pressure and temperature
profiles and volume mixing ratio (VMR) profiles of over 40 atmospheric trace
gases and more than 20 isotopologue species. ACE-FTS profiles the limb
between 5 and 150 km with a vertical sampling of <inline-formula><mml:math id="M46" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 to 6 km,
depending on the orbital geometry and tangent height, and the vertical
extent of the instrument field-of-view at the tangent altitude is on the
order of 3–4 km. Two different versions of the level 2 ACE-FTS O<inline-formula><mml:math id="M47" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data
are used in this study, version 3.6 (v3.6) and version 4.1 (v4.1).</p>
      <p id="d1e914">The retrieval algorithm for trace species concentrations is described by
Boone et al. (2005, 2013, 2020), and it uses a non-linear, least-squares,
global-fitting technique that fits observed spectra to forward modelled
spectra in species-dependent microwindows. The modelled spectra are
calculated using spectral line parameters from the HITRAN2004 database
(Rothman et al., 2005) with various updates (Boone et al., 2013) for version 3.6, and the v4.1 retrieval uses HITRAN2016 (Gordon et al., 2017). In March
2021, the processing environment for the v4 retrievals was changed, and the
current operational version is currently v4.1/4.2, with no significant
differences in the retrieval results between v4.1 and 4.2.</p>
      <p id="d1e917">Both versions 3.6 and 4.1 of the ACE-FTS O<inline-formula><mml:math id="M48" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> retrieval use 40
microwindows between 829 and 2673 cm<inline-formula><mml:math id="M49" 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> and account for CFC-12,
HCFC-22, CFC-11, N<inline-formula><mml:math id="M50" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, CH<inline-formula><mml:math id="M51" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>, HCOOH, and various isotopologues as
interfering species. The retrievals have a lower altitude limit of 5 km and
an upper altitude limit of 95 km. Horizontal homogeneity is assumed in the
retrievals, and diurnal variation along the line of sight is not taken into
account. ACE-FTS v2.2 O<inline-formula><mml:math id="M52" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> was validated by Dupuy et al. (2009), and
Sheese et al. (2017) compared ACE-FTS v3.5 O<inline-formula><mml:math id="M53" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to correlative data from
MIPAS and MLS. The ACE-FTS v2.2 O<inline-formula><mml:math id="M54" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles are known to have a
positive bias on the order of 15 %–20 % in the upper stratosphere to lower
mesosphere, near 50–60 km, and on average typically agree with correlative
data sets to within <inline-formula><mml:math id="M55" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>5 % in the middle lower to middle stratosphere
(<inline-formula><mml:math id="M56" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 20–40 km) with a slight positive bias on the order of a few
percent. The average bias found between ACE-FTS v3.5 and Aura MLS and MIPAS
is within 2 % from 10–45 km and up to 19 % between 46 and 60 km.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>MAESTRO</title>
      <p id="d1e1009">The MAESTRO instrument (McElroy et al., 2007) consists of two
spectrophotometers designed to cover the spectral range 210–1015 nm, with
1.5–2 nm spectral resolution. The solar occultation measurements are used to retrieve profiles of aerosol extinction and concentrations of O<inline-formula><mml:math id="M57" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>,
NO<inline-formula><mml:math id="M58" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>, and H<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O in the upper troposphere and stratosphere
(<inline-formula><mml:math id="M60" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5–52 km) with a vertical resolution on the order of 1 km.
The O<inline-formula><mml:math id="M61" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> retrieval algorithm (McElroy et al., 2007) fits apparent optical
depth spectra to modelled spectra in order to derive slant column densities.
The forward model assumes temperature-independent O<inline-formula><mml:math id="M62" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and NO<inline-formula><mml:math id="M63" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
absorption cross sections from Burrows et al. (1998, 1999). The slant
columns are then used in a Chahine inversion technique (Chahine, 1968) to
retrieve O<inline-formula><mml:math id="M64" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles.</p>
      <p id="d1e1083">This study uses v3.13 of the MAESTRO O<inline-formula><mml:math id="M65" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data, which have not yet been
independently validated. Kar et al. (2007) compared version 1.2 MAESTRO
O<inline-formula><mml:math id="M66" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data to correlative data from ozonesondes and satellite instruments,
including ACE-FTS. They found that between 16 and 50 km MAESTRO typically
agreed with ozonesonde data to within <inline-formula><mml:math id="M67" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 %–10 % and that
MAESTRO and ACE-FTS tended to agree within <inline-formula><mml:math id="M68" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 %–15 % in the
stratosphere up to 50 km. They also found that while MAESTRO sunset profiles
typically agreed with satellite measurements to within 5 %–10 % in the
16–40 km region, MAESTRO sunrise profiles exhibited a positive bias of up
to <inline-formula><mml:math id="M69" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 %–30 % in the 40–55 km region and a negative bias of
<inline-formula><mml:math id="M70" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 %–15 % near 20–30 km. Similar results were found by
Dupuy et al. (2009) when comparing v1.2 MAESTRO O<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data to correlative
data from satellite, balloon, airborne, and ground-based instruments. Hubert
et al. (2016) found no significant drift between MAESTRO v1.2 and balloon-borne measurements for the period 2004–2010.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>MLS on Aura</title>
      <p id="d1e1152">The Aura satellite was launched in 2004 into a sun-synchronous orbit
(ascending node of 13:45 LT) near 700 km. On board is the MLS instrument
(Waters et al., 2006), which observes thermal emission in the Earth's limb
in a spectral range of 118 GHz to 2.5 THz in order to retrieve profiles of
temperature, geopotential height, and concentrations of over 15 atmospheric
trace species on a vertical pressure grid.</p>
      <p id="d1e1155">The MLS v5 O<inline-formula><mml:math id="M72" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles, which are used in this study, are retrieved
from the 240 GHz radiometer measurements and are scientifically useful
between pressure levels of 261 and 0.001 hPa (<inline-formula><mml:math id="M73" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 10 and 90 km),
