spectroscopic determination of atmospheric water vapor

Spectroscopic Determination of Atmospheric Water VaporAuthor(s): R. R. Querel, D. A. Naylor and F. KerberSource: Publications of the Astronomical Society of the Pacific, Vol. 123, No. 900 (February2011), pp. 222-229Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/658285 .

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Spectroscopic Determination of Atmospheric Water Vapor

R. R. QUEREL,1 D. A. NAYLOR,1 AND F. KERBER2

Received 2010 October 27; accepted 2010 November 23; published 2011 February 9

ABSTRACT. Atmospheric water vapor is the principal source of opacity at infrared wavelengths. Spectral ob-servations of a star with a featureless continuum, such as a white dwarf, provide a method of determining atmo-spheric absorption along the line of sight to the star. Through fitting a site-specific atmospheric transmission modelto high-resolution atmospheric absorption measurements, it is possible to determine the water vapor column abun-dance expressed in millimeters of precipitable water vapor (PWV). While more challenging in interpretation, emis-sion spectra can also be used to derive PWV. This article describes a general algorithm that we have developed forretrieving PWV from both atmospheric transmission and emission spectra. The retrieved PWV values have beenvalidated by intercomparison with contemporaneous measurements provided by radiosonde balloons and emissionradiometers.

Online material: color figures

1. OVERVIEW

This article describes an automated method to determine pre-cipitable water vapor (PWV) by fitting a simulated atmosphericspectrum to measured absorption or emission-line spectra.

Atmospheric water vapor is the principal source of opacity atinfrared wavelengths. Spectral observations of a star with an al-most featureless continuum, such as a white dwarf, provide amethod of determining atmospheric absorption along the lineof sight to the star. A serendipitous by-product of these spectrais that they provide a simultaneous measure of the many absorp-tion lines due to atmospheric water vapor. Since these transi-tions occur at visible and near-infrared wavelengths, they havehigh excitation energies, and the derived column abundancesare thus less sensitive to the atmospheric model used in theretrieval process, because the corresponding levels are not pop-ulated at typical atmospheric temperatures. The measured spec-trum can be iteratively fitted to a model atmospheric spectrum toretrieve PWV. In principle, this technique can used to fit bothabsorption and emission spectra.

2. INTRODUCTION

The impetus behind the development of a spectral line-fittingtechnique to retrieve PWV data from a range of spectroscopicinstruments was to provide an independent method of cross-calibrating an infrared radiometer developed by our group.

The Infrared Radiometer for Millimetre Astronomy (IRMA)(Naylor et al. 2008) measures atmospheric emission in a care-fully selected spectral band (∼2 μm wide), defined by a band-pass optical filter, centered at a wavelength of ∼20 μm, near thepeak of the Planck curve for typical atmospheric temperatures(∼260 K). The detected flux is converted to PWV by use of asophisticated atmospheric radiative transfer model. Since IRMAoperates in the thermal-infrared region, however, it is sensitiveto any source of stray radiation from ambient temperaturesources that may be in the field of view and thus requires carefulcalibration.

While the IRMA units have been shown to provide accuratePWVmeasurements in a relative sense (i.e., when two colocatedIRMA units are measuring the same patch of sky), their calibra-tion in terms of retrieving absolute PWV values has remained achallenge (Querel et al. 2008). To further investigate this issue,researchers at the Las Campanas Observatory (LCO) comparedPWV values derived from IRMA with those extracted fromstandard star calibration measurements taken with the MagellanInamori Kyocera Echelle (MIKE) spectrograph (Bernsteinet al. 2003).

