Transmission Spectroscopy with the ACE-FTS Infrared Spectral Atlas of Earth: A Model Validation and Feasibility Study
Franz Schreier, Steffen Städt, Pascal Hedelt, Mareike Godolt
TTransmission Spectroscopy with the ACE-FTS Infrared Spectral Atlas of Earth:A Model Validation and Feasibility Study
Franz Schreier a, ∗ , Steffen St¨adt a , Pascal Hedelt a , Mareike Godolt b a DLR — Deutsches Zentrum f¨ur Luft- und Raumfahrt,Institut f¨ur Methodik der Fernerkundung,Oberpfaffenhofen, 82234 Weßling, Germany b TUB — Technische Universit¨at Berlin, Zentrum f¨ur Astronomie und Astrophysik, Hardenbergstr. 36, 10623 Berlin, Germany
Abstract
Infrared solar occultation measurements are well established for remote sensing of Earth’s atmosphere, and the corre-sponding primary transit spectroscopy has turned out to be valuable for characterization of extrasolar planets. Ourobjective is an assessment of the detectability of molecular signatures in Earth’s transit spectra.To this end, we take a limb sequence of representative cloud-free transmission spectra recorded by the space-borneACE-FTS Earth observation mission (Hughes et al., ACE infrared spectral atlases of the Earth’s atmosphere, JQSRT2014) and combine these spectra to the effective height of the atmosphere. These data are compared to spectra modeledwith an atmospheric radiative transfer line-by-line infrared code to study the impact of individual molecules, spectralresolution, the choice of auxiliary data, and numerical approximations. Moreover, the study serves as a validation of ourinfrared radiative transfer code.The largest impact is due to water, carbon dioxide, ozone, methane, nitrous oxide, nitrogen, nitric acid, oxygen, andsome chlorofluorocarbons (CFC11 and CFC12). The effect of further molecules considered in the modeling is eithermarginal or absent. The best matching model has a mean residuum of 0 . Keywords:
Extrasolar planets; Solar occultation spectra; Atmospheric composition; Biosignatures
1. Introduction
More than 20 years after the discovery of the first extra-solar planet around a solar-like star [1] about 3700 exoplan-ets have been detected ( http://exoplanet.eu/ ), includ-ing a few dozen super-Earths [e.g. 2, 3], a few potentiallyEarth-sized planets (e.g. in the Trappist-1 system [4, 5],Kepler-22b [6], or K2-137b [7]) and a few Earth-mass plan-ets [e.g. 8, 9]. In the last decade the characterization ofthese remote worlds has attracted increasingly more atten-tion. The question of the spectral appearance of terrestrialexoplanets and the possibility to identify signatures of lifehas been the focus of a series of modeling studies, whereasthe quantitative characterization by atmospheric retrievaltechniques is so far mainly confined to larger objects suchas hot Jupiters and Neptune-sized planets.One of the first comprehensive modeling studies ofbiosignatures of terrestrial exoplanets has been performedby Des Marais et al. [10] who used a line-by-line (lbl) atmo-spheric radiative transfer code to assess spectral signatures ∗ Corresponding author
Email address: [email protected] (Franz Schreier) known from Earth, Mars, and Venus in the mid / thermalinfrared (MIR, TIR) and visible to near IR (NIR). Seguraet al. [11] generated synthetic Vis-NIR and TIR spectra ofan Earth-like planet orbiting around M dwarfs, and transitspectra of Earth and an Earth-like exoplanet orbiting anM star have been modeled by Kaltenegger and Traub [12].The impact of the host star’s type or distance on the spec-tral appearance of Earth-like planets has been consideredby, e.g., Segura et al. [13], Rauer et al. [14], Hedelt et al.[15], Vasquez et al. [16, 17], Rugheimer et al. [18] and [19].For an assessment of exoplanet atmospheric remotesensing Earth seen from space is an ideal test case; infact it is the only planet that can be used for validationof exoplanet retrieval codes (to some extent, solar systemplanets, esp. Mars and Venus, can be used, too). Chris-tensen and Pearl [20] presented observed spectra of Earthobtained with the Thermal Emission Spectrometer (TES)aboard NASA’s Mars Global Surveyor at a distance of4.7 million km. Tinetti et al. [21] has compared visibleand IR spectra modeled with an lbl multiple scatteringcode and observations made by TES and the OMEGAinstrument aboard ESA’s Mars Express as well as ground-
Molecular Astrophysics, received 25 July 2017, accepted 8 February 2018, doi: 10.1016/j.molap.2018.02.001 March 15, 2018 a r X i v : . [ a s t r o - ph . E P ] M a r ased Earth-shine observations. Visible or near IR Earth-shine spectra have been analysed by, e.g., Woolf et al.[22], Pall´e et al. [23], Garc´ıa Mu˜noz et al. [24]. Watervapor and biogenic oxygen and ozone have been identifiedin high resolution Vis-NIR transmission spectra of Earthseen during the December 2010 Moon eclipse by Arnoldet al. [25]. EPOXI (Extrasolar Planet Observation andCharacterization — Deep Impact eXtended Investigation)observations of Earth have been used by Rugheimer et al.[19], Kaltenegger et al. [26], Robinson et al. [27] for ra-diative transfer code validation. Furthermore, Irwin et al.[28] calculated transit spectra of Earth using the NEME-SIS code [29] and used Rosetta/VIRTIS observations forvalidation.To our knowledge, data from space-borne missions ded-icated to Earth observation have been rarely used todemonstrate the capabilities of exoplanet atmosphericstudies. For validation of their radiative transfer code,Misra et al. [30] used solar occultation spectra observedby the ATMOS Fourier transform spectrometer [31] on-board the ATLAS 3 Space Shuttle (November 1994) intheir assessment of the impact of refraction on transitspectroscopy of Earth-like exoplanets. Likewise, ATMOSdata were used by Kaltenegger and Traub [12] for vali-dation purposes. Disk-averaged MIR spectra have beengenerated from nadir observations with the AtmosphericInfrared Sounder (AIRS) instrument [32] aboard NASA’sAqua satellite by Hearty et al. [33], these data were alsoused in the Robinson et al. [27] validation study. G´omez-Leal et al. [34] studied the disk-integrated MIR thermalemission of Earth seen as a point source using a variety ofsatellite measurements acquired over more than 20 years.Solar occultation data obtained with SCIAMACHY (Scan-ning Imaging Absorption Spectrometer for AtmosphericCHartographY) on ESA’s Envisat satellite were consid-ered in Garc´ıa Mu˜noz et al. [24].NIR observations of Venus by SCIAMACHY were usedfor validation of a line-by-line single scattering code byVasquez et al. [35]. The Swedish small satellite missionOdin originally had a dual role: aeronomy and astronomy;among others, it has been used for measurements of wateron Mars and Jupiter [36, 37].Similar to the ATMOS instrument, the Canadian Atmo-spheric Chemistry Experiment — Fourier Transform Spec-trometer (ACE-FTS) observes the Earth’s limb in solaroccultation [38, 39]. Hundreds of spectra recorded in the2004 to 2008 time frame have been averaged by Hugheset al. [40] to compile five “infrared spectral atlases” forvarious seasons and latitude bands.In this study we use the ACE-FTS infrared atlas to gen-erate effective height spectra of Earth’s atmosphere and tocompare these with model spectra generated with an lblcode in order to assess the visibility and detectability ofatmospheric gases in transit spectra. In the next sectionwe briefly review the data and models used for this study,and in section 3 we present the results. First, we study theimpact of individual molecular absorbers, auxiliary data, and numerical approximations using the ACE-FTS arc-tic winter atlas degraded to moderate resolution, and insubsection 3.2 we investigate the molecular visibility anddetectability for various resolutions using a mix of all fiveatlases to mimic a global view. After a discussion in sec-tion 4 we summarize our study in section 5 and concludewith a brief outlook.
2. Data and Models
The Atmospheric Chemistry Experiment — FourierTransform Spectrometer is one of two science instrumentsaboard the Canadian SCISAT orbiting Earth at 650 kmaltitude with an inclination of 74 ◦ [38, 39]. ACE-FTS ob-serves the atmospheric absorption in the infrared (750 to4400 cm − or 2.2 to 13 . µ m) with high spectral resolution(0 .
