Self- and Air-Broadening, Shifts, and Line Mixing in the

ν2 Band of CH4

M. A. H. Smith1, D. Chris Benner2, V. Malathy Devi2, and A. Predoi-Cross3

1Science Directorate, NASA Langley Research Center, Hampton, VA 23681-2199, USA

2Department of Physics, The College of William and Mary, Williamsburg, VA 23187-8795, USA

3Department 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 (CH4).

Significant uncertainties existed in line broadening and shift parameters, line shapes, and line mixing especially for weak lines in these CH4 bands. These uncertainties impact remote sensing retrievals.

Status of CH4 ν2 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 ν4 (Smith et al., 1992; Malathy Devi et al., 1988).

• Broadening and shift parameters were not known for many weak CH4 lines in the ν4 and ν2 bands. Accurate parameters are needed because methane interferes with retrievals of other atmospheric species (e.g., H2O, NO2).

• Line mixing had not been observed in laboratory spectra of the CH4 ν2 band.

Methane Spectrum at 5 – 9 µm

Recorded at room temperature with 1.5 m cell. Sample is 2.58% CH4 in air at a total pressure of 425 torr. Residual H2O lines appear above ~1330 cm-1.

Zooming in on the ν2 Band

Experimental Conditions: McMath-Pierce FTS(National Solar Observatory at Kitt Peak)

Source:Glower

Beam splitter: KClDetectors:

As:SiSpectral coverage: 750–2850 cm-1

Maximum path difference (L): 94.34 cmUnapodized resolution (FWHM): 0.005 cm-1

FTS input aperture size: 8 mmNumber of co-added scans: 8–12Recording time: ~1 hrSignal-to-RMS noise: ~350

Details of this 50-cm coolable cell are described by Smith et al. (1992).

CH4 at 6 – 9 µm: Experimental Summary

McMath-Pierce FTS at Kitt PeakResolution: 0.005 to 0.010 cm-1

Bandpass: 750 – 2850 cm-1

Calibration: ν2 band of H2O

Self-Broadened Spectra

Pressures: 1 to 650 torr

Path lengths: 1 to 150 cm

Temperatures: 22°C to 30°C

Samples: “natural” CH4

and 99% 13CH4

Air-Broadened Spectra

Pressures: 50 to 550 torr

Path lengths: 5 to 150 cm

Temperatures: −63°C to 41°C

Samples: 13CH4 (room temp.)

and “natural” CH4

Dilute mixtures: 0.4% to 2.7% CH4

At least 64 useful spectra collected to date (since 1985)!

29 of these were useful for analysis of the ν2 band.

Analysis Details

• Wavenumber scales of all spectra were calibrated using the ν2 lines of residual H2O 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 ν2 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

2

000

01

000

0 ),)(()1)(,)((),(n

L

n

LL T

TTpselfb

T

TTpairbpTpb

Where bL (p, T) is the Lorentz halfwidth (in cm-1) of the spectral line at pressure p and temperature T, and the broadening coefficient bL

0(Gas)(p0, T0) is the Lorentz halfwidth of the line at the reference pressure p0 (1 atm) and temperature T0 (296 K), and χ is the ratio of the partial pressure of CH4 to the total sample pressure in the cell.

The temperature dependence exponents of the pressure-broadening coefficients are n1 and n2.

Where ν0 is the zero-pressure line position (in cm-1), ν is the line position corresponding to the pressure p, δ0 is the pressure-induced line shift coefficient at the reference pressure p0 (1 atm) and temperature T0 (296 K) of the broadening gas (air), and χ is as defined above.

)()1)(( 000 selfairp

).(')()( 0000 TTTT

The temperature dependence of the pressure induced shift coefficient (in cm-1 atm-1 K-1) is δ′. δ0(T) and δ0(T0) represent the pressure induced shift coefficients (in cm-1 atm-1) at T and T0 (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 ωo and ρ are N × N diagonal matrices

Diagonal elements are:

ω(jj) = wavenumber

ωo (jj) = zero pressure line position

ρ(jj) = number density of the transition lower states

Off-diagonal elements are:

ω(jk) = ωo (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

Wjj = diagonal elements are functions of Lorentz widths and pressure-induced shifts

Wjk = off-diagonal elements are line mixing coefficients

Wjk are related by energy densities ρ calculated via Boltzmann terms where

E" is lower state energy

C2 is 2nd radiation term = 1.4387 K/cm where

Fit of CH4 ν4 Manifold With and Without Line Mixing

Room-temperature spectra; pmax = 550 Torr for air-broadening and 453 Torr for self-broadening.

