Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm

J. Quant. Spectrosc. Radiat. Trans[er VoL 22, pp. 315-331 Pergamon Press Ltd.. 1979. Printed in Great Britain

I N T E N S I T I E S A N D N2 C O L L I S I O N - B R O A D E N I N G COEFFICIENTS MEASURED FOR SELECTED H20 A B S O R P T I O N L I N E S B E T W E E N 715 A N D 7 3 2 n m t T. D. WILKERSON,:~G. SCHWEMMER,§and B. GENTRY§ Institute for Physical Science and Technology,University of Maryland, College Park, MD 20742, U.S.A.

and L. P. GIVER Space Sciences Division,Ames Research Center, NASA, Moffett Field, CA 94035, U.S.A. (Received 31 October 1978)

Abstract--Intensities and N2 collision-broadeningcoefficientswere measured for 62 lines of H20 vapor between 715 and 732 nm. The lines selected are potentially useful for remote laser measurements of H20 vapor in the earth's atmosphere. The spectra were obtained with several different H20 vapor abundances and N2 broadeninggas pressures; the spectral resolution was 0.05 cm-~. Measured H20 line strengths range from 4×10 -25 to 4×10-23cm-1/(molec./cm2), and N2 collision broadening coefficients are approx. 0.1 cm ~/atm. 1. INTRODUCTION

THIs PAVER summarizes the results of measurements on the strength and width of selected H20 absorption lines lying between 715 and 732 nm. This research was carried out at the Long Path Gas Cell facility at NASA-Ames Research Center, in collaboration with the University of Maryland where the development of remote laser sensing of water vapor requires accurate H20 line parameters in the near i.r. Applications to remote sensing are briefly discussed in Section 1.3. Our results on H20 will also be useful in atmospheric optics generally, because the 720 nm lines are prominent as telluric lines in solar spectra and can either serve as indicators of H20 column content or provide a calibration for other observed lines in wavelength regions such as 580, 650, 690, 820, and 940 nm. In a subsequent paper we will report strengths, widths and pressure shifts for lines in the ptrr band of H20 near 940 nm. 1.1 P r e v i o u s m e a s u r e m e n t s

Past work on the absolute photometry of H20 lines below l/zm is relatively sparse because the lines are weaker than in the prominent i.r. bands. The work of BURCH et al. "'2) stands out as a comprehensive survey of band strength and spectral signature, at medium resolution ( - 1 2 cm -~) down to 690 nm. The Utrecht Atlas (3) provides better resolution ( - 0 . 0 8 cm-1), and the companion volume by MOORE et al. (4~ gives equivalent widths for telluric lines of H20 that can be compared with estimates of the total column content of H20 responsible for the lines. Also, the atlas by DELBOUILLE and ROLAND(5) and its companion line list by SWENSSON et al. ~6~ extend down to 750 nm with a resolution of order - 0 . 0 5 cm -2. Strengths of a few individual lines have been reported by FARMERt7) (820 nm band), MEREDITr~ et a l f l ~ (940 nm band), and BRAVLT et al. ~9) (694.3 nm line plus seven other lines in the i.r. from 1-2.5/zm). In recent years, very high resolution spectra of solar and telluric lines have been obtained at Kitt Peak National Observatory. Preliminary work on the visible spectrum has been reported by BRAULT and TESTERMAN,O°) and we have been able to make improved plans for the present work on the basis of unpublished H20 results kindly provided by J. W. Brault and W. S. +,Research supported in part by NASA GRANT No. NSG-2216, by NASA-Ames Research Consortium Grant No. NCA2-OR420-701, and by the University of Maryland. ¢VisitingScientist at Ames Research Center, NASA. §Present address: Code 941, Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A. 315

316

T.D. WILKERSONet al.

Benedict (private communication, 1973). Comments on the comparison of our results with Brault's are given in Section 6. According to L. S. Rothman (private communication, 1978), the Kitt Peak data for the region 550-770 nm will be made available on the atmospheric transmission tape compiled at the Air Force Geophysical Laboratory. Previous updating of this tape has been described by ROTHMANand MCCLATCHEY.(11) 1.2 Laser remote sensing applications

The principal application of molecular line absorption data to atmospheric lidar comes about through the differential absorption lidar (DIAL) method that has been described by MEASURES and PILON, (12) AHMED,O3) BYER and GARBUNY,O4) SCHOTLAND,O5A6) and REMSBERGand GORDLEY.(17) This method makes use of the differences observed in pulsed laser backscatter when a pulsed laser transmitter is tuned on and off an absorption line. Molecular density at any given range is obtained from a logarithmic derivative of the ratio of the "on" and "off" lidar returns, divided by the difference in absorption cross sections at the two wavelengths in question. Thus, for example, the measurement of [H20], the concentration of water vapor, by this method depends directly on cross sections and therefore on line strengths and widths. Moreover, it is clear that to determine [H20] in a manner which is free from temperature effects, one needs to use lines whose absorption cross sections are relatively temperature independent. This led to one of the line selection criteria for our measurements and is discussed further in Section 2.1 below. WILKERSON et al. "s) and ELLINGSONet al. ~19) made preliminary estimates of the suitability of H20 lines below 1/zm wavelength for lidar probing of atmospheric water vapor profiles, based on data sources such as Refs. 1-4, 7, and 8. The generally favorable results have led to successful demonstrations by NOaTHAMet al. ~2°) and BROWELLet al. ~2~) of a water vapor lidar system, and to further lidar simulations by SCHWEMMERand WILKERSON(22'23) exploring a variety of applications. The quantitative study o n H 2 0 absorption reported here was undertaken in part to obtain higher accuracy data for remote sensing applications, so that "temperature insensitive" lidar operation would be possible over a wide range of atmospheric humidity. 2. SELECTION OF LINES FOR MEASUREMENT

Each H20 absorption line was singled out for measurement on the basis of temperature insensitivity of the absorption cross section at the line center, resolvability from other atmospheric absorption lines (H20, O2), and being located in a good spectral region containing other H20 lines having a wide range of absorption strength. 2.1 Energy levels Many lines that occur in a molecular band are not ideally suited for determining molecular concentration, because they originate from lower levels E" whose populations depend noticeably or even markedly on temperature. Line width also depends on temperature via the mean speed of colliding molecules that are responsible for pressure broadening. At high altitude in the earth's atmosphere Doppler broadening dominates collision broadening, and temperature again determines the degree to which any given line's absorption cross section is spread out into a profile g(v - v0) where v0 is the frequency at line center. The integrated cross section S = f g(v - v0) dv and g0 = o-(0) are slightly different functions of temperature, so that one has a choice of different temperature-insensitive parametric relations E"(T), i.e. Ogo=o 3S c~T ~ v s - ~ = 0 , depending on whether one envisions a narrow-band optical measurement system operating at the line center vs a broader transmission device covering an entire H20 line. To obtain the strongest optical interaction for lidar purposes, the use of sufficiently narrow-band lasers to operate at v0 is preferable and entirely feasible; hence we employed &ro/OT = 0 here to select the energy levels E" appropriate to temperature-insensitive operation over the temperature range T = 200-400K which is more than adequate for the earth's

Intensities and N2 collision-broadeningcoefficients

317

Table 1. H20 rotationalenergylevels E" in (0, 0, 0) for temperature-insensitiveabsorptionat line centers. d"

r"

K'~

K" c

2

l

2

l

E"{cm'l) a

Approx.

