- Email: [email protected]
Air-Broadening and Shift Coefficients of O3Lines in the ν2Band and Their Temperature Dependence
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO .
182, 221–238 (1997)
MS967139
Air-Broadening and Shift Coefficients of O3 Lines in the n2 Band and Their Temperature Dependence V. Malathy Devi,* D. Chris Benner,* M. A. H. Smith,† and C. P. Rinsland† *The College of William and Mary, Williamsburg, Virginia 23187-8795; and †Atmospheric Sciences Division, NASA Langley Research Center, Hampton, Virginia 23681-0001 Received May 23, 1996; in revised form July 16, 1996
Room temperature measurements of self- and air-broadening coefficients are reported for over 370 transitions covering a range of 0 £ J 9 £ 45 and 1 £ K a9 £ 12 for the n2 ozone band in the 630 to 800 cm01 spectral region. In addition, the temperature dependence of air-broadened halfwidth and air-induced pressure shift coefficients have been determined for over 350 spectral lines. A total of 29 O3 absorption spectra (0.005-cm01 resolution) recorded at various temperatures (29 to 0637C) with a Fourier transform spectrometer were used in the analysis. The spectral line parameters were deduced by analyzing all of the 29 spectra simultaneously using a nonlinear least-squares fitting technique. The results are compared with similar measurements obtained in the ozone n1 band. q 1997 Academic Press INTRODUCTION
Reliable values for spectral line parameters such as zero pressure position n0 , intensity S(T ), halfwidth coefficient b 0L (T, P), pressure-induced shift coefficient d 0 (T, P), the temperature dependence n of the halfwidth coefficient, and d*, the temperature dependence of the pressure-induced shift coefficient of ozone spectral lines are required for accurate quantification of radiative transfer properties of O3 in the Earth’s atmosphere. Precise knowledge of O3 spectroscopic parameters are also needed, especially in the infrared, for remote sensing studies of the terrestrial atmosphere such as the Halogen Occultation Experiment (HALOE). Many of these spectroscopic line parameters have recently been published from analyses of high-resolution laboratory measurements of O3 in several spectral regions (1–23). From some of these studies halfwidth and pressure-induced shift coefficients for several hundred lines of ozone broadened by air, nitrogen, and oxygen are known (7, 20, 23). The majority of the studies made measurements at ambient temperatures. Spencer and co-workers recently published measurements of n for several nitrogen- and oxygenbroadened ozone transitions in the n3 band (20, 22). In the microwave spectral region, Colmont and Monnanteuil (8) and Connor and Radford (9) published measurements of the temperature dependent exponent n for a few pure rotational transitions. Using Quantum Fourier Transform theory (QFT) Gamache and Rothman (24) reported theoretical halfwidth and pressure-induced shift coefficients for all unique rotational transitions of ozone perturbed by nitrogen for J £ 35. Using the same method, Gamache ( 25) published the temperature dependence of N2-broadened halfwidth coeffi-
cients for the same 126 transitions of ozone from J 9 Å 1 to 35. Later Gamache and Davies (26) reported halfwidth and pressure-induced shift coefficients for N2 , O2 , and air broadening of ozone calculated by the ATC (Anderson–Tsao– Curnutte) method and by the QFT method. More recently, Hartmann and co-workers (27) made new calculations of ozone broadening by N2 and O2 for B-type bands. Apart from Spencer et al.’s (20, 22) measurements in the n3 band, the experimental measurements of broadening and pressureshift coefficients of Smith et al. (28) for more than 440 transitions in the n1 band are the only other measurements below room temperature. In the infrared region the majority of ozone broadening and pressure-induced shift coefficients reported in the literature pertain to the n1 and the n3 fundamentals. Except for the self-broadened halfwidth coefficients of 72 transitions measured by Smith et al. (16), there are no other experimental or calculated halfwidth or pressureinduced shift measurements published for n2 lines. In this paper we present the first experimental determination of airbroadened halfwidth coefficients for 393 rovibrational transitions in the n2 fundamental. For almost all of these lines we also present the first experimental measurements of the air-induced pressure shift coefficient and its temperature dependence, and the temperature dependence of the air-broadened halfwidth coefficients. In addition, self-broadening coefficients at room temperature have been determined for 374 of these lines. EXPERIMENTAL DETAILS
The 0.005 cm01 resolution spectra used in this study are the same as those analyzed for the n1 band by Smith et al.
221 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7139
/
6t12h$$221
03-11-97 16:10:26
mspas
222
MALATHY DEVI ET AL.
TABLE 1 Experimental Conditions
(28). They were obtained at various temperatures between room temperature and 0637C using the McMath–Pierce Fourier transform spectrometer (FTS) of the National Solar Observatory (NSO) on Kitt Peak. The spectra were recorded during two different experiments, both using 50 cm absorption cells, one at room temperature and the other coolable. Two room temperature spectra of pure O3 and seven room temperature air-broadened O3 spectra were analyzed in combination with 20 additional spectra of ozone diluted with dry air at temperatures between 17C and 0637C. The two pure ozone spectra provided additional information to determine the self-broadening coefficients at room temperature. These two spectra also constrained the zero pressure line center positions. The FTS experimental setup consisted of a glower light source at approximately 2000 K, a KCl beam splitter, and two liquid helium cooled As-doped Si detectors. The spectral band pass for five of the room temperature spectra was limited to 450–1450 cm01 and for the low-temperature spectra it was 550–2750 cm01 . For the room temperature data we used a Pyrex absorption cell 50-cm long, 5.08 cm in diameter fitted with Teflon valves. Potassium chloride windows cemented to the cell were slightly wedged (5–10 mrad) to prevent channeling resulting from multiple reflections. For the low-temperature measurements we used a 50 cm cooled cell, a double walled Pyrex glass tube with KCl wedged windows which was enclosed in an evacuated metal chamber with wedged KCl windows. The cell temperature was regulated by circulating chilled ethanol through the space between the double glass wall. Further details regarding the coolable cell may be found in Ref. (29).
Ozone samples were prepared using the silent electric discharge and a research grade natural isotopic sample of oxygen. A summary of the experimental conditions of the present work is given in Table 1. For the low-temperature spectra lean O3 –air mixtures were prepared by initially filling the cell with pure O3 (5 to 28 Torr) and then adding research grade dry air to the sample until the total pressure reached about 250 Torr. In each series of spectra (Table 1) the spectrum with the highest total pressure was recorded first, and the subsequent lower pressure spectra were obtained by pumping out some of the gas sample. For each spectrum the sample pressure and temperature were monitored continuously during the approximately 1 hr integration time. The total pressure measurements are accurate to {0.1% and the temperature measurements are accurate to {17C. Calibration of the wavelength scale of the spectra was achieved using the n2 band water vapor line positions reported by Toth (30). These water vapor lines appeared in our spectra due to residual H2O within the evacuated interferometer tank and the dry nitrogen purged atmospheric paths between the source and the entrance aperture of the interferometer where the absorption cell containing the ozone sample was kept. The positions of the narrow (low pressure) component of these H2O lines were used for the calibration. DATA ANALYSIS
The room temperature self- and air-broadened halfwidth coefficient, the air-induced pressure shift coefficient, and the temperature dependence of air-broadened halfwidth and
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$222
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
223
pressure-induced shift coefficients were determined by fitting all 29 spectra (Table 1) together using a simultaneous least-squares fitting program (31). The spectra were analyzed by fitting 1 to 2 cm01 segments at a time using the program interactively. Using this technique, we retrieved several line parameters (e.g., zero pressure position, pressure-induced shift, temperature dependence of the pressureinduced shift, pressure-broadened halfwidth coefficient, and the temperature dependence of the halfwidth coefficient) simultaneously. The absorption lines were assumed to have Voigt lineshapes. Initial values for the line parameters were taken from the 1992 HITRAN database (32). In the global least-squares fitting program, except for the temperature dependence of pressure shift coefficients, d*, the various retrieved parameters were determined using the following expressions: bL Å b 0L (T )p, n Å n0 / d 0 (T )p,
[1]
b 0L (T ) Å b 0L (T 0 )(T 0 /T ) n , and
d 0 (T ) Å d 0 (T 0 ) / d* (T 0 T 0 ).