MIKE is a facility instrument on the Clay Magellan 6.5 mtelescope, located at LCO. Several rapidly rotating A- and B-type stars, with magnitudes between 4 and 6, were chosen ascalibration targets, as they are expected to have few broadenedphotospheric features in the wavelength range of interest.Furthermore, there are a sufficient number of these stars distrib-uted across the sky to make feasible their use as calibration tar-gets. PWV measurements with MIKE are routinely made onceper night under clear sky conditions (Thomas-Osip et al. 2007).While dedicating a 6.5 m class telescope to monitoring PWV is

1Institute for Space Imaging Science, Department of Physics and Astronomy,University of Lethbridge, Lethbridge, Alberta, Canada, T1K 3M4.

2 European Southern Observatory, Karl-Schwarzschild Strasse 2, 85748Garching bei München, Germany.

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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 123:222–229, 2011 February© 2011. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.



impractical, these spot measurements provide a useful databasefor comparison with other instruments.

Currently, MIKE-derived PWV values are based on a fewcarefully selected, isolated, weak atmospheric water vapor lines,using the equivalent-width method first proposed by Brault et al.(1975) and addressed further by Thomas-Osip et al. (2007).This method uses a simple single-layer atmospheric model.The spectral region in which these weak lines are found, how-ever, contains over 1000 water vapor lines of varying strengthsand overlaps. A single-layer atmospheric model accurately re-presents the absorption spectrum of molecular oxygen, due tothe fact that the species has a well-defined mixing ratio and ver-tical distribution profile, defined by its scale height. The mixingratio and vertical distribution of atmospheric water vapor, how-ever, are highly variable. A more realistic multilayer atmo-spheric model based on average site-specific meteorologicalparameters discussed later allows a more accurate determinationof PWV.

Our group has developed a sophisticated radiative transfermodel, the Blue Sky Transmission and Radiance AtmosphericModel (BTRAM),3 which has been used to simulate the atmo-sphere above a variety of observing sites around the world.BTRAM is a user-friendly, line-by-line, layer-by-layer full ra-

diative transfer model that uses the HITRAN 2008 database ofmolecular parameters (Rothman et al. 2009). One of the keyfeatures of BTRAM is that it allows the user to input site-specific meteorological parameters, often obtained from radio-sondes, meteorological towers, etc., to produce a more realistictransmission or emission spectrum. These include, but are notlimited to, the base temperature and pressure, the vertical pro-files of temperature and pressure, and the scale height of watervapor. For example, typical values for the scale height of watervapor can vary between 1.5 and 2.5 km, leading to a high degreeof uncertainty in retrieved PWV values: i.e., on the orderof ∼25%. Since radiosondes offer the best source of verticaldistribution data, and thus the scale height of water vapor, in-corporating this site-derived information into the model isinvaluable.

A model atmospheric transmission spectrum is shown in Fig-ure 1. The upper plot shows the absorption due to atmosphericwater vapor for a column abundance of 1 mm PWV. The lowerplot shows the equivalent spectrum containing the other princi-pal constituents responsible for absorption in this range (mostlyCO2 and O2), excluding water vapor. Examination of these plotsshows that there are several spectral regions where water vaporis the sole source of opacity and can be isolated for analysis. Inthis study we have selected the regions delineated by the verticallines, which were chosen because they include a wide range ofwater vapor transition lines strengths.

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FIG. 1.—Transmission spectrum produced by BTRAM for the atmosphere above the Las Campanas Observatory. Top: Transmission spectrum for water vapor alone(PWV ¼ 1 mm). Bottom: Transmission due to CO2 and O2—the only other significant sources of opacity in this spectral region. The vertical bars delineate three regionsused for fitting to the echelle data, centered at ∼720, ∼830, and ∼930 nm. See the electronic edition of the PASP for a color version of this figure.

3See http://blueskyspectroscopy.com/; (Chapman et al. 2011, in preparation).

