Line mixing and speed dependence in CO2 at 6227.9 cm−1: Constrained multispectrum analysis of intensities and line shapes in the 30013 ← 00001 band

Journal of Molecular Spectroscopy 245 (2007) 52–80 www.elsevier.com/locate/jms

Line mixing and speed dependence in CO2 at 6227.9 cm1: Constrained multispectrum analysis of intensities and line shapes in the 30013 ‹ 00001 band V. Malathy Devi a, D. Chris Benner b

a,*

, L.R. Brown b, C.E. Miller b, R.A. Toth

b

a Department of Physics, The College of William and Mary, Box 8795, Williamsburg, VA 23187-8795, USA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Received 27 April 2007 Available online 18 July 2007

Abstract Line position, intensity and line shape parameters (Lorentz widths, pressure shifts, line mixing, speed dependence) are reported for transitions of the 30013 ‹ 00001 band of 16O12C16O (m0 = 6227.9 cm1). The results are determined from 26 high-resolution, high signal-to-noise ratio spectra recorded at room temperature with the McMath-Pierce Fourier transform spectrometer. To minimize the systematic errors of the retrieved parameters, we constrained the multispectrum nonlinear least squares retrieval technique to use quantum mechanical expressions for the rovibrational energies and intensities rather than retrieving the individual positions and intensities line by line. Self- and air-broadened Lorentz width and pressure-induced shift, speed dependence and line mixing (off-diagonal relaxation matrix elements) coefficients were adjusted individually. Errors were further reduced by simultaneously fitting the interfering absorptions from the weak 30012 ‹ 00001 band of 16O13C16O as well as the weak hot bands 31113 ‹ 01101, 32213 ‹ 02201, 40014 ‹ 10002 and 40013 ‹ 10001 of 16O12C16O in this spectral window. This study complements our previous work on line mixing and speed dependence in the 30012 ‹ 00001 band (m0 = 6347.8 cm1) [V.M. Devi, D.C. Benner, L.R. Brown, C.E. Miller, R.A. Toth, J. Mol. Spectrosc. 242 (2007) 90-117] and provides key data needed to improve atmospheric remote sensing of CO2.  2007 Elsevier Inc. All rights reserved. Keywords: CO2; Positions; Intensities and pressure broadening; Off-diagonal relaxation matrix element coefficients; Line mixing; Lorentz widths; Pressure shifts; Near infrared; Speed dependent line shape

1. Introduction This paper continues our systematic study of the near infrared (NIR, 4000–7500 cm1) spectroscopy of CO2. In a recent study [1] we employed a constrained multispectrum analysis technique [2] to obtain accurate line position, intensity, Lorentz width (self- and air-broadened), pressure shift (self- and air-induced), line mixing (self- and airbroadened) and speed dependence parameters for the 30012 ‹ 00001 band of 16O12C16O (m0 = 6347.8 cm1). The present study determines these parameters for the *

Corresponding author. Fax: +1 757 221 3540. E-mail address: [email protected] (D.C. Benner).

0022-2852/$ - see front matter  2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2007.05.015

30013 ‹ 00001 band (m0 = 6227.9 cm1) using the same spectra, molecular line shapes and analysis procedure. This follows our earlier analysis of line positions [3,4] and our ongoing measurements of intensities of over 150 vibration–rotation bands for eight isotopologues [5–7]. We also determined self- and air-broadened width and shift parameters for 15 and 11 vibration–rotation bands, respectively, of 16O12C16O [8,9]. The retrievals [5–9] used a common set of spectral data but employed the standard Voigt line profile [10] and retrieval software in which only one spectrum is analyzed at a time [11] rather than the one used in the present work and Ref. [1]. Until recently, near-IR measurements of air-broadened CO2 spectra, critical for accurate remote sensing of the

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Earth’s atmosphere, were particularly sparse, as were the self broadening coefficients needed for studies of Mars and Venus. In Table 1 we summarize the air- and self-broadened halfwidth and shift coefficients published for the 30013 ‹ 00001 band of 16O12C16O at 6227.9 cm1 [8,9,12– 17]. Several of these studies [12–14] as well as [18–20] also investigated line intensities. The majority of studies used the usual Voigt profile [10] to fit the line shapes while a few employed a Galatry line shape [21]. Few of the studies measured air-broadening halfwidth or shift coefficients directly. The most extensive self- and air-shift coefficients in the nearinfrared were reported only by Toth et al. [8,9]. To support carbon cycle science [22], our combined research was undertaken specifically to enable remote sensing retrievals of total column CO2 data with 0.3% accuracy. Although line positions of some bands were previously upgraded [3,4] in HITRAN 2004 [23], the available CO2 spectroscopic measurements of intensities and broadening were insufficient to achieve such a high level of accuracy. In the present work we determined accurate air-broadened halfwidth and shift coefficients also for a large number of transitions (54) for the strongest band (30013 ‹ 00001) in the fitted region, in addition to selfwidths and shifts. In our study of 30012 ‹ 00001 [1], we concluded that a better molecular line shape was needed to reproduce high quality laboratory spectra [24] and perhaps atmospheric data as well. In the present paper, we make the first comparison of the speed dependence and line mixing parameters (for self and air broadening) retrieved directly for two different near infrared bands of CO2. 2. Experiment The data used in the present work are the same used in [1] and are summarized in Table 2. Briefly, 26 laboratory spectra (Fig. 1) were recorded at 0.01 cm1 unapodized resolution with the McMath-Pierce FTS configured with a quartz-halogen source and two liquid nitrogen cooled

Table 1 Summary of widths and shifts measurements for the 30013 ‹ 00001 band of

53

InSb detectors. Fifteen spectra were pure carbon dioxide in natural abundance (16O12C16O = 0.9842), and 11 were CO2 + air mixtures (prepared by adding dry air to pure samples of CO2 in natural abundance). Nineteen spectra were recorded with absorption path lengths ranging from 25 to 121 m using a stainless steel multipass absorption cell with a 6 m base path length. Seven self-broadened spectra were obtained using a single pass stainless steel absorption cell with a path length of 2.46 m. Sample pressures were monitored continually using calibrated capacitance manometers (MKS) with 0–10, 0–100 and 0–1000 torr ranges. Sample temperatures were measured and monitored throughout the data acquisition period using high accuracy (±0.05 K) platinum resistance thermometers. Further details about the experimental set up, White cell configuration, calibration procedures and experimental precautions taken to minimize systematic errors have been discussed previously [1,5]. 3. Data reduction and retrievals The 6120–6280 cm1 region contains strong 16O12C16O absorptions arising from the 30013 ‹ 00001 band, as well as interfering absorptions from several weaker CO2 bands. As seen in Fig. 1, all these bands can be fitted simultaneously to retrieve the essential line parameters (positions, intensities, Lorentz widths and pressure shifts). Generating a single multispectrum least squares solution [25] produces internal consistency across all spectra while fitting a band over its entire spectral interval minimizes errors arising from experimental measurement sources such as the 100% transmission level and residual phase errors. This method also forces the 100% transmission level to be continuous and reduces the correlations between intensity and broadening parameters because the same solution must work for all spectra analyzed and under all measurement conditions (e.g. pressure, temperature, path length). For this particular dataset, we found that the standard Voigt line shape did not reproduce the observed spectra

12

C16O2

Reference

Instrument

Line shape

No. self-widths (range)

No. self-shifts (range)

No. air-widths (range)

No. air-shifts (range)

Present worka

FTS

65 (P66–R62)

65 (P66–R62)

58 (P58–R56)

54 (P54–R54)

Toth et al. [8] Toth et al. [9] Re´galia-Jarlot [13] Hikida et al. [14] Hikida and Yamadab [15] Pouchet et al. b [12] Nakamichi et al. b [17] Valero and Suarez [16]

FTS FTS FTS TDL TDL TDL Cavity Ringdown FTS

Speed dependent Voigt/line mixing Voigt Voigt Voigt Voigt and Galatry Galatry Voigt Voigt Equivalent width

57 (P58–R56)

55 (P58–R54) 44 (P44–R46)

42 (P44–R46)

a b

48 (P44–R50) 11 (P28–R28) 11 (P28–R28)

44 (P44–R44) 3 Temperatures

Line mixing measured using the off-diagonal relaxation matrix elements formalism. The air broadening coefficients were calculated from measured N2 and O2 broadening.

10 (P28–R28) 5 (R12–R20) 5 (R0, P8–P38)

54

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Table 2 Summary of experimental conditions of the CO2 spectra analyzed in this work CO2 in air

Pure CO2 a

Temp. (K)

Pressure (torr)

Path length (m)

Temp. (K)

Pressure (torr)

CO2Volume mixing ratio

Path length (m)

293.99 293.68 293.49 293.09 293.89 293.88 293.94 294.05 293.37 294.37 293.58 294.09 292.79 293.57 293.38

896.84b 556.56 252.42 52.14 450.93 101.95 26.10 11.04 252.01 94.65 75.27 50.70 30.31 25.61 9.973

49.00 49.00 49.00 49.00 24.94 24.94 24.94 24.94 2.46 2.46 2.46 2.46 2.46 2.46 2.46

292.92 293.07 292.79 293.34 293.05 293.17 293.03 293.17 292.88 292.63 292.75

923.52 250.38 100.86 551.29 549.545 200.25 100.00 50.07 49.79 26.05 25.09

0.0593 0.0595 0.0605 0.0152 0.0499 0.0155 0.0160 0.0749 0.0160 0.0679 0.0170

121.18 121.18 121.18 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00

a b

Pure natural CO2 samples (Volume mixing ratio = 1 with 0.9842 Not used by Toth et al. [5,8].

16

O12C16O); 1 atm = 101.3 kPa = 760 torr.

within experimental measurement uncertainty [24] and that line mixing was occurring. To avoid masking line shape effects, we did not adjust the positions and intensities on a line-by-line basis but rather solved for the rovibrational energy (G, B, D and H) and transition moment constants (vibrational band strength Sv, and the Herman-Wallis-type coefficients a1 and a2) for each vibrational state using Eqs. (1) and (2), respectively. This strategy proved adequate since all bands measured in this work are free of obvious perturbations for the range of J considered. mi ¼ G0  G00 þ ðB0 J 0 ½J 0 þ 1  D0 fJ 0 ½J 0 þ 1g

2

3

þ H 0 fJ 0 ½J 0 þ 1g Þ  ðB00 J 00 ½J 00 þ 1  D00 fJ 00 ½J 00 þ 1g2 þ H 00 fJ 00 ½J 00 þ 1g3 Þ     S m mi Li F C 2 E00 C 2 mi Si ¼ exp 1  exp Q r m0 T0 T0

ð1Þ

d0 ðT Þ ¼ d0 ðT 0 Þ þ d0 ðT  T 0 Þ ð2Þ

where F ¼ ð1 þ a1 m þ a2 m2 þ a3 m3 þ a4 J 0 ðJ 0 þ 1ÞÞ

2

ting technique and the method of calculating the uncertainties in the retrieved values are given in Benner et al. [2]. As in our study of the 30012 ‹ 00001 region [1], the selfand air-broadened Lorentz halfwidth and pressure-induced shift coefficients, defined in Eqs. (4)–(6), were determined on a line-by-line basis using the constrained multispectrum least squares fitting [2]. "  n1 T0 0 bL ðp; T Þ ¼ p bL ðairÞðp0 ; T 0 Þð1  vÞ T #  n2 T0 þb0L ðselfÞðp0 ; T 0 Þv ð4Þ T   ð5Þ m ¼ m0 þ p d0 ðairÞð1  vÞ þ d0 ðselfÞv

