Precise methane absorption measurements in the 1.64 μm spectral region for the MERLIN mission

Abstract

In this article we describe a high-precision laboratory measurement targeting the R(6) manifold of the 2ν₃ band of ¹²CH₄. Accurate physical models of this absorption spectrum will be required by the Franco-German, Methane Remote Sensing LIDAR (MERLIN) space mission for retrievals of atmospheric methane. The analysis uses the Hartmann-Tran profile for modeling line shape and also includes line-mixing effects. To this end, six high-resolution and high signal-to-noise absorption spectra of air-broadened methane were recorded using a frequency-stabilized cavity ring-down spectroscopy apparatus. Sample conditions corresponded to room temperature and spanned total sample pressures of 40 hPa – 1013 hPa with methane molar fractions between 1 μmol mol⁻¹ and 12 μmol mol⁻¹. All spectroscopic model parameters were simultaneously adjusted in a multispectrum nonlinear least-squares fit to the six measured spectra. Comparison of the fitted model to the measured spectra reveals the ability to calculate the room-temperature, methane absorption coefficient to better than 0.1% at the on-line position of the MERLIN mission. This is the first time that such fidelity has been reached in modeling methane absorption in the investigated spectral region, fulfilling the accuracy requirements of the MERLIN mission. We also found excellent agreement when comparing the present results with measurements obtained over different pressure conditions and using other laboratory techniques. Finally, we also evaluated the impact of these new spectral parameters on atmospheric transmissions spectra calculations.

1. Introduction

Methane (CH₄) is the second most important anthropogenic greenhouse gas after carbon dioxide. It is responsible for about 20% of the warming induced by long-lived greenhouse gases [Kirschke et al., 2013]. Since pre-industrial times, the background molar fraction of atmospheric methane has increased approximately 2.5 times to its present value of 1.8 μmol mol⁻¹. Methane emissions are caused by human activities as well as natural sources [Kirschke et al., 2013]. The lack of precise global measurements of atmospheric methane is a major problem which limits our understanding of methane source- and sink-processes. Existing surface measurements of methane do not have sufficient spatial coverage to adequately quantify the worldwide distribution of methane emissions. Thus, high-precision, space-borne measurement techniques are necessary to obtain global coverage. Passive remote sensors such as SCIAMACHY [Frankenberg et al., 2011], GOSAT [Parker et al., 2011], CarbonSat [Buchwitz et al., 2013], and Sentinel 5 [Butz et al., 2012] measure the wavelength-resolved solar backscattered radiation from the surface of the Earth. However, these sensors are unable to measure at high altitudes during the winter months and their data are subject to bias in regions with aerosols layers or thin ice clouds [Morino et al., 2011]. Space-borne active remote sensing is thus a complementary approach because it can be more sensitive near the surface of the Earth, essentially has zero aerosol/cloud biases and can measure during both daytime and nighttime. In order to realize this goal, Deusches Zentrum für Luft- und Raumfahrt (DLR) and Centre National d’Etudes Spatiales (CNES) proposed the “Methane Remote Sensing Lidar Mission” (MERLIN) in 2010 within the framework of a German-French climate-monitoring initiative [Stephan et al., 2011]. This approach is based on the integrated-path differential-absorption (IPDA) LIDAR technique which measures the difference in atmospheric transmission between a laser emitting at a wavelength near the center of a methane absorption feature [Measures, 1992], denoted on-line, and a reference off-line wavelength with no significant absorption ([Kiemle et al., 2013] and references therein). For MERLIN, the selected on-line wavelength is situated at the trough (λ=1645.55 nm) between two strong absorption features which belong to the R(6) manifold of the 2ν₃ band of ¹²CH₄ [Kiemle et al., 2011]. By positioning the on-line wavelength in this local absorption minimum, the laser frequency stability requirement can be relaxed. The primary objective of the mission is to obtain spatial and temporal gradients of atmospheric methane columns with high precision and unprecedented accuracy on a global scale. For that, a statistical relative uncertainty (precision) of 1% with a spatial resolution of 50 km and a temporal resolution of 1 month and 0.1% for systematic relative uncertainty (accuracy) for the measured methane columns are required [Stephan et al., 2011; Kiemle et al., 2013]. Therefore, the temperature-, pressure- and wavelength- dependent absorption cross-sections which describe the attenuation of the radiation by methane have to be known with extremely high accuracy in order to achieve this objective.

