Temperature dependent air-broadened linewidths of ozone rotational transitions

Journal of Molecular Spectroscopy 251 (2008) 194–202

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Temperature dependent air-broadened linewidths of ozone rotational transitions Brian J. Drouin a,*, Robert R. Gamache b a

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail Stop 183-301, Pasadena, CA 91109-8099, USA Department of Environmental, Earth, and Atmospheric Sciences, University of Massachusetts Lowell, and University of Massachusetts School of Marine Sciences, 265 Riverside Street, Lowell, MA 01854, USA

b

a r t i c l e

i n f o

Article history: Received 13 December 2007 In revised form 21 February 2008 Available online 29 February 2008 Keywords: Ozone Air broadening Atmospheric chemistry

a b s t r a c t Ozone resonant features in the rotational band are useful for composition measurements in the stratosphere and upper troposphere. However, the density of ozone features in the long wavelengths often decreases precision of other trace species measurements, especially when insufficient spectral parameters exist. This work presents systematic studies of temperature dependent air-broadened linewidth parameters for ozone. Eighteen new experimental measurements are presented and compared with 57 calculated parameters that cover spectral regions currently probed by the Earth Observing System— Microwave Limb Sounder. Comparisons with previous measurements and similar broadening studies in the infrared wavelengths are made. Published by Elsevier Inc.

1. Introduction We dedicate this work to the distinguished careers of Herbert M. Pickett and Edward A. Cohen. These two stratospheric spectroscopists forged the path of atmospheric broadening measurements that have enabled many quantitative concentration profile retrievals from limb emission measurements. It is our honor to continue in this tradition as the atmospheric sciences demand more expansive and more precise data. The ozone rotational spectrum is second only to water for dominance of the long wavelength radiance from the Earth’s atmosphere. The nature of the ozone emission spectrum differs from water in that the intensity is distributed among a large number of ro-vibrational states. Observers of ozone radiance often opt for measurements of single, strong, temperature independent transitions within this manifold. The largest concentrations of ozone are located in the stratosphere where individual resonant lines may be readily observed with radiometric instruments such as the current space-bourne limb-sounding mission, the Earth Observing System—Microwave Limb Sounder (EOS-MLS) [1]. Meanwhile, the remaining ozone features interfere with retrievals of other trace species. This issue is most prevalent in the fourth radiometric band (R4) of EOS-MLS located near 500 lm. Accurate retrieval of atmospheric trace species with weak resonant emission features (less than 1 K) requires that the background radiance (off-target) be fit to a high tolerance. Initial work addressed deficiencies in the target lineshape a-priori knowledge, specifically, air-broadened linewidth parameters. In general, a

* Corresponding author. Fax: +1 818 354 0966. E-mail address: [email protected] (B.J. Drouin). 0022-2852/$ - see front matter Published by Elsevier Inc. doi:10.1016/j.jms.2008.02.016

practical requirement on (both target and background) lineshape precision is <3%. At this point, most targeted line positions and intensities for EOS-MLS are considered well understood for mission purposes [2]. Since launch in August 2004 the new broadening data [3–7] has been useful in the retrieval algorithms for the radiance calibration data. The MLS radiances are distributed as a calibrated Level 1 data product. Additionally a Level 2 product, which incorporates the spectroscopic parameters and geophysical data, is produced through non-linear fitting of a state-vector (temperature or concentration vs. pressure) to the radiance data. The optimization of this algorithm has been the subject of numerous validation efforts [8–14] and different versions of the algorithm are systematically numbered. Initial Level 2 data released to the public was v1.5, currently the entire data set is being reprocessed with the v2.2 algorithm. Studies prior to the v1.5 data had revealed systematic dependencies of several trace species in the MLS 640 GHz (R4) region [8]. A systematic error (or bias) in species profile (for weak R4 species such as BrO, HOCl, and HO2) was characterized and found to be proportional to the ozone concentration. In order to produce a less biased output for EOS MLS v1.5 data products, separate baseline retrievals were performed throughout the 640 GHz band. Until this point only one ozone lineshape, a targeted line in the 640 GHz band, had been measured directly—the remaining lines all used values from the HITRAN 2000 database [15], which were then based on scaled calculations of Gamache [16]. In the millimeter wavelengths this tabulation was found to be only accurate to within approximately 10% of measurements [5]. Therefore, the possibility of reducing systematic retrieval biases for weak emissions through a more comprehensive study of the ozone temperature dependent lineshapes prompted this work.