ð3Þ

mi denotes the wavenumber (cm1) of the ith transition, and prime and double prime denote the upper and lower vibrational levels, respectively. In Eq. (2), Li are the Ho¨nl-London factors (described in Toth et al. [5]), C2 represents the second radiation constant and other terms have their usual significance. The terms a1 and a2 in Eq. (3) were sufficient to describe the bands to the noise level of the spectra once the speed dependence and line mixing were utilized. The lower state rovibrational constants were constrained to the values found by Miller and Brown [3,4]. We emphasize that the line positions and intensities presented in this study were not individually measured and that corresponding values given in Appendices A–E, are calculated from the constants determined using Eqs. (1)–(3). Details of this fit-

ð6Þ

In Eqs. (4)–(6) bL 0 and d0 represent pressure broadening (in cm1 atm1 at 296 K) and pressure shift coefficients (in cm1 atm1 at 294 K), respectively. bL (p, T) is the Lorentz halfwidth (in cm1) of the spectral line at pressure p and temperature T, and bL 0 ðGasÞðp0 ; T 0 Þ is the Lorentz halfwidth coefficient of the line at the reference pressure p0 (1 atm) and temperature T0 (296 K) of the broadening gas (either air or CO2), and v is the ratio of the partial pressure of CO2 to the total sample pressure in the cell. Further details can be found in Section 4.2 of Ref. [1]. We tested different line shapes and found that the largest non-Voigt deviations were due to line mixing [26,27]. Spectra were first fit using standard Voigt profiles. Significant residuals remained in the fit. The fit residuals were considerably reduced when the Voigt profile was modified with off-diagonal relaxation matrix element coefficients. The remaining small residuals were further reduced when speed dependence [28] was also included in the fit (see Fig. 1). The multispectrum fit illustrated in Fig. 1 shows the final

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

55

Fig. 1. Multispectrum fitting of CO2 from 6120 to 6280 cm1. (a) Twenty-six experimental spectra recorded at 0.01 cm1 resolution using the Fourier transform spectrometer at Kitt Peak. This set consists of 15 high-purity CO2 spectra in natural mixture of the isotopologues and 11 CO2 + air spectra; all gas samples are at room temperature. Positions of transitions included in the multispectrum fit are indicated by tick marks shown at the top of panel. Each spectrum is normalized to the highest signal in the fitted interval. The 100% absorption line is shown by dotted line at the bottom of panel. Each spectrum was assigned a weight such that the weighted RMS residuals are almost the same in each spectrum. The three other panels are the corresponding weighted residuals (observed minus calculated on an expanded vertical scale) obtained by applying different line shapes. (b) A Voigt profile modified with speed dependence and line mixing (via relaxation matrix element coefficients); (c) the weighted residuals from a fit using the Voigt profile modified with line mixing (via relaxation matrix element coefficients) but without speed dependence; (d) the weighted residuals from a fit using only the Voigt profile. To show the effects of line mixing, only the residuals from the 6 highest-pressure self-broadened and 3 air-broadened spectra are plotted.

retrieval for the entire 30013 ‹ 00001 band (both the P- and R-branches) using all 26 spectra listed in Table 2. As before [1], a weight of 1.0 is assigned to the spectrum with the highest signal to noise ratio, and the weights for all other spectra are set proportional to the square of the ratio of the signal-to-noise ratios. Including weak absorption features (of the 31113 ‹ 01101 hot band of 16O12C16O and 3 other weaker bands, as well as 30012 ‹ 00001 of 16 13 16 O C O) is necessary but that alone did not achieve an

accurate fit. As seen in Fig. 1b, the weighted fit residuals determined using a speed-dependent Voigt line shape [28] and line mixing calculated from relaxation matrix element coefficients [27] are better than those obtained using either a Voigt line shape without speed dependence but with a similar line mixing calculation (Fig. 1c) or the retrieval with a standard Voigt profile [10] with no modifications as shown in Fig. 1d. For simplicity, in the bottom panel we present only the residuals from the six highest pressure

56

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

self-broadened spectra and the three highest air-broadened spectra where the effects of line mixing are most evident. It also illustrates the fact that line mixing influences other spectral line parameters such as intensities, widths and pressure-induced shifts.

The individual line parameters for the 30013 ‹ 00001 band and the four 16O12C16O hot bands in the 6120– 6280 cm1 region are given in Appendices A–E; results for the 30012 ‹ 00001 band of 16O13C16O will be reported separately. The parameters include the calculated zero pressure line position (m in cm1), calculated line intensity (cm1/molecule cm2 at 296 K), the Lorentz pressurebroadening coefficients bL 0 ðairÞ and bL 0 ðselfÞ in cm1 atm1 at 296 K, and the pressure-induced shift coefficients d0(air) and d0(self) in cm1 atm1 at 294 K. Line mixing (off-diagonal relaxation matrix element coefficients) and speed-dependent parameters are listed only for the 30013 ‹ 00001 band. The weaker bands were fit without line mixing and speed dependence since the signal-to-noise ratios in the spectra were insufficient to detect non-Voigt behavior in these transitions. The uncertainties in the pressure-induced shift coefficients are given in parentheses in

units of the least significant digit reported. In all cases the uncertainty represents one standard deviation in the measured quantity. The measured parameters for the hot bands are less accurate and less extensive due to the weaker absorption strengths. For the 31113 ‹ 01101 hot band we obtained positions and intensities for several transitions in the P-, Q- and R-branches in both the e and f sub-levels and broadening and shift parameters in the P- and R-branches. However, only self broadening values were measured for the 40014 ‹ 10002 band. The two remaining hot bands were sufficiently weak that only the positions and intensities could be obtained with the current dataset. We note that by using constraints even the parameters of weak bands could be retrieved with reasonable accuracy (see Figs. 2 and 3). Table 3 lists the rovibrational (G, B, D, H, . . .) and intensity (band strength Sv, and the Herman-Wallis-type coefficients a1 and a2) parameters retrieved for the 30013 ‹ 00001 region. The intensity parameters correspond to a CO2 sample in natural abundance (0.9842 16 12 16 O C O). The correlation coefficients between appropriate pairs of the fitted parameters are also listed; these are required to calculate the uncertainties of the positions and intensities of the individual lines, as explained by Benner et al. [2]. There are no significant correlations between

Fig. 2. Uncertainties in the fitted line positions (cm1) are plotted as a function of J 0 for each measured band. Curves corresponding to specific bands are labeled with the upper vibrational state. See the text for details.

Fig. 3. The percent intensity uncertainties (ratio of intensity uncertainty to intensity · 100) are plotted as a function of m for P and R branches and as a function of J 00 for Q branches for each measured band. For example, the uncertainty in intensity varies from 0.01% to <0.1% as jmj increases from 0 to 100 for the strongest band (30013 ‹ 00001). See the text for details.

4. Results

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80 Table 3 Rovibrational and band intensity constants and correlation coefficients of measured Band

Upper state rotational constants in cm 0

G G 30013 ‹ 00001 31113 ‹ 01101 31113 ‹ 01101 32213 ‹ 02201 32213 ‹ 02201 40014 ‹ 10002 40013 ‹ 10001

e f e f

00

6170.10897 (51) 6175.11304 (21) 6205.50986 (33)

C16O2 bands: 6120–6280 cm1

12

1

Intensity constants D · 10

H · 10

Sv · 1024

A1 · 104

A2 · 105

0.3867111479 (144) 0.386922332 (150) 0.388334816 (150) 0.38860808 (212) 0.38860698 (212) 0.38735008 (68) 0.38555499 (188)

1.717038 (144) 1.353711 (189) 1.48926 (188) 1.600 (17) 1.447 (17) 1.9933 (44) 0.835 (27)

10.552 (38) 1.932 (60) 1.124 (60) 0.0 fixed 0.0 fixed 0.0 fixed 11.33 (100)

441.331 (53) 32.545 (19)

+2.880 (11) +3.72 (6)

+1.7106 (44) +1.213 (31)

1.248 (5)

0.0 fixed

0.0 fixed

2.233 (4) 1.48 (4)

5.21 (45) 0.0 fixed

0.0 fixed 0.0 fixed

0.39021894900 0.39063910900 0.391254698 0.3916667620 0.3916667620 0.3901889160 0.3904708290

1.334088000 1.3539300 1.3616060 1.373660 1.381250 1.149427 1.57157070

B

6227.9165646 (40) 6196.175974 (29)

57

0

0

7

0

12

Lower state constants 00001 01101 01101 02201 02201 10001 10002

(fixed) e (fixed) f (fixed) e (fixed) f (fixed) (fixed) (fixed)

0. 667.3798265 1335.1313992 1388.1840918 1285.4081123

Band

30013 ‹ 00001 31113 ‹ 01101 31113 ‹ 01101 32213 ‹ 02201 32213 ‹ 02201 40014 ‹ 10002 40013 ‹ 10001

0.1918 0.2967 0.3040 3.765 0.7380 1.86596 2.33398

Correlation coefficients for upper state constants

e f e f

Correlation coefficients for intensity constants

G 0  G 00 & B 0

G 0  G 00 & D 0

G 0  G 00 & H 0

B0 & D0

B0 & H0

D0 & H0

S v & A1

S v & A2

A1 & A2

0.698 0.767 0.767 0.784 0.779 0.853 0.865

0.547 0.587 0.586 0.604 0.601 0.690 0.760

0.442 0.464 0.464

+0.943 +0.933 +0.932 +0.929 +0.929 +0.932 +0.965

+0.834 +0.820 +0.820

+0.961 +0.959 +0.960

+0.071 +0.019

0.652 0.745

0.046 +0.076

+0.892

+0.975

0.659

+0.085

The band centers and rotational constants are in cm1. The rotational constants for the lower states (ground state, 01101, 02201, 10001, 10002) are from Ref. [3]. Note that L00 (10001) = 0.5663 · 1018 and L00 (10002) = 0.9928 · 1018. The intensity constants are the same for the e and f levels of the 31112 ‹ 01101 and 32212 ‹ 02201 bands. The band strengths (Sv) are in cm1/(molecule cm2) · 1024 at 296 K. The 12C16O2 samples used were at natural abundance (16O12C16O = 0.9842). The rotational partition function used for 12C16O2 at 296 K is 263.60.

the intensity parameters Sv, a1 and a2; the largest correlation coefficient for the 30013 ‹ 00001 band is 0.652 between Sv and a2. There are significant correlations between the rotational constants B, D, and H, but the parameters determined in this work generally agree with the values determined by Miller and Brown [3] within the mutual 3r uncertainties. In Fig. 2, uncertainties in the zero pressure positions are plotted as a function of J 0 for each measured band with curves labeled according to the upper vibrational state. For the 30013 ‹ 00001 band, the uncertainties in positions are less than 3 · 106 cm1 for J 0 < 40, less than 4 · 105 cm1 for 40 < J 0 < 60, and less than 4 1 5 · 10 cm for 60 < J 0 < 80. The uncertainties in position for the 31113 ‹ 01101 band reach 1 · 104 cm1 when J 0  45. The extrapolation of the uncertainties beyond the range of measured lines is only an estimate and assumes that there are no perturbations. Fig. 3 shows the numerical precision in the intensities obtained from the multispectrum fit expressed as a percentage of the retrieved intensity (ratio of calculated intensity uncertainty to retrieved intensity times 100) versus m or

