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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0"><?xmltex \hack{\allowdisplaybreaks}?><?xmltex \hack{\hyphenation{MIPAS}}?><?xmltex \hack{\hyphenation{MAESTRO}}?><?xmltex \hack{\hyphenation{GOMOS}}?><?xmltex \hack{\hyphenation{ACE-FTS}}?>
  <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-11-4435-2018</article-id><title-group><article-title><?xmltex \hack{\vskip 6mm}?>The SPARC water vapour assessment II: comparison of stratospheric and lower mesospheric water vapour time series observed from satellites</article-title><alt-title>Comparison of <inline-formula><mml:math id="M1" 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> time series</alt-title>
      </title-group><?xmltex \runningtitle{Comparison of {$\chem{H_{{2}}O}$} time series}?><?xmltex \runningauthor{F. Khosrawi et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Khosrawi</surname><given-names>Farahnaz</given-names></name>
          <email>farahnaz.khosrawi@kit.edu</email>
        <ext-link>https://orcid.org/0000-0002-0261-7253</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Lossow</surname><given-names>Stefan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2833-0522</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Stiller</surname><given-names>Gabriele P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2883-6873</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Rosenlof</surname><given-names>Karen H.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0903-8270</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff15">
          <name><surname>Urban</surname><given-names>Joachim</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-7026-793X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <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="aff5">
          <name><surname>Damadeo</surname><given-names>Robert P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1466-839X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Eriksson</surname><given-names>Patrick</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8475-0479</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>García-Comas</surname><given-names>Maya</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2323-4486</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7 aff8">
          <name><surname>Gille</surname><given-names>John C.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Kasai</surname><given-names>Yasuko</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Kiefer</surname><given-names>Michael</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff10">
          <name><surname>Nedoluha</surname><given-names>Gerald E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Noël</surname><given-names>Stefan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5216-9110</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff11">
          <name><surname>Raspollini</surname><given-names>Piera</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5408-1809</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff12">
          <name><surname>Read</surname><given-names>William G.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Rozanov</surname><given-names>Alexei</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4525-3223</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff13">
          <name><surname>Sioris</surname><given-names>Christopher E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff14">
          <name><surname>Walker</surname><given-names>Kaley A.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-3420-9454</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Weigel</surname><given-names>Katja</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6133-7801</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Karlsruhe Institute of Technology, Institute of Meteorology and Climate Research, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>NOAA Earth System Research Laboratory, Global Monitoring Division, 325 Broadway, Boulder, CO 80305, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Chalmers University of Technology, Department of Space, Earth and Environment, Hörsalsvägen 11,<?xmltex \hack{\newline}?> 41296 Gothenburg, Sweden</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>University of Bremen, Institute of Environmental Physics, Otto-Hahn-Allee 1, 28334 Bremen, Germany</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>NASA Langley Research Center, Mail Stop 401B, Hampton, VA 23681, USA</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada, Spain</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>National Center for Atmospheric Research, Atmospheric Chemistry Observations and Modeling Laboratory, P.O. Box 3000, Boulder, CO 80307-3000, USA</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>University of Colorado, Atmospheric and Oceanic Sciences, Boulder, CO 80309-0311, USA</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>National Institute of Information and Communications Technology, Terahertz Technology Research Center, 4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan</institution>
        </aff>
        <aff id="aff10"><label>10</label><institution>Naval Research Laboratory, Remote Sensing Division, 4555 Overlook Avenue Southwest, Washington, DC 20375, USA</institution>
        </aff>
        <aff id="aff11"><label>11</label><institution>Istituto di Fisica Applicata N. Carrara Del Consiglio Nazionale delle Ricerche (IFAC-CNR), Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Italy</institution>
        </aff>
        <aff id="aff12"><label>12</label><institution>Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA</institution>
        </aff>
        <aff id="aff13"><label>13</label><institution>Environment and Climate Change Canada, Atmospheric Science and Technology Directorate, 4905 Dufferin St., <?xmltex \hack{\newline}?> ON, M3H 5T4, Canada</institution>
        </aff>
        <aff id="aff14"><label>14</label><institution>University of Toronto, Department of Physics, 60 St. George Street, Toronto, ON, M5S 1A7, Canada</institution>
        </aff>
        <aff id="aff15"><label>†</label><institution>deceased, 14 August 2014</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Farahnaz Khosrawi (farahnaz.khosrawi@kit.edu)</corresp></author-notes><pub-date><day>25</day><month>July</month><year>2018</year></pub-date>
      
