Temperature Dependence of Air-Broadening and Shift Coefficients of O3Lines in the ν1Band

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

182, 239–259 (1997)

MS967232

Temperature Dependence of Air-Broadening and Shift Coefficients of O3 Lines in the n1 Band M. A. H. Smith,* V. Malathy Devi,† D. Chris Benner,† and C. P. Rinsland* *Atmospheric Sciences Division, NASA Langley Research Center, Mail Stop 401A, Hampton, Virginia 23681-0001; and †Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795 Received May 28, 1996; in revised form November 18, 1996

High-resolution Fourier transform absorption spectra of ozone broadened by dry air have been recorded at a number of temperatures from 0637C to 297C. Using a multispectrum nonlinear least-squares procedure, we fit 29 of these spectra simultaneously to determine the air-broadening and shift coefficients and their temperature dependences for 450 lines in the 9-mm region; most of these belong to the n1 band. Partial air-broadening results were obtained for 104 additional lines, and room-temperature self-broadening coefficients were also determined for most of the 554 lines measured. These results cover a wide range of rotational quantum numbers, particularly in the R branch, with J 9 £ 55 and K a9 £ 12. The variation of the retrieved broadening and shift parameters with the rotational quantum numbers has been examined; particularly interesting behavior of the broadening coefficients is noted as the value of K a9 approaches that of J 9. The broadening and shift coefficients compare well with previous room-temperature measurements in the n1 and other bands. The temperature-dependence results are also consistent (within the stated uncertainties) with the few previous measurements of the temperature dependence of air- and N2-broadening coefficients in other O3 bands, but disagree with the mean value given in the HITRAN compilation. q 1997 Academic Press

beamsplitter and liquid helium cooled As:Si detectors. A glower heated to approximately 2000 K was used as the light Knowledge of infrared pressure broadening and line shift source. The 50-cm Pyrex coolable absorption cell with potascoefficients for ozone–air mixtures is important for atmo- sium chloride windows is the same as that used in our studies spheric remote sensing studies. Accurate parameters are es- of low-temperature air- and N2-broadening of CH4 (27, 28). pecially needed in the 9–11 mm region which is used for The ozone samples were prepared from ultra-high-purity O2 ozone retrievals by a number of different measurement sys- (Matheson) having natural isotopic composition; we used the tems. Most of the ozone broadening and shift coefficient same silent-discharge ozone generation system as in our previmeasurements reported to date (1–26) have been concen- ous studies (25, 29, 30). At each temperature, the cell was trated in the n1 and n3 fundamental bands and the pure rota- first filled with 21 to 34 Torr of nearly pure ozone, and the tional band. However, less than a third of these studies (7, spectrum was recorded. Then Ultra-Zero air (Alphagaz) was 9, 10, 17, 19, 21, 23, 24, 26) have addressed the temperature added to achieve a total pressure of approximately 250 Torr. dependence of the broadening coefficients (none in the n1 After recording the spectrum at this highest pressure, the O3 – band), and none have looked at the temperature dependence air sample was partially pumped out to record the next specof the shifts. In this paper we report measurements of air- trum. O3 –air spectra were recorded at four different total broadening and shift coefficients and their temperature de- pressures between 100 and 252 Torr for each temperature. A pendences, as well as self-broadening coefficients, for 450 thermostatically controlled circulating refrigerator was used to ozone lines in the n1 fundamental band and several lines in stabilize the temperature of the ethanol coolant at six different the n3 band. In addition, partial results (typically no shift temperatures from room temperature down to 0637C, which coefficients, no temperature dependence, or both) were ob- was the lowest temperature achievable with the present refrigtained for 104 weaker lines in the same spectral region. erator and thermal insulation. The sample pressure was monitored continuously during the recording of each spectrum using a 0- to 1000-Torr DataEXPERIMENTAL DETAILS metrics Barocel 570A-series pressure transducer. Sample For this study new spectra of ozone and ozone–air mixtures temperatures were monitored by six T-type thermocouples were recorded at 0.005 cm01 resolution using the Fourier mounted on the outside of the double-walled Pyrex cell, transform spectrometer at the McMath–Pierce telescope facil- two at each end and two at the midpoint. Details of the ity of the National Solar Observatory on Kitt Peak near Tuc- thermocouple arrangement may be found in Ref. (27). The son, Arizona. The spectrometer was set up using the KCl temperature readings of the individual thermocouples difINTRODUCTION

239 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.