In these expressions, bL represents the Lorentz halfwidth coefficient (in cm01 ) at pressure p, n0 is the zero pressure line position (in cm01 ), and n is the line position at pressure p. The temperature dependence of the halfwidth coefficient is n, b 0L (T ) is the halfwidth coefficient at temperature T. The Lorentz broadening coefficient at the reference temperature T 0 (296 K) is b 0L (T 0 ). The temperature dependence of the pressure-induced shift coefficient is d*, and d 0 (T ) and d 0 (T 0 ) represent the pressure-induced shift coefficient at temperatures T and T 0 (296 K), respectively. RESULTS AND DISCUSSION
In Fig. 1 we show an example of a multispectrum fit of O3 lines near 722 cm01 . This figure illustrates that all 29 spectra could be simultaneously fit with one unique set of line parameters. This is very important with halfwidths and shift measurements at various temperatures. Such a fit constrains well the position of each line needed for accurate shift coefficients. When the spectra are fit individually in a crowded overlapping region such as that shown in this figure, the positions and widths of neighboring lines may wander and not be accurately determinable. Figure 1 proves that all 29 spectra are simultaneously fit to the same noise level and indicates that there are no major discrepancies in the parameters derived. The residuals from the least-squares fit (magnified by a factor of 10) are displayed in the top panel. Because the n2 region is close to the edge of the spectral band pass, the signal-to-noise ratio (S/N) is relatively poor
FIG. 1. Example of a 29 spectra nonlinear least-squares fit in the 722 cm01 region in the n2 band of ozone. The experimental conditions of the fitted spectra are summarized in Table 1. The calculated spectra are shown in the lower panel and the magnified residuals (observed minus calculated) resulting from the least-squares fit expressed as a fraction of peak intensity in the fitted region are shown in the upper panel. The positions of absorption lines included in the least-squares fit are shown by tick marks on the top axis of the lower panel.
(100 to 250) in comparison to that in the region of the n1 band (200 to 500). We were not able to determine reliable O3 self-shift coefficients from the spectra because of the limited S/N and the low O3 pressures used in the experiments. Self-broadened halfwidth coefficients for 72 n2 transitions were reported earlier by Smith et al. (16). The values determined for b 0L (self), b 0L (air), n(air), d 0 (air), and d* (air) from this work are listed in Table 2. Room temperature air-broadening coefficients, b 0L (air), have been determined for 393 lines.
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$222
03-11-97 16:10:26
mspas
224
MALATHY DEVI ET AL.
TABLE 2 Measured Spectral Line Parameters for the n2 Band of Ozone
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
225
226
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
227
228
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
229
230
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
231
TABLE 2—Continued
In addition, room temperature air-broadening coefficients for five 2n2 – n2 lines are also determined, and are listed in the last five rows of Table 2. Because of the inherent weakness of this band (compared to n3 and n1 ) and the low ( õ15%) volume mixing ratios of O3 samples used, for many weak n2 transitions we were able to determine only room
temperature air-broadening coefficients. Transitions for which we were unable to determine the temperature dependence of the air-broadening or pressure-induced shift coefficients had n(air) and d* values constrained to 0.55 and 0, respectively, and are indicated by blank spaces in Table 2. Initial measurements of several strong, well separated lines
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
232
MALATHY DEVI ET AL.
FIG. 2. (a) Measured air-broadening coefficient, b 0L (air), at 296 K vs J 9; (b) the temperature-dependent exponent n(air) of air-broadening coefficients plotted as a function of J 9; (c) measured self-broadening coefficient, b 0L (self), at 296 K plotted as a function of J 9; and (d) temperature-dependent exponent n(air) as a function of b 0L (air). The error bars indicate one standard deviation uncertainty in the measured quantities. Where no error bars are displayed, the standard deviation is smaller than the size of the symbol. In (a) – (d), open circles correspond to K a9 £ J 9 transitions and filled circles correspond to transitions with K a9 Å J 9.
gave n(air) values varying between 0.5 and 0.6 and therefore we chose to use the value of n(air) Å 0.55 for these weak lines instead of n(air) Å 0.76 given in the 1992 HITRAN database (32). If the room temperature self-broadening coefficient of a transition was not determined, its value was constrained to that given in Ref. (32). Column 1 of Table 2 gives the wavenumber (cm01 ) of each measured spectral line along with its standard error in units of the last digit obtained from the present least-squares analysis. The assignments given in columns 2–7 are from Ref. (32). The values given in parentheses indicate onesigma standard error in the measured quantities in units of the last digit quoted. As discussed in our previous studies (31, 33), in the multispectrum fitting technique, the quoted errors in the retrieved parameters represent the uncertainties due to random errors such as the noise level in the spectra and other fitted parameters only. By fitting a large number of spectra simultaneously these random errors are decreased to very small values. However, in order to determine the absolute uncertainties in the retrieved parameters, errors associated with the measurements of gas pressure and gas
temperature, uncertainties in the line parameters such as position and intensity, uncertainties in the wavelength calibration of the spectra, and errors involved in the spectral line shape must also be considered. The determination of all these uncertainties is certainly a nontrivial problem. Based upon our knowledge of the accuracies in these parameters we estimate that the absolute uncertainties in our broadening and shift measurements and their temperature dependences may, however, be determined by adding an additional 2% in b 0L , 0.0002 cm01 atm01 in d 0 , 0.05 in n(air), and 0.00001 cm01 atm01 K 01 in d* to the errors indicated in Table 2. The uncertainties indicated in Table 2 are appropriate for comparison between values in the table. (a) b 0L (air) and n(air) The broadening coefficients b 0L (air) and their temperature dependence n(air) listed in Table 2 are plotted as a function of J 9 in Figs. 2a and 2b, respectively. The error bars denote one standard deviation listed in Table 2. In Fig. 2c we have plotted b 0L (self) as a function of J 9. Consistent with our
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
233
FIG. 3. (a) Observed air-broadening coefficient, b 0L (air), for J 9 Å 11 at 296 K and (b) the temperature dependence n(air), of the air-broadened halfwidth coefficient for J 9 Å 11 as a function of the lower state rotational quantum number K a9 . The open circles correspond to results for the n2 band and the filled circles correspond to those for the n1 band. The values for the n1 band are from Ref. (28). The solid curve in (b) corresponds to calculated n values for N2 broadening from Gamache (25). Because no calculated values have been explicitly reported for b 0L (N2 ) for J 9 Å 11 there is no solid curve plotted in (a). (c) and (d) display the same parameters for J 9 Å 20.
earlier studies on other ozone bands (10, 16, 23, 28), it is clearly seen in Figs. 2a and 2c that b 0L decreases with increasing J 9 for both air and self broadening. However, such a definite trend is not observed among the n values plotted in Fig. 2b. The scatter in the n(air) values for a fixed J 9 in Fig. 2b reflect the K-dependent variations in n for any given J 9 value. In Fig. 2d we have examined the correlation between the halfwidth coefficient and its temperature dependence. A very weak negative correlation of n(air) with respect to b 0L (air) may be noticed. The open circles in these figures represent K 9a £ J 9 lines and the filled circles correspond to K 9a Å J 9 transitions. It is clearly seen that for a particular J 9, the halfwidth coefficients have the smallest value for the J 9 Å K 9a transitions. The selection rule governing the ozone transitions is K 9a / K 9c Å J 9 or J 9 / 1 and the highest K 9a value we were able to observe in this study was 12 (Table 2). While a small decrease in n with J 9 was observed in the n1 band (28), the n value in the n2 band does not reveal any noticeable dependence on the rotational quantum number J 9. This may be attributed to the higher
uncertainties in the retrieved parameters in the n2 region due to lower S/N in this region of the spectra. Details of the K 9a dependence of the broadening coefficients and n values for one of the J 9 (J 9 Å 11) values are shown in Fig. 3. In Figs. 3a and 3b the open circles show the results obtained for the n2 band and the filled circles correspond to those for the n1 lines (28). In both bands the values for b 0L gradually increase with K 9a , reach a maximum around K 9a Å 6 or 7, and then decrease rapidly to reach the minimum value when K 9a Å J 9. In Fig. 3b one may notice a slight decrease of n with increasing K 9a values in both the n1 and n2 bands. It is obvious that the n values are larger in the n1 band than in the n2 band. The solid curve in Fig. 3b shows n vs K 9a calculated for nitrogen broadening for ozone by Gamache (25). Since no calculated N2-broadening coefficients were explicitly reported in Ref. (25), a solid curve similar to that in Fig. 3b is not available in Fig. 3a. Based upon his calculations, Gamache suggested an average n value of 0.76 for air broadening in all ozone bands. Following the conventional Anderson–Tsao–Curnutte theory, Tej-
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
234
MALATHY DEVI ET AL.
