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<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" dtd-version="3.0">
  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</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/acp-16-11671-2016</article-id><title-group><article-title>The Zugspitze radiative closure experiment for quantifying water vapor
absorption over the terrestrial and solar infrared –
Part 3: Quantification of the mid- and near-infrared water vapor continuum
in the 2500 to 7800 cm<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral range under atmospheric conditions</article-title>
      </title-group><?xmltex \runningtitle{The Zugspitze radiative closure experiment -- Part 3}?><?xmltex \runningauthor{A. Reichert and R. Sussmann}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Reichert</surname><given-names>Andreas</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Sussmann</surname><given-names>Ralf</given-names></name>
          <email>ralf.sussmann@kit.edu</email>
        </contrib>
        <aff id="aff1"><institution>Karlsruhe Institute of Technology, IMK-IFU, Garmisch-Partenkirchen, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Ralf Sussmann (ralf.sussmann@kit.edu)</corresp></author-notes><pub-date><day>21</day><month>September</month><year>2016</year></pub-date>
      
      <volume>16</volume>
      <issue>18</issue>
      <fpage>11671</fpage><lpage>11686</lpage>
      <history>
        <date date-type="received"><day>13</day><month>April</month><year>2016</year></date>
           <date date-type="rev-request"><day>25</day><month>April</month><year>2016</year></date>
           <date date-type="rev-recd"><day>30</day><month>August</month><year>2016</year></date>
           <date date-type="accepted"><day>2</day><month>September</month><year>2016</year></date>
      </history>
      <permissions>
        