Many laboratory studies have been devoted to improving our spectroscopic knowledge of methane. The various spectroscopic parameters needed for calculating the absorption spectrum are line position, line-integrated intensity and line shape (i.e. line width, line pressure-induced shift etc.). From a remote sensing point of view, the absorption line-shape parameter appears to be the most critical parameter. Inadequate modeling of the line shape, e.g. caused by erroneous spectroscopic broadening parameters or by the use of a deficient line-shape model, typically results in gas concentration retrieval errors that exhibit latitudinal, seasonal or other regionally varying biases. An overview of recent measurements of the line-shape parameters of the 2ν₃ band of ¹²CH₄ can be found in Devi et al. [2015]. The R(6) manifold was investigated by four studies, [Frankenberg et al., 2008; Lyulin et al.,2009; Lyulin et al., 2011; Devi et al., 2015], all of which were based on Fourier transform spectroscopy (FTS). Except for Devi et al. [2015], the other studies adopted the Voigt profile (VP) to represent the line shapes of isolated methane transitions. This profile is now considered as obsolete for many applications since it cannot reproduce absorption spectra to within a precision of a few percent [Ngo et al., 2013; Hartmann et al., 2008; Birk and Wagner, 2016]. Generally, other collisional (i.e. pressure-dependent) effects such as line-mixing, Dicke narrowing and speed dependence have to be taken into account in the line-shape calculation in order to represent more accurately measured spectra. Furthermore, instrument-induced line-shape distortion makes the precise determination of line shape parameters more challenging with traditional FTS methods. Also, the limited optical path length of the cells used in FTS spectrometers (leading to the need for samples with high absorber concentration) can render the contribution of methane self-broadening non-negligible, which is a situation unfavorable for the precise determination of air-broadened line shapes.

The frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) technique [Hodges et al., 2004; Long et al., 2012] offers a powerful alternative to traditional FTS methods, especially for precise measurements of optically thin spectra that are well below the detection limit of conventional spectrometers. In FS-CRDS technique, absorption spectra are acquired by locking the probe-laser frequency to successive modes of a length-stabilized, high-finesse optical resonator and by measuring the cavity decay rate associated with each mode. In this fashion, FS-CRDS spectra are obtained from measurements of time and frequency, resulting in accurate detuning (x) and absorption coefficient axes (y) and negligible instrumental line broadening. Importantly, this unique approach to CRDS provides the spectral resolution and linearity required for precise fits of non-Voigt line profiles and the concomitant determination of various line shape parameters [Lisak et al., 2010; Long et al., 2010; Long et al., 2011; Lamouroux et al., 2014; Sironneau et al., 2015]. FS-CRDS typically yields spectrum signal-to-noise ratios in the 5×10³:1 to 2×10⁴:1 range, with some reported measurements ranging from 2×10⁵:1 [Cygan et al., 2012] to 10⁶:1 [Lin et al., 2015]. The accurate measurement of isolated transition areas on samples of known composition and density [Sironneau et al., 2015; Polyansky et al., 2015] also yields low-uncertainty determinations (0.2% relative uncertainty level) of line intensities. With regard to measurements of transition frequencies and pressure shifting coefficients, FS-CRDS can be referenced to highly accurate RF frequency standards via an optical frequency comb (OFC) [Truong et al., 2013]. This scheme provides absolute transition frequencies (uncertainties from 10 kHz – 100 kHz) as well as pressure shifting coefficients with relative uncertainties well below 1%.

In this work, an FS-CRDS apparatus [Lin et al., 2015] recently developed at the National Institute of Standard and Technology (NIST) in Gaithersburg, Maryland USA was used to record spectra of methane diluted in air. We measured spectra in the R(6) manifold region of the 2ν₃ band of ¹²CH₄ for six pressures in the range 40 hPa to 1013 hPa. These spectra were analyzed using multispectrum fitting of the model to the measured spectra, whereby the model parameters were adjusted simultaneously for all pressure conditions. The recently recommended line-shape model, the Hartmann-Tran profile (HTP) [Tennyson et al., 2014; Ngo et al., 2013], was used to calculate the isolated line shapes associated with the individual rotation-vibration transitions of the manifold. This profile takes into account Dicke narrowing, speed dependence effects and correlation between velocity-changing and internal-state-changing collisions. In addition, collisional interferences between lines (i.e. line-mixing) were also accounted for by using the first-order approximation of Rosenkranz [Ngo et al., 2013; Rosenkranz, 1975].