      <volume>11</volume>
      <issue>7</issue>
      <fpage>4435</fpage><lpage>4463</lpage>
      <history>
        <date date-type="received"><day>29</day><month>January</month><year>2018</year></date>
           <date date-type="rev-request"><day>6</day><month>March</month><year>2018</year></date>
           <date date-type="rev-recd"><day>25</day><month>June</month><year>2018</year></date>
           <date date-type="accepted"><day>12</day><month>July</month><year>2018</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/11/4435/2018/amt-11-4435-2018.html">This article is available from https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018.pdf</self-uri>
      <abstract>
    <p id="d1e375">Time series of stratospheric and lower mesospheric water vapour
using 33 data sets from 15 different satellite instruments were compared in
the framework of the second SPARC (Stratosphere-troposphere Processes And
their Role in Climate) water vapour assessment (WAVAS-II). This comparison
aimed to provide a comprehensive overview of the typical uncertainties in the
observational database that can be considered in the future in observational
and modelling studies, e.g addressing stratospheric water vapour trends. The
time series comparisons are presented for the three latitude bands, the
Antarctic (80<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S), the tropics
(15<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) and the Northern Hemisphere mid-latitudes
(50<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) at four different altitudes (0.1, 3, 10 and
80 <inline-formula><mml:math id="M8" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) covering the stratosphere and lower mesosphere. The<?pagebreak page4436?> combined
temporal coverage of observations from the 15 satellite instruments allowed
the consideration of the time period 1986–2014. In addition to the
qualitative comparison of the time series, the agreement of the data sets is
assessed quantitatively in the form of the spread (i.e. the difference
between the maximum and minimum volume mixing ratios among the data sets),
the (Pearson) correlation coefficient and the drift (i.e. linear changes of
the difference between time series over time). Generally, good agreement
between the time series was found in the middle stratosphere while larger
differences were found in the lower mesosphere and near the tropopause.
Concerning the latitude bands, the largest differences were found in the
Antarctic while the best agreement was found for the tropics. From our
assessment we find that most data sets can be considered in future
observational and modelling studies, e.g. addressing stratospheric and lower
mesospheric water vapour variability and trends, if data set specific
characteristics (e.g. drift) and restrictions (e.g. temporal and spatial
coverage) are taken into account.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.Sx1" specific-use="unnumbered">
  <title>Dedication to Jo Urban</title>
      <p id="d1e447">We would like to dedicate this paper to our highly valued colleague Jo Urban,
who would have certainly been the lead author of this study had he not passed
away so soon. Without his devoted work on UTLS water vapour over many years,
this work would not have been possible. In particular, the retrieval of water
vapour from the SMR observations and the combination of these data with other
data sets to understand the long-term development of this trace constituent
comprised a large part his life's work. With his passing, we lost not only
a treasured colleague and friend, but also a leading expert in the microwave
and sub-millimetre observation community.</p>
</sec>
<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e456">Water vapour is the most important greenhouse gas and plays a
key role in the chemistry and radiative balance of the atmosphere. Any
changes in atmospheric water vapour have important implications for the
global climate <xref ref-type="bibr" rid="bib1.bibx54 bib1.bibx46" id="paren.1"/> and need to be monitored and
understood <xref ref-type="bibr" rid="bib1.bibx29" id="paren.2"/>. Accurate knowledge of the water vapour
distribution and its trends from the upper troposphere up to the mesosphere
is therefore crucial for understanding climate change and chemical forcing
<xref ref-type="bibr" rid="bib1.bibx14" id="paren.3"/>.</p>
      <p id="d1e468">Water vapour is the source of the hydroxyl radical (OH) which controls the
lifetime of shorter-lived pollutants, tropospheric and stratospheric ozone
and other longer-lived greenhouse gases such as methane <xref ref-type="bibr" rid="bib1.bibx52" id="paren.4"/>.
Further, water vapour is an essential component of polar stratospheric clouds
(PSCs) which play a key role in Antarctic and Arctic ozone depletion during
winter and spring <xref ref-type="bibr" rid="bib1.bibx53" id="paren.5"/>. Accordingly, water vapour has an
important influence on stratospheric chemistry through its ability to form
ice particles. Dehydration, that is, the removal of water vapour from the gas
phase, can either be a reversible or an irreversible process depending on the
lifetime of water-containing particles and their size. However, ice particles
generally live long enough and grow sufficiently large to fall and remove
water vapour permanently from an air mass so that dehydration can generally
be defined as an irreversible process. Dehydration in the stratosphere is
generally observed over the Antarctic during winter
<xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx63 bib1.bibx30 bib1.bibx32" id="paren.6"><named-content content-type="pre">e.g.</named-content></xref> and to a
lesser extent also over the Arctic
<xref ref-type="bibr" rid="bib1.bibx8 bib1.bibx35 bib1.bibx21 bib1.bibx27" id="paren.7"><named-content content-type="pre">e.g.</named-content></xref> as well as at the
tropical tropopause <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx42 bib1.bibx49" id="paren.8"><named-content content-type="pre">e.g.</named-content></xref>.</p>
      <p id="d1e492">In addition to its role in the Earth's radiative budget and middle
atmospheric chemistry, water vapour is an important tracer for transport in
the stratosphere and lower mesosphere. Dynamical circulations that can be
diagnosed with water vapour in the middle atmosphere are the Brewer–Dobson
circulation in the stratosphere and the pole-to-pole circulation in the
mesosphere
<xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx44 bib1.bibx28 bib1.bibx38 bib1.bibx51 bib1.bibx24 bib1.bibx45" id="paren.9"/>.
In the stratosphere, the water vapour abundance is primarily governed by two
main sources: (1) the transport from the troposphere through the tropical
tropopause layer (TTL), where the minimum temperature (the so-called cold
point temperature) determines how much water vapour enters the stratosphere
<xref ref-type="bibr" rid="bib1.bibx9" id="paren.10"/>; (2) the oxidation of methane, which is the only
important chemical source of water vapour in the stratosphere
<xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx23" id="paren.11"/>.</p>
      <?pagebreak page4437?><p id="d1e504">A major research focus in relation to water vapour has been on the detection
and attribution of long-term changes in stratospheric and mesospheric water
vapour based on in situ and remote sensing measurements <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx34 bib1.bibx47 bib1.bibx31 bib1.bibx48 bib1.bibx16 bib1.bibx15 bib1.bibx6" id="paren.12"/>. Many of these measurements have indicated an increase in
stratospheric and mesospheric water vapour that has significant implications
for atmospheric temperature. Increases in stratospheric water vapour cool the
stratosphere but warm the troposphere <xref ref-type="bibr" rid="bib1.bibx54" id="paren.13"/>. Model simulations
predict a <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M10" display="inline"><mml:mi mathvariant="normal">K</mml:mi></mml:math></inline-formula> decrease in stratospheric temperature per decade
along with a 0.5–1 <inline-formula><mml:math id="M11" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula> increase of water vapour in the 21st century
<xref ref-type="bibr" rid="bib1.bibx10" id="paren.14"/>. Both the future cooling of the stratosphere and the
future increase in water vapour enhance the potential for the formation of
PSCs, which would have significant implications on Arctic and Antarctic
dehydration and ozone loss <xref ref-type="bibr" rid="bib1.bibx22 bib1.bibx58" id="paren.15"/>. The methane
increase in the stratosphere can only explain part of the observed water
vapour changes <xref ref-type="bibr" rid="bib1.bibx47 bib1.bibx16" id="paren.16"><named-content content-type="pre">e.g.</named-content></xref>. A complete
understanding of water vapour changes also requires good knowledge of
short-term variability, such as the annual oscillation (AO) and semi-annual
oscillation (SAO)
or the
variations caused by the quasi-biennial oscillation
<xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx43 bib1.bibx19 bib1.bibx25" id="paren.17"><named-content content-type="pre">e.g.</named-content></xref>.</p>
      <p id="d1e555">In addition to an observed long-term increase in stratospheric water vapour,
pronounced drops have occasionally been observed. One drop (sometimes denoted
as the millennium drop) occurred in 2000
<xref ref-type="bibr" rid="bib1.bibx40 bib1.bibx48 bib1.bibx54 bib1.bibx61 bib1.bibx4" id="paren.18"/>, with water
vapour abundances starting to recover around 2004–2005 onwards. This
decrease was caused by a reduced transport of water vapour across the
tropical tropopause in response to lower cold point temperatures. The exact
driving mechanism is still in question, but has been suggested to be due to
variations of the QBO (quasi-biennial oscillation), ENSO (El Niño
Southern Oscillation) and the Brewer–Dobson circulation that collectively
acted in the same direction lowering the tropopause temperatures. In 2011 and
2012 another drop occurred, which however was shorter-lived than the
millennium drop <xref ref-type="bibr" rid="bib1.bibx62" id="paren.19"/>. Recently, another sharp decrease was
observed in connection with the QBO disruption and the unusual El Niño
event in 2015 and 2016 <xref ref-type="bibr" rid="bib1.bibx60 bib1.bibx1" id="paren.20"/>, but this decrease has
also already recovered.</p>
      <p id="d1e567">Within the framework of the second SPARC water vapour assessment (WAVAS-II),
we compared time series of stratospheric and lower mesospheric water vapour
derived from a number of different satellite data sets. The time series
comparison was performed for the Antarctic (80<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S), the
tropics (15<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) and the Northern Hemisphere
mid-latitudes (50<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) at four different altitudes (0.1,
3, 10 and 80 <inline-formula><mml:math id="M18" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). This selection of latitude bands covers all three
basic climatic regions (i.e. tropics, mid-latitudes and polar region) and
allows the inclusion of all stratospheric WAVAS-II data sets in the
comparison. The combined temporal coverage of the 15 satellite instruments
allows the consideration of the time period 1986–2014. This work aims to
provide estimates of the typical uncertainties in the time series from
satellite observations that should be taken into account in observational and
modelling studies. A brief overview of the data sets used in this study is
provided in the next section followed by a description of the analysis
approach in Sect. <xref ref-type="sec" rid="Ch1.S3"/>. In Sect. <xref ref-type="sec" rid="Ch1.S4"/> the
results are presented, focusing on the comparison of the de-seasonalised
water vapour time series. Comparison results for the absolute time series are
given in the Supplement. Finally, our results will be summarised and
conclusions will be given in Sect. <xref ref-type="sec" rid="Ch1.S5"/>.</p>
</sec>
<sec id="Ch1.S2">
  <title>Data sets</title>
      <p id="d1e645">For the comparison of water vapour products
performed within the second SPARC WAVAS-II assessment, 40 data sets (not
including data sets of minor water vapour isotopologues) have been
considered, primarily focusing on the time period from 2000 to 2014
<xref ref-type="bibr" rid="bib1.bibx66" id="paren.21"/>. In the present study, we included all 33 data sets that
have observational coverage in the stratosphere. A list of these data sets is
provided in Table <xref ref-type="table" rid="Ch1.T1"/>, along with the effective time
periods available for analysis. In addition, this table provides the data
set labels and numbers used in the figures. Overall, data sets from the
following 15 instruments have been considered (listed in alphabetical order):
ACE-FTS, GOMOS, HALOE, HIRDLS, ILAS-II, MAESTRO, MIPAS, MLS (aboard the Aura
satellite, not the instrument on the Upper Atmosphere Research Satellite –
UARS), POAM III, SAGE II, SAGE III, SCIAMACHY, SMILES, SMR and SOFIE. For a
number of instruments there are multiple data sets based on different data
processors, measurement geometries, retrieval versions and spectral
signatures used to derive the water vapour information. This especially holds
for MIPAS, where 13 data sets have been included in this comparison. The MIPAS
measurements are processed by four different processing centres: (1) the
University of Bologna <xref ref-type="bibr" rid="bib1.bibx7" id="paren.22"/>, (2) the European Space Agency
(ESA; <xref ref-type="bibr" rid="bib1.bibx41" id="altparen.23"/>), (3) IMK/IAA
<xref ref-type="bibr" rid="bib1.bibx64 bib1.bibx55" id="paren.24"/> and (4) Oxford <xref ref-type="bibr" rid="bib1.bibx36" id="paren.25"/>. The
four processors differ in several respects, such as their choices of spectral
ranges (so called micro-windows), the vertical grid on which the retrievals
are performed (pressure or geometric altitude), the choice of regularisation
(and related to this, the vertical resolution), the choice of spectroscopic
database, the sophistication of the radiative transfer (in particular,
whether or not non-local thermodynamic equilibrium, NLTE,
emissions are considered) and whether or not any
attempt is made to account for horizontal inhomogeneities, and the a priori
and the assumed <inline-formula><mml:math id="M19" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M20" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
profile. Indeed, the temperature used might be a large
source of error for species retrieved in LTE regions. Some of the different
processing schemes also make use of different level-1b data versions (here V5
and V7) based on different ESA calibrations. The spread of results seen for
MIPAS indicates how specific choices within a retrieval approach may
influence the retrieval results. The HALOE, POAM III and SAGE II data sets
also include observations before 2000. These were considered in the
comparisons, so that the combined temporal coverage of all data sets ranges
from 1986 to 2014. A complete description of the data sets and their
characteristics can be found in the WAVAS-II data set overview paper by
<xref ref-type="bibr" rid="bib1.bibx66" id="text.26"/>. In comparison to our previous SPARC WAVAS-II paper
<xref ref-type="bibr" rid="bib1.bibx25" id="paren.27"/> the following two data related changes have been made:
(1) the ACE-FTS v3.5 and MAESTRO data sets have been extended from March 2013
until December 2014 (see Table 1 of <xref ref-type="bibr" rid="bib1.bibx25" id="altparen.28"/>). (2) The
MIPAS ESA v7 data set has been completed. In the aforementioned study, this data set
comprised only a sample of 200 000 observations (instead of 1 800 000), though
at the<?pagebreak page4438?> time the temporal coverage on a monthly basis had already been completed.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p id="d1e692">Overview over the water vapour data sets from
satellites used in this study.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <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="center"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Instrument</oasis:entry>
         <oasis:entry colname="col2">Data set</oasis:entry>
         <oasis:entry colname="col3">Label</oasis:entry>
         <oasis:entry colname="col4">Number</oasis:entry>
         <oasis:entry colname="col5">Time period</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">ACE-FTS</oasis:entry>
         <oasis:entry colname="col2">v2.2</oasis:entry>
         <oasis:entry colname="col3">ACE-FTS v2.2</oasis:entry>
         <oasis:entry colname="col4">1</oasis:entry>
         <oasis:entry colname="col5">03/2004–09/2010</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">v3.5</oasis:entry>
         <oasis:entry colname="col3">ACE-FTS v3.5</oasis:entry>
         <oasis:entry colname="col4">2</oasis:entry>
         <oasis:entry colname="col5">03/2004–12/2014</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">GOMOS</oasis:entry>
         <oasis:entry colname="col2">LATMOS v6</oasis:entry>
         <oasis:entry colname="col3">GOMOS</oasis:entry>
         <oasis:entry colname="col4">3</oasis:entry>
         <oasis:entry colname="col5">09/2002–07/2011</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">HALOE</oasis:entry>
         <oasis:entry colname="col2">v19</oasis:entry>
         <oasis:entry colname="col3">HALOE</oasis:entry>
         <oasis:entry colname="col4">4</oasis:entry>
         <oasis:entry colname="col5">10/1991–11/2005</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">HIRDLS</oasis:entry>
         <oasis:entry colname="col2">v7</oasis:entry>
         <oasis:entry colname="col3">HIRDLS</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">01/2005–03/2008</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">ILAS-II</oasis:entry>
         <oasis:entry colname="col2">v3/3.01</oasis:entry>
         <oasis:entry colname="col3">ILAS-II</oasis:entry>
         <oasis:entry colname="col4">6</oasis:entry>
         <oasis:entry colname="col5">04/2003–08/2003</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAESTRO</oasis:entry>
         <oasis:entry colname="col2">Research</oasis:entry>
         <oasis:entry colname="col3">MAESTRO</oasis:entry>
         <oasis:entry colname="col4">7</oasis:entry>
         <oasis:entry colname="col5">03/2004–12/2014</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MIPAS</oasis:entry>
         <oasis:entry colname="col2">Bologna V5H v2.3 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-Bologna V5H</oasis:entry>
         <oasis:entry colname="col4">8</oasis:entry>
         <oasis:entry colname="col5">07/2002–03/2004</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Bologna V5R v2.3 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-Bologna V5R NOM</oasis:entry>
         <oasis:entry colname="col4">9</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" colname="col2">Bologna V5R v2.3 MA</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">MIPAS-Bologna V5R MA</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">10</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">ESA V5H v6 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-ESA V5H</oasis:entry>
         <oasis:entry colname="col4">11</oasis:entry>
         <oasis:entry colname="col5">07/2002–03/2004</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">ESA V5R v6 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-ESA V5R NOM</oasis:entry>
         <oasis:entry colname="col4">12</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">ESA V5R v6 MA</oasis:entry>
         <oasis:entry colname="col3">MIPAS-ESA V5R MA</oasis:entry>
         <oasis:entry colname="col4">13</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" colname="col2">ESA V7R v7 NOM</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">MIPAS-ESA V7R</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">14</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">IMKIAA V5H v20 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-IMKIAA V5H</oasis:entry>
         <oasis:entry colname="col4">15</oasis:entry>
         <oasis:entry colname="col5">07/2002–03/2004</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">IMKIAA V5R v220/221 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-IMKIAA V5R NOM</oasis:entry>
         <oasis:entry colname="col4">16</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" colname="col2">IMKIAA V5R v522 MA</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">MIPAS-IMKIAA V5R MA</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">17</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Oxford V5H v1.30 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-Oxford V5H</oasis:entry>
         <oasis:entry colname="col4">18</oasis:entry>
         <oasis:entry colname="col5">07/2002–03/2004</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Oxford V5R v1.30 NOM</oasis:entry>
         <oasis:entry colname="col3">MIPAS-Oxford V5R NOM</oasis:entry>
         <oasis:entry colname="col4">19</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Oxford V5R v1.30 MA</oasis:entry>
         <oasis:entry colname="col3">MIPAS-Oxford V5R MA</oasis:entry>
         <oasis:entry colname="col4">20</oasis:entry>
         <oasis:entry colname="col5">01/2005–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MLS</oasis:entry>
         <oasis:entry colname="col2">v4.2</oasis:entry>
         <oasis:entry colname="col3">MLS</oasis:entry>
         <oasis:entry colname="col4">21</oasis:entry>
         <oasis:entry colname="col5">08/2004 – 12/2014</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">POAM III</oasis:entry>
         <oasis:entry colname="col2">v4</oasis:entry>
         <oasis:entry colname="col3">POAM III</oasis:entry>
         <oasis:entry colname="col4">22</oasis:entry>
         <oasis:entry colname="col5">04/1998–11/2005</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SAGE II</oasis:entry>
         <oasis:entry colname="col2">v7.00</oasis:entry>
         <oasis:entry colname="col3">SAGE II</oasis:entry>
         <oasis:entry colname="col4">23</oasis:entry>
         <oasis:entry colname="col5">01/1986–08/2005</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SAGE III</oasis:entry>
         <oasis:entry colname="col2">Solar occultation v4</oasis:entry>
         <oasis:entry colname="col3">SAGE III</oasis:entry>
         <oasis:entry colname="col4">24</oasis:entry>
         <oasis:entry colname="col5">04/2002–06/2005</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCIAMACHY</oasis:entry>
         <oasis:entry colname="col2">Limb v3.01</oasis:entry>
         <oasis:entry colname="col3">SCIAMACHY limb</oasis:entry>
         <oasis:entry colname="col4">25</oasis:entry>
         <oasis:entry colname="col5">08/2002–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Lunar occultation v1.0</oasis:entry>
         <oasis:entry colname="col3">SCIAMACHY lunar</oasis:entry>
         <oasis:entry colname="col4">26</oasis:entry>
         <oasis:entry colname="col5">04/2003–04/2012</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Solar occultation – OEM v1.0</oasis:entry>
         <oasis:entry colname="col3">SCIAMACHY solar OEM</oasis:entry>
         <oasis:entry colname="col4">27</oasis:entry>
         <oasis:entry colname="col5">08/2002–08/2011</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Solar occultation – Onion peeling v4.2.1</oasis:entry>
         <oasis:entry colname="col3">SCIAMACHY solar Onion</oasis:entry>
         <oasis:entry colname="col4">28</oasis:entry>
         <oasis:entry colname="col5">08/2002–08/2011</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMILES</oasis:entry>
         <oasis:entry colname="col2">NICT v2.9.2 band A</oasis:entry>
         <oasis:entry colname="col3">SMILES-NICT band A</oasis:entry>
         <oasis:entry colname="col4">29</oasis:entry>
         <oasis:entry colname="col5">01/2010–04/2010</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">NICT v2.9.2 band B</oasis:entry>
         <oasis:entry colname="col3">SMILES-NICT band B</oasis:entry>
         <oasis:entry colname="col4">30</oasis:entry>
         <oasis:entry colname="col5">01/2010–04/2010</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMR</oasis:entry>
         <oasis:entry colname="col2">v2.0 544 GHz</oasis:entry>
         <oasis:entry colname="col3">SMR 544 GHz</oasis:entry>
         <oasis:entry colname="col4">31</oasis:entry>
         <oasis:entry colname="col5">11/2001–12/2014</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">v2.1 489 GHz</oasis:entry>
         <oasis:entry colname="col3">SMR 489 GHz</oasis:entry>
         <oasis:entry colname="col4">32</oasis:entry>
         <oasis:entry colname="col5">11/2001–08/2014</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SOFIE</oasis:entry>
         <oasis:entry colname="col2">v1.3</oasis:entry>
         <oasis:entry colname="col3">SOFIE</oasis:entry>
         <oasis:entry colname="col4">33</oasis:entry>
         <oasis:entry colname="col5">08/2007–09/2014</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S3">
  <title>Approach</title>
<sec id="Ch1.S3.SS1">
  <title>Time series calculation</title>
      <p id="d1e1327">For the first step, we screened the individual data sets according to the
criteria recommended by the data providers. A complete list of these criteria
is given in the WAVAS-II data set overview paper by <xref ref-type="bibr" rid="bib1.bibx66" id="text.29"/>. After
the screening we interpolated the data onto a regular pressure grid. This
comprises 32 levels per pressure decade, which corresponds to a fine vertical
sampling of about 0.5 km. The uppermost level we consider is 0.1 hPa. The
interpolated profiles were then binned monthly and for the three latitude
bands chosen: 80<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S, 15<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and
50<inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. The monthly zonal means <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are
given as
            <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M28" display="block"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:munderover><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1515">In the equation above <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> describes the individual observations
that fall into a given time <inline-formula><mml:math id="M30" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> (i.e. month) and latitude <inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula> bin,
<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates their total number and <inline-formula><mml:math id="M33" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> denotes the altitude
level. Before this calculation the data in the given bin were screened using
the median and the median absolute difference (MAD, <xref ref-type="bibr" rid="bib1.bibx18" id="altparen.30"/>) in
an attempt to remove unrepresentative observations that occasionally occur.
Data points outside the interval <inline-formula><mml:math id="M34" display="inline"><mml:mo>〈</mml:mo></mml:math></inline-formula>median[<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn></mml:mrow></mml:math></inline-formula> MAD[<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>]<inline-formula><mml:math id="M37" display="inline"><mml:mo>〉</mml:mo></mml:math></inline-formula>, with <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></inline-formula>…<inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, were discarded, targeting the most prominent
outliers <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx25" id="paren.31"/>. For a normally distributed data set,
7.5 MAD corresponds to about <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>. For individual data sets this
concerned on average between 0.03 % and 3.2 % percent of the data in
a given bin. Averaged over all data sets typically 0.6 % of the data in a
given bin were removed by this screening. In addition to the monthly zonal
means, the corresponding standard error <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was
calculated by