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TABLE 1 Summary of Measured Ozone Spectra

fered by no more than 17C during the recording of each spectrum, indicating that the cell temperature was nearly constant along its entire length. In addition to the 24 air-broadened O3 spectra recorded using the coolable cell and covering the interval from approximately 550 to 2750 cm01 , we included in the analysis five other room temperature self-broadened and air-broadened O3 spectra recorded previously with the same FTS. These spectra were obtained using a different 50-cm cell (also constructed of Pyrex with wedged KCl windows) but the same source, detectors, and beamsplitter; they cover the region from 450 to 1450 cm01 at the same resolution (0.005 cm01 ) as the new spectra. Three of these older spectra were recorded with samples of O3 in dry air at total pressures of 107 to 316 Torr, and they were previously analyzed to obtain room-temperature air-broadening and shift coefficients for 68 lines in the n1 band (12). The other two older spectra, recorded with 8 and 23 Torr of pure O3 , had been used in our earlier study of ozone self-broadening at room temperature (15). They were included in the present study to constrain the retrieved O3 line positions in the air-shift calculations and to improve the determination of the self-broadening coefficients. The volume mixing ratio, pressure, and temperature conditions for all 29 spectra used in the present analysis are summarized in Table 1. The signal-to-noise ratios of the spectra were between 200 and 500. Calibrations of the wavelength scales of the spectra were performed using the measured positions of n2 vibration–rotation lines of H2O. These lines appeared as sharp peaks in each spectrum due to 5– 20 mTorr residual water vapor in the nearly evacuated FTS tank. The H2O line positions given by Toth (31) were used as the reference standards for the calibration of all the spectra. DATA ANALYSIS

The 29 spectra were analyzed using the same multispectrum nonlinear least-squares spectral fitting technique (32) as in our recent study of the temperature dependence of CH4

broadening and shifts in the 2.3 mm region (28). All spectral lines were modeled using the Voigt line shape function convolved with the instrument line shape function appropriate for the McMath–Pierce FTS setup used for recording each spectrum. Initial values for the line parameters were taken from the 1992 HITRAN database (33). The free parameters for each line in the fit included the line position in vacuum ( n0 ), the line intensity, the Lorentz air-broadening (b AO ) and self-broadening (b SO ) coefficients, the air-broadening temperature dependence exponent (n), the air-shift coefficient ( d 0 ), and its temperature dependence ( d* ). The slope and height of the background level for each spectrum within the 1–2 cm01 interval being fitted were also included as free parameters. For a few crowded intervals, the number of free parameters exceeded the capacity of the software, and three to four intermediate-pressure air-broadened spectra were removed from the fit. The broadening parameters were assumed to have the following relationship b(p, T ) Å (1 0 q)r bA (p, T ) / qrbS (p, T ),

where b(p, T ) is the Lorentz halfwidth (in cm01 ) at total sample pressure p and temperature T, q is the volume mixing ratio of O3 in the sample, and bA (p, T ) and bS (p, T ) are the Lorentz halfwidths for air- and self-broadening, respectively. bX ( p, T ) (where X is either A or S) is calculated by bX ( p, T ) Å b XO r pr(296 K/T ) n x

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[2]

where nX is the temperature-dependence exponent and b XO is the broadening coefficient in cm01 atm01 at 296K. The measured line position n in a given spectrum may be expressed as n Å n0 / d (T )r p

[3]

where n0 is the line position in vacuum and d (T ) is the line shift coefficient (in cm01 atm01 ) at T due to all gases. Because of the small O3 partial pressures in each sample ( £34 Torr), no meaningful values can be obtained for self-shifts from the present set of spectra. Therefore we assumed the self-shift coefficient to be zero for all ozone transitions. Henceforth in this paper d will denote the air-induced line shift coefficient. Its temperature dependence is expressed by (27, 28) d (T ) Å d 0 / d*r(T 0 TO ),