02 cm − , i.e. about two times the ATMOS resolution)in limb viewing geometry. Each measurement essentiallycomprises a sequence of transmission spectra for differenttangent altitudes and is used to derive altitude dependentprofiles of temperature and trace gas concentrations.Since its launch in August 2003 ACE-FTS has recordedtens of thousands of occultation spectra. Representativespectral “atlases” of these data have been generated byaveraging about 800 cloud-free spectra for a series of alti-tudes from 4 to 128 km in 4 km steps [40]. Five atlases with31 spectra each are provided for Arctic summer and winter(ASU, AWI; latitude range 60 ◦ – 90 ◦ N), midlatitude sum-mer and winter (MLS, MLW; 30 ◦ – 60 ◦ N), and the tropics(30 ◦ S – 30 ◦ N). The data (with 39 MB per file/spectrumfor 1 960 001 wavenumbers in 100 – 5000 cm − ) are avail-able at alongwith representative plots for 10 km, 30 km, 70 km, and110 km tangent heights in pdf format. Fig. 1 shows anexcerpt of the arctic winter atlas indicating the high reso-lution and low noise level (due to the averaging).Except for a few dips a single ACE-FTS occultationspectrum has a typical signal-to-noise (SNR) ratio of about100 to 450 for wavenumbers 800 – 3500 cm − [40, Fig. 1,SNR >
50 up to 4000 cm − ]. Because typically 800 spec-tra have been averaged, the atlas spectra can be expectedto have an SNR of some thousands.ACE-FTS is characterized by a very high resolution,and the spectra are given with a wavenumber grid spac-ing δν = 0 . − . To study the impact of lowerresolution, we considered degraded spectra obtained byconvolution with a Gaussian response function. Initiallywe take an optimistic point of view and consider spectraconvolved with a Gaussian of HWHM (half width at halfmaximum) Γ = 1 . − . Additionally, we examine theimpact of spectral resolution with more realistic HWHMsΓ = 2 , , ,
20 and 50 cm − . In a gaseous, non-scattering atmosphere the attenuationof radiation along the path s is described by Beer’s law2
40 850 860 870 880 890 900
Wavenumber ν [cm − ]0 . . . . . . T r a n s m i ss i o n T
4- 8 km24-28 km32-36 km
Figure 1: Zoom into three of 31 high resolution limb transmission spectra of the arctic winter atlas. (The large peaks around 879 and896 cm − are due to HNO , the three peaks around 850 cm − are due to H O.) [41] for transmission T and optical depth τ as a functionof wavenumber ν , T ( ν, s ) = e − τ ( ν,s ) (1)= exp − s (cid:90) d s (cid:48) (cid:88) m k m ( ν, p ( s (cid:48) ) , T ( s (cid:48) )) n m ( s (cid:48) ) , where p and T are the atmospheric pressure and temper-ature, and the integrand constitutes the absorption coeffi-cient essentially determined by the sum of the absorptioncross sections k m scaled by the molecular number densities n m . In high resolution lbl models, the absorption cross sec-tion of molecule m is given by the superposition of manylines l with line center positions ˆ ν l , each described by theproduct of a temperature–dependent line strength S l anda normalized line shape function g describing the broaden-ing mechanisms (for brevity the subscript m is omitted), k ( ν, p, T ) = (cid:88) l S l ( T ) g ( ν ; ˆ ν l , γ l ( p, T )) . (2)The combined effect of pressure broadening (correspond-ing to a Lorentzian line shape) and Doppler broadening(corresponding to a Gaussian line shape) can be repre-sented by a convolution, i.e. the Voigt line profile [42, 43]with width γ (cid:0) γ L ( p, T ) , γ G ( T ) (cid:1) . The “Generic Atmospheric Radiation Line-by-lineInfrared-microwave Code” [44, 45] has been developed in the last two decades with an emphasis on efficient and re-liable numerical algorithms. It is suitable for arbitrary ob-servation geometry, instrumental field-of-view (FoV), andspectral response functions (SRF). More recently, GAR-LIC (or its Fortran 77 predecessor) has also been used fora variety of exoplanet studies, e.g. [14–17].The core of GARLIC’s subroutines constitutes the basisof forward models used to implement inversion codes to re-trieve atmospheric state parameters [e.g. 46, 47]. For veri-fication, GARLIC has contributed to several intercompar-ison studies [e.g. 48–50]. For validation, modeled spectrahave been successfully compared with limb thermal emis-sion spectra observed by the MIPAS instrument aboardENVISAT [51] and with Venus observations [35, 52].For the lbl computation of cross sections (2), GARLICuses a (default) cut-off δν = 10 cm − in the line wings(25 cm − for H O with continuum). Wavenumber gridpoints are sampled with a (default) spacing of δν = γ/ γ is the (Voigt) half width depending on molecule,pressure, and temperature. All spectral lines listed in thedatabase are considered, i.e. weak lines are not neglected. Line parameter databases are a mandatory input forlbl modeling. For the 700 – 4400 cm − wavenumber rangeconsidered here, the HITRAN 2016 database [53] lists2.94 million lines of 43 molecules (the entire database hasmore than nine million lines of 49 molecules), whereasthe GEISA 2015 database [54] has 2.48 million lines of51 molecules (total 52 molecules with five million lines).Data of molecular masses and rotational and vibrational3artition sums (required for the temperature conversion ofline strengths) are taken from the ATMOS data set [55].In addition to the lbl cross sections described by Eq. (2)there is a further contribution commonly known as thecontinuum [56]. The pressure and temperature dependentcontinuum varies slowly with wavenumber and is especiallyimportant for water. Until recently, the continuum imple-mented in GARLIC was based on code and data extractedfrom the FASCODE3 lbl model [57] and essentially corre-sponds to the “CKD continuum” [58] comprising water(self and foreign), carbon dioxide, oxygen and nitrogencontributions. For the ongoing intercomparison of GAR-LIC with the ARTS and KOPRA lbl models [59] and forthe study reported here an upgrade of the continuum hasbeen made, i.e. the “MT-CKD continuum” [60] (version2.5) has been implemented. Pressure, temperature and volume mixing ratio pro-files for the seven “main” gases (corresponding to themolecules considered in the very first version of the HI-TRAN database [61]) and six “scenarios” (tropical, mid-latitude summer and winter (MLS, MLW), subarctic sum-mer and winter (SAS, SAW), US Standard) have beencompiled by Anderson et al. [62] for the 0 – 120 km altituderange. Furthermore, this dataset (a.k.a. the “AFGL pro-files”) provides concentration profiles of further 21 tracegases.Alternatively, the Committee on Space Research(COSPAR) International Reference Atmosphere (CIRA)provides monthly mean profiles of pressure vs. tempera-ture for the altitude range 0 – 120 km and latitudes 80 ◦ Nto 80 ◦ S with 5 ◦ spacing [63, http://badc.nerc.ac.uk/data/cira/ ].Concentration profiles of heavy species, in particularchlorofluorocarbons (CFC) etc., were taken from the MI-PAS model atmospheres [64, and http://eodg.atm.ox.ac.uk/RFM/atm/ ]. For an exoplanet seen from afar it is not possible to dis-tinguish between limb spectra corresponding to individualtangent heights. Using (primary) transit observations oneessentially measures the effective height h ( ν ) = (cid:90) ∞ (cid:16) − T ( ν, z t ) (cid:17) d z t (3)where the integral includes all limb transmission spec-tra with tangent altitude z t terminating at “top-of-atmosphere” (ToA). In this study, the ToA of 120 km wasdefined by the available atmospheric data [62–64].Numerically, effective height spectra are summed ac-cording to the trapezoid quadrature approximation of (3) h ( ν ) ≈ δz t (cid:32) L (cid:88) l =1 (cid:0) − T ( ν, z l ) (cid:1) + T ( ν, z ) + T ( ν, z L )2 − (cid:33) (4) taken a limb sequence with equidistant tangent points from z to z L . As an alternative to the trapezoid quadraturerule, the integral (3) can be approximated using a mid-point quadrature.Some studies of exoplanet transit spectroscopy con-sider the mean transmission of a limb sequence, (cid:104)T (cid:105) ( ν ) = L (cid:80) l T l ( ν ) [e.g. 12, 14, 65]. However, it should be notedthat this quantity depends on the choice of the ToA al-titude: Limb rays traversing only the upper layers of theatmosphere have a transmission close to one, and theseones considerably contribute to the overall sum (the divi-sion by the number of limb spectra L hardly compensatesthis), whereas those rays with A ( ν, z t ) = 1 − T ( ν, z t ) ≈ band indicatingthat the mesosphere has some non-negligible absorption.Furthermore note that the mean transmission also dependson the choice of the tangent altitudes: for example, a non-equidistant set of tangent points with dozens of points inthe troposphere and just a few in the stratosphere andmesosphere will significantly change the mean transmis-sion.The additional transit depth due to the atmosphere isdefined as [14, 15] δd t ( ν ) = (cid:0) R p + h ( ν ) (cid:1) − R R (5)with R p and R s the planetary and solar radius. Thesquared ratio of the radii is also known as the geometrictransit depth d geo = R /R . For a quantitative estimate of the agreement betweenobserved and modeled effective height spectra the meanand maximum (absolute) difference and the norm of theresidual are considered, (cid:104)| ∆ h |(cid:105) = 1 m m (cid:88) i =1 | h obs ( ν i ) − h mod ( ν i ) | (6)∆ h max = max i | h obs ( ν i ) − h mod ( ν i ) | (7) (cid:107) ∆ h (cid:107) = (cid:34) m (cid:88) i =1 (cid:0) h obs ( ν i ) − h mod ( ν i ) (cid:1) (cid:35) / (8)where m is the number of data points in the spectra.Whereas (cid:104)| ∆ h |(cid:105) and ∆ h max are more intuitive, the resid-ual norm (cid:107) ∆ h (cid:107) is the quantity to be minimized in a least4
000 1500 2000 2500
Wavenumber ν [cm − ]010203040 E ff e c t i v e H e i g h t [ k m ] ∆ h ≤ .