with a vertical resolution of 2.5–4 km in the stratosphere (Livesey et al.,
2022). The MLS retrieval algorithm, as described by Livesey et al. (2006,
2022), uses a Newtonian optimal estimation technique (Rodgers, 2008), with a
forward model that does not assume horizontal homogeneity, given the Aura
MLS line-of-sight viewing conditions (Livesey and Read, 2000). The
absorption cross sections used in the forward model are from the JPL
Spectral Line Catalogue (Pickett et al., 1998) with updates.</p>
      <p id="d1e1174">The v2.2 O<inline-formula><mml:math id="M74" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> product has been validated by Jiang et al. (2007),
Froidevaux et al. (2008), and Livesey et al. (2008); in the stratosphere,
the results of those validation studies are generally applicable to the v5.1
stratospheric O<inline-formula><mml:math id="M75" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data (Livesey et al., 2022). When comparing to
ground-based O<inline-formula><mml:math id="M76" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles, Hubert et al. (2016) found the v3.3 MLS
O<inline-formula><mml:math id="M77" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data to be stable within 2 % per decade in the upper stratosphere
and within 1.5 % per decade in the middle stratosphere.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Instruments on Odin</title>
      <p id="d1e1221">The Odin satellite (Murtagh et al., 2002) was launched in 2001 into a
sun-synchronous orbit (ascending node of 06:00 LT) at an altitude of
<inline-formula><mml:math id="M78" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 600 km. There are two limb sounding instruments aboard the
satellite that are currently in operation, OSIRIS (Llewellyn et al., 2004)
and SMR (Frisk et al., 2003).</p>
<sec id="Ch1.S2.SS3.SSS1">
  <label>2.3.1</label><title>OSIRIS</title>
      <p id="d1e1238">The OSIRIS instrument uses an optical spectrograph operating in the
spectral range of 280–810 nm to observe Rayleigh and Mie scattered sunlight
in the Earth's limb and retrieves profiles of O<inline-formula><mml:math id="M79" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, NO<inline-formula><mml:math id="M80" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>, and BrO
concentrations and aerosol extinction. Scans are made between altitudes of
approximately 7 and 110 km with a vertical field-of-view of approximately 1 km. As detailed by Bourassa et al. (2012), O<inline-formula><mml:math id="M81" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations are
retrieved using the Multiplicative Algebraic Reconstruction Technique (MART) (Roth et al., 2007; Degenstein et al., 2009) between approximately
10 and 60 km, with a vertical resolution on the order of 2 km, and
pressure and temperature profiles from the European Centre for Medium-Range
Weather Forecasts (ECMWF) ERA-Interim reanalysis are used (Dee et al., 2011). Within
the O<inline-formula><mml:math id="M82" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> retrieval, UV and visible absorption is taken into account, and
aerosols and NO<inline-formula><mml:math id="M83" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> are both considered interfering species and are
pre-retrieved.</p>
      <p id="d1e1286">The version 5.10 OSIRIS data are used in this study. Hubert et al. (2016)
found there to be a significant positive drift in the v5.07 OSIRIS O<inline-formula><mml:math id="M84" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
data above 20 km with respect to ozonesonde and lidar data. Between 22 and
35 km, the OSIRIS drift is on the order of 1 %–3 % per decade, and above 37 km the positive drift increases to 8 % per decade near 42 km. However,
Bourassa et al. (2018) determined that these drifts were due to a systematic
error in the pointing knowledge and showed that the drifts were
significantly reduced in v5.10. Adams et al. (2014) determined that
throughout the stratosphere the v5.07 OSIRIS drift relative to the GOMOS
(Global Ozone Monitoring by Occultation of Stars) was less than 3 %
per decade, and v5.07 was shown to be in excellent agreement (within
<inline-formula><mml:math id="M85" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 5 %) with coincident SAGE II profiles throughout the
stratosphere by Adams et al. (2013).</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <label>2.3.2</label><title>SMR</title>
      <p id="d1e1313">The SMR instrument uses four tuneable receivers within 486–581 GHz and a
millimetre-wave receiver at 119 GHz to observe thermal emissions in the Earth's
limb. The SMR observations are used to retrieve profiles of temperature and
O<inline-formula><mml:math id="M86" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, H<inline-formula><mml:math id="M87" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, N<inline-formula><mml:math id="M88" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, HNO<inline-formula><mml:math id="M89" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, and ClO concentrations. Three
different O<inline-formula><mml:math id="M90" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> products are retrieved, one from emissions measured at the
544.6 GHz line, one from the 501.8 GHz, and one from the 488 GHz line;
however, only the 544 GHz O<inline-formula><mml:math id="M91" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> retrievals are used in this study.</p>
      <p id="d1e1371">The O<inline-formula><mml:math id="M92" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> retrieval algorithm (Urban et al., 2005) makes use of
measurements in a 1 GHz band (centred at 544.6 GHz) and uses a Newtonian
Levenberg–Marquardt optimal estimation technique (Rodgers, 2008). The
forward model used in the retrievals is the open-source ARTS (Atmospheric
Radiative Transfer Simulator) forward model (Buehler et al., 2005). Version 3.0 O<inline-formula><mml:math id="M93" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, used in this study, is retrieved at altitudes between 11 and 109 km, with a vertical resolution of <inline-formula><mml:math id="M94" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2–3 km.</p>
      <p id="d1e1399">Jones et al. (2007) compared v2.1 501 GHz O<inline-formula><mml:math id="M95" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to correlative data from
satellite and balloon measurements, and Sagi and Murtagh (2016) compared the
v2.1 501 and 544 GHz O<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data sets, showing that the two data sets are
within 10 % of each other at altitudes between 15 and 40 km. Sagi et al. (2017) used v2.1 544 GHz O<inline-formula><mml:math id="M97" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data in their study on O<inline-formula><mml:math id="M98" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> depletion in the Northern Hemisphere.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>SABER on TIMED</title>
      <p id="d1e1447">The TIMED (Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics)
satellite was launched in 2001 into a non-sun-synchronous orbit, sweeping
through 24 h of local time every 36 d. On board is the SABER instrument