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An algorithm was developed in the IDL® programmingenvironment using the Levenberg-Marquardt nonlinear least-squares (NLLS) minimization routine (Markwardt 2009) tofit high-resolution spectrograph measurements to a simulatedatmospheric spectrum. When this algorithm was first appliedto MIKE data, the resulting PWV was found to be ∼25% higherthan the values determined using the simpler Brault method(Querel et al. 2008). The source of this discrepancy has sincebeen identified as resulting from their use of the natural log ofthe line flux, which Brault et al. (1975) had claimed as a quickmethod for obtaining PWV for lines with central depths lessthan 50%. A rigorous analysis has shown that the Brault methodonly returns accurate values for central-line depths less than20%, thus limiting its range of applicability (Thomas-Osipet al. 2010).

3. FITTING SPECTRAL DATA: ABSORPTION

The method we have developed to fit the theoretical BTRAMspectrum to generic echelle spectra is outlined in Figure 2. Byway of illustration, this method has been used to analyze MIKEdata. The MIKE data we used were reduced using the standardpipeline, for which the final data product is a Flexible ImageTransport System file containing spectra for the source and vari-ous housekeeping data for every diffraction order of the MIKEobservation.4 After ingesting the MIKE data, the wavelengthscale is first corrected for vacuum wavelengths and the contin-uum established. The wavelengths at which the continuum is

evaluated are determined by first examining the regions ofthe BTRAM spectrum that have absorption less than 0.2%;these corresponding regions are mapped onto the MIKE data.A low-order polynomial is fitted to these selected continuumregions to establish a normalized transmission spectrum.

The theoretical atmospheric transmission spectrum is itera-tively fitted to the normalized MIKE spectrum using the NLLSalgorithm. The fit parameters include PWV, the instrumentalline shape, and a wavelength-dependent shift. In principle,a spectrometer-specific instrumental line shape (ILS) couldbe used; however, in general, the ILS for an echelle spectro-graph is well approximated by a Gaussian profile, which wehave adopted. The model spectrum is computed at a higherresolution (Δλ ¼ 0:001 nm or, typically, a factor of 10) thanthe MIKE data to retain computational accuracy followingconvolution with the ILS. Under the assumption that the dis-tribution of water vapor in the atmosphere is constant, thecomputation can proceed in opacity space. In this space,the opacity, τ(λ), can be linearly scaled by the fitting algorithmand, upon convergence, converted into a resultant transmissionspectrum, T ðλÞ ¼ e�τðλÞ.

3.1. Results

Comparisons of the MIKE data and the best-fit BTRAMmodel for two spectral ranges, 715–730 and 813–838 nm,are shown in Figures 3 and 4 for both a dry night (left) anda wet night (right). The top graphs in each figure show a10 nm range: i.e., 715–725 and 814–824 nm, respectively.The middle and bottom plots show two different expanded re-gions of the upper plots, each 2 nm wide: i.e., 718–720, 723–725, 814–816, and 822–824 nm, respectively. In each plot theupper trace is the MIKE data, the middle trace is the fittedBTRAM spectrum displaced for clarity, and the bottom traceis the residual difference between the MIKE data and BTRAMmodel. There is seen to be excellent agreement across the com-plex manifold of water vapor lines observed by MIKE, whichjustifies the underlying assumption that the ILS is well repre-sented by a Gaussian. It can also be seen that the signal-to-noiseratio in the 720 nm band is superior to that observed in the830 nm band. Instrumental artifacts become apparent in the930 nm band, making removal of the continuum more challeng-ing. For this reason, derivation of water vapor using the 930 nmband has not been included in the current analysis.

3.2. Effect of Varying Resolution

In principle, the fitting routine should work effectively for aspectrum of any resolution. To verify this effect, we analyzeddata taken from the Ultraviolet and Visual Echelle Spectrograph(UVES) (Dekker et al. 2000). UVES is installed at the Nasmythplatform of one of the 8.2 m telescopes at the European South-ern Observatory’s (ESO) Very Large Telescope (VLT) at theParanal observatory site in northern Chile. In a dedicated test,

Identify the continuum

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FIG. 2.—Flowchart depicting the fitting of a simulated spectrum to a genericabsorption spectrum.