57 km
Wavenumber ν [cm − ]0 . . . . . . . M e a n T r a n s m i ss i o n Figure 2: Comparison of ACE-FTS effective height (left) and mean transmission (right) spectra for three different ToA altitudes (arcticwinter, smoothed by convolution with a Gaussian of width Γ = 10 cm − ). The yellow curve (left plot) is the difference of the effective heightsfor ToA=120 km and ToA=80 km. squares fitting procedure. Note that the mean residuum islargely independent of the number m of data points, andthe maximum residual is linked to the spectral resolution.The detectability of a certain molecule will depend onthe spectral resolution and the noise of the observation.For a quantitative assessment the relative change of theresidual norm due to the inclusion/exclusion of a moleculewill be used, i.e.( (cid:107) ∆ h m +1 (cid:107) − (cid:107) ∆ h m (cid:107) ) / (cid:107) ∆ h m (cid:107) (9)with m indicating the number of absorbing molecules.This is in analogy to the “ y –convergence” test consider-ing the relative change of the residuals from iteration toiteration, that is commonly used for the iterative solutionof nonlinear least squares problems [66, 67]: if this ratio issmaller than a given threshold (cid:15) (essentially proportionalto the reciprocal of the SNR), the iteration is stopped. For an estimate of the signal-to-noise ratio to be ex-pected for Earth seen from afar, we use the noise model ofRauer et al. [14]. The SNR T of a spectral feature observedin transmission is the product of the stellar SNR S and thechange of the additional transit depth ∆ δd t ,SNR T = SNR S ∆ δd t with SNR S = (cid:114) R D I S At λ hc qR , (10)where D is the observer-star distance, I S the stellar spec-tral energy flux, A the telescope area, t the integration time, R the resolving power, q a measure of the instru-ment’s throughput, λ wavelength, and h , c Planck’s con-stant and the speed of light, respectively.
3. Results
The observed effective height spectra derived from thefive IR atlases by combination of all limb transmissionspectra according to Eq. (3) and smoothing with a Gaussof half width Γ = 10 cm − are compared in Fig. 3. Ignor-ing the long wavelength end, the difference between theheights can be as large as a few kilometers. Large differ-ences occur for relative transparent spectral regions as wellas for regions characterized by strong absorption (e.g. thetwo CO bands and the ozone band at 10 µ m). Also notethe large spread of the effective heights in the HNO bandaround 11 µ m with strongly enhanced absorption for thearctic winter.The volume mixing ratio of 330 ppm and 1 . and a CH profile scaled by a fac-tor 1.3 yield the best agreement. For recent satellite andground-based measurements of these carbon species see,e.g.,[68].5 Wavelength λ [ µ m]01020304050 E ff e c t i v e H e i g h t [ k m ] cm − O HNO , CFCCO CO CO CH CH O O tropics: 4.05 – 48.20 kmmls: 3.75 – 49.00 kmmlw: 2.58 – 46.64 kmasu: 3.34 – 49.82 kmawi: 3.34 – 49.82 km Figure 3: Comparison of effective height spectra resulting from the five IR atlases. The yellow line indicates the maximum difference h max − h min . The lower x -axis shows wavelengths in micrometer whereas the upper axis shows wavenumbers ν = 1 /λ in cm − . The numbersin the legend indicate the minimum and maximum effective height. Molecules responsible for some of the major features are indicated (H Oabsorbs “almost everywhere” and is not indicated).Table 1: Comparison of mean, extremum, and norm residual for themoderate resolution arctic winter runs as a function of the numberof absorbing molecules. The “relNorm” column gives the relativechange of the norm as defined in (9), all other columns give heightsin kilometers. Except for the “GEISA” column all model runs havebeen using the HITRAN database. A tripled HNO and doubledCFC11, CFC12 concentrations have been used. The very first row isfor CO alone. The second column identifies the molecule added tothe list of absorbers. m mean max norm GEISA relNorm ∆ h max1 CO2 8.003 33.849 1219.99 1219.651 H2O 7.978 47.961 1460.76 1461.842 +CO2 4.721 33.616 893.33 893.68 0.3884 48.8843 +O3 3.058 22.085 564.35 565.06 0.3683 34.0034 +N2O 2.381 19.943 445.09 446.52 0.2113 14.3635 +CO 2.341 19.943 442.00 443.48 0.0069 3.5236 +CH4 1.141 11.213 244.23 245.61 0.4474 21.3857 +O2 1.022 11.213 230.08 231.18 0.0580 4.8138 +NO 1.020 11.213 230.05 231.15 0.0001 0.3559 +SO2 1.020 11.213 229.98 231.09 0.0003 0.08910 +NO2 1.014 11.212 229.74 230.81 0.0010 2.30711 +NH3 1.013 11.212 229.51 230.58 0.0010 0.22612 +HNO3 0.773 6.914 161.74 163.22 0.2953 10.38113 +OH 0.773 6.914 161.74 163.22 0.0000 0.00814 +HF 0.773 6.914 161.76 163.24 0.0001 0.23615 +HCl 0.772 6.914 161.70 163.17 0.0004 0.25116 +HBr 0.772 6.914 161.69 163.17 0.0000 0.00317 +HI 0.772 6.914 161.69 163.17 0.0000 0.00218 +ClO 0.772 6.914 161.69 163.17 0.0000 0.00119 +OCS 0.764 6.914 161.06 162.61 0.0039 1.13820 +H2CO 0.762 6.914 161.00 162.56 0.0003 0.05821 +HOCl 0.762 6.914 160.97 162.52 0.0002 0.02722 +N2 0.575 5.424 108.03 110.58 0.3289 7.98423 +HCN 0.573 5.424 107.99 110.53 0.0004 0.12724 +CH3Cl 0.572 5.424 107.86 110.40 0.0012 0.12525 +H2O2 0.572 5.424 107.81 110.34 0.0005 0.03126 +C2H2 0.572 5.424 107.81 110.34 0.0001 0.01327 +C2H6 0.569 5.424 107.23 109.59 0.0053 0.37828 +PH3 0.569 5.424 107.23 109.59 0.0000 0.00029 +COF2 0.566 5.424 106.89 109.25 0.0032 0.14230 +SF6 0.566 5.424 106.82 109.22 0.0007 0.17431 +CCl3F 0.543 5.424 100.70 103.24 0.0573 4.91932 +CCl2F2 0.489 2.635 81.94 84.95 0.1863 5.01933 +CClF3 0.489 2.635 81.94 84.95 0.0000 0.00034 +CF4 0.487 2.635 81.67 84.56 0.0033 1.08135 +C2Cl3F3 0.485 2.630 81.14 84.04 0.0066 0.13936 +CHClF2 0.480 2.627 79.87 82.80 0.0156 0.21437 +ClONO2 0.472 2.376 77.97 80.86 0.0237 0.84138 +N2O5 0.462 2.375 76.06 78.84 0.0246 0.969 In the following we will first study the effective heightspectrum resulting from the combined arctic winter IRatlas for two reasons: First, water is highly variable inEarth’s atmosphere, and it is hence difficult to select arepresentative H O profile. Furthermore, laboratory spec-troscopy of water is not trivial mainly because of the dif-ficulty to exactly quantify the amount of water in the gasabsorption cell. The appropriate line shape, uncertaintiesdue to pressure broadening parameters and due to con-tinuum contributions further complicate matters [69–72].Accordingly we have chosen the arctic winter case char-acterized by a relatively dry atmosphere. The subarcticwinter profile of Anderson et al. [62] has an integrated wa-ter content of 4 . / m compared to 40 . / m for thetropical profile.Unless otherwise noted, the subarctic winter pressure,temperature and concentration profiles of the main ab-sorbers [62] were used along with spectroscopic data (lbland cross sections) from HITRAN 2016 and CKD contin-uum data. A key question of exoplanet science is the detectabilityof various molecules, esp. biosignatures, by atmospheric re-mote sensing. Not surprisingly the carbon dioxide bands at4 . µ m (partially only), the water band at 6 . µ m,and the combined H O and CO absorption at 2 . µ m arereadily recognizable, see Fig. 3. Moreover, the atmospheric6 able 2: Impact of a missing molecule on the residual norm for themoderate resolution arctic winter runs. The “relNorm” column givesthe relative change of the norm with the 38 molecules spectrum asreference (in analogy to Eq. (9) with m = 37). The third column isthe maximum change of the effective height δh = h − h . norm relNorm δh max [km] [km]none 76.06H2O 448.42 4.896 19.219CO2 790.42 9.392 35.288O3 620.50 7.158 33.801N2O 156.49 1.057 7.813CO 76.19 0.002 2.657CH4 339.33 3.461 21.366O2 95.78 0.259 4.596NO 76.12 0.001 0.354SO2 76.07 0.000 0.088NO2 76.63 0.007 2.307NH3 76.18 0.002 0.199HNO3 165.68 1.178 10.328OH 76.06 0.000 0.008HF 76.02 0.001 0.236HCl 76.18 0.002 0.250HBr 76.06 0.000 0.001HI 76.06 0.000 0.003ClO 76.06 0.000 0.001OCS 77.06 0.013 1.137H2CO 76.15 0.001 0.058HOCl 76.10 0.001 0.027N2 141.50 0.860 7.983HCN 76.10 0.001 0.127CH3Cl 76.20 0.002 0.119H2O2 76.09 0.000 0.030C2H2 76.07 0.000 0.013C2H6 76.55 0.006 0.378PH3 76.06 0.000 0.000COF2 76.39 0.004 0.140SF6 76.14 0.001 0.173CCl3F 83.13 0.093 4.904CCl2F2 94.96 0.248 4.976CClF3 76.06 0.000 0.000CF4 76.26 0.003 1.059C2Cl3F3 76.58 0.007 0.138CHClF2 77.36 0.017 0.214ClONO2 77.97 0.025 0.841N2O5 77.97 0.025 0.969 window around 10 µ m is visible, albeit with interruptionsdue to ozone and nitric acid absorption features.For an assessment of the impact of atmospheric gaseson the observed spectrum a series of spectra has beenmodeled, starting with H O or CO alone, and addingmolecule-by-molecule in the order of the HITRAN lbldatabase up to m ≤