W X YZ

Line Mixing Selection Rules (Pieroni et al., 1999a)

A1 ↔ A2 but not A2 ↔ A2F1 ↔ F2 but not F2 ↔ F2E ↔ 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 12CH4 ν2 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 12CH4 ν2 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 12CH4 ν2 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 12CH4 Parameters Retrieved

Parameter ν4 rotational quanta range

ν4 number of values

ν2 rotational quanta range

ν2 number of values

Self-widths 1 ≤ |m| ≤ 20 538 3 ≤ |m| ≤ 16 145

Self-shifts 1 ≤ |m| ≤ 20 419 3 ≤ |m| ≤ 16 140

Self-mixing 3 ≤ |m| ≤ 19 57 5 ≤ |m| ≤ 16 11

Air-widths 1 ≤ |m| ≤ 19 428 3 ≤ |m| ≤ 16 144

Air-shifts 1 ≤ |m| ≤ 19 381 3 ≤ |m| ≤ 16 135

Air-mixing 3 ≤ |m| ≤ 19 57 5 ≤ |m| ≤ 16 11

Temperature-dependences were determined only for 12CH4 widths and shifts.We also obtained self- and air-broadening, shift, and mixing parameters for transitions in the 13CH4 ν4 band.

Measured 12CH4 ν2 Air- and Self-Broadened Widths

Measured 12CH4 ν2 Air- and Self-Induced Line Shifts

T-Dependence Exponents for Air- and Self-Broadening

Measured Mixing Coefficients in the ν2 12CH4 band and comparisons with those in the ν4a,b and ν1+ν4

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) F 15F2 19←16F1 415F1 20←16F2 4

1399.79521399.8475

0.0283(14)0.0286(2)a

0.0261(19)0.0300(5) b

0.05231.1333

P(15) A 14A2 6←15A1 114A1 7←15A2 2

1405.79541405.8655

0.0286(17)0.0289(2)a

0.0314(10)0.0302(4)b

0.07010.8548

P(9) F 8F1 10←9F2 28F2 10←9F1 3

1448.86091448.9011

0.0204(17)0.0150(1)a

0.0231(16)0.0175(0)b

0.04020.6834

P(9) F 8F1 10←9F2 28F2 11←9F1 2

1448.86091449.1832

0.0134(4) 0.0089(3) 0.3223

P(7) F 6F2 8←7F1 26F1 8←7F2 2

1465.71271465.9530

0.0064(1)0.0087(1)a

0.0079(5)c

0.0049(1)0.0100(1)b

0.0055(2)c

0.24031.41740.3533

P(6) F 5F2 7←6F1 15F1 7←6F2 2

1474.69051474.7684

0.0053(1)0.0098(1)a

0.0038(1)0.0101(1)b

0.07790.6085

R(5) F 6F2 7←5F1 26F1 7←5F2 1

1599.01101599.5594

0.0090(1)0.0048(1)a

0.0128(3)0.0067(0)b

0.54840.6351

R(6) F 7F2 8←6F1 17F1 8←6F2 2

1610.59601610.7779

0.0105(1)0.0093(1)a

0.0088(4)c

0.0131(1)0.0108(0)b

0.0079(2)c

0.18190.18090.1693

R(6) A 7A2 3←6A1 17A1 3←6A2 1

1610.09141610.9510

0.0151(1)0.0210(1)a

0.0169(11)c

0.0154(2)0.0198(0)b

0.0178(5)c

0.85961.03250.9873

R(7) F 8F2 9←7F1 28F1 9←7F2 2

1621.86221622.2160

0.0126(1) 0.0166(4) 0.3538

R(8) F 9F1 10←8F2 29F2 10←8F1 2

1633.15071633.5662

0.0154(1)0.0165(2)a

0.0188(3)0.0143(1)b

0.41550.4685

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 ν2 transitions of 12CH4 (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 ν2 band.

– First experimental determination of temperature dependence exponents for air- and self-broadening in the ν2 band.

• Line mixing has been measured in the ν2 band system of 12CH4.

– Mixing coefficients (off-diagonal relaxation matrix elements) were determined from self- and air-broadened spectra for 11 pairs of transitions in ν2 P and R manifolds.

– No mixing was observed in most ν2 manifolds.

– Line mixing cannot be neglected in atmospheric retrievals (Mondelain et al., 2007).

References

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L. Darnton and J. S. Margolis, J. Quant. Spectrosc. Radiat. Transfer, 13 (1973) 969-976.

A. Levy, N. Lacome and C. Chackerian, Jr., Collisional line mixing, in Spectroscopy of the Earth’s

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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