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M42" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msqrt><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:msqrt></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mover accent="true"><mml:mrow><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:munderover><mml:msup><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e1918">To avoid spurious data, averages that are smaller than their corresponding
standard errors in an absolute scale were discarded. Also, monthly averages
based on less than 20 observations for dense data sets (e.g. HIRDLS, MIPAS,
MLS, SCIAMACHY limb, SMILES-NICT and SMR) and less than 5 observations for
sparse data sets (e.g. ACE-FTS, GOMOS, HALOE, ILAS-II, MAESTRO, POAM III,
SAGE II, SAGE III, SCIAMACHY occultation and SOFIE) were not considered any
further. This is a slightly more relaxed approach than used in the time
series analysis by <xref ref-type="bibr" rid="bib1.bibx25" id="text.32"/>, where a minimum of 20 observations was
required for all data sets. However, additional tests have shown that such a
conservative criterion is not required for the sparser data sets.</p>
      <p id="d1e1924">In our analysis we consider both absolute time series and de-seasonalised
time series. The ILAS-II and SMILES data sets cover less than one year, so
that a de-seasonalisation is not meaningful. There are multiple ways to
achieve a de-seasonalisation. The most common and simplest approach is to
calculate for a given calendar month the average over several years.
Subsequently this average is subtracted from the individual months
contributing to this climatological average (i.e. average approach). This
approach requires that a data set covers every calendar month at least twice.
For the MIPAS V5H data sets this requirement is not fulfilled as they cover
only 21 months. To accomplish a de-seasonalisation even for these data sets a
regression approach was used. Every data set was regressed with the following
regression model:

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M43" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">offset</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">AO</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>sin⁡</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">AO</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><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:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">AO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>cos⁡</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">AO</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">SAO</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>sin⁡</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">SAO</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">SAO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>cos⁡</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">SAO</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e2172">This model contained an offset as well as the annual oscillation (AO) and semi-annual
oscillation (SAO). The AO and SAO are parameterised by orthogonal sine and
cosine functions. <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the fit of the regressed time series
and <inline-formula><mml:math id="M45" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> are the regression coefficients of the individual model components.
<inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">AO</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> year is the period of the annual oscillation; likewise
<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">SAO</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> years is the period of the semi-annual oscillation. In
accordance to <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">AO</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">SAO</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> given in years, the
time <inline-formula><mml:math id="M50" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> is here also used on a yearly scale. To calculate the regression
coefficients we followed the method outlined by <xref ref-type="bibr" rid="bib1.bibx65" id="text.33"/> using
the standard errors <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (their inverse squared) of the
monthly zonal means as statistical weights. Autocorrelation effects and
empirical errors <xref ref-type="bibr" rid="bib1.bibx56" id="paren.34"/> were not considered in this regression.
The de-seasonalised time series <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, thus the anomalies for
each time <inline-formula><mml:math id="M53" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>, are then given as
            <disp-formula id="Ch1.E4" content-type="numbered"><mml:math id="M54" display="block"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e2395">For the sake of simplicity we do not assign any error to the regression fit,
so that the standard error of the de-seasonalised time series is given by
            <disp-formula id="Ch1.E5" content-type="numbered"><mml:math id="M55" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<?pagebreak page4439?><sec id="Ch1.S3.SS2">
  <title>Comparison parameters</title>
      <p id="d1e2452">To assess how the different time series compare between two data sets or
altogether we use a number of parameters, namely the spread (i.e. the
difference between the maximum and minimum volume mixing ratios among the
data sets), the (Pearson) correlation coefficient and the drift (i.e. linear
changes of the difference between time series over time). In the following
subsections, the calculation of these parameters is described in more detail.</p>
<sec id="Ch1.S3.SS2.SSS1">
  <title>Spread</title>
      <p id="d1e2460">We define the spread as the difference between the maximum and minimum volume
mixing ratio among the data sets at a given time and place. As such, the
spread is a simple measure of the collective consistency among the time
series from the different data sets. We have chosen this approach for the
spread calculation since for the other approaches based on standard deviation
or percentiles, assumptions have to be made. However, we have also calculated
the spread using<?pagebreak page4440?> the other two approaches and derived qualitatively the same
results as for the maximum–minimum calculation. Prior to the spread
calculation, we performed an additional screening among the data sets to
avoid unrepresentative spread estimates. The screening is again based on the
median and median absolute difference, as done before for the monthly zonal
mean calculation. Monthly zonal means outside the interval <inline-formula><mml:math id="M56" display="inline"><mml:mo>〈</mml:mo></mml:math></inline-formula>median[<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>]</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn></mml:mrow></mml:math></inline-formula>
MAD[<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>]<inline-formula><mml:math id="M59" display="inline"><mml:mo>〉</mml:mo></mml:math></inline-formula> were not considered, with <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> denoting the number of data sets at a
given time, latitude and altitude. The subscript <inline-formula><mml:math id="M62" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is used as a placeholder
either for the absolute or the de-seasonalised data. This screening removed
overall 2.6 % of the data for the latitude band between 80<inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and
70<inline-formula><mml:math id="M64" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S. For the tropical and the mid-latitude bands, respectively 3.6 % and 3.7 %
of the data were removed. Subsequently, the spread was derived.
We did not impose any additional criterion on the number of data sets
available for a spread estimate to be valid (two data sets is the natural
minimum). However, for much of the 1990s the only available satellite data
sets are HALOE and SAGE II. Since both instruments provide solar occultation
measurements, the number of coincidences is limited. Thus, their time series
do not constantly overlap, there are many gaps in the spread. Therefore, we
focus in the results section on the time period between 2000 and 2014.</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <title>Correlation</title>
      <p id="d1e2634">To describe the consistency between two time series we employed the
correlation coefficient <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M66" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E6"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>r</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{7.0}{7.0}\selectfont$\displaystyle}?><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msubsup><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mfenced open="[" close="]"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mo>⋅</mml:mo><mml:msqrt><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mfenced close="]" open="["><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

              with

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M67" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E7"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:munderover><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E8"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:munderover><mml:msub><mml:mi>y</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e3210">The subscripts at the end of the variables refer to the two data
sets. <inline-formula><mml:math id="M68" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is again a placeholder for the absolute and de-seasonalised data.
<inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the number of months the two time series actually overlap,
i.e. where both data sets yield valid monthly means. Correlation coefficients
were only considered if the overlap was at least 12 months. We did not
perform any significance analysis for the coefficients since we simply want
to show if the expected high correlation between two time series exist.</p>
</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Drift</title>
      <p id="d1e3248">As drift we consider the linear change of the difference between two time
series, which indicates if the longer-term variation of the two time series
is the same or not. The difference time series was calculated as
            <disp-formula id="Ch1.E9" content-type="numbered"><mml:math id="M70" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where the subscripts at the end once more denote the two data sets.
As indicated by this equation the drift analysis focuses on de-seasonalised
time series. The standard error corresponding to the difference time series
is given by
            <disp-formula id="Ch1.E10" content-type="numbered"><mml:math id="M71" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:msubsup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e3414">Due to the lack of appropriate covariance data, this calculation
omits any covariance between the different data sets. The difference time
series were then regressed with a regression model containing an offset, a
linear term (which describes the drift) and the QBO parameterised by the
Singapore (1<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 104<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E) winds at 50 hPa (QBO<inline-formula><mml:math id="M74" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:math></inline-formula>) and
30 hPa (QBO<inline-formula><mml:math id="M75" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>) provided by Freie Universität Berlin
(<uri>http://www.geo.fu-berlin.de/met/ag/strat/produkte/qbo/qbo.dat</uri>):

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M76" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">offset</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">linear</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mtd></mml:mtr><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:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">QBO</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">QBO</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E11"><mml:mtd/><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:msub><mml:mi>C</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">QBO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">QBO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>t</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="d1e3609">The calculation of the regression coefficients followed again the
method by <xref ref-type="bibr" rid="bib1.bibx65" id="text.35"/>, using the inverse square of the
corresponding standard error <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as weight. Here,
unlike in the regression for the de-seasonalisation, auto-correlation effects
and empirical errors were considered to derive optimal uncertainty estimates
for the drifts. This consideration used the approach outlined by
<xref ref-type="bibr" rid="bib1.bibx56" id="text.36"/>. We show drift results if the overlap period between the
two time series is at least 36 months. As overlap period we define the time
between the first and the last month both data sets yield a valid monthly
mean. We also provide the information regarding how many months both data
sets actually overlap, but we did not put any additional constraint on this
quantity. In addition, we have performed tests with more advanced regression
models, which yielded qualitatively the same results.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>Results</title>
      <p id="d1e3652">In this section, the results for the time series
comparison are presented. First, we provide an example
(Fig. <xref ref-type="fig" rid="Ch1.F1"/>) of the typical altitude–time
distribution (contour time series) to describe the general characteristics of
the water vapour distribution in the three latitude bands considered:
Antarctic (80<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S), tropics
(15<inline-formula><mml:math id="M80" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) and the Northern Hemisphere mid-latitudes
(50<inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N). These latitude bands were selected since these
cover all three basic climatic regions and allow the inclusion of all
stratospheric WAVAS-II data sets in<?pagebreak page4441?> the comparison. Contour time series of
water vapour in these three latitude bands derived from all of the data sets
considered in this study are provided in the Supplement (Figs. S1–S3). These
figures give a good first overview of the altitude and temporal coverage of
the individual data sets and their representation of the characteristics of
the water vapour distribution at the three latitude bands.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p id="d1e3714">Water vapour time series for the latitude bands 80<inline-formula><mml:math id="M84" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> to
70<inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S <bold>(a)</bold>, 15<inline-formula><mml:math id="M86" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 15<inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N
<bold>(b)</bold> and 50<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> to 60<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N <bold>(c)</bold> based on the MLS
data. The light grey and white lines indicate the tropopause as derived from
the MERRA reanalysis data. The black dots and the corresponding <inline-formula><mml:math id="M90" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axes on
the right show the average latitude of the monthly mean data. White areas
indicate that there are no data.</p></caption>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f01.pdf"/>

