Self- and Air-Broadening, Shifts, and Line Mixing in the ν 2 Band of CH 4 M. A. H. Smith 1, D. Chris Benner 2, V. Malathy Devi 2, and A. Predoi-Cross 3 1 Science Directorate, NASA Langley Research Center, Hampton, VA , USA 2 Department of Physics, The College of William and Mary, Williamsburg, VA , USA 3 Department of Physics, The University of Lethbridge, Lethbridge, AB T1K 3M4, Canada.

Research Objectives Enhance scientific return from AURA and other remote sensing missions by improving fundamental knowledge of the spectroscopic parameters in the 7.5-μm band system of methane (CH 4 ). Significant uncertainties existed in line broadening and shift parameters, line shapes, and line mixing especially for weak lines in these CH 4 bands. These uncertainties impact remote sensing retrievals.

Status of CH 4 ν 2 Parameters Before This Work HITRAN 2004 parameters (Rothman et al., 2005). –Line positions and intensities from Brown et al. (2003). –Air-broadening and shift parameters, and self-broadened widths, are based on our previously reported results for ν 4 (Smith et al., 1992; Malathy Devi et al., 1988). Broadening and shift parameters were not known for many weak CH 4 lines in the ν 4 and ν 2 bands. Accurate parameters are needed because methane interferes with retrievals of other atmospheric species (e.g., H 2 O, NO 2 ). Line mixing had not been observed in laboratory spectra of the CH 4 ν 2 band.

Methane Spectrum at 5 – 9 µm Recorded at room temperature with 1.5 m cell. Sample is 2.58% CH 4 in air at a total pressure of 425 torr. Residual H 2 O lines appear above ~1330 cm -1.

Zooming in on the ν 2 Band

Experimental Conditions: McMath-Pierce FTS (National Solar Observatory at Kitt Peak) Source:Glower Beam splitter:KCl Detectors:As:Si Spectral coverage: 750–2850 cm -1 Maximum path difference (L):94.34 cm Unapodized resolution (FWHM):0.005 cm -1 FTS input aperture size:8 mm Number of co-added scans:8–12 Recording time:~1 hr Signal-to-RMS noise:~350 Details of this 50-cm coolable cell are described by Smith et al. (1992).

CH 4 at 6 – 9 µm: Experimental Summary McMath-Pierce FTS at Kitt Peak Resolution: to cm -1 Bandpass: 750 – 2850 cm -1 Calibration: ν 2 band of H 2 O Self-Broadened Spectra Pressures:1 to 650 torr Path lengths:1 to 150 cm Temperatures:22°C to 30°C Samples: “natural” CH 4 and 99% 13 CH 4 Air-Broadened Spectra Pressures:50 to 550 torr Path lengths: 5 to 150 cm Temperatures:−63°C to 41°C Samples: 13 CH 4 (room temp.) and “natural” CH 4 Dilute mixtures: 0.4% to 2.7% CH 4 At least 64 useful spectra collected to date (since 1985)! 29 of these were useful for analysis of the ν 2 band.

Analysis Details Wavenumber scales of all spectra were calibrated using the ν 2 lines of residual H 2 O and present in the optical paths outside the sample cells. An interactive multispectrum nonlinear least squares fitting technique (Benner et al., 1995) was used to analyze limited wavenumber intervals (5 to 15 cm -1 each) of about 30 to 60 spectra simultaneously, depending on the spectral region. A Voigt line shape profile was assumed. Including speed-dependence or Dicke narrowing in our spectral profiles did not significantly improve the residuals. Line mixing (off-diagonal relaxation matrix element coefficients) was necessary to accurately model the absorption in some ν 2 P- and R-branch manifolds. Initial values for all line parameters were taken from the HITRAN 2004 database, where available. Self-shift coefficients had initial values of zero, and an initial value of 0.7 was assumed for all temperature-dependence exponents of self-broadening. Spectral backgrounds (including some channeling), zero transmission levels, FTS phase errors, and FTS instrument line shapes were appropriately modeled.