[4]

where d 0 is the shift coefficient in cm01 atm01 at T0 Å 296K and d* is in units of cm01 atm01 K 01 . Because of the relatively small ozone pressures and the fact that all the low-temperature O3 spectra included in this analysis were air-broadened, we could not obtain reliable

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results for the temperature dependence of self-broadening. In our retrievals we fixed the self-broadening temperature dependence exponent to be the same as the 1992 HITRAN value (33) for air-broadening, 0.76 for all ozone lines. We note that this value is consistent with the few nS values determined for millimeter-wave ozone lines (9). Since nS was held fixed in our retrievals, for convenience of notation we will use n to denote nA in the remainder of this paper. For weak lines, including some belonging to the n3 and n1 / n2 0 n2 bands, only air-broadening coefficients and some temperature dependences could be determined. Parameters which could not be determined for weak lines were fixed to their 1992 HITRAN values (33), i.e., n Å 0.76, d 0 Å 0, and d* Å 0 for air-broadening, with b 0A and b 0S based on calculations normalized to measurements. We note that in the recently released 1996 update of the HITRAN compilation (L. S. Rothman, private communication), the line parameters for O3 in the 1070–1200 cm01 region are the same as in the 1992 version (33). Figure 1 is an example of the calculated spectra and residuals from a multispectrum least-squares fit in one of the spectral regions studied. RESULTS AND DISCUSSION

Table 2 lists the broadening and shift coefficients and their temperature dependences determined for each of the 554 lines examined, along with their vibration–rotation assignments (33) and measured positions. This total includes 533 lines in the n1 band, 18 lines in the n3 band, and 3 lines in the n1 / n2 0 n2 band. As mentioned earlier, for many weaker lines we could not determine all of the broadening and shift parameters (particularly temperature dependences). Nevertheless, we are able to report all five retrieved broadening and shift parameters (b 0A , n, b 0S , d 0 , and d* ) for 450 lines: 444 in the n1 band and 6 in the n3 band. The value given in parentheses after each measured parameter reported in Table 2 represents one standard deviation in units of the last digit quoted. These standard deviations represent only the statistical uncertainties due to random errors such as the noise level in each spectrum or errors in other fitted parameters. Because of the large number of spectra fit simultaneously, the standard deviations are quite small. As can be observed in Table 2 and Figs. 2–6, the retrieved parameters for transitions with higher J 9 and K 9a (and also with very low J 9 ), which are weaker and have smaller signals in the spectra, have larger statistical uncertainties. Additional contributions to the total uncertainty of each retrieved parameter arise from uncertainties in spectroscopic parameters that were held fixed in our analysis, as well as systematic errors in experimental parameters such as pressure, temperature, ozone concentration, and wavelength calibration. The relationships of these uncertainties would seem to be calculable in a straightforward way. For example, one should be able to calculate the uncertainty in n, the temperature