        
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016.html">This article is available from https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016.pdf</self-uri>
      <abstract>
    <p id="d1e96">We present a first quantification of the near-infrared (NIR) water vapor
continuum absorption from an atmospheric radiative closure experiment carried
out at the Zugspitze (47.42<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 10.98<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E; 2964 m a.s.l.).
Continuum quantification is achieved via radiative closure using
radiometrically calibrated solar Fourier transform infrared (FTIR) absorption spectra covering the 2500 to
7800 cm<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral range. The dry atmospheric conditions at the
Zugspitze site (IWV 1.4 to 3.3 mm) enable continuum quantification even
within water vapor absorption bands, while upper limits for continuum
absorption can be provided in the centers of window regions. Throughout
75 % of the 2500 to 7800 cm<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral range, the Zugspitze results agree within our estimated uncertainty with the widely used MT_CKD
2.5.2 model (Mlawer et al., 2012). In the wings of water vapor absorption
bands, our measurements indicate about 2–5 times stronger continuum
absorption than MT_CKD, namely in the 2800 to 3000 cm<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 4100 to
4200 cm<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral ranges. The measurements are consistent with the
laboratory measurements of Mondelain et al. (2015), which rely on cavity
ring-down spectroscopy (CDRS), and the calorimetric–interferometric
measurements of Bicknell et al. (2006). Compared to the recent FTIR
laboratory studies of Ptashnik et al. (2012, 2013), our measurements are
consistent within the estimated errors throughout most of the spectral range.
However, in the wings of water vapor absorption bands our measurements
indicate typically 2–3 times weaker continuum absorption under atmospheric
conditions, namely in the 3200 to 3400, 4050 to 4200, and 6950 to
7050 cm<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral regions.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e185">Atmospheric water vapor is the most important contributor to the absorption
of incoming solar radiation in the near infrared (NIR; 4000–14 000 cm<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Kiehl and Trenberth, 1997). Water vapor
absorption comprises both the effect of spectral line absorption and the
broadband so-called continuum absorption (e.g., Shine et al., 2012). Depending
on the atmospheric state and the choice of continuum model, up to 6 % of
the clear-sky water vapor absorption can be attributed to the continuum
(Paynter and Ramaswamy, 2011). Consequently, quantitative knowledge of this
contribution is a prerequisite for realistic atmospheric radiative transfer
calculations employed in, e.g., climate models (Paynter and Ramaswamy, 2014;
Rädel et al., 2015; Turner et al., 2012).</p>
      <p id="d1e203">However, the NIR atmospheric water vapor continuum currently still lacks
sufficient experimental constraints. Recently, a number of laboratory studies
based on different experimental techniques investigated this open question.
Several efforts were made to quantify continuum absorption, including the
contributions of both the self- and foreign-broadened continuum. Several
studies made use of cell measurements with grating spectrometers (e.g., Burch,
1982, 1985; Burch and Alt, 1984) and FTIR (Fourier transform infrared)
spectrometers (Baranov et al., 2008; Baranov and Lafferty, 2011; Paynter et
al., 2009; Ptashnik et al., 2011, 2012, 2013, 2015). Furthermore, a number of
spectral regions were covered by cavity ring-down spectroscopy (CRDS)
measurements (Cormier et al., 2002, 2005; Mondelain et al., 2013, 2014,
2015), by the related technique of optical-feedback cavity-enhanced
spectroscopy (OF-CEAS; Ventrillard et al., 2015), and by
calorimetric–interferometric measurements (Fulghum and Tilleman, 1991;
Bicknell et al., 2006). However, no consensus has been reached among these
studies. As noted by, e.g., Mondelain et al. (2014) and Ptashnik et al. (2013),
the individual results feature differences far beyond the respective
uncertainty estimates whose attribution to causative processes remains
tentative. A further challenge for laboratory studies is that they are
typically carried out at higher temperatures than those encountered in the
atmosphere in order to detect the weak continuum absorption in the limited
optical path length of the cells. Note that CDRS and related techniques in
principle enable measurements at atmospheric temperature (see, e.g., Cormier et
al., 2005), but such measurements are not yet available for many spectral
regions). To date, the temperature dependence of the self-continuum has been
investigated by measurements in a number of spectral regions (e.g., Cormier et
al., 2005; Mondelain et al., 2014; Ptashnik et al., 2011; Ventrillard et al.,
2015). However, the remaining uncertainty of the self-continuum temperature
dependence (see, e.g., Paynter and Ramaswamy, 2011) and the lack of
measurements of the foreign-continuum temperature dependence cause
considerable uncertainties in the application of the laboratory results to atmospheric radiative transfer calculations.</p>
      <p id="d1e206">The continuum has been investigated for atmospheric conditions using
measurements of atmospheric emitted infrared radiance for other spectral
regions (e.g., Tobin et al., 1999; Rowe and Walden, 2009). However,
atmospheric measurements are available only for a fraction of the spectral
region covered by this study (Newman et al., 2012; 2400 to 3200 cm<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
while for the remaining interval from 3200 to 7800 cm<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, no atmospheric
measurements have been reported. A validation of continuum absorption
strength under atmospheric conditions is therefore highly desirable to
address these shortcomings. To this aim, we conducted a radiative closure
experiment with the objective of quantifying the NIR water vapor continuum
absorption from atmospheric measurements. The study is carried out at the
high-altitude Zugspitze site and relies on the solar FTIR measurements
implemented at this site (Sussmann and Schäfer, 1997) in the framework of
the Network of the Detection of Atmospheric Composition Change (NDACC;
<uri>http://www.ndacc.org</uri>). While such atmospheric closure studies enable us
to avoid some limitations of laboratory measurements as outlined above, they
are also subject to a number of major challenges: absorption in the NIR due
to aerosols can become comparable to the magnitude of the water vapor
continuum absorption of interest (Ptashnik et al., 2015) and requires an
accurate separation of continuum and aerosol contribution. Furthermore, the
characterization of the atmospheric state (e.g., IWV, water vapor profile,
temperature profile, and further trace gas column amounts) is more
challenging and typically less accurate than the characterization of
experimental conditions in a laboratory study.</p>
      <p id="d1e236">This paper is part of a three-paper series about different aspects of the
Zugspitze radiative closure experiment. The first paper, hereafter referred
to as Part 1 (Sussmann et al., 2016, same issue), describes the instrumental
setup, evaluates the sensitivity of the closure experiment in the far
infrared (FIR; 2–667 cm<inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the mid-infrared (MIR; 667–4000 cm<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and the NIR, and provides results on the FIR water
vapor continuum. A novel radiometric calibration method for solar FTIR
spectra in the NIR is presented in a second paper, referred to as Part 2
(Reichert et al., 2016, same issue). Part 3 (this paper) contains the NIR
continuum quantification method and results. Continuum quantification in the
NIR is achieved by comparing calibrated radiance spectra, obtained with the
method presented in Part 2, to radiative transfer model calculations. The
results derived from our data set are presented and compared to results from
laboratory studies as well as the widely used MT_CKD 2.5.2 continuum model
(Mlawer et al., 2012).</p>
      <p id="d1e270">This paper is structured as follows. Sect. 2 contains an overview of the
instrumental setup used in the closure experiment. Section 3 outlines the
method for water vapor continuum quantification. In Sect. 4, the results
obtained with this method are presented and compared to previous studies.
Finally, Sect. 5 contains a summary and conclusions.</p>
</sec>
<sec id="Ch1.S2">
  <title>Setup of the closure experiment</title>
      <p id="d1e279">The closure experiment relies on a quantitative comparison of measurements of
spectral radiance with synthetic spectra calculated using the line-by-line
radiative transfer model (LBLRTM; Clough et al., 2005). Spectral line
parameters were set according to the aer_v3.2 line list provided alongside
the LBLRTM model. Water vapor continuum absorption is then quantified via the
spectral residuals, i.e., the difference between simulated and measured
spectra. We adopt the definition of the water vapor continuum given in Turner
and Mlawer (2010); i.e., water vapor continuum is defined as all absorption by
water vapor exceeding a Voight line shape within <inline-formula><mml:math id="M14" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>25 cm<inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> of each
line center minus the value of the Voight line shape at <inline-formula><mml:math id="M16" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>25 cm<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
(“plinth”).</p>
      <p id="d1e320">The instruments used in the Zugspitze radiative closure experiment and the
related uncertainties are described in detail in Part 1. In summary, spectral
radiances in the NIR are measured using a solar FTIR spectrometer setup at
the Zugspitze (47.42<inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 10.98<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E; 2964 m a.s.l.) summit
observatory (Sussmann and Schäfer, 1997). Radiative calibration of
measured spectra is achieved via a novel calibration method presented in
Part 2, which relies on a combination of the Langley method and measurements
of a medium-temperature blackbody source.</p>
      <p id="d1e341">The atmospheric state at the time of the radiance measurements is required
as input to the LBLRTM radiative transfer calculations. To enable
accurate quantification of the water vapor continuum from spectral
residuals, the atmospheric state has to be constrained precisely using a
number of additional measurements listed in the following.</p>
      <p id="d1e344">Vertically integrated water vapor (IWV) constitutes the key input parameter
and is derived directly from the solar FTIR spectra (e.g., Sussmann et al.,
2009; Schneider et al., 2012). Temperature and pressure profiles are taken
from four-times-daily National Center for Environmental Prediction (NCEP)
resimulation data. NCEP resimulation data is also used to constrain the shape
of the water vapor profile. Column-averaged mixing ratios of CO<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>,
CH<inline-formula><mml:math id="M21" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>, and N<inline-formula><mml:math id="M22" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O are measured using the nearby Garmisch TCCON (Total
Carbon Column Observing Network) solar FTIR instrument (Sussmann and
Rettinger, 2014). O<inline-formula><mml:math id="M23" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> columns were constrained by combined Brewer–Dobson
measurements made at the nearby Hohenpeißenberg observatory (Köhler,
1995).</p>
      <p id="d1e384">Aerosol optical depth (AOD) has to be constrained precisely in order to
enable continuum quantification in the wings of the strong NIR water vapor
bands and within window regions. A great advantage of the Zugspitze site is
that AOD is typically very low; i.e., the AOD for the Zugspitze data set is
about a factor of 10 lower than at typical lowland midlatitude sites. The
AOD levels encountered in our closure data set (for data set description and
selection criteria see Sect. 3.3) are in the range of 0.0005–0.00075 at
2500 cm<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and in the range of 0.0024–0.0032 at 7800 cm<inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> at air mass
1. AOD was measured using the Sun-Sky Automatic Radiometer –
Zugspitze (SSARA-Z) sun photometer (Toledano et al., 2009) developed by the
Meteorological Institute of the University of Munich and set up at
Schneefernerhaus (2675 m a.s.l.; 680 m horizontal distance to the
Zugspitze solar FTIR). The instrument includes 13 spectral channels from 340
to 1640 nm. Only information from five channels whose central wavelengths are
in the spectral region between 439.6 and 781.1 nm was used in the analysis.
The exact filter wavelengths and full width at half maximum (FWHM) values of
these channels are listed in Table 1. The reason for the channel selection is
that in the ultraviolet (UV) to visible range, water vapor continuum
absorption can be considered negligible compared to AOD, whereas for the NIR
channels continuum absorption will lead to biased AOD results. The channels
below 440 nm were excluded since the high influence of Rayleigh scattering in
the UV leads to increased AOD uncertainties.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><caption><p id="d1e414">Central wavelength and FWHM of the sun photometer (SSARA-Z) filters
used for AOD analysis.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="right"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"><inline-formula><mml:math id="M26" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> (nm)</oasis:entry>  
         <oasis:entry colname="col2">FWHM (nm)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">439.6</oasis:entry>  
         <oasis:entry colname="col2">9.7</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">498.7</oasis:entry>  
         <oasis:entry colname="col2">12.3</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">531.9</oasis:entry>  
         <oasis:entry colname="col2">11.2</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">672.5</oasis:entry>  
         <oasis:entry colname="col2">10.9</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">781.1</oasis:entry>  
         <oasis:entry colname="col2">9.7</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e492">The data analysis of the SSARA-Z measurements was implemented in a similar way to the
approach outlined by Toledano et al. (2009). Specifically, we used standard
Langley calibration for cloud-free periods. Rayleigh scattering was accounted
for using the formula given by Bodhaine et al. (1999). In the analysis, a
Gaussian shape was assumed for the filter transmissivity curves. The
influence of absorption by O<inline-formula><mml:math id="M27" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> was subtracted as outlined in
Guyemard (1995). NIR AOD was then deduced by assuming AOD wavelength
dependence according to the Ångstrom relation:
          <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M28" display="block"><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M29" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> designates AOD. The Ångstrom exponent <inline-formula><mml:math id="M30" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and scaling
<inline-formula><mml:math id="M31" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> are determined by a fit to the UV/visible AOD measurements. More
sophisticated descriptions of the AOD wavelength dependence such as the
relation given by Molineaux et al. (1998) may be used instead of Eq. (1).
However, the number of sun photometer wavelength channels included in our
analysis is not sufficient to place tight constraints on the higher number of
parameters used in such models. Furthermore, the very low AOD at the Zugspitze
leads to high relative errors in the AOD determined from sun photometer
measurements, which removes the benefits of more advanced models compared to
Eq. (1).</p>
      <p id="d1e556">The AOD uncertainty comprises several contributions: first of all, the AOD
determined from the sun photometer measurements is affected by uncertainty in
the radiance measurements. This uncertainty contribution was set according to
the 2<inline-formula><mml:math id="M32" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> radiance measurement noise. The calibration uncertainty ensues
from the uncertainty of the Langley fit. Additional uncertainty arises from
the Rayleigh scattering correction, where central wavelength and FWHM errors
of optical filters and atmospheric pressure errors contribute. The treatment
of O<inline-formula><mml:math id="M33" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> absorption is also prone to additional errors, due to filter
parameter and O<inline-formula><mml:math id="M34" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> column errors. In addition to these contributions,
further uncertainty is induced by the fit to Eq. (1), which enables
constraining the NIR AOD from the UV/visible measurements. The overall AOD
uncertainty that ensues from these contributions for our data set at air mass
1 is <inline-formula><mml:math id="M35" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.0015 at 2500 cm<inline-formula><mml:math id="M36" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math id="M37" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.0025 at 7800 cm<inline-formula><mml:math id="M38" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S3">
  <title>NIR continuum determination</title>
<sec id="Ch1.S3.SS1">
  <title>Method overview</title>
      <p id="d1e634">The aim of this study is to constrain the NIR water vapor continuum
absorption under atmospheric conditions. We make use of the radiative closure
experiment setup at the Zugspitze observatory that is described in detail in
Part 1. Generally, radiative closure experiments comprise a quantitative
comparison of spectral radiance measurements to synthetic spectra. The
strategy for water vapor continuum quantification employed in this study
relies on radiometrically calibrated solar FTIR spectra in the 2500 to
7800 cm<inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> range. An alternative method that has been proposed by Mlawer
et al. (2014) and relies on the Langley method is presented in Appendix C.</p>
      <p id="d1e649">Spectra were recorded with the solar FTIR instrument described in Sect. 2 and
Part 1, using no optical filter, a spectral resolution of 0.02 cm<inline-formula><mml:math id="M40" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
(resolution is defined as 0.9<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>/</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></inline-formula>optical path difference), and averaging over
four to eight scans which leads to a 75–150 s repeat cycle per spectrum. The
measured spectra are radiometrically calibrated by means of the calibration
method outlined in Part 2. Briefly, the calibration approach relies on
Langley calibration in suitable spectral windows with little atmospheric
absorption. In addition to the Langley technique, which enables highly accurate
calibration in selected windows, the shape of the calibration curve between
the windows is constrained using spectral radiance measurements of a
high-temperature blackbody source. The calibration uncertainty achieved with
this novel method is 1–1.7 % (2<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> throughout the spectral range
considered. Synthetic radiance spectra are generated using the LBLRTM. Figure 1 shows the mean measured and synthetic
radiance spectra for the closure data set that will be presented in
Sect. 3.3. The atmospheric state used as input to the calculations was set
based on the measurements described in Sect. 2. Given the calibrated spectral
radiance measurements and the synthetic spectra, radiance residuals <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math></inline-formula> can then be calculated for a set of spectra selected according to the
criteria that will be presented in Sect. 3.3:
            <disp-formula id="Ch1.E2" content-type="numbered"><mml:math id="M44" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">FTIR</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant="normal">LBLRTM</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="normal">no</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi mathvariant="normal">continuum</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">AOD</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mtext>FTIR</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> designates the radiometrically calibrated solar FTIR
spectra, <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mtext>LBLRTM, no continuum</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> the synthetic LBLRTM spectra not
including continuum absorption, and AOD the aerosol optical depth. Continuum
optical depth <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is calculated from the spectral
residuals as follows:</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p id="d1e775">Mean measured (black) and synthetic (red) radiance spectra for the
closure data set selected according to the criteria presented in Sect. 3.3.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f01.png"/>