134.91

Energy Group

A (140 cm- l )

2

2

2

0

136.17

A

3

-3

0

3

136.77

A

3

-2

l

3

142.28

A

3

-I

T*(approx.)

200 K

l

2

173.36

B (]75 cm- l )

230 K

3

0

2

2

206.30

C (2]5 cm" l )

275 K

3

l

2

l

212.15

C

3

2

3

1

285.23

D (285 cm" I )

3

3

3

0

285.43

D

4

-4

0

4

222.06

C

4

-3

l

4

224.83

C

4

-2

l

3

275.52

D

4

-I

2

3

300.35

D

0

2

2

315.79

E (320 cm" ] )

5

-5

0

5

325.35

E

5

-4

l

5

326.64

E

4

340 K

370 K

(a) Reference 5

atmosphere. These levels are listed in Table 1, along with their rotational quantum number assignments, and are lumped into live approximate categories (A . . . . . E) for future reference. The column labeled T* gives the temperatures for which lines having E"= 140, 175, 215, 285, and 320 cm -l would be exactly temperature independent; i.e. (&ro/0T)r. = 0. This association between E" and T* differs from that employed by BP.AULTet a/. (9) which was based on the temperature dependence of S as opposed to fro. Figure I shows the variation with temperature of (&ro/OT)/o'o for different values of E", along with a scale depicting the \ relevant rotational energy levels for H20. In calculating the line-center cross section, we employed not only the thermal dependence of the level populations and partition function, but also a Voigt profile incorporating the Doppler width and the temperature dependence of the iinewidth due to H20 collision broadening in air, as in calculations by SC~IWEMMERand W I L K E R S O N (22) a n d

by H E A T O N .

+0001

(24)

i

i

rotational j excitation level energy J"K~K~c~J E"(c re'l) 422

425

300

413

+0.0005

250 414

(9% dT %

321

3ZZ

(OK-i) 0

20O

3~2 305

ZZO ZZl

- 0.0005

0

211 IOO

zo

- 0.001 I00 K

200K

30OK

400K

Temperoture

Fig. 1. Watervaporenergy levels E" (right) and the temperaturedependenceof the line-centerabsorption cross section(left) as a functionof E". QSRT Vol. 22, No. 4--B

318

T.D. WILKERSONet al.

2.2 Wavelength separation For the most part, we have restricted our measurements to H20 lines separated by 0.02 nm or more from any nearby observed line of H20 or 02. This ensures that lidar operation with a laser bandwidth <0.005 nm can resolve the lines. In some cases, smaller interline separations were considered when the estimated line strengths are such as to suggest the lines might be resolved with a narrowband laser. 2.3 Wavelength interval The range 714-733 nm was selected for the present measurement program at NASA-Ames. This range contains 85 lines satisfying the above criteria on energy levels and resolvability, and the approximate strengths of these lines are distributed over at least two orders of magnitude. Moreover, lines from the various energy level subsets (A . . . . . E) are fairly evenly distributed in strength and wavelength between 714 and 733 nm so that this region is suitable for temperatureinsensitive absorption work more or less equally at any temperature from 200 to 400°K. As well as containing the strongest useful H20 lines, the chosen range has parts that are dominated by lines approximately an order of magnitude weaker, so that absorption measurements can be carried out readily even under high humidity conditions. This is useful from the standpoint of lidar engineering, and absorption measurements generally, because the range of known line strengths will then permit a corresponding range of humidities to be measured with uniform accuracy. In differential absorption lidar work particularly, it is important to have a variety of line strengths available for atmospheric probing to different distances. The interplay of lidar range, molecular absorption, distance resolution of the lidar system, and errors in observed molecular concentration have been discussed in detail in Refs. (16), (17), and (22). 3. EXPERIMENTAL PROCEDURES A multipass absorption cell with a base path length of 25 m was used, which permitted spectra to be obtained with path length of 50 m, 100 m, and multiples of 100 up to 2500 m. This "White cell" has D-shaped primary mirrors 91 cm in diameter, and is equipped with internal focusing optics near the entrance and exit windows which add 7 m to the total optical path length. The spectra were obtained with a Jarrell-Ash Czerny-Turner 5 m scanning spectrometer filled with dry N2 using the eighth order of a 300 l/ram Bausch and Lomb grating blazed at 5.7/~m in the first order. The current from an RCA 31034 A gallium arsenide phototube operated at -40°C was displayed on a Hewlett Packard strip chart recorder and simultaneously stored on magnetic tape. The source of continuum radiation was a 1000 watt tungsten quartz-iodine lamp. A quartz prism was used as a predispersor to isolate the 720 nm region prior to the entrance slit of the 5 m spectrometer. The spectra subsequently used for data analysis were all obtained with entrance and exit slit widths set at 0.040 mm. All spectra were taken at a room temperature of approx. 20°C, and the cell temperature was determined for each spectral scan. Spectra were taken of pure H20 vapor and also H20 vapor broadened with N2. The partial pressure of H20 vapor was measured with a calibrated Baratron diaphragm pressure gauge accurate to 0.008 Torr over the range 0-10 Torr. The H20 partial pressure was limited to 5 Torr to avoid possible problems of condensation in the cell. Matheson dry N2 was then added to the H20 vapor and the total pressure measured with a Wallace & Tiernan 0-50 psi gauge accurate to 0.3% full scale. Spectra were obtained with the pressure and path length conditions given in Table 2. The total H20 vapor column abundance in the White cell is given in this table in molec./cm 2 for each combination used. In addition of H20 vapor in the White cell, the optical path of 8.6 m between the White cell and the spectrometer was in ambient air. Records of the relative humidity and temperature were maintained so the data could be corrected for this additional H20 vapor, which is described in a following section. 4. DATA ANALYSIS Line strengths have often been determined by using equivalent widths. These methods enjoy the advantage of the independence of the equivalent width from instrumental effects. However, this method has several shortcomings. The level corresponding to no absorption must

Intensities and N2 collision-broadeningcoefficients

319

Table 2. H20 abundancesin the Whitecell in units of 102jrnol/crnz.

Path Lenqth

PH20 = 1.52 Torr

1.52 Torr

2.37 Torr

5.01 Tort

PN2= 0 and 252 Torr

505 Torr

0 Torr

0 Torr

57 m

.

.

.

.

.

.

.

107 m

.

.

.

.

.

.

.

207 m

1.02

.

.

.

.

.

.

.

.

.

.

1.02

1.60

607 m

2.99

2.99

4.68

1407 m

6.93

6.93

....

1907 m

.

2407 m

II.9

2507 m

....

.

.

.

.

.

.

. .

.

.

.

.

.

.

369 and 754 Torr

0.96

....