dependence of the air-broadening coefficient, from the uncertainties in the measured halfwidths and information on the temperature range of the data. However, this is only true if the uncertainties in the halfwidth determinations at different temperatures are completely uncorrelated. In fact, they are not. For instance, a systematic pressure gauge calibration error may increase or decrease all of the measured halfwidths in the same direction by similar amounts. This may introduce an error in the broadening coefficient, but if the error is exactly proportional to the pressure, will not cause an error in n. Similarly, a weak line blended with a stronger one may need its parameters constrained because the spectra do not contain enough information about these parameters that is uncorrelated with the parameters of the stronger line. An error in a constrained parameter of a weak line may have the same effect as a systematic problem with either pressure or temperature, or both. Thus the retrieved values of b 0X and n are not necessarily affected equally. The multispectrum nonlinear least squares fitting technique (32) reveals some of the systematic errors missed by single-spectrum fits. The multispectrum fit constrains b 0X and nX to behave mathematically as specified by Eq. (2) and constrains the line center to behave as described in Eqs. (3) and (4). If the behavior of a systematic error does not follow the constraining equations, this error will be apparent in the residuals from the fit. Since single-spectrum fits cannot involve these constraining equations, the results may appear satisfactory when appreciable systematic errors are present. In order to minimize the multispectrum residuals (see Fig. 1), it was necessary to carefully examine and account for some systematic errors; this accounting was not done (because the need was not apparent) in our previous studies of broadening and shifts in O3 vibration–rotation bands (12, 15, 25) using single-spectrum fitting. We also note that these previous studies involved at most four room-temperature spectra per broadening gas, and thus their results have intrinsically higher statistical uncertainties than the present work. From our current knowledge of likely remaining systematic errors in the n1 study reported here, we estimate that the absolute uncertainties in our derived parameters may be found by adding the following quantities to the standard deviations reported in Table 2: 2% for b 0A and b 0S , 0.05 for n, 0.0002 cm01 atm01 for d 0 , and 1 1 10 05 cm01 atm01 K 01 for d*. The relative precisions, i.e., the uncertainties in comparing the measurements to each other, are smaller than these absolute values, but are at least as large as the standard deviations listed in Table 2. Based upon our spectral resolution, signal-to-noise ratio, and the number of spectra analyzed simultaneously, our theoretical precision in determining the unshifted ozone line positions should be 5 1 10 06 cm01 or better. The absolute accuracy of the O3 line positions reported in Table 2 is approximately the same as that of our H2O calibration lines (31), 2 1 10 05

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FIG. 1. Calculated spectra and residuals from a multispectrum fit of air-broadened and self-broadened O3 spectra recorded at various temperatures. Although 29 spectra were included in the fit, for clarity only the six air-broadened spectra with total pressures around 150 Torr are shown here along with a self-broadened spectrum recorded with 8 Torr O3 at room temperature.

cm01 . However, other random and systematic errors contribute significantly to the uncertainties in d 0 and d*, which appear quite large relative to the retrieved values. Because pressureinduced line shifts and their temperature-dependences can have either positive or negative signs and can vary greatly from line to line (for examples, see Refs. (12, 14, 25, 27, 28)), the determination of a value near zero for the d 0 or d* of a single

line is not necessarily insignificant, regardless of the uncertainty. Our retrieved values for d* are reported in Table 2 for this reason and because they are consistent with the other reported broadening and shift parameters determined by multispectrum fitting and constrained by Eqs. (3) and (4). Although uncertain, they represent the reasonable range of d* values to be expected in the n1 band, which is comparable to the range of

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TABLE 2 Measured 16O3 Line Parameters in the n1 and Other Bands

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

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TABLE 2 —Continued

d* values determined for air-broadening in several bands of methane (27, 28). Figure 2 shows the n1 results from Table 2 plotted as functions of J 9. The tendency of b 0A and b 0S to decrease with increasing J 9 is quite obvious, while trends in n, d 0 , and d* are not so readily apparent. Closer inspection of Fig. 2(c) shows a trend toward more negative shifts with increasing J 9; this trend has also been observed in previous shift measurements in the n1 (12) and other bands (16, 25). Some J 9dependence of the air-broadening temperature dependence exponent n also appears for high and very low J 9 values; average n values are about 0.73 for J 9 £ 8, nearly constant around 0.68 for 9 £ J 9 £ 30, falling to 0.64 for J 9 near 40 and 0.61 for J 9 near 50. The trends in broadening parameters appear somewhat more clearly in Fig. 3, which shows the measured values as functions of J 9 only for lines in the n1 band with K 9a Å 0. For comparison, we have also included in these plots symbols representing other published measurements of the same