30 (i.e. SF ). Note that pressure andtemperature are left unchanged, i.e. the surface pressureis about 1 bar for all runs. The progress is monitored bythe mean, maximum, and norm residuals listed in Tab. 1.The effective height spectrum modeled with H O, CO and O already shows the main features of the observedeffective height spectrum, esp. the largest peaks aroundthe centers of their main absorption bands, cf. Fig. 4 (firstand second from top). Note that although water is mainlypresent in the (lower) troposphere, the pure H O effec-tive height spectrum reaches up to 20 km in its absorptionbands. Inclusion of nitrous oxide N O significantly reducesthe discrepancies at its fundamental bands around 1250and 2200 cm − , and less drastically at 2500 and 3500 cm − .The impact of carbon monoxide is clearly seen for the firstfundamental band at 2150 cm − , whereas the first over-tone around 4250 cm − is barely visible, and the change of the residual mean and norm is minimal. For methane thelargest contribution to the spectrum occurs in the pentadband around 3000 cm − (from ∆ h as large as 20 km to al-most zero), but the reduction in the dyad (1300 cm − ) andoctad (4300 cm − ) is also quite dramatic with more than10 km in the peaks. The strong reduction of the discrep-ancy around 1600 cm − is due to oxygen (Fig. 4 bottom).The following four molecules in the HITRAN list (NO,SO , NO , and NH ) do not significantly reduce the resid-ual. The large underestimate of the effective height around900 cm − can be largely attributed to nitric acid, seeFig. 5a). The default profile given by Anderson et al.[62] turned out to be inadequate and increasing the HNO mixing ratio by a factor four leads to a satisfying agree-ment in this band; however, this also yields an excess ab-sorption at 1300 and 1700 cm − , and a tripled nitric acidconcentration is used henceforth. Indeed, the HNO pro-files collected in the ACE-FTS Climatology [73, 74] con-firm elevated concentrations for Northern latitudes, andthe polar summer and winter HNO concentrations of theMIPAS model atmospheres [64] are about a factor twolarger than the midlatitude summer and winter profiles(which are identical to the profiles used here [62]). En-hanced nitric acid total columns in polar winter have alsobeen measured by the Infrared Atmospheric Sounding In-terferometer (IASI) [75]. Note that the chlorofluorocar-bons CFC11 and CFC12 also have strong absorption inthe 830 – 930 cm − interval, see discussion below.The next large reduction of the residual is due to the ni-trogen molecule, where both lbl and continuum contributeto the absorption in the 1900 – 2800 cm − region (Fig. 5b).As Tab. 1 indicates, inclusion of lbl contributions frommore molecules (23 to 29) does not further reduce theresidual remarkably.To further improve the model spectra it is necessary toconsider contributions from molecules with spectroscopicproperties available as cross sections (instead of lbl data)only. Note that for SF HITRAN line data are provided ina supplementary folder only, and the use of cross sectiondata is recommended. The CFCs CCl F and CCl F bothhave strong bands in the region of the HNO band men-tioned above: Adding CFC11 (CCl F) reduces the resid-ual norm from 106.8 to 100 . h max ≈ . − un-changed; CFC12 (CCl F ) has its peak absorption here,and its inclusion largely eliminates this deviation and fur-ther reduces the residual norm to 82 km, compare Fig. 5c.The contributions of further heavy molecules, in partic-ular N O , have also a small impact on the effective heightspectrum. The final mean and norm residual (Fig. 5d) for38 molecules is 0 .
46 km and 76 km, respectively, comparedto 1.02 and 230 km for the first seven HITRAN (or GEISA)molecules.Adding the CFCs to the model atmosphere actuallycompensates for some of the extra HNO required to re-duce the discrepancies around 900 cm − . Scaling both theCFC11 and CFC12 profile by a factor two and scaling7 µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m ACE-FTS H2O CO2 +O3 +N2O E ff e c t i v e h e i g h t [ k m ] +CO +CH4 Wavenumber ν [cm − ]01020304050 +O2 Figure 4: Effective height spectra for the main gases (arctic winter, moderate resolution Γ = 1 cm − ). In the top the model spectra ofpure water or carbon dioxide atmospheres are compared to the ACE-FTS observation. In the following plots absorption due to the speciesindicated in the legend is added. The bottom shows the model spectrum for seven absorbers. HNO by a factor three gives the smallest residuum with0 .
46 km mean residuum and norm 76 . The GEISA database [54] is a widely used alternativeto HITRAN in Earth science. The effective height residu-als shown in Fig. 6 (top) indicate that line parameters ofHITRAN 16 yield a slightly better agreement with the ob-servations compared to GEISA 15. Tab. 1 and some modelruns with input data mixed from both databases show thatthis superiority can be largely attributed to the differentH O spectroscopic data, for all the other molecules bothdatabases perform equally well. This is also confirmed by acomparison of model spectra with 37 absorbing molecules,i.e. all molecules except for water (see the subsection 3.1.5 below), giving almost identical residuals. Note that withHITRAN 12 (with 2.3 million lines contributing) the resid-uals are slightly smaller, with a mean and norm 0.455 and75 .
62 km, respectively. Also note that, in contrast to HI-TRAN, the GEISA database contains 46031 SF lines in920 – 976 cm − (the HITRAN supplementary listing com-prises almost three million SF lines).Inclusion of continuum absorption in the radiative trans-fer modeling is clearly important, as demonstrated by thecomparison of effective height spectra modeled with andwithout continuum in Fig. 6 (mid). Without continuum,the maximum deviation of the observed and modeled ef-fective height is as large as 14 km, and the mean residual isabout twice as large. Replacing the CKD water continuumdata with more recent data of the MT-CKD continuum(version 2.5) has only a little effect on the spectra (notshown), i.e. the mean residuum is slightly changed from8 E ff . H e i g h t [ k m ] ACE-FTS11 molecules+HNO3
800 1000 1200 1400 1600 1800 ν [cm − ] − ∆ H e i g h t [ k m ] a E ff . H e i g h t [ k m ] ACE-FTS21 molecules+N2 ν [cm − ] − − ∆ H e i g h t [ k m ] b E ff . H e i g h t [ k m ] ACE-FTS30 molecules+CFC11+CFC12
750 800 850 900 950 1000 1050 1100 1150 1200 ν [cm − ] − − ∆ H e i g h t [ k m ] c E ff . H e i g h t [ k m ] ACE-FTS36 molecules+ClONO2+N2O5
800 1000 1200 1400 1600 1800
Wavenumber ν [cm − ] − − ∆ H e i g h t [ k m ] d Figure 5: Zoom into effective height spectra and residuals: a) impact of nitric acid; b) nitrogen; c) CFC11 and CFC12; d) chlorine nitrateand nitrogen pentoxide. The numbers in the legend are the mean (6), maximum (7), and norm (8) residual computed for the whole spectrum.
000 1500 2000 2500 3000 3500 4000 − . − . − . − . . . . . . . ∆ H e i g h t [ k m ] µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m − ∆ H e i g h t [ k m ] ν [cm − ] − − − − − ∆ H e i g h t [ k m ] Figure 6: Impact of auxiliary data on effective height residuals for 38 molecules H O, . . . , N O : Top: HITRAN (red) vs. GEISA (blue); Mid:CKD continuum on (red) vs. off (blue); Bottom: SAW (red) vs. MLS (blue) pressure, temperature, and concentrations. Legend numbers asin Fig. 5. .