In the remainder of this article we describe the FS-CRDS measurements of air-broadened methane and the associated multispectrum fitting results. Line parameters and their uncertainties for the investigated ¹²CH₄ transitions are reported. We also compare the present results to previous FTS measurements and existing spectroscopic line lists. Finally, using our measured methane line parameters and external database parameters for carbon dioxide and water vapor, we discuss calculated absorption spectra for an atmospheric column spanning the 4 cm⁻¹ - wide wave number region relevant to the MERLIN mission.

2. Experimental apparatus

Here we provide only a brief overview of the FS-CRDS apparatus used in this work. For a more detailed description see Ref. [Lin et al., 2015]. The sample cell comprises an all-stainless-steel vacuum-compatible enclosure (internal volume ≈ 250 cm³) containing two high-finesse mirrors (R=0.99997 at λ = 1.65 μm, radius of curvature = 1 m). The ring-down cavity length (≈ 138 cm) is actively stabilized by referencing to the simultaneous cavity transmission of an iodine-stabilized HeNe laser, which results in a long-term cavity mode frequency stability of approximately 10 kHz. The probe beam is provided by an external cavity diode laser followed by a booster-optical amplifier used for power amplification and rapid switching to initiate the ring-down decay events. At each spectrum step, the probe laser frequency is actively stabilized to a TEM₀₀ mode of the ring-down cavity using a high-update-rate (400 Hz) wavelength meter with a frequency resolution of 1 MHz. At the beginning of each scan, the frequency axis is referenced to the heterodyne beat signal between the probe laser beam and a Cs-clock-referenced optical frequency comb (OFC) having a fractional stability of 10⁻¹³ (1 s averaging time). Frequency detuning relative to the first point of the scan is determined by counting ring-down cavity mode orders as the laser is tuned from mode-to-mode of the ring-down cavity. The mode spacing or cavity free spectral range (FSR) is measured by step-scanning the laser from mode-to-mode of the evacuated ring-down cavity and measuring the laser frequency at each step with a high-precision wavelength meter (resolution of 1 MHz), resulting in unc(FSR) = 2 kHz. At each pressure condition, we correct the empty-cavity FSR value for the effect of air density on optical pathlength using dFSR/dp = −0.285 Hz/Pa (based on the calculated dependence of air refractive index with density for a wavelength λ = 1645.75 nm and temperature T = 23 °C). The combined standard uncertainty for the first point of the spectrum frequency axis is approximately 100 kHz and is limited by the precision of the laser frequency lock. There is a cumulative error along the detuning axis which is equal to Δq×u(FSR) where Δq is the number of mode jumps. For all spectra reported here Δq < 500, yielding a maximum uncertainty of about 1 MHz for the absolute frequency at all points. As previously described, [Lin et al., 2015], this spectrometer has a minimum detectable absorption coefficient of 1.5×10⁻¹² cm⁻¹ (10 s averaging time). In the present study, each spectral point is based on the average of 320 decay events, with successive spectrum points acquired every 7 s. We acquired absorption spectra on static charges of the methane/air sample at temperatures near 296 K. We measured the gas pressure and temperature in the ring-down cell using NIST-calibrated pressure and temperature sensors having relative combined standard uncertainties generally less than 0.05% and 20 mK, respectively. The temperature sensor was in good thermal contact with the outside surface of the bounding stainless steel tube (1 m long, 2.5 cm diameter) containing the sample gas. We observed that the largest driver of temperature uncertainty was caused by axial gradients (maximum absolute difference < 80 mK) in the cell wall temperature. Assuming ideal gas conditions and adding the pressure and temperature uncertainties in quadrature yields a relative combined standard uncertainty in sample gas density of 0.02%. In order to optimize the spectrum signal-to-noise ratio over the pressure range considered, we used a pair of high- (11.8736 μmol mol⁻¹ ± 0.0039 μmol mol⁻¹) and low- (1.192 μmol mol⁻¹ ± 0.01 μmol mol⁻¹) concentration mixtures of methane in air. Both mixtures were certified at NIST by reference to primary gravimetric standards. The specified concentrations correspond to total methane at natural isotopic abundance. For the spectrum model described below, we assumed the relative abundance of ¹²CH₄ in the total methane to be 0.98827. Table 1 summarizes the experimental conditions of the analyzed spectra, the corresponding standard uncertainties and other experimental specifications.

Table 1.