parameters in the n1 and other B-type ozone bands (2, 9– 12, 15, 19, 24) and dashed lines representing the ozone broadening and shift parameters given in the 1992 HITRAN database (33) for R-branch lines with DKa Å /1. The HITRAN air-broadening coefficients are based upon N2-broadening values calculated by Gamache and Rothman (34), and the n value of 0.76 given for all O3 transitions is based upon the mean value from calculations of Gamache (35) for 126 transitions. HITRAN self-broadening coefficients are calculated values from the empirical polynomial expression of Smith et al. (15). Air-induced line shift coefficients are zero for all ozone transitions in the 1992 HITRAN database, and no temperature-dependence of the shifts is given. For the K 9a Å 0 transitions, the HITRAN values are in good agreement with the measurements of b 0A and b 0S (except for selfbroadening for J 9 § 30), but the HITRAN mean n is larger than all but three of the measured values, and most of the measured d 0 values are nonzero. Within their absolute uncertainties, all the various mea-

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FIG. 2. Broadening and shift parameters as functions of J 9 for all lines analyzed in the n1 band. (a) Air-broadening coefficients b 0A . (b) Temperaturedependence exponents n for air broadening. (c) Air-shift coefficients d 0 . (d) Temperature-dependence factors d* for air-shifts. (e) Self-broadening coefficients b 0S . Error bars represent standard deviations as listed in Table 2.

surements of air- and self-broadening parameters in B-type ozone bands are in agreement. Self-broadening coefficients were previously measured in four B-type bands, but airbroadening and shift parameters have been reported for only two of these bands, the pure rotational and n1 transitions. Table 3 compares the mean air-broadening parameters from the present study and other published works (4, 5, 10–12, 19, 24) for B-type bands. Some differences in the mean values occur from one study to another, but most of these can be attributed to variations in the quantum number ranges and distributions of the lines measured. For example, a mean

value of n Å 0.74 was derived from studies of only 13 rotational lines predominantly with J 9 £ 10, while our present study found a mean n Å 0.67 from measurements of over 470 lines with J 9 values mostly between 7 and 47. In Table 4 are given the results of line-by-line comparisons of the present measurements with our previous n1 measurements (12, 15), measurements of rotational lines with the same quantum numbers (10, 11, 19, 24), and the 1992 HITRAN parameters (33). The agreement of the measured broadening coefficients is excellent, with differences of 3% or less for most lines. As can be seen in Fig. 3a for transitions

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FIG. 3. As in Fig. 2 for transitions with K a9 Å 0. Solid circles represent present measurements in the n1 band; open circles: previous measurements in the n1 band (12, 15); open squares: previous self-broadening measurements in the n2 band (15); open inverted triangles: measurements in the pure rotational band (2, 9–11, 19, 24 ); dashed lines in (a), (b), (c), and (e): 1992 HITRAN (33) values for R-branch lines with DKa Å /1. Error bars represent standard deviations for Present Work and Refs. ( 12, 15) and reported uncertainties (if any) for other references.

with K 9a Å 0 the measured air-broadening coefficients agree with the 1992 HITRAN values within {3%. Similar agreement occurs for transitions with K 9a Å 1 and 2. However, for K 9a § 3 the measured air-broadening coefficients are significantly larger than their corresponding HITRAN values, particularly for transitions with J 9 £ 20. Considering these discrepancies, examples of which can be seen in Fig. 4a, it is not surprising that, on average, the 1992 HITRAN air-broadening coefficients are nearly 6% lower than our measured values. The line-by-line comparison also shows

the measured temperature-dependence n values for n1 and rotational lines to be in good agreement, but the 1992 HITRAN n value (0.76 for all ozone lines) is on average 12% higher than our n1 measurements. The air-shift coefficients determined in the present study are somewhat more positive than those from our previous study of the n1 band (12), but the differences are within the uncertainties of the older measurements. We have also examined the available measurements of air- and self-broadening parameters in A-type ozone bands

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FIG. 4. Measured and 1992 HITRAN (33) broadening parameters as functions of K a9 for O3 n1 transitions with J 9 Å 10. Symbols and lines have the same meanings as in Fig. 3.