B.J. Drouin, R.R. Gamache / Journal of Molecular Spectroscopy 251 (2008) 194–202

Ozone pressure broadening of rotational transitions has been studied by a variety of techniques over the world. Early rotational broadening measurements were made in the millimeter wavelengths by Connor and Radford [17] as well as Oh and Cohen [18]. Measurements in the 1 mm region can be found in work supporting the MASTER instrument that ESA plans to launch soon [19]. More recently Priem et al. [20], Yamada and Amano [21], and Drouin et al. [5] made similar style measurements which ventured into the submillimeter wavelengths. However, only two of these submillimeter measurements lie within the MLS radiometric band near 500 lm. Finally, Larsen et al. [22] has provided the most comprehensive data set in the rotational band through Fourier Transform spectroscopy in the far-infrared (wavelengths less than 300 lm). A number of semiclassical theoretical models have been used to predict the pressure-broadening parameters of O3. Tejwani and Yeung [23] have made calculations using Anderson–Tsao–Curnutte theory [24–26]; however, their calculations needed scaled molecular constants to agree with measurement. Gamache and Davies [27] and Gamache and Rothman [28] have made calculations using the quantum Fourier transform (QFT) theory of Davies [29]. The QFT method incorporates a scaling parameter that was adjusted theoretically. Hartmann et al. [30] using the real components of Robert–Bonamy (RB) theory [31], have made calculation of halfwidths for a small number of ozone transitions. Neshyba and Gamache [32] also used the real components of RB theory to study nitrogen broadening of ozone. More recently Priem et al. [20] made complex Robert–Bonamy (CRB) calculations for N2- and O2-broadening of the 500.4 GHz line of ozone. Drouin et al. [5] made complex Robert–Bonamy calculations for N2- and O2-broadening and then used these results to determine air-broadening for 22 pure rotation transitions of O3. One advantage of the complex Robert– Bonamy calculations is they allow the simultaneous determination of the half-width and line shift. There have been fewer calculations on the temperature dependence of the half-width for ozone transitions; Ref. [16] reports the temperature exponent for 126 N2-broadened ozone lines studied in the range from 200 to 500 K from QFT calculations. Weighted average temperature exponents for A- and B-type bands for N2-, O2-, and air-broadening can be derived from the ATC calculations of Tejwani and Yeung [23]. Hartmann et al. [30] have reported the temperature exponents for N2- and O2-broadening of four transitions of ozone from real component RB calculations. Priem et al. [20] reported the temperature dependence of the 500.4 GHz transition of ozone perturbed by nitrogen, oxygen, and air determined by CRB calculations. Drouin et al. [5] also reported the temperature dependence of the half-width determined by CRB calculations for 22 rotation band transitions. All of these calculations used the power-law model of the temperature dependence of the halfwidth. 2. Experiment The general experimental setup was very similar to that described earlier [5]. Two differences were the change in frequency range and the addition of programmed mass-flow controllers. Despite the similarities to previous work, the potential for systematic errors in these types of experiments gives good reason to fully describe the present apparatus in detail. Tunable radiation in the 600–700 GHz range is produced via cascaded frequency multiplication [33]. The radiation is passed twice through a one meter temperature controlled cell with inset, ‘top hat’, polypropylene windows. Secondary windows at the base of the ‘top-hat’ are used to prevent water condensation on the inner, cold window surface. Temperatures from 205 to 300 K are

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achieved and regulated to within 1.5 K using a circulation methanol/isopropanol bath that is passively cooled with liquid nitrogen. Ozone is prepared as needed using an RF discharge of O2 and stored on cold (200 K), dry silica gel. A short period of strong pumping on the silica gel (up to half hour) improves the purity of the ozone and produces a stable mixture (O3/O2) for 1–2 days of slow flow out of the trap. Air-broadened ozone features are measured by streaming the ozone off the cold silica and combining this with synthetic air in the flow cell. The computer records the demodulated FM signal that is adjusted for optimal signal to noise (S/N) for linewidths of a few MHz, corresponding to approximately 500 mTorr of air pressure. A survey scan used to verify frequency precision of the JPL spectral line catalog compilation for this region is shown in Fig. 1. A mass-flow controller was used to create a stable, programmable flow rate that was controlled by the same computer as the data acquisition. A computer program that records the spectrometer signal simultaneously with the system temperature and pressure is then allowed to automatically scan each transition (18 transitions total) (±10–15 MHz) for the given temperature and pressure. The spectral recording cycle is then repeated for a different, preprogrammed flowmeter setting. After one or more cycles through the range of flowmeter settings the system is paused and the temperature regulation is adjusted to a new set point. After the temperature equilibrates the cycles are resumed. Recorded spectra are analyzed individually for each temperature and spectral window, but collectively for all pressures, utilizing the convolution method [34]. This method allows the instrument lineshape, in this case due to the modulation, to be treated implicitly when determining changes in linewidth between two spectra recorded at different pressures. When utilizing this method it is important that background features are removed via baseline subtraction from a ‘blank’ scan. Blank scans are achieved via large air-flow rates (pressures >5 Torr) that effectively broaden the absorption signal to a point where the modulation is no longer sensitive to the absorption, the resulting spectra contain only background effects that are due primarily to standing waves within the instrument. The 18 transitions have been measured in two, overlapping, series of experiments in which some effects of systematic choices in the data capture might be discernable. The primary difference in the two sets of measurements is the frequency range, the first run utilized frequency scans of ±10 MHz, the second ±15 MHz. The only other differences are the choices of flow settings and the transitions probed. The frequency window was widened for the second set of measurements because the high pressure measurements of the first run often had non-zero line intensity at the edges of the scans. A discussion of potential systematic biases will be given in the section 5. Each measurement (mi ) of a specific transition at a given pressure (pi ) and temperature (T i ) is compared (convoluted) with every other measurement (mk , where pk > pi ) in the pressure series such that M pressure measurements results in M(M-1)/2 comparisons. The results of the convolution fits are differences in linewidth, DCi;k that depend on pressure and temperature as such:  n 296 DCi;k ¼ c0 Dp ð1Þ T where c0 is the pressure broadening parameter at the reference temperature of 296 K. The exponential temperature dependence is given by n. The pressures Dp ¼ pk  pi are measured during each scan as the average reading from calibrated capacitance monometers located at ports of the flow cell. Temperature is measured using a ‘T’ type thermocouple embedded in the exit port of the circulating coolant and T ¼ ðT i þ T k Þ=2. The thermocouple is referenced to an ice bath at 0 °C. Eq. (1) is readily derived via the empirical power-

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595000

610000 620000 630000 640000 650000 660000 670000 680000 690000

705000

Frequency (MHz) Fig. 1. Survey scan of ozone at room temperature and 50 mTorr. The gray trace is source power measured and the box represents the MLS window where broadening measurements have been done.