Upper. Experimental conditions for the measured spectra where P, T, and x are the total sample pressure, temperature, methane-in-air and molar fraction, respectively. For each quantity, uncertainty components are added in quadrature. In the case of pressure and temperature, the component uncertainties include the standard deviation of the respective measurements for each spectrum and the combined standard uncertainty in the pressure or temperature gauge. The temperature uncertainty also includes a component associated with temperature gradients in the sample gas. The final column gives the relative combined standard uncertainty for the total methane concentration n, which is assumed to be at natural isotopic abundance. Lower. Experimental specifications for ring-down apparatus.

spectrum	P (hPa)	unc(P)/P (%)	T (K)	unc(T)/T (%)	x (umol mol−1)	unc(x)/x (%)	unc(n)/n (%)
1	40.535	0.046	296.225	0.025	11.8736	0.033	0.062
2	133.64	0.028	296.183	0.027	11.8736	0.033	0.051
3	402.89	0.025	296.097	0.028	11.8736	0.033	0.050
4	506.49	0.019	296.129	0.030	11.8736	0.033	0.048
5	760.69	0.014	296.110	0.028	1.192	0.839	0.839
6	1013.53	0.013	296.106	0.029	1.192	0.839	0.840
System Parameters
* ring-down cavity length (cm)				137.84
* empty cavity FSR (MHz)				108.75
unc(FSR) (kHz)				2
unc(ν) (MHz)				1
* mirror reflectivity				0.99997
number of ring-down acquisitions per frequency step				320

^*denotes a nominal value.

3. Spectrum analysis

The measured spectra were analyzed using a multispectrum fitting technique [Benner et al., 1995] in which all six measured spectra (Table 1) were fit by simultaneous adjustment of the model parameters. This technique allows one to constrain the linear pressure dependence of line shape parameters and to decrease the numerical correlation between these parameters. The fitting procedure was realized using code that we recently developed, and which provides adjustable parameters related to each spectrum considered and to each spectral line. A particular feature of this code is that we can calculate complex line profiles, such as the HTP [Ngo et al., 2013; Tennyson et al., 2014], along with line-mixing through the first-order approximation of Rosenkranz [Rosenkranz, 1975]. Moreover, because methane molar fractions for all measured spectra did not exceed 12 μmol mol⁻¹, we were able to safely neglect the effects of methane self-broadening. Only parameters of the six R(6) manifold lines of ¹²CH₄ were adjusted during the fitting process. Contributions of weak interfering lines having intensities lower than 1.0×10⁻²³ cm/molecule at temperature T = 296 K were calculated using the HITRAN 2012 [Rothman et al., 2013; Brown et al., 2013; Campargue et al., 2013] line parameters and then fixed. Fig. 1 shows that the contribution of weak lines in the considered spectral range is satisfactorily reproduced using line-parameter data from the 2012 version of the HITRAN database [Rothman et al., 2013].

Figure 1.

Comparison between the present FS-CRDS-measured spectra and HITRAN-calculated values for air-broadened methane at room temperature and P=133 hPa. The upper and lower panels correspond to HITRAN 2008 [Rothman et al., 2009] and HITRAN 2012 [Rothman et al., 2013], respectively.

Using the HTP to represent the line shape and taking into account the line-mixing effect, the absorption coefficient versus wavenumber σ (cm⁻¹) is calculated through [Ngo et al., 2013]

$$\alpha (\sigma )={\sum }_l\frac{S_{\iota }{n}_{{\mathrm{CH}}_4}}{\pi }[\mathrm{Re}\{I_l^{\mathit{\text{HTP}}}(\sigma )\}-Y_l\mathrm{Im}\{I_l^{\mathit{\text{HTP}}}(\sigma )\}].$$ (1)

The sum in Eq. (1) is over the six lines of the R(6) manifold, Y_l = Pζ_l is the first-order line-mixing parameter, representing the coupling between the line l and other lines. S_l and $n_{{\text{CH}}_4}$ are the line-integrated intensity (at natural isotopic abundance) and the number density of total methane, respectively. Using the ideal gas law and the known molar fraction of methane, $x_{{\text{CH}}_4}$, we calculate $n_{{\text{CH}}_4}=x_{{\text{CH}}_4}P/(k_{\mathrm{B}}T)$ where P and T are the total gas pressure and temperature, respectively, and k_B is the Boltzmann constant.