(Russell et al., 1999), which uses observations of infrared emissions to
retrieve O<inline-formula><mml:math id="M99" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations throughout the stratosphere to lower
thermosphere in a 9.6 <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m channel and in the mesosphere to lower
thermosphere in a 1.27 <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m channel, both with a vertical resolution of <inline-formula><mml:math id="M102" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 km. This study makes use of the v2.0 O<inline-formula><mml:math id="M103" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> 9.6 <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m
data, the retrieval of which is described by Rong et al. (2009) and uses an
iterative onion peel retrieval method, taking into account non-LTE (local
thermodynamic equilibrium) effects.</p>
      <p id="d1e1500">The version 1.07 O<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data products are discussed and validated by Rong
et al. (2009), where they found the 9.6 <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m O<inline-formula><mml:math id="M107" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data to have a
positive bias in the stratosphere on the order of 5 %–15 % (above what can
be explained by systematic uncertainties). Corrections for this bias have
been formulated and are under active study by the SABER team. An updated
data set is expected to be produced in the next year (James Russell, personal
communication, 2021​​​​​​​, Hampton University, Hampton, VA). To the
authors' knowledge, no studies have been published on the differences
between the v1.07 and v2.0 9.6 <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m O<inline-formula><mml:math id="M109" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data products; however,
Fytterer et al. (2015) discuss how v1.07 can be used to supplement v2.0
where there are data gaps without the need for systematic corrections. The
SABER O<inline-formula><mml:math id="M110" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data were not considered in the drift analysis study of Hubert
et al. (2016).</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Methodology</title>
      <p id="d1e1565">In this and the following sections, the term INST will be used in general to
refer to any of the instruments (other than ACE-FTS). The coincidence
criteria used in all of the comparisons were such that ACE-FTS and INST
profiles must have been measured within 6 h and 300 km of each other.
These coincidence criteria were chosen in order to ensure that coincident
profiles were as close to common volume as possible while still having
enough profiles to ensure results are statistically significant, and, as
discussed by Sheese et al. (2021), these criteria keep the estimated O<inline-formula><mml:math id="M111" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
geophysical variability (1<inline-formula><mml:math id="M112" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>) between ACE and Odin measurements to
less than 5 %. The geophysical variability between ACE-FTS and MLS and
between ACE-FTS and SABER is assumed to be similar to the geophysical
variability between ACE and Odin.</p>
      <p id="d1e1584">Prior to analysis, all MAESTRO, OSIRIS, SABER, and SMR profiles, which do
not have simultaneously retrieved pressure values, have been linearly
interpolated onto the ACE-FTS 1 km grid. The MLS profiles have been
interpolated to corresponding coincident ACE-FTS pressure values (on a 1 km
grid) in order to avoid any uncertainties inherent in the retrieved MLS
geopotential height values. None of the profiles were vertically smoothed,
as the vertical resolutions of all the instruments are relatively similar
and smoothing the data has little to no effect on comparison results (e.g.
Sheese et al., 2016). In cases where an ACE-FTS profile was coincident with
multiple profiles from an INST data set, only the profile measured closest
in latitude to the ACE-FTS occultation was used.</p>
      <p id="d1e1587">For direct comparisons between ACE-FTS and INST, the relative mean
differences are calculated with respect to ACE-FTS data as
          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M113" display="block"><mml:mrow><mml:mi mathvariant="normal">diff</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:msubsup><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>Y</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="M114" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes the ACE-FTS values at a given height and <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes the
corresponding INST values. The dual-instrument mean is used in the
denominator as ACE-FTS and most other INST retrievals allow for negative
concentrations. When the average of two compared values is near zero (due to
allowing negative values), this can cause unrealistically large percent
differences.</p>
      <p id="d1e1668">A similar approach to Bourassa et al. (2012) was taken to determine
estimates of the ACE-FTS precision. Following the methodology in their
Sect. 3.2, the ACE-FTS relative precision, <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is given by
          <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M117" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">A</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">I</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">A</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="normal">I</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:mfenced></mml:mrow></mml:msqrt><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the standard deviation of the ACE-FTS measurements, <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">I</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the standard deviation of the INST measurements, and <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">A</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="normal">I</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the standard deviation of the differences. In order to
avoid imaginary values in the overall mean precision profiles, mean profiles
of the absolute precision-squared values were calculated, of which the square roots were then calculated.</p>
      <p id="d1e1777">When determining the multi-instrument averages for the ACE-FTS comparison
results, the INST values (relative to ACE-FTS) are weighted using the
inverse square of the standard deviation of the differences,
          <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M121" display="block"><mml:mrow><mml:mi>W</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mi mathvariant="normal">comp</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mi>W</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mi mathvariant="normal">comp</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is the INST weight at height <inline-formula><mml:math id="M123" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>,
and <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the standard deviation of the differences between INST
and ACE-FTS. This, rather than a simple mean, is done to account for the