Plots of DC vs. Dp for each pressure run (i.e., same temperature and transition, see Fig. 2) were utilized to inspect the data quality. At this stage pressure limits for each transition are imposed to ensure that only data with good S/N, or unsaturated absorption was utilized for further analysis. The culling of the data set at this point is necessary because all lines were treated equally by the automatic scanning routine. However, the S/N depends on the linestrength and linewidth. Therefore, the weaker lines (or slightly broader) had poorer S/N, especially at the highest pressures measured, and therefore these data sets contain fewer high pressure measurements. Alternatively, the strongest lines are often saturated in absorption and the convolution method does not return a reliable result until the low pressure comparison point is sufficiently diluted. For many of the strong lines, there are fewer low pressure measurements in the final, culled, data set. Values of c0 and n are fitted to measured Dp; T; DC values over the entire set of culled measurements. This parametric fit simultaneously determines both lineshape parameters and their statistical

3 2.5 2 1.5 1 0.5 0 0

0.2

0.4 0.6 0.8 Differential Pressure (Torr)

1

3. Theory The calculations are made using the complex implementation of the Robert–Bonamy (CRB) theory [31]. The method has been described previously [35–37] here we present only a review of salient features as they apply to the current calculations. The method is complex valued yielding the half-width and line shift from a single calculation. The dynamics use curved trajectories based on the isotropic part of the intermolecular potential [31], which has important consequences in the description of close intermolecular collisions (small impact parameters). Within the CRB formalism the half-width, c, and line shift, d, of a ro-vibrational transition f i are given by minus the imaginary part and the real part, respectively, of the diagonal elements of the complex relaxation

b 3.5 Differential Linewidth (MHz)

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

Differential Intensity

Differential Linewidth (MHz)

a 3.5

uncertainties. These values are listed in Table 1. Most of the transitions measured in this study comprise data sets of more than 500 values of DC; the total number of measurements used in the analysis is given by N in Table 1. Similar data for differential line shift are created during the convolution fitting process. This data was also inspected for each transition studied and none of it showed any systematic and reproducible pressure dependence.

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

3 2.5 2 1.5 1 0.5 0 0

0.2

0.4

0.6

0.8

Differential Intensity

law equation (Eq. (2)) by taking the finite valued derivative with respect to pressure.  n T0 CðT; pÞ ¼ cðT 0 Þp ð2Þ T

1

Differential Pressure (Torr)

Fig. 2. Example inspection plots for (a) 156;10 165;11 at 625 372 MHz, a strong, initially saturated absorption and (b) 244;20 243;21 at 623 688, a weaker, ultimately noisy (when broadened) absorption. Black represent data that was not used in the parametric fitting analysis. Squares show differential linewidths and triangles represent the differential peak intensity.

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B.J. Drouin, R.R. Gamache / Journal of Molecular Spectroscopy 251 (2008) 194–202 Table 1 Values of electrostatic moments for O3 ; N2 , and O2 Molecule O3

N2 O2

Multipole moment 18

m ¼ 0:532  10 esu Q xx ¼ 1:40  1026 esu 26 Q yy ¼ 0:70  10 esu Q zz ¼ 2:10  1026 esu 26 Q zz ¼ 1:4  10 esu Q zz ¼ 0:4  1026 esu

Reference [46] [46] [46] [46] [47] [48]

Table 2 Values of the heteronuclear atom–atom parameters for the collision pairs considered in this work Atomic pair

r (Å)