        </fig>

      <p id="d1e784"><disp-formula id="Ch1.E3" content-type="numbered"><mml:math id="M48" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>ln⁡</mml:mi><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant="normal">LBLRTM</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi mathvariant="normal">no</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="normal">continuum</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">AOD</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          After the calculation of the continuum optical depth (OD), absorption
coefficients were derived from these results. The continuum OD <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>cont</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is linked to the continuum absorption coefficient <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>cont</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
as follows:

                <disp-formula id="Ch1.E4" content-type="numbered"><mml:math id="M51" display="block"><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mtext>cont</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mo>⋅</mml:mo><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:munderover><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">wv</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">wv</mml:mi></mml:msub><mml:mtext>d</mml:mtext><mml:mi>h</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M52" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> designates the relative air mass, <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mtext>obs</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> the altitude of
the observing instrument, <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>wv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> the water vapor number density, and
<inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>air</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> the dry-air number density.</p>
      <p id="d1e971"><inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>cont</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can be further decomposed into self- and foreign-continuum
contributions according to
            <disp-formula id="Ch1.E5" content-type="numbered"><mml:math id="M57" display="block"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mrow><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:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> designate the self- and foreign-continuum coefficients and <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mrow><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:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are the densities of water vapor, dry
air, and a reference density, respectively. Specifically,
<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1013</mml:mn></mml:mrow></mml:math></inline-formula> mbar,
<inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the Boltzmann constant, and <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">296</mml:mn></mml:mrow></mml:math></inline-formula> K. In addition to
their different dependence on water vapor density according to Eq. (5), self-
and foreign-broadened continua are characterized by their distinct
temperature dependence: while the self-continuum shows strong negative
temperature dependence, the foreign continuum is assumed to have no or only
weak temperature dependence.</p>
      <p id="d1e1186">The separation of <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>cont</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> into self- and foreign-continuum
contributions from atmospheric measurements is challenging. In principle, an
assignment to self- and foreign continuum is possible using a large set of
measurements covering a wide range of atmospheric conditions, i.e., IWV and
temperature. However, the available data do not permit such an assignment
given the sensitivity of our setup as discussed in Sect. 4. Therefore, in the
following, we characterize continuum strength using the mean continuum
absorption coefficient <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, defined as follows:
            <disp-formula id="Ch1.E6" content-type="numbered"><mml:math id="M69" display="block"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:munderover><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">wv</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">wv</mml:mi></mml:msub><mml:mtext>d</mml:mtext><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">obs</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:munderover><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">wv</mml:mi></mml:msub><mml:mtext>d</mml:mtext><mml:mi>h</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">IWV</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Low-uncertainty constraints on <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can only be placed
in a number of spectral windows. The selection of such suitable windows is
outlined in Sect. 3.4. The continuum results for each spectrum were computed
as the median of <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in all selected spectral windows
within 10 cm<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wide bins. Finally, an error-weighted mean of
<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was calculated from the set of 52 spectra selected
according to the criteria listed in Sect. 3.3. The uncertainty estimate of
the continuum results is presented in Sect. 3.2.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Uncertainty estimate</title>
      <p id="d1e1380">An interpretation of the residual OD and assignment to causative absorption
processes requires a comprehensive uncertainty budget of the closure
experiment. The uncertainty estimate of our experimental setup is described
in detail in Part 1 except for contributions only relevant for the NIR
closure measurements. The total residual uncertainty and its various
contributions are also shown in Part 1, Fig. 5. A description of the
NIR-specific contributions and a brief outline of the remaining sources of
uncertainty are given below. All uncertainty values are quoted at a 2<inline-formula><mml:math id="M74" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>
confidence level.
<list list-type="custom"><list-item><label>i.</label>
      <p id="d1e1392">Absorption line parameter uncertainties of water vapor and other
absorbing species. These uncertainties were set to the mean value of the
uncertainty range specified by the error codes provided in the line parameter
file (aer_v3.2) provided alongside the LBLRTM model. Line parameter
uncertainties are the dominant contribution to the error budget within
absorption bands.</p></list-item><list-item><label>ii.</label>
      <p id="d1e1396">A further significant contribution to the error budget results from the
IWV measurement uncertainty. The IWV precision was set to 0.8 %, the bias
to 1.1 % according Schneider et al. (2012). The uncertainty resulting from
NCEP water vapor profile shape errors was estimated using a comparison of
NCEP profiles to radiosonde data (see Part 1 for details).</p></list-item><list-item><label>iii.</label>
      <p id="d1e1400">The OD uncertainty resulting from NCEP temperature profile errors was
deduced from a temperature error covariance matrix estimate for the NCEP
resimulation profiles. The error covariance matrix estimate was constructed
from the comparison of coincident NCEP profiles to a radiosonde campaign
conducted at the site (see Part 1 for details).</p></list-item><list-item><label>iv.</label>
      <p id="d1e1404">Column uncertainties for further trace gases (e.g., CO<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>, CH<inline-formula><mml:math id="M76" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>,
N<inline-formula><mml:math id="M77" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, and O<inline-formula><mml:math id="M78" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>) are also included in the uncertainty estimate. The
respective column accuracies are listed in Part 1 (Table 2 therein).</p></list-item><list-item><label>v.</label>
      <p id="d1e1444">The AOD uncertainty is of crucial importance for the OD uncertainty
budget in the window regions. As outlined in Sect. 2, the AOD uncertainty at
air mass 1 is <inline-formula><mml:math id="M79" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.0025 for the closure data set throughout the 2500 to
7800 cm<inline-formula><mml:math id="M80" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> range.</p></list-item></list>
The uncertainty contributions i to v listed above are linked to the accuracy
of the atmospheric-state input for LBLRTM calculations. Aside from that, an
additional group of error contributions stems from the solar FTIR spectral
radiance measurements:
<list list-type="custom"><list-item><label>vi.</label>
      <p id="d1e1469">The radiance uncertainty due to the radiometric calibration is about 1–1.7 % and is described in detail in Part 2.</p></list-item><list-item><label>vii.</label>
      <p id="d1e1473">A further uncertainty contribution results from the solar FTIR
measurement noise. It is determined directly from solar FTIR spectra and is
among the few uncertainty contributions in the closure experiment that are of a strictly
statistical character. It is therefore largely reduced by taking mean results
from a larger set of spectra.</p></list-item><list-item><label>viii.</label>
      <p id="d1e1477">Ice layer formation on the liquid-nitrogen-cooled InSb detector can
occur in the case of leaks in the detector's vacuum enclosure. Ice formation
leads to additional absorption in certain spectral regions, most notably in
the 3000 to 3400 cm<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> range. The uncertainty contribution by varying
ice absorption was estimated using lamp spectra routinely recorded with the
solar FTIR. Variations in ice absorption during the time period covered by
the experiment can be detected as a change in the ratio of measured signal
outside and inside the ice absorption band. The maximum variation of this
ratio detected in the lamp spectra (1.6 %) was taken as an estimate of
the error due to ice absorption.</p></list-item><list-item><label>ix.</label>
      <p id="d1e1493">Only a fraction of the solar tracker mirrors is covered by the
instrument's field of view (FOV). Due to the nonideal alignment of optical
elements, the exact location of the area observed by the instrument on the
mirror changes depending on the azimuth and elevation of the instrument's
line of sight. The reflectivity of the tracker mirrors features spatial
inhomogeneity due to dirt and aging effects. In combination with the moving
area covered by the FOV, this results in a variation in measured radiance
which leads to spurious variations in the measured OD. An estimate of this
uncertainty contribution can be gained by using an outgoing laser beam aligned
with the instrument's optical axis that enables constraining the mirror area
covered by the FOV depending on the instrument's azimuth and elevation. A
detailed description of this analysis is given in Part 2, Sect. 4.1.</p></list-item><list-item><label>x.</label>
      <p id="d1e1497">The uncertainty due to inaccuracies in the extra-atmospheric solar spectrum (ESS) was estimated from
repeating the continuum retrieval using the ESS versions by Kurucz (2005) and
Menang et al. (2013), which differ by about 5 % (see Sect. 4). The
corresponding uncertainty contribution corresponds to 11.1 % of the
remaining continuum uncertainty budget on average (see also Fig. 9 of the
companion publication Part 1).</p></list-item></list></p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Spectra selection</title>
      <p id="d1e1506">We analyzed spectra recorded under cloud-free conditions in the
December 2013–February 2014 period. Due to inaccuracies in the air mass
calculation at high solar zenith angle, the air mass was required to be below <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">9.0</mml:mn></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e1521">In Sect. 3.2, we outlined a source of radiance error in the solar FTIR
measurements due to the pointing variation on the tracker mirrors and give an
estimate of this contribution. For spectra included in the closure data set,
this uncertainty contribution was required to be negligible compared to other
sources of uncertainty; more specifically, the selection threshold was set to a
maximum radiance error of 0.1 %. These selection criteria lead to a final
data set of 52 selected solar FTIR spectra covering an IWV range from 1.4 to
3.3 mm, for which the continuum results are presented in Sect. 4. The mean
atmospheric state of the closure data set is listed in Appendix A.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <title>Micro-window selection</title>
      <p id="d1e1530">To select suitable windows for continuum quantification, a number of
selection criteria were applied to the spectra. Several criteria make use of
upper or lower envelopes to the spectra, which were constructed as follows:
the upper/lower envelope is defined as the linear interpolation between the
highest/lowest values encountered within each 10 cm<inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wide wavenumber
bin. Specifically, the following filtering criteria were applied to the spectra:</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p id="d1e1547">Mean continuum absorption coefficient <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
determined in the Zugspitze closure experiment and corresponding 2<inline-formula><mml:math id="M85" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>
uncertainties (black). The figure only includes data points for which the
measured continuum exceeds the estimated uncertainty. A representation of the
full set of measurement results is shown in Fig. B1. Results are compared to
the MT_CKD 2.5.2 model (self- and foreign continuum: light blue; foreign
continuum: dark blue), the BPS-MTCKD 2.0 model (purple line), and the
following laboratory studies carried out at room temperature or below: the
CRDS measurements of Mondelain et al. (2015) (orange), the
calorimetric–interferometric measurements of Bicknell et al. (2006) (green),
and the FTIR measurements of Ptashnik et al. (2012, 2013) (red).</p></caption>
          <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f02.png"/>