      </fig>

      <p id="d1e3794">The comparison of the time series is then performed qualitatively for all
data sets at the three latitude bands and at four selected altitudes covering
the stratosphere and lower mesosphere (0.1, 3, 10 and 80 <inline-formula><mml:math id="M91" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>).
Subsequently, we assess the agreement of the data sets quantitatively in form
of the spread over all data sets as well as the correlations and drifts among
the individual data sets. While the example is based on absolute data, the
comparison results presented in this section were derived from
de-seasonalised data. The corresponding results based on absolute data
(except for the drift) are provided in the Supplement.</p>
<sec id="Ch1.S4.SS1">
  <title>General characteristics of the water vapour time series</title>
      <p id="d1e3809">Figure <xref ref-type="fig" rid="Ch1.F1"/> shows contour time series of
water vapour in the Antarctic (80<inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S), tropics
(15<inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) and mid-latitudes
(50<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) based on the MLS data set for the time period
2004–2014. Here, the typical characteristics of the water vapour
distributions in these latitude regions become visible. The water vapour
distribution in the polar regions
(Fig. <xref ref-type="fig" rid="Ch1.F1"/> top) is determined by the
following three processes: (1) dehydration of the lower stratosphere during
polar winter caused by the sedimentation of ice containing polar
stratospheric cloud particles <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx8" id="paren.37"/>; (2) vertical
transport of dry/moist air. During polar winter, dry air from the upper
mesosphere descends within the polar vortex to the upper stratosphere, while during summer and early autumn moist air from the upper
stratosphere is transported into the
mesosphere; (3) enhanced
production of water vapour by methane oxidation during summer due to the
higher insolation <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx23" id="paren.38"/>.</p>
      <p id="d1e3877">In the tropics (Fig. <xref ref-type="fig" rid="Ch1.F1"/> middle), the
most prominent feature in the water vapour time series is the “atmospheric
tape recorder” <xref ref-type="bibr" rid="bib1.bibx28" id="paren.39"/>. This feature is a consequence of the annual
oscillation of dehydration (or freeze-drying) at the tropical tropopause due to
the annual oscillation of the tropical tropopause temperature. The tape
recorder signal is transported upwards to about 15 <inline-formula><mml:math id="M98" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> by the
ascending branch of the Brewer–Dobson circulation and maintains its integrity
because of the subtropical mixing barrier in the lower stratosphere. Around
the stratopause (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) a pronounced semi-annual oscillation is
found that is induced by an interplay of transport and momentum deposition of
different types of waves <xref ref-type="bibr" rid="bib1.bibx13" id="paren.40"/>.</p>
      <p id="d1e3913">The water vapour distribution in the mid-latitudes
(Fig. <xref ref-type="fig" rid="Ch1.F1"/> bottom) is primarily
influenced by transport within the Brewer–Dobson circulation and the
overturning circulation in the mesosphere. In the lower stratosphere, low
volume mixing ratios are transported from the lower latitudes to the
mid-latitudes in late spring/early summer <xref ref-type="bibr" rid="bib1.bibx37" id="paren.41"/>. Likewise, in
the lower mesosphere the effect of upwelling in summer and downwelling in
winter can be clearly seen, as described for the Antarctic.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <title>Qualitative time series comparisons</title>
      <p id="d1e3928">In the following, the time series from the
different satellite data sets are compared qualitatively. The time series in
the three considered latitudes bands cover generally the time period from
1991 to 2014 (0.1 <inline-formula><mml:math id="M101" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>), from 1986 to 2014 (3 and 10 <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) and
1988 to 2014 (80 <inline-formula><mml:math id="M103" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). A necessary requirement for the analyses of the
de-seasonalised time series was a minimum data set length of one year, ruling
out some shorter data sets (see Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/>). However,
these data sets are considered in the Supplement, where the time series in
absolute terms derived from all satellite instruments considered in this
study are provided (Figs. S3–S6). Some data sets, e.g. the MAESTRO data set,
only have coverage up to the lowest pressure level (80 <inline-formula><mml:math id="M104" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>)
considered here and thus these data can only be found in bottom subfigures
(Figs. <xref ref-type="fig" rid="Ch1.F2"/>–<xref ref-type="fig" rid="Ch1.F4"/>
and S3–S6). Overall, 25 data sets have been considered in the comparison
for the Antarctic while 24 data sets have been considered in the comparison
for the tropics. In the Northern Hemisphere mid-latitudes, the best temporal
and spatial coverage of the satellite data sets is found and therefore, 27
out of the 33 satellite data sets are considered in this comparison.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2" specific-use="star"><caption><p id="d1e3968">De-seasonalised time series at four different altitudes considering
the latitude band 80<inline-formula><mml:math id="M105" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> to 70<inline-formula><mml:math id="M106" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S. In the legend the average
latitude of the individual time series is indicated, which was calculated in
two steps. First, for an individual monthly mean the latitudes of all
profiles contributing to it were averaged. Any altitude dependence due to
missing or screened data was ignored in this step. Finally, the mean
latitudes over the entire time series were averaged. The same anomaly range
(<inline-formula><mml:math id="M107" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) has been used in all panels so that the differences in the anomaly
and the spread can be more easily compared. On the <inline-formula><mml:math id="M108" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis the ticks are
given in the middle of the year.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f02.pdf"/>

        </fig>

<sec id="Ch1.S4.SS2.SSS1">
  <?xmltex \opttitle{Antarctic (80{${}^{{\circ}}$}--70{${}^{{\circ}}$}\,S)}?><title>Antarctic (80<inline-formula><mml:math id="M109" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–70<inline-formula><mml:math id="M110" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S)</title>
      <p id="d1e4033">Figure <xref ref-type="fig" rid="Ch1.F2"/> shows the de-seasonalised
water vapour time series for the southern polar latitudes. The HIRDLS,
SCIAMACHY (solar occultation) and SAGE III observations have no coverage in
this latitude region, while the GOMOS observations' coverage is too limited
to allow derivation of de-seasonalised time series. In the de-seasonalised
time series, a spread among the data sets can be found at the four altitudes
considered in the comparison. The largest anomalies and the largest spread
are found at 0.1 <inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> (up to <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M113" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>), while the smallest
anomalies and thus the smallest spread is found at 3 <inline-formula><mml:math id="M114" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> (generally
in the range of <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M116" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>).</p>
      <p id="d1e4087">At 0.1 <inline-formula><mml:math id="M117" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the time series start from 1991 onwards with HALOE, since
SAGE II measurements are not available at this altitude. Large differences in
the seasonal variation of the de-seasonalised time series are found,
resulting in a considerable spread among the data sets, larger than at other
altitudes. Large anomalies (up to <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M119" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>), and thus large
inter-annual variation, are found
for the MIPAS-Oxford V5H, MIPAS-ESA V5R and MIPAS-ESA V7R data sets, while
quite small anomalies are found for both ACE-FTS data sets. These large
anomalies in the above mentioned MIPAS data sets are a consequence of the
pronounced (spiky)<?pagebreak page4442?> seasonal
variation in the absolute data (see Fig. S1 in the Supplement) that is
difficult to be accounted for in the sinusoidal regression used for the
de-seasonalisation.</p>
      <p id="d1e4114">Decadal changes in water vapour are found in the de-seasonalised time series
at 3 <inline-formula><mml:math id="M120" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Several periods of water vapour increases are followed by
water vapour decreases. Negative anomalies are found around 1992 while
positive anomalies are found around 1996 (HALOE). Water vapour then shows
positive anomalies again in <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2003</mml:mn></mml:mrow></mml:math></inline-formula> (HALOE, POAM III, SAGE II), followed
by a decrease in 2003–2004, which again is followed by a slight increase in
water vapour that lasts until 2010. From 2010 onwards water vapour remains
unchanged. The last increase in water vapour is most strongly pronounced in
SMR 489 <inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> indicating a
drift in the SMR 489 <inline-formula><mml:math id="M123" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data relative to
the other data sets (see also Sect. <xref ref-type="sec" rid="Ch1.S4.SS5"/>). A large spread
between the de-seasonalised time series is found between 1999 and 2004
(mainly between POAM III, SAGE II and SMR 489 <inline-formula><mml:math id="M124" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>). Between 2005 and
2014, good agreement between the de-seasonalised time series is found.
However, SMR 489 <inline-formula><mml:math id="M125" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> has somewhat higher anomalies (from 2011
onwards) than the other satellite data sets.</p>
      <p id="d1e4165">At 10 <inline-formula><mml:math id="M126" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, the spread among the data sets is quite similar to that
observed at 3 <inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, but the variability in water vapour is more
pronounced. There is a decrease in the SAGE II de-seasonalised water vapour
time series of 1986–1990. An increase in the de-seasonalised water vapour
time series is found in POAM III around 2001. Also from 2009 onwards there
seems to be a slight increase in water vapour in all data sets. The
SMR 489 <inline-formula><mml:math id="M128" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> de-seasonalised time series at 10 <inline-formula><mml:math id="M129" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is in good
agreement with the de-seasonalised time series of the water vapour products
derived from the other satellite instruments. However, the
SMR 489 <inline-formula><mml:math id="M130" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> as well as the SOFIE anomalies are low relative to MLS.
This becomes quite obvious at the end of the time series (2012–2014), when
only ACE-FTS, MLS, SMR 489 <inline-formula><mml:math id="M131" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and SOFIE were taking measurements. Also, the
influence of the QBO is clearly visible at this altitude level. Distinct
positive anomalies are found in 2007–2008, 2011 and 2013.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><caption><p id="d1e4214">As Fig. <xref ref-type="fig" rid="Ch1.F2"/>, but considering
the latitude band between 15<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 15<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f03.pdf"/>

          </fig>

      <p id="d1e4243">At 80 <inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the water vapour distribution is strongly influenced by
dehydration (Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>). The de-seasonalised time
series at 80 <inline-formula><mml:math id="M135" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> once again depict
the spread between the individual
instruments in this latitude band. At 80 <inline-formula><mml:math id="M136" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> similar results as for
10 <inline-formula><mml:math id="M137" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> are derived (except that here no long-term changes are
visible). However, here the deviations between HALOE and SAGE II are smaller
than at 10 and 3 <inline-formula><mml:math id="M138" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. As at 10 <inline-formula><mml:math id="M139" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, a decrease in the
anomalies of the SAGE II de-seasonalised time series is found for 1986–1990.
The de-seasonalised time series then remains constant until 1998 (HALOE and
SAGE II). From 1998 onwards the spread between the data sets increases. There
is an increase in the anomalies found in 2001, which is followed by a
decrease, which lasts until 2004. Another decrease in water vapour is found
in 2009. At 80 <inline-formula><mml:math id="M140" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, POAM III shows stronger inter-annual
variation and higher/lower anomalies than at 10 and 3 <inline-formula><mml:math id="M141" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, depending on which
year is considered.</p>
</sec>
<?pagebreak page4444?><sec id="Ch1.S4.SS2.SSS2">
  <?xmltex \opttitle{Tropics (15{${}^{{\circ}}$}\,S--15{${}^{{\circ}}$}\,N)}?><title>Tropics (15<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M143" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N)</title>
      <?pagebreak page4445?><p id="d1e4330">Figure <xref ref-type="fig" rid="Ch1.F3"/> shows the de-seasonalised
water vapour time series for the tropics. The POAM III, SAGE III, SCIAMACHY
(solar and lunar occultation) and SOFIE data sets have no coverage in this
latitude band. In the SAGE II time series some data gaps occur which are due
to the aftermath of the Pinatubo eruption (resulting in unrealistically high
water vapour values that were filtered out) as well as the “short
events” between June 1993 and April 1994, when too few measurements were
available <xref ref-type="bibr" rid="bib1.bibx57" id="paren.42"/>. In the tropics, good consistency between the
data sets is found except at 0.1 <inline-formula><mml:math id="M144" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, where again the spread between
the data sets is largest. At 0.1 <inline-formula><mml:math id="M145" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> some data sets exhibit larger
anomalies (<inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M147" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>; e.g. MIPAS-Oxford V5H and MIPAS-ESA V7R),
while others exhibit rather small anomalies (<inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M149" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>; e.g.
ACE-FTS and MLS). The HIRDLS, GOMOS and MAESTRO (80 <inline-formula><mml:math id="M150" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) data sets
show generally larger anomalies and thus larger spread than the other
satellite data sets. The de-seasonalised time series in the tropics reflect
the decadal changes in water vapour that have been documented in the
literature, such as the drop in stratospheric water vapour after 2000 and in
2012 <xref ref-type="bibr" rid="bib1.bibx39 bib1.bibx40 bib1.bibx62" id="paren.43"/>. Further, at 3 and
10 <inline-formula><mml:math id="M151" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, a variability in water vapour on an approximate 2-year
timescale associated with the QBO is clearly visible.</p>
      <p id="d1e4404">At 0.1 <inline-formula><mml:math id="M152" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the time series starts in 1991 with the HALOE data set,
which is also the only one available for these altitude and latitude regions
until 2001. The de-seasonalised time series from HALOE shows an increase
between 1992 and 1996 followed by a period with rather constant anomalies
that lasts until 2001. Afterwards a decrease is visible until 2005.
SMR 489 <inline-formula><mml:math id="M153" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> observes, in contrast to HALOE, an increase in water
vapour between 2001 and 2005. Therefore, at the beginning of the
SMR 489 <inline-formula><mml:math id="M154" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> record the anomalies at 0.1 <inline-formula><mml:math id="M155" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> are clearly lower
than those from HALOE or the other satellite data sets measuring from 2001
onwards. However, a large spread between the data sets is also found during
this time period. A similar increase (but somewhat stronger) is found in the
MIPAS Oxford V5H data set between 2001 and 2003, but here the anomalies are
higher than the ones from the other satellite data sets. While the
MIPAS Oxford V5H and SMR 489 <inline-formula><mml:math id="M156" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets show increasing anomalies, the other data sets show decreasing
anomalies. From 2006 onwards all data sets show increasing anomalies. Between
2012 and 2014, ACE-FTS, MLS and SMR 489 <inline-formula><mml:math id="M157" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> are the only data sets
covering this time period and deviations among them are quite visible.
SMR 489 <inline-formula><mml:math id="M158" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> anomalies are higher and show larger inter-annual
variability than ACE-FTS and MLS. MLS (together with ACE-FTS) exhibit
generally the lowest anomalies (<inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M160" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>) compared to the other
satellite data sets at this altitude.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p id="d1e4476">As Figs. <xref ref-type="fig" rid="Ch1.F2"/> and
<xref ref-type="fig" rid="Ch1.F3"/>, but here the time series for the
latitude band between 50<inline-formula><mml:math id="M161" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 60<inline-formula><mml:math id="M162" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N are shown.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f04.pdf"/>