quality of the INST data sets used in the comparisons and assumes that all
data sets, in comparison with ACE-FTS, exhibit similar geophysical
variability.</p>
      <p id="d1e1861">Similar to the analyses by Hubert et al. (2016), the drift and its
corresponding error at each altitude are determined by fitting the 30 d
mean relative difference time series to a linear model using iterative
reweighting least-squares fitting with a bisquare weighting function (Street
et al., 1988). Using 30 d mean values as opposed to daily means eliminates
the need to deseasonalize the data prior to analysis within specific
latitude bands. A Student's <inline-formula><mml:math id="M125" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> test is then performed to determine the
uncertainty of the linear drift for a confidence level of 99 %. When
determining the multi-instrument average of the ACE-FTS drift, the drift
values for ACE-FTS – INST are weighted using the inverse square of the
uncertainty of the drift,
          <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M126" display="block"><mml:mrow><mml:mi>W</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mi mathvariant="normal">drft</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:mi>W</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mi>t</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi><mml:mi mathvariant="normal">drft</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is the INST weight at height <inline-formula><mml:math id="M128" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>,
and <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi mathvariant="normal">INST</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the uncertainty of the calculated
linear drift between INST and ACE-FTS. The drift is considered to be
non-zero when the weighted-average error bounds are less than 100 % of the drift value.</p>
      <p id="d1e1957">Prior to analysis, the ACE-FTS data were screened using the ACE-FTS quality
flags as described by Sheese et al. (2015). For all other data sets, all
recommended quality, status, and convergence flags were taken into account
when such flags were available. Quality flags were generated for the MAESTRO
data using the same algorithm as the ACE-FTS quality flags and were used to
screen out unphysical outliers. For MLS data, no profile that was flagged as
having cloud contamination at any pressure level was used in the analysis.
For SABER data, as recommended by Fytterer et al. (2015), no data with
values greater than 20 ppmv were used. Only SMR data where the corresponding
measurement response (sum of the rows of the averaging kernels) values were
greater than 0.8 were used.</p>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Global comparisons</title>
      <p id="d1e1975">Figure 1 shows the results of comparing v3.6 and v4.1 ACE-FTS O<inline-formula><mml:math id="M130" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
profiles to coincident MAESTRO, MLS, OSIRIS, SABER, and SMR using all
available data from 2004 to 2020 with coincidence criteria of being within 6 h
and 300 km (excluding MAESTRO PM data below 23 km, as will be discussed in
Sect. 4.2). The thick black lines are the multi-instrument weighted averages
and are shown without the individual INST comparisons in Fig. 2. As can be
seen in Fig. 1, both versions 3.6 and 4.1 yield similar average standard
deviations of differences and correlation coefficient profiles. At all
altitudes examined, the correlation coefficients are on the order of
0.8–0.9, and the standard deviations are on the order of 15 %
(<inline-formula><mml:math id="M131" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 0.3 ppmv) in the upper stratosphere, 10 %
(<inline-formula><mml:math id="M132" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 0.5 ppmv) in the middle stratosphere, and 20 % (0.1 ppmv)
in the lower stratosphere. It should be noted that the coincidence criteria
were chosen so that the estimated 1<inline-formula><mml:math id="M133" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> natural variability
(variability due to sampling differences) is less than or on the order of
<inline-formula><mml:math id="M134" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 % (Sheese et al., 2021). For comparisons between
atmospheric measurements, it is desirable to have coincidence criteria that
allow for the natural variability to be less than the combined accuracies,
and the value of 5 % is the minimum accuracy recommended by the Global
Climate Observing System (GGOS) for stratospheric O<inline-formula><mml:math id="M135" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (GCOS, 2011).
Figure 2 highlights the difference in the ACE-FTS bias between versions 3.6
and 4.1, showing that the bias in the upper and lower stratosphere improved
in 4.1 but worsened in the middle stratosphere. In the 15–20 km region, the bias decreased from <inline-formula><mml:math id="M136" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 %–5 % (<inline-formula><mml:math id="M137" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 0.05 ppmv) to
about <inline-formula><mml:math id="M138" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 % to 5 % (<inline-formula><mml:math id="M139" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>0.02 to 0.05 ppmv) and is in part due to updates in
spectroscopic parameters from HITRAN2004 to HITRAN2016. Above 45 km the bias
decreased slightly from 2 %–13 % to 2 %–11 % due to an improvement in the
ACE-FTS altitude registration, which is now generated from measurements of
the N<inline-formula><mml:math id="M140" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> continuum (Boone et al., 2020). In the 20–45 km region, where
ozone concentrations peak, the bias was on the order of <inline-formula><mml:math id="M141" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 % to 3 % (maximum of 0.2 ppmv near 33 km) in v3.6 and increased to <inline-formula><mml:math id="M142" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2 %–9 % (maximum of just over 0.5 ppmv near 30 km). Although the overall bias with
respect to other limb sounders worsened, the increase is in part due to the
improved instrument line shape modelling, which now allows for asymmetry and
improved wavenumber variation (Boone et al., 2020).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e2079">Comparisons between ACE-FTS O<inline-formula><mml:math id="M143" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and MAESTRO (blue), MLS (red),
OSIRIS (yellow), SABER (purple), and SMR (green) with coincidence criteria
of within 6 h and 300 km for all coincident profiles within 2004–2020. ACE-FTS v3.6 (top) and v4.1 (bottom). From left to right the plots show the mean of the differences between ACE-FTS and INST in ppmv, the standard deviation of the differences between ACE-FTS and INST in ppmv, the mean of the relative differences between ACE-FTS and INST in percent, the standard
deviation of the relative differences between ACE-FTS and INST in percent,
and the correlation coefficients. The black line in each plot provides the
weighted average (see text).</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f01.png"/>