        </fig>

      <p id="d1e1577"><list list-type="custom">
            <list-item><label>i.</label>

      <p id="d1e1582">To avoid spectral regions affected by line absorption, only the spectral
points with the lowest OD compared to the surrounding spectral region were
used. Specifically, only points for which the OD exceeds the lower envelope by
less than the 2<inline-formula><mml:math id="M86" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> OD uncertainty were used.</p>
            </list-item>
            <list-item><label>ii.</label>

      <p id="d1e1595">Regions around solar lines were excluded. This was implemented as an
exclusion of all points for which the extra-atmospheric solar radiance
according to the ESS of Kurucz (2005) is more than 0.5 % below the upper
envelope. Note that recent studies indicate that many solar lines are missing
in this ESS (see Menang et al., 2013). However, solar lines omitted in the
ESS of Kurucz (2005) are discarded from further analysis by applying the
selection criterion i. As outlined in Sect. 4, a repetition of the continuum
analysis using the ESS of Menang et al. (2013), which includes many
additional solar lines, only leads to very minor changes in the continuum
results, thereby indicating that the solar line removal scheme according to
criteria i and ii is appropriate.</p>
            </list-item>
            <list-item><label>ii.</label>

      <p id="d1e1601">Only regions with low-OD uncertainty are included. Therefore, we select
points less than 10 % above the lower envelope to the uncertainty.</p>
            </list-item>
            <list-item><label>iv.</label>