1.76

1.76

3.40

3.40

9.97

9.97

23.1

14.7

12.3

5.01Torr

.

.

23.1 .

.

.

.

.

.

.

39.5

39.5

....

41.2

....

be determined very accurately. The lines that can be measured are restricted to those sufficiently far from neighboring lines that wing overlap is not serious; even for well isolated lines, wing corrections must be made. These limitations are minimized for weak, Doppler profile lines, but for the lidar applications discussed previously, it is also necessary to determine the pressure broadening coefficients near atmospheric pressure, which cannot be achieved under low pressure, nearly Doppler conditions. The objective in the present work was therefore to determine the absorption cross sections, line intensities and N2 pressure broadening coefficients directly from the spectra obtained under the laboratory conditions given above. To do this we had to correct for finite instrumental resolution (see 4.2) and for the combination of both Lorentz and Doppler broadening. Methods such as those discussed by KOSTKOWSKIand BASS(25) and more recently by MEREDITH(26) led us to use a parametric deconvolution routine to correct for both of these effects; this is discussed in detail in Sections 4.2 and 4.3. Also, we corrected for residual water vapor in the laboratory air path as described in Section 4.4. The final results for line strength and halfwidth are expressed as Lorentz line parameters that do not include any other effects of temperature and instrument broadening. This procedure is detailed in Section 4.5. For each line, the central intensity Ic = (Ip- Z)/(Io-Z) was determined, where I0 is the measured "continuum" or "baseline" on the spectrum determined from regions of no absorption, Z is the zero level representing complete absorption, and Ip is the measured height of each line center. The observed half-width of each line, Yobs,was measured on the spectrum at a height corresponding to X/It. These measured quantities were then corrected in several steps to yield the Lorentz parameters for each line: rL, the Lorentz optical depth at the line center, and yL, the Lorentz half-width in cm -~ measured at rU2. Then, since the cross section trL = r~JnL, where n is the H20 vapor number density and L is the path length, we determined the line intensity S at the conditions of measurement from the Lorentz relation

(1)

S = 7"ro'LYL;

S has units of cm-l/(molec./cm2). These quantities were then normalized to STP conditions using the following relationships f r o m MCCLATCHEY et at.: (27)

yLO= yL (Po/P )( T/ To)°'62, iT\

I''

[hcE"(1

(2)

1~]

S O= S k~00,] exp I_---k- \ - T - Too/J

(3)

o trL°= S o /¢ryL,

(4)

and

320

T.D. WtLKERSONet al.

where Po = 1 atm and To = 273°K. These normalized data were then averaged. The final results for the average values of S °, 3'L°, and ~rL° are presented after the correction procedures are described. 4.1 Central intensities and hall-widths Direct measurements of /c and 3'ob~ were made from the strip chart recordings. The scattered light level Z and intensity baseline 10 had first to be determined. The former was found directly from measurements of opaque O2 lines near 760 nm in both the 7th and 8th orders when the White cell contained ambient air. Scattered light was 3.4% of total intensity in these cases and was assumed to have the same value for the 720nm region in 8th order; Z = 0.03410. The baseline Io was generally determined from regions of no absorption; there is a sufficient nunber of gaps in this H20 band to permit this procedure, and the I0 determined in this manner was usually applicable to the stronger lines measured. In cases where the wings of several lines overlap, the I0 for the total spectrum is not what is desired for calculating I~. Iterative corrections were made in these cases on a line-by-line basis to determine a "local I0" for each line of interest, where the "local I0" includes the effects of the wings of the nearby lines. As an example, consider a group of three slightly merged lines. The initial Io was determined from clear regions outside the overlap region, and I~ and 3'ob~were measured for the first line (1). Using the Lorentz approximation for the line profile, the absorption due to line 1 was calculated at the centers of lines 2 and 3. Using this "local I0", I~, and 3'obs were measured for line 2 and absorption due to this line calculated at the centers of lines 1 and 3. Similarly, line 3 was measured using its "local Io", and then line 1; the process was iterated until each local baseline converged and a self consistent set of measurements was produced. Usually two complete iterations were sufficient for convergence. 4.2 Spectral resolution determination The slit width was determined from measurements of 3'obsand lc on lines of pure H20 vapor taken at conditions of low pressure and medium path length (PH2o = 1.52 torr, L = 607 and 1407 m). The Doppler half-width is 3'0 = 0.0201 cm -1 at 720nm for H20 vapor at ambient temperature. BENEDICTand KAPLANt28) show that 3,L° ~ 0.55 cm-J/atm for H20 self-broadening; so, for these spectra, 7L ~ 0.0011 cm -1 ~ 0.055~/~ These values of 3'o and 3'L were used in the Voigt computer program of YouNc, ~29~which combines the Doppler and Lorentz profiles. The Voigt profile parameters are summarized in Appendix A. Using the Voigt program, theoretical absorption lines were calculated for a range of line intensities. (Since 3'L was much smaller than 3'o, the fact that 3'L~0.0011cm -1 is an approximate value had negligible effect on the calculated Voigt absorption lines.) Next, these calculated absorption lines were convolved with a Gaussian spectral slit assuming a range of slit halfwidths, a. The functional relationship between Ic and 3'obs,where a enters as a parameter, is depicted in Fig. 2. Also shown are the observed values of I¢ and 3'obsfor 55 well-isolated H20 lines, each of which yields an empirical value of a. Using JEFFREY'SO°) weighted averaging, the slit half-width was determined to be a = 0.0249 cm -j +0.0002 cm -~ st. err. The resolving power was thus 280,000, which was 46% of theoretical for the particular grating used. 4.3 Correcting for instrumental resolution Having determined the slit half-width, a, we corrected the apparent pressure-broadened line widths for finite resolution in the following manner. A series of Voigt absorption profiles was calculated, again using yo = 0.0201 cm -1 for this band and parametrically varying the true central depth Iv and Voigt width, yr. After convolving these Voigt lines with the slit function of half-width a, we calculated what the observed central intensity,/o and observed half width, Yobs, should be. Approximately 200 such convolutions were made, and the resulting points were fitted to smooth curves of constant 7v and Iv using cubic splines. The results are summarized in Fig. 3, from which it is apparent that, given the measured quantities Ic and Yobs, we could efficiently correct for the finite spectral resolution to obtain Iv and yr. Since the resolution was high, the corrections were quite small for the range of conditions we used: only the data obtained with PN2 = 369, 505, and 754 torr were used to cletermine H20 line intensities, cross sections, and pressure broadening coefficients. This procedure introduced errors less than 0.3%

Intensities and N2 collision-broadening coefficients a

=.028

.033

a =.027

~ o ~

a

321

=.026

O~''''~

a=,024

o

"~ ~.032

e.=,023

~1 '031

a=.021

v,.

~ .029 .028 .027 0.2

0.3

I I L 0.4 0.5 0.8 0.7 0.8 OBSERVED CENTRAL INTENSITY, Ic

I 0.9

Fig. 2. I~ and yob, measured on 55 spectral lines of pure H20 vapor at a pressure of P -'- 1.52 Tort. The slit half-width was determined by comparing the calculated curves with the measurements; ~r= 0.0249_+ 0.0002 cm-~, where the uncertainty is the standard error of the mean.