FIG. 4. (a) Measured b 0L (air) vs K a9 for J 9 Å 8, 9, 10, 11, and 12. (b) Measured n(air) vs K a9 for J 9 Å 8, 9, 10, 11, and 12. (c) Measured pressure shift coefficients, d 0 (air), vs K a9 for J 9 Å 8 through 12 in the n2 band of ozone. The horizontal solid line corresponds to zero pressure shift coefficients. Most measured shift coefficients are negative. (d) Measured temperature dependence exponent d* of shift coefficients vs K a9 are plotted for J 9 values of 8 through 12. The horizontal solid line represents d* Å 0.
wani and Yeung (34) reported mean temperature exponent values of n Å 0.68 and n Å 0.73 for A- and B-type transitions, respectively. Both the n1 and n2 bands of ozone are B-type transitions. Gamache (25) in his calculations did not find any difference in the average temperature exponent values between A- and B-type transitions. However, his results showed that n values are transition dependent and the fluctuation about the average value was small ( {6%). Our measurements also showed n values to be transition dependent, but the variations are found to be much larger than {6%. From the 357 measurements in the n2 band we obtained a mean and standard deviation of n Å 0.53 { 0.08. This is significantly smaller than the mean n value of 0.67 { 0.07 obtained for over 440 n1 lines measured in the same spectra (28). Note that the standard deviations associated with the mean values are in fact one standard deviation scatter in the mean values and do not represent the measurement uncertainties. Figures 3c and 3d show the variations with K 9a of the airbroadening coefficients at 296 K and n values for lines with J 9 Å 20 in both the n2 and n1 bands. For the purpose of
comparisons, we have also included in these figures solid curves indicating the calculated N2-broadening coefficients at 296 K from Gamache and Rothman (24) and the calculated n values from Gamache (25). The air-broadening coefficients in the 1992 HITRAN database (32) are based upon a scaling of these calculated N2-broadening values. It is clear from these figures that the calculated broadening coefficients are too small and the n values too large compared to corresponding measured values in the present work on the n2 band. Previous calculations of O3 line broadening made with the Anderson–Tsao–Curnutte approach or the QFT-ID models both seem to systematically underestimate O3 broadening, especially broadening by O2 . Bouazza et al. (21) discussed this subject. Comparisons made between the 394 measured air-broadened halfwidth coefficients presented in Table 2 and those reported in the 1992 HITRAN database (32) gave 1.09 { 0.07 as the mean and standard deviation for the ratio of measurement to calculation. Gamache (25) observed dependence of n upon K 9a by plotting calculated values of n vs K 9a for a series of lines with J Å 5, 11, and 20. In cases where several transitions (for a given J 9 ) had
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
235
the same K 9a , the n values were averaged and the mean values were used in producing the plots. In Figs. 4a and 4b we have plotted b 0L (air) vs K 9a and n(air) vs K 9a , respectively, for J 9 values of 8 through 12. We plot all measured values of b 0L and n (without averaging the values of b 0L and n for cases where for a given J 9 there was more than one transition with same K 9a ). As expected, variation in b 0L with K 9a is clearly seen in Fig. 4a and a weak decrease of n with K 9a is vaguely noticeable in Fig. 4b. The use of the multispectrum fitting technique allowed us to also determine over 375 self-broadened halfwidth coefficients compared to only 72 values in our previous work (16) obtained from a spectrum-by-spectrum analysis technique. From the 63 lines that are common in both studies we obtained the mean and standard deviation of 1.01 { 0.04 for the ratio of the present results divided by the previous results. We also compared the self-broadening coefficients in the n2 band with those obtained from these same spectra for n1 transitions having the same rotational quantum numbers. For the approximately 150 identical (both upper and lower rotational quantum numbers same) transitions compared, on average n2 values are 5% larger. The results are given in Table 3. (b) d 0 (air) and d* (air) Similar to the broadening coefficients, b 0L (air), the pressure-induced shift coefficients, d 0 (air), and their temperature dependence, d* (air), also depend upon the transition studied. In an attempt to reveal any trends in d 0 (air) or d* (air), we have plotted d 0 (air) and d* (air) for J 9 Å 8 through 12 in Figs. 4c and 4d, respectively, vs K 9a . There is no observable dependence of either d 0 (air) or d* (air) on J 9 or K 9a in our measurements. In Figs. 5a and 5b we have plotted d0 (air) vs J 9 and d* (air) vs J 9, respectively. About 70% of measured pressure-induced shift coefficients and 52% of d* values were found to be negative. From approximately 360 measurements, we obtained means and standard deviations of 00.0008 { 0.0017 cm01 atm01 at 296 K and 00.2 { 2.9 1 10 05 cm01 atm01 K 01 for the d 0 and d* values, respectively. Except for the one previous study on self-broadening coefficients for 72 lines (16), no other measurements or calculations seem to be reported on broadening coefficients, pressure-induced shift coefficients, or their temperature dependences for lines of the n2 band. However, b 0L (self), b 0L (air), n(air), d 0 (air), and d* (air) for the n1 band of O3 using the same set of spectra as in this work have recently been measured by Smith et al. (28) and in Table 3 we have compared the average values determined for these two bands. In Figs. 6a–6d we have plotted the measured airbroadening and pressure-induced shift coefficients and their temperature dependence for the 150 identical rovibrational transitions in the n2 and the n1 bands. From Fig. 6a it appears
FIG. 5. (a) Observed pressure-induced shift coefficient d 0 (air) and (b) the temperature dependence of measured shift coefficients d* (air) vs J 9 for all measured transitions in this study.
that there is a small vibrational dependence of the Lorentz air-broadening coefficients. From the 150 measurements for which comparisons could be made, the average and standard deviation for the ratio of b 0L (air) in the n2 to n1 band are found to be 1.03 and 0.04, respectively. Although the magnitude of this vibrational dependence is not significant relative to absolute uncertainties, the differences seem to be real as shown in Fig. 6a. We have observed vibrational dependence in broadening and pressure-induced shift coefficients previously in several O3 and CH4 bands (23, 28, 33). However, vibrational dependences in the n and d* values have not been observed or predicted so far for any of the ozone bands. As shown in Fig. 6b the differences in the n values between these two bands are more pronounced than the differences in the air-broadening coefficients. The means and standard deviations of the n(air) values in the n2 and n1 bands (from the 150 identical transitions) are 0.53 { 0.07 and 0.68 { 0.08, respectively. At this time we are not able to explain the reason for this large difference. In Figs. 6c and 6d the
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
236
MALATHY DEVI ET AL.