          </fig>

      <p id="d1e4508">At 3 and 10 <inline-formula><mml:math id="M163" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the time series begins with SAGE II in 1986. From
1991 onwards HALOE observations are also available. Both SAGE II and HALOE
provide here a much better representation of the temporal development of the
water vapour time series and the inter-annual variability than in the
Antarctic since both data sets have a much better temporal coverage in the
tropics (see Figs. S1 and S2 in the Supplement). SAGE II shows somewhat
larger anomalies than HALOE. Generally, the de-seasonalised time series show
good agreement with each other at these two altitude levels (3 and
10 <inline-formula><mml:math id="M164" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). Further, at these altitude levels, the lowest anomalies and
the lowest spread between the data sets is found, especially at
10 <inline-formula><mml:math id="M165" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The deviations between MLS (or ACE-FTS) and
SMR 489 <inline-formula><mml:math id="M166" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> found during the time period 2012–2014 are still evident
at 3 <inline-formula><mml:math id="M167" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> but to a much lesser extent than at 0.1 <inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. At
3 <inline-formula><mml:math id="M169" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, inter-annual variations
(with anomalies roughly on the order
of <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M171" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>) due to the QBO are clearly visible. At 10 <inline-formula><mml:math id="M172" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>
this variability is far less obvious. Also, the differences between
SMR 489 <inline-formula><mml:math id="M173" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and the other data sets measuring during the time period
2001–2005 (SAGE II and HALOE) are found to a lesser extent at 3 <inline-formula><mml:math id="M174" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>,
but not at 10 <inline-formula><mml:math id="M175" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The GOMOS data set exhibits large scatter. At
10 <inline-formula><mml:math id="M176" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the HIRDLS data set indicates stronger inter-annual
variability than the other satellite instruments. This level is the uppermost
altitude where HIRDLS can be retrieved and accordingly the data here are more
uncertain. Both drops in water vapour, the one in 2001 and the one in 2012,
are clearly visible in the de-seasonalised time series at 10 <inline-formula><mml:math id="M177" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The
latter one is strongly pronounced in the three remaining data sets covering
that time period (ACE-FTS v3.5, MLS and SMR 489 <inline-formula><mml:math id="M178" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>). There is also a
clear variability on an approximate 2-year timescale associated with the QBO
visible at this altitude level, although not at all times are as clearly
pronounced as at 3 <inline-formula><mml:math id="M179" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e4635">Similar to the other three pressure levels, at 80 <inline-formula><mml:math id="M180" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> relatively good
agreement between SAGE II and HALOE is found. However, SAGE II typically
shows somewhat lower anomalies than HALOE. At 80 <inline-formula><mml:math id="M181" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, higher
variability with larger anomalies than at 10 and 3 <inline-formula><mml:math id="M182" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is found
(generally around <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M184" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>). The data sets agree well in terms
of the inter-annual variation.
The drops in 2000 and 2011 are consistently observed, as are the recoveries
afterwards. This is also true for the pronounced QBO in 2006–2008. In 2005
the MIPAS-Bologna V5R NOM and MIPAS-ESA V5R NOM data sets show strong
negative anomalies (up to <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M186" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>) which are not found in the other
data sets. Similar behaviour of these data sets is found in 2011, when they
show strong positive anomalies (up to 1.6 <inline-formula><mml:math id="M187" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>), while in the other
satellite data sets, anomalies up to only 0.4–0.8 <inline-formula><mml:math id="M188" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula> are found.
MAESTRO shows strong scatter, mainly because 80 <inline-formula><mml:math id="M189" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is near the upper
altitude limit of the MAESTRO water vapour retrieval. Another distinctive
characteristic in the de-seasonalised time series at 80 <inline-formula><mml:math id="M190" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is the
increase in water vapour that lasts until mid-2014 (ACE-FTS v3.5, MLS and
SMR 544 <inline-formula><mml:math id="M191" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>) which is anti-correlated with the time series at
10 <inline-formula><mml:math id="M192" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p id="d1e4739">The difference between the maximum and minimum volume mixing ratio
among the different de-seasonalised data sets as a function of time and
altitude for the three latitude bands. The light grey and white lines
indicate the tropopause as derived from MERRA reanalysis data. The right
<inline-formula><mml:math id="M193" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axes and the corresponding red dots indicate the maximum number of data
sets available for this analysis at a given time considering all altitudes.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f05.pdf"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS3">
  <?xmltex \opttitle{Northern mid-latitudes
(50{${}^{{\circ}}$}--60{${}^{{\circ}}$}\,N)}?><title>Northern mid-latitudes
(50<inline-formula><mml:math id="M194" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M195" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N)</title>
      <p id="d1e4781">Figure <xref ref-type="fig" rid="Ch1.F4"/> shows the de-seasonalised time
series for the Northern Hemisphere mid-latitudes. The GOMOS, SCIAMACHY lunar and SOFIE
data sets have no coverage in this latitude region. As for the other latitude
bands the largest spread between the satellite data sets is found at
0.1 <inline-formula><mml:math id="M196" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. This is accompanied by large inter-annual variability. The
ACE-FTS v3.5, MIPAS-Bologna V5H, MIPAS-Oxford V5H and SMR 489 <inline-formula><mml:math id="M197" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>
data sets are among the data sets showing the largest inter-annual
variability and also the largest anomalies at 0.1 <inline-formula><mml:math id="M198" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The
MIPAS-Oxford V5H data set covers the time period of 2002–2004 and here the
largest anomalies (exceeding 2 <inline-formula><mml:math id="M199" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>) are found. The largest negative
anomalies are found in 2005 and 2006 with <inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M202" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>,
respectively. The differences between ACE-FTS v3.5 and the other satellite
data sets become most pronounced at the end of the data record when only
SMR 489 <inline-formula><mml:math id="M203" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and MLS were still measuring. Here, ACE-FTS v3.5 shows
some larger variability. At this altitude, the drift in the
SMR 489 <inline-formula><mml:math id="M204" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set is again visible. The anomalies are
typically more negative<?pagebreak page4447?> compared to the other data sets until 2004, while they are more
positive after 2012. The HALOE data set indicates an increase in water vapour
until about 1997 and a decrease afterwards. There appears to be a decrease in
water vapour for all data sets from 2007 to 2010, followed by a pronounced
increase that lasts until early 2012.</p>
      <p id="d1e4856">At 3 <inline-formula><mml:math id="M205" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, the de-seasonalised time series show generally good
agreement, while at 10 <inline-formula><mml:math id="M206" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the best agreement is found. Differences at
3 <inline-formula><mml:math id="M207" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> are that SMR 489 <inline-formula><mml:math id="M208" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> exhibits lower anomalies during
the time period 2001 to 2006 and higher anomalies than the other data sets
from 2010 to 2014 and that SAGE II shows higher anomalies than the other
satellite instruments at the end of their data record (2004–2005).
Differences at 10 <inline-formula><mml:math id="M209" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> are found in the time period 2004–2008, when
SAGE II and HIRDLS show stronger inter-annual variability, and during
2010–2012, when SMR 489 <inline-formula><mml:math id="M210" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> exhibits somewhat higher anomalies than
the other satellite data sets. In both altitude levels, an increase in water
vapour between 1992 and 2000 (10 <inline-formula><mml:math id="M211" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) and 1992 and 1998
(3 <inline-formula><mml:math id="M212" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) is found. The two water vapour drops that
occurred after 2000 and in 2011 in the tropics <xref ref-type="bibr" rid="bib1.bibx39 bib1.bibx40 bib1.bibx62" id="paren.44"/> are also visible at 10 <inline-formula><mml:math id="M213" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> in the Northern Hemisphere
mid-latitudes, however with a temporal delay.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F6" specific-use="star"><caption><p id="d1e4928">Example correlations between de-seasonalised MIPAS-Oxford V5R NOM
time series and those from other data sets. Results are only shown when the
two data sets have an overlap of at least 12 valid monthly means. The dashed
orange lines indicate the four altitudes for which the correlations between
all data sets are shown in the following figures.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f06.pdf"/>