462 to 0 .
467 km.
Transmission spectroscopy is primarily used for com-position retrieval and is thought to have only little valuefor temperature retrieval [76, 77]. On the other hand, forthe operational data processing of ACE-FTS observationstemperature is first retrieved from the relative and abso-lute intensity of CO lines [39]. However, the ACE-FTSdata processing exploits about 30 spectra of a limb scanindividually to infer the profile information on tempera-ture (and gas abundances), whereas here we use a kindof mean transmission spectrum to resemble exoplanet re-mote sensing. Nevertheless it is instructive to assess thetemperature sensitivity of the effective height spectra.The ACE-FTS arctic winter atlas comprises measure-ments of December to February in the 60 to 90 ◦ N latitudebelt. Accordingly we have recalculated the effective height(with all 38 molecules included) with the SAW tempera-ture [62] replaced by the fifteen arctic winter CIRA tem-perature profiles [63]. The resulting residua means spanthe 0.448 to 0 .
522 km interval with the smallest mean forthe 60 ◦ N February CIRA profile (the corresponding normis 73.47), i.e. with this profile the height is fitted slightlybetter than with the SAW profile.Note that in addition to 33 ×
12 temperature profilesCIRA also provides a single pressure profile as functionof altitude. This profile significantly differs from the SAW profile, it is about a factor of 1.46 larger around 40 km anda factor 0.65 smaller at ToA. The effective height spectrumobtained with both CIRA pressure and temperature pro-files shows larger deviations from the observed spectrumand is not considered further on.As a further test of the temperature sensitivity of theeffective height spectra the transmission has also been cal-culated with the other pressure and temperature profilesof the Anderson et al. [62] dataset. For all five p, T profilesthe residuals are significantly larger, the norms lie in therange 93 to 178 km. If, in addition, the concentration pro-files of H O, O , N O, CH , and CO are also replaced, thedeviations get even larger, with residua norms from 105 to233 km. Note that in all cases the maximum residuum is inthe CO band at 4 . µ m. Fig. 6 (bottom) shows effectiveheights and residuals for MLS with the largest mean differ-ence of 1 .
715 km. The results clearly confirm the choice ofthe SAW profile and emphasize the importance of choos-ing an appropriate pressure, temperature profile for fittingeffective height observations.
The effective height spectra presented so far have beenevaluated with the trapezoid quadrature (4) given a seriesof GARLIC limb spectra with equidistant tangent pointsfrom 4 to 100 km in δz t = 4 km steps. A denser tan-gent point grid does not significantly change the effectiveheight: the difference of the δz t = 4 km and δz t = 2 km10pectra is less than 0 . .
572 km (Fig. 7 top).The effective height integral (3) approximated with themidpoint quadrature and a limb sequence with tangentpoints at 6 , , , . . . ,
98 km altitude also shows largerdeviations to the observed effective height, with a meanresiduum of 0 .
525 km. Using a denser tangent grid spacingfor the midpoint quadrature (i.e., 5 , , , . . . ,
99 km)reduces this difference to 0 .
112 km.Note, however, that with midpoint quadrature contribu-tions from the lowest atmospheric layers are missing if theindividual transmission spectra are computed for pencil-beams. Limb paths with different tangent heights probedifferent parts of the atmosphere, i.e. the temperature de-creases by more than 10 km from z t = 4 km to z t = 6 km,and the “effective” path lengths through the atmosphere(ToA – tangent – ToA) is shortened by more than 20 km(for a pure geometric case ignoring refraction). Model-ing the limb transmissions with a rectangular field-of-viewwith half width 1 km improves the quality of the midpointquadrature estimate (mean residuum 0 .
498 km, see Fig. 7bottom).
In subsection 3.1.1 the relevance of a particular moleculehas been inferred from its impact on the residual spectrumand estimated quantitatively by the decrease of the resid-ual mean, maximum, or norm. An alternative approachis to study the increase of the residual due to the neglectof a single molecule in the list of absorbers. Accordinglywe have computed a series of effective height spectra with37 molecules (denoted as h ), i.e. with one of those gasesexcluded from the list of absorbers.Tab. 2 reveals that the omission of H O, CO , O ,N O, CH , HNO , or N drastically increases the residuumnorm. Note that for HF the residuum norm is slightlysmaller, this might be a hint on inadequacies of the spec-troscopic data and/or concentration profile. The relativechange of the residuum norm (9) can be as large as a factorten, e.g. for carbon dioxide and ozone. The importance ofthese molecules essentially confirms the results from thebottom-up analysis compiled in Tab. 1.The last column of Tab. 2 indicates that without H O,CO , O , CH , or HNO the effective height spectrumchanges by more than 10 km. Note that with all 38molecules included in the model ( h ), the residuum spec-trum h − h obs is ideally a noisy zero, hence the maxi-mum of h − h ≈ h obs − h ≡ ∆ h is a measure of thestrength of the neglected molecule’s spectral feature. Thismaximum residuum may overestimate the actual strength,but appears to be somewhat more objective than the com-monly used difference of the center absorption and theneighboring “continuum” absorption. The bottom-up and top-down analysis summarized inthe two tables can be used to define a (preliminary) listof important molecules for the Earth’s transmission spec-trum. Clearly gases such as PH or CClF do not haveany significant absorption and can be ignored. Remov-ing further species such as the heavy halogens also doesnot substantially increase the residuum. Fig. 8 shows thatwith 23 absorbing molecules (i.e. ignoring 15 molecules)the mean and norm residuum increases only slightly to0 .
471 and 77 .
26 km. Note that also ignoring absorption ofNH , C H or CHClF would lead to an increase of themean residuum by more than a hundred meters. The study of the (sub)arctic winter atlas presented inthe previous subsection has demonstrated the validity ofour radiative transfer modeling approach, the impact of“auxiliary” data such as molecular spectroscopy and at-mospheric state parameters, and has allowed to define alist of relevant molecules. Modeling effective height spec-tra for the (sub)arctic summer, the two midlatitude andthe tropical case and comparing these with the correspond-ing ACE-FTS IR atlas leads to the same conclusions. Themean or norm of the residuals as a function of the numberof molecules modeled is essentially identical to Tab. 1 andconfirms the list of “important” molecules given above.When a planet is observed as a distant point source, itwill likely be impossible to distinguish contributions frompolar, midlatitude, or tropical regions. Thus, when usingthe transit spectra generated from the ACE-FTS atlas asremote observations of an exoplanet, a disk-averaged spec-trum can be approximated by combining one sixth of thearctic summer, arctic winter, midlatitude summer, midlat-itude winter, and one third of the tropical spectrum.
For exoplanets little is known about seasonal and latitu-dinal climatologies, however, 3D model calculations havealready been used successfully to study Earth-like exoplan-ets [e.g. 78–83]. These advanced models can be used toconstruct a priori and or initial guess atmospheric stateparameters for the retrieval from exoplanet observations.In the following, however, we will only consider the six“scenarios” of the Anderson et al. [62] dataset (see sub-section 2.5). In particular, we will use the “US Standard”(USS) profile of the Anderson et al. [62] dataset for mod-eling the global effective height spectra in the followingsubsections. As for nitric acid and the CFC’s, the factor3 enhancement of HNO found for the arctic winter is notappropriate elsewhere, but increased CFC concentrationscan be observed in all cases. Thus, the HNO , CCl F andCCl F concentrations have been doubled henceforth.Before studying the detectability of various molecules,we compare the impact of atmospheric data on the disk-averaged spectrum. As a reference we computed the11 − − ∆ H e i g h t [ k m ] µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m
500 1000 1500 2000 2500 3000 3500 4000 4500 ν [cm − ] − − ∆ H e i g h t [ k m ] Figure 7: Comparison of quadrature methods for effective height residua spectra. Top: trapezoid ( δz t = 4 km) vs. 8 km. Bottom: midpointquadrature with infinitesimal (pencil beam) vs. finite field-of-view ( δz t = 4 km). ACE-FTS arctic winter; model spectra with 38 molecules asdiscussed in subsection 3.1. The numbers in the legend are the mean, maximum, and norm residuum of observation vs. model as defined insubsection 2.7. E ff . H e i g h t [ k m ] ACE-FTSall 38main23 ν [cm − ] − . − . − . − . . . . . . . ∆ H e i g h t [ k m ] µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m Figure 8: Comparison of transit spectra modeled with the 23 “important” gases or with all 38 gases. (Sub)-arctic winter, moderate resolutionΓ = 1 cm − . Legend numbers as in Fig. 5. T = 250 K. The discrep-ancies between observed and model spectrum are clearlyvisible, and the mean and norm residuals are increasedby roughly 20%. For a discussion of transmission spec-tra of hot Jupiter isothermal atmospheres see Heng andKitzmann [77].In view of the little improvement and the higher compu-tational cost of the “mix” scenario compared to the USSscenario, we will henceforth use the USS profiles to com-pute the effective height spectra. The impact of a missing molecule on the model spec-trum is listed in Tab. 3, and residual spectra are shown inFig. 10. Molecules that were prominent in the (sub)arcticspectra are also prominent for the global view. In partic-ular, the relative change of the residuum norm due to theneglect of carbon dioxide is greater than ten, and H O,O , N O, CH , N , and N O increase the norm by morethan a factor two. Note that the ranking of the relativenorm changes in Tab. 2 and 3 is identical for the strongestabsorbers, indicating a similar molecular impact for theglobal and arctic case.These large changes of the residuum norm are alsoclearly visible as differences between the effective heightspectra, that become larger than 30 km for CO and O (third numeric column in Tab. 3). Note that for somegases (CO, NO, CF ) the exclusion leads to slightly smallerresidual norms, what might be attributed to imperfectconcentration profiles or spectroscopic data. Furthermorenote that the max( δh ) given in Tab. 3 are similar to themaximum residual max(∆ h ) given in the legend of Fig. 10(see the discussion in subsection 3.1.5).Molecules that do not show a significant impact on theresidua are candidates for a further consolidation of thelist of important absorbers: Neglecting C H , CF , OCS,CH Cl, HOCl, NH , NO, or SO leads to a relative in-crease of the residuum norm of less than one percent.Note, however, that OCS, NO, and CF change the ef-fective height spectrum by about 1 .