TABLE 3 Comparison of Line Parameters between the n2 and n1 Bands of O3
d 0 (air) and d* (air) values measured for these two bands are plotted and no noticeable vibrational dependence in either d 0 (air) or d* (air) is apparent. One has to be very careful in interpreting the accuracy we have stated for the various retrieved parameters. We have given an estimate for the absolute uncertainties as well as the precision for the retrieved parameters. The uncertainties associated with each measured quantity given in Tables 2 and 3 are based upon systematic errors (errors in wavelength calibration, temperature and pressure measurements etc.) which appear in both studies we have compared. The values determined for air-induced shift coefficients d 0 (air) and their temperature dependence d* (air) are indeed very small quantities. This is especially true in the n2 band, where they are often small enough to be below our measurement capability. The measurements, however, provide an upper limit to these parameters. When results are compared between the two bands (e.g., b 0L and n in n2 and n1 ) the errors we have quoted in Table 3 are in fact the scatter from the mean measured values and errors of the systematic nature described previously should not be added. CONCLUSIONS
The data presented in this investigation are the first experimental measurements of air-broadened Lorentz halfwidth coefficients, pressure-induced shift coefficients, and the temperature-dependent air-broadened halfwidth and pressure-induced shift coefficients for ozone in the n2 fundamental
band. In addition, we have determined ozone self-broadened halfwidth coefficients for a larger number of transitions than were measured in our previous study. We have measured 393 air-broadened halfwidth coefficients, b L0 ( air ) , 374 self-broadened halfwidth coefficients, b 0L (self), 362 pressure-induced shift coefficients d 0 (air), 357 temperature-dependent halfwidth coefficients, n(air), and 355 temperaturedependent pressure-induced shift coefficients d* (air). Comparisons of self-broadened halfwidth coefficients determined in this work using the multispectrum fitting technique gave good agreement with our previous study made by a spectrum-by-spectrum analysis procedure, but the new technique made it possible to reduce the uncertainties in the measured halfwidth coefficients and to derive many more self-broadened halfwidth coefficients. The measured self- and air-broadened halfwidth coefficients, pressure-induced shift coefficients, and their temperature dependence are found to be transition dependent. Of the total, 70% of the shift coefficients and 52% of the coefficients of the temperature dependence of the pressure-induced shifts are negative. Comparisons between the n2 and n1 ozone bands revealed some interesting results. The mean values obtained for the self- and air-broadened halfwidth coefficients in the n2 band are 3 and 5% larger, respectively, than the corresponding values measured in the n1 band. The mean values of pressureinduced shift coefficients and their temperature exponents for the two bands are within their respective experimental uncertainties. The largest difference is observed between the temperature dependence of air-broadened halfwidth coefficients. The
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
237
OZONE n2 BROADENING AND SHIFTS
FIG. 6. Comparison of (a) air-broadened halfwidth coefficients b 0L (air), (b) temperature dependence n(air) of the air-broadened halfwidth coefficients, (c) pressure-induced shift coefficients d 0 (air), and (d) temperature dependence d* (air) of the pressure shift coefficients between the n2 and the n1 lines of ozone. The results for the n1 band are from Ref. (28). The error bars denote one standard deviation in the measured quantities. The straight lines passing through the origin in these graphs correspond to equality of the plotted quantities.
average value for n(air) in the n2 band is 0.53 with a one standard deviation scatter of 0.08 and for the n1 band the average n(air) value is 0.67 with a one standard deviation scatter of 0.07. Both these values are significantly smaller than the HITRAN n(air) value of 0.76 assumed to be the same for all bands of ozone. The results presented in this investigation should prove useful for interpreting infrared remote sensing studies of the terrestrial atmosphere and for radiative transfer calculations. The measured parameters from this study will be made available for inclusion in the next update of the HITRAN database. ACKNOWLEDGMENTS We thank Charles T. Solomon and Harry G. Walthall of the Fabrication Division at NASA Langley Research Center for their help in designing and building the coolable glass cell. We also thank Claude Plymate and Jeremy Wagner of the National Solar Observatory (NSO) for their assistance in recording the data and Gregg Ladd at NSO for the initial processing of the spectra. Research at the College of William and Mary is supported by cooperative agreements with the National Aeronautics and Space Administration. NSO is operated by the Association of Universities for Research in Astronomy, Inc., under contract with NSF.
REFERENCES 1. R. T. Menzies, Appl. Opt. 15, 2597–2599 (1976). 2. S. Lundqvist, J. Margolis, and J. Reid, Appl. Opt. 21, 3109–3113 (1982). 3. C. Meunier, P. Marche, and A. Barbe, J. Mol. Spectrosc. 95, 271–275 (1982). 4. J. M. Hoell, C. N. Harward, C. H. Bair, and B. S. Williams, Opt. Eng. 21, 548–552 (1982). 5. A. Barbe, P. Marche, C. Meunier, and P. Jouve, J. Physique 44, 1015– 1017 (1983). 6. N. Monnanteuil and J. M. Colmont, J. Quant. Spectrosc. Radiat. Transfer, 29, 131–136 (1983). 7. J. S. Margolis, J. Quant. Spectrosc. Radiat. Transfer 29, 539–542 (1983). 8. J. M. Colmont and N. Monnanteuil, J. Mol. Spectrosc. 104, 122–128 (1984). 9. B. J. Connor and H. E. Radford, J. Mol. Spectrosc. 117, 15–29 (1986). 10. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, D. Chris Benner, and K. B. Thakur, J. Opt. Soc. Am. B. 5, 585–592 (1988). 11. J.-M. Flaud, C. Camy-Peyret, C. P. Rinsland, M. A. H. Smith, and V. Malathy Devi, ‘‘Atlas of Ozone Spectral Parameters from Microwave to Medium Infrared.’’ Academic Press, Cambridge, MA, 1990. 12. C. Flannery, J. J. Klassen, M. Gojer, J. I. Steinfeld, M. Spencer, and C. Chackerian, Jr., J. Quant. Spectrosc. Radiat. Transfer 46, 73–80 (1991).
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$224
03-11-97 16:10:26
mspas
238
MALATHY DEVI ET AL.
13. M. N. Spencer and C. Chackerian, Jr., J. Mol. Spectrosc. 146, 135– 142 (1991). 14. A. Barbe, S. Bouazza, and J. J. Plateaux, Appl. Opt. 30, 2431–2436 (1991). 15. J. J. Plateaux, S. Bouazza, and A. Barbe, J. Mol. Spectrosc. 146, 314– 325 (1991). 16. M. A. H. Smith, C. P. Rinsland, and V. Malathy Devi, J. Mol. Spectrosc. 147, 142–154 (1991). 17. J. J. Oh and E. A. Cohen, J. Quant. Spectrosc. Radiat. Transfer 48, 405–408 (1992). 18. A. Barbe, J. J. Plateaux, S. Bouazza, J.-M. Flaud, and C. Camy-Peyret, J. Quant. Spectrosc. Radiat. Transfer 48, 599–610 (1992). 19. N. Sokabe, M. Hammerich, T. Pedersen, A. Olafsson, and J. Henningsen, J. Mol. Spectrosc. 152, 420–433 (1992). 20. M. N. Spencer, C. Chackerian, Jr., C. Flannery, and J. I. Steinfeld, Spectrochim. Acta A 48, 1273–1281 (1992). 21. S. Bouazza, A. Barbe, J. J. Plateaux, L. Rosenmann, J. M. Hartmann, C. Camy-Peyret, and J.-M. Flaud, J. Mol. Spectrosc. 157, 271–289 (1993). 22. M. N. Spencer, C. Chackerian, Jr., C. Flannery, and J. I. Steinfeld, J. Quant. Spectrosc. Radiat. Transfer 49, 525–533 (1993). 23. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, and E. S. Prochaska, J. Mol. Spectrosc. 164, 239–259 (1994); Erratum, J. Mol. Spectrosc. 165, 596 (1994).
24. R. R. Gamache and L. S. Rothman, Appl. Opt. 24, 1651–1656 (1985). 25. R. R. Gamache, J. Mol. Spectrosc. 114, 31–41 (1985). 26. R. R. Gamache and R. W. Davies, J. Mol. Spectrosc. 109, 283–299 (1985). 27. J. M. Hartmann, C. Camy-Peyret, J.-M. Flaud, J. Bonomy, and D. Robert, J. Quant. Spectrosc. Radiat. Transfer 40, 489–495 (1988). 28. M. A. H. Smith, V. Malathy Devi, D. Chris Benner, and C. P. Rinsland, manuscript submitted to J. Mol. Spectrosc. (1996). 29. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, and D. Chris Benner, Spectrochim. Acta A 48, 1257–1272 (1992). 30. R. A. Toth, J. Opt. Soc. Am. B 8, 2236–2255 (1991). 31. D. Chris Benner, C. P. Rinsland, V. Malathy Devi, M. A. H. Smith, and D. Atkins, J. Quant. Spectrosc. Radiat. Transfer 53, 705–721 (1995). 32. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. Chris Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 48, 469 – 507 ( 1992 ) . 33. V. Malathy Devi, D. Chris Benner, M. A. H. Smith, and C. P. Rinsland, J. Quant. Spectrosc. Radiat. Transfer 51, 439–465 (1994). 34. G. D. T. Tejwani and E. S. Yeung, J. Chem. Phys. 63, 1513–1517 (1975).