0.15 0.14

-r

0.12

0.12

0.II

0.11

010 I Q 0.09 LIJ > n,." 0 0 8 0.07 rn 0

0.15

0,15

0.I0

0.09 ,~

o

0.08 / 0.07~

i o.o6~

006 0.05 0.04 - 0

o1, o12 o'~ 04

o!5 o6

o!7 olB- o19 G.o

C E N T R A L IN'I:ENSITY IC

Fig. 3. Graphical representation of the corrections for the spectrograph slit function, used to determine 3'v and Iv from the measured quantities 3'ob~(the observed halfwidtb at half maximum) and It (the observed central intensity). These corrections were computed for the specific case a=0.0249cm -~, yo = 0.0201 cm -I.

in yv; errors of sevoral per cent could have occurred in yv if the Lorentz profile had been used as an approximation for the Voigt profile in this step of the data reduction. 4.4 Air path corrections T h e H 2 0 vapor measurements were made with the 5 m spectrometer filled with dry N2. This procedure reduced the problem of extra absorption caused by H20 vapor that was not in the White cell, but the optical transfer path of 8.6 m between the White cell and the spectrometer was still at ambient air conditions. In the worst case used in the data reductions (PH,o = 1.52 torr, PN2 = 505 torr, L = 207 m), there was only 3.2 times more H20 vapor in the White cell than in the outside air path. For most cases, however, there was much more HzO vapor in the cell. As in dealing with blended lines, Lorentz line profiles were assumed adequate to determine the contributions to Ic and 7oh, from the two regions of H20 vapor. This method produced good agreement between sets of data taken at different White cell path lengths. In actuality, both spectra created inside and outside the White cell multiply before being convolved with the Gaussian spectrometer slit. In general, convolution is not distributive with respect to multiplication, but after comparing synthetic profiles convolved independently before multiplication with profiles convolved after multiplication, it was found that very little difference resulted for our slit function and range of pressures and abundance. We could treat the profiles as if they

322

T.D. WILKERSONet al. 1.0 - -

--

u

oi, pot,

q

-

I ~.--.±

I

~/

/

2.95 x I0 z° molec/cm a O.9

//~a"

~°

/ / /:2"

absorption cell

~

/'~-~ "~----.. final sl~t convolution

~

e

c

l

.

obsOrp~ion (curve)

L.76 xtOZ' molec/cm z , ~ /

.~

~

0.6--005

~.

1"-~ combined cell and air path I I 0 0.05

~ .

product of seporotely

T= 2 9 4 K [ 0.10

P = 0.5182 atrnos 1 1 0.15 0.20

v-v.

[ 0.25

0.30

(cm5

Fig. 4. Comparison of a slit-convolvedtotalabsorption profile(solidline)for the White cell and outside air path in tandem vs the product (solid points) of the two separately convolved profiles multipled together. Agreement under all of the conditions employed (see Table 2) facilitatesthe correction for the air path of H20. A Gaussian slitfunction is assumed.

were convolved separately, and still maintain errors from this source at less than 0.3% in the half-widths. Figure 4 shows an example in which profiles convolved independently before combining are compared with profiles combined before convolution with the slit function. The equations used to correct yv and Iv for the outside air path are given in Appendix B.

4.5 Lorentz parameters Having obtained the Voigt parameters for each measurement, yv and Iv, we could have proceeded in a similar manner to determine yL and IL using the same computed Voigt absorption line profiles. However, an expression is available in closed form relating yv, YL, and YD- WHITING(M) and KIELKOPF'S(n) work was improved by OLIVEROand L O N G B O T H U M (33)to give the expression Yv = l/2[ClyL + "~v/(C2YL2 + 4C3y2)].

(5)

Wtih the constants C1 = 1.0692, C2 = 0.86639, and C3 = 1.0, they have shown this expression to be accurate to better than 0.02%. Solving for yL, we determined YL= YV[7.7254 -- 6.7254%/(1 + 0.3195(yo/yv)2)].

(6)

From the Voigt central intensity Iv, we calculated the optical depth rv = - In Iv. From rv and yL, we computed zL through the equation TV

ZL X/~yK(0,y)'

(7)

y = x/0n 2)YdYD

(8)

where y is the Voigt parameter

and K(0, y) is the Voigt function at the line center, following the notation of YouN6: 29) Equation (7) is derived in Appendix A and rdZv is tabulated as a function of y. S a, yL°, and crL° were then computed from yL, ru and the physical conditions existing during the spectral scan, according to Eqs. (1-4). The individual determinations of these normalized quantities were assigned weights based on the quality of each spectral measurement, as is discussed in Appendix C. The final results of these measurements are listed in the next section.

Intensities and N2 collision-broadeningcoefficients

323

5. RESULTS Table 3 lists the vibration-rotation assignments for the 62 lines selected for measurement according to the criteria discussed in Section 2. This spectral region is dominated by the fourand five-quantum jumps in which the upier vibrational states are (v~v~v~)=301,202, and 221. As summarized in Table I and Fig. 1, the appropriate range of lower state angular momentum J" is 2 to 5 for temperature insensitive lines in the atmospheric temperature range, and the values J"= 3 and 4 predominate. Table 4 presents the measurement results for the 62 lines, giving the wavelength, number of measurements of each line (n), the strength S °, N2-pressurebroadened halfwidth yL°, and corresponding line-center absorption cross section trL° (all at STP conditions). To save space, a common exponential unit of 10-24 is used for both S O and trL°, though their dimensions are different. Appendix C describes the assignment of weights to each of the individual spectral measurements of these quantities. The quantities listed in Table 4 are weighted averages of S °, yo, and ~L°. The standard deviation of the mean for each of these weighted averages was calculated line by line, using the expression of Pu~I~ and W|NSLOW(34)

. / ( L''d2)

sm= V \ ( n - 1)Xw}

(9)