(7, 13–16, 25), and found them to be consistent with the results of the present study in the B-type n1 band. Because of the lack of temperature-dependent air-broadening measurements outside the rotational band, we have also compared our n1 air-broadening results with temperature-dependent N2-broadening measurements in the A-type n3 (21) and n1 / n3 (26) bands for transitions with matching lower-state quantum numbers. The results are summarized in Table 5. It is interesting to note that the n3 N2-broadening coefficients of Ref. (21) are on average 4% smaller than the corresponding n1 air-broadened values. Other studies where air- or O2and N2-broadening coefficients were measured in the same

band (10, 12, 19, 22, 25, 26) all indicate that the N2-broadening coefficient is usually about 3% larger than the air-broadening value for the same line. Indeed, Table 5 also shows that the n1 / n3 N2-broadening coefficients (26) average 3% larger than the air-broadening coefficients for corresponding n1 transitions. We are not able to unambiguously determine whether the differences with Ref. (21) are due to vibrational-band dependence or to systematic errors in the measurements (or both). We also note that our n1 n exponents for air-broadening average 6% to 8% lower than the those determined for N2-broadening (21, 26). This mean difference is marginally significant, being of the same mag-

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nitude as our absolute uncertainty in determining n, but is not supported by experimental studies of the temperaturedependence of N2- and O2-broadening in the n3 (21, 23) and n1 / n3 (26) vibration–rotation bands and in several rotational transitions (10, 11, 19). Within the uncertainties of these other measurements (typically 10 to 25%), the n value for O2-broadening has always been observed to be equal to or slightly less than the corresponding value for N2broadening for the same ozone transition. In Fig. 3e and Table 4 it appears that the n1 self-broadening coefficients for lines with J 9 £ 6 and K 9a Å 0 determined in the present study may be systematically lower than those determined in our previous study (15) or in studies of rotational lines (2, 9). However, we note that the infrared studies involved spectra measured with O3 partial pressures up to 28 Torr, while the rotational-line studies used sample pressures up to only 1 Torr. Also, our previous determinations of self-broadening coefficients in the n1 band (15) were based on separate least-squares fits of one to four individual spectra, while the present results were determined through simultaneous fitting of 25 to 29 spectra. Therefore we believe

FIG. 5. Measured b 0A and b 0S vs K a9 for n1 R-branch lines with DKa Å /1 and J 9 Å 8–12. For clarity, symbols for the same J 9 values are connected by solid, dashed, or dotted lines. Error bars represent standard deviations as given in Table 2.

FIG. 6. Comparison of broadening coefficients vs J 9 for R-branch ( D J Å /1) O3 transitions with K a9 Å 1. Large circles: n1 air-broadening measurements (present work); triangles: n1 / n3 N2-broadening measurements (22, 26); small circles connected by lines: calculated N2-broadening (36). Error bars represent absolute uncertainties of the measured values. Open symbols indicate transitions with K c9 Å J 9, while solid symbols correspond to K c9 Å J 9 0 1. Note that DKa Å {1 in the n1 band, while DKa Å 0 in the n1 / n3 band and in the calculations.

that our present results are more reliable. We note that the 1992 HITRAN (33) self-broadening coefficients, calculated using an empirical expression derived from our previous study (15), are in very good agreement with the present measurements for J 9 £ 30. For each J 9 in Fig. 2 there is usually a range of values of the broadening and shift parameters. The distributions of these values are not entirely due to random error; particularly for the broadening coefficients there appears to be a strong dependence on the second rotational quantum number K 9a . As an illustration, in Fig. 4 the broadening and shift parameters for lines in the n1 band with J 9 Å 10 are plotted as functions of K 9a along with previous measurements and 1992 HITRAN values (33) as in Fig. 3. The remarkable features of the curve defined by the solid circles in Fig. 4a are the nearly constant air-broadening coefficient values over most of the range of K 9a and the sharp drop-off as K 9a approaches J 9. We note that the HITRAN values show a nearly opposite trend: broadening coefficients decreasing as K 9a increases from 0 to 4, then leveling off. For self-broadening (Fig. 4(e)), the measured b 0S coefficients also decrease as K 9a approaches J 9, but do not fall off as abruptly as for airbroadening. These distributions of air- and self-broadening coefficents with K 9a are observed in the n1 band not only for J 9 Å 10, but also for four other series of lines with J 9 Å 8 through J 9 Å 12 (see Fig. 5). A series of significantly smaller-than-average air-broadening coefficients for K 9a Å J 9 lines also appears distinctly in Fig. 2a for 5 £ J 9 £ 12. In Fig. 4b the distribution of n values with K 9a for J 9 Å 10 shows a small decrease in n as K 9a increases. This trend also appears for other J 9 values in the n1 band. For all the