Within the HTP model, the $I_l^{\mathit{\text{HTP}}}(\sigma )$ line shape quantity is a function of eight parameters [Ngo et al., 2013], i.e.,

$$I_{\mathit{\text{HTP}}}(\sigma )=f(\sigma -{\sigma }_0,{\Gamma }_D,{\Gamma }_0,{\Gamma }_2,{\Delta }_0,{\Delta }_2,{\nu }_{vc},\eta ),$$ (2)

with σ₀ representing the unperturbed position of the line. The HTP model takes into account the main processes affecting the shape of an isolated line in the binary-collision regime. These include the following four effects. 1) Doppler broadening (through the Doppler broadening halfwidth Γ_D); 2) velocity-changing (VC) collisions (Dicke narrowing) induced by intermolecular collisions, which is described through the hard-collision model [Nelkin and Ghatak, 1964; Rautian and Sobel’man, 1967] and parameterized in terms of the rate of velocity-changing collisions ν_vc (or the Dicke narrowing frequency); 3) speed dependences (SD) of the collisional halfwidth Γ(v) and shift Δ(v) modeled by the quadratic law and first proposed by Refs. [Rohart et al., 1994; Rohart et al., 1997] $\Gamma (v)+i\Delta (v)={\Gamma }_0+i{\Delta }_0+({\Gamma }_2+i{\Delta }_2)[{(v/\stackrel{\sim }{v})}^2-3/2]$ where $\stackrel{\sim }{v}=\sqrt{2k_{B}T/m}$ is the most probable speed for an absorbing molecule of mass m; and 4) temporal correlation between velocity-changing and internal-state-changing collisions, which is accounted for through the correlation parameter η. The line parameters of the HTP vary simply with the total pressure P: σ₀, and η are constant while ν_vc, Γ₀, Γ₂, Δ₀ and Δ₂ are proportional to P. Note that from Eq. (2) the majority of models used to describe measured absorption spectra [Ngo et al., 2013 and references therein] can be directly obtained as limits of the HT profile, by fixing appropriate parameters to zero.

In our fitting procedure, for each line, the shared parameters (i.e. common parameters for all considered pressures) are then $\frac{{\Gamma }_0}{P},\frac{{\Gamma }_2}{P},\frac{{\Delta }_0}{P},\frac{{\Delta }_2}{P},\frac{{\nu }_{vc}}{P},\eta ,\frac{Y}{P}$ together with the zero-pressure position of the line σ₀ and the relative integrated line intensity, i.e. S_i/S_tot with S_tot the spectrum area. Note that the Dicke narrowing parameter $\frac{{\nu }_{vc}}{P}$ was fitted but imposed to be the same for all six transitions during the fitting procedure. Finally, for each spectrum, a linear base line with two adjustable parameters, representing the zero absorption level, and the total area were also retrieved. Note that the Doppler contribution is calculated from the considered temperature for each transition and then fixed. In total, (49+3×6 spectra) parameters were adjusted for the six transitions with a total of six measured spectra. Because the CH₄ concentrations of the first four spectra (see Table 1) in the mixtures were known with a very high precision, these spectra were used to deduce absolute intensity for the 6 considered transitions.

4. Results

4.1 Fit residuals and obtained parameters

As shown in Fig. 2, the considered 2ν₃ R(6) manifold is formed by two distinct groups of three transitions each, which remain almost unresolved even at low pressure. It is thus particularly challenging to correctly retrieve parameters for each line of the manifold. The initial 2ν₃ R(6) parameters are set as follows: line positions σ_0,l and line intensities were taken from HITRAN 2012, line broadening and shifting coefficients, Γ_0,l/P and Δ_0,l/P, were based on those of the ν₃ manifold [Pine et al., 1997] as done in [Tran et al., 2010], and the first-order line-mixing parameters ζ_l, were calculated from the relaxation matrix elements of Refs. [Tran et al., 2010; Tran et al., 2006].

Figure 2.

Multispectrum fit results of the six air-broadened spectra in the 2ν₃ R(6) ¹²CH₄ manifold region. All the spectra (normalized to their peak absorption) considered here are overlaid in the top panel (a): measurements are represented using dots while lines are for the modeled absorptions. The fit residuals (observed minus calculated) using the first-order line-mixing HTP are plotted (expanded scale ×100) in the second panel (b), those obtained using the first-order line-mixing Speed-Dependent Voigt profile in the third panel (c), while in the bottom panel (d) the fit residuals obtained with the VP are plotted. The wave number position of the MERLIN on-line case is also indicated as a thick black line.