where w is the weight of each measurement, d is the deviation from the mean, and n is the number of measurements. Before accepting sm as a good evaluation of the uncertainty of the results for each line measured, we divided the data into several subsets of different conditions of measurement to check for possible systematic effects. When the data were grouped into the 3 subsets corresponding to the N2 pressure conditions employed, it became evident that there was often greater dispersion of those three individual 3, o values for a given line than was reasonable to expect from its value of sm calculated from the entire data set. This probably reflects the increasing difficulties of measuring yobsat the higher pressures. The wing overlap of neighboring lines sometimes distorted the measured shape of the line, and this could not always be exactly corrected. Therefore, the standard deviations of the mean for all quantities were recalculated using Eq. (9) for the data subsets grouped by pressure; in this case, d is the deviation of a subset from the mean, w is the weight of a subset (which was set equal to the number of measurements in that subset), and n is the number of subsets. The standard deviation of the mean for each line presented in Table 4 is the larger value of sm calculated by these two methods. 6. DISCUSSION The values given in Table 4 are the results of many independent measurements (on the average, eleven measurements per line) of recorded absorption line profiles under the variety of physical conditions indicated in Table 2. Each measurement was an absolute one, rather than being made relative to a few standard lines. Systematic errors were eliminated as far as possible by using absolute pressure measurements of the H20 vapor in the absorption cell prior to adding N2 as a pressure-broadening gas, rather than relying on a psychrometer or other classical device for humidity determinations. When the data analysis was complete, we made a few spot checks to show that the S o and yL° quoted in Table 4, when used to generate synthetic spectral line profiles, indeed agreed with the profiles observed in specific experimental runs. Figure 5 shows one such comparison at 1/2 atm N2, including the effects of the spectrograph slit smearing. Agreement of synthetic and actual line profiles was good in all cases and is an important corroboration of the profile assumptions that were necessitated by the finite resolution of the spectrograph. A residual systematic error, of the order of a few per cent, may be present in the quoted values for the pressure-broadening coefficient yL°. Comparing subsets of these results for one atm N2 vs one half atm N2, one finds an average value (over all the lines) of 1.053 for the ratio yL° (1 atm)/yL° (1/2 atm), w~de the corresponding average of the standard errors for this ratio is -+4.3%. Thus the distinction between the low and high pressure data seems to be real, though not large in magnitude. One can speculate that: (i) the one atmosphere (N2) results on yL° are

324

T.D. WILKERSON et aL

Table 3. H20 absorption lines measured in this study. Air wavelengths and vacuum wavenumbers as listed by J. W. Brault and W. S. Benedict (private communication, 1973). The level are specified in the same manner in Ref. (5). x(nm)

C(cm"I )

E"(cm- l )

J"K'~K'~

J'K~K~

714.7639

13986.778

715.3750

13974 830

715.9322

vlv~v ~

136.77

303

422

301

315.79

422

533

202

13963 954

212.15

321

432

202

717.5986

13931 527

173.36

312

423

202

717.6152

13931 205

315.79

422

523

301

717.7625

13928 346

275.52

413

514

301

718.1537

13920 759

325.35

505

606

301

718.1760

13920 327

326.64

515

616

301

718.2836

13918 241

326.64

515

606

202

718.6144

13911 834

222.06

404

505

301

718 6379

13911 380

212.15

321

422

301

718 7404

13909 395

224.83

414

515

301

719 1488

13901 497

136.77

303

404

301

7191866

13900.766

206.30

322

423

301

719 2472

13899.595

136.77

303

414

202

719 3765

13897.095

142.28

313

414

301

719,7869

13889.173

136.17

220

321

301

720,0024

13885.016

222.06

404

423

301

720 0541

13884.019

134.91

221

322

301

7201492

13882.184

136.77

303

322

301

720 2871

13879.528

206.30

322

413

202

721,1216

13863.473

224.83

414

413

301

721,5545

13855.149

134.91

221

312

202

721 8029

13850.382

142.28

313

312

301

723 0708

13826.095

212.15

321

404

301

7232236

13823.173

300.35

423

422

301

723.4400

13819.039

206.30

322

321

301

723.4734

13818.400

134.91

221

220

301

723.6133

13815.728

136.17

220

221

301

724.0828

13806.770

212.15

321

322

301

724.3477

13801.721

285.23

331

330

301

724.3717

13801.265

285.43

330

331

301

724.9389

13790.466

173.36

312

331

221

725.0221

13788.883

173.36

312

313

301

725 2096

13785.318

315.79

422

523

221

725 8654

13772.864

285.43

330

431

221

725,9121

13771.978

285.23

331

432

221

726,0068

13770.182

275.52

413

514

221

726 2976

13764.668

136.77

303

212

202

726 3392

13763,879

275.52

413

414

301

726 5594

13759,703

136.77

303

202

301

727 0129

13751.126

325.35

505

606

221

727 5407

13741.148

212.15

321

220

301

727 6314

13739.436

224,83

414

515

221

727 6549

13738.993

224.83

414

331

221

727 6846

13738.433

222.06

404

313

202

727 7388

13737.409 13736.106

224.83

414

313

301

727.8078

222.06

404

303

301

727.9691

13733.063

134.91

221

322

221

728.2282 728.3214

13728.176

136.77

303

404

221

13726.420

728,7379

13718.575

142.28 300.35

313 423

414 322

221 301

72B.8126

13717.169

275.52

413

312

301

729.1401

13711.007

729.2169

13709.563

325.35 315.79

505 422

414 321

202 301

729.7061

13700.372

224.83

414

413

221

730.5630

13684.304

212.15

321

202

301

730.8701

13678.553

285.23

331

330

221

730.8782 730.9619

13678.401 13676.835

285.43 285,43

330 330

331 313

221 301

731.1245 731.5514

13673.794 13665.814

300.35 134.91

423 221

422 220

221 221

Intensities and N2 collision-broadening coefficients

325

Table 4. Measured strengths, widths and line center cross sections for HzO absorption lines. Standard temperature and pressure (STP) are assumed, and the exponential unit for S o and ~o is 10-24. k(nm)

n

S°(cm-1/molec./cm 2)

y~{cm -1 )

a~(cm 2)

714.7639

9

1.89

± 0.08

0.1062

± 0.0040

5.67

-+ 0.08

715.3750

4

0.440

-+ 0.017

0.099

+ 0.006

1,42

~

0.06

715.9322

7

1.022

± 0.027

O.lO|O

± 0.0038

3.23

±

0.05

±

0.08

717. 5986

II

2.82

± O.lO

O.1051

±

0.0039

8.57

717.6152

14

5.36

± 0.13

0.1981

±

0.0028

15.78

......

20.9

....

O.ll2

4__ 0.13 ....

717.7625

l

7.38

718.1537

II

22.57

-+ 0.25

0.0878

±

0.0017

82,1

±

718.1769

14

7.23

-+ 0.15

0.9919

_+ 0.0032

25.2

-+ 0.6

0.661

718.2836

4

i

0.030

0.0933

_+ 0.0047

±

0.06

718.6144

16

II.I0

±

0.29

0.0961

+_ 0.0030

37.0

±

0.6

718.6379

15

20.9

±

9.6

0,I075

_+ 0.0015

61.8

±

l.l

718,7404

II

34.5

-+ 0.7

O.lO01

+_ 0.0023

I09.7

±

3.6

719,1488

18

40.1

±

0.I079

_+ 0.0012

I18.6

±

2.5

719.1866

23

7.07

-+ 0 . I 0

0.1028

_+ 0.0017

21,99

+

0.29

719.2472

21

4.44

-+ 0.15

0.1064

_+ 0.0032

13.30

±

0.18

719.3765

24

13.22

±

0.20

0.I025

±

0.0025

41.1

±

0.5

719.7869

23

6.09

+-

0.26

0.I045

±

0.0036

18.55

-+ 0.29

720.0024

l

0.49

....

0.091

720.0541

19

±

0.7

0.1093

±

720.1492

3

1.83

-+

0.20

0.III

_+ O.OlO

720.2871

1

0.40

....