        </fig>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2099">Weighted averages of the mean differences <bold>(a)</bold> and mean percent differences <bold>(b)</bold> for comparisons between ACE-FTS and all instruments. Dashed lines represent ACE-FTS v3.6 and solid lines represent v4.1.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f02.png"/>

        </fig>

      <p id="d1e2115">The ACE-FTS relative precision profiles (relative to INST) and weighted-mean
precision estimates are shown in Fig. 3. For v3.6, Fig. 3a shows that for
each comparison the ACE-FTS relative precision is <inline-formula><mml:math id="M144" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1–0.2 ppmv above 40 km, <inline-formula><mml:math id="M145" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1–0.5 ppmv between 20–40 km, and
<inline-formula><mml:math id="M146" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1–0.4 ppmv below 20 km. For v4.1 (Fig. 3b) the ACE-FTS
relative precision profiles have a more consistent variation with altitude
between INST comparisons, with values of <inline-formula><mml:math id="M147" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1–0.3 ppmv above
45 km, 0–0.4 ppmv below 25 km, and peak (worst) values near 30 km on the
order of 0.7–0.8 ppmv. The weighted-mean relative precision values for both
v3.6 and 4.1 are on the order of 0.1–0.2 ppmv (<inline-formula><mml:math id="M148" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 6 %–10 %)
below 20 km and <inline-formula><mml:math id="M149" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.15 ppmv (<inline-formula><mml:math id="M150" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 %–8 %) above 45 km. In the intermediate altitudes, the v3.6 precision is typically within
4 %–6 %, whereas it is slightly worse for v4.1, typically within
6 %–10 %.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2170">ACE-FTS relative precision estimates for <bold>(a)</bold> v3.6 relative to INST in ppmv, <bold>(b)</bold> v4.1 relative to INST in ppmv, and <bold>(c)</bold> weighted mean profiles in percent.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f03.png"/>

        </fig>

      <p id="d1e2188">The source of the change in precision can in part be explained by the change
in the tangent height retrieval algorithm. The update of CO<inline-formula><mml:math id="M151" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
spectroscopic parameters between versions 3 and 4, along with fixing the
pressure near 18 km to the results of the N<inline-formula><mml:math id="M152" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> continuum analysis (Boone
et al., 2020), leads to an increase in O<inline-formula><mml:math id="M153" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> number density variability of
<inline-formula><mml:math id="M154" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 % throughout the stratosphere. Further contributions to
the reduction of precision in v4.1 are currently being investigated.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2227">Drift profiles (curves) and corresponding 99 % confidence bounds (semitransparent shaded regions) for comparisons between v3.6 and v4.1
ACE-FTS O<inline-formula><mml:math id="M155" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and MAESTRO (blue), MLS (red), OSIRIS (yellow), SABER
(purple), and SMR (green) with coincidence criteria of within 6 h and 300 km for all coincident profiles within 2004–2020. Results in ppmv per decade (top) and in percent per decade (bottom).</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f04.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2248">Relative drift profiles for each INST relative to ACE-FTS v3.6 <bold>(a)</bold> and v4.1 <bold>(b)</bold> and the corresponding inter-instrument stability
(magenta), represented by the standard deviation of the drift profiles.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f05.png"/>