4 MIKE pipeline: http://obs.carnegiescience.edu/Code/mike.

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the resolution of UVES was varied by adjusting the slit widthbetween 0.3, 0.5, 1, 2, 5, and 10" over a period of 1 hr whileobserving a calibration star (HR 6141) under stable seeing con-ditions estimated at 1". Under these conditions, increasing theslit width past 1" does not lead to a reduction in the spectralresolution, since the latter is determined by the seeing-limiteddisk of the star on the entrance aperture to the spectrograph. Thedata were reduced in a homogeneous manner similar to theUVES reprocessing project5 using validated master calibration

files. An example of UVES spectra taken at the lowest and high-est resolutions are shown in the middle and lower traces of Fig-ure 5, together with the model fits. The PWV derived in eachcase is ∼1:3 mm, with an estimated uncertainty of 5%. Figure 6summarizes the derived PWVobtained at the six different reso-lutions over this 1 hr observing period. It can be seen that theretrieved PWV values are independent of spectral resolution,which validates the resolution independence of the technique.

The basic Echelle spectrograph (BACHES) (Avila et al.2007) is a lower-resolution instrument (R ∼ 15; 000) with awavelength range of 390–750 nm. BACHES was attached to a40 cm telescope and operated on Paranal in concert with the

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FIG. 3.—Transmission plots of MIKE spectra (upper traces) and the corresponding fitted BTRAM spectra (middle traces), displaced for clarity, over the 700 nmregion for a dry night (PWV ∼ 1:5 mm), left column, and a wet night (PWV ∼ 4:8 mm), right column. In each case the difference is shown to the same scale. See theelectronic edition of the PASP for a color version of this figure.

5 UVES reprocessed data set: http://www.eso.org/qc/reproUVES/processing.html.


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facility instrumentation during a dedicated PWV measurementcampaign. An example BACHES spectrum recorded in atmo-spheric conditions similar to those present during the slit-varying test described previously (PWV ∼ 1:3 mm) is shownin the upper trace of Figure 5, together with the fitted atmo-spheric model. Although the resolving power is on the orderof seven times lower than the best UVES spectra, the algorithmgenerates a good fit to the observed data.

The preceding spectra-fitting technique has been applied toarchival data from facility echelle instruments in order to recon-struct the history of PWVover both sites of the La Silla Paranalobservatory. Results will be reported in another article.

When comparing the correlation between PWV derivedfrom several astronomical spectrographs by line-fitting to thatdetermined from contemporaneous radiosonde measurements,we find quantitative agreement of 10–15%, with a confidencelevel of 80% or better. This is quite remarkable, given the factthat an astronomical instrument such as UVES will sample anatmospheric PWV in a pencil beam in the line of sight to a starwhile the radiosonde makes an in situ measurement of the airalong its trajectory. The two methods will not measure thesame parts of the atmosphere. A detailed analysis of the vari-ous instruments and methods will be given in a subsequentarticle.

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FIG. 4.—Transmission plots of MIKE spectra (upper traces) and the corresponding fitted BTRAM spectra (middle traces), displaced for clarity, over the 800 nmregion for a (left) dry night (PWV ∼ 1:5 mm) and for a (right) wet night (PWV ∼ 4:8 mm). In each case the difference is shown to the same scale. See the electronicedition of the PASP for a color version of this figure.


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4. FITTING SPECTRAL DATA: EMISSION

In the case of absorption spectroscopy at visible and near-infrared wavelengths, where the atmosphere is not a significantsource of emission, it is relatively easy to establish the spectralcontinuum and the baseline, both of which are required to de-termine the integrated line absorption. By contrast, emissionmeasurements of atmospheric water vapor are more challeng-ing, because the effective temperature of the atmosphere(∼260 K) is similar to the temperature of the telescope and in-strument preoptics. Since even the best mirrors have emissivitiesof a few percent, they will radiate as graybodies at typical tem-peratures of ∼273 K and thus can contribute significant flux tothe measured signal. In principle, it is possible to account forthis continuum contribution to the measured signal, by radiativetransfer modeling of all the optical components from the pri-mary mirror to the detector. In practice, however, analysis showsthat the error incurred in assuming that the continuum contribu-tion is constant (i.e., independent of wavelength) is �1:5% overthe 5 μm band and �1:3% in the 20 μm band.