The multispectrum fit of the 2ν₃ R(6) ¹²CH₄ manifold, extending from 6076.7 to 6077.3 cm⁻¹ is shown in Fig. 2 (upper panel), along with the fit residuals (middle panel) for the six considered spectra. The results obtained with the same measured spectra but by using the commonly used VP (no line-mixing, nor Dicke narrowing and speed dependence) and with the Speed Dependent Voigt Profile (SDVP) combined with the first order line-mixing are also reported for comparison (bottom panel). As can be observed, the VP leads to large deviations with respect to the measured spectra, with differences of up to ±2% (Fig. 2d). When line-mixing and speed dependence effects are taken into account (Fig. 2c), the fit residuals are of about ±0.2%. Finally, when the HTP (Fig. 2b) is used together with the first-order line-mixing, excellent agreement is obtained with a maximum residual deviation of ±0.12% for all considered pressures. Particularly, the fit residuals are always lower than 0.1% around the MERLIN on-line wave number near σ= 6077 cm⁻¹. This is the first time that such an accuracy is reached in the modeling of the 2ν₃ R(6) ¹²CH₄ manifold, completely fulfilling the accuracy requirements for MERLIN [Kiemle et al., 2011; Kiemle et al., 2013; Stephan et al., 2011]. Note that sources of uncertainty associated with the measured spectra should not be critical here because of the high signal-to-noise ratio (>20,000:1), the small relative combined uncertainty of the pressure and temperature measurements (around 0.02%) and the accuracy of absolute and relative frequency scales (standard uncertainty of nominally 1 MHz ≈ 3.3×10⁻⁵ cm⁻¹) of the FS-CRDS experiment.

The retrieved spectroscopic parameters for the 2ν₃ R(6) ¹²CH₄ manifold are listed in Table 2 together with their associated standard deviations (1-σ statistical errors reported by the fitting program). The illustrated variation in the intensity ratios from the expected 5:3:2 values can be interpreted as perturbations between nearby levels. Nonetheless, it is apparent that these parameters remain close to their initial values derived from HITRAN2012 [Rothman et al., 2013], resulting in a fine tuning of the initial parameters. With regard to other parameters, the direct comparison with previous studies is difficult because of differences in the line-shape models considered. We noticed for example that our values of the broadening parameters $\frac{{\Gamma }_0}{P}$ were slightly lower than those of other studies [Pine, 1997; Devi et al., 2015]. Nevertheless, our set of parameters together with our line shape model provide the best available modelling of the absorption in the R(6) manifold of the 2ν₃ band of ¹²CH₄. A meaningful way to test the ascribed accuracy is to compute the residuals obtained through comparisons of modeled spectra (based on the present HTP-line mixing fits) with previous high-precision measurements.

Table 2.

Measured line parameters for the R(6) manifold in the 2ν₃ band of ¹²CH₄. The uncertainties in parentheses are 1-sigma internal statistical errors in the last quoted digit(s); as an example, 6076.92716(9) cm⁻¹ means 6076.92716(0.00009) cm⁻¹. Values can be converted to SI units using the factor 1 cm⁻¹ atm⁻¹ = 0.295872 MHz Pa⁻¹.

R6 TRANSITION	FITTED POSITION (cm−1)	INTENSITY (cm/molecule)	${\Gamma }_{\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−3 cm−1/atm)	${\Delta }_{\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−3 cm−1/atm)	${\zeta }_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−1 cm−1/atm)	${\nu }_{\raisebox{1ex}{$vc$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−3 cm−1/atm)	${\Gamma }_{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−3 cm−1/atm)	${\Delta }_{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$ (10−3 cm−1/atm)	η
7E ← 6E 1	6076.92716(9)	4.52(6).10−22	66.75(71)	−25.65(66)	–		24.95(83)	−1.97(72)	0.540(24)
7F1 ← 6F2 1	6076.93411(9)	7.91(7).10−22	53.16(40)	−3.43(41)	−3.9(26)		3.08(45)	12.85(35)	0.273(22)
7A1 ← 6A2 1	6076.95316(1)	1.22(1).10−21	65.29(14)	−9.48(12)	−0.96(16)	19.36(99)	13.49(21)	−3.27(17)	0.239(18)
7F1 ← 6F2 2	6077.02785(1)	7.29(6).10−22	54.35(26)	−6.15(32)	3.89(25)		0.0*	−5.63(23)	0.123(21)
7F2 ← 6F1 1	6077.04639(2)	7.35(7).10−22	43.68(16)	−13.79(31)	2.31(15)		3.54(34)	−5.30(26)	0.614(33)
7A2 ← 6A1 1	6077.06296(1)	1.20(1).10−21	60.45(16)	−9.05(16)	−0.24(8)		11.39(19)	−1.37(21)	0.257(16)

^*Ill-defined parameter, set to 0.