1, 0 .
3, and 1 . The observed effective height analyzed so far has beenobtained by convolution of the high resolution ACE-FTSspectra with a Gauss response function of half widthΓ = 1 . − , and the model spectra have been degraded analogously. For an assessment of the relevance of molec-ular species with lower resolution, both the ACE-FTS andGARLIC spectra have been convolved with a Gauss ofΓ = 10 cm − .The effective height spectra for all but one molecule aredepicted in Fig. 11. As already discussed in the previ-ous subsection 3.2.2, leaving out molecules such as carbondioxide or ozone does not reduce the effective height tozero. Because of other interfering gases in the 4 . µ m band,excluding carbon dioxide reduces the effective height from48 km to about 10–20 km. Likewise, in the 9 . µ m regionthe absence of ozone in the model reduces h to roughly5 km. The strong absorption features of these gases aresuperimposed on a non-negligible background contributionof interfering gases, e.g. water vapor, which will make thequantification of the molecules abundance difficult.The last four columns of Tab. 3 quantify the impact ofan ignored molecule on effective height residuals and tran-sit depths. Note that the residual norms are much smallerfor the low resolution case (roughly a factor √ ≈ O, CO , O , and CH have adrastic effect on the spectra (Fig. 12) and their omissionsignificantly increases the residuum norm. Excluding ni-trous oxide, oxygen, nitric acid, and nitrogen also lead tomarked increases of the residual. As for the moderate res-olution case (Fig. 10), removing carbon monoxide reducesthe residuum mean and norm only slightly, but can beclearly seen in the spectrum.The importance of including heavy species, esp. someCFCs, in the modeling is also evident here. Along withHNO , both CCl F and CCl F significantly contributeto the absorption around 900 cm − , see Fig. 12 (bottomright). In this spectral region the Gaussian width ofΓ = 10 cm − is equivalent to a resolution ν/ Γ ≈ δh is only slightlysmaller for CO and O , hence the transit depth change isstill close to 1 ppm. Smearing of the fine peak structure ofmethane reduces δh by more than a factor two, whereas forH O, N O, O , N , HNO , and the CFC’s the reductionis less than a factor two. For an estimate of the SNR and its dependence on res-olution further runs with response function half widthsΓ = 2 , ,
20 and 50 cm − have been performed. Notethat for HNO the absorption peak around 890 cm − doesnot show up anymore for Γ = 50 cm − . Given the effec-tive height spectrum of all 23 molecules and the spectrumof 22 molecules the change of the additional transit depthis estimated by max (cid:0) d t,23 − d t,22 (cid:1) (see Tab. 3). For the13
000 1500 2000 2500 3000 3500 400001020304050 E ff . H e i g h t [ k m ] µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m ACE-FTSmixuss ν [cm − ] − . − . − . − . . . . . . . ∆ H e i g h t [ k m ] mix: 0.412 2.04 64.17uss: 0.420 2.03 65.66 ν [cm − ] − − − ∆ H e i g h t [ k m ] mix: 0.412 2.04 64.17iso: 0.499 2.87 77.84 Figure 9: Comparison of global moderate resolution (Γ = 1 cm − ) spectra: The ACE-FTS spectrum is a combination of the tropical,midlatitude, and arctic spectra. Model spectra (23 molecules) calculated as a mix with tropical, MLS, MLW, SAS, and SAW climatologies(red) or with the USS atmosphere (blue, top and center) or with an isothermal ( T = 250 K) atmosphere (blue, bottom, residuals only).Legend numbers as in Fig. 5. SNR T according to Eq. (10) we assume (similar to Hedeltet al. [15], see his Table 3) a James Webb Space Telescope(JWST) configuration with A = 240 m and q = 0 .
15, astellar radius and temperature as for the Sun (6 . · kmand 5770 K), an integration time of 12 .
98 h for the Sun-Earth system, and an observer-star distance of 10 pc. Theresolving power is estimated by the FWHM (full width athalf maximum) of the Gaussian spectral response functionat the band center, i.e. R = ν band / ∼ √ t/D , reasonable SNRs mayalso be possible for ozone when an exo-Earth at a few par-secs is observed for multiple transits with R ≤
20. Note,however, that “simply” co-adding spectra recorded at mul-tiple transits might be challenging because of the temporalvariability of the host star or the degradation of the detec-tor performance. In this respect, a planet orbiting closerto its host star allowing more observations in a shorterperiod of time would be advantageous. For example, anEarth-like planet at 1 AU could only be observed five times during JWST’s lifetime, leading to a factor ≈ Clouds cover more than half of Earth’s surface and playa dominant role in the climate system [85]. Although theACE-FTS atlases have been compiled by averaging cloud-free spectra only, it is nevertheless instructive to exploitthese data for an assessment of the impact of clouds. Fol-lowing Garc´ıa Mu˜noz et al. [24] clouds are assumed toblock the radiation traversing the lower most limb ray at4 km, i.e. the very first transmission contributing to the in-tegral/sum in Eqs. (3) and (4) is set to T ( ν, z ) = 0. (Notethat “typical” water clouds can be expected for somewhatlower regions, whereas ice clouds are typically found inaltitudes around/up to the tropopause.) Furthermore weassume a 50% cloud cover for each of the 5 latitude bands/ seasons, so the final spectra are given by the mean of thecloud-free and fully cloud-contaminated global spectra.Fig. 14 demonstrates that a cloud layer changes theglobal effective height spectrum essentially for smallheights, whereas spectral regions characterized by strong14
000 1500 2000 2500 3000 3500 4000 − H2O 2.694 19.52 510 − CO2 2.646 35.73 815.4 − ∆ H e i g h t [ k m ] O3 1.809 34.22 618.7 − N2O 0.710 8.35 159.2 − . − . − . − . . . . . . . CO 0.410 2.14 64.78 − CH4 1.428 20.75 330.3 − − O2 0.512 4.36 86.75 − − HNO3 0.559 6.58 114.7 − ∆ H e i g h t [ k m ] N2 0.604 7.16 139.5 − . − . − . − . . . . . . . NOx 0.446 2.14 70.37 ν [cm − ] − . − . − . − . . . . . . . OCS 0.424 2.03 66.12 ν [cm − ] − − CFCs 0.487 5.49 89.83
Figure 10: Impact of a missing species on global residual spectra (moderate resolution Γ = 1 cm − ). The bottom right plot shows CCl F,CCl F , and CF combined. For the reference spectrum (blue) with 23 molecules the residuum mean and norm are 0 .