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$224
03-11-97 16:10:26
mspas
182, 221–238 (1997)
MS967139
Air-Broadening and Shift Coefficients of O3 Lines in the n2 Band and Their Temperature Dependence V. Malathy Devi,* D. Chris Benner,* M. A. H. Smith,† and C. P. Rinsland† *The College of William and Mary, Williamsburg, Virginia 23187-8795; and †Atmospheric Sciences Division, NASA Langley Research Center, Hampton, Virginia 23681-0001 Received May 23, 1996; in revised form July 16, 1996
Room temperature measurements of self- and air-broadening coefficients are reported for over 370 transitions covering a range of 0 £ J 9 £ 45 and 1 £ K a9 £ 12 for the n2 ozone band in the 630 to 800 cm01 spectral region. In addition, the temperature dependence of air-broadened halfwidth and air-induced pressure shift coefficients have been determined for over 350 spectral lines. A total of 29 O3 absorption spectra (0.005-cm01 resolution) recorded at various temperatures (29 to 0637C) with a Fourier transform spectrometer were used in the analysis. The spectral line parameters were deduced by analyzing all of the 29 spectra simultaneously using a nonlinear least-squares fitting technique. The results are compared with similar measurements obtained in the ozone n1 band. q 1997 Academic Press INTRODUCTION
Reliable values for spectral line parameters such as zero pressure position n0 , intensity S(T ), halfwidth coefficient b 0L (T, P), pressure-induced shift coefficient d 0 (T, P), the temperature dependence n of the halfwidth coefficient, and d*, the temperature dependence of the pressure-induced shift coefficient of ozone spectral lines are required for accurate quantification of radiative transfer properties of O3 in the Earth’s atmosphere. Precise knowledge of O3 spectroscopic parameters are also needed, especially in the infrared, for remote sensing studies of the terrestrial atmosphere such as the Halogen Occultation Experiment (HALOE). Many of these spectroscopic line parameters have recently been published from analyses of high-resolution laboratory measurements of O3 in several spectral regions (1–23). From some of these studies halfwidth and pressure-induced shift coefficients for several hundred lines of ozone broadened by air, nitrogen, and oxygen are known (7, 20, 23). The majority of the studies made measurements at ambient temperatures. Spencer and co-workers recently published measurements of n for several nitrogen- and oxygenbroadened ozone transitions in the n3 band (20, 22). In the microwave spectral region, Colmont and Monnanteuil (8) and Connor and Radford (9) published measurements of the temperature dependent exponent n for a few pure rotational transitions. Using Quantum Fourier Transform theory (QFT) Gamache and Rothman (24) reported theoretical halfwidth and pressure-induced shift coefficients for all unique rotational transitions of ozone perturbed by nitrogen for J £ 35. Using the same method, Gamache ( 25) published the temperature dependence of N2-broadened halfwidth coeffi-
cients for the same 126 transitions of ozone from J 9 Å 1 to 35. Later Gamache and Davies (26) reported halfwidth and pressure-induced shift coefficients for N2 , O2 , and air broadening of ozone calculated by the ATC (Anderson–Tsao– Curnutte) method and by the QFT method. More recently, Hartmann and co-workers (27) made new calculations of ozone broadening by N2 and O2 for B-type bands. Apart from Spencer et al.’s (20, 22) measurements in the n3 band, the experimental measurements of broadening and pressureshift coefficients of Smith et al. (28) for more than 440 transitions in the n1 band are the only other measurements below room temperature. In the infrared region the majority of ozone broadening and pressure-induced shift coefficients reported in the literature pertain to the n1 and the n3 fundamentals. Except for the self-broadened halfwidth coefficients of 72 transitions measured by Smith et al. (16), there are no other experimental or calculated halfwidth or pressureinduced shift measurements published for n2 lines. In this paper we present the first experimental determination of airbroadened halfwidth coefficients for 393 rovibrational transitions in the n2 fundamental. For almost all of these lines we also present the first experimental measurements of the air-induced pressure shift coefficient and its temperature dependence, and the temperature dependence of the air-broadened halfwidth coefficients. In addition, self-broadening coefficients at room temperature have been determined for 374 of these lines. EXPERIMENTAL DETAILS
The 0.005 cm01 resolution spectra used in this study are the same as those analyzed for the n1 band by Smith et al.
221 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7139
/
6t12h$$221
03-11-97 16:10:26
mspas
222
MALATHY DEVI ET AL.
TABLE 1 Experimental Conditions
(28). They were obtained at various temperatures between room temperature and 0637C using the McMath–Pierce Fourier transform spectrometer (FTS) of the National Solar Observatory (NSO) on Kitt Peak. The spectra were recorded during two different experiments, both using 50 cm absorption cells, one at room temperature and the other coolable. Two room temperature spectra of pure O3 and seven room temperature air-broadened O3 spectra were analyzed in combination with 20 additional spectra of ozone diluted with dry air at temperatures between 17C and 0637C. The two pure ozone spectra provided additional information to determine the self-broadening coefficients at room temperature. These two spectra also constrained the zero pressure line center positions. The FTS experimental setup consisted of a glower light source at approximately 2000 K, a KCl beam splitter, and two liquid helium cooled As-doped Si detectors. The spectral band pass for five of the room temperature spectra was limited to 450–1450 cm01 and for the low-temperature spectra it was 550–2750 cm01 . For the room temperature data we used a Pyrex absorption cell 50-cm long, 5.08 cm in diameter fitted with Teflon valves. Potassium chloride windows cemented to the cell were slightly wedged (5–10 mrad) to prevent channeling resulting from multiple reflections. For the low-temperature measurements we used a 50 cm cooled cell, a double walled Pyrex glass tube with KCl wedged windows which was enclosed in an evacuated metal chamber with wedged KCl windows. The cell temperature was regulated by circulating chilled ethanol through the space between the double glass wall. Further details regarding the coolable cell may be found in Ref. (29).
Ozone samples were prepared using the silent electric discharge and a research grade natural isotopic sample of oxygen. A summary of the experimental conditions of the present work is given in Table 1. For the low-temperature spectra lean O3 –air mixtures were prepared by initially filling the cell with pure O3 (5 to 28 Torr) and then adding research grade dry air to the sample until the total pressure reached about 250 Torr. In each series of spectra (Table 1) the spectrum with the highest total pressure was recorded first, and the subsequent lower pressure spectra were obtained by pumping out some of the gas sample. For each spectrum the sample pressure and temperature were monitored continuously during the approximately 1 hr integration time. The total pressure measurements are accurate to {0.1% and the temperature measurements are accurate to {17C. Calibration of the wavelength scale of the spectra was achieved using the n2 band water vapor line positions reported by Toth (30). These water vapor lines appeared in our spectra due to residual H2O within the evacuated interferometer tank and the dry nitrogen purged atmospheric paths between the source and the entrance aperture of the interferometer where the absorption cell containing the ozone sample was kept. The positions of the narrow (low pressure) component of these H2O lines were used for the calibration. DATA ANALYSIS
The room temperature self- and air-broadened halfwidth coefficient, the air-induced pressure shift coefficient, and the temperature dependence of air-broadened halfwidth and
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$222
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
223
pressure-induced shift coefficients were determined by fitting all 29 spectra (Table 1) together using a simultaneous least-squares fitting program (31). The spectra were analyzed by fitting 1 to 2 cm01 segments at a time using the program interactively. Using this technique, we retrieved several line parameters (e.g., zero pressure position, pressure-induced shift, temperature dependence of the pressureinduced shift, pressure-broadened halfwidth coefficient, and the temperature dependence of the halfwidth coefficient) simultaneously. The absorption lines were assumed to have Voigt lineshapes. Initial values for the line parameters were taken from the 1992 HITRAN database (32). In the global least-squares fitting program, except for the temperature dependence of pressure shift coefficients, d*, the various retrieved parameters were determined using the following expressions: bL Å b 0L (T )p, n Å n0 / d 0 (T )p,
[1]
b 0L (T ) Å b 0L (T 0 )(T 0 /T ) n , and
d 0 (T ) Å d 0 (T 0 ) / d* (T 0 T 0 ).