          </fig>

      <p id="d1e4938">Although the inter-annual and decadal variability at 80 <inline-formula><mml:math id="M214" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is low,
some satellite data sets (MAESTRO, POAM III and SMR 544 <inline-formula><mml:math id="M215" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>) show
larger deviations from the other satellite data sets. In the MAESTRO data,
high inter-annual variability is found with anomalies reaching up to
1.6 <inline-formula><mml:math id="M216" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>. In this altitude region, MAESTRO has its best temporal
coverage in the mid-latitudes, but still 80 <inline-formula><mml:math id="M217" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is at the upper limit
of the MAESTRO measurements and therefore not every measured profile reaches
that high up. This explains why higher variability (scatter) than in the
other satellite data sets is found for the MAESTRO time series. POAM III
exhibits much larger anomalies than the other satellite data sets
(<inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M219" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula> compared to <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M221" display="inline"><mml:mi mathvariant="normal">ppmv</mml:mi></mml:math></inline-formula>). Although the POAM III
anomalies decrease with time, they still remain higher than the anomalies
from the other satellite data sets. The differences between POAM III and the
other satellite data sets are caused by the limited temporal sampling (only
summer months are measured) of POAM III in this latitude region making the
de-seasonalisation by regression apparently fail. In the SMR 544 <inline-formula><mml:math id="M222" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>
data set, larger inter-annual variability is found, but with much smaller
anomalies than MAESTRO. In the SAGE II data, the anomalies are decreasing
slightly in the time period 1987–2002. Further, there is some pronounced QBO
alongside an overall increase from 2004 to 2012.</p>
      <?pagebreak page4449?><p id="d1e5011">Overall, in the Northern Hemisphere mid-latitudes, the lowest inter-annual
variability is found, especially at 80 <inline-formula><mml:math id="M223" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Similar to the
comparisons in the Antarctic and tropics, the largest inter-annual and
decadal variability as well as the largest spread between the data sets is
found at 0.1 <inline-formula><mml:math id="M224" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The drops in stratospheric water vapour after 2000
and in 2011 that are observed in the tropics are also found at 10 <inline-formula><mml:math id="M225" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>
in the mid-latitudes, but with a temporal delay and to a lesser extent than
in the tropics.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F7" specific-use="star"><caption><p id="d1e5037">The correlations between de-seasonalised time series in the latitude
band between 80<inline-formula><mml:math id="M226" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 70<inline-formula><mml:math id="M227" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S. The upper panel considers the
0.1 hPa <bold>(a)</bold> and 3 hPa <bold>(b)</bold> pressure levels, while in the
lower panel the results at 10 hPa <bold>(c)</bold> and 80 hPa <bold>(d)</bold> are
shown. Only data sets yielding any result at a given altitude are shown.
Thus, the number of data sets can vary from altitude to altitude. Comparisons
yielding no results are indicated by grey crosses. For comparisons with
results (the coloured boxes) the number of months the two data sets actually
overlap (i.e. both yield a valid monthly mean) are indicated.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f07.pdf"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S4.SS3">
  <title>Spread assessment</title>
      <p id="d1e5084">In the following, the spread between the data sets is
quantitatively assessed to provide an estimate of the uncertainty in the
observational database. Figure <xref ref-type="fig" rid="Ch1.F5"/> shows the difference between
the maximum and minimum volume mixing ratio among the different
de-seasonalised water vapour data sets as a function of time and altitude for
the three latitude bands: Antarctic, tropics and Northern Hemisphere
mid-latitudes. The spread of the absolute time series is shown in the
Supplement in Fig. S7. The spread is calculated for the years 2000–2014.
Earlier years are not considered due to the lack of a sufficient number of
satellite instruments measuring during that time period. Before 2000 only
HALOE, POAM III and SAGE II data were available which results in a too sparse
and not meaningful picture (similar to the gaps found for the early years in
Fig. <xref ref-type="fig" rid="Ch1.F5"/>). The spread estimates become more meaningful as
more satellite data sets become available. This can be seen from
Fig. <xref ref-type="fig" rid="Ch1.F5"/> for 2002 onwards. For the years
2000–2001 and 2012–2014 between two and four data sets were available. In
these cases the differences among the data sets are not as pronounced and
probably less meaningful than for the years 2002–2012, when the majority of
satellite instruments were measuring.</p>
      <p id="d1e5093">In all three latitude bands the spread is large at the highest and lowest
altitude level considered in this study, which correspond to the upper
troposphere/tropopause region and the lower mesosphere. The large spread in
these altitude regions is related to large uncertainties in the
water vapour observations (e.g. due to increased measurement noise) as well as to the variability of the atmosphere and its different
representation in the individual data sets. In addition, large spread is
found in the Antarctic lower stratosphere (Fig. <xref ref-type="fig" rid="Ch1.F5"/> top) in
winter and spring, when the water vapour distribution in the lower
stratosphere is affected by dehydration and transport of low water vapour
from the mesosphere into the stratosphere
(Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>). In the tropics
(Fig. <xref ref-type="fig" rid="Ch1.F5"/> middle), the lowest spread compared to the other
latitude bands is found. Increased values are found here as in the other
regions at the highest and lowest levels. The spread is lowest in the time
period 2006 to 2010. Similar behaviour is found for the mid-latitudes
(Fig. <xref ref-type="fig" rid="Ch1.F5"/> bottom), also here the spread seems to be lower
around 10 <inline-formula><mml:math id="M228" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> during the time period 2006–2010. The mid-latitudes
show features similar to the tropics and polar regions. In the Northern Hemisphere mid-latitudes, the largest spread occurs in the lower
stratosphere,
where low water vapour is found due to air masses that are freeze dried when
entering the stratosphere in the tropics (atmospheric tape recorder), and in
the lower mesosphere due to the descent of air within the polar vortex.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><caption><p id="d1e5113">As Fig. <xref ref-type="fig" rid="Ch1.F7"/>, but here the results for
the latitude band between 15<inline-formula><mml:math id="M229" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 15<inline-formula><mml:math id="M230" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N are shown.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f08.pdf"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS4">
  <title>Correlation assessment</title>
      <p id="d1e5148">To assess the temporal consistency between
individual data sets, the correlation coefficients between all possible
combinations of data sets are considered. In this section, the results for
the de-seasonalised time series are presented, while the results for the
absolute time series are given in the Supplement. We start by presenting an
example correlation of the MIPAS-Oxford V5R NOM time series with those from
the other data sets and then present all correlations in the form of
matrices.</p>
<sec id="Ch1.S4.SS4.SSS1">
  <title>Correlation example</title>
      <p id="d1e5156">Figure <xref ref-type="fig" rid="Ch1.F6"/> shows the correlation between the
de-seasonalised MIPAS-Oxford V5R NOM time series and those from the other
data sets for the Antarctic, tropics and the Northern Hemisphere
mid-latitudes. The largest spread in the correlation between the satellite
data sets is found in the Antarctic (Fig. <xref ref-type="fig" rid="Ch1.F6"/>
top), also where the lowest correlation over all altitude levels is found
(rarely exceeding a correlation coefficient of 0.8). MIPAS-ESA V5R NOM and
MIPAS-ESA V7R are among the data sets showing the highest correlation with
MIPAS-Oxford V5R NOM over all altitude levels while the lowest correlation
with MIPAS-Oxford V5R NOM is found for SCIAMACHY lunar throughout most
altitudes. The SOFIE and SMR 544 <inline-formula><mml:math id="M231" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets show very low
correlations (even negative for SOFIE) at the lowest altitude levels (below
10 <inline-formula><mml:math id="M232" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) as well as above 3 <inline-formula><mml:math id="M233" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> (but here SMR 489 <inline-formula><mml:math id="M234" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>
instead of SMR 544 <inline-formula><mml:math id="M235" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>). In between these altitudes levels the SOFIE
and SMR 489 <inline-formula><mml:math id="M236" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets show similar correlation to
MIPAS-Oxford V5R NOM as the other data sets.</p>
      <p id="d1e5206">In the tropics (Fig. <xref ref-type="fig" rid="Ch1.F6"/> middle), the
correlation coefficients vary between 0.8 and 1 for most data sets between 30
and 1 <inline-formula><mml:math id="M237" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Low correlations are found for all data sets between 100
and 30 hPa, except the MIPAS-IMKIAA V5R NOM data set, which shows a high
correlation (<inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula>) up to 1 <inline-formula><mml:math id="M239" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> with MIPAS-Oxford V5R NOM. The data
sets that show the lowest correlation with MIPAS-Oxford V5R NOM (even in some
occasions negative) are GOMOS and MAESTRO. These data sets thus deviate from
the typical correlation of most other data sets. Above 60 hPa and above
25 <inline-formula><mml:math id="M240" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> this is also true for HIRDLS and
SMR 544 <inline-formula><mml:math id="M241" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>, respectively.
These two data sets show reasonable correlation with MIPAS-Oxford V5R NOM
at the lowest altitude levels, but then the correlation coefficients decrease
rapidly with increasing altitude, most likely due to increased measurement
noise. At altitudes above 0.7 <inline-formula><mml:math id="M242" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the correlation decreases for all
data sets and the spread between the data sets increases. For
MIPAS-ESA V5R NOM, the correlation, although decreasing, remains rather high
with a correlation coefficient of 0.7. The lowest correlation at
0.1 <inline-formula><mml:math id="M243" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is found for the ACE-FTS v2.2, ACE-FTS v3.5, MIPAS
Bologna V5R NOM and MIPAS-Bologna V5R MA data sets.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><caption><p id="d1e5266">As Figs. <xref ref-type="fig" rid="Ch1.F7"/> and
<xref ref-type="fig" rid="Ch1.F8"/>, but considering the latitude band between
50<inline-formula><mml:math id="M244" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 60<inline-formula><mml:math id="M245" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f09.pdf"/>

          </fig>

      <?pagebreak page4452?><p id="d1e5297">In the Northern Hemisphere mid-latitudes
(Fig. <xref ref-type="fig" rid="Ch1.F6"/> bottom), the correlation coefficients
vary between 0.4 and almost 1 in the altitude region between 0.7 <inline-formula><mml:math id="M246" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>
and 10 <inline-formula><mml:math id="M247" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> depending on which data set is considered. The spread in
the Northern Hemisphere mid-latitudes is almost as large as the spread in the
Antarctic. Very high correlation (correlation coefficient of around 0.9–1)
between MIPAS-Oxford V5R NOM and the other data sets is found at, for
example, around 1 <inline-formula><mml:math id="M248" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> for the MIPAS-ESA V5R NOM and MIPAS-ESA V7R
data sets. The lowest correlation between MIPAS-Oxford V5R NOM and the other
data sets is found above 1 <inline-formula><mml:math id="M249" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> for the two ACE-FTS data sets while
the SMR 489 <inline-formula><mml:math id="M250" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set shows a rather low correlation throughout
the entire altitude region considered in this study. Below 10 <inline-formula><mml:math id="M251" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the
lowest correlations (even negative correlations) are found for HIRDLS,
MAESTRO, SCIAMACHY limb and SMR 544 <inline-formula><mml:math id="M252" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets. These data sets
also deviate from the usual spread in correlation of the data sets.</p>
</sec>
<?pagebreak page4453?><sec id="Ch1.S4.SS4.SSS2">
  <title>Correlation matrices</title>
      <p id="d1e5358">The correlation of all data sets is given in
Figs. <xref ref-type="fig" rid="Ch1.F7"/>–<xref ref-type="fig" rid="Ch1.F9"/> in
form of matrix plots for the three latitude bands and four altitude levels.
In addition to the correlation coefficient, the number of months of overlap
between the time series is given (requiring a minimum of 12 months; see
Sect. <xref ref-type="sec" rid="Ch1.S3.SS2.SSS2"/>). The same figures for the correlation of the
absolute time series are given in the Supplement (Figs. S8–S10). The
correlation matrix shown in Fig. <xref ref-type="fig" rid="Ch1.F7"/> gives a
good overview over the temporal consistency of all data sets in the
Antarctic. The correlations between the data sets are generally positive
(green), but in some cases negative correlations (red) are found, for
example, in the case of the correlation between the MIPAS-IMKIAA V5H and
POAM III data sets at 10 <inline-formula><mml:math id="M253" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> or that between the MLS and
SCIAMACHY lunar data sets at 3 <inline-formula><mml:math id="M254" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. However, in these two cases, the
number of overlapping months is not that high (14 and 28) and this may
explain the low correlation between these data sets. An example of where
a negative correlation is found
despite the high number of overlapping months (70) is the correlation between
the MIPAS-Bologna V5R NOM and MLS data sets at 0.1 <inline-formula><mml:math id="M255" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. An example of
a high number of overlapping months (114) and high correlation coefficient is
the correlation between the MLS and SMR 489 <inline-formula><mml:math id="M256" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets at
10 <inline-formula><mml:math id="M257" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Nevertheless, although in the Antarctic the correlation is
generally positive, the correlation coefficient rarely exceeds 0.5. An
exception is the 3 hPa level, where a generally high correlation among the
MIPAS data sets is found. Similar behaviour between the MIPAS data sets is
found at 10 <inline-formula><mml:math id="M258" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><caption><p id="d1e5414">The left panel shows the drifts between the de-seasonalised time
series of the SMR 489 GHz data set and the other data sets. In the right
panel the corresponding significance levels of the drift estimates are shown
and the <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> level is marked by a vertical line. This example considers
the latitude band between 50<inline-formula><mml:math id="M260" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 60<inline-formula><mml:math id="M261" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. In the legend, the
first number given in parentheses indicates the overlap period (over all altitudes) of the two
data sets, i.e. the time between the first and the last month during which the data sets
yield a valid monthly mean. Results are only shown here when this time period
is at least 36 months. The second number indicates the number of months for
which both data sets actually yield a valid monthly mean.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f10.pdf"/>