The method we have developed to fit the theoretical BTRAMemission spectra to the measured echelle spectrum is outlined inFigure 7. The first step is to ingest the spectrum and the relevanthousekeeping data (wavelength range, spectral resolution, am-bient temperature, and pressure). The measured spectrum is

fitted to a series of precomputed simulated spectra, which havebeen computed for a range of 0–5 mm PWV, in steps of 0.1 mmPWV. The specific series is drawn from a precomputed hyper-cube that covers the expected range of base temperatures andpressures. The use of a precomputed hypercube having dimen-sions of radiance, wavelength, base temperature, base pressure,and PWVallows the real-time determination of PWV from mea-sured emission spectra. The parameters allowed to vary in theNLLS fit are the half-width of a Gaussian ILS, a gain, and anoffset. For each simulated spectrum in the series, the resultingχ2, together with the fit parameters, are stored. At the end of thisprocess, the simulated spectra with the lowest χ2 parameter isidentified as the best fit, from which the PWV is derived.

4.1. Results

To illustrate the use of the emission fitting routine, wehave analyzed emission spectra measured with a cryogenic

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FIG. 5.—An example of three spectra taken at different resolutions undersimilar observing conditions (PWV ∼ 1:3 mm). Top: The measured data areshown and the best model fit is shown displaced for clarity. BACHES:R ∼ 15; 000. Middle: UVES with a wide (10") slit, and hence seeing-limitedresolution: R ∼ 40; 000. Bottom: UVES with a 0.3" slit: R ∼ 100; 000. See theelectronic edition of the PASP for a color version of this figure.

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FIG. 6.—Fitted PWV values derived from measurements of the same targetstar made under stable seeing conditions with different slit widths. The legendvalues denote slit width in arcseconds. The resolving power for the 0.3" slit is∼100; 000; the seeing-limited resolving power of ∼40; 000 is reached at 1". ThePWV error bars of 5% have been omitted for clarity.

INPUT SPECTRA (Flux, )

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simulated spectrumwith different PWVStore and fit parametersX2

Once completed, sort by X2 todetermine the best fitting spectrum,associate its PWV to the input data

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FIG. 7.—Flowchart depicting the fitting of a simulated spectrum to a genericemission spectrum.


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high-resolution infrared Echelle spectrograph (CRIRES)(Kaeufl et al. 2004), operated from 5.038–5.063 μm at a resolu-tion of 50,000, and emission spectra measured by the VLT im-ager and spectrometer for mid-Infrared (VISIR) (Lagage et al.2004), operated from 19.35–19.57 μm at a resolution of 4500.CRIRES and VISIR are infrared facility instruments at Paranalthat, during their normal operations, periodically take measure-ments of atmospheric emission when their respective telescopesare pointing at zenith.

Figure 8 shows the measured emission spectra obtained withCRIRES and VISIR on two nights, one dry and one wet, to-gether with best-fit model spectra. There is seen to be very goodagreement between the modeled and measured spectra. Slightasymmetries in the residual are more likely due to instrumentaleffects, or perhaps the data processing pipeline, than to uncer-tainties in the molecular database. For example, since a non-linear correction is required for the wavelength scale in anechelle spectrograph, residual asymmetry could result from hav-ing a not-quite-optimal correction algorithm. Both sets of plotsshow the measured and modeled spectra and the residual to thesame scale. The model and residual have been offset for clarity.While it is difficult to establish uncertainties through minimiza-tion techniques, an investigation of the local minima in χ2 space

indicates that the uncertainties are no more than 5%. As a cross-check of this error estimate, we studied the signal-to-noise ratioas the fitted PWV was varied, resulting in a similar 5% limit tothe uncertainty in the retrieved PWV value.