In these expressions, bL represents the Lorentz halfwidth coefficient (in cm01 ) at pressure p, n0 is the zero pressure line position (in cm01 ), and n is the line position at pressure p. The temperature dependence of the halfwidth coefficient is n, b 0L (T ) is the halfwidth coefficient at temperature T. The Lorentz broadening coefficient at the reference temperature T 0 (296 K) is b 0L (T 0 ). The temperature dependence of the pressure-induced shift coefficient is d*, and d 0 (T ) and d 0 (T 0 ) represent the pressure-induced shift coefficient at temperatures T and T 0 (296 K), respectively. RESULTS AND DISCUSSION
In Fig. 1 we show an example of a multispectrum fit of O3 lines near 722 cm01 . This figure illustrates that all 29 spectra could be simultaneously fit with one unique set of line parameters. This is very important with halfwidths and shift measurements at various temperatures. Such a fit constrains well the position of each line needed for accurate shift coefficients. When the spectra are fit individually in a crowded overlapping region such as that shown in this figure, the positions and widths of neighboring lines may wander and not be accurately determinable. Figure 1 proves that all 29 spectra are simultaneously fit to the same noise level and indicates that there are no major discrepancies in the parameters derived. The residuals from the least-squares fit (magnified by a factor of 10) are displayed in the top panel. Because the n2 region is close to the edge of the spectral band pass, the signal-to-noise ratio (S/N) is relatively poor
FIG. 1. Example of a 29 spectra nonlinear least-squares fit in the 722 cm01 region in the n2 band of ozone. The experimental conditions of the fitted spectra are summarized in Table 1. The calculated spectra are shown in the lower panel and the magnified residuals (observed minus calculated) resulting from the least-squares fit expressed as a fraction of peak intensity in the fitted region are shown in the upper panel. The positions of absorption lines included in the least-squares fit are shown by tick marks on the top axis of the lower panel.
(100 to 250) in comparison to that in the region of the n1 band (200 to 500). We were not able to determine reliable O3 self-shift coefficients from the spectra because of the limited S/N and the low O3 pressures used in the experiments. Self-broadened halfwidth coefficients for 72 n2 transitions were reported earlier by Smith et al. (16). The values determined for b 0L (self), b 0L (air), n(air), d 0 (air), and d* (air) from this work are listed in Table 2. Room temperature air-broadening coefficients, b 0L (air), have been determined for 393 lines.
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$222
03-11-97 16:10:26
mspas
224
MALATHY DEVI ET AL.
TABLE 2 Measured Spectral Line Parameters for the n2 Band of Ozone
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
225
226
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
227
228
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
229
230
MALATHY DEVI ET AL.
TABLE 2—Continued
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$7139
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
231
TABLE 2—Continued
In addition, room temperature air-broadening coefficients for five 2n2 – n2 lines are also determined, and are listed in the last five rows of Table 2. Because of the inherent weakness of this band (compared to n3 and n1 ) and the low ( õ15%) volume mixing ratios of O3 samples used, for many weak n2 transitions we were able to determine only room
temperature air-broadening coefficients. Transitions for which we were unable to determine the temperature dependence of the air-broadening or pressure-induced shift coefficients had n(air) and d* values constrained to 0.55 and 0, respectively, and are indicated by blank spaces in Table 2. Initial measurements of several strong, well separated lines
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
232
MALATHY DEVI ET AL.
FIG. 2. (a) Measured air-broadening coefficient, b 0L (air), at 296 K vs J 9; (b) the temperature-dependent exponent n(air) of air-broadening coefficients plotted as a function of J 9; (c) measured self-broadening coefficient, b 0L (self), at 296 K plotted as a function of J 9; and (d) temperature-dependent exponent n(air) as a function of b 0L (air). The error bars indicate one standard deviation uncertainty in the measured quantities. Where no error bars are displayed, the standard deviation is smaller than the size of the symbol. In (a) – (d), open circles correspond to K a9 £ J 9 transitions and filled circles correspond to transitions with K a9 Å J 9.
gave n(air) values varying between 0.5 and 0.6 and therefore we chose to use the value of n(air) Å 0.55 for these weak lines instead of n(air) Å 0.76 given in the 1992 HITRAN database (32). If the room temperature self-broadening coefficient of a transition was not determined, its value was constrained to that given in Ref. (32). Column 1 of Table 2 gives the wavenumber (cm01 ) of each measured spectral line along with its standard error in units of the last digit obtained from the present least-squares analysis. The assignments given in columns 2–7 are from Ref. (32). The values given in parentheses indicate onesigma standard error in the measured quantities in units of the last digit quoted. As discussed in our previous studies (31, 33), in the multispectrum fitting technique, the quoted errors in the retrieved parameters represent the uncertainties due to random errors such as the noise level in the spectra and other fitted parameters only. By fitting a large number of spectra simultaneously these random errors are decreased to very small values. However, in order to determine the absolute uncertainties in the retrieved parameters, errors associated with the measurements of gas pressure and gas
temperature, uncertainties in the line parameters such as position and intensity, uncertainties in the wavelength calibration of the spectra, and errors involved in the spectral line shape must also be considered. The determination of all these uncertainties is certainly a nontrivial problem. Based upon our knowledge of the accuracies in these parameters we estimate that the absolute uncertainties in our broadening and shift measurements and their temperature dependences may, however, be determined by adding an additional 2% in b 0L , 0.0002 cm01 atm01 in d 0 , 0.05 in n(air), and 0.00001 cm01 atm01 K 01 in d* to the errors indicated in Table 2. The uncertainties indicated in Table 2 are appropriate for comparison between values in the table. (a) b 0L (air) and n(air) The broadening coefficients b 0L (air) and their temperature dependence n(air) listed in Table 2 are plotted as a function of J 9 in Figs. 2a and 2b, respectively. The error bars denote one standard deviation listed in Table 2. In Fig. 2c we have plotted b 0L (self) as a function of J 9. Consistent with our
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
233
FIG. 3. (a) Observed air-broadening coefficient, b 0L (air), for J 9 Å 11 at 296 K and (b) the temperature dependence n(air), of the air-broadened halfwidth coefficient for J 9 Å 11 as a function of the lower state rotational quantum number K a9 . The open circles correspond to results for the n2 band and the filled circles correspond to those for the n1 band. The values for the n1 band are from Ref. (28). The solid curve in (b) corresponds to calculated n values for N2 broadening from Gamache (25). Because no calculated values have been explicitly reported for b 0L (N2 ) for J 9 Å 11 there is no solid curve plotted in (a). (c) and (d) display the same parameters for J 9 Å 20.
earlier studies on other ozone bands (10, 16, 23, 28), it is clearly seen in Figs. 2a and 2c that b 0L decreases with increasing J 9 for both air and self broadening. However, such a definite trend is not observed among the n values plotted in Fig. 2b. The scatter in the n(air) values for a fixed J 9 in Fig. 2b reflect the K-dependent variations in n for any given J 9 value. In Fig. 2d we have examined the correlation between the halfwidth coefficient and its temperature dependence. A very weak negative correlation of n(air) with respect to b 0L (air) may be noticed. The open circles in these figures represent K 9a £ J 9 lines and the filled circles correspond to K 9a Å J 9 transitions. It is clearly seen that for a particular J 9, the halfwidth coefficients have the smallest value for the J 9 Å K 9a transitions. The selection rule governing the ozone transitions is K 9a / K 9c Å J 9 or J 9 / 1 and the highest K 9a value we were able to observe in this study was 12 (Table 2). While a small decrease in n with J 9 was observed in the n1 band (28), the n value in the n2 band does not reveal any noticeable dependence on the rotational quantum number J 9. This may be attributed to the higher
uncertainties in the retrieved parameters in the n2 region due to lower S/N in this region of the spectra. Details of the K 9a dependence of the broadening coefficients and n values for one of the J 9 (J 9 Å 11) values are shown in Fig. 3. In Figs. 3a and 3b the open circles show the results obtained for the n2 band and the filled circles correspond to those for the n1 lines (28). In both bands the values for b 0L gradually increase with K 9a , reach a maximum around K 9a Å 6 or 7, and then decrease rapidly to reach the minimum value when K 9a Å J 9. In Fig. 3b one may notice a slight decrease of n with increasing K 9a values in both the n1 and n2 bands. It is obvious that the n values are larger in the n1 band than in the n2 band. The solid curve in Fig. 3b shows n vs K 9a calculated for nitrogen broadening for ozone by Gamache (25). Since no calculated N2-broadening coefficients were explicitly reported in Ref. (25), a solid curve similar to that in Fig. 3b is not available in Fig. 3a. Based upon his calculations, Gamache suggested an average n value of 0.76 for air broadening in all ozone bands. Following the conventional Anderson–Tsao–Curnutte theory, Tej-
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
234
MALATHY DEVI ET AL.