=kB ðKÞ

O–N O–O

3.148 3.010

43.90 51.73

ozone–nitrogen collision pair and =k ¼ 51:73 K and r = 3.01 Å for the ozone–oxygen collision pair. matrix. In computational form the half-width and line shift are usually expressed in terms of the Liouville scattering matrix [38,39] h iE n2 D R ðc  idÞf i ¼ v  1  e S2 ðf ;i;J2 ;v;bÞ ei½S1 ðf ;i;J2 ;v;bÞþS2 ðf ;i;J2 ;v;bÞ v;b;J2 2pc ð3Þ where n2 is the number density of perturbers and h. . . iv;b;J2 represents an average over all trajectories (impact parameter b and initial relative velocity v) and initial rotational state J 2 of the collision partI ner. S1 (real) and S2 ¼R S2 þ i S2 are the first and second order terms in the expansion of the scattering matrix, they depend on the rovibrational states involved and associated collision induced jumps from these levels, on the intermolecular potential and characteristics of the collision dynamics The exact forms of the S2 and S1 terms are given in Refs. [35–37]. Here only transitions within the rotation band are considered thus the S1 term is zero. The intermolecular potential employed in the calculations consists of the leading electrostatic components for the O3–N2 or –O2 system (the dipole and quadrupole moments of O3 with the quadrupole moment of N2 or O2) and atom–atom interactions [32]. The atom–atom terms are defined as the sum of pair-wise Lennard– Jones 6–12 interactions [40] between atoms of the radiating and the perturbing molecules. The heteronuclear Lennard–Jones parameters for the atomic pairs are determined using the ‘‘combination rules” of Hirschfelder et al. [41]. The atom–atom distance, rij is expressed in terms of the center of mass separation, R, via the expansion in 1=R of Sack [42]. Here the formulation of Neshyba and Gamache [32] expanded to eighth order is used. To evaluate the reduced matrix elements rotational–vibrational wave functions are needed. For ozone, the reduced matrix elements are evaluated using wavefunctions determined by diagonalizing the Watson-Hamiltonian [43] in a symmetric top basis. The ground vibrational state wavefunctions used in the calculations are determined with the Watson–Hamiltonian constants of Barbe [44]. The molecular constants for N2 and O2 are from Huber and Herzberg [45]. All molecular parameters for the O3 —N2 or O3 —O2 systems used in this work are the best available values from the literature. No molecular constants are adjusted to give better agreement with experiment. The dipole and quadrupole moments of ozone are taken from Ref. [46]. The quadrupole moment of nitrogen is from Mulder et al. [47] and that for oxygen is from Stogryn and Stogryn [48]. The numerical values are listed in Table 1. The atom–atom parameters were obtained using the standard combination rules [41] with the atom–atom parameters for homonuclear diatomics determined by Bouanich [49] by fitting to second virial coefficient data. These parameters are reported in Table 2. The atom–atom potential is expanded to eighth-order in the molecular centers of mass separation. In the parabolic trajectory approximation the isotropic part of the interaction potential is taken into account in determining the distance, effective velocity, and force at closest approach [31]. To simplify the trajectory calculations the isotropic part of the atom–atom expansion is fit to an isotropic Lennard– Jones 6–12 potential, giving =k ¼ 43:9 K and r = 3.15 Å for the

4. Calculations The calculations were made for 57 rotation band transitions of O3 broadened by N2 and by O2 at seven temperatures (200, 250, 296, 300, 350, 500, 700 K) by explicitly performing the averaging over the Maxwell–Boltzmann distribution of velocities. At each of the temperatures studied, the half-width and line shift for air as the buffer gas were obtained assuming binary collisions and Dalton’s law cair ¼ 0:79cN2 þ 0:21cO2

ð4Þ

and dair ¼ 0:79dN2 þ 0:21dO2

ð5Þ

For applications to atmospheres, the temperature dependence of the half-widths must be known. Theoretical consideration of the temperature dependence of the half-width for a one term intermolecular potential gives the power-law model [50], see Eq. (2). However, for certain types of radiator–perturber interactions the power law model is being questioned. Wagner et al. [51] have observed that for certain transitions of water vapor perturbed by air, N2 , or O2 the power-law does not correctly model the temperature dependence of the half-width. This fact was also demonstrated by Toth et al. [52] in a study of air-broadening of water vapor transitions in the region from 696 to 2163 cm1. In both studies it was found that the temperature exponent, n, can be negative for many transitions. In such cases the power-law equation (2) is not valid. The mechanism leading to negative temperature exponents is called the resonance overtaking effect and was discussed by Wagner et al. [51], Antony et al. [53] and Hartmann et al. [54]. Other, better models for the temperature dependence of the half-width have been proposed. Pack [55] in a study of CO2 broadened by He and Ar, proposed a polynomial in T for the temperature dependence of the half-width. In a study of the temperature dependence of the half-width of the 500.4 GHz transition (342;32 341;33 ) of the ground vibrational state of ozone Gamache [56], at the suggestion of Rossi [57], proposed a double power-law model, which more correctly modeled the temperature dependence over a large temperature range. 5. Discussion 5.1. Experimental results The results of the experimental work are summarized in Table 3. This section will compare the individual broadening parameters as well as offer comparisons with complementary literature data. General correlations can be drawn upon comparison with polynomial derived values [58] tabulated in HITRAN [59]. Fig. 3(a) plots experimental and theoretical values of the broadening parameter at 296 K vs. the HITRAN 2004 values. The solid line represents a 1:1 correspondence. Only one of the new experimental measurements is in agreement with the tabulation based on the estimated

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Table 3 Ozone air broadening parameters Frequency (MHz)

J0Ka0 ;Kc0

J00Ka00 ;Kc00

c0

n

N

620 686 620 826 623 688a 625 372a 632 177a 633 353 634 462a 634 520 638 903 642 350 644 805 647 840a 650 733 651 476a 651 557 653 762 658 815 661 459

63;3 260;26 244;20 156;10 281;27 227;15 224;18 403;37 192;18 204;16 73;5 184;14 146;8 164;12 122;10 144;10 217;15 274;24

52;4 251;25 243;21 165;11 272;26 236;18 223;19 394;36 181;17 203;17 62;4 183;15 155;11 163;13 111;11 143;11 226;16 273;25

3.089(14) 2.564(21) 2.687(10) 2.906(15) 2.575(11) 2.843(16) 2.734(11) 2.756(21) 2.730(13) 2.705(12) 3.072(15) 2.760(14) 3.006(11) 2.759(13) 2.938(10) 2.832(11) 2.668(40) 2.651(10)

0.720(17) 0.760(30) 0.814(15) 0.723(21) 0.901(17) 0.678(26) 0.755(17) 0.504(39) 0.805(18) 0.823(17) 0.739(18) 0.713(19) 0.598(17) 0.785(18) 0.735(14) 0.763(15) 1.171(69) 0.806(14)