      <p id="d1e1607">In order to avoid biases of the retrieved continuum due to measurement
noise, only regions with a signal-to-rms-noise ratio <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M88" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 5 were
included.</p>
            </list-item>
          </list>The selection thresholds cited above were adjusted in order to provide
sufficiently dense coverage with selected points while maintaining optimum
selection quality. Different experimental setups may therefore require
different selection threshold values. The final continuum OD results were
computed as the median value of all selected spectral points within
10 cm<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wide bins.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>Results</title>
      <p id="d1e1651">Figure 1 shows the mean continuum absorption coefficient
<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> determined from the Zugspitze data set in comparison
to the MT_CKD 2.5.2 model predictions and several recent laboratory
studies. The figure includes laboratory measurements carried out at or below
room temperature, which provided constraints on both the self- and foreign
continuum using the same or a very similar experimental setup. The mean
atmospheric state of the closure data set is listed in Appendix A, while a
table with our results for <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the relative scaling
of our results vs. the MT_CKD 2.5.2 predictions and associated
uncertainties are available as a Supplement (Supplement A). The
results shown in Fig. 2 are in very good agreement with the
<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values derived using the Langley method as outlined
in Appendix C. The assignment of the residual OD to water vapor continuum
absorption was made based on two arguments: as outlined in Part 1, great care
was taken to construct a comprehensive uncertainty budget including thorough
estimates of all relevant error contributions to the closure experiment.
Therefore, contributions to the residual OD from processes other than water
vapor continuum absorption far beyond the indicated error bars seem unlikely.
Furthermore, the IWV dependence of the measured residual OD is consistent
with that expected from water vapor continuum absorption. As
<inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> includes contributions due to both foreign and
self-continuum, it is expected to scale as the sum of a constant and a linear
term with respect to water vapor density and therefore also with respect to
IWV. The closure data set covers an IWV range of
1.4 mm <inline-formula><mml:math id="M94" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> IWV <inline-formula><mml:math id="M95" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 3.5 mm, which enables the investigation of the IWV
dependence of <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Due to the narrow range of
atmospheric temperatures covered in the data set, temperature dependence of
the self-continuum can be neglected in this analysis. A fraction of
98.6 % of all measured continuum absorption coefficients in the Zugspitze
data set are consistent with a combination of constant and linear scaling
with respect to IWV, i.e., with being caused by a combination of foreign and
self water vapor continuum. However, 94.2 % of the data are also
consistent with a purely constant scaling, i.e., with being solely due to
foreign-continuum absorption. This is due to the fact that at the atmospheric
conditions covered by the data, in all spectral regions where continuum
absorption is detectable beyond the experiment's sensitivity, the foreign
continuum constitutes by far the dominant contribution, assuming that the
partitioning into self- and foreign continuum given by the MT_CKD model is
approximately correct. Note that this assumption has to be considered
tentative since for both self- and foreign continuum the results of recent
laboratory studies deviate from the MT_CKD model, especially in window
regions (e.g., Ptashnik et al., 2012, 2013; Mondelain et al., 2015). Examples
of the measured <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the best-fit constant and
linear scaling for wavenumber bins within water vapor bands, in the wings of
bands, and in window regions are shown in Fig. A3.</p>
      <p id="d1e1753">This analysis shows that the contribution of the self-continuum is not
unambiguously detectable due to the limited sensitivity of our experiment. We
therefore provide values of the mean continuum absorption coefficient
<inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as defined by Eq. (6), including contributions from
both self- and foreign continuum instead of the more commonly used continuum
coefficients <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>s</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. If values for <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are
required, further assumptions on the self-continuum have to be made before
subtracting this contribution. As an example, Supplement B to this paper contains a list of <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values for all spectral bins where
<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> exceeds the uncertainty estimate. The results were calculated
from our measurements assuming the self-continuum to be consistent with the
MT_CKD model. Recent laboratory measurements (e.g., Ptashnik et al., 2013)
suggest that this assumption may not be appropriate. However, alternative
sources of the self-continuum do not constitute a more robust estimate either,
given the inconsistencies between different laboratory results, the
uncertainty of the self-continuum temperature dependence, and the fact that
the foreign continuum is likely to be the dominant contribution to the
overall continuum absorption for the dry atmospheric conditions of our study
and the spectral windows covered by the measurements (see Fig. 1). A 50 %
uncertainty was assumed for the self-continuum as suggested by Paynter and Ramaswamy (2011) and is included in the uncertainty of <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in addition to
the uncertainty budget presented in Sect. 3.2.</p>
      <p id="d1e1837">As outlined in the companion paper Part 2, recent studies on the NIR ESS have
yielded results that feature differences of up to 5–10 % (see, e.g.,
Menang et al., 2013; Bolsée et al., 2014; Thuillier et al., 2014, 2015;
Weber, 2015). Furthermore, the number of solar lines differs significantly
between, e.g., the ESS versions of Kurucz (2005) and Menang et al. (2013). To
investigate the influence of inaccuracies in the ESS on the continuum
results, the continuum retrieval was repeated using the ESS determined by
Menang et al. (2013) instead of the ESS by Kurucz (2005) that was used to
generate the results presented in Fig. 2. This is a good test to assess the
sensitivity of the results to ESS uncertainty since these ESS versions differ
by about 5 %, while recent ESS results generally feature differences of
up to <inline-formula><mml:math id="M105" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>5 % compared to the ESS of Kurucz (2005). Note that the Menang
et al. (2013) ESS only covers the spectral region <inline-formula><mml:math id="M106" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 4000 cm<inline-formula><mml:math id="M107" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The
comparison is therefore restricted to 4233 cm<inline-formula><mml:math id="M108" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M109" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M110" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M111" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 7800 cm<inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, which corresponds to the first Langley point covered
by the Menang et al. (2013) ESS and the maximum wavenumber value covered by
our analysis. For this region, the median of the absolute value of the
difference between the Menang et al. (2013) and Kurucz (2005) continuum
results corresponds to 11 % of the continuum uncertainty estimate (see
Figs. 3 and 4). Therefore, ESS uncertainty does not constitute a major
accuracy limitation of our analysis, which is due to the fact that the same
ESS is used for both synthetic spectra calculation and the radiometric
calibration presented in the companion paper Part 2. The ESS-related
continuum uncertainty was estimated from the difference of the Menang et
al. (2013) and Kurucz (2005) results and included in the uncertainty budget
as described in Sect. 3.2 (see also Fig. 9 of the companion paper Part 1).
For the spectral region <inline-formula><mml:math id="M113" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M114" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 4233 cm<inline-formula><mml:math id="M115" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, where no direct
comparison is available, the ESS-induced continuum uncertainty was assumed to
correspond to 11 % of the remaining overall uncertainty as suggested by
the median value in the spectral range <inline-formula><mml:math id="M116" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M117" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 4233 cm<inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p id="d1e1967">Mean continuum absorption coefficient derived with the method and
data set described in Sect. 3 using the ESS by Menang et al. (2013) (blue
data points) and by Kurucz (2005) (black data points). The different ESS
sources differ by about 5 % and many solar lines not present in Kurucz (2005)
were included in Menang et al. (2013).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f03.png"/>

      </fig>

      <p id="d1e1977">The prediction of the MT_CKD 2.5.2 model is shown alongside our results
for <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. 1. The MT_CKD 2.5.2 values of
<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were computed in an analogous way to the values
derived from our data set; i.e., <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was calculated
according to Eq. (6) for the set of atmospheric states encountered in the
data set. The results shown in Fig. 1 represent the mean of the MT_CKD
predictions for the set of selected measurements. Overall, there is good
agreement of our results with the MT_CKD values. Consistency within a
2<inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> range is observed for 75 % of the spectral range covered by
our measurements. The most apparent discrepancy between MT_CKD and our
results occurs in the 2800 to 3000 cm<inline-formula><mml:math id="M123" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> range, where our results are
about a factor of 5 higher than the MT_CKD predictions. However, care has
to be taken in the interpretation of this discrepancy since the 2800 to
3000 cm<inline-formula><mml:math id="M124" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral range coincides with a methane absorption band.
Therefore, the accuracy of the continuum result in this range depends on
whether the HITRAN error estimate for methane line parameters is correct and
whether line coupling effects where treated in a sufficiently realistic way
in the LBLRTM model. Further significant discrepancies ensue in the 4100 to
4200 cm<inline-formula><mml:math id="M125" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wavenumber region. The higher measurement results from the
Zugspitze data indicate that the MT_CKD model underestimates the continuum
absorption in the wings of the 4000 to 5000 cm<inline-formula><mml:math id="M126" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> window region. In the
centers of water vapor absorption bands (i.e., <inline-formula><mml:math id="M127" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5200–5400
and <inline-formula><mml:math id="M128" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 7100–7300 cm<inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, our results are significantly lower than
the MT_CKD predictions for a number of spectral points. However, the
continuum results in these regions are highly sensitive to accurate input and
uncertainty estimates for IWV and water vapor line parameters. Therefore, the
slight differences found in the band centers do not provide robust evidence
for the necessary adjustments of the MT_CKD model.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p id="d1e2109">Same as Fig. 3 but using a linear scale to show the results in the
window regions.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f04.png"/>