Definitions of Broadening and Shift Parameters Where b L (p, T) is the Lorentz halfwidth (in cm -1 ) of the spectral line at pressure p and temperature T, and the broadening coefficient b L 0 (Gas)(p 0, T 0 ) is the Lorentz halfwidth of the line at the reference pressure p 0 (1 atm) and temperature T 0 (296 K), and χ is the ratio of the partial pressure of CH 4 to the total sample pressure in the cell. The temperature dependence exponents of the pressure-broadening coefficients are n1 and n2. Where ν 0 is the zero-pressure line position (in cm -1 ), ν is the line position corresponding to the pressure p, δ 0 is the pressure-induced line shift coefficient at the reference pressure p 0 (1 atm) and temperature T 0 (296 K) of the broadening gas (air), and χ is as defined above. The temperature dependence of the pressure induced shift coefficient (in cm -1 atm -1 K -1 ) is δ′. δ 0 (T) and δ 0 (T 0 ) represent the pressure induced shift coefficients (in cm -1 atm -1 ) at T and T 0 (296 K), respectively. An initial estimate of zero was assumed for δ′ for both air- and self-broadening.

Line shape of N Lorentz line profiles as a function of ω (cm -1 ) described by Levy et al. (1992) ω and ω o and ρ are N × N diagonal matrices Diagonal elements are: ω (jj) = wavenumber ω o (jj) = zero pressure line position ρ (jj) = number density of the transition lower states Off-diagonal elements are: ω (jk) = ω o (jk) = ρ (jk) = 0 W is the relaxation matrix to include line mixing in the fit. Χ is a 1 × N matrix S is the transition intensity T is the transpose Line Mixing W jj = diagonal elements are functions of Lorentz widths and pressure-induced shifts W jk = off-diagonal elements are line mixing coefficients W jk are related by energy densities ρ calculated via Boltzmann terms where E" is lower state energy C 2 is 2 nd radiation term = K/cm where

Fit of CH 4 ν 4 Manifold With and Without Line Mixing Room-temperature spectra; p max = 550 Torr for air-broadening and 453 Torr for self-broadening. W X Y Z Line Mixing Selection Rules (Pieroni et al., 1999a) A1 ↔ A2 but not A2 ↔ A2 F1 ↔ F2 but not F2 ↔ F2 E ↔ E Sum of mixing coefficients = 0. Retrieval indicates that F-species lines W and X mix only with each other, and Y and Z do not mix.

Multispectrum Fit in the 12 CH 4 ν 2 P(8) Manifold 28 Spectra 8 self- and 20 air- broadened Cell lengths 0.5 and 1.5 m T = 226 to 298 K Max. pressure ~ 645 torr No line mixing observed for these weak transitions!

Multispectrum Fit in the 12 CH 4 ν 2 P(14) Manifold 26 Spectra 9 self- and 17 air- broadened Cell lengths 0.5 and 1.5 m T = 226 to 298 K Max. pressure ~ 645 torr No line mixing, but a forbidden transition!

Multispectrum Fit in the 12 CH 4 ν 2 R(7) Manifold with Mixing 29 Spectra 11 self- and 18 air- broadened Cell lengths 0.5 and 1.5 m T = 226 to 298 K Max. pressure ~ 645 torr

Summary of 12 CH 4 Parameters Retrieved Parameterν 4 rotational quanta range ν 4 number of values ν 2 rotational quanta range ν 2 number of values Self-widths1 ≤ |m| ≤ ≤ |m| ≤ Self-shifts1 ≤ |m| ≤ ≤ |m| ≤ Self-mixing3 ≤ |m| ≤ ≤ |m| ≤ 1611 Air-widths1 ≤ |m| ≤ ≤ |m| ≤ Air-shifts1 ≤ |m| ≤ ≤ |m| ≤ Air-mixing3 ≤ |m| ≤ ≤ |m| ≤ 1611 Temperature-dependences were determined only for 12 CH 4 widths and shifts. We also obtained self- and air-broadening, shift, and mixing parameters for transitions in the 13 CH 4 ν 4 band.