505 442 770 + 821 537 + 681 657 + 831 608 679 + 770 403 686 619 582 589 + 687 619 604 + 809 747 740 345 779

The parameters c0 and n are defined in Eq. (1). One sigma uncertainties are given in parenthesis. N is the number of convolutions included in the parametric analysis. a Two sets of data were averaged for each of these measurements, see text.

statistical errors. The remaining values are completely below the 1:1 line, indicating a bias of +8% compared with these measurements. Fig. 3(b) displays the measured and calculated temperature exponents from this study vs. the polynomial derived values [58] from HITRAN 2004. Again the solid line represents a 1:1 correspondence. The experimental values have no average bias vs. HITRAN 2004, however, there is a large variation in the measured values (9% standard deviation) that is not represented in the tabulation (3% standard deviation). This behavior is also observed if one compares the air-broadening measurements [60,61] of the m1 and m2 bands with the polynomials described in Ref. [58]. Additionally, a weak negative correlation between measured values of c0 and n was noted one of the infrared studies [61]. This behavior is also exemplified in the present data set as shown in Fig. 4. Comparisons with the definitive infrared data sets for m2 [60] and m1 [61] show similarities in the J; K a (or just K c ) dependances of the room temperature broadening. Fig. 5 shows 1:1 plots of c0 and n for matched sets of transitions in this work and Refs. [60,61]. In the figures two parameters are compared if one energy level of the pair is equivalent, i.e., the lower state of the vibrational transition is either the upper or lower state of the rotational transition. Two interesting features are easily discernable from this comparison: (1) the vibrational c0 values are all larger than corresponding rotational values; (2) the n values are bifurcated with the m1 group roughly aligning 1:1 with the rotational and the m2 group falling in a similar distribu-

5.2. Theoretical results While calculations were made for N2 -;O2 -, and air-broadening of ozone, only the air-broadened results are discussed here. The data for the other broadening molecules are available, see below. The half-widths range from 2.8 to 3.4 MHz/Torr with J 00 ranging from 4 to 40. These data are given in Table 4. The theoretical results are compared directly with the HITRAN 2004 database in Fig. 3. The reference broadening values are in excellent agreement with HITRAN 2004. This agreement is likely due to the fact that the theoretical vibrational contributions are very small for this molecule, and the HITRAN listing is based on work done for the vibrational modes. Consequently the theory is in excellent agreement for the analogous vibrational transitions corresponding to the rotational transitions studied experimentally here. The tight grouping of points in the comparison of n values in Fig. 3(b) reiterates this point. It also points out the smoothing effect that the polynomial fitting of the infrared data of Wagner et al. [58] which has no doubt reduced the spread of the n values that are seen in similar infrared studies [60,61]. The temperature dependence of the half-width was determined using the power-law model, Eq. (2), for 57 rotation band transitions, using the seven points in the range 200–700 K where the reference temperature T0 was taken as 296 K. Birnbaum [50] has shown that for a system that has only the ‘‘dipole–quadrupole” interaction, the leading interaction of the O3 —N2 or the O3 —O2 systems, the temperature exponent is 0.83. The temperature exponents range from 0.84 to 0.81 indicating that the broadening of ozone in the rotation band is dominated by rotational contributions (the real part of the S2 term). It is also noted from the correlation coefficients of the fits indicate that the power-law model does not work perfectly over this temperature range. Estimated error in the temperature power-law exponent was determined as follows. The temperature exponents were calculated using the half-width values at any two of the temperatures studied. With seven temperatures this yields twenty 2-point temperature exponents. The difference between each 2-point temperature exponent and the 7-point fit value is calculated. The error is taken as the largest of these differences. This procedure yields the maximum error in the temperature exponent and is thought to be more reasonable than a statistical value taken from the fit. The n values are reported in Table 4 along with their error. In Fig. 4, the calculated c296 values are plotted vs. the calculated n

b

3.5

3.1 2.9 2.7 2.5 2.5

1 0.9

3.3 This Work n

This Work γ296 (MHz/Torr)

a

tion—but with significantly smaller values. The first point simply shows that the work of Wagner et al. [58], which is the basis for HITRAN 04, is in general agreement with these earlier works. The second point emphasizes the fact that, experimentally, there is still a quite large variance in measured n values.

0.8 0.7 0.6 0.5

2.7

2.9 3.1 HIT04 γ 296 (MHz/Torr)

3.3

3.5

0.4 0.4

0.5

0.6

0.7 HIT04 n

0.8

0.9

1

Fig. 3. Comparisons of measured and HITRAN values for (a) pressure induced half-width values at 296 K and (b) for pressure induced half-width temperature exponents values. Black diamonds are this work’s experimental results, gray circles are this work’s theoretical results.