      </fig>

      <p id="d1e2118">Figure 1 also includes a comparison of our results to several current
laboratory studies using different experimental approaches for continuum
quantification. For the comparison, <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values were
calculated for the same set of atmospheric states as our results using the
continuum coefficients given in the respective studies. For the Mondelain et
al. (2015) and Bicknell et al. (2006) results, we used the MT_CKD
temperature dependence. Since the results of Bicknell et al. (2006) do not
allow a dissociation of self- from foreign continuum, we
assumed the self-to-foreign ratio suggested by the MT_CKD model to
calculate the corresponding value of <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.The self-continuum temperature dependence proposed by Rädel et al. (2015), which,
which was deduced from the measurements of Ptashnik et al. (2011), was used
for all laboratory studies. Note, however, that the importance of the
continuum temperature dependence is limited (5 to 20 %, see below) for
our data set. This is due to the fact that no temperature dependence is
assumed for the foreign continuum, which is by far dominant for most spectral
regions given the dry atmospheric conditions encountered in our data set. A
fraction of the spectral range covered by this study, namely
2500–3200 cm<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, was also included in the airborne measurements by
Newman et al. (2012). Newman et al. (2012) conclude that the increase in the
self-continuum in MT_CKD 2.5 compared to MT_CKD 2.4 led to reduced
spectral residuals, while no firm conclusion can be drawn in the
2500–3200 cm<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> range on whether MT_CKD 2.5 or the results of
Ptashnik et al. (2011) represent a more appropriate quantitative description
of the water vapor self-continuum. These findings are in agreement to the
results of this study, given that both are not consistent with continuum
absorption being weaker than indicated by MT_CKD 2.5. Our results show
very good agreement with the CDRS-based measurements of Mondelain et al. (2015). Due to the dominant role of the foreign continuum in the 4100 to
4200 cm<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> spectral range, this agreement mainly corresponds to a
comparison of the foreign-continuum results of Mondelain et al. (2015) and
our measurements. Therefore, our results are consistent with the finding of
Mondelain et al. (2015) and Ptashnik et al. (2012) that the foreign continuum
is underestimated by the MT_CKD model in this spectral region. For the
spectral range examined by Bicknell et al. (2006) with
calorimetric–interferometric measurements, only the upper limit of the
continuum absorption is constrained by our data, which is consistent with all
laboratory studies cited here. The comparison of our results to the
BPS_MTCKD 2.0 continuum proposed by Paynter and Ramaswamy (2014) is mostly
equivalent to the comparison to MT_CKD. This is due to the fact that the
BPS_MTCD 2.0 foreign continuum, which constitutes the dominant contributor
for the dry atmospheric conditions encountered in our data set, was mostly
adopted from MT_CKD. Exceptions include the spectral regions from 2500 to
3000, 5200 to 5600, and 6800 to 7000 cm<inline-formula><mml:math id="M135" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, where our results show
better consistency with the MT_CKD 2.5.2 model. The FTIR-based results of
Ptashnik et al. (2012, 2013) in combination with the temperature dependence
proposed by Rädel et al. (2015) lead to higher absorption coefficients
than our data in several spectral regions. Significant inconsistencies beyond
the uncertainty range occur mostly in the wings of water vapor absorption
bands, e.g., in the 3200 to 3400 and 4000 to 4200 cm<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ranges, as seen in Fig. 1. In these ranges the absorption coefficients provided by
the FTIR laboratory measurements are typically a factor of 2–3 higher
compared to our data. Further FTIR laboratory measurements were carried out
by Baranov and Lafferty (2011) at temperatures of 311 to 363 K on the self-continuum and by Baranov and Lafferty (2011) at 326 to 363 K on the foreign continuum at
<inline-formula><mml:math id="M137" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M138" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 3500 cm<inline-formula><mml:math id="M139" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The results of these studies generally agree
well within the estimated errors with the findings of Ptashnik et al. (2012,
2013). As noted by, e.g., Ptashnik et al. (2015), weak lines not included in
the line list used for the synthetic spectra calculation may bias the
retrieved continuum results. This effect is largely reduced in our analysis
due to the spectral selection criteria applied, namely the selection of
low-OD windows as outlined in Sect. 3.4, criterion i. An issue not accounted
for in our analysis is the uncertainty of the continuum temperature
dependence, since an uncertainty estimate is provided neither for the
MT_CKD nor the Rädel et al. (2015) relations. However, under the
atmospheric conditions covered by our data set and assuming the MT_CKD
self-to-foreign ratio, the self-continuum contributes only 10 to 30 % to
the total continuum absorption at the spectral points for which we detect
significant continuum absorption. While no temperature dependence is assumed
for the dominant foreign contribution, the temperature dependence of the self-continuum changes the mean continuum absorption coefficient by 5 to 20 %
within the spectral range considered here and assuming the Rädel et
al. (2015) relation. Therefore, it seems unlikely that the differences
between the results of Ptashnik et al. (2012, 2013) and our data are solely
due to inaccuracies in the continuum temperature dependence. Note, however
that the assumption that the foreign continuum has no significant temperature
dependence, which was used in the data analysis, has not been robustly
confirmed by measurements under atmospheric conditions yet. Due to the
dominant role of the foreign continuum in the wings of water vapor absorption
bands, inaccuracies in the foreign-continuum temperature dependence would
have a significant influence on the conversion of the findings of Ptashnik et
al. (2012, 2013) to atmospheric temperatures.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Summary and conclusions</title>
      <p id="d1e2243">We present a quantification of the water vapor continuum absorption in the
NIR spectral range (2500 to 7800 cm<inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> from an atmospheric radiative
closure experiment. To our knowledge, prior to this study no precise
constraints on the continuum absorption under atmospheric conditions were
available for most of this spectral range. The mean continuum absorption
coefficient was determined from a set of 52 solar FTIR spectra. The method to
achieve continuum quantification relies on the use of radiometrically
calibrated spectra obtained by the method presented in Part 2. Continuum
constraints are presented in the wings and some spectral windows in the
centers of water vapor absorption bands. Due to the low IWV encountered
throughout our measurement period, only the upper boundary of the continuum
can be constrained in the centers of atmospheric windows.</p>
      <p id="d1e2261">The results show good consistency with the widely used MT_CKD 2.5.2 model,
although they indicate a need for increasing the absorption strength compared
to the model in some spectral regions such as the wings of water vapor
absorption bands. Our results were compared to a number of recent laboratory
studies using different experimental techniques. A first group of studies
relies on FTIR cell measurements. Our data generally indicate lower continuum
absorption than implied by the studies of Ptashnik et al. (2012, 2013) in
combination with the self-continuum temperature dependence given in Rädel
at al. (2015). However, significant deviations from these studies only occur
in the wings of water vapor absorption bands. There are also several regions
where our results are in good agreement with the findings of Ptashnik et
al. (2012, 2013), most notably around 3000 cm<inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Further experimental
techniques used for continuum quantification in laboratory experiments
include CRDS. A comparison to the CDRS results of Mondelain et al. (2015) in
the spectral region around 4250 cm<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> shows very good agreement with our
findings. Bicknell et al. (2006) quantified continuum absorption using a
calorimetric–spectrometric technique. While our results agree with the findings
of Bicknell et al. (2006), their measurements cover spectral regions where
only an upper limit for the continuum absorption can be deduced from our
data.</p>
      <p id="d1e2288">An assignment of the detected continuum absorption to self- and foreign
continuum requires improvements of the experimental sensitivity or a
data<?xmltex \hack{\vadjust{\newpage}}?> set covering a broader range of IWV values. The
same is true for a detection of the continuum beyond the uncertainty limit in
window regions which requires improved sensitivity or a data set covering
higher IWV values. Aside from these limitations, our results provide a
valuable foundation for an improved quantification of the NIR water vapor
continuum under atmospheric conditions. Most notably, our analysis provides a
tool for atmospheric validation of the predictions of current laboratory
studies and the MT_CKD continuum model in the NIR spectral range. This is
of crucial importance since the results of recent studies carried out using
different experimental techniques show inconsistent results and to date no