        </fig>

      <p id="d1e2263">Figure 4 shows the calculated v3.6 and v4.1 ACE-FTS drift profiles relative
to INST, given the coincidence criteria of within 6 h and 300 km. All INST
profiles exhibit similar differences in drifts versus ACE-FTS profiles
between v3.6 and v4.1. All ACE-FTS – INST profiles show no significant
change in drift between ACE-FTS data versions below <inline-formula><mml:math id="M156" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 22 km
and a significant positive shift in drift, on the order of 1 %–3 % per decade, above <inline-formula><mml:math id="M157" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 22 km. These changes in drift between
ACE-FTS versions are more clearly seen in Fig. 5, which shows that the
largest differences in drift are exhibited in the 40–45 km region. Also
shown is the inter-instrumental stability, which is calculated (for both
v3.6 and v4.1) as the standard deviation of all ACE-FTS drifts relative to
INST. For both versions of ACE-FTS, the best inter-instrumental stability is
0.8 % per decade near 22 km, and between 17 and 46 km, the
inter-instrumental stability is below 2 % per decade. Figure 6 shows the
ACE-FTS MLS time series (30 d mean values) at 42.5 km as an example of
the calculated trends and their uncertainty (represented as 99 %
confidence intervals). At this altitude level, the ACE-FTS v3.6 drift
relative to MLS is <inline-formula><mml:math id="M158" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.3 <inline-formula><mml:math id="M159" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 % per decade (<inline-formula><mml:math id="M160" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>0.06 <inline-formula><mml:math id="M161" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.05 ppmv per decade), whereas the drift in v4.1 relative to MLS is not significant with a value of 0.9 <inline-formula><mml:math id="M162" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.3 % per decade (0.04 <inline-formula><mml:math id="M163" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.06 ppmv per decade). The global drift results, seen in Fig. 7, clearly show that not
only is there a significant difference in drift values between v3.6 and v4.1
at nearly all altitudes above <inline-formula><mml:math id="M164" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 25 km, but that there is a
significant drift in v3.6 O<inline-formula><mml:math id="M165" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> at all altitudes above 20 km and no drift
in v4.1 at any analyzed altitude. ACE-FTS v3.6 data exhibit a mean drift on
the order of 1 <inline-formula><mml:math id="M166" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5 % per decade between 20 and 35 km and on the
order of 2.5 <inline-formula><mml:math id="M167" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 % per decade in the 40–50 km region. This drift
is due to an inaccurate trend in the assumed CO<inline-formula><mml:math id="M168" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentrations used in
the v3.6 pressure and temperature retrieval (which are used in the O<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
retrievals). In version v4.1, CO<inline-formula><mml:math id="M170" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentrations are determined using a
more accurate model (Boone et al., 2020).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e2383">Linear fits (lines) to the 30 d average differences (circles)
between ACE-FTS and MLS at an altitude of 42.5 km for <bold>(a)</bold> ACE-FTS v3.6 and <bold>(b)</bold> ACE-FTS v4.1. Shaded areas represent the 99 % confidence bounds.</p></caption>
          <?xmltex \igopts{width=352.814173pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f06.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e2400">Weighted average ACE-FTS drift profiles for v3.6 (dashed lines)
and v4.1 (solid lines) in <bold>(a)</bold> absolute differences and <bold>(b)</bold> relative differences. Shaded regions (semitransparent) represent the 99 % confidence bounds.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f07.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Regional comparisons</title>
      <p id="d1e2423">The ACE-FTS weighted-average bias was calculated for data that were binned
by ACE-FTS measurement local time (AM and PM) and by latitude – Arctic
(50–90<inline-formula><mml:math id="M171" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N; Arc), Antarctic (50–90<inline-formula><mml:math id="M172" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S; Ant), and
extra-polar (50<inline-formula><mml:math id="M173" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–50<inline-formula><mml:math id="M174" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N; EP). The results, Fig. 8, show
that in the middle stratosphere there is little change with local time and
latitude in the ACE-FTS bias. At all local times and latitudes between 20–40 km, the v3.6 bias is typically positive and on the order of 0 %–4 %, and the
v4.1 bias is positive and greater than 1 %, peaking near 30 km at
<inline-formula><mml:math id="M175" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 8 %–9 %. As shown in Sect. 4.1, these biases include a
positive bias introduced by FOV modelling error, which, for globally averaged
data, is on the order of a couple of percent near 20 and 40 km and
<inline-formula><mml:math id="M176" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 7 % near 27 km. The weighted-average biases seen in Fig. 8
have not been corrected for FOV modelling errors, as those errors have not
yet been calculated on a regional basis.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e2479">Weighted-average percent biases between ACE-FTS O<inline-formula><mml:math id="M177" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and INST
for comparisons in different local time and latitudinal bins of Arctic
(Arc), extra-polar (EP), and Antarctic (Ant), and with coincidence criteria
of within 6 h and 300 km. <bold>(a)</bold> ACE-FTS v3.6 and <bold>(b)</bold> v4.1.</p></caption>
          <?xmltex \igopts{width=361.35pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f08.png"/>

        </fig>

      <p id="d1e2503">When comparing ACE-FTS O<inline-formula><mml:math id="M178" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to INST profiles that were binned according
to measurement local time, MAESTRO was the only instrument that exhibited a
significant difference in drift values with respect to ACE-FTS between AM
and PM measurements. As seen in Fig. 9, below 23 km, the PM comparisons
exhibit a statistically significant drift on the order of 5 %–10 %,
whereas the AM comparisons exhibit a non-significant drift of
<inline-formula><mml:math id="M179" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 %–2 %. As none of the other instruments exhibit this type
of difference with respect to local time (not shown), it is likely that it
is the MAESTRO PM data that have a positive drift. Due to this, all global
comparisons in Sect. 4.1 exclude MAESTRO PM data below 23 km. The source of
this drift has not yet been identified but is being investigated by the
MAESTRO team.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e2525">Drift profiles between ACE-FTS v4.1 and MAESTRO for AM (blue) and
PM (purple) measurements. Shaded regions (semitransparent) represent 99 %
confidence bounds.</p></caption>
          <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f09.png"/>

        </fig>

      <?xmltex \floatpos{p}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e2536">Weighted-average ACE-FTS drift profiles for AM and PM comparisons
in relative terms. <bold>(a)</bold> ACE-FTS v3.6, <bold>(b)</bold> v4.1. Shaded regions (semitransparent) represent 99 % confidence bounds.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f10.png"/>