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1

0.9

This s Work n

0.8

0.7

0.6

0.5

0.4 2.5

2.7

2.9

3.1

This Work γ 296 (MHz/Torr) Fig. 4. Correlation between broadening values and temperature exponents. The black diamonds are the experimental, and the gray circles are the theoretical, results from this work.

b

3.2

1 0.9

3

This Work n

This Work γ 296 (MHz/Torr)

a

2.8

0.8 0.7 0.6

2.6 0.5

2.4 2.5

2.7

2.9

3.1

3.3

3.5

γ 296 IR (MHz/Torr)

0.4 0.4

0.5

0.6

0.7 n IR

0.8

0.9

1

Fig. 5. Comparisons of measured rotational and infrared values (m2 , open diamonds [60]; m3 , filled diamonds [61]) for pressure induced half-width (a) values at 296 K and for pressure induced half-width temperature exponent values (b).

values and the spread in n values is given as an ‘error bar’. Unlike the experimental data there does not appear to be much of a negative correlation between these values. However, the n values decrease with J m until about J m ¼ 18 and then increase again. It is also seen that there is variation with K m as a function of J m . As noted above the overall variation in n is small. There is a smooth variation from the large values of the halfwidth to the small values as a function of J m , which is defined as the larger of J 00 and J 0 , with some spread as a function of K m (larger of K 00a and K 0a ). This behavior is visible in the Q-branches plotted in Fig. 6. It is well known for ozone, from both measurement [62] and from calculation [27], that the range of the pressure-broadened half-widths as a function of J is not large when compared to a light asymmetric rotor like H2 O. Here roughly a 19% decrease is observed in going from high to low J m . By comparison, for H2 O the half-width changes by a factor of 30 from high to low J. The pressure-induced line shifts calculated in this work are very small, in agreement with the insensitivity of any laboratory experiment to the phenomenon. The calculated values range from 0.006 to +0.012 MHz/Torr. Due to the small magnitude of the values the line shifts are not reported here. A complete listing of the theoretical data for N 2 ; O2 , and air-broadening can be found at www.faculty.uml.edu/Robert_Gamache.

ering the relative difficulty of the measurements and demands on theory, the growing data set is formidable and worth discussing in the context of this work. A literature survey identified 40 independent measurements of air-broadened ozone transitions measured by the monochromatic scanning of a millimeter or submillimeter radiation source. Furthermore, 101 air-broadened transitions (all in the far-IR) have been measured via Fourier Transform Spectroscopy. The 17 measurements presented here bring this data set to 158. Only a small fraction of the measurements overlap the same transitions, however, these occasions offer much more information on systematic errors. For this section the focus is on a large overview and systematic errors will be discussed in Section 5.4. It can be seen from Fig. 6 that the low K a Q-branches dominate this work and other studies directed at submillimeter limb sounding studies. Twenty-nine of the 57 non-FT measurements are in this subset. With more than twenty data points a graph such as that shown in Fig. 6 can be interpreted as a general critique of the rotational linewidth tabulation in HITRAN 2004, which is shown as the smooth lines connecting each set of K c values in a Q-branch. Only the lowest K c values in the 1 Q R branch are above the tabulated values.

5.3. Literature comparisons

Sources of systematic errors in linewidth measurements are numerous. In this final section potential error due to pressure calibration, temperature calibration/measurement, finite analysis methods and model biases will each be discussed.

There is a growing, now substantive, number of published ozone rotational transition air-broadening measurements. Consid-

5.4. Systematic errors

200

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Table 4 CRB calculated half-widths at 296 K in units of MHz/Torr for N2 -;O2 -, and airbroadening of ozone transitions in the rotation band

3.8

HIT04 Connor PhLAM

3.6

Frequency (MHz)

J 0Ka0 ;Kc0

J 00Ka00 ;Kc00

c0 (MHz/Torr)

n (unc)

195430.363 206132.049 208642.415 231281.511 235709.855 237146.116 239093.279 242318.688 243453.776 244158.390 247761.753 248183.390 249788.552 249961.960 273050.900 288959.140 535922.659 591248.915 610365.187 620686.697 620825.695 623687.733 625371.112 632176.937 633352.692 634461.604 634520.173 638903.096 642349.703 644804.926 647839.917 650732.726 651475.845 651556.974 653762.450 654713.487 654853.037 655005.256 655120.330 655203.576 655290.198 655606.308 655872.589 655962.099 656005.734 656223.761 656252.556 656383.998 656419.754 656461.535 656477.701 658038.638 658814.978 661458.303 2509561.816 2543209.100

141;13 245;19 51;5 161;15 162;14 142;12 182;16 122;10 120;12 83;5 154;12 202;18 71;7 102;8 181;17 91;9 281;27 301;29 251;25 63;3 260;26 244;20 156;10 281;27 227;15 224;18 403;37 192;18 204;16 73;5 184;14 146;8 164;12 122;10 144;10 194;16 174;14 214;18 124;8 154;12 271;27 134;10 104;6 114;8 234;20 94;6 84;4 74;4 64;2 54;2 44;0 254;22 217;15 274;24 379;29 3110;22

140;14 254;22 40;4 160;16 161;15 141;13 181;17 121;11 111;11 92;8 163;13 201;19 60;6 101;9 180;18 80;8 280;28 300;30 240;24 52;4 251;25 243;21 165;11 272;26 236;18 223;19 394;36 181;17 203;17 62;4 183;15 155;11 163;13 111;11 143;11 193;17 173;15 213;19 123;9 153;13 260;26 133;11 103;7 113;9 233;21 93;7 83;5 73;5 63;3 53;3 43;1 253;23 226;16 273;25 368;28 309;21

3.0864 2.8954 3.2424 3.0376 3.0304 3.0767 2.9875 3.1239 3.1331 3.2188 3.0539 2.9505 3.2203 3.1711 3.0025 3.1897 2.8754 2.8535 2.9007 3.2891 2.8899 2.9055 3.0939 2.8747 2.9424 2.9266 2.8007 2.9772 2.9500 3.2629 2.9905 3.1247 3.0364 3.1385 3.0885 2.9669 3.0137 2.9399 3.1419 3.0623 2.8802 3.1161 3.1947 3.1676 2.9144 3.2235 3.2511 3.2767 3.2983 3.3036 3.2420 2.8923 2.9635 2.8744 2.8075 2.8703