0.087

721.1216

15

2.95

-+

0.05

0.I095

±

0.0020

8.57

±

721.5545

3

0.50

±

0.07

O.lOl

±

0.015

1.567

-+ 0.030

721.8029

8

2.15

_+ 0.08

0.I159

±

0.0035

5.89

-+ 0.06

723.0708

4

0.66

±

0.08

0,II0

-+

0.014

1.914

±

723.2236

13

6.62

±

0.14

0.I082

-+

0.0021

723.4400

13

5.30

±

0.I0

0.I040

±

0.0021

723.4734

lO

38.8

-+

1.3

0.I069

±

0.0023

723.6133

15

12.92

±

0.22

O.1081

±

0.0017

724.0828

16

15.4

±

0.5

0.I022

*

724.3477

25

-+

0.21

0.0919

19.0

8.77

1.2

...... 0.0012

......

2.25

1.6

1.70 55.2 5.27

.... -+ 1.5 +

1.48

0.22 .... 0.08

0.030

19.49

-+ 0.34

16.21

±

0.12

+

3.2

38.06

±

0.39

0.0038

48.2

±

0.6

±

0.0028

30.45

-+ 0.36

90.I

-+ 2.2

I15.7

-+

0.7

0.0971

-+

0.0015

0.453

±

0.038

0.085

+-

0.012

24

5.67

-+

0.28

0.I132 ±

0.0045

725.2096

2

1.14

±

0.I0

0.145

O.Oll

2.495

-+ 0.025

725.8654

8

1.472 ±

0.039

0.0960 -+

0.0028

4.90

-+ 0.16

725.9121

3

0.417 ±

0.036

0.0770 ±

0.0041

1.73

±

726.0068

4

0.92

-+

0.18

0.I18

0.018

2.46

+- 0.14

726.2976

13

3.99

+

0.09

0.I074 ±

0.0026

1.184

-+ 0.017

726.3392

6

1.04

±

0.18

0.102

0.016

3.25

±

-+

1.0

0.I190 +-

9.0019

724.3717

19

724.9389

3

725.0221

27.4

32.3

±

-+

±

1.70

±

0.08

15.95

±

0.37

86.4

O.lO

0.19

-+ 3.0

726.5594

II

727.0129

II

2.54

±

0.16

0.0859 ±

0.0035

727,5407

16

14.31

±

0.45

O.ll06 -+

0.0020

41.2

±

727.6314

13

3.30

-+

0.09

0.0919 -+

0.0020

II.45

+- 0.29

727.6549

II

3.13

±

0.12

0.I026 ±

0.0027

9.70

-+ 0.16

727.6846

13

4.10

-+

0.13

0,I064 -+

0.0023

12.25

-+ 0.28

727.7388

13

±

0.9

0.I097 -+

0.0018

70.I

+

727.8078

17

±

0.16

0.1092 ±

0.0028

16.79

-+ 0.45

727.9691

13

2.27

±

0.06

0.1036 -+

0.0020

6,95

-+ 0 . I 0

728.2282

12

4.74

±

0.24

0.I076 -+

0.0033

14.02

-+ 0.27

728.3214

4

0.029

0,0960 -+

0.0023

728.7379

14

14.53

+-

0.31

0.I074 -+

0,0013

43.1

728,8126

16

7.05

*

0.19

0.1075 -+

0.0013

20.87

± 0.45

729.1401

8

1.39

+

0.05

0,I019 ±

0.0030

4.34

+- 0.16

729.2169

15

4.71

+

14.78

729.7061

3

0.398 ±

24.1 5.75

1.345 ±

9.41

4.466

0.6

1.8

-+ 0.023 ± 0.7

0.14

O.lOl5 ±

0.0026

0.016

0.102

±

0.006

1.244

-+ 0.031

-+

-+ 0.031

730.5630

3

0.85

0.07

O,lOl

0.008

2.689

730.8701

4

1.311 -+

0.048

0.0702 ±

0.0017

5.95

730. 8782

6

4.1

-+

O. 5

O.lOl

±

0.008

730.9619

3

0.89

±

0.08

0.097

+- 0.008

731.1245

3

0.93

±

0.05

0.989

±

731.5514

12

4.73

±

0.13

0.0964

+_ 0.0031

-+

-+ 0.22

0.006

13.0

+

0.19

± 0.09 ±

0.6

2,940

_+ 0.025

3.349

±

0.027

±

0.35

15.68

326

T.D. WILKERSONet al. I00

8O

0,o,,e \/

Observed line

////

~

Colculo'ted profile

60

O3 Z

4O H20: X= 723.6155 nm

20

I

+0.50

L

]

,

I

+0.25

t

0 v-v °

L

-0.25

~

I

-0.50

(cm -~)

Fig. 5. Comparison of observed profile of an H20 absorption line with the profile calculated using the results for ~,0 and S o listed in Table 4. Convolution calculations include the thermal Doppler effect (Voigt function) and the spectrograph slit function.

rendered artificially large by the blending of many very faint lines lying nearby the measured ones, or (ii) the half atmosphere profiles are the less reliable ones with which to find ~/L° because the slit correction is percentage-wise more important, or (iii) the pressure broadening of H20 lines by N2 molecules is slightly nonlinear with pressure. Higher resolution measurements are needed to settle these speculations. The average values for yL° quoted in Table 4 are not likely to be systematically in error by more than 2-3%. The linewidths may be compared in a few salient respects with the calculations by BENEDICT and KAPLAN(35)for rotational linewidths of H20. The comparison is far from complete, since our measurements cover only a small fraction of the lines (and of the range of J, the total angular momentum), and the calculations do not include lines for which AJ = - 1. Nonetheless, we can look at the relationship between the measured 3'L° and certain average values ~ that BENEDICT and KAPLAN(35) obtained for all lines (AJ = 0, +1) arising from a given rotational level (e.g. J"K"K'~= 413) in the ground state. It is useful to see whether yL° and 37 display similar dependences on J and whether, for any given J"K"K", yL° varies systematically with the upper vibrational state (v~, v~, v~). The rotational levels are "even" or "odd" according as the parity of (J + K,, + Kc).