FIG. 4. (a) Measured b 0L (air) vs K a9 for J 9 Å 8, 9, 10, 11, and 12. (b) Measured n(air) vs K a9 for J 9 Å 8, 9, 10, 11, and 12. (c) Measured pressure shift coefficients, d 0 (air), vs K a9 for J 9 Å 8 through 12 in the n2 band of ozone. The horizontal solid line corresponds to zero pressure shift coefficients. Most measured shift coefficients are negative. (d) Measured temperature dependence exponent d* of shift coefficients vs K a9 are plotted for J 9 values of 8 through 12. The horizontal solid line represents d* Å 0.
wani and Yeung (34) reported mean temperature exponent values of n Å 0.68 and n Å 0.73 for A- and B-type transitions, respectively. Both the n1 and n2 bands of ozone are B-type transitions. Gamache (25) in his calculations did not find any difference in the average temperature exponent values between A- and B-type transitions. However, his results showed that n values are transition dependent and the fluctuation about the average value was small ( {6%). Our measurements also showed n values to be transition dependent, but the variations are found to be much larger than {6%. From the 357 measurements in the n2 band we obtained a mean and standard deviation of n Å 0.53 { 0.08. This is significantly smaller than the mean n value of 0.67 { 0.07 obtained for over 440 n1 lines measured in the same spectra (28). Note that the standard deviations associated with the mean values are in fact one standard deviation scatter in the mean values and do not represent the measurement uncertainties. Figures 3c and 3d show the variations with K 9a of the airbroadening coefficients at 296 K and n values for lines with J 9 Å 20 in both the n2 and n1 bands. For the purpose of
comparisons, we have also included in these figures solid curves indicating the calculated N2-broadening coefficients at 296 K from Gamache and Rothman (24) and the calculated n values from Gamache (25). The air-broadening coefficients in the 1992 HITRAN database (32) are based upon a scaling of these calculated N2-broadening values. It is clear from these figures that the calculated broadening coefficients are too small and the n values too large compared to corresponding measured values in the present work on the n2 band. Previous calculations of O3 line broadening made with the Anderson–Tsao–Curnutte approach or the QFT-ID models both seem to systematically underestimate O3 broadening, especially broadening by O2 . Bouazza et al. (21) discussed this subject. Comparisons made between the 394 measured air-broadened halfwidth coefficients presented in Table 2 and those reported in the 1992 HITRAN database (32) gave 1.09 { 0.07 as the mean and standard deviation for the ratio of measurement to calculation. Gamache (25) observed dependence of n upon K 9a by plotting calculated values of n vs K 9a for a series of lines with J Å 5, 11, and 20. In cases where several transitions (for a given J 9 ) had
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
OZONE n2 BROADENING AND SHIFTS
235
the same K 9a , the n values were averaged and the mean values were used in producing the plots. In Figs. 4a and 4b we have plotted b 0L (air) vs K 9a and n(air) vs K 9a , respectively, for J 9 values of 8 through 12. We plot all measured values of b 0L and n (without averaging the values of b 0L and n for cases where for a given J 9 there was more than one transition with same K 9a ). As expected, variation in b 0L with K 9a is clearly seen in Fig. 4a and a weak decrease of n with K 9a is vaguely noticeable in Fig. 4b. The use of the multispectrum fitting technique allowed us to also determine over 375 self-broadened halfwidth coefficients compared to only 72 values in our previous work (16) obtained from a spectrum-by-spectrum analysis technique. From the 63 lines that are common in both studies we obtained the mean and standard deviation of 1.01 { 0.04 for the ratio of the present results divided by the previous results. We also compared the self-broadening coefficients in the n2 band with those obtained from these same spectra for n1 transitions having the same rotational quantum numbers. For the approximately 150 identical (both upper and lower rotational quantum numbers same) transitions compared, on average n2 values are 5% larger. The results are given in Table 3. (b) d 0 (air) and d* (air) Similar to the broadening coefficients, b 0L (air), the pressure-induced shift coefficients, d 0 (air), and their temperature dependence, d* (air), also depend upon the transition studied. In an attempt to reveal any trends in d 0 (air) or d* (air), we have plotted d 0 (air) and d* (air) for J 9 Å 8 through 12 in Figs. 4c and 4d, respectively, vs K 9a . There is no observable dependence of either d 0 (air) or d* (air) on J 9 or K 9a in our measurements. In Figs. 5a and 5b we have plotted d0 (air) vs J 9 and d* (air) vs J 9, respectively. About 70% of measured pressure-induced shift coefficients and 52% of d* values were found to be negative. From approximately 360 measurements, we obtained means and standard deviations of 00.0008 { 0.0017 cm01 atm01 at 296 K and 00.2 { 2.9 1 10 05 cm01 atm01 K 01 for the d 0 and d* values, respectively. Except for the one previous study on self-broadening coefficients for 72 lines (16), no other measurements or calculations seem to be reported on broadening coefficients, pressure-induced shift coefficients, or their temperature dependences for lines of the n2 band. However, b 0L (self), b 0L (air), n(air), d 0 (air), and d* (air) for the n1 band of O3 using the same set of spectra as in this work have recently been measured by Smith et al. (28) and in Table 3 we have compared the average values determined for these two bands. In Figs. 6a–6d we have plotted the measured airbroadening and pressure-induced shift coefficients and their temperature dependence for the 150 identical rovibrational transitions in the n2 and the n1 bands. From Fig. 6a it appears
FIG. 5. (a) Observed pressure-induced shift coefficient d 0 (air) and (b) the temperature dependence of measured shift coefficients d* (air) vs J 9 for all measured transitions in this study.
that there is a small vibrational dependence of the Lorentz air-broadening coefficients. From the 150 measurements for which comparisons could be made, the average and standard deviation for the ratio of b 0L (air) in the n2 to n1 band are found to be 1.03 and 0.04, respectively. Although the magnitude of this vibrational dependence is not significant relative to absolute uncertainties, the differences seem to be real as shown in Fig. 6a. We have observed vibrational dependence in broadening and pressure-induced shift coefficients previously in several O3 and CH4 bands (23, 28, 33). However, vibrational dependences in the n and d* values have not been observed or predicted so far for any of the ozone bands. As shown in Fig. 6b the differences in the n values between these two bands are more pronounced than the differences in the air-broadening coefficients. The means and standard deviations of the n(air) values in the n2 and n1 bands (from the 150 identical transitions) are 0.53 { 0.07 and 0.68 { 0.08, respectively. At this time we are not able to explain the reason for this large difference. In Figs. 6c and 6d the
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
236
MALATHY DEVI ET AL.