0.818(0.083) 0.815(0.113) 0.840(0.068) 0.813(0.089) 0.814(0.093) 0.816(0.086) 0.813(0.099) 0.819(0.077) 0.822(0.073) 0.821(0.066) 0.811(0.090) 0.814(0.104) 0.836(0.067) 0.822(0.071) 0.813(0.095) 0.831(0.068) 0.818(0.113) 0.818(0.114) 0.811(0.109) 0.825(0.063) 0.812(0.111) 0.816(0.112) 0.813(0.086) 0.817(0.112) 0.812(0.106) 0.813(0.110) 0.819(0.103) 0.811(0.099) 0.811(0.106) 0.824(0.063) 0.809(0.099) 0.815(0.082) 0.809(0.092) 0.820(0.074) 0.811(0.084) 0.810(0.103) 0.809(0.096) 0.812(0.108) 0.813(0.076) 0.810(0.088) 0.814(0.112) 0.812(0.079) 0.816(0.070) 0.814(0.073) 0.815(0.112) 0.818(0.068) 0.820(0.066) 0.821(0.065) 0.823(0.065) 0.824(0.065) 0.827(0.070) 0.817(0.114) 0.812(0.104) 0.819(0.114) 0.816(0.102) 0.813(0.101)

JPL

The pressure gauge used in this study is a MKS capacitance manometer calibrated to 0.25% of its reading. The calibration, performed by MKS is traceable to NIST standards [63]. The signal generated by the capacitance measurement is read directly into the computer data acquisition interface (DAQ). Small offsets in the pressure measurement, typically a few mTorr, are often observed and attributed to zero drift (typically from the ambient temperature of the manometer) and due to DAQ grounding (a constant). This pressure, with offsets, is recorded continuously during spectral acquisition of each lineshape and the average value stored in the data file with the spectral trace and other engineering parameters. During analysis the pressure measurements for each of the two scans being compared via the convolution method are differ-

γ296 ((air) MHz/Torr

LMSB

3.4

Theory

3.2

3

2.8

2.6 1

1.5

2

2.5

3 3.5 K am + K cm /30

4

4.5

5

Fig. 6. Comparisons of measured rotational broadening parameters with HITRAN 2004.

enced—removing constant or slowly varying offsets in the pressure measurements. With this scheme the only error that propagates through to the pressure dependent lineshape parameters is due to inaccuracies in the pressure calibration. The propagation exercise, which is described in more detail in Ref. [5], reveals that the S/N of the measurements contributes more to the error than any potential bias within the pressure calibration accuracy. Temperature is measured using ‘T’ type thermocouples which produce a characteristic voltage as a function of temperature. In this work, two thermocouples are placed in anti-parallel configuration and the differential voltage (1 to 3 mV) is measured at the DAQ using the highest gain setting. One thermocouple is immersed in a zero degree ice bath and the second is in the cooling jacket of the spectrometer cell. The voltage is converted to temperature using a polynomial fit to the temperature vs. voltage table for a ‘T’ type thermocouple available in the CRC [64]. Over the temperature range of this experiment the polynomial is essentially an exact fit and therefore the uncertainty of 1 K given in the tabulation can be transferred onto this measurement. In cases where the S/N of measurement is very good, resulting in statistical data fits with random errors <2%, the error associated with this temperature measurement becomes the (random) dominant error and should be propagated through when calculating the error in a given pressure, temperature linewidth. The placement of the thermocouple in the cooling jacket is a matter of convenience and may introduce some bias through the inference that the gas temperature is equivalent to the temperature of the cell walls. This potential bias could manifest as a linear temperature offset with an intercept at room temperature, i.e., T gas ¼ T jacket þ að296  T jacket Þ. A numerical test of the effects of such an error indicate that, for (a measured value of) n near 0.7, values of a between zero and 0.3 produce a nearly equivalent bias in the perceived value for n,with the measured value always smaller in magnitude than the true value. The bias is stronger for larger values of n in a non-linear fashion. A value for a of 0.1 would indicate that the measurements reported here for 200 K were actually for a gas at 210 K, and that an n value reported as 0.68(3) would actually be 0.78(3). As such, the value of a remains unknown for this spectrometer and the results reported here assume an a of zero. This simple model does not address the possibility of an inhomogeneous gas. An inhomogeneous gas may result from temperature differentials at the ends of the cell (perhaps near the inset windows) and would likely manifest as a negative bias in n in the same manner as described above. Some error in the application of the convolution method can be generated simply by the finite measurement window around each

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5.5. Theoretical improvements A more extensive treatment of the velocity effects in the statistical ensemble of broadening partners has been implemented in this study through the use of a full integration in the velocity domain. A comparison of this ‘velocity integral’ (VI) treatment to the previously used ‘MRTV’ approximation (mean-relative thermal velocities) is given to demonstrate the improvements. As can be seen in Fig. 7 the theory and measurement still do not agree, however, the measured J-dependence is much more accurately reproduced. Similar comparisons of measurements and the VI calculations reveal that the difference increases with the K m quanta. This behavior is exemplified in Fig. 6 wherein the Q-branches are depicted with lower K m values to the left and higher values to the right. At K m 6 2 the VI calculations are, on the average, in agreement with experiment, i.e., less than 2%. However, the K m ¼ 4 Qbranch, which was the focus of approximately half of the current measurements, has an average deviation of about 8%. 5.6. MLS improvements The data set presented here was incorporated into the EOSMLS v2.2 spectroscopy tables and thus part of the current EOS-