        </fig>

      <p id="d1e2551">The weighted average ACE-FTS drift was calculated for different local times
and latitude regions for v4.1 only. The v3.6 drift identified in Sect. 4.1
exists at all local time and latitudes and therefore the v3.6 O<inline-formula><mml:math id="M180" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data
are not recommended for use in trend studies. As seen in Fig. 10, when the
v4.1 data are binned by local time there are small but significant drifts of
approximately <inline-formula><mml:math id="M181" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.8 <inline-formula><mml:math id="M182" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8 % per decade in the AM data near 21 km
and approximately <inline-formula><mml:math id="M183" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 <inline-formula><mml:math id="M184" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 % per decade in the PM data at 44.5 km. When the AM and PM data were further partitioned into Arctic, Antarctic, and
extra-polar latitudinal bins, no significant trend was detectable near 45 km
in the PM data at any latitude region, and the AM data only exhibited a
significant drift in the extra-polar region near 21 km, as shown in Fig. 11.
Unfortunately, the ACE sampling is too sparse to detect a statistically
significant drift result in sub-regions of the AM EP bin, which could help
to further elucidate the cause of the drift. However, it should be noted
that in every latitudinal region there are no significant differences
between AM and PM mean drifts, and similarly, for both AM and PM data there
are no significant differences in drift between latitudinal regions.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e2593">Weighted-average ACE-FTS v4.1 drift profiles for comparisons in
Antarctic (Ant), extra-polar (EP), and Arctic (Arc) latitude bands and
separated by AM and PM local times. Shaded regions (semitransparent)
represent 99 % confidence bounds.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/1233/2022/amt-15-1233-2022-f11.png"/>

        </fig>

      <p id="d1e2602">GCOS recommends that for long-term stratospheric O<inline-formula><mml:math id="M185" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> trend studies, data
sets should have a stability of within 1 % per decade (GCOS, 2011),
and the European Space Agency Ozone Climate Change Initiative program
(ozone_CCI) recommends a stability of less than 1 %–3 % per decade at all latitudes throughout the stratosphere (van Weele,
2016). Both of the significant AM and PM drifts detected in the ACE-FTS v4.1
O<inline-formula><mml:math id="M186" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data (<inline-formula><mml:math id="M187" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>1 % per decade near 45 km and 0.8 % per decade near 21 km, respectively) are at or below the recommended limits.</p>
      <p id="d1e2631">Figure 11 also shows that in the upper altitude regions, above 50 km, the
Antarctic data exhibit a positive drift on the order of 2 %–4 % per decade, which is more prominent for PM data. When the data are not binned by local time, the SH results exhibit a positive drift that is significant above 51 km and has a maximum value of 2.4 <inline-formula><mml:math id="M188" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.5 %, which is within the
ozone_CCI stability recommendations but only just meets the
stricter recommendations of GCOS within the uncertainty.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Summary</title>
      <p id="d1e2651">Both versions 3.6 and 4.1 of stratospheric ACE-FTS O<inline-formula><mml:math id="M189" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles have
been compared to correlative measurements from the limb-viewing satellite
instruments MAESTRO, MLS, OSIRIS, SABER, and SMR. On a global scale, the
v3.6 profiles exhibit a mean bias that is positive on the order of
<inline-formula><mml:math id="M190" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 % in the 17–35 km region and a bias that increases with
altitude from <inline-formula><mml:math id="M191" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 % near 40 km up to <inline-formula><mml:math id="M192" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 13 % near 52 km. The
v4.1 O<inline-formula><mml:math id="M193" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> bias profile tends to be more positive than that of v3.6 in the
middle stratosphere, reaching up to 9 % near 30 km, and more negative by
<inline-formula><mml:math id="M194" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 3 %–4 % percent above 46 km as well as below 20 km.</p>
      <p id="d1e2701">In the middle stratosphere (<inline-formula><mml:math id="M195" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 20–45 km), neither version
varies drastically (typically <inline-formula><mml:math id="M196" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 3 %) as a function of local time
or latitude; however, above 45 km and below 20 km, there are significant
differences in the mean biases between AM and PM profiles. Below 20 km, the
bias in the AM data is up to 5 % greater than the PM bias, and above 45 km the PM bias is up to <inline-formula><mml:math id="M197" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 6 % greater than the AM bias. It
should be noted that above <inline-formula><mml:math id="M198" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40 km O<inline-formula><mml:math id="M199" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> undergoes large
diurnal variation and the time coincidence criterion of 6 h could be a
source of the larger bias at these altitudes. Similarly, ACE-FTS does not
account for the increased horizontal inhomogeneity across the day–night
terminator at these altitudes.</p>
      <p id="d1e2741">Similar to the bias, the estimated ACE-FTS precision in the middle
stratosphere worsened from v3.6 to v4.1. The v3.6 relative precision was
estimated to be between 5 % and 6 %, whereas that of v4.1 was estimated to be <inline-formula><mml:math id="M200" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 7 %–10 %. The source of the change in precision between versions is currently under investigation.</p>
      <p id="d1e2751">The GCOS recommendations for O<inline-formula><mml:math id="M201" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profile accuracy are within 5 %–20 % in
the upper stratosphere and within 10 % in the upper troposphere to lower
stratosphere (GCOS, 2011). At all analyzed altitude levels both the v3.6 and
v4.1 O<inline-formula><mml:math id="M202" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data meet these accuracy recommendations. ESA
ozone_CCI, however, has stricter recommendations. Above 20 km,
ozone_CCI recommends an O<inline-formula><mml:math id="M203" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> accuracy of within 8 %, and
an accuracy of 16 % below 20 km. The v3.6 PM data meet these requirements at all analyzed altitude levels below 47 km, and at all altitude levels below 51 km for the AM data. The v4.1 data, on the other hand, only meet the ozone_CCI requirements near 30 km in certain sub-regions, as the bias can range between 7 % and 9 %, depending on local time and latitude. However, it should be noted that the results presented in this
study are not strictly measurements of accuracy, but rather of bias relative to
other limb sounders where the true O<inline-formula><mml:math id="M204" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> profiles are unknown.</p>
      <p id="d1e2791">In terms of drift, ACE-FTS v4.1 O<inline-formula><mml:math id="M205" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is a significant improvement over
v3.6. The v3.6 data exhibited a significant drift at all analyzed altitude
levels above 21 km, peaking at <inline-formula><mml:math id="M206" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.14 <inline-formula><mml:math id="M207" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02 ppmv per decade at 40.5 km, and on the order of <inline-formula><mml:math id="M208" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.0 <inline-formula><mml:math id="M209" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.4 % within <inline-formula><mml:math id="M210" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20–35 km and <inline-formula><mml:math id="M211" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.5 <inline-formula><mml:math id="M212" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8 % per decade within <inline-formula><mml:math id="M213" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40–50 km. The <inline-formula><mml:math id="M214" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M215" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.5 % per decade drift in the upper stratosphere technically meets the ozone_CCI stability recommendation of
within 1 %–3 % per decade but not the GCOS recommendation of within 1 % per decade. Therefore, v3.6 ACE-FTS O<inline-formula><mml:math id="M216" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> data above 35 km are not
recommended for use in trend studies and should only be used with caution in
the 20–35 km region. The v4.1 data, when analyzed on a global scale, exhibit
no significant drift at any analyzed altitude and drift values are within
<inline-formula><mml:math id="M217" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0.4 % below 52 km. When the data are binned by local time, there
is a small drift in the AM data near 21 km of approximately <inline-formula><mml:math id="M218" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.8 <inline-formula><mml:math id="M219" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8 % per decade and approximately <inline-formula><mml:math id="M220" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1 <inline-formula><mml:math id="M221" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 % per decade near 44 km in the PM data; however, both these subsets adhere to the GCOS and ozone_CCI stability recommendations. This study also found that there is likely a significant positive O<inline-formula><mml:math id="M222" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> drift (<inline-formula><mml:math id="M223" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 2 %–10 % with respect to ACE-FTS) in the MAESTRO PM data below 23 km that worsens with decreasing altitude.</p>
</sec>