J00 , as appropriate, for each band analyzed. For the 30013 ‹ 00001 band, the intensity uncertainty varies from 0.01% to <0.1% as jmj increases from 0 to 100. The use of constraints [2] produced high precision in positions and intensities. The absolute accuracy of individual 30013 ‹ 00001 line intensities is estimated to be 0.3%, limited in large part by the uncertainty in the calculation of the concentration of (CO2)2 that may be present in the cell [2]. The estimated accuracies for the weaker bands range from 0.3% to 1.0%. The question of absolute accuracy is addressed further in Section 4.1. 4.1. Intensities The intensity data shown in Fig. 4 illustrate the challenge in establishing CO2 spectroscopic reference standards to support atmospheric remote sensing with accuracies of 0.3%. The retrieved line intensities for the six vibrational bands observed in the 30013 ‹ 00001 region are plotted as a function of m on both linear (Fig. 4a) and logarithmic (Fig. 4b) scales; the corresponding uncertainties are shown on a logarithmic scale in Fig. 4c. The 30013 ‹ 00001 tran-

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V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Fig. 4. Line intensities in natural abundance determined for the P and R branches of the six vibrational bands are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines) on a (a) linear scale and (b) logarithmic scale. The uncertainties in fitted intensities on a logarithmic scale are shown in (c).

sitions reach a maximum intensity near 1.8 · 1023 cm1/ molecule cm2 at 296 K. As seen in Fig. 4b, four of the five other vibrational bands have transitions that would interfere with 30013 ‹ 00001 intensity determinations at the 0.3% level (Sv > 6 · 1026 cm1/molecule cm2) and all five bands have transitions that would interfere at the 0.1% level (Sv > 2 · 1026 cm1/molecule cm2). Failure to characterize all CO2 absorptions that contribute to observed spectral intensity at the desired accuracy level will introduce systematic errors into remote sensing retrievals.

Fig. 4c illustrates that the individual line intensity uncertainties of the hot band 40014 ‹ 10002 of 16O12C16O and 30012 ‹ 00001 of 16O13C16O are comparable to those for the same quantum numbers of 31113 ‹ 01101 even though these bands are approximately an order of magnitude weaker than 31113 ‹ 01101. In fact, 30012 ‹ 00001 of 16 13 16 O C O has intensity uncertainties exceeding those of the 31113 ‹ 01101 band for several P-branch lines. This is because the relative uncertainties of all bands are limited by the signal-to-noise of the spectra. The intensity uncer-

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80 Table 4 Comparison of band intensity parameters of Parameter

C16O2

30013 ‹ 00001 band a

This work Sv a1 a2 N Jmax

12

31113 ‹ 01101 band Toth et al. [5]

22

4.4133 (5) · 10 0.2880 (11) · 103 0.1711 (4) · 104 74 74

59

22

4.420 (4) · 10 0.2782 (80) · 103 0.1826 (26) · 104 60 67

This worka

Toth et al. [5]

0.32545 (19) · 1022 0.372 (6) · 103 0.1213 (31) · 104 136 60

0.3281 (3) · 1022 0.2308 (248) · 103 0.0482 (98) · 104 74 53

The intensities are obtained from a natural CO2 sample with a 16O12C16O abundance of 0.9842 and are in units of cm1/(molecule cm2) at 296 K. The results from this work are determined by the multispectrum least squares fitting technique by incorporating position and intensity constraints in the solution (see the text for details). a

Fig. 5. Line intensities of the 30013 ‹ 00001 band from this work are compared to observed line intensities from Toth et al. [5] and plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines) on (a) a linear scale and (b) a logarithmic scale. In panel (c), the ratios of measured line intensities [Toth et al. [5] divided by values from present work] are displayed. The error bars shown in (c) are dominated by the uncertainties in [5].

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tainties are J-dependent because we have constrained the intensities to follow a theoretical relationship, and the uncertainties track with this formula. The 30013 ‹ 00001 band strength and Herman-Wallis coefficients obtained by Toth et al. [5] using a Voigt line shape and an unconstrained line-by-line retrieval procedure compare well to present values (Table 4). The fractional integrated band strength difference between Toth et al. [5] and present work {(Toth et al. [5]  Present work)/(Present work) · 100} is +0.15%. In Fig. 5, the individual 30013 ‹ 00001 line intensities determined in the present work are compared to those of Toth et al. [5] on both linear (Fig. 5a) and logarithmic (Fig. 5b) scales. Fig. 5c presents ratio of the Toth et al. values [5] to those from the present work (PW). The associated error bars are dominated by measurement uncertainties from [5]. The intensities of individual lines differ by less than 1.0%; the unweighted mean difference is +0.40 ± 0.39% with no obvious m dependence. We attribute the offset between the Toth et al. [5] results and the present work to the difference in retrieval techniques (unconstrained line by line vs. constrained multispectrum) and line shape parameterizations (Voigt vs. speed dependent Voigt with line mixing), even though both analyses were performed on a common set of spectral data (see Refs. [1,5]). Our previous work on the 30012 ‹ 00001 band (m0 = 6348 cm1) yielded an intensity ratio of 1.003 (6) for the analogous comparison [1]. We conclude that the relative intensities of the 30013 ‹ 00001 and 30012 ‹ 00001 bands have been determined with a precision of 0.1%, and that the line by line/Voigt retrievals overestimate the individual rovibrational transition intensities by 0.4%, mostly due to the inadequacies of the Voigt line shape. This has direct implications for atmospheric remote sensing since an overestimation of the CO2 line strengths would lead to remote sensing retrievals that underestimated the true atmospheric CO2 level. In fact, Washenfelder et al. [29] reported atmospheric column CO2 retrievals using a Voigt line shape parameterization from the 30013 ‹ 00001 and 30012 ‹ 00001 bands that were 2.16 ± 0.39% and 2.40 ± 0.42%, respectively, higher than in situ column CO2 measurements. Their results deviate from the in situ measurements due to the effects of inaccuracies in the intensities, line shapes and atmospheric modeling that they used. More accurate line shape parameterizations will clearly be required to enable atmospheric CO2 remote sensing with accuracies better than 0.3% [22,30]. Fig. 6 displays the differences between our 30013 ‹ 00001 line intensities, with intensities determined in five other recent investigations [5,12–14,18], and the HITRAN04 database [23]. Boudjaadar et al. [18] retrieved 58 rovibrational transition intensities (P60 to R54) from FTS spectra using a multispectrum fitting procedure. They reported accuracies of 3% and 5%, respectively, for strong and weak (high J) transitions. Re´galia-Jarlot et al. [13] measured 48 rovibrational transition intensities (P44 to R50) from three FTS spectra using a multispectrum fitting

procedure. They repeated the intensity measurements of 13 transitions between R6 and R30 obtained using a tunable diode laser spectrometer and found agreement within 1%. Recently, Boudjaadar et al. [19] confirmed that the previous Boudjaadar et al. [18] and Re´galia-Jarlot et al. [13] intensities agreed to within 0.5% despite larger absolute uncertainties reported for both data sets. In two other diode laser experiments Pouchet et al. [12] reported absolute intensities of 13 lines between R6 and R30 and Hikida et al. [14] studied 11 transitions between P28 and R28. The intensity differences seen in Fig. 6 and listed in Table 5 are rather small: +0.40 (39)% with Toth et al. [5], +1.7 (8)% with Boudjaadar et al.[18], +1.7(4)% with Re´galia-Jarlot et al. [13], +0.40(1.3)% with Pouchet et al. [12] and 1.7(2.7)% with Hikida et al. [14] compared to the differences observed with HITRAN04 [23] (for J 0 up to 72) and present work (4 ± 13)%. Given the effort by the other studies to achieve better intensity accuracies and the prior comparisons for 30012 ‹ 00001 at 6348 cm1 (see Table 13 in Toth et al. [5]), we expected to see better agreement of the measured intensities. 4.2. Self and air broadening coefficients The measured self- and air-broadened halfwidth and shift coefficients and the corresponding uncertainties for the 30013 ‹ 00001 and 31113 ‹ 01101 bands are listed in Appendices A and B, respectively. The uncertainties in positions and intensities are not directly listed in Appendices A and B, but are displayed in Figs. 2 and 3, respectively. The 40014 ‹ 10002 hot band was sufficiently intense that we were able to determine the self-broadening widths and shifts for a few transitions, but not the air broadening coefficients (Appendix D). The 32213 ‹ 02201 and 40013 ‹ 10001 bands were too weak for an accurate determination of any self or air broadening parameters (Appendices C and E, respectively). The measured self- and air-broadened halfwidth coefficients of 30013 ‹ 00001 are plotted as a function of m in Fig. 7. Unlike the line positions and intensities, we have not constrained the halfwidth coefficients to a quantum mechanical function that varies smoothly with m. Despite this, the line to line variation is smooth at almost the 0.1% level for self broadening and only a bit larger for the air broadening, with few exceptions (see Appendix A). The two solid curves in Fig. 7a correspond to selfand air-halfwidth coefficients calculated using empirical expressions given in Toth et al. [8]. The air-broadened halfwidth coefficients are smaller than the corresponding selfbroadened values. The ratios of self- to air-halfwidth coefficients vary with m because the self-broadening coefficients fall off more rapidly with increasing m than do the airbroadening coefficients. In Fig. 7b, the percentage difference between the observed and empirically calculated self-broadened halfwidth coefficients, plotted as a function of m, are within ±1% except for a few weak high-J transitions. However, as seen in Ref. [1], close inspection of

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Fig. 6. Intensity differences between other studies [5,12–14,18,23] and the present work in percent are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines) for (a) Toth et al. [5]  Present work, (b) Boudjaadar et al. [18]  Present work, (c) Re´galia-Jarlot et al. [13]  Present work, (d) Pouchet et al. [12]  Present work, (e) Hikida et al. [14]  Present work and (f) HITRAN04 [23]  Present work. The mean and standard deviations of the differences obtained in each case are also included in the panels.