The lines listed in Tables 3 and 4 fall into four groups of even levels (K" = 0, 1, 2, 3) and three groups of odd levels having K" = 1, 2, 3. Only a few lines having K" = 3 were studied. Hence, most of the comments given below are based on the other five groups. Also, the largest class of measured lines as regards the upper vibrational state is (v[, v~, v~)= (3, 0, 1), the following remarks are confined to this case unless ortherwise explicitly noted. Discernible trends in ~ vs J" are predicted for lines associated with even levels J"K"K~ = 303, 404 and 505 in the group K ~ = 0 and for the odd levels 313, 414 and 515 in the group K,' = 1; measurement bears out that y o indeed decreases by about 15% as J" increases from 3 to 5 within each of these groups. The values of yL° are of order 10% greater than 1; in most cases. Constancy of ~ with J is predicted for these groups: J " = 3, 4 in the even levels where K,' = 1; J " = 2, 3, 4 in the even levels having Katt _- 2; and j t t = 3, 4, 5 in the odd levels where K~ = 1. Indeed, 3'L° is reasonably constant within these groups and is typically 15% greater than the calculated 17. Comparison of linewidths between differing upper vibrational states is scanty. We will make note of a few instances here in which a particular level J"K',;K" absorbs to the same type of level J ' K ' K " in a different vibrational state, in particular (v~, v~, v~) = (2, 2, I) instead of (3, 0, 1). For even rotational levels, this comparison shows no striking difference between (2, 2, 1) and (3, 0, 1). For odd levels on the other hand, the ratio 3°(2, 2, 1)/~°(3, 0, 1) decreases with increasing J" and K~. Sample values of this ratio are 0.95 for 221 ~ 322, 0.82 for 423-->422 and 0.76 for 331 -->330. Thus, it appears that the J dependence of H20 linewidths may be modulated significantly in some cases by vibrational effects. On the other hand, the agreement of the

Intensities and N2 collision-broadeningcoefficients

327

measured y o for four- and five-quantum transitions in the near i.r. with calculations by BENEDICTand KAPLANof q for the far i.r. is in general remarkably good. Further discussion of H20 linewidths will be given in a subsequent paper, when new results on the ptr¢ band near 940 nm are presented. We will comment briefly on the applicability of our results to H20 linewidths in atmospheric air. This problem has been addressed frequently and holds continuing interest as knowledge accumulates on the quadrupole moments of N2 and 02 and on theoretical calculations of pressure broadening. DAVIES and OLIt36) have recently presented new calculations which are compared with those of BENEDICTand KAPLAN~28"35)and with measurements in the 5#m region by ENG, KELLEY, MOORADIAN,CALAWA, and HARMAN(37) and by ENG, KELLEY, CALAWA,HARMAN, and NILE. (as) For the present it appears reasonable to adopt the result y(air)/y(N2) = 0.9 as accurate within a few percent for low J lines of H20, reflecting the approximation T(O2)/T(N2) ~ 0.5 which unfortunately was not tested in the present measurements. More complete measurements are indeed required, both of the lines themselves and of the effective quadrupole moments Q2 of N2 and 02. For the present, QE(N2) appears to be close to four times Q2(O2), as noted by ENG et al. (3s) Therefore one can use the nitrogen results for yL° given in Table 4 to estimate the corresponding quantities for ambient air at about 90% of the values shown. Finally we wish to cite the comparison of our scale of absolute strengths S Owith the only other available compilation for these lines, namely the unpublished results of Brault and Benedict (private communication, 1973) alluded to previously. The latter compilation is very useful because it contains - 2 0 times as many lines as we have measured absolutely here. Figure 6 is given to enable the reader to convert between the two scales of strengths. The comparison is shown logarithmically, and a slightly curved, quadratic fit is indicated in the figure. The equation for this curve is loglo (1024z) = O.024563[lOglo(lO24x)]2 + 1.043911 lOglo(lO24x) -- 0.072352,

(10)

where z is the line strength we measured in the present work, and x is the line strength according to Brault and Benedict. As seen in Eq. (10), a normalizing factor of 102'1was adopted in the determination of the quadratic fit. For line having strengths S o>- 10-23 cm -j cm2/mol, the two scales are in close agreement. The slope of the data-fitting curve is nearly constant and is greater than unity, so that for S o - 10-24 cm -I cm2/mol there is a 15% excess in the previously measured strengths relative to ours. We believe this discrepancy is a systematic overestimation of the weaker H20 line strengths by Brault and Benedict, perhaps arising from the geometry of their long, low angle slant paths through the atmosphere and the influence of high altitude humidity on the observable absorption by weak vs strong lines. Generally speaking, the estimation of humidity b

~o

_z

10 -23

m

I--

~,

10 -24

.J

3 X 10 -25

10 -24

10 -23

L I N E S T R E N G T H S M E A S U R E D BY 8 R A U L T A N D B E N E D I C T

Fig. 6. Logarithmic comparison of line strengths of Brault and Benedict (private communication, 1973)with those measured in the present study. The quadratic "best fit" curve is described in Section 6.

328

T.D. WILKERSONet al.

b y B r a u l t a n d B e n e d i c t r e l a t i v e to t h e f o r m a t i o n o f t h e s t r o n g e r lines a p p e a r s to h a v e b e e n q u i t e a c c u r a t e . F o r t h e e n t i r e c o l l e c t i o n of lines t r e a t e d h e r e , w e p r e f e r o u r a b s o l u t e scale of s t r e n g t h s b e c a u s e w e m e a s u r e d t h e H 2 0 a b u n d a n c e a n d t h e l e n g t h of t h e a b s o r b i n g c o l u m n a b s o l u t e l y . F o r t h e m a n y lines n o t m e a s u r e d b y us b u t s t u d i e d b y B r a u l t a n d B e n e d i c t , o n e c a n p r o v i s i o n a l l y u s e t h e d a t a r e p r e s e n t a t i o n s h o w n in Fig, 6 to t r a n s f e r t h e p r e v i o u s r e s u l t s into o n e s w h i c h w o u l d b e c o n s i s t e n t w i t h o u r a b s o l u t e scale.

Acknowledgements--We wish to thank R. W. BOESEfor his continued support and encouragement of this work. Frequent discussions with W. S. BENEDICTwere invaluable, and the use of his and J. W. BRAULT'Sdata was very helpful in planning the measurements. The contribution of J. BRASSEURin setting up and running the early experiments, and of M. LIU and W. ZABORin obtaining and reducing data, are gratefully acknowledged.