4.2 Intercomparisons with FTS measurements

In order to test the model for the wavenumber region presented above, we compared the resulting predictions with spectra measured by other groups. We note that these previous data were based on different experimental techniques and corresponded to other pressure conditions. Specifically, we used two sets of measured spectra of Refs. [Frankenberg et al., 2008] and [Devi et al., 2015]. For the first set (Set 1), four spectra of methane diluted in N₂ were measured at room temperature for pressures ranging from 126 hPa to 900 hPa using a high resolution FTS spectrometer [Frankenberg et al., 2008]. In the second set (Set 2), four air-broadened, room-temperature methane FTS spectra of Ref. [Devi et al., 2015] were measured at pressures from 331 hPa to 1179 hPa. Details of the experimental setups and conditions can be found in the corresponding references.

From the spectroscopic parameters obtained in this work (see Table 2), synthetic spectra were calculated for exactly the same temperature and pressure conditions as those of the previous measurements. The contribution of methane self-broadening to the spectra is not negligible in these prior cases (i.e. the relative partial pressure of CH₄ of Set 1 was about 1–2% while it was of 0.3–1% for the Set 2) and therefore was taken into account. The contributions of self-broadening, and line-mixing coefficients for pure methane were taken from the values of Ref. [Devi et al., 2015] and estimated as discussed by [Tran et al. 2015]. The instrument line shape functions of the two FTS spectrometers were also accounted for by using data provided by the authors of [Frankenberg et al., 2008] and [Devi et al., 2015] and by using the LINEFIT software developed by F. Hase [Hase et al., 1999]. Finally, except for a scaling factor for the spectrum area, the calculated spectra were directly compared with measured transmittances without using any adjustable parameters.

Figure 3 presents the comparison between the measured spectra of Set 1 and those calculated using the different spectroscopic line parameter data sets. Line shape parameters for N₂-broadened methane were obtained from those of air-broadened methane using the corresponding ratios of Ref. [Pine et al., 2003]. In the left panel (Fig. 3a), spectra were calculated using line positions and intensities provided in HITRAN 2008 [Rothman et al., 2008] and line-broadening and -shifting coefficients estimated from data of Ref. [Pine, 1997]. The latter were obtained from high-quality measurements in the ν₃ band of methane. In the left panel (Fig. 3a), residuals obtained for the four considered pressures with line-mixing (black lines) and without line-mixing (red lines) taken into account are plotted. These results illustrate the importance of the line-mixing contribution to the shape of methane spectra. In the right panel (Fig. 3b), measured spectra are compared with those calculated using the spectroscopic line parameters obtained in the present work, using the HTP and taking line-mixing into account. The corresponding residuals are plotted in blue. The black residuals of Fig. 3a are also plotted in Fig. 3b for comparison. As can be observed, the new spectroscopic parameters, used together with our code lead to very good agreement with measured spectra, much better than with previous line-parameter data, with the obtained residuals being almost within the experimental noise level.

Figure 3.

Top (a) and (b): Transmittance spectra measured by an FTS spectrometer (Set 1, [Frankenberg et al., 2008]) and differences (lower panels) between these measurements and calculated spectra. Black and red residuals correspond to a model based on positions and intensities from HITRAN 2008 and line-broadening and -shifting coefficients estimated from the data of Ref. [Pine, 1997], with (black) and without (red) line mixing taken into account. Blue residuals correspond to the present model (obtained from fits to the FS-CRDS data).