Fig. 7b reveals small systematic m-dependent variations that are significantly larger than the line to line variation. The same effect occurs in the air-broadened halfwidths (Fig. 7c), where the P- and R-branches exhibit systematic differences in their residuals. This is due to the fact that the empirical expression used in fitting the measurements does not fully represent the observed variations in the halfwidth coefficients with m. The residuals presented in Fig. 7b and c are therefore real deviations in the empirical

fits from the actual behavior occurring within the self- and air-broadening mechanisms. In Fig. 7d we show the ratio of self to air broadened halfwidth coefficients as a function of m. Within the range of m shown this ratio varies from approximately 1.08 to 1.35. In Fig. 8, we compare the 30013 ‹ 00001 self- and airbroadened halfwidth coefficients from the present work with the corresponding values for 30012 ‹ 00001 at 6348 cm1 [1]. Figs. 8b and c show the ratios of self to self

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Table 5 Comparison of line intensities: %(other  present)/present Other studies [Reference]

30013 at 6227.9 cm1 # lines

Toth et al. [5] Boudjaadar et al. [18] Re´galia-Jarlot et al. [13] Henningsen and Simonsen [20] Hikida et al. [14] Pouchet et al. [12]

30012 at 6348 cm1 [1] %diff

61 57 49

0.40 1.65 1.73

11 13

1.72 0.40

Mean % difference (others  present)/present

and air- to air-halfwidth coefficients, respectively, as a function of m. The values of the self-broadened widths for the two bands are identical within experimental error through jmj 6 50, and yield an average ratio of 0.999 ± 0.004. The values of the air-broadened widths behave similarly for jmj 6 50, and yield an average ratio of 0.999 ± 0.006. Thus, the values from the two bands are essentially the same. The measured self- and air-induced pressure shift coefficients (in units of cm1 atm1 at 294 K) for 30013 ‹ 00001 (present work) and 30012 ‹ 00001 [1] are plotted as a function of m in Fig. 9. The increased scatter observed in both the self- and air-shift coefficients at higher m values is due to the weaker absorption strengths and correspondingly larger uncertainties in the shift coefficient for these lines. The measured self- and air-shift coefficients for both bands exhibit the same qualitative variation with m, although the 30013 ‹ 00001 self-shift coefficients are systematically lower (larger in magnitude) than the 30012 ‹ 00001 selfshift coefficients. The differences between self- and airinduced shift coefficients for the two bands are plotted in Fig. 9b and c, respectively. A dashed line corresponding to zero difference has been added to each plot to aid the viewer. The mean difference between the 30013 ‹ 00001 and 30012 ‹ 00001 self-shift coefficients is 0.0004 (2) cm1 atm1 at 294 K calculated for the transitions with jmj 6 52. The mean difference between the 30013 ‹ 00001 and 30012 ‹ 00001 air-shift coefficients is 0.0001 (3) cm1 atm1 at 294 K calculated for the transitions with jmj 6 40. The small range obtained for m and the larger uncertainty in the air-shift coefficients reflect the smaller range of CO2 optical depths in the air broadening data set than in the self broadening data set. 4.3. Line mixing and speed-dependent line shape Our previous work on the 30012 ‹ 00001 band centered at 6348 cm1 revealed that a regular Voigt line shape was insufficient to simulate the data to within experimental uncertainty [1]. The retrievals that minimized statistical and systematic errors in that study combined a speed dependent Voigt line shape [28] with line mixing calculated using the relaxation matrix formalism [27]. In determining the off-diagonal relaxation matrix elements, we considered line mixing only between the nearest neighbor lines in the

0.49 (±1.39)

# lines

%diff

62 58 48 42

0.22 1.1 0.24 3.3

0.56(±1.91)

P- and R-branches; all other off-diagonal relaxation matrix elements were constrained to zero. We determined the relaxation matrix elements for the 30013 ‹ 00001 band in the same fashion, and the retrieved values are given in Table 6. We assume that the temperature dependence exponent of the self- and air-broadened widths (n = 0.75) also describes the temperature dependence of the off-diagonal relaxation matrix element coefficients. We estimate that this assumption will introduce errors no larger than 0.05% for the range of temperatures encountered in our data, 292.6 K to 294.4 K. For transitions with jmj > 40, the off-diagonal relaxation matrix element coefficients could not be determined directly from the experimental spectra and have been assigned a value of 0.004 cm1 atm1 at 296 K. The off-diagonal relaxation matrix element coefficients for self- and air-broadening of the 30013 ‹ 00001 band are plotted vs. m in Fig. 10a. The relaxation matrix elements and the speed-dependent line shape factor could be measured only for transitions in the 30013 ‹ 00001 band, since it was the only band in the present study strong enough to have significant far wing absorption. Fig. 10a shows that the off-diagonal relaxation matrix elements are larger for self broadening than for air broadening. The ratio of the off-diagonal relaxation matrix elements for self and air broadening varies with m. The mean and standard deviation of the unweighted ratios of the off-diagonal relaxation matrix element coefficients of self- to airbroadening for the P- and R-branch pairs of transitions are found to be 1.46 ± 0.56 and 1.48 ± 0.32, respectively. These ratios have to be considered only approximate, and proper judgment has to be exercised in using these values in any rigorous treatment involving these coefficients. It is clear from Fig. 10a that the off-diagonal relaxation matrix element coefficients for self- broadening are not the same for lines with same jmj in the P and R branches. Such a noticeable difference is not observed for the air broadening off-diagonal relaxation matrix element coefficients. The self-broadening off-diagonal relaxation matrix element coefficients were determinable for J up to 40 in the Pbranch and for J up to 44 in the R-branch. The air broadening off-diagonal relaxation matrix element coefficients were determined up to J = 38 and J = 40 in the P- and R-branches, respectively. Beyond those J, a fixed value of 0.004 cm1 atm1 was used for J up to 60 in both branches

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63

Fig. 7. Comparison of halfwidth coefficients for the 30013 ‹ 00001 band of 12C16O2. (a) The measured self- and air-broadened halfwidth coefficients (cm1 atm1 at 296 K) are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). Both sets are fitted to the empirical expression given in [8] and the corresponding calculated values are shown by solid curves. (b) The percentage observed minus calculated residuals obtained for self-broadened halfwidth coefficients are plotted as a function of m. (c) The percentage observed minus calculated residuals obtained for air-broadened halfwidth coefficients are plotted as a function of m. (d) Ratios of measured self- to air-broadened halfwidth coefficients are plotted as a function of m. Where error bars are not visible the uncertainties are smaller than the size of the symbols used. The dashed horizontal lines in (b) and (c) correspond to zero difference.

and for both self and air broadening. The data provide better sensitivity to line mixing in the R-branch due to smaller wavenumber intervals between transitions and thus greater overlap of the line wings. For comparison we have included in Fig. 10a the self- and air- off diagonal relaxation matrix element coefficients determined in our previous study of the 30012 ‹ 00001 band [1]. The off-diagonal relaxation

matrix element coefficients measured for self- and air-mixing of the two bands are remarkably similar, although not identical. We continue to investigate the possible reasons for these differences. The measured speed-dependence parameters for transitions in the 30013 ‹ 00001 band are listed in Appendix A along with other line parameters determined for that

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Fig. 8. Comparison of the measured 30013 ‹ 00001 and 30012 ‹ 00001 [1] halfwidth coefficients of 12C16O2 retrieved using the same spectral data and retrieval procedure. (a) Measured self- and air-broadened halfwidth coefficients (cm1 atm1 at 296 K) are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines.) (b) The ratios of self-broadened halfwidth coefficients from present work to those in Ref. [1] are plotted versus m. (c) The ratios of air-broadened halfwidth coefficients from present work to those in Ref. [1] are plotted versus m. Where error bars are not visible the uncertainties are smaller than the size of the symbols used.

band. The speed-dependence parameters are plotted in Fig. 10b. Reliable values for the speed dependence were determinable only for J values up to 40. Beyond those J (for 42 6 J 6 60) the speed-dependence parameters were fixed to a value of 0.1, in both branches and for both self and air broadening. From Fig. 10b we see that speed dependence as a function of m follows a pattern similar to the Lorentz halfwidth coefficients and the off-diagonal relaxation matrix element coefficients. In our analysis we have assumed that speed dependence is independent of the broadening gas, hence a single value is determined for both self and air broadening. Speed dependence parame-

ters determined in [1] for the 30012 ‹ 00001 band compare well with present measurements as seen in Fig. 10b. References to other approaches on line mixing in CO2 absorption spectra by other approximations such as ECS are given in [1,2]. 5. Comparison of broadening coefficients from other studies In this section we compare and contrast the self- and airbroadened widths and shifts for the 30013 ‹ 00001 and 30012 ‹ 00001 bands determined via constrained multispectrum retrievals with the corresponding values obtained

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65

Fig. 9. Comparison of the measured 30013 ‹ 00001 and 30012 ‹ 00001 [1] shift coefficients of 12C16O2 retrieved using the same spectral data and retrieval procedure. (a) Measured self- and air-induced pressure shift coefficients (cm1 atm1 at 294 K) are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). (b) The differences in the self-induced shift coefficients for the 30013 ‹ 00001 and 30012 ‹ 00001 bands plotted versus m. The dashed horizontal line corresponds to equal self-shift coefficients in the two bands. (c) The differences in the air-induced shift coefficients for the 30013 ‹ 00001 and 30012 ‹ 00001 bands plotted versus m. The dashed horizontal line in (c) corresponds to equal air-shift coefficients in the two bands. Where error bars are not visible the uncertainties are smaller than the size of the plot symbols.

by Toth et al. using unconstrained line by line retrievals [8,9]. We also examine the consistency between present values and the other investigations summarized in Table 1. 5.1. Comparison with Toth et al. studies Toth et al. [8,9] fitted empirical expressions to the average values of the measured self- and air-broadening coefficients for the entire 3001n ‹ 00001 (n = 1–4) tetrad. The empirical fit coefficients listed by Toth et al. [8] in their Table 9 simulated their measured self-broadened widths with a standard deviation of 2.27%. Since that study pro-

vided a detailed assessment of self-broadened halfwidth and shift coefficients reported in the literature for the 30013 ‹ 00001 and 30012 ‹ 00001 bands [8], we restrict our comparison of the present results of self widths for the 30013 ‹ 00001 band to those from [1,8]. The measured self- and air-broadened halfwidth coefficients from present work and those from our previous work [1] as well as by Toth et al. [8,9] are plotted as a function of m in Fig. 11a. The ratios of self-broadened halfwidth coefficients measured by Toth et al. [8] divided by present results for the 30013 ‹ 00001 band as a function of m are shown in Fig. 11b. The mean and standard deviation of the

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Table 6 Self- and air-broadened off-diagonal relaxation matrix element coefficientsa Wij for 30013 ‹ 00001 band of Line mixing between

Self W

P2 & P4 P4 & P6 P6 & P8 P8 & P10 P10 & P12 P12 & P14 P14 & P16 P16 & P18 P18 & P20 P20 & P22 P22 & P24 P24 & P26 P26 & P28 P28 & P30 P30 & P32 P32 & P34 P34 & P36 P36 & P38 P38 & P40 P40 & P42 P42 & P44 P44 & P46 P46 & P48 P48 & P50

0.0065 0.0119 0.0148 0.0185 0.0215 0.0241 0.0267 0.0284 0.0288 0.0290 0.0293 0.0294 0.0294 0.0288 0.0264 0.0245 0.0223 0.0203 0.0179 0.004b 0.004b 0.004b 0.004b 0.004b

a b

CO2 –CO2 ð296 ij

(1) (1) (1) (2) (2) (2) (2) (2) (2) (2) (2) (3) (3) (3) (4) (4) (3) (3) (3)

KÞ

Air W

CO2 –air ð296 ij

KÞ

0.0072 (7) 0.0140 (7) 0.0140 (7) 0.0174 (7) 0.0191 (7) 0.0225 (7) 0.02171(7) 0.0214 (8) 0.0209 (8) 0.0208 (9) 0.0204 (10) 0.0204 (11) 0.0206 (12) 0.0183 (13) 0.0150 (15) 0.0140 (16) 0.0135 (17) 0.0103 (18) 0.0053 (17) 0.004b 0.004b 0.004b 0.004b 0.004b

Line mixing between

Self W

R0 & R2 R2 & R4 R4 & R6 R6 & R8 R8 & R10 R10 & R12 R12 & R14 R14 & R16 R16 & R18 R18 & R20 R20 & R22 R22 & R24 R24 & R26 R26 & R28 R28 & R30 R30 & R32 R32 & R34 R34 & R36 R36 & R38 R38 & R40 R40 & R42 R42 & R44 R44 & R46 R46 & R48 R48 & R50