          </fig>

      <p id="d1e5451">In Fig. <xref ref-type="fig" rid="Ch1.F8"/> the correlation matrix for the
tropics is shown. The large spread between the data sets we found in
Fig. <xref ref-type="fig" rid="Ch1.F6"/> at 0.1 <inline-formula><mml:math id="M262" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is also reflected in
the correlations among all data sets. The same holds for the good
correlations that are found at 3 and 10 <inline-formula><mml:math id="M263" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. An exception here is the
GOMOS data set that shows negative correlations with all instruments at
3 <inline-formula><mml:math id="M264" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, but the number of overlapping months is rather low. At
80 <inline-formula><mml:math id="M265" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the spread between the data sets is not as large as at
0.1 <inline-formula><mml:math id="M266" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, but still larger than at 3 and 10 <inline-formula><mml:math id="M267" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. At
80 <inline-formula><mml:math id="M268" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> occasionally negative correlations are found. This primarily
concerns comparisons involving the GOMOS, HALOE, MAESTRO and MIPAS-Oxford V5H
data sets. The lowest (negative) correlation is found between
SMR 489 <inline-formula><mml:math id="M269" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and SAGE II data sets, but here the number of
overlapping months (21) was also rather low.</p>
      <p id="d1e5515">The correlation matrix shown in Fig. <xref ref-type="fig" rid="Ch1.F9"/> gives a
good overview of the temporal consistency of all data sets in the
mid-latitudes. The majority of the correlations are positive, but for some
comparisons negative correlation is found. One such example is the
correlation between the MIPAS Bologna V5H and SMR 489 <inline-formula><mml:math id="M270" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets
at 3 <inline-formula><mml:math id="M271" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. However, again the number of overlapping months was rather low
and may explain the negative correlation between these data sets. An example
of negative correlation, despite a high number of overlapping months, is
found between MIPAS-Bologna V5R NOM and
MIPAS-Bologna-V5R-MA with MLS at 0.1 <inline-formula><mml:math id="M272" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The correlation of these
two data sets with the other data sets is also generally low at
0.1 <inline-formula><mml:math id="M273" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Also, for the two ACE-FTS data sets the correlation of most
data sets is often low despite a sufficient number of overlapping months.
Positive correlations are found for the ACE-FTS v2.2/v3.5 data sets in
comparison to the MIPAS-IMKIAA V5R MA, MIPAS-Oxford V5R MA, MLS and
SMR 489 <inline-formula><mml:math id="M274" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>. The highest correlation at 0.1 <inline-formula><mml:math id="M275" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> is found
between the two ACE-FTS data sets and between ACE-FTS v2.2 and MLS. At 3 and
10 <inline-formula><mml:math id="M276" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> generally high correlations among the MIPAS data sets are
found. At 10 <inline-formula><mml:math id="M277" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the correlation of HIRDLS with some data sets is
high, but low with the other data sets. At 80 <inline-formula><mml:math id="M278" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> low correlations
between MAESTRO and all other instruments are found.</p>
      <p id="d1e5585">In summary, a high number of overlapping months does not necessarily
guarantee a good correlation between
two data sets, but generally the chances are quite high if this is the case.
On the other hand, if data sets overlap only for a low number of months, good
agreement between these data sets can still be found. Therefore, for
assessing the agreement between two data sets, both the number of overlapping
months and the correlation coefficient should be taken into account. The
correlation assessment again confirms what we found before from the
qualitative time series comparison, namely that the best agreement between
the satellite data sets is found in the tropics, while in
the Antarctic and Northern Hemisphere
mid-latitudes a large spread between the data sets is found. Generally, the
lowest correlations are found in the Antarctic. Further, in each latitude
band the correlation is lower in the lower stratosphere and lower mesosphere
than in the middle stratosphere.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F11" specific-use="star"><caption><p id="d1e5590">Drifts between the different data sets in the latitude band between
80<inline-formula><mml:math id="M279" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 70<inline-formula><mml:math id="M280" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S at four specific altitudes. The drift
estimates are based on the difference time series between the data sets given
on the <inline-formula><mml:math id="M281" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis and the data sets given on the <inline-formula><mml:math id="M282" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis. Additional
information is given in the result boxes: the overall time period the two
data sets overlap, how many months the data sets actually overlap (upper
left corner) and if the drifts are significant (green frame) or not significant
(slant) at the <inline-formula><mml:math id="M283" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> uncertainty level. The significance level is given in
the lower right corner in cases where the drift is significant.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f11.pdf"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S4.SS5">
  <title>Drift assessment</title>
      <p id="d1e5648">In addition to the spread and correlations, the drifts
among the satellite data sets are considered. As drift we consider the linear
change of the difference between two time series, which indicates if the
longer-term variation of the two time series is the same or not
(Sect. <xref ref-type="sec" rid="Ch1.S3.SS3"/>). As before, we start with an example. In
Fig. <xref ref-type="fig" rid="Ch1.F10"/> the drifts between the de-seasonalised time
series of the SMR 489 <inline-formula><mml:math id="M284" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and all other data sets are shown for the
Northern Hemisphere mid-latitudes (left panel) as well as the corresponding
significance level (right panel). The significance level is given by the
absolute ratio of the drift to the drift uncertainty. We consider a drift as
statistically significant when the significance level is larger than
<inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> (corresponding to the 95 % confidence level).</p>
<sec id="Ch1.S4.SS5.SSS1">
  <title>Drift example</title>
      <p id="d1e5677">Figure <xref ref-type="fig" rid="Ch1.F10"/> shows that below 20 <inline-formula><mml:math id="M286" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> large
drifts (up to 2.5 <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and even higher) are found
between SMR 489 <inline-formula><mml:math id="M288" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and the other satellite data sets. In the
altitude region between 20 and 1 <inline-formula><mml:math id="M289" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, good<?pagebreak page4454?> consistency
between the satellite data sets is found despite the different time periods
of measurements. The smallest drifts, ranging
from about 0 to 0.5 <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, are found around 20 <inline-formula><mml:math id="M291" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The drifts consistently
increase with altitude and maximise around 0.4 <inline-formula><mml:math id="M292" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Above
1 <inline-formula><mml:math id="M293" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> the drifts of SMR 489 <inline-formula><mml:math id="M294" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> vary between about 0.75 and
1.5 <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> depending on which data set the
SMR 489 <inline-formula><mml:math id="M296" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set is compared to, but decrease with altitude
towards 0.1 <inline-formula><mml:math id="M297" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The drifts range here between 0 and
1.25 <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The drifts between SMR 489 <inline-formula><mml:math id="M299" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and
the other satellite data sets are in most cases significant at the <inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>
uncertainty level as can be seen from Fig. <xref ref-type="fig" rid="Ch1.F10"/> (right
panel). Larger drifts between SMR 489 <inline-formula><mml:math id="M301" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and the other data sets
that obviously deviate from the majority of data sets are found for the
comparison to the POAM III, SAGE II, SAGE III and HALOE data sets. However,
this is due to the fact that for these data sets not only the overlap period
with SMR 489 <inline-formula><mml:math id="M302" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> is relatively short (4 years, 2001–2005), but
also the number of months for which both data sets actually yield a valid
monthly mean is small (see numbers given in figure legend). Additionally,
these drifts are in most cases not statistically significant at the <inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>
uncertainty level.</p>
</sec>
<sec id="Ch1.S4.SS5.SSS2">
  <title>Drift matrices</title>
      <p id="d1e5865">In Figs. <xref ref-type="fig" rid="Ch1.F11"/>–<xref ref-type="fig" rid="Ch1.F13"/> the drift
estimates between the time series of all data sets are summarised as matrix
plots for the three latitude bands and four altitudes. In the matrix plots,
data sets are only shown if they yield any result at a given altitude. The
drift estimates are based on the difference time series between the data sets
given on the <inline-formula><mml:math id="M304" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis and the data sets given on the <inline-formula><mml:math id="M305" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis. Additional
information that is given in the matrix plots includes the overlap period of
the two data sets, how many months the two data sets actually overlap and if the drift is significant or not
at the <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> uncertainty level as well as the corresponding significance
level for significant drift.</p>
      <?pagebreak page4456?><p id="d1e5896">In the Antarctic (Fig. <xref ref-type="fig" rid="Ch1.F11"/>), almost no significant
drifts are found between the satellite data sets at the two lowest altitude
levels (80 and 10 <inline-formula><mml:math id="M307" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). An exception here is the MAESTRO data set
which shows a significant (negative) drift of <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> to
<inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (significance level up to 3.7) and POAM III
which shows a significant positive drift (2 to 3 <inline-formula><mml:math id="M311" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)
compared to SAGE II and SMR 544 <inline-formula><mml:math id="M312" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> (at 80 <inline-formula><mml:math id="M313" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). While the
overall time period MAESTRO had overlap
with other data sets was sufficiently long (<inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">85</mml:mn></mml:mrow></mml:math></inline-formula> months), the number of
coincident months for these data sets was rather low (9 months). Further, at
80 <inline-formula><mml:math id="M315" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, a significant
negative drift is found between some MIPAS data sets and SOFIE. At
10 <inline-formula><mml:math id="M316" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, a significant (positive) drift
(0.8 <inline-formula><mml:math id="M317" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) is found between the MIPAS-Oxford V5R NOM and
ACE-FTS v2.2 data sets (significance level of 3.2) and of
2 <inline-formula><mml:math id="M318" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> between the SMR 489 GHz and POAM III data sets
(significance level 3.0). Additionally, significant drifts are found between
different MIPAS data sets relative to SMR 489 <inline-formula><mml:math id="M319" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> and between the MLS
and SMR data sets. At 3 <inline-formula><mml:math id="M320" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> most drifts are significant. Most MIPAS
data sets exhibit significant positive drifts relative to the ACE-FTS
(significance level up to 5.7) and MLS (significance level up to 8.1) data
sets. While in the comparisons to the ACE-FTS data sets the actual number of
overlapping months is limited, this is not the case in the comparison to MLS.
As before, for the SMR 489 <inline-formula><mml:math id="M321" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set significant positive drifts
are found (significance level up to 4.8) relative to most other data sets. A
large variety of drifts is found at 0.1 <inline-formula><mml:math id="M322" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, but in most cases the
drift is not significant. Data sets for which most drifts are significant at
this altitude level are SMR 489 <inline-formula><mml:math id="M323" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M324" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M325" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>,
significance level up to 6.4) and MIPAS-Bologna V5R MA (significance level up
to 3.2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><caption><p id="d1e6101">As Fig. <xref ref-type="fig" rid="Ch1.F11"/>,
but here for the tropics, i.e. between 15<inline-formula><mml:math id="M326" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and
15<inline-formula><mml:math id="M327" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f12.pdf"/>

          </fig>

      <p id="d1e6130">In the tropics (Fig. <xref ref-type="fig" rid="Ch1.F12"/>), larger drifts are found
than in the Antarctic, especially at 0.1 <inline-formula><mml:math id="M328" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Here, most drifts are
significant. Significant drifts are found for the MIPAS-Bologna V5R NOM,
MIPAS-Bologna V5R MA, MIPAS-ESA V5R, MIPAS-IMKIAA V5R NOM,
MIPAS-Oxford V5R NOM and SMR 489 <inline-formula><mml:math id="M329" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data sets. For example, for
MIPAS-Bologna V5R NOM and MIPAS-Bologna V5R MA drift (significance level up
to 6.5) in comparison to most other satellite data sets is found. For
MIPAS-Bologna V5R NOM this is also the case at 3 <inline-formula><mml:math id="M330" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> (significance
level up to 9.8). Large negative drifts are found for GOMOS (<inline-formula><mml:math id="M331" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M332" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, significance level up to 3.9) compared to
most data sets. Also for SMR 489 <inline-formula><mml:math id="M333" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> significant positive drifts (up
to <inline-formula><mml:math id="M334" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, significance level up to 8.5) for almost
all data sets are found at 3 <inline-formula><mml:math id="M336" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Good consistency is found among
the MIPAS data sets. The drifts are low and in most cases not significant. An
exception here is MIPAS-Oxford V5R NOM
(<inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula>–1 <inline-formula><mml:math id="M338" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, significance level up to 9.8). For
the tropics the best agreement among the data sets is found at
10 <inline-formula><mml:math id="M339" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. In most cases the drift is not significant and in cases where
the drift is significant the drifts are relatively low with
0.2–0.4 <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Larger drifts are found at this altitude
for GOMOS (up to <inline-formula><mml:math id="M341" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M342" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and HIRDLS (up to
<inline-formula><mml:math id="M343" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M344" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). For GOMOS the drifts are significant in most
cases (significance level up to 4.3), while this is not the case for HIRDLS.</p>
      <p id="d1e6335">At 80 <inline-formula><mml:math id="M345" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> a wide variety is found. Some data sets show positive
drift, some negative. In some cases the drift is significant and in other
cases not. For example, a positive drift (2 <inline-formula><mml:math id="M346" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)
relative to almost all data sets is found for MIPAS-Bologna V5R NOM
(significance level up to 6.4). For the HIRDLS data set a significant
positive drift (also <inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M348" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) is found compared to
MIPAS-IMKIAA V5R NOM, MIPAS-IMKIAA-V5R MA and MIPAS-Oxford V5R NOM
(significance level 2.0–4.6). A large drift (<inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M350" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>)
at this altitude level is found for MIPAS-ESA V5R MA compared to
MIPAS-IMKIAA V5R NOM (significance level 4.8). Also the MIPAS-Oxford V5R NOM
shows significant drifts compared to a number of data sets.</p>
      <p id="d1e6417">The patterns of the estimated drifts in the Northern Hemisphere mid-latitudes
shown in Fig. <xref ref-type="fig" rid="Ch1.F13"/> are quite similar to the drifts in
the tropics and Antarctica. However, the estimated change in
<inline-formula><mml:math id="M351" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> seems to be somewhat lower in the mid-latitudes than
in the tropics or Antarctic. The highest variety is again found at
0.1 <inline-formula><mml:math id="M352" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Similar to the tropics significant drifts are found, e.g., for the MIPAS-Bologna V5R NOM and MIPAS-Bologna V5R MA (up to
<inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M354" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, significance level up to 3.9) data sets
relative to the SMR 489 <inline-formula><mml:math id="M355" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set. At 3 <inline-formula><mml:math id="M356" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, for most data
sets the drifts are small and/or not significant. Significant negative drifts
are found for both ACE-FTS data sets and for SMR 489 <inline-formula><mml:math id="M357" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>. For SMR
489 GHz drift is found relative to most other data sets which is also in
most cases significant. At 10 <inline-formula><mml:math id="M358" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> HIRDLS shows pronounced drifts
compared to the other data sets. However, these drifts are not significant
except for the comparison with MLS (drift of 3 <inline-formula><mml:math id="M359" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>,
significance level 2.3). Otherwise for most data sets the drifts are small
and/or not significant at 10 and 80 <inline-formula><mml:math id="M360" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Exceptions are HIRDLS
(<inline-formula><mml:math id="M361" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M362" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and MAESTRO
(<inline-formula><mml:math id="M363" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M364" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>),
which show negative drift at 80 <inline-formula><mml:math id="M365" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. For HIRDLS in most cases the
drift is significant (significance level up to 4.1), but for MAESTRO in most
cases not. For MIPAS-Bologna-V5R NOM significant positive drifts are found
for all instruments that are in most cases around
0.2–0.4 <inline-formula><mml:math id="M366" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, but higher compared to HIRDLS
(significance level 4.1), MAESTRO (significance level 2.2), SCIAMACHY limb
(significance level 10.6) and SCIAMACHY solar OEM (significance level 6.6).
Other data sets for which drifts are found compared to most other data sets
are SCIAMACHY limb, SCIAMACHY solar Onion and SMR 489 <inline-formula><mml:math id="M367" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13" specific-use="star"><caption><p id="d1e6615">As Figs. <xref ref-type="fig" rid="Ch1.F11"/> and
<xref ref-type="fig" rid="Ch1.F12"/>, but here the results for the latitude band
between 50<inline-formula><mml:math id="M368" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 60<inline-formula><mml:math id="M369" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N are shown.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://amt.copernicus.org/articles/11/4435/2018/amt-11-4435-2018-f13.pdf"/>