TABLE 3 Comparison of Line Parameters between the n2 and n1 Bands of O3
d 0 (air) and d* (air) values measured for these two bands are plotted and no noticeable vibrational dependence in either d 0 (air) or d* (air) is apparent. One has to be very careful in interpreting the accuracy we have stated for the various retrieved parameters. We have given an estimate for the absolute uncertainties as well as the precision for the retrieved parameters. The uncertainties associated with each measured quantity given in Tables 2 and 3 are based upon systematic errors (errors in wavelength calibration, temperature and pressure measurements etc.) which appear in both studies we have compared. The values determined for air-induced shift coefficients d 0 (air) and their temperature dependence d* (air) are indeed very small quantities. This is especially true in the n2 band, where they are often small enough to be below our measurement capability. The measurements, however, provide an upper limit to these parameters. When results are compared between the two bands (e.g., b 0L and n in n2 and n1 ) the errors we have quoted in Table 3 are in fact the scatter from the mean measured values and errors of the systematic nature described previously should not be added. CONCLUSIONS
The data presented in this investigation are the first experimental measurements of air-broadened Lorentz halfwidth coefficients, pressure-induced shift coefficients, and the temperature-dependent air-broadened halfwidth and pressure-induced shift coefficients for ozone in the n2 fundamental
band. In addition, we have determined ozone self-broadened halfwidth coefficients for a larger number of transitions than were measured in our previous study. We have measured 393 air-broadened halfwidth coefficients, b L0 ( air ) , 374 self-broadened halfwidth coefficients, b 0L (self), 362 pressure-induced shift coefficients d 0 (air), 357 temperature-dependent halfwidth coefficients, n(air), and 355 temperaturedependent pressure-induced shift coefficients d* (air). Comparisons of self-broadened halfwidth coefficients determined in this work using the multispectrum fitting technique gave good agreement with our previous study made by a spectrum-by-spectrum analysis procedure, but the new technique made it possible to reduce the uncertainties in the measured halfwidth coefficients and to derive many more self-broadened halfwidth coefficients. The measured self- and air-broadened halfwidth coefficients, pressure-induced shift coefficients, and their temperature dependence are found to be transition dependent. Of the total, 70% of the shift coefficients and 52% of the coefficients of the temperature dependence of the pressure-induced shifts are negative. Comparisons between the n2 and n1 ozone bands revealed some interesting results. The mean values obtained for the self- and air-broadened halfwidth coefficients in the n2 band are 3 and 5% larger, respectively, than the corresponding values measured in the n1 band. The mean values of pressureinduced shift coefficients and their temperature exponents for the two bands are within their respective experimental uncertainties. The largest difference is observed between the temperature dependence of air-broadened halfwidth coefficients. The
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$223
03-11-97 16:10:26
mspas
237
OZONE n2 BROADENING AND SHIFTS
FIG. 6. Comparison of (a) air-broadened halfwidth coefficients b 0L (air), (b) temperature dependence n(air) of the air-broadened halfwidth coefficients, (c) pressure-induced shift coefficients d 0 (air), and (d) temperature dependence d* (air) of the pressure shift coefficients between the n2 and the n1 lines of ozone. The results for the n1 band are from Ref. (28). The error bars denote one standard deviation in the measured quantities. The straight lines passing through the origin in these graphs correspond to equality of the plotted quantities.
average value for n(air) in the n2 band is 0.53 with a one standard deviation scatter of 0.08 and for the n1 band the average n(air) value is 0.67 with a one standard deviation scatter of 0.07. Both these values are significantly smaller than the HITRAN n(air) value of 0.76 assumed to be the same for all bands of ozone. The results presented in this investigation should prove useful for interpreting infrared remote sensing studies of the terrestrial atmosphere and for radiative transfer calculations. The measured parameters from this study will be made available for inclusion in the next update of the HITRAN database. ACKNOWLEDGMENTS We thank Charles T. Solomon and Harry G. Walthall of the Fabrication Division at NASA Langley Research Center for their help in designing and building the coolable glass cell. We also thank Claude Plymate and Jeremy Wagner of the National Solar Observatory (NSO) for their assistance in recording the data and Gregg Ladd at NSO for the initial processing of the spectra. Research at the College of William and Mary is supported by cooperative agreements with the National Aeronautics and Space Administration. NSO is operated by the Association of Universities for Research in Astronomy, Inc., under contract with NSF.
REFERENCES 1. R. T. Menzies, Appl. Opt. 15, 2597–2599 (1976). 2. S. Lundqvist, J. Margolis, and J. Reid, Appl. Opt. 21, 3109–3113 (1982). 3. C. Meunier, P. Marche, and A. Barbe, J. Mol. Spectrosc. 95, 271–275 (1982). 4. J. M. Hoell, C. N. Harward, C. H. Bair, and B. S. Williams, Opt. Eng. 21, 548–552 (1982). 5. A. Barbe, P. Marche, C. Meunier, and P. Jouve, J. Physique 44, 1015– 1017 (1983). 6. N. Monnanteuil and J. M. Colmont, J. Quant. Spectrosc. Radiat. Transfer, 29, 131–136 (1983). 7. J. S. Margolis, J. Quant. Spectrosc. Radiat. Transfer 29, 539–542 (1983). 8. J. M. Colmont and N. Monnanteuil, J. Mol. Spectrosc. 104, 122–128 (1984). 9. B. J. Connor and H. E. Radford, J. Mol. Spectrosc. 117, 15–29 (1986). 10. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, D. Chris Benner, and K. B. Thakur, J. Opt. Soc. Am. B. 5, 585–592 (1988). 11. J.-M. Flaud, C. Camy-Peyret, C. P. Rinsland, M. A. H. Smith, and V. Malathy Devi, ‘‘Atlas of Ozone Spectral Parameters from Microwave to Medium Infrared.’’ Academic Press, Cambridge, MA, 1990. 12. C. Flannery, J. J. Klassen, M. Gojer, J. I. Steinfeld, M. Spencer, and C. Chackerian, Jr., J. Quant. Spectrosc. Radiat. Transfer 46, 73–80 (1991).
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$224
03-11-97 16:10:26
mspas
238
MALATHY DEVI ET AL.
13. M. N. Spencer and C. Chackerian, Jr., J. Mol. Spectrosc. 146, 135– 142 (1991). 14. A. Barbe, S. Bouazza, and J. J. Plateaux, Appl. Opt. 30, 2431–2436 (1991). 15. J. J. Plateaux, S. Bouazza, and A. Barbe, J. Mol. Spectrosc. 146, 314– 325 (1991). 16. M. A. H. Smith, C. P. Rinsland, and V. Malathy Devi, J. Mol. Spectrosc. 147, 142–154 (1991). 17. J. J. Oh and E. A. Cohen, J. Quant. Spectrosc. Radiat. Transfer 48, 405–408 (1992). 18. A. Barbe, J. J. Plateaux, S. Bouazza, J.-M. Flaud, and C. Camy-Peyret, J. Quant. Spectrosc. Radiat. Transfer 48, 599–610 (1992). 19. N. Sokabe, M. Hammerich, T. Pedersen, A. Olafsson, and J. Henningsen, J. Mol. Spectrosc. 152, 420–433 (1992). 20. M. N. Spencer, C. Chackerian, Jr., C. Flannery, and J. I. Steinfeld, Spectrochim. Acta A 48, 1273–1281 (1992). 21. S. Bouazza, A. Barbe, J. J. Plateaux, L. Rosenmann, J. M. Hartmann, C. Camy-Peyret, and J.-M. Flaud, J. Mol. Spectrosc. 157, 271–289 (1993). 22. M. N. Spencer, C. Chackerian, Jr., C. Flannery, and J. I. Steinfeld, J. Quant. Spectrosc. Radiat. Transfer 49, 525–533 (1993). 23. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, and E. S. Prochaska, J. Mol. Spectrosc. 164, 239–259 (1994); Erratum, J. Mol. Spectrosc. 165, 596 (1994).
24. R. R. Gamache and L. S. Rothman, Appl. Opt. 24, 1651–1656 (1985). 25. R. R. Gamache, J. Mol. Spectrosc. 114, 31–41 (1985). 26. R. R. Gamache and R. W. Davies, J. Mol. Spectrosc. 109, 283–299 (1985). 27. J. M. Hartmann, C. Camy-Peyret, J.-M. Flaud, J. Bonomy, and D. Robert, J. Quant. Spectrosc. Radiat. Transfer 40, 489–495 (1988). 28. M. A. H. Smith, V. Malathy Devi, D. Chris Benner, and C. P. Rinsland, manuscript submitted to J. Mol. Spectrosc. (1996). 29. M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, and D. Chris Benner, Spectrochim. Acta A 48, 1257–1272 (1992). 30. R. A. Toth, J. Opt. Soc. Am. B 8, 2236–2255 (1991). 31. D. Chris Benner, C. P. Rinsland, V. Malathy Devi, M. A. H. Smith, and D. Atkins, J. Quant. Spectrosc. Radiat. Transfer 53, 705–721 (1995). 32. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. Chris Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 48, 469 – 507 ( 1992 ) . 33. V. Malathy Devi, D. Chris Benner, M. A. H. Smith, and C. P. Rinsland, J. Quant. Spectrosc. Radiat. Transfer 51, 439–465 (1994). 34. G. D. T. Tejwani and E. S. Yeung, J. Chem. Phys. 63, 1513–1517 (1975).
Copyright q 1997 by Academic Press
AID
JMS 7139
/
6t12h$$224
03-11-97 16:10:26
mspas