The comparison between the air-broadened methane measured spectra of Set 2 [Devi et al., 2015] and calculated transmittances is presented in Fig. 4. Residuals between measurements and spectra calculated using spectroscopic parameters obtained in this work and the associated spectral profiles (first-order line-mixing HTP) are plotted in blue in the lower panels. Recall that calculations were done for exactly the same pressure and temperature conditions as those of the measurements and no adjustable parameters were used for these comparisons. In order to compare our results with the different existing spectroscopic data sources, calculations were also performed using spectroscopic parameters of the 2008 [Rothman et al., 2009] and the 2012 [Rothman et al., 2013] versions of the HITRAN database. The corresponding residuals for all considered pressures are plotted in black and red lines, respectively. Surprisingly, the spectroscopic data set of HITRAN2008 lead to much better agreement with measured spectra than those of HITRAN2012. This is probably a result of the inconsistency between the line-broadening coefficients provided in HITRAN 2012 for these lines and the use of the VP. As can be observed in Fig. 4, our new data lead to much better agreement with measured spectra. Differences between all measured spectra and our calculations are almost always better than about 0.2%, except for the case of the lowest pressure (i.e. the lowest panel) where a slightly larger set of residuals is obtained. The latter is probably caused by uncertainty in the assumed FTS instrument line shape function, determined from low-pressure HCl spectra which were recorded simultaneously with air-broadened methane spectra [Devi et al., 2015].

Figure 4.

Top: Transmittances measured by an FTS spectrometer (Set 2, [Devi et al., 2015]) and differences (lower panels) between these measurements and calculated spectra. Calculations are based on first-order line mixing with the HTP (present case, blue lines), VP with HITRAN 2012 line parameters (red lines, [Rothman et al., 2013]) and VP with HITRAN 2008 (black lines, [Rothman et al., 2009]).

5. Discussion and conclusions

Absorption of methane in the 1.64 μm region was precisely measured using a frequency-stabilized cavity ring-down spectroscopy spectrometer at room temperature and various pressures. These spectra were analyzed using the latest standard line shape profile which takes into account line-mixing, Dicke narrowing and speed dependence effects. The obtained data and model enable calculation of synthetic spectra to within 0.12% of measurements and yield even better agreement at the on-line position of the MERLIN mission. Using the spectroscopic data derived from implementing the commonly used Voigt profile led to deviations of up to 2% between the calculated and measured absorption coefficients. Note that for MERLIN and atmospheric applications in general, data at lower temperature are also required. For that, high sensitivity CRDS measurements at low temperatures will be recorded. The same line-shape model will be used for their analysis. The temperature dependence issue of the non-Voigt line-shape parameters will be studied. Such studies will be performed and presented in a forthcoming paper. The other issue concerning the spectroscopy for MERLIN is the broadening of methane lines with water vapor. For that, a study has been performed by our group showing that broadening of methane lines with water vapor is much more efficient (1.34 times) than that with dry air [Delahaye et al., 2016].

In order to quantify the influence of these new spectroscopic data and model for atmospheric observations, we carried out simple radiative transfer calculations assuming the US-standard-atmospheric-condition model. The results are shown in Fig. 5 in which atmospheric spectra (including absorption by methane, water vapor and carbon dioxide) calculated by using HITRAN 2008 parameters (black) and our new model for the R(6) manifold along with HITRAN 2012 parameters for other lines (red) are plotted. The relative difference observed between the two spectra, plotted in the lower panel of Fig. 5, is of the order of 5% and 1.5% in the off- and on-line MERLIN spectral regions, respectively. The latter is consistent with residuals observed using VP to describe absorption by ¹²CH₄ in the R(6) manifold (Fig. 2c). This again emphasizes the importance of properly modeling the line shape and choice of spectroscopic parameters for precise remote sensing atmospheric applications. For the off-line region (6075.896 cm⁻¹), analyzing the contribution of each species (Fig. 6) shows that there are significant differences between absorbances calculated using HITRAN 2008 and HITRAN 2012 for methane and water vapor. As already shown in Fig. 1, spectroscopic data in HITRAN 2012 for ¹²CH₄ in this 1.64 μm region are much more complete than in HITRAN 2008. Similarly, several weak lines of H₂O were also added in the 2012 version of the database. Hence, these lines must be taken into account in any performance calculation for MERLIN.

Figure 5.

Upper panel: comparison of the total column-integrated absorption spectra (including CH₄, H₂O and CO₂ absorption) derived using HITRAN 2008 parameters (black) and our new model for the R(6) manifold along with HITRAN 2012 parameters for other weak lines (red). Lower panel: Relative difference between the two spectra, in percent. Meteorological data were obtained from the US-Standard model. Vertical lines mark off- and on-line MERLIN instrument operating wavelengths, respectively.

Figure 6.

Comparisons of the CH₄, CO₂ and H₂O total column-integrated absorption spectra calculated using spectroscopic data of HITRAN 2008 (dots) and our data for the 2ν₃ R(6) manifold of ¹²CH₄ together with HITRAN 2012 for other lines and species (lines).