experimental validation under atmospheric conditions was available.</p>
</sec>
<sec id="Ch1.S6">
  <title>Data availability</title>
      <p id="d1e2299">The mean water vapor continuum absorption coefficients derived in this
study and shown in Figs. 2, 3 ,4, and B1 are provided in the Supplement. Additional underlying data can be obtained at any time from the corresponding author on
demand.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <title>Mean atmospheric state of the closure data set</title>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.T1"><caption><p id="d1e2315">Mean atmospheric state of the closure data set: <?xmltex \hack{\mbox\bgroup}?>pressure,<?xmltex \hack{\egroup}?>
temperature, and water vapor density profiles. The data set was selected
from Zugspitze solar FTIR spectra measured from December 2013 to February 2014 and
contains 52 spectra. Spectra selection criteria are listed in Sect. 3.3.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.96}[.96]?><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="39.833858pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="51.214961pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="39.833858pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="51.214961pt"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Altitude</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math id="M143" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math id="M144" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><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:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">(km a.s.l.)</oasis:entry>  
         <oasis:entry colname="col2">(mbar)</oasis:entry>  
         <oasis:entry colname="col3">(K)</oasis:entry>  
         <oasis:entry colname="col4">(g m<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">2.964 <?xmltex \hack{\hfill\break}?>2.975 <?xmltex \hack{\hfill\break}?>2.987 <?xmltex \hack{\hfill\break}?>3.009 <?xmltex \hack{\hfill\break}?>3.032 <?xmltex \hack{\hfill\break}?>3.066 <?xmltex \hack{\hfill\break}?>3.099 <?xmltex \hack{\hfill\break}?>3.147 <?xmltex \hack{\hfill\break}?>3.262 <?xmltex \hack{\hfill\break}?>3.497 <?xmltex \hack{\hfill\break}?>3.600 <?xmltex \hack{\hfill\break}?>3.700 <?xmltex \hack{\hfill\break}?>3.800 <?xmltex \hack{\hfill\break}?>3.900 <?xmltex \hack{\hfill\break}?>4.000 <?xmltex \hack{\hfill\break}?>4.100 <?xmltex \hack{\hfill\break}?>4.200 <?xmltex \hack{\hfill\break}?>4.300 <?xmltex \hack{\hfill\break}?>4.400 <?xmltex \hack{\hfill\break}?>4.500 <?xmltex \hack{\hfill\break}?>4.600 <?xmltex \hack{\hfill\break}?>4.700 <?xmltex \hack{\hfill\break}?>4.800 <?xmltex \hack{\hfill\break}?>4.900 <?xmltex \hack{\hfill\break}?>5.000 <?xmltex \hack{\hfill\break}?>5.500 <?xmltex \hack{\hfill\break}?>6.000 <?xmltex \hack{\hfill\break}?>6.500 <?xmltex \hack{\hfill\break}?>7.000 <?xmltex \hack{\hfill\break}?>8.000 <?xmltex \hack{\hfill\break}?>9.000 <?xmltex \hack{\hfill\break}?>10.00 <?xmltex \hack{\hfill\break}?>15.00 <?xmltex \hack{\hfill\break}?>20.00 <?xmltex \hack{\hfill\break}?>30.00 <?xmltex \hack{\hfill\break}?>40.00 <?xmltex \hack{\hfill\break}?>60.00 <?xmltex \hack{\hfill\break}?>100.0 <?xmltex \hack{\hfill\break}?>120.0</oasis:entry>  
         <oasis:entry colname="col2">714.074 <?xmltex \hack{\hfill\break}?>713.085 <?xmltex \hack{\hfill\break}?>712.008<?xmltex \hack{\hfill\break}?>710.036 <?xmltex \hack{\hfill\break}?>707.982 <?xmltex \hack{\hfill\break}?>704.946 <?xmltex \hack{\hfill\break}?>702.000 <?xmltex \hack{\hfill\break}?>697.763 <?xmltex \hack{\hfill\break}?>687.664 <?xmltex \hack{\hfill\break}?>667.380 <?xmltex \hack{\hfill\break}?>658.649 <?xmltex \hack{\hfill\break}?>650.259 <?xmltex \hack{\hfill\break}?>641.950 <?xmltex \hack{\hfill\break}?>633.727 <?xmltex \hack{\hfill\break}?>625.592 <?xmltex \hack{\hfill\break}?>617.538 <?xmltex \hack{\hfill\break}?>609.570 <?xmltex \hack{\hfill\break}?>601.680 <?xmltex \hack{\hfill\break}?>593.871 <?xmltex \hack{\hfill\break}?>586.147 <?xmltex \hack{\hfill\break}?>578.503 <?xmltex \hack{\hfill\break}?>570.935 <?xmltex \hack{\hfill\break}?>563.441 <?xmltex \hack{\hfill\break}?>556.027 <?xmltex \hack{\hfill\break}?>548.693 <?xmltex \hack{\hfill\break}?>513.149 <?xmltex \hack{\hfill\break}?>479.451 <?xmltex \hack{\hfill\break}?>447.548 <?xmltex \hack{\hfill\break}?>417.379 <?xmltex \hack{\hfill\break}?>361.924 <?xmltex \hack{\hfill\break}?>312.542 <?xmltex \hack{\hfill\break}?>68.744 <?xmltex \hack{\hfill\break}?>123.703 <?xmltex \hack{\hfill\break}?>54.6496 <?xmltex \hack{\hfill\break}?>10.775 <?xmltex \hack{\hfill\break}?>2.488 <?xmltex \hack{\hfill\break}?>0.179<?xmltex \hack{\hfill\break}?>2.77 <inline-formula><mml:math id="M147" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>2.38 <inline-formula><mml:math id="M149" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M150" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">270.570 <?xmltex \hack{\hfill\break}?>270.522 <?xmltex \hack{\hfill\break}?>270.469 <?xmltex \hack{\hfill\break}?>270.372 <?xmltex \hack{\hfill\break}?>270.271 <?xmltex \hack{\hfill\break}?>270.121 <?xmltex \hack{\hfill\break}?>269.974 <?xmltex \hack{\hfill\break}?>269.671 <?xmltex \hack{\hfill\break}?>268.899 <?xmltex \hack{\hfill\break}?>267.256 <?xmltex \hack{\hfill\break}?>266.536 <?xmltex \hack{\hfill\break}?>265.838 <?xmltex \hack{\hfill\break}?>265.139 <?xmltex \hack{\hfill\break}?>264.440 <?xmltex \hack{\hfill\break}?>263.741 <?xmltex \hack{\hfill\break}?>263.042 <?xmltex \hack{\hfill\break}?>262.342 <?xmltex \hack{\hfill\break}?>261.644 <?xmltex \hack{\hfill\break}?>260.919 <?xmltex \hack{\hfill\break}?>260.186 <?xmltex \hack{\hfill\break}?>259.455 <?xmltex \hack{\hfill\break}?>258.723 <?xmltex \hack{\hfill\break}?>257.991 <?xmltex \hack{\hfill\break}?>257.260 <?xmltex \hack{\hfill\break}?>256.528 <?xmltex \hack{\hfill\break}?>252.871 <?xmltex \hack{\hfill\break}?>249.366 <?xmltex \hack{\hfill\break}?>245.966 <?xmltex \hack{\hfill\break}?>242.567 <?xmltex \hack{\hfill\break}?>235.748 <?xmltex \hack{\hfill\break}?>228.923 <?xmltex \hack{\hfill\break}?>222.463 <?xmltex \hack{\hfill\break}?>213.438 <?xmltex \hack{\hfill\break}?>209.890 <?xmltex \hack{\hfill\break}?>212.607 <?xmltex \hack{\hfill\break}?>248.853 <?xmltex \hack{\hfill\break}?>239.829 <?xmltex \hack{\hfill\break}?>213.601 <?xmltex \hack{\hfill\break}?>378.719</oasis:entry>  
         <oasis:entry colname="col4">1.270 <?xmltex \hack{\hfill\break}?>1.266 <?xmltex \hack{\hfill\break}?>1.263 <?xmltex \hack{\hfill\break}?>1.256 <?xmltex \hack{\hfill\break}?>1.249 <?xmltex \hack{\hfill\break}?>1.239 <?xmltex \hack{\hfill\break}?>1.229 <?xmltex \hack{\hfill\break}?>1.201 <?xmltex \hack{\hfill\break}?>1.127 <?xmltex \hack{\hfill\break}?>0.966 <?xmltex \hack{\hfill\break}?>0.898 <?xmltex \hack{\hfill\break}?>0.833 <?xmltex \hack{\hfill\break}?>0.769 <?xmltex \hack{\hfill\break}?>0.707 <?xmltex \hack{\hfill\break}?>0.645 <?xmltex \hack{\hfill\break}?>0.585 <?xmltex \hack{\hfill\break}?>0.526 <?xmltex \hack{\hfill\break}?>0.468 <?xmltex \hack{\hfill\break}?>0.446 <?xmltex \hack{\hfill\break}?>0.436 <?xmltex \hack{\hfill\break}?>0.425 <?xmltex \hack{\hfill\break}?>0.415 <?xmltex \hack{\hfill\break}?>0.405 <?xmltex \hack{\hfill\break}?>0.395 <?xmltex \hack{\hfill\break}?>0.385 <?xmltex \hack{\hfill\break}?>0.338 <?xmltex \hack{\hfill\break}?>0.261 <?xmltex \hack{\hfill\break}?>0.169 <?xmltex \hack{\hfill\break}?>0.087 <?xmltex \hack{\hfill\break}?>0.027 <?xmltex \hack{\hfill\break}?>9.69 <inline-formula><mml:math id="M151" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>2.96 <inline-formula><mml:math id="M153" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M154" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>4.17 <inline-formula><mml:math id="M155" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M156" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>2.35 <inline-formula><mml:math id="M157" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M158" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>6.27 <inline-formula><mml:math id="M159" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M160" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>1.41 <inline-formula><mml:math id="M161" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M162" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>9.17 <inline-formula><mml:math id="M163" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M164" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>1.13 <inline-formula><mml:math id="M165" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M166" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>8.74 <inline-formula><mml:math id="M167" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M168" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \hack{\newpage}?><?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.T2"><caption><p id="d1e2941">Mean atmospheric state of the closure data set: trace gas column
amounts. The data set was selected from Zugspitze solar FTIR spectra
measured from December 2013 to February 2014 and contains 52 spectra. Spectra
selection criteria are listed in Sect. 3.3.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">IWV</oasis:entry>  
         <oasis:entry colname="col2">2.26 mm</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">XCO<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">395.3 ppm</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">XCH<inline-formula><mml:math id="M170" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">1781 ppb</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">XN<inline-formula><mml:math id="M171" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O</oasis:entry>  
         <oasis:entry colname="col2">311.8 ppb</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">O<inline-formula><mml:math id="M172" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> column</oasis:entry>  
         <oasis:entry colname="col2">279.9 DU</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\clearpage}?>
</app>