0.0056 0.0171 0.0225 0.0263 0.0295 0.0318 0.0326 0.0335 0.0335 0.0335 0.0334 0.0324 0.0308 0.0299 0.0286 0.0275 0.0265 0.0240 0.0226 0.0213 0.0196 0.0176 0.0138 0.0110 0.0073

12

C16O2

CO2 –CO2 ð296 ij

(1) (1) (1) (1) (1) (1) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (3) (3) (3) (3)

KÞ

Air W ijCO2 –air ð296 KÞ 0.0043 0.0134 0.0167 0.0197 0.0198 0.0212 0.0213 0.0212 0.0230 0.0236 0.0227 0.0235 0.0231 0.0229 0.0210 0.0202 0.0169 0.0172 0.0155 0.0077 0.004b 0.004b 0.004b 0.004b 0.004b

(5) (7) (6) (6) (6) (5) (5) (5) (5) (5) (5) (5) (6) (6) (7) (6) (7) (6) (6) (7)

Units are cm1 atm1 near 296 K. The values given in parentheses represent one standard deviation measurement error in the last quoted digit. Fixed to a default value of 0.004 cm1 atm1 near 296 K.

unweighted ratios are 0.982 ± 0.016, close to the value of 0.98 ± 0.01 obtained for the 30012 ‹ 00001 band [1]. Thus, we find that the line by line/Voigt profile retrievals systematically underestimate the self broadening coefficients by 2.0% while overestimating the intensities by 0.4% compared to our constrained multispectrum/speed dependence with line mixing retrievals. Inspection of Fig. 11b clearly indicates an m-dependent pattern in these ratios. The measured self-broadened halfwidths for both, the 30013 ‹ 00001 and the 30012 ‹ 00001 bands in Fig. 11a show small but noticeable differences with respect to corresponding measurements by Toth et al. [8], especially for m < 24. The self-broadened halfwidth differences are attributed to the two different analysis techniques, as discussed above. The empirical fit coefficients for air-broadened halfwidths determined in [9] simulate their measured air halfwidths with a standard deviation of 0.67%. The ratios of air-broadened halfwidth coefficients measured by Toth et al. [9] divided by present results for the 30013 ‹ 00001 band as a function of m are shown in Fig. 11c. Inspection of Fig. 11c clearly indicates that there is a small but noticeable systematic differences in the air-broadened halfwidths measured in [9] and in present work. The mean and standard deviation of the unweighted ratios (values from Toth et al. [9] divided by values from present work) are 0.985 ± 0.011. The measured self-shift coefficients are plotted as a function of m for the 30013 ‹ 00001 band in Fig. 12a. The present measured pressure-induced shift coefficients are fitted to

the same empirical expression used in Ref. [8], and the results are also shown in Fig. 12a by the solid curve. The residuals between measured and calculated self-shift coefficients (from present work) are plotted as a function of m in Fig. 12b. Agreement within ±10% is seen between measurements and calculations. The mean and RMS standard deviation between our measured values and smoothed curve is 5 ± 9%, but the deviations between them are systematic, and it is apparent that the empirical expression is not adequate to represent the measured values. The measurement precision in our self-shift values is at the 2–3% level. The measured air-induced shift coefficients are also plotted as a function of m for the 30013 ‹ 00001 band in Fig. 12a. Similar to self-shift coefficients, our measured air- shift coefficients are fitted to the empirical expression used in Ref. [8,9] and the calculated curve (dashed) is plotted in Fig. 12a. The residuals between measured and calculated air-induced shift coefficients are plotted in Fig. 12c. Measurements and calculations agree within ±15%. Again, the empirical expression is not adequate to reproduce our air shift coefficients within the measurement precision. Comparisons of self- and air-shift coefficients between 30013 ‹ 00001 and 30012 ‹ 00001 bands from present work and [1] and from Toth et al. [8,9] are shown in Fig. 13. The self-shift coefficients are plotted versus m in Fig. 13a with comparisons of the air-shift coefficients in Fig. 13b. The self-shift coefficients from the two studies agree fairly well, although the present results are slightly smaller in absolute value than those in Ref. [8]. A value of 1.12 ± 0.30 is obtained as the unweighted ratio for mea-

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67

Fig. 10. Comparison of the measured 30013 ‹ 00001 and 30012 ‹ 00001 [1] line mixing and speed dependence coefficients of 12C16O2 retrieved using the same spectral data and retrieval procedure. (a) Measured off-diagonal relaxation matrix element coefficients (cm1 atm1 at 296 K) for self- and airbroadening are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). (b) The measured speed-dependent parameters in the P and R branches are plotted against m. The speed-dependent parameter is assumed to be independent of broadening gas and a single value fits each transition. In (a) and (b) similar values determined in the 30012 ‹ 00001 band are also shown for comparisons. Where error bars are not visible the uncertainties are smaller than the plot symbol.

sured self-shifts by Toth et al. [8] divided by present measurements. For the 30012 ‹ 00001 band, a ratio of 1.09 ± 0.14 was obtained as the unweighted ratio for measured self-shifts by Toth et al. [8] by values determined in [1]. For the air-induced shifts the corresponding unweighted ratios were determined to be 1.08 ± 0.09 for the 30013 ‹ 00001 and 1.06 ± 0.09 for the 30012 ‹ 00001 bands, respectively. Fig. 14a and b compare values from the present work and Toth et al. [8] for the self-broadened halfwidth and self-shift coefficients, respectively, determined for the 31113 ‹ 01101 hot band. The absorption features of this band were weak in our spectra and therefore the results for this band (Appendix B) are less accurate than those

for the stronger 30013 ‹ 00001 band. The mean and standard deviations of the unweighted ratios (Ref. [8] / Present work) of self-broadened halfwidth and self-shift coefficients are 0.98 ± 0.01 and 1.21 ± 0.44, respectively. The agreement between the two studies is remarkable given the relatively weak absorption of this band and the significant differences in the analysis techniques used in the two studies. As with our observation in the 31112 ‹ 01101 band [1], the 31113 ‹ 01101 self-shift coefficients behave much more like the air-shifts of the 30013 ‹ 00001 band than the self-shift coefficients determined for the 30013 ‹ 00001 band. The Pbranch pressure shifts have relatively constant negative values as opposed to the slowly increasing negative value with m for the R-branch transitions.

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Fig. 11. Comparison of the measured halfwidth coefficients using similar spectral data but a different retrieval procedure. (a) Eight sets of measured selfand air-broadened halfwidth coefficients are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). The present values and Ref. [1] were obtained from the multispectrum fitting with speed dependence and line mixing while the Toth et al. values [8,9] were determined using single spectrum fitting with a Voigt profile. (b) The ratios of self-broadened halfwidth coefficients measured for the 30013 ‹ 00001 band in [8] divided by corresponding values from the present work are plotted as a function of m. (c) The ratios of air-broadened halfwidth coefficients measured for the 30013 ‹ 00001 band in [9] divided by corresponding values from the present work are plotted as a function of m. Where error bars are not visible the uncertainties are smaller than the plot symbol.

5.2. Comparison with other investigations and HITRAN Until recently, experimental measurements of airbroadened halfwidth coefficients for CO2 bands reported in the literature were limited to only a few bands compared to other spectroscopic line parameters such as line positions and intensities. Because of this lack of direct measurements for different CO2 vibrational bands, the HITRAN database [23,31] assumes that the air broaden-

ing for CO2 is independent of the vibrational transition, and lists a single set of air-broadened halfwidth coefficients as a function of m for all CO2 vibrational bands. The first extensive set of air-broadened halfwidths and shift coefficients for a near-IR CO2 band has recently been reported by us [1]. In this work we are reporting a similar set of accurate air broadened halfwidths and shift coefficients for the 30013 ‹ 00001 band. Concurrent with the present study, Toth et al. [9] have measured air-

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69

Fig. 12. Comparison of the measured self- and air-shift coefficients from present work with those of Toth et al. [8,9]. (a) The measured self- and air-shift coefficients for the 30013 ‹ 00001 band from present work and Toth et al. [8,9] are plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). The experimental self- and air-shift coefficients from this work are fitted to the same empirical expression used in [8,9] and the calculated self- and air-shifts are plotted as curves. (b) The percentage observed minus calculated differences between self-shift coefficients from the present work and the fitted curve is plotted as a function of m. (c) The percentage observed minus calculated differences between air-shift coefficients from the present work and the fitted curve are plotted as a function of m. Where error bars are not visible the uncertainties are smaller than the plot symbol.

broadened halfwidths coefficients for 11 near infrared CO2 bands in the 4750–7000 cm1 spectral region, including the band investigated in [1] and the band measured in present work. Fig. 15 compares the air-broadened halfwidth coefficients of the 30013 ‹ 00001 band determined in the present work to those reported for the 30012 ‹ 00001 band [1]. The values determined for these two bands are very close as seen in Fig. 15. For comparison, we have

included in Fig. 15 the air-broadened halfwidths measured for these two bands by Toth et al. [9]. We have also included the air-broadened halfwidth coefficients computed from separate N2 and O2 broadening coefficients determined for the 30013 ‹ 00001 band [12,15,17] using the formula: b0L ðairÞ ¼ 0:79b0L ðN2 Þ þ 0:21b0L ðO2 Þ

ð7Þ

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V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Fig. 13. The present measured self- and air-shift coefficients of 30013 ‹ 00001 are compared to corresponding values of 30012 ‹ 00001 band in [1] and to values from Toth et al. [8,9] for both bands. In Fig. 13a the self-shift coefficients are plotted as a function of m. In Fig. 13b the air-shift coefficients versus m are displayed. Where error bars are not visible the uncertainties are smaller than the plot symbol.