42 km and 65 . able 3: Norm (8), relative change of norm (9), maximum change max( δh ) = max( h − h ) of effective height (3), and the change of theadditional transit depth (5) due to omission of a single molecule. The norm for the spectra with all 23 molecules included is given in the veryfirst row. Note that the δh columns give the maximum change, e.g. the peak at 1040 cm − for ozone and at 3030 cm − for methane, compareFig. 10 and Fig. 12. moderate resolution low resolutionnorm relNorm δh ∆ δd t norm relNorm δh ∆ δd t [km] [km] [km] [km]65.656 19.279CO2 815.414 11.419 36.386 9.6e-07 253.121 12.129 34.364 9.1e-07O3 618.729 8.424 34.966 9.2e-07 189.244 8.816 32.519 8.6e-07H2O 509.956 6.767 19.296 5.1e-07 152.659 6.918 12.541 3.3e-07CH4 330.335 4.031 22.055 5.8e-07 93.601 3.855 10.393 2.7e-07N2O 159.233 1.425 8.950 2.4e-07 47.058 1.441 8.069 2.1e-07N2 139.539 1.125 8.046 2.1e-07 42.818 1.221 6.616 1.7e-07HNO3 114.697 0.747 8.110 2.1e-07 33.768 0.752 5.636 1.5e-07O2 86.748 0.321 4.130 1.1e-07 25.622 0.329 3.240 8.5e-08CCl2F2 83.632 0.274 4.615 1.2e-07 24.261 0.258 2.919 7.7e-08CCl3F 72.621 0.106 4.535 1.2e-07 20.804 0.079 2.455 6.5e-08NO2 70.396 0.072 2.427 6.4e-08 20.760 0.077 1.850 4.9e-08ClONO2 66.968 0.020 0.873 2.3e-08 19.649 0.019 0.505 1.3e-08N2O5 66.835 0.018 1.000 2.6e-08 19.637 0.019 0.731 1.9e-08CHClF2 66.532 0.013 0.198 5.2e-09 19.564 0.015 0.116 3.1e-09CO 64.777 0.013 2.383 6.3e-08 18.692 0.030 1.098 2.9e-08C2H6 65.913 0.004 0.307 8.1e-09 19.344 0.003 0.132 3.5e-09CF4 65.831 0.003 1.042 2.7e-08 19.261 0.001 0.350 9.2e-09OCS 66.122 0.007 1.090 2.9e-08 19.361 0.004 0.720 1.9e-08CH3Cl 65.718 0.001 0.109 2.9e-09 19.287 0.000 0.057 1.5e-09HOCl 65.691 0.001 0.028 7.3e-10 19.290 0.001 0.019 5e-10NH3 65.711 0.001 0.119 3.1e-09 19.297 0.001 0.026 7e-10NO 65.630 0.000 0.311 8.2e-09 19.269 0.001 0.193 5.1e-09SO2 65.655 0.000 0.065 1.7e-09 19.278 0.000 0.035 9.2e-10absorption due to, e.g., carbon dioxide or ozone are notaffected. Accordingly one can expect that clouds do notsignificantly change the detectability of these strong ab-sorbers.
4. Discussion
Our analysis has demonstrated that ten gases substan-tially contribute to Earth’s transit spectrum as observedby the ACE-FTS instrument: CO , O , H O, CH , N O,N , HNO , O , and the CFCs CCl F and CCl F orderedaccording to the relative change of the residual norm (seeTab. 3). However, the transit spectrum modeled withthese 10 “main” gases only results in large residua esp.around 1630 cm − , that can be attributed to NO . The ne-glected absorption due to NO is especially seen in the lowresolution spectrum around 1900 cm − . Carbon monoxidehas a substantial impact at 2150 cm − (and much smalleraround 4300 cm − ). Furthermore, the omission of OCSleads to noticeable residuals at 2070 cm − , and CF is vis-ible around 1285 cm − . ClONO clearly shows up at 800and 1745 cm − (the band around 1300 cm − is less promi-nent in the spectra), and N O at 750 and 1240 cm − .Hence, adding nitrogen oxides, carbon monoxide, carbonyl sulfide, tetrafluoromethane, chlorine nitrate, and nitrogenpentoxide in the model removes these discrepancies, al-though these five species do not alter the mean and normresidual. In conclusion, the preliminary list of “impor-tant” absorbers defined in subsection 3.1.5 can thereforebe further shortened by deletion of C H , CH Cl, CHClF ,HOCl, NH , and SO .The comparison of spectra modeled with the 17 “main”gases and with 23 molecules is shown in Fig. 15. Althoughthe residual is somewhat larger, the selection of the rel-evant molecules is especially important for the quantita-tive estimate of concentrations using inversion techniques:First, ignoring irrelevant species helps to speed up the for-ward modeling; secondly, limiting the number of unknowngas concentrations, i.e. reducing the size of the state vec-tor, will lead to a better conditioning of the inverse prob-lem. Nevertheless, neglecting further gases in the modelingleads to a visible increase of the low or moderate resolu-tion residual spectra. However, the importance of thesegases for the modeling does not necessarily imply theirdetectability in noisy low resolution spectra.Except for CO, NO, OCS, CF , ClONO , and N O ourlist is identical to the eleven “spectroscopically most sig-nificant molecules” used by Kaltenegger and Traub [12].16
000 1500 2000 2500 3000 3500 4000
Wavenumber ν [cm − ]01020304050 E ff e c t i v e h e i g h t h [ k m ] µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m ACE-FTSH2OCO2O3N2OCOCH4O2HNO3N2CFC
Figure 11: Impact of a missing species on the global effective height spectrum (low resolution Γ = 10 cm − ). Rugheimer et al. [19] modeled Earth’s reflection and emis-sion spectra using “21 of the most spectroscopically signif-icant molecules”. For the validation of the SMART code[86] with AIRS [32] and ATMOS [31] observations eightspecies (H O, CO , O , N O, CO, CH , and O ) havebeen included in the modeling by Robinson et al. [27] andMisra et al. [30], respectively. Barstow et al. [87] consid-ered H O, CO , O , CO, CH , O , SO , OCS, N forretrieval tests of exo-Earths and exo-Venuses, but foundSO and OCS to be negligible for Earth. Also note thatour list of seventeen gases is appropriate for Earth andmay change for other planets.The limited spectral resolution can mask the molec-ular absorption features, and we have assessed this byconvolution of the high resolution ACE-FTS spectra andmonochromatic model spectra with a Gaussian responsefunction. In particular, we have assumed that the widthof the Gaussian is constant over the entire spectral do-main. Note that for modeling the ACE-FTS spectrathe monochromatic transmission (1) has to be convolvedwith an instrument line shape given approximately by2 L sinc(2 πLν ) where L is the maximum optical path dif-ference ( L = ±
25 cm for ACE-FTS).In contrast to the constant width FTS, instrumentsfor exoplanet observations are frequently characterizedby a constant resolving power R = ν/δν . The In-fraRed Spectrograph (IRS) of the Spitzer Space Tele-scope had two modules for moderate and low resolutionin the 5 – 38 µ m region where the moderate resolution R = 600 corresponds to our HWHM Γ = 1 cm − at the low wavenumber end. The IR and NIR spectrographs of theARIEL (Atmospheric Remote sensing Infrared ExoplanetLarge survey) ESA mission candidate aim to observe the1 .
95 – 7 . µ m interval with a resolving power of R = 100and the 1 .
25 – 1 . µ m interval with R = 10, respectively[88]. The Mid InfraRed Instrument (MIRI) on the JamesWebb Space Telescope (JWST) will offer two spectrome-ter modes, the low resolution spectrograph with R = 100in 5 – 12 µ m and the medium resolution spectrometer with R = 1300 – 3700 in 5 – 28 µ m, and JWST’s Near-InfraRedSpectrograph (NIRSpec) covers four wavelength regionsup to 5 . µ m with medium ( R = 1000) or high (2700) res-olution [e.g. 89].Our spectra (both observed and modeled) are in agree-ment with other transit spectra published before. Themaximum effective height in the CO ν band around2340 cm − (about 48 km for the moderate resolution and ≈
46 km for the low resolution) is compatible with spectramodeled by Misra et al. [30] and Kaltenegger and Traub[12]. The effective height in the center of the ozone bandof about 35 km is somewhat lower than shown in [12], andthe minimum effective height of roughly 1 – 4 km (depend-ing on resolution) is considerably smaller here, both forthe observed and model spectrum (presumably because ofthe absence of clouds). The “atmospheric radius” of anEarth-like planet shown by Meadows et al. [90] has a max-imum of about 60 km in the ν and ν bands of CO , asimilar peak at 9 . µ m at the ozone band, and the min-imum radius is larger than observed by ACE-FTS. Themaximum of the effective tangent height around the CO
000 1500 2000 2500 3000 3500 4000 − H2O 2.658 12.47 152.7 − CO2 2.610 33.89 253.1 − ∆ H e i g h t [ k m ] O3 1.774 31.83 189.2 − N2O 0.663 7.53 47.06 − . − . − . . . . . . CO 0.367 1.88 18.69 − CH4 1.404 9.82 93.6 − − O2 0.478 3.34 25.62 − − HNO3 0.527 5.12 33.77 − − ∆ H e i g h t [ k m ] N2 0.563 6.35 42.82 − . − . − . . . . . . NOx 0.413 1.88 20.75 ν [cm − ] − . − . − . . . . . . OCS 0.389 1.88 19.36 ν [cm − ] − − CFCs 0.449 3.66 25.69
Figure 12: Effective height residual spectra due to the exclusion of a single molecule (low resolution Γ = 10 cm − , see also Fig. 10). Forthe reference spectrum (blue) with 23 molecules the residuum mean and norm are 0 .
38 km and 19 .