3.1

Experiment velocity integral'

3 'MRTV' Γ296 (air) MHz/Torr

line. In theory, the lineshape extends to infinity with ever decreasing intensity. In practice, most of the line intensity is captured within the frequency scans. However, if the broadening moves intensity out of the scan window, the algorithm will attempt to compensate during the least-squares minimization. This affects the stronger lines at higher pressures where the wings of the lines are sloped enough to produce signal at 10 MHz from line-center. The effect of truncation is to limit the accuracy of the convolution algorithm. The first order effect being a reduction of the line intensity (which is used as an indicator of the partial pressure consistency within a pressure run). A second order effect is to artificially increase the fitted linewidth because the least-squares analysis will attempt to reduce the residuals of the wings, which, due to the truncation, can only be partially done ‘from the outside’ of the line, and therefore intensity from ‘inside’ is borrowed via increased width. Six of the strongest lines measured in this work were reinvestigated with extended scan windows in order to determine if a systematic effect was discernable. Five of these six measurements revealed smaller c296 values and larger n values, the sixth was opposite in both respects. The magnitudes of the differences were 62% for the c296 values and up to 20% for the n values. This large difference in n cannot be completely attributed to one systematic error, since the intensity of each transition is also temperature dependent. It is believed that, for most of the reported transitions this systematic error is more represented by the 2% spread in c296 values. In order to present a unified data set, these separate measurements were combined for presentation in Table 3 using the N values to determine weighted averages for the parameters, these measurements are indicated with a superscript ‘a’ in Table 3. Finally, some systematic error may be introduced simply through the power law model. This model is a well-established empirical method for characterizing lineshape pressure and temperature dependence. However, it is also known that the power-law model only holds up over certain temperature intervals, outside of these intervals the lineshape may have mode-specific interactions with the bath gas (or gases) which can only be predicted with quantized versions of the collision theory. These effects are unusual in the 200–300 K range studied here, where collision rates dominate over quantum statistics, and no systematic deviations from the power-law model could be discerned from the data.

2.9

2.8

2.7

2.6 12

16

20

24

28

J m (r Q3) Fig. 7. Comparisons of new experimental measurements, new theoretical calculations and simpler calculations using the MRTV approximation. [33]

MLS R4 Level 2 data products [10–14]. Several improvements to the data products were executed during the process of conversion from v1.5 to v2.2 and, as such, not all of the changes can be attributed to this spectroscopy. For R4 products the prime mover is considered to be in how gain compression in the instrument back-end is dealt with. The change affects the largest signals most. Another augmentation of the algorithm involves an ad hoc adjustment to the dry nitrogen continuum. These issues combine in the relatively large continuum contribution of the R4 baseline and a dramatic improvement in the overall background corrections was observed across the band. The spectroscopy update, which is primarily the ozone parameters described here, provided a balancing component for these background improvements in R4. After inspection of over one month of data the systematic bias in R4 trace species retrievals that tracked ozone concentration was not discernable, as it had been prior to development of v1.5. Because the ad hoc baseline correction has been removed in v2.2, MLS retrievals of products such as BrO, HO2 and HOCl can be considered more accurate (lessbiased) and more reliable for long term averages. Acknowledgments This research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. One of the authors (R.R.G.) is pleased to acknowledge support of this research by the National Science Foundation (NSF) through Grant No. ATM-0242537. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF. References [1] J.W. Waters, W.G. Read, L. Froidevaux, R.F. Jarnot, R.E. Cofield, D.A. Flower, G.K. Lau, H.M. Pickett, M.L. Santee, D.L. Wu, M.A. Boyles, J.R. Burke, R.R. Lay, M.S. Loo, N.J. Livesey, T.A. Lungu, G.L. Manney, L.L. Nakamura, V.S. Perun, B.P. Ridenoure, Z. Shippony, P.H. Siegel, R.P. Thurstans, R.S. Harwood, H.C. Pumphrey, M.J. Filipiak, J. Atmos. Sci. 56 (1999) 194. [2] H.M. Pickett, R.L. Poynter, E.A. Cohen, M.L. Delitsky, J.C. Pearson, H.S.P. Müller, J. Quant. Spectrosc. Radiat. Transfer 60 (5) (1998) 883–890. Available from: . [3] M.M. Yamada, M. Kobayashi, H. Habara, T. Amano, B.J. Drouin, J. Quant. Spectrosc. Radiat. Transfer 82 (1–4) (2003) 391–399. [4] B.J. Drouin, J. Quant. Spectrosc. Radiat. Transfer 83 (3–4) (2004) 321–331. [5] B.J. Drouin, J. Fischer, R.R. Gamache, J. Quant. Spectrosc. Radiat. Transfer 83 (1) (2004) 63–81. [6] B.J. Drouin, J. Quant. Spectrosc. Radiat. Transfer 105 (3) (2007) 450–458. [7] B.J. Drouin, J. Quant. Spectrosc. Radiat. Transfer 103 (3) (2007) 558–564.

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