Excellent agreement is seen in the air-broadened halfwidth coefficients between the present measurements and those in [1]. It is clear from Fig. 15 that for the 30013 ‹ 00001 band, the air-broadened halfwidths computed from separate N2 and O2 broadening by Hikida and Yamada [15] are lower than the present measurements by more than the experimental uncertainties. The values calculated by Pouchet et al. [12] are even lower, but the discrepancy approximately equals the uncertainty in their measurements. The measured air-broadened halfwidth coefficients for the two Fermi tetrad bands from this study compare with each other almost within their experimental uncertainties. The mean percent difference between present work and [1] is found to be 0.07(0.57). The percent differences in the air-broadened halfwidth coefficients measured by Toth et al. [9] and present work for the

30013 ‹ 00001 band is 1.6(1.1) while the difference between HITRAN database [23] and present work for the 30013 ‹ 00001 band is calculated to be 1.10(2.8)%. We attribute the deviations in the measured air-broadened halfwidth coefficients between the present study and by Toth et al. [9] to the differences in line shape profiles used in the two analyses. 6. Conclusion The present work demonstrates that line mixing and speed dependence are required to simulate room temperature laboratory spectra for the 30013 ‹ 00001 band of 16 12 16 O C O within the experimental noise level. This confirms the conclusions from our study of the 30012 ‹ 00001 band [1] that CO2 spectral simulations employing a Voigt line shape introduce systematic errors

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

71

Fig. 14. (a) Measured self-broadened halfwidth coefficients of the 31113 ‹ 01101 hot band of 12C16O2(cm1 atm1 at 296 K) plotted as a function of m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines). (b) Measured self-shift coefficients of 31113 ‹ 00001 band of 12C16O2(cm1 atm1 at 294 K) are shown as a function of m. For purpose of comparisons the measured self-broadened halfwidth and self-shift coefficients from Toth et al. [8] are included in panels (a) and (b), respectively. Error bars are visible if the uncertainties are larger than the plot symbol (see text for details).

in the fit residuals. Moreover, both the relaxation matrix element coefficients for air broadening and speed dependent parameters of these two bands have very similar values and behavior as a function of m. There are some small differences in the self broadening line mixing coefficients, however, and further study is needed. In the present work we fit our data within the experimental noise level with a specific line mixing model that considered only nearest neighbor matrix elements. This choice affects all of our spectral line parameters. Our spectral parameters are based upon experimental data rather than theoretical values from a fully populated or purely diagonal relaxation matrix. To reproduce our accuracy, it is essential that a consistent set of line parameters be used. Therefore, we included a full set of consistent positions,

intensities, Lorentz widths, pressure shifts, off-diagonal matrix elements and speed-dependent parameters in the Appendices. We conclude that the accuracy in our spectroscopic parameters should enable atmospheric remote sensing of CO2 with an absolute uncertainty of 0.3% near room temperature. We note that this accuracy is achieved when using the complete set of line parameters presented here; this high accuracy would be seriously compromised if our parameters were used in another line shape/line mixing model or with a mixture of parameters from our study and other studies. For more general atmospheric remote sensing applications, the temperature dependence for the relaxation matrix elements and speed-dependant parameters must still be determined.

72

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Fig. 15. The measured air-broadened halfwidth coefficients for the 30013 ‹ 00001 band from present work are plotted versus m (m = J 00 for P-branch lines and J 00 + 1 for R-branch lines) and compared to other measurements [1,9,12,15,17,23]. Air-broadened halfwidth coefficients from Refs. [12,15,17] are computed from reported N2 and O2 broadening. Error bars are visible if the uncertainties are larger than the plot symbol (see text for details).

was performed under contract with National Aeronautics and Space Administration. The authors express sincere appreciation to M. Dulick of NOAO (National Optical Astronomy Observatory) for the assistance in obtaining the data. We thank NASA’s Upper Atmosphere Research Program for support of the McMath-Pierce laboratory facility.

Acknowledgments The material presented in this investigation is based upon work supported by the National Science Foundation under Grant No. ATM-0338475 to the College of William and Mary. The research at the Jet Propulsion Laboratory (JPL), California Institute of Technology, Appendix A Spectral line parameters for the 30013 ‹ 00001 band of Line

Positiona

Intensityb

P74e P72e P70e P68e P66e P64e P62e P60e P58e P56e P54e P52e

6150.476816 6153.129771 6155.749435 6158.335954 6160.889485 6163.410199 6165.898278 6168.353914 6170.777304 6173.168656 6175.528178 6177.856086

3.8493E27 6.4769E27 1.0730E26 1.7499E26 2.8096E26 4.4407E26 6.9087E26 1.0579E25 1.5943E25 2.3646E25 3.4509E25 4.9553E25 0.06737

a

1

16

O12C16O

bL 0 ðairÞc %unc. bL 0 ðselfÞc %unc. d0(air)d

1.08

0.06856 0.06904 0.07110 0.07203 0.07238 0.07352

0.77 0.62 0.36 0.25 0.18 0.14

unc. d0(self)d

0.00402 (72)

0.01113 0.00946 0.00895 0.00953 0.00902 0.00897

unc. SDe %unc.

(52) (43) (25) (17) (13) (10)

Zero pressure line positions in cm . The line positions are calculated using the rovibrational constants listed in Table 3. Refer to Fig. 2 for position uncertainties. b Line intensities are in cm1/(molecule cm2) at 296 K for a natural CO2 sample (16O12C16O fraction of 0.9842). The listed intensities are values calculated using the vibrational band intensity and the Herman-Wallis factors listed in Table 3. Refer to Fig. 3 for intensity uncertainties. c The measured Lorentz halfwidth coefficients are in cm1 atm1 at 296 K. d The measured pressure shift coefficients are in cm1 atm1 at the temperature of spectra (294 K, see Table 2). e Speed-dependent parameter (unitless).

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

73

Appendix A (continued) Line

Positiona

Intensityb

bL 0 ðairÞc %unc. bL 0 ðselfÞc %unc. d0(air)d

P50e P48e P46e P44e P42e P40e P38e P36e P34e P32e P30e P28e P26e P24e P22e P20e P18e P16e P14e P12e P10e P8e P6e P4e P2e R0e R2e R4e R6e R8e R10e R12e R14e R16e R18e R20e R22e R24e R26e R28e R30e R32e R34e R36e R38e R40e R42e R44e R46e R48e R50e R52e R54e R56e

6180.152596 6182.417925 6184.652290 6186.855909 6189.028995 6191.171758 6193.284405 6195.367137 6197.420146 6199.443622 6201.437743 6203.402679 6205.338591 6207.245631 6209.123937 6210.973638 6212.794851 6214.587680 6216.352216 6218.088537 6219.796708 6221.476778 6223.128784 6224.752748 6226.348677 6228.689986 6230.215765 6231.713419 6233.182890 6234.624105 6236.036977 6237.421403 6238.777268 6240.104444 6241.402787 6242.672143 6243.912344 6245.123209 6246.304549 6247.456161 6248.577833 6249.669344 6250.730463 6251.760953 6252.760567 6253.729054 6254.666157 6255.571615 6256.445161 6257.286530 6258.095453 6258.871660 6259.614885 6260.324863

7.0003E25 9.7279E25 1.3296E24 1.7871E24 2.3616E24 3.0679E24 3.9168E24 4.9131E24 6.0531E24 7.3221E24 8.6923E24 1.0121E23 1.1552E23 1.2913E23 1.4122E23 1.5090E23 1.5728E23 1.5951E23 1.5689E23 1.4892E23 1.3540E23 1.1644E23 9.2486E24 6.4331E24 3.3064E24 1.6745E24 4.9779E24 8.0947E24 1.0893E23 1.3264E23 1.5126E23 1.6431E23 1.7170E23 1.7362E23 1.7057E23 1.6326E23 1.5256E23 1.3939E23 1.2467E23 1.0925E23 9.3880E24 7.9145E24 6.5495E24 5.3223E24 4.2488E24 3.3328E24 2.5696E24 1.9476E24 1.4515E24 1.0639E24 7.6701E25 5.4396E25 3.7954E25 2.6057E25

0.06817 0.06733 0.06694 0.06726 0.06796 0.06823 0.06815 0.06865 0.06929 0.06918 0.07018 0.07030 0.07092 0.07208 0.07280 0.07404 0.07529 0.07624 0.07804 0.07973 0.08133 0.08319 0.08509 0.08753 0.09171 0.09550 0.08869 0.08528 0.08363 0.08204 0.07987 0.07827 0.07659 0.07499 0.07376 0.07269 0.07203 0.07095 0.07025 0.06959 0.06929 0.06875 0.06807 0.06827 0.06709 0.06783 0.06669 0.06681 0.06669 0.06754 0.06665 0.06477

0.94 0.56 0.60 0.34 0.29 0.22 0.18 0.16 0.14 0.13 0.13 0.11 0.10 0.12 0.10 0.09 0.11 0.09 0.09 0.10 0.10 0.10 0.12 0.14 0.22 0.41 0.17 0.12 0.11 0.10 0.10 0.09 0.09 0.09 0.09 0.10 0.10 0.10 0.10 0.11 0.12 0.13 0.13 0.16 0.18 0.22 0.25 0.33 0.43 0.55 0.74 1.02

0.07515 0.07543 0.07589 0.07795 0.07975 0.08062 0.08212 0.08465 0.08616 0.08826 0.09017 0.09223 0.09404 0.09663 0.09821 0.09980 0.10180 0.10308 0.10537 0.10727 0.10946 0.11188 0.11495 0.11791 0.12228 0.12868 0.11975 0.11608 0.11372 0.11106 0.10780 0.10588 0.10377 0.10162 0.09998 0.09784 0.09672 0.09439 0.09286 0.09087 0.08900 0.08642 0.08450 0.08294 0.08070 0.07925 0.07796 0.07697 0.07605 0.07489 0.07396 0.07238 0.07140 0.07093

0.13 0.08 0.25 0.12 0.10 0.09 0.07 0.07 0.07 0.07 0.07 0.05 0.05 0.07 0.05 0.05 0.06 0.05 0.05 0.06 0.05 0.05 0.06 0.07 0.08 0.12 0.07 0.06 0.06 0.05 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.10 0.07 0.07 0.07 0.07 0.09 0.09 0.10 0.13 0.08 0.10 0.13 0.17 0.24

0.00530 0.00477 0.00616 0.00625 0.00665 0.00588 0.00674 0.00675 0.00628 0.00661 0.00677 0.00675 0.00668 0.00638 0.00634 0.00636 0.00629 0.00629 0.00610 0.00574 0.00549 0.00486 0.00519 0.00399 0.00371 0.00366 0.00440 0.00417 0.00435 0.00415 0.00456 0.00484 0.00493 0.00541 0.00546 0.00545 0.00574 0.00587 0.00595 0.00609 0.00608 0.00581 0.00682 0.00669 0.00593 0.00720 0.00714 0.00780 0.00785 0.00740 0.00828 0.00852

unc. d0(self)d (62) (37) (37) (21) (17) (18) (15) (12) (10) (9) (10) (8) (7) (8) (6) (6) (6) (6) (6) (7) (7) (8) (10) (13) (25) (49) (17) (11) (9) (7) (7) (6) (6) (6) (6) (6) (6) (6) (7) (7) (8) (9) (10) (12) (14) (13) (15) (20) (26) (36) (48) (65)

unc. SDe

0.00946 (12) 0.00909 (8) 0.00834 (10) 0.00843 (5) 0.00807 (5) 0.00778 (4) 0.00797 (4) 0.00775 (4) 0.00751 (4) 0.00728 (4) 0.00715 (4) 0.00688 (4) 0.00673 (4) 0.00674 (4) 0.00651 (4) 0.00638 (4) 0.00618 (5) 0.00571 (4) 0.00544 (4) 0.00515 (4) 0.00511 (4) 0.00444 (4) 0.00460 (4) 0.00392 (5) 0.00367 (6) 0.00472 (10) 0.00486 (5) 0.00438 (4) 0.00459 (4) 0.00507 (4) 0.00534 (4) 0.00531 (4) 0.00576 (4) 0.00580 (4) 0.00624 (4) 0.00640 (4) 0.00650 (4) 0.00701 (4) 0.00717 (4) 0.00758 (4) 0.00784 (5) 0.00776 (4) 0.00821 (4) 0.00868 (4) 0.00886 (4) 0.00921 (4) 0.00908 (5) 0.00950 (5) 0.00984 (6) 0.00974 (7) 0.01003 (7) 0.01147 (9) 0.01118 (12) 0.01046 (17) (continued

0.099 0.108 0.088 0.093 0.105 0.109 0.105 0.106 0.110 0.107 0.129 0.130 0.131 0.141 0.126 0.147 0.143 0.140 0.132 0.131 0.124 0.117 0.091 0.125 0.114 0.139 0.137 0.134 0.132 0.135 0.127 0.120 0.114 0.126 0.108 0.104 0.092 0.097 0.086 0.071 0.096 0.074 0.076 0.082 0.096 0.104

%unc.