Measured 12 CH 4 ν 2 Air- and Self-Broadened Widths

Measured 12 CH 4 ν 2 Air- and Self-Induced Line Shifts

T-Dependence Exponents for Air- and Self-Broadening

Measured Mixing Coefficients in the ν 2 12 CH 4 band and comparisons with those in the ν 4 a,b and ν 1 +ν 4 c bands. Mixing pair(s)Assignments (cm -1 ) Off-diagonal relaxation matrix element coefficients (cm -1 atm -1 at 296K) Self-Air-Line separation (cm -1 ) P(16) F15F2 19←16F1 4 15F1 20←16F (14) (2) a (19) (5) b P(15) A14A2 6←15A1 1 14A1 7←15A (17) (2) a (10) (4) b P(9) F8F1 10←9F2 2 8F2 10←9F (17) (1) a (16) (0) b P(9) F8F1 10←9F2 2 8F2 11←9F (4)0.0089(3) P(7) F6F2 8←7F1 2 6F1 8←7F (1) (1) a (5) c (1) (1) b (2) c P(6) F5F2 7←6F1 1 5F1 7←6F (1) (1) a (1) (1) b R(5) F6F2 7←5F1 2 6F1 7←5F (1) (1) a (3) (0) b R(6) F7F2 8←6F1 1 7F1 8←6F (1) (1) a (4) c (1) (0) b (2) c R(6) A7A2 3←6A1 1 7A1 3←6A (1) (1) a (11) c (2) (0) b (5) c R(7) F8F2 9←7F1 2 8F1 9←7F (1)0.0166(4) R(8) F9F1 10←8F2 2 9F2 10←8F (1) (2) a (3) (1) b a Smith et al. (2008a), b Smith et al. (2008b), c Predoi-Cross et al. (2007)

Summary Air- and self-broadening and shift parameters have been determined for over 130 ν 2 transitions of 12 CH 4 (and temperature dependences for most of these). –Good agreement with previous room-temperature air-broadening and shift measurements of 47 transitions by Rinsland et al. (1988). –First measurements of self-broadened widths and shifts in the ν 2 band. –First experimental determination of temperature dependence exponents for air- and self-broadening in the ν 2 band. Line mixing has been measured in the ν 2 band system of 12 CH 4. –Mixing coefficients (off-diagonal relaxation matrix elements) were determined from self- and air-broadened spectra for 11 pairs of transitions in ν 2 P and R manifolds. –No mixing was observed in most ν 2 manifolds. –Line mixing cannot be neglected in atmospheric retrievals (Mondelain et al., 2007).

References D. Chris Benner et al., J. Quant. Spectrosc. Radiat. Transfer, 53 (1995) L. R. Brown et al., J. Quant. Spectrosc. Radiat. Transfer, 82 (2003) L. Darnton and J. S. Margolis, J. Quant. Spectrosc. Radiat. Transfer, 13 (1973) A. Levy, N. Lacome and C. Chackerian, Jr., Collisional line mixing, in Spectroscopy of the Earth’s Atmosphere and Interstellar Medium, K. N. Rao and A. Weber Eds., Ch. 2, pp , Academic Press, Boston, MA (1992). D. Mondelain et al., J. Mol. Spectrosc. 244 (2007) D. Pieroni et al., J. Chem. Phys., 110 (1999a) D. Pieroni et al., J. Chem. Phys., 111 (1999b) D. Pieroni et al., J. Chem. Phys., 113 (2000) A. Predoi-Cross et al., J. Mol. Sepctrosc., 246 (2007) C. P. Rinsland et al., Appl. Opt., 27 (1988) L. S. Rothman et al., J. Quant. Spectrosc. Radiat. Transfer, 96 (2005) M. A. H. Smith et al., Spectrochimica Acta, 48A (1992) M. A. H. Smith et al., Manuscripts in preparation (2008a,b).

SignOffPage The research at the College of William and Mary and NASA Langley was performed under cooperative agreements with the National Aeronautics and Space Administration (NASA) funded though NASA’s Upper Atmosphere Research Program and AURA Validation Program. We thank Mike Dulick and Detrick Branston of the National Solar Observatory for their assistance in obtaining the data recorded at Kitt Peak. NSO is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under contract with the National Science Foundation. We also thank NASA’s Upper Atmosphere Research Program for their support of the McMath-Pierce FTS facility. Acknowledgements