ESO has developed a pipeline6 to determine PWV fromCRIRES and VISIR spectra (Smette et al. 2008). The ESO re-trieval algorithm uses the Reference Forward Model7 and thetropical atmospheric profile from FASCODE. On analyzingthe same data, we found that our method for retrieving PWVfrom emission spectra yielded PWV values that were ∼10%lower than those produced from the ESO pipeline and in betteragreement with contemporaneous radiosondes launched fromthe site during the observations (Querel et al. 2010; Kerberet al.2010). We attribute our more accurate PWV derivationto the use of a realistic site-specific atmospheric model.

5. CONCLUSION

In this article, we describe a robust line-fitting routine for theretrieval of atmospheric water vapor from emission or absorption

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FIG. 8.—Examples of measured emission spectra from CRIRES and VISIR (upper traces) and the corresponding fitted BTRAM spectra (middle traces), displaced forclarity, from four different nights. Dry nights are on the left side and wet nights are on the right side. The CRIRES-derived PWV values were 0.5 mm (upper left) and6.8 mm (upper right). The VISIR-derived PWV values were 0.8 mm (lower left) and 4.4 mm (lower right). In each case the difference is shown to the same scale; theintensity is in arbitrary units. See the electronic edition of the PASP for a color version of this figure.

6 ESO, PWV measurements: http://www.eso.org/sci/facilities/paranal/sciops/CALISTA/pwv/data.html.

7 Reference Forward Model: http://www.atm.ox.ac.uk/RFM/.


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spectra in real time. The algorithm yieldsmore accurate estimatesof PWV than other methods currently in use. This improvementarises from the use of a site-specific atmospheric model(BTRAM) and results in derived PWV values that are in goodagreement with contemporaneous radiosonde measurements,which are considered to be the gold standard in atmosphericsounding.

Given the robustness of the fitting algorithm, in the contextof site-testing work for the ESO European Extremely LargeTelescope, we have reprocessed calibration standard star mea-surements to extract PWV and create a historical record of thewater vapor above the La Silla and Paranal observatory sites(Querel et al. 2010; Kerber et al. 2010). This study includedspectral data from the Fiber-fed Extended Range Optical Spec-trograph (Kaufer et al. 1999) (∼1700 spectra spanning 4 yr;5 GB of data) and UVES (∼1500 spectra spanning 7 yr;600 MB of data). Using the techniques described in this article,we were able to derive PWV from these 3200 spectra in a matterof hours on a standard desktop PC.

The authors would like to thank Brad Gom for his continu-ing work with the Blue Sky Transmission and Radiance Atmo-spheric Model, Reinhard Hanuschik for the pipeline-processedUltraviolet and Visual Echelle Spectrograph spectra, AlainSmette for providing the cryogenic high-resolution infraredEchelle spectrograph and VLT imager and spectrometer formid-infrared pipeline-processed spectra, Carlos Guirao formanually processing the basic Echelle spectrograph spectra,and Joanna Thomas-Osip for providing access to processedMagellan Inamori Kyocera Echelle spectra. Thank you to theAstroMeteorology Group from the Universidad de Valparaísofor launching the radiosondes during the PWV measurementcampaigns. It is a pleasure to thank the directors of La SillaParanal observatory for granting technical time. D.A.N. ac-knowledges funding from Natural Sciences and EngineeringResearch Council, and R.R.Q. recognizes European SouthernObservatory for funding the precipitable water vapor site-testingcampaigns. The authors would like to thank the referee for pro-viding timely and constructive feedback.

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Querel, R. R., et al. 2008, Proc. SPIE, 7014, 701457———. 2010, Proc. SPIE, 7733, 773349Rothman, L. S., et al. 2009, J. Quant. Spectrosc. Radiat. Transfer,

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spectroscopic determination of atmospheric water vapor

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