<app id="App1.Ch1.S2">
  <title>Appendix figures</title>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.F1"><caption><p id="d1e3045">Mean continuum absorption coefficient <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
determined in the Zugspitze closure experiment and corresponding 2<inline-formula><mml:math id="M174" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>
uncertainties (black). Results are compared to the MT_CKD 2.5.2 model
(self- and foreign continuum: light blue; foreign continuum: dark blue), the
BPS-MTCKD 2.0 model (purple line), and the following laboratory studies
carried out at room temperature or below: the CRDS measurements of Mondelain
et al. (2015) (orange), the calorimetric–interferometric measurements of
Bicknell et al. (2006) (green), and the FTIR measurements of Ptashnik et al. (2012, 2013) (red).</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=412.564961pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f05.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.F2"><caption><p id="d1e3079">Examples of the scaling of the mean continuum absorption
coefficient <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (black data points) with respect to
IWV <bold>(a)</bold> within a water vapor absorption band (4100 cm<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <bold>(b)</bold> in the
wings of an absorption band (4700 cm<inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <bold>(c)</bold> in a window region
(2700 cm<inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The blue line corresponds to the best-fit constant
scaling, the red line to the best-fit linear scaling.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=312.980315pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f06.png"/>

      </fig>

<?xmltex \hack{\clearpage}?>
</app>

<app id="App1.Ch1.S3">
  <title>Continuum quantification using the Langley method</title>
      <p id="d1e3167">Langley measurements (see, e.g., Liou, 2002 and Part 2) are part of the
radiometric calibration method employed in this study which is presented
in the companion paper Part 2. These Langley measurements can be used to
directly quantify the water vapor continuum as outlined by Mlawer et
al. (2014), thereby offering a validation of the results obtained with the
method presented in Sect. 3. For continuum quantification according to this
strategy, spectrally resolved atmospheric optical depth is determined using
the Langley method for all wavenumber values according to the analysis scheme
presented in Part 2. The atmospheric optical depth without water vapor
continuum absorption is then calculated using the LBLRTM model using the
atmospheric-state input set as outlined in Sect. 3 and the companion paper
Part 1. Residual optical depth between Langley result and model calculation
in spectral windows selected according to Sect. 3.4 is interpreted as water
vapor continuum absorption.</p>
      <p id="d1e3170">The OD uncertainty budget required for the window selection in the case of
the Langley method is largely similar to the uncertainty estimate described
in Sect. 3.2. Differences include the absence of the calibration uncertainty,
which is replaced by the OD uncertainty of the Langley fit, including the
uncertainty contribution due to air mass inaccuracies. Furthermore, the error
due to changing ice absorption on the detector is not included in the error
budget, since, by construction, the Langley method is only sensitive to
atmospheric absorption. The mean continuum absorption coefficient is then
calculated from the residual OD as described in Sect. 3.1.</p>
      <p id="d1e3173">Figure C1 shows the mean continuum absorption coefficients derived from the
Langley measurements made on 12 December 2013 (black data points). The
results are compared to<?xmltex \hack{\vadjust{\newpage}}?> the MT_CKD 2.5.2 model (blue line) and the results
obtained with the calibrated method according to Sect. 3. (orange data
points), which were calculated for the same set of 16 spectra used in the
Langley method. Throughout 98.0 % of spectral range for which results
from both methods are available, the absorption coefficients are consistent
within the 2<inline-formula><mml:math id="M179" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> error estimate. While in window regions both methods
are equally suitable for continuum quantification, large errors due to air
mass uncertainties make the use of the calibrated method presented in Sect. 3
preferable in the vicinity of water vapor absorption bands.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.F3"><caption><p id="d1e3187">Mean continuum absorption coefficient <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">cont</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
determined from 12 December 2013 spectra using the Langley method and
corresponding 2<inline-formula><mml:math id="M181" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> uncertainties (black). Results are compared to the
calibrated method for the same spectral data set (orange) and the MT_CKD
2.5.2 model (blue).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/16/11671/2016/acp-16-11671-2016-f07.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><supplementary-material position="anchor"><p id="d1e3219"><bold>The Supplement related to this article is available online at <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-16-11671-2016-supplement" xlink:title="zip">https://doi.org/10.5194/acp-16-11671-2016-supplement</inline-supplementary-material>.</bold></p></supplementary-material>
</app>
  </app-group><ack><title>Acknowledgements</title><p id="d1e3227">We are grateful for the constructive and helpful reviews and short comments, which
led to significant improvements of this paper. We furthermore thank
H. P. Schmid (KIT/IMK-IFU) for his continual interest in this work. Funding
by the Bavarian State Ministry of the Environment and Consumer Protection
(contracts TLK01U-49581 and VAO-II TP I/01) and Deutsche Bundesstiftung
Umwelt is gratefully acknowledged. It is our pleasure to thank E. Mlawer
(AER) for suggesting the exploitation of our Zugspitze solar FTIR
measurements for NIR continuum quantification, which is the subject of this
paper. The authors are indebted to D. D. Turner (NOAA) for helpful
conversations during the definition phase of the Zugspitze radiance closure
project. We furthermore thank Ulf Köhler (Meteorologisches Observatorium
Hohenpeißenberg, DWD) for providing ozone column measurements,
Matthias Wiegner (LMU München) for access to sun photometer measurement
data, and Petra Hausmann (KIT/IMK-IFU) for providing IWV retrievals. We are
grateful for support by the Deutsche Forschungsgemeinschaft and the Open Access
Publishing Fund of the 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: H.
Maring<?xmltex \hack{\newline}?> Reviewed by: P. Rowe and one anonymous referee</p></ack><ref-list>
    <title>References</title>

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    <!--<article-title-html>The Zugspitze radiative closure experiment for quantifying water vapor absorption over the terrestrial and solar infrared – Part 3: Quantification of the mid- and near-infrared water vapor continuum in the 2500 to 7800 cm<sup>−1</sup> spectral range under atmospheric conditions</article-title-html>
<abstract-html><p class="p">We present a first quantification of the near-infrared (NIR) water vapor
continuum absorption from an atmospheric radiative closure experiment carried
out at the Zugspitze (47.42° N, 10.98° E; 2964 m a.s.l.).
Continuum quantification is achieved via radiative closure using
radiometrically calibrated solar Fourier transform infrared (FTIR) absorption spectra covering the 2500 to
7800 cm<sup>−1</sup> spectral range. The dry atmospheric conditions at the
Zugspitze site (IWV 1.4 to 3.3 mm) enable continuum quantification even
within water vapor absorption bands, while upper limits for continuum
absorption can be provided in the centers of window regions. Throughout
75 % of the 2500 to 7800 cm<sup>−1</sup> spectral range, the Zugspitze results agree within our estimated uncertainty with the widely used MT_CKD
2.5.2 model (Mlawer et al., 2012). In the wings of water vapor absorption
bands, our measurements indicate about 2–5 times stronger continuum
absorption than MT_CKD, namely in the 2800 to 3000 cm<sup>−1</sup> and 4100 to
4200 cm<sup>−1</sup> spectral ranges. The measurements are consistent with the
laboratory measurements of Mondelain et al. (2015), which rely on cavity
ring-down spectroscopy (CDRS), and the calorimetric–interferometric
measurements of Bicknell et al. (2006). Compared to the recent FTIR
laboratory studies of Ptashnik et al. (2012, 2013), our measurements are
consistent within the estimated errors throughout most of the spectral range.
However, in the wings of water vapor absorption bands our measurements
indicate typically 2–3 times weaker continuum absorption under atmospheric
conditions, namely in the 3200 to 3400, 4050 to 4200, and 6950 to
7050 cm<sup>−1</sup> spectral regions.</p></abstract-html>
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