500 1000 1500 2000
Resolving Power . . . . . . . . . S NR t r an s m i ss i on H2O 3800CO2 2325O3 1040CH4 3030N2O 2200N2 2450O2 1600HNO3 890
Figure 13: Single-to-noise ratios of Earth’s transmission spectrum seen from a 10 pc distance. The numbers in the legend indicate the bandcenter wavenumber in cm − . . µ m band shown by Rauer et al. [14] is somewhat lower,whereas the maximum around the O . µ m band is largerthan ours.The SNR’s reported here are also comparable with thosegiven by Rauer et al. [14] (Table 3). Differences can beattributed to, e.g., the atmospheric setup (here “US Stan-dard” [62] with enhanced carbon dioxide, methane, and ni-tric acid concentrations and additional trace gases), spec-troscopic database (HITRAN 2016 vs. 2004, see also re-mark below), and the actual estimate of the effective heightchanges. Furthermore note that the analysis of subsection3.2.4 only provides a rough SNR estimate assuming anideal detector and non-variable sources; for an extendednoise model see, e.g., Hedelt et al. [15].In our analysis we have used atmospheric profiles asgiven by standard Earth climatologies [62–64]. Only ina few cases, where the default was either clearly inade-quate (outdated CO and CH concentrations) or wherediscrepancies between observation and model were obvi-ous (HNO and CFC 11 and 12), profiles were adjusted byvisual inspection of the spectra. Fitting atmospheric stateparameters (e.g. concentration scaling factors) by meansof numeric optimization techniques is clearly advantageousand this study serves as a preparation for an analysis ofthe ACE-FTS spectra with nonlinear least squares inver-sion [cf. 46]. Although transmission spectra are primarily used for concentration retrievals, the analysis of subsection3.1.3 has indicated the importance of pressure and tem-perature profiles that are hardly available for exo-Earths;clearly the retrieval of p and T will make the inverse prob-lem even more challenging. Note that for the data analysisof the ACE-FTS spectra pressure, temperature, and theCO mixing ratio are determined in a first step before thetrace gas concentration retrieval [39].Success or failure of the inversion critically depends onthe proper initial guess or a priori atmospheric profiles.The temperature profile has been shown to impact theeffective height (cf. subsection 3.1.3), on the other handFig. 3 shows a surprisingly little spread of the observedspectra for the five seasons/latitudes. Nevertheless, thechoice of appropriate temperatures is clearly an impor-tant issue for the analysis of the ACE-FTS spectra or,more generally, planetary transmission spectra. Amongall IR relevant atmospheric species water has the highestvariability (esp. in the troposphere), however, accordingto Fig. 3 this is only partly propagated into the effectiveheight spectra near its band centers and the choice of theH O profile might be less critical for the performance ofthe fitting.Due to the mature quality of the current spectroscopicdatabases, the modeled effective height is essentially in-dependent of the choice of HITRAN or GEISA. However,19
000 1500 2000 2500 3000 3500 400001020304050 E ff e c t i v ehe i gh t[ k m ] µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m wavenumber [cm − ]01020304050 E ff e c t i v ehe i gh t[ k m ] Cloud freeFully cloudy
Figure 14: Impact of clouds on global effective height spectrum (top: moderate resolution Γ = 1 cm − , bottom: low resolution Γ = 10 cm − ) using the much older HITRAN 86 database with 233 thou-sand lines of 28 molecules significantly increases the meanand norm residual to 0 .
81 km and 154 km (compare the m = 28 row in Tab. 1), with large peaks up to almost 10 kmin the residuum spectrum in the center of the methanebands. Moreover, the version of the continuum did notchange the model spectrum notably (the H O continuumis especially important in the lower troposphere). Espositoet al. [91] noted that “typical differences introduced by thetwo H O continuum models are of one order of magnitudeless than typical differences arising from different line pa-rameters.” In conclusion, the choice of spectroscopic inputdata is not expected to impact the analysis substantially.However, this may be different for water-rich and hot at-mospheres [e.g. 70, 72].Our main objective has been to identify molecular sig-natures in Earth’s transit spectra useful for atmosphericretrieval of terrestrial exoplanets. Alternatively, one canview this study as a validation of the GARLIC forwardmodel. A similar validation study for the SMART code[86] using ATMOS observations [31] has been presentedby Misra et al. [30]. However, the approach used here ap-pears to be suboptimal for a thorough validation: First,it would be more appropriate to compare model andobserved transmission spectra corresponding to individ-ual tangent heights (similar to Kaltenegger and Traub[12], Misra et al. [30]). Secondly, the comparison shouldbe performed for high spectral resolution of the ACE-FTSobservations. Both the integration or summation in thespatial and spectral domain could lead to a cancellation or compensation of model errors. Furthermore, modelspectra would be computed for all molecules known to berelevant for Earth’s atmosphere, the impact of individualmolecules is of little interest. Finally, the state of the at-mosphere should be known precisely; sophisticated closureexperiments have been performed for this purpose [e.g. 92–95]. Note that there appears to be no direct link betweenthe ACE climatology [73, 74] and the ACE-FTS atlas [40].
5. Summary and Outlook
Effective height transit spectra of Earth have beengenerated by combining representative limb transmissionspectra observed by the ACE-FTS solar occultation instru-ment. These spectra have been degraded to moderate andlow resolution and compared with spectra computed withan lbl radiative transfer code using HITRAN (or GEISA)spectroscopic data. Inclusion of exclusion of moleculesconsidered in the modeling allowed to study their impacton the transit spectra. The main infrared absorbers wa-ter, carbon dioxide, ozone, nitrous oxide, and methane canbe clearly identified in the effective height spectra. Fur-thermore, nitric acid is very prominent around 900 cm − ,and the main constituents of Earth’s atmosphere, molecu-lar oxygen and nitrogen, are also important for modelingthe spectra. To further reduce the discrepancies, heavymolecules had to be considered, too. In particular, the“technosignatures” CFC11 and CFC12 are visible in themoderate and low resolution spectra.20
000 1500 2000 2500 3000 3500 4000 − . − . − . − . . . . . . . ∆ H e i g h t [ k m ] µ m 6.7 µ m 5.0 µ m 4.0 µ m 3.0 µ m 2.5 µ m
23 gases: 0.420 2.03 65.6617 gases: 0.427 2.07 66.97 ν [cm − ] − . − . − . . . . . . ∆ H e i g h t [ k m ]
23 gases: 0.385 1.88 19.2817 gases: 0.391 1.88 19.67
Figure 15: Comparison of transit spectra residuals modeled with the 23 gases (see Tab. 3) or with 17 gases: H O, CO , O , N O, CO, CH ,O , NO, NO , HNO , OCS, N , CCl F, Cl F , CF , ClONO , N O . Moderate resolution Γ = 1 cm − (top) and low resolution Γ = 10 cm − (bottom). Legend numbers as in Fig. 5. Transit observations of extrasolar Earth-like planetsavailable for analysis in the near future will likely not en-compass the large spectral range nor will they have thehigh resolution and low noise of the ACE-FTS spectraused in this study. When ACE-FTS observations are usedfor a feasibility study of Earth-like exoplanet transit spec-troscopy, the impact of spectral interval, resolution, andsignal-noise ratio will be an important aspect. Despite theclear visibility of a dozen or more molecules in the moder-ate and low resolution spectra, our SNR estimates indicatethat only a few species may actually be detectable undervery favorable conditions.For the quantitative estimation of atmospheric stateparameters from spectroscopic observations, inversion bynumerical optimization techniques is well established forEarth and Solar System planets. More recently, thesetechniques have also been applied successfully for remotesensing of exoplanets [e.g. 96–100]. So far these retrievalsare confined mostly to large objects such as hot Jupiters,whereas the analysis of smaller objects such as super-Earths and Earth-like exoplanets is clearly more challeng-ing [101, 102]. Nevertheless, we are adapting our GARLICcode (already used for analysis of microwave, far, thermal,and near IR Earth observation data [e.g. 46, 47]) to exo-planet studies.Verification and validation of exoplanet retrieval codesis an important aspect. Whereas verification can be read-ily accomplished using synthetic measurements and codeintercomparison (similar to [e.g. 103]), validation is chal- lenging due to the lack of reference “truth” data (e.g. insitu measurements). Thus, testing an exoplanet retrievalwith Earth (or other Solar System planets such as Mars orVenus) is an attractive alternative. The spectra providedin the ACE-FTS atlases provide an unique opportunity togenerate a representative effective height spectrum (simi-lar to the ATMOS spectra [31]), and our inverse problemsolver currently being developed on the basis of the GAR-LIC forward model will be validated against this dataset.
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Acknowledgments
First we would like to thank Thomas Trautmann andAdrian Doicu (Oberpfaffenhofen) and Lee Grenfell andHeike Rauer (Berlin) for useful discussions and criticalreading of the manuscript. The atmospheric spectra pro-vided by the MIPAS group in Oxford have been quiteuseful for this study, see http://eodg.atm.ox.ac.uk/ATLAS/http://eodg.atm.ox.ac.uk/ATLAS/