4.0 3.2 3.4 3.1 2.4 2.1 2.2 2.4 2.0 2.0 1.9 1.5 1.4 1.4 1.5 1.2 1.2 1.2 1.3 1.4 1.6 2.2 5.0 1.7 1.8 1.2 1.3 1.3 1.4 1.4 1.5 1.7 1.8 1.6 2.0 2.2 2.7 2.7 3.2 4.3 2.8 4.5 4.6 4.5 4.1 4.3

on next page)

74

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Appendix A (continued) Line

Positiona

Intensityb

R58e R60e R62e R64e R66e R68e R70e R72e

6261.001333 6261.644037 6262.252726 6262.827159 6263.367103 6263.872336 6264.342648 6264.777846

1.7607E25 1.1704E24 7.6582E26 4.9323E26 3.1269E26 1.9514E26 1.1989E26 7.2513E27

bL 0 ðairÞc %unc. bL 0 ðselfÞc %unc. d0(air)d unc. d0(self)d 0.07005 0.06934 0.06985

unc. SDe %unc.

0.01220 (24) 0.00982 (36) 0.01268 (53)

0.34 0.51 0.75

Appendix B Spectral line parameters for the 31113 ‹ 01101 band of Line

Positiona

Intensityb

P59e P57e P55e P53e P51e P49e P47e P45e P43e P41e P39e P37e P35e P33e P31e P29e P27e P25e P23e P21e P19e P17e P15e P13e P11e P9e P7e P5e P3e Q17e Q15e Q13e

6137.39451 6139.81579 6142.20567 6144.56445 6146.89240 6149.18975 6151.45669 6153.69341 6155.90006 6158.07677 6160.22363 6162.34076 6164.42821 6166.48605 6168.51432 6170.51305 6172.48227 6174.42200 6176.33223 6178.21296 6180.06419 6181.88590 6183.67809 6185.44072 6187.17379 6188.87726 6190.55111 6192.19531 6193.80985 6195.46956 6195.62215 6195.75614

4.561E27 6.839E27 1.009E26 1.465E26 2.092E26 2.938E26 4.060E26 5.516E26 7.369E26 9.677E26 1.249E25 1.584E25 1.973E25 2.413E25 2.897E25 3.411E25 3.939E25 4.455E25 4.933E25 5.339E25 5.640E25 5.804E25 5.800E25 5.606E25 5.207E25 4.598E25 3.787E25 2.789E25 1.605E25 3.949E27 5.055E27 6.482E27

bL 0 ðairÞc

0.07041 0.07304 0.07190 0.07214 0.07137 0.07430 0.07514 0.07676 0.07876 0.08189 0.07966 0.08601

%unc.

1.59 1.38 1.22 1.11 1.02 1.19 0.97 0.98 1.02 1.12 1.37 1.55

16

O12C16O bL 0 ðselfÞc

0.09071 0.09302 0.09398 0.09593 0.09730 0.09996 0.10087 0.10291 0.10532 0.10673 0.11077 0.11462 0.11679 0.12509

%unc.

d0(air)d

unc.

d0(self)d

unc.

0.07964 0.08171 0.08157 0.08285

1.01 0.78 0.63 0.62

0.00441 0.00795 0.00803 0.00581

(81) (64) (51) (51)

0.08615 0.08696 0.08900 0.21 0.17 0.16 0.14 0.13 0.17 0.13 0.13 0.13 0.16 0.22 0.19 0.26 0.49

0.37 0.28 0.25

0.00603 0.00648 0.00693

(31) (23) (22)

0.00548 0.00582 0.00572 0.00552 0.00505 0.00583 0.00516 0.00489 0.00523 0.00371 0.00493 0.00528 0.00107

(16) (14) (13) (13) (18) (13) (13) (13) (16) (27) (22) (30) (59)

0.00861 0.00637 0.00490 0.00386 0.00749 0.00512 0.00407  0.00669 0.00351 0.00753

(88) (80) (73) (89) (72) (74) (80) (92) (110) (134)

a Zero pressure line positions in cm1. The line positions are calculated using the rovibrational constants listed in Table 3. Refer to Fig. 2 for position uncertainties. b Line intensities are in cm1/(molecule cm2) at 296 K for a natural CO2 sample (16O12C16O fraction of 0.9842). The listed intensities are values calculated using the vibrational band intensity and the Herman-Wallis factors listed in Table 3. Refer to Fig. 3 for intensity uncertainties. c The measured Lorentz halfwidth coefficients are in cm1 atm1 at 296 K. d The measured pressure shift coefficients are in cm1 atm1 at the temperature of spectra (294 K, see Table 2).

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

75

Appendix B (continued) Line

Positiona

Intensityb

Q11e Q9e Q7e Q5e Q3e Q1e R1e R3e R5e R7e R9e R11e R13e R15e R17e R19e R21e R23e R25e R27e R29e R31e R33e R35e R37e R39e R41e R43e R45e R47e R49e R51e R53e R55e R57e R59e P60f P58f P56f P54f P52f P50f P48f P46f P44f P42f P40f P38f P36f P34f P32f P30f P28f

6195.87157 6195.96848 6196.04689 6196.10683 6196.14832 6196.16854 6197.71623 6199.22672 6200.70742 6202.15831 6203.57937 6204.97055 6206.33184 6207.66321 6208.96461 6210.23602 6211.47739 6212.68868 6213.86985 6215.02082 6216.14154 6217.23193 6218.29192 6219.32139 6220.32024 6221.28835 6222.22558 6223.13175 6224.00670 6224.85022 6225.66208 6226.44203 6227.18978 6227.90503 6228.58741 6229.23656 6138.79535 6141.06221 6143.30293 6145.51782 6147.70716 6149.87121 6152.01023 6154.12442 6156.21399 6158.27912 6160.31997 6162.33669 6164.32941 6166.29824 6168.24330 6170.16467 6172.06244

8.372E27 1.099E26 1.487E26 2.138E26 3.520E26 9.225E26 9.242E26 2.272E25 3.422E25 4.408E25 5.209E25 5.805E25 6.189E25 6.363E25 6.342E25 6.148E25 5.812E25 5.367E25 4.848E25 4.289E25 3.718E25 3.161E25 2.638E25 2.160E25 1.738E25 1.373E25 1.066E25 8.137E26 6.105E26 4.504E26 3.268E26 2.332E26 1.637E26 1.131E26 7.685E27 5.139E27 3.664E27 5.542E27 8.248E27 1.208E26 1.740E26 2.466E26 3.438E26 4.713E26 6.353E26 8.419E26 1.097E25 1.404E25 1.765E25 2.179E25 2.642E25 3.143E25 3.666E25

bL 0 ðairÞc

%unc.

0.08138 0.08136 0.08157 0.07888 0.07274 0.07480 0.07312 0.07077 0.07128 0.06963 0.06829 0.06827

1.71 1.33 1.34 1.05 0.93 0.95 1.16 0.95 1.02 1.69 1.83 1.45

0.06828

1.79

0.07131 0.06995

1.71 1.47

bL 0 ðselfÞc

%unc.

0.10888

0.79

0.12049 0.11651 0.11191 0.10787 0.10684 0.10385 0.10159 0.10023 0.09835 0.09717 0.09621 0.09271 0.09096 0.09185 0.08865 0.08759 0.08666

0.46 0.23 0.18 0.25 0.17 0.13 0.16 0.26 0.14 0.16 0.47 0.30 0.31 0.37 0.26 0.49 0.38

0.07929 0.07677 0.08571 0.08147 0.08208 0.08343 0.08584 0.08706 0.09071 0.09025

1.19 0.87 2.00 0.64 0.46 0.41 0.29 0.28 0.22 0.21

d0(air)d

unc.

0.00299 0.00513 0.00687 0.00698 0.00319 0.00287 0.00391 0.00380 0.00566 0.00949

(108) (111) (82) (67) (70) (87) (66) (73) (121) (125)

0.00607

(122)

0.00667

d0(self)d

0.00072 0.00350 0.00305 0.00401 0.00465 0.00521 0.00590 0.00622 0.00698 0.00716 0.00541 0.00861 0.00687 0.00469 0.00695 0.00723 0.00809

0.00653 0.00801 0.00682 0.00584 0.00989 0.00464 0.00565 0.00539 (122) 0.00524 0.00529 (continued on next

unc.

(56) (26) (20) (27) (18) (14) (15) (26) (14) (16) (44) (27) (28) (34) (23) (43) (33)

(94) (68) (171) (52) (37) (33) (25) (23) (20) (19) page)

76

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Appendix B (continued) Line

Positiona

Intensityb

bL 0 ðairÞc

%unc.

bL 0 ðselfÞc

%unc.

d0(air)d

P26f P24f P22f P20f P18f P16f P14f P12f P10f P8f P6f P4f P2f Q16f Q14f Q12f Q10f Q8f Q6f Q4f Q2f R2f R4f R6f R8f R10f R12f R14f R16f R18f R20f R22f R24f R26f R28f R30f R32f R34f R36f R38f R40f R42f R44f R46f R48f R50f R52f R54f R56f R58f R60f

6173.93667 6175.78742 6177.61474 6179.41868 6181.19927 6182.95653 6184.69049 6186.40115 6188.08853 6189.75262 6191.39343 6193.01093 6194.60512 6194.99759 6195.26619 6195.50014 6195.69942 6195.86405 6195.99402 6196.08933 6196.14998 6198.48845 6200.00084 6201.48980 6202.95527 6204.39720 6205.81555 6207.21025 6208.58125 6209.92845 6211.25180 6212.55121 6213.82657 6215.07778 6216.30475 6217.50733 6218.68541 6219.83883 6220.96745 6222.07108 6223.14956 6224.20267 6225.23021 6226.23193 6227.20760 6228.15693 6229.07964 6229.97540 6230.84389 6231.68474 6232.49755

4.192E25 4.693E25 5.139E25 5.498E25 5.736E25 5.820E25 5.725E25 5.430E25 4.927E25 4.216E25 3.310E25 2.222E25 9.140E26 4.464E27 5.718E27 7.353E27 9.560E27 1.271E26 1.764E26 2.674E26 5.086E26 1.632E25 2.867E25 3.937E25 4.832E25 5.532E25 6.021E25 6.298E25 6.371E25 6.259E25 5.989E25 5.593E25 5.106E25 4.563E25 3.994E25 3.428E25 2.886E25 2.384E25 1.934E25 1.541E25 1.207E25 9.286E26 7.023E26 5.223E26 3.819E26 2.747E26 1.943E26 1.352E26 9.257E27 6.236E27 4.134E27

0.06725 0.07411 0.07250 0.07140 0.07358 0.07539 0.07867 0.07949 0.08240 0.08575 0.08947

1.27 1.19 1.08 1.01 0.96 0.97 1.66 1.06 1.18 1.39 1.96

0.09343 0.09472 0.09679 0.09826 0.09984 0.10180 0.10505 0.10594 0.10931 0.11205 0.11388 0.11741

0.16 0.15 0.14 0.13 0.13 0.13 0.37 0.14 0.16 0.18 0.26 0.38

0.00547 0.00635 0.00625 0.00366 0.00752 0.00733

(86) (88) (78) (71) (71) (73)

0.00721 0.01028 0.00332

(84) (97) (119)

0.07797 0.08003 0.07857 0.07955 0.06993 0.07706 0.07443 0.07109 0.06847 0.07177 0.07072

2.64 1.23 1.06 0.99 2.37 0.93 0.94 1.08 1.21 1.76 1.35

0.11669 0.11010 0.11018 0.10681 0.10440 0.10301 0.10015 0.09834 0.09643 0.09543 0.09464 0.09156

0.27 0.77 0.18 0.15 0.15 0.80 0.15 0.14 0.21 0.24 0.29 0.27

0.08826 0.08666

0.25 0.29

unc.

d0(self)d

unc.