          </fig>

</sec>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Summary and conclusions</title>
      <p id="d1e6654">In the
framework of the second SPARC water vapour assessment, time series of
stratospheric and lower mesospheric water vapour derived from satellite
observations were compared. The comparison results presented comprise 33 data
sets from 15 satellite instruments. These comparisons provide a comprehensive
overview of the typical uncertainties in the observational database that
should be considered in the future in observational and modelling studies
addressing stratospheric and lower mesospheric water vapour variability and
trends.</p>
      <?pagebreak page4457?><p id="d1e6657">The time series comparison was performed for three latitude bands: the
Antarctic (80–70<inline-formula><mml:math id="M370" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S), the tropics (15<inline-formula><mml:math id="M371" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–15<inline-formula><mml:math id="M372" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) and
the Northern Hemisphere mid-latitudes (50<inline-formula><mml:math id="M373" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>–60<inline-formula><mml:math id="M374" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) at four
altitudes levels (0.1, 3, 10, 80 <inline-formula><mml:math id="M375" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) covering the stratosphere and
lower mesosphere. The combined temporal coverage of observations from the 15
satellite instruments allows consideration of the time period 1986–2014. In
addition to the qualitative comparison of the time series, a quantitative
comparison was provided based on the spread, correlation and drift between
the individual time series.</p>
      <p id="d1e6713">The qualitative time series comparison shows that the largest differences
between the de-seasonalised time series are in the Antarctic and in the lower
mesosphere (0.1 <inline-formula><mml:math id="M376" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) and tropopause region (80 <inline-formula><mml:math id="M377" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). In the
stratosphere (3 and 10 <inline-formula><mml:math id="M378" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>) and the tropics, good agreement between
the satellite data sets was found. These differences were quantitatively
confirmed by the correlation assessment, where the best agreement between the
satellite data sets was also found in the tropics, while in Antarctic and
Northern Hemisphere mid-latitudes, large spread between the data sets was
found. Generally, the lowest correlations between the individual data sets
were found in the Antarctic. In each latitude band<?pagebreak page4459?> the correlation was lower
in the lower stratosphere and lower mesosphere than in the middle
stratosphere.</p>
      <p id="d1e6737">There are multiple factors that give rise to the observed differences between
the individual data sets. A thorough discussion on this is given in
<xref ref-type="bibr" rid="bib1.bibx25" id="text.45"/>. From this study we know that the most important
contributions arise from differences in temporal and spatial sampling, the
influence of clouds or NLTE effects. Other factors include systematic
differences, for example calibration problems. However, for the time series comparison we would rank sampling
biases and systematic errors as the most important reasons for the
differences as was discussed by <xref ref-type="bibr" rid="bib1.bibx59" id="text.46"/> based on trace gas
climatologies.</p>
      <p id="d1e6747">The reason why the largest differences between the data sets are found in the
tropopause region, in the lower mesosphere and in the Antarctic is
that these are also the locations where the highest variability in water vapour is found. Given the
limited vertical resolution of the satellite data sets, tropospheric
influences start to play a role near the tropopause. Sampling differences
become more pronounced due to the large variability, e.g. due to the fact
that the satellite observations are influenced differently by clouds. In the
lower mesosphere, diurnal variation becomes more important. The satellite
data sets do not have the same local time coverage. For example there is the
influence of NLTE effects in most MIPAS
data sets except MIPAS-IMKIAA V5R MA, where these NLTE effect are explicitly
considered. Larger deviations in the lower mesosphere occur, e.g. in the case
of the MIPAS NOM data sets, which are close to their upper retrieval limit
there, and thus more uncertain.</p>
      <p id="d1e6750">Less agreement between the data sets was found for the Antarctic, especially
in the lower stratosphere in winter and spring when dehydration occurs. Large
differences between the data sets were found in both the absolute and
de-seasonalised data. In the absolute data, these differences are primarily
caused by differences in the influence of clouds on the measurements.
However, sampling biases can also play a role. In the de-seasonalised data
some differences between the data sets could be related to the
de-seasonalisation approach used in our study (e.g. POAM III). Since the dehydration
is more a seasonal phenomenon, and accordingly is less characterised by a
sinusoidal behaviour, the usage of sinusoidal functions for the
de-seasonalisation is not optimal. Instead, the average approach
(see Sect. <xref ref-type="sec" rid="Ch1.S3.SS1"/>) would be more suitable for
de-seasonalisation in this region.</p>
      <p id="d1e6755">In addition to the assessment of the spread and correlations, the drifts
between the individual data sets were also assessed, which indicates if the
longer-term variations (drifts) of two time series are the same or not. From
the drift comparison we found that the drift patterns are quite similar for
the three latitude bands considered. The drifts are highest at the highest
and lowest considered altitude levels (0.1 and 80 <inline-formula><mml:math id="M379" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>). The majority
of significant drifts were found in the tropics (the latitude region with the
lowest spread/variability), which makes the drift detection considerably easier. Further, it is possible that
some of the drifts (especially for the low-density samplers) are caused by
sampling biases <xref ref-type="bibr" rid="bib1.bibx5" id="paren.47"/>. The same drift approach as used here has
been used by <xref ref-type="bibr" rid="bib1.bibx26" id="text.48"/> to calculate drifts from profile-to-profile
comparisons (using coincident data). However, no statistically significant
difference was found between the two sets of drifts in 95 % of the
comparisons.</p>
      <p id="d1e6771">Further, from the drift assessment we found that the MIPAS data sets show
positive drifts relative to the ACE-FTS data sets in the Antarctic and
Northern Hemisphere mid-latitudes at 3 <inline-formula><mml:math id="M380" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. Interestingly, no drifts
of MIPAS relative to ACE-FTS are found in the tropics. The reason for this is
currently not understood. The drifts found in the MIPAS data sets are
consistent with the time dependence unaccounted for
in the correction coefficient for the non-linearity in the
detector response function used in the data sets based on calibration
version 5 <xref ref-type="bibr" rid="bib1.bibx66" id="paren.49"/>. Some improvement is seen in the
MIPAS ESA V7R NOM data set, where a time dependence of the correction
coefficient is implemented, though not at all altitudes. Additionally, even
drifts among the different MIPAS data sets were found. This might be related
to the different retrieval choices (as well as to the usage of different
micro-windows) by the different processors and to sampling differences
between the NOM and MA observations. Further, from the drift comparison, we
found that the SMR 489 <inline-formula><mml:math id="M381" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set shows a significant drift relative to the other data sets, except at around
10 <inline-formula><mml:math id="M382" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The drifts of the SMR 489 <inline-formula><mml:math id="M383" display="inline"><mml:mi mathvariant="normal">GHz</mml:mi></mml:math></inline-formula> data set are largest at
around 50 and 0.5 <inline-formula><mml:math id="M384" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> with approximately 1.5 and
<inline-formula><mml:math id="M385" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:mi mathvariant="normal">ppmv</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">decade</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, respectively depending on the data set used
for comparison.</p>
      <p id="d1e6840">Further, within this assessment study we encountered the following
difficulties in our analyses using the HIRDLS, GOMOS and MAESTRO data sets.
The GOMOS time series exhibit larger scatter from month to month (coverage
only in the tropics for de-seasonalised data here) despite extended
screening <xref ref-type="bibr" rid="bib1.bibx66" id="paren.50"/>, resulting in low correlations to the other data
sets and pronounced negative drifts at 10 and 3 <inline-formula><mml:math id="M387" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>. The
quality of the HIRDLS data set deteriorates towards 10 <inline-formula><mml:math id="M388" display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, resulting
in low correlations, larger anomalies and larger drifts. However,
the drifts were mostly not statistically significant. It should be noted here
that in addition to correcting for the effects of the obstruction in the
optics, changes in the calibration were made within the HIRDLS mission
<xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx12" id="paren.51"/>. This change in calibration may also have an
influence on the drift estimates. The MAESTRO data set encounters large
uncertainty (noise) at 80 hPa (in the correlations and drifts) which is
related to the vicinity to the uppermost limit of these retrievals. Similar
behaviour is also found for the SCIAMACHY limb and the SMR 544 GHz data sets.</p>
      <p id="d1e6863">Nevertheless, although the water vapour data sets have been thoroughly
assessed in this study it is difficult or rather impossible to decide which
data set is most suitable for future modelling and observational studies.
This can only be<?pagebreak page4460?> answered with respect to the specific scientific application
to which the data set is intended to be applied. For future studies, e.g. on
water vapour trends, we can state that the data sets that provide the longest
measurement record with high spatial and temporal coverage have an advantage
over the ones which provide only observations in specific latitude bands
and/or altitude regions. For data sets that show drift relative to other data
sets (e.g. SMR 489 GHz), a drift
has to be taken into account, and data sets that are simply too short (less
than 1 year; e.g. ILAS-II and SMILES) cannot be used for trend studies at
all. Thus, from our assessment we find that most data sets can be considered
in future observational and modelling studies, e.g addressing stratospheric
and lower mesospheric water vapour variability and trends, if data set
specific characteristics (e.g. an
instrument drift) and restrictions (e.g. spatial and temporal coverage) are
taken into account.</p>
</sec>

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

      <p id="d1e6870">Data are available upon request.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e6873">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/amt-11-4435-2018-supplement" xlink:title="pdf">https://doi.org/10.5194/amt-11-4435-2018-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution">

      <p id="d1e6882">The study was designed by JU, FK and SL with
contributions from the WAVAS-II core members GS, KR, JCG, MK, GEN, WGR and KAW.
FK wrote the manuscript and SL performed the analyses and contributed to the
writing of the manuscript. JU performed the first version of the analyses.
GS helped with the selection of results to be presented in the paper. KHR
contributed to the discussion of the results. Satellite data used in this
study were provided by GPS, JPB, RD, PE, MGC, JG, YK, MK, SN, PR, WGR, AR, CS,
KAW and KW. Valuable comments on the manuscript were provided by GPS, KHR, RPD,
PR, MG, SN, CS, JG, AR and KW.</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e6889">The authors declare that they have no competing
interests.</p>
  </notes><notes notes-type="sistatement">

      <p id="d1e6895">This article is part of the special issue “Water vapour in the
upper troposphere and middle atmosphere: a WCRP/SPARC satellite data quality
assessment including biases, variability, and drifts (ACP/AMT/ESSD
inter-journal SI)”. It does not belong to a conference.</p>
  </notes><?xmltex \hack{\newpage}?><ack><title>Acknowledgements</title><p id="d1e6902">The Atmospheric Chemistry Experiment (ACE), also known as SCISAT, is a
Canadian-led mission mainly supported by the Canadian Space Agency and the
Natural Sciences and Engineering Research Council of Canada. We would like to
thank the European Space Agency (ESA) for making the MIPAS level-1b data set
available. MLS data were obtained from the NASA Goddard Earth Sciences and
Information Center. Work at the Jet Propulsion Laboratory, California
Institute of Technology, was done under contract with the National
Aeronautics and Space Administration. SCIAMACHY spectral data have been
provided by ESA. The work on the SCIAMACHY water vapour data products has
been funded by DLR (German Aerospace Center) and the University of Bremen.
The SCIAMACHY limb water vapour data set v3.01 is a result of the DFG (German
Research Council) Research Unit “Stratospheric Change and its Role for
Climate Prediction” (SHARP) and the ESA SPIN (ESA SPARC Initiative) project
and were partly calculated using resources of the German HLRN
(High-Performance Computer Center North). We would like to thank Mark Hervig
for providing the SOFIE data and Takafumi Sugita for providing the ILAS-II
data. We acknowledge the HALOE science team and the many members of the HALOE
project for producing and characterising the high-quality HALOE data set.
Further, we would like to thank Ellis Remsberg for valuable comments on the
manuscript. Stefan Lossow was funded by the SHARP project under contract
STI 210/9-2. We want to express our gratitude to SPARC and WCRP (World
Climate Research Programme) for their guidance, sponsorship and support of
the WAVAS-II programme. We acknowledge support by Deutsche
Forschungsgemeinschaft and Open Access Publishing Fund of Karlsruhe Institute
of Technology.<?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: Stefan
Buehler<?xmltex \hack{\newline}?>
Reviewed by: Hugh C. Pumphrey and one anonymous referee</p></ack><ref-list>
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<abstract-html><p>Time series of stratospheric and lower mesospheric water vapour
using 33 data sets from 15 different satellite instruments were compared in
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observational database that can be considered in the future in observational
and modelling studies, e.g addressing stratospheric water vapour trends. The
time series comparisons are presented for the three latitude bands, the
Antarctic (80°–70°&thinsp;S), the tropics
(15°&thinsp;S–15°&thinsp;N) and the Northern Hemisphere mid-latitudes
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assessed quantitatively in the form of the spread (i.e. the difference
between the maximum and minimum volume mixing ratios among the data sets),
the (Pearson) correlation coefficient and the drift (i.e. linear changes of
the difference between time series over time). Generally, good agreement
between the time series was found in the middle stratosphere while larger
differences were found in the lower mesosphere and near the tropopause.
Concerning the latitude bands, the largest differences were found in the
Antarctic while the best agreement was found for the tropics. From our
assessment we find that most data sets can be considered in future
observational and modelling studies, e.g. addressing stratospheric and lower
mesospheric water vapour variability and trends, if data set specific
characteristics (e.g. drift) and restrictions (e.g. temporal and spatial
coverage) are taken into account.</p></abstract-html>
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