      
      </body>
    <back><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e2940">The MATLAB code used in the analyses for this paper is available at <ext-link xlink:href="https://doi.org/10.5683/SP3/TDCB7J" ext-link-type="DOI">10.5683/SP3/TDCB7J</ext-link> (Sheese and Walker, 2022).</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2949">The ACE-FTS and MAESTRO Level 2 data can be obtained via the ACE database (registration required), <uri>https://databace.scisat.ca/level2/</uri> (ACE-FTS, 2022; MAESTRO, 2022). The ACE-FTS data quality flags used for filtering the dataset can be accessed at <ext-link xlink:href="https://doi.org/10.5683/SP2/BC4ATC" ext-link-type="DOI">10.5683/SP2/BC4ATC</ext-link> (Sheese and Walker, 2020). The MLS data can be obtained via the Goddard Earth Sciences Data and Information Services Center archive, <uri>https://disc.gsfc.nasa.gov/</uri> (last access: 2 March 2022, registration required; <ext-link xlink:href="https://doi.org/10.5067/Aura/MLS/DATA2516" ext-link-type="DOI">10.5067/Aura/MLS/DATA2516</ext-link>, Schwartz et al., 2020). The OSIRIS data can be obtained via <uri>ftp://odin-osiris.usask.ca/</uri> (last access: 2 March 2022, registration required; <ext-link xlink:href="https://doi.org/10.5281/zenodo.4532249" ext-link-type="DOI">10.5281/zenodo.4532249</ext-link>, Bourassa et al., 2021). The SABER data can be obtained via <uri>ftp://saber.gats-inc.com/</uri> (SABER, 2022). The SMR data can be obtained via <ext-link xlink:href="https://doi.org/10.5270/OD1-d98abd8" ext-link-type="DOI">10.5270/OD1-d98abd8</ext-link> (European Space Agency, 2020).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2980">PES wrote the manuscript, performed the analysis, and helped develop the project. KAW helped develop the project and provided insight into the ACE-FTS and MAESTRO data. CDB provided insight into the ACE-FTS data. AEB and DAD provided insight into the OSIRIS data. LF provided insight into the MLS data. CTM and JZ provided insight into the MAESTRO data. DM provided insight into the SMR data. and JMR provided insight into the SABER data. Valuable comments on the manuscript were provided by all coauthors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2986">The contact author has declared that neither they nor their co-authors have any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2992">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e2998">This article is part of the special issue “New developments in atmospheric limb measurements: instruments, methods, and science applications (AMT/ACP inter-journal SI)”. It is a result of the 10th international limb workshop, Greifswald, Germany, 4–7 June 2019.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e3004">The Atmospheric
Chemistry Experiment is a Canadian-led mission mainly supported by the CSA.
We thank Peter Bernath, who is the PI of the ACE mission. Odin is a
Swedish-led satellite project funded jointly by Sweden (Swedish National
Space Board), Canada (CSA), France (Centre National d'Études Spatiales),
and Finland (Tekes), with support by the third-party mission programme of the
European Space Agency (ESA). Work at the Jet Propulsion Laboratory was
performed under contract with the National Aeronautics and Space
Administration.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e3009">This research has been supported by the Canadian Space Agency (contract no. 9F045-180034/001/MTB).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e3015">This paper was edited by Chris McLinden and reviewed by Chris Sioris and Chris McLinden.</p>
  </notes><ref-list>
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