0.00499 0.00583 0.00616 0.00492 0.00533 0.00582 0.00487 0.00489 0.00480 0.00371 0.00361 0.00087

(15) (14) (14) (13) (12) (13) (32) (15) (16) (19) (30) (44)

0.00094

(31)

0.00478 0.00269 0.00002

(98) (83) (79)

0.00303 0.00322 0.00407

(20) (15) (15)

0.00319 0.00463 0.00512 0.00672 0.00545

(72) (69) (76) (84) (127)

0.00483 0.00520 0.00504 0.00598 0.00633 0.00782

(14) (13) (20) (23) (27) (25)

0.00761 0.00761

(22) (25)

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

77

Appendix C Line positions and intensities for the 32213 ‹ 02201 band of

16

O12C16O

Line

Positiona

Intensityb

Line

Positiona

Intensitya

P40e P38e P36e P34e P32e P30e P28e P26e P24e P22e P20e P18e P16e P14e P12e P10e P8e P6e P4e Q4e Q2e R2e R4e R6e R8e R10e R12e R14e R16e R18e R20e R22e R24e R26e R28e R30e R32e R34e R36e R38e R40e

6134.02139 6136.05731 6138.06880 6140.05586 6142.01854 6143.95683 6145.87077 6147.76035 6149.62558 6151.46648 6153.28305 6155.07528 6156.84317 6158.58672 6160.30592 6162.00075 6163.67122 6165.31729 6166.93895 6170.04779 6170.09062 6172.42224 6173.93377 6175.42075 6176.88314 6178.32090 6179.73400 6181.12238 6182.48602 6183.82485 6185.13883 6186.42791 6187.69202 6188.93112 6190.14514 6191.33401 6192.49768 6193.63606 6194.74909 6195.83669 6196.89878

4.1443E27 5.3173E27 6.7005E27 8.2900E27 1.0066E26 1.1991E26 1.4003E26 1.6022E26 1.7944E26 1.9651E26 2.1010E26 2.1890E26 2.2163E26 2.1722E26 2.0485E26 1.8403E26 1.5460E26 1.1643E26 6.8313E27 8.2017E27 7.7993E27 3.9011E27 9.5746E27 1.4057E26 1.7674E26 2.0444E26 2.2356E26 2.3421E26 2.3689E26 2.3243E26 2.2196E26 2.0675E26 1.8818E26 1.6757E26 1.4613E26 1.2489E26 1.0469E26 8.6100E27 6.9513E27 5.5111E27 4.2920E27

P41f P39f P37f P35f P33f P31f P29f P27f P25f P23f P21f P19f P17f P15f P13f P11f P9f P7f P5f P3f Q3f R3f R5f R7f R9f R11f R13f R15f R17f R19f R21f R23f R25f R27f R29f R31f R33f R35f R37f R39f

6132.95502 6135.01034 6137.04022 6139.04475 6141.02405 6142.97823 6144.90739 6146.81160 6148.69097 6150.54556 6152.37546 6154.18071 6155.96138 6157.71751 6159.44914 6161.15631 6162.83903 6164.49732 6166.13119 6167.74063 6170.07225 6173.18109 6174.68035 6176.15502 6177.60503 6179.03032 6180.43081 6181.80643 6183.15707 6184.48263 6185.78301 6187.05809 6188.30775 6189.53185 6190.73025 6191.90282 6193.04939 6194.16980 6195.26390 6196.33150

3.6345E27 4.7048E27 5.9825E27 7.4702E27 9.1567E27 1.1013E26 1.2990E26 1.5018E26 1.7002E26 1.8832E26 2.0382E26 2.1518E26 2.2109E26 2.2037E26 2.1206E26 1.9551E26 1.7040E26 1.3663E26 9.3822E27 3.8539E27 8.0962E27 6.9431E27 1.1930E26 1.5971E26 1.9166E26 2.1507E26 2.2992E26 2.3650E26 2.3549E26 2.2787E26 2.1486E26 1.9780E26 1.7805E26 1.5688E26 1.3543E26 1.1462E26 9.5161E27 7.7540E27 6.2034E27 4.8743E27

Zero pressure line positions in cm1. The line positions are calculated using the rovibrational constants listed in Table 3. Refer to Fig. 2 for position uncertainties. b Line intensities are in cm1/(molecule cm2) at 296 K for a natural CO2 sample (16O12C16O fraction of 0.9842). The listed intensities are values calculated using the vibrational band intensity and the Herman-Wallis factors listed in Table 3. Refer to Fig. 3 for intensity uncertainties. a

78

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

Appendix D Spectral line parameters for 40014 ‹ 10002 band of Line

Positiona

Intensityb

P48e P46e P44e P42e P40e P38e P36e P34e P32e P30e P28e P26e P24e P22e P20e P18e R16f P14e P12e P10e P8e P6e P4e P2e R0e R2e R4e R6e R8e R10e R12e R14e R16e R18e R20e R22e R24e R26e R28e R30e R32e R34e R36e R38e R40e R42e R44e

6130.41236 6132.58315 6134.72525 6136.83902 6138.92479 6140.98287 6143.01356 6145.01713 6146.99385 6148.94395 6150.86765 6152.76518 6154.63670 6156.48240 6158.30243 6160.09693 6161.86602 6163.60980 6165.32836 6167.02178 6168.69011 6170.33348 6171.95163 6173.54485 6175.88774 6177.41832 6178.92378 6180.40413 6181.85902 6183.28863 6184.69274 6186.07123 6187.42394 6188.75072 6190.05138 6191.32572 6192.57353 6193.79458 6194.98861 6196.15538 6197.29458 6198.40592 6199.48909 6200.54374 6201.56952 6202.56607 6203.53299

4.9056E27 6.7267E27 9.0685E27 1.2017E26 1.5650E26 2.0025E26 2.5167E26 3.1059E26 3.7624E26 4.4716E26 5.2112E26 5.9512E26 6.6545E26 7.2779E26 7.7751E26 8.0994E26 8.2075E26 8.0638E26 7.6440E26 6.9386E26 5.9552E26 4.7195E26 3.2745E26 1.6783E26 8.4643E27 2.5059E26 4.0595E26 5.4409E26 6.5960E26 7.4869E26 8.0933E26 8.4131E26 8.4606E26 8.2642E26 7.8627E26 7.3012E26 6.6272E26 5.8869E26 5.1224E26 4.3692E26 3.6555E26 3.0013E26 2.4191E26 1.9150E26 1.4893E26 1.1381E26 8.5476E27

16

O12C16O bL 0 ðselfÞc

%unc.

d0(self)d

unc.

0.09254 0.09470 0.09390

1.17 1.04 0.94

0.00696

(107)

0.00331

(85)

0.09396 0.10492 0.10089 0.10617 0.11092 0.10857 0.11072 0.12086 0.11386 0.14194

2.27 0.92 0.79 0.84 0.86 0.94 1.18 1.61 2.45 4.30

0.01407 0.00263 0.00469 0.00725 0.00305

(212) (98) (78) (88) (96)

0.00674

(134)

0.10346

0.92

0.00418

(95)

0.09903 0.09436 0.09503

0.82 0.82 0.99

0.01112 0.01018

(80) (76)

0.07077

2.86

V.M. Devi et al. / Journal of Molecular Spectroscopy 245 (2007) 52–80

79

Appendix D (continued) Line

Positiona

Intensityb

R46e R48e R50e

6204.46987 6205.37629 6206.25180

6.3110E27 4.5815E27 3.2741E27

bL 0 ðselfÞc

%unc.

d0(self)d

unc.

a Zero pressure line positions in cm1. The line positions are calculated using the rovibrational constants listed in Table 3. Refer to Fig. 2 for position uncertainties. b Line intensities are in cm1/(molecule cm2) at 296 K for a natural CO2 sample (16O12C16O fraction of 0.9842). The listed intensities are values calculated using the vibrational band intensity and the Herman-Wallis factors listed in Table 3. Refer to Fig. 3 for intensity uncertainties. c The measured self-broadened Lorentz halfwidth coefficients are in cm1 atm1 at 296 K. d The measured self-shift coefficients are in cm1 atm1 at the temperature of spectra (294 K, see Table 2).

Appendix E Spectral line parameters for 40013 ‹ 10001 band of 16 12 16 O C O Line

Positiona

P46e P44e P42e P40e P38e P36e P34e P32e P30e P28e P26e P24e P22e P20e P18e P16e P14e P12e P10e P8e P6e P4e P2e R0e R2e R4e R6e R8e R10e R12e R14e R16e R18e R20e R22e R24e R26e R28e

6160.09723 6162.47929 6164.82264 6167.12787 6169.39544 6171.62574 6173.81906 6175.97562 6178.09560 6180.17909 6182.22617 6184.23685 6186.21113 6188.14899 6190.05037 6191.91520 6193.74343 6195.53496 6197.28973 6199.00767 6200.68870 6202.33277 6203.93984 6206.28097 6207.79538 6209.27270 6210.71294 6212.11612 6213.48225 6214.81136 6216.10348 6217.35866 6218.57690 6219.75824 6220.90267 6222.01019 6223.08076 6224.11431

Intensityb 4.2734E27 5.7724E27 7.6643E27 1.0001E26 1.2821E26 1.6146E26 1.9964E26 2.4231E26 2.8854E26 3.3693E26 3.8553E26 4.3193E26 4.7333E26 5.0666E26 5.2884E26 5.3697E26 5.2862E26 5.0210E26 4.5669E26 3.9276E26 3.1190E26 2.1685E26 1.1137E26 5.6344E27 1.6716E26 2.7137E26 3.6447E26 4.4279E26 5.0367E26 5.4564E26 5.6842E26 5.7287E26 5.6079E26 5.3471E26 4.9762E26 4.5268E26 4.0300E26 3.5144E26 (continued on next column)

Appendix E (continued) Line

Positiona

Intensityb

R30e R32e R34e R36e R38e R40e R42e R44e R46e

6225.11073 6226.06987 6226.99153 6227.87543 6228.72124 6229.52853 6230.29679 6231.02541 6231.71365

3.0043E26 2.5191E26 2.0728E26 1.6745E26 1.3285E26 1.0354E26 7.9301E27 5.9692E27 4.4170E27

Zero pressure line positions in cm1. The line positions are calculated using the rovibrational constants listed in Table 3. Refer to Fig. 2 for position uncertainties. b Line intensities are in cm1/(molecule cm2) at 296 K for a natural CO2 sample (16O12C16O fraction of 0.9842). The listed intensities are values calculated using the vibrational band intensity and the HermanWallis factors listed in Table 3. Refer to Fig. 3 for intensity uncertainties. a

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