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TABLE 3 O3 Air-Broadening Measurements in B-Type Bands

J 9 values measured, average n values are about 0.70 for lines with K 9a £ 4, falling to about 0.63 for lines with K 9a § 8. The calculations of Gamache (35) for the temperaturedependence of N2-broadening show some decrease in n for K 9a § 7 or 8, but the magnitude of this decrease is less than we have observed for air-broadening in the n1 band. TABLE 4 Results of Line-by-Line Comparison of Parameters

We observe in Fig. 4 that there are no apparent trends in the air-shift parameters d 0 and d* with K 9a for lines with J 9 Å 10, and this is also true for the transitions with other J 9 values we have measured. Variations in these parameters with K 9a may be undetectable because of the small magnitudes and relatively large uncertainties of the measured d 0 and d* values in the n1 band. More comprehensive studies in the higher vibration–rotation bands, which have larger pressure-induced line shifts, should provide greater insight. Recently Neshyba and Gamache (36) have developed an improved calculation of broadening coefficients for asymmetric rotor molecules which appears to reproduce well observed N2broadening coefficients in the n1 / n3 band of O3 (22). In Fig. 6 we have expanded Fig. 3 of Ref. (36) to include an TABLE 5 Comparison of Temperature-Dependent Air- and N2-Broadening Parameters for Transitions with Matching J9 K9a K9c

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O3 n1 BROADENING AND SHIFTS

additional measured N2-broadening value in the n1 / n3 (26) band and our measured air-broadening coefficients for the n1 band. For clarity, only measurements and calculations for Rbranch ( D J Å /1) transitions with K 9a Å 1 are plotted. There is reasonably good agreement between the calculations and the measurements over the relatively small range of 15 £ J 9 £ 25 for which the calculated values are given. However, a visual extrapolation of the calculated curves toward lower J 9 suggests that the calculations may overestimate the measured values at low J 9. We note that our n1 air-broadening measurements for J 9 § 13 verify the theoretical prediction of larger broadening coefficients for transitions with K 9c Å J 9 0 1, relative to those for K 9c Å J 9. CONCLUSIONS

We have determined air-broadening and shift coefficients and their temperature dependences, as well as self-broadening coefficients, for 450 O3 absorption lines in the 9-mm region. Few of these parameters had previously been measured; however, the present measurements are in agreement with most previous measurements in the n1 band and other bands. The present measurements cover an extensive range of rotational quantum numbers in the n1 band, allowing for the first time a detailed examination of the variation of broadening parameters within the band. Significant discrepancies between the measured air-broadening coefficients and those on the 1992 HITRAN database (33) were found for lines with K 9a § 3. In addition, the values of the air-broadening temperature-dependence exponent n determined from the measurements were on average 12% smaller than the 1992 HITRAN value. The airshift coefficients are consistent with and have improved accuracy over previous measurements (12), and their temperature dependences are reported here for the first time, although with considerable uncertainty. Additional theoretical studies are needed to accurately model these observations. ACKNOWLEDGMENTS We are grateful to Charles T. Solomon and Harry G. Walthall of the glass shop at NASA Langley Research Center for assistance in the design, construction, and testing of the ozone generator system and the sample cells. We also thank Claude Plymate and Jeremy Wagner of the National Solar Observatory for their assistance in recording the FTS spectra, Greg Ladd for initial processing of the spectra at NSO, and the late Carolyn Sutton of SAIC for preliminary processing of the spectra at NASA Langley Research Center. Research at the College of William and Mary is supported by the National Aeronautics and Space Administration.

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