REFERENCES 1. D. E. BURCHand D. A. GRYVNAK,Absorption by H20 between 5045 and 14,485cm -~ (0.69-1.98/zm). AeronutronicPhilco Ford Report No. U-3704 (July 1966). 2. D. E. BtJRCH, D. A. GRVVr~AK,and R. R. PArry, Absorption by H20 between 2800 and 4500cm -1 (2.7#m region). Aeronutronic-Philco Ford Report No. U-3202 (Sept. 1%5). 3. M. MrNNAERT,G. W. F. MULDERS,and J. HOtITGAST(Utrecht) Photometric Atlas of the Solar Spectrum. D. Schnabel and Kampert-Helm, Amsterdam (1940). 4. C. E. MOORE, M. G. J. MIN~rAER'r,and J. HOUT6AST, The Solar Spectrum 2935 A to 8770 A, National Bureau of Standards Monograph 61 (1%6). 5. L. DELBOUILLEand G. ROLAND,Photometric Atlas of the Solar Spectrum from A7498 to ,~12016, M6moires de la Societ6 Royale des Sciences de Li6ge, Special Vol. 4 (1963). 6. J. W. SWENSSON,W. S. BENEDICt,L. DELBOtJ~LLE,and G. ROLAND,The Solar Spectrum from A7498 to ,t 12016, Institut d'Astrophysique de l'Universite de Li6ge, Special Vol. 5 (1970). 7. C. B. FARMER,Icarus 15, 190 (1970). 8. R. E. MEREDITH,T. S. CHANG,F. G. SMITHand D. R. WOODS,Investigations of Molecular Absorption Line Parameters for Atmospheric Constituents, Science Applications Inc. Report No. SAI-73-004-AA(II) on ARPA/STO Contract No. DAAH-01-73-C-0786 (Dec. 1973). 9. J. W. BRAULT,J. S. FEHDER,and D. N. B. HALL, JQSRT 15, 549 (1975). 10. J. W. BRAULTand L. TESTERMAN,Preliminary Edition of the Kitt Peak Solar Atlas, unpublished (1972). II. L. S. RO'rHMAHand R. A. MCCLATCHEY,Appl. Opt. 15, 2616 (1976). 12. R. M. MEASURESand G. PILON, Optoelectronics 4, 141 (1972). 13. S. A. AHMED,AppL Opt. 12, 901 (1973). 14. R. L. BYERand M. GARBI/NY,Appl. Opt. 12, 1496 (1973). 15. R. M. SCEOTLAND,Proc. of the 4th Syrup. on Remote Sensing of the Environment, pp. 273-283. University of Michigan at Ann Arbor (April 1966). 16. R. M. SCHOTLAHD,J. Appl. Meteorology 13, 71 (1974). 17. E. E. REMSBERGand L. L. GORDLEY,Appl. Opt. 17, 624 (1978). 18. T. D. WILgERSON,B. ERCOLI,and F. S. TOMKINS,Atmospheric absorption spectra, University of Maryland, Tech. Rep. (to SRI) BN-784 (Feb. 1974). 19. R. G. ELLISGSON,T. J: MclLRATH,G. SCHWEMMER,and T. D. WtLKERSON,Water vapor lidar. University of Maryland, Tech. Rep. BN-816 (Jan. 1976). 20. G. B. NORrHAM, E. V. BROWELL,M. L. BRUMEIELD,T. D. WlLS:ERSON,and T. J. MCILRATH,Proc. on a workshop on remote sensing of the marine boundary layer, pp. 308-316. Vail. Colorado, (Aug. 1976), NRL Memor. Rep. 3430 (June 1977). 21. E. V. BROWELL,M. L. BRUMFIELD,J. H. SIVITER,JR., G. B. NORTHAM,T. D. WILKERSOt~,and T. J. MCILRATrl,Proc. of the 8th Int. Laser Radar Conf. Drexel University, Philadelphia, Pennsylvania (June 1977). 22. G. SCHWEMMERand T. D. WILKERSON,Proc. on a Workshop on Remote Sensing of the Marine Boundary Layer, pp. 288-299. Vail, Colorado (Aug. 1976), NRL Memo. Rep. 3430 (June 1977). 23. G. SCHWEMMERand T. D. WILKERSO~, Proc. of the 8th Int. Laser Radar Conf. Drexel University, Philadelphia, Pennsylvania (June 1977). 24. H. I. HEATON,JQSRT 16, 801 (1976). 25. H. J. KOSTgOWSKIand A. M. BASS,J. Opt. Soc. Am. 46, 1060 (1956). 26. R. E. MEREDITH,JQSRT 12, 455 (1972). 27. R. A. M¢CLATCHEY,W. S. BENEDICT,S. A. CLOUGH,D. E. BtIRCH, R. F. CALFEE, K. FOX, L. S. ROTHMAN,and J. S. GARING, AFCRL atmospheric absorption line parameters compilation. Air Force Cambridge Research Laboratory. Rep. No. TR-0096 (Jan. 1973). 28. W. S. BENEDICTand L. D. KAPLAN,JQSRT 4, 453 (1964). 29. C. YOUNG,JQSRT 5, 549 (1965). 30. H. JEFFREYS, Theory of Probability, p. 129. Clarendon Press, Oxford (1948). 31. E. E. WHITIr~G,JQSRT 8, 1379 (1968). 32. J. F. KIELKOPF,J. Opt. Soc. Am. 63, 987 (1973). 33. J. J. OUVEROand R. L. LONGEOTHUM,JQSRT 17, 233 (1977). 34. E. M. PUG~Iand G. H. WINSLOW, The Analysis of Physical Measurements, p. 107. Addison-Wesley, Reading, Mass. (1%6). 35. W. S. BEr~EDICTand U D. KAPLAN,J. Chem, Phys. 30, 388 (1959). 36. R. W. DAWESand B. A. OLI, JQSRT 20, 95 (1978). 37. R. S. ENG, P. L. KELLEY,A, MOORADIAN,A. R. CALAWA,and T. C. HARMAN,Chem. Phys. Lett. 19, 524 (1973). 38. R. S. ENG, P. L. KELLEY,A. R. CALAWA,T. C. HARMAS,and K. W. NILL, Molecular Phys. 28, 653 (1974).

Intensities and N2 collision-broadening coefficients

329

APPENDIX A Voigt [unction

Following the notation of YOUNG,ag) the Voigt profile is the convolution of the Lorentz profile and the Doppler profile, determined through the integral k~

y /'® e x p ( - t 2) .

K(x,y)=~: g j_=yT~(-Zz~_t)~at.

(i)

Here k. is the (Voigt) absorption coefficient, and ko = (S/yo)(ln 2/Ir) tt2,

(2)

y = (yL/yD)(In 2) m is the Voigt parameter,

(3)

x = [(v - ~o)/yo](ln 2) 1/2,

(4)

S = ~r~LyL is the line strength,

(5)

YL = YL°P/Po is the Lorentz half-width,

(6)

yo = (volC)(2kT In 2/m) t/2 is the Doppler half-width,

(7)

vo = the wavenumber of the line center, and v = the wavenumber being evaluated. At the line center, ~'v = k~nL; since "rL = o'LnL, we can combine Eqs. (1), (2), and (5) at v = vo into the expression

YD \ ~ ' / Substituting Eq. (3), we get ~'t

7v

X/~'yK(0, y)'

(9)

which is the relationship of the Lorentz optical depth to the Voigt optical depth given by Eq. (7) of the main text. Values of K(0, y) were taken from the tables of YouNo, (29J and the factor (V'~ryK(0, y))-~ is given in Table 5 for 1.8 < y <_-10. This range of values for y exceeds our applications for the present H20 measurements. For y - 2, applicable for our 0.5 atm data, z L - l.H'v; so this factor (X/~ry(K0, y))-i can be regarded as a correction factor to obtain ~'z.from rv. APPENDIX B Correction for absorption in the air path outside the gas cell

The analysis of the correction problem proceeds on the assumption that both the gas cell and outside air path absorption profiles are Lorentzian. This is allowed because the Gaussian contributions to broadening are small and are the same in both cases, and because the air path correction is small compared to the principal absorption in the gas cell. For the case of two absorptions in tandem, each given by a Lorentz optical depth • i = Aio'i = SAiyi/Tr[(v- vo)2+ 712]

(1)

~',. = ~'j + 72,

(2)

the measured total optical depth is

where the Ai = n~Li are abundances in mol/cm2, o-i are the absorption cross-sections in cmZ/mol, S is the line strength in Table 5. Correction factor for computing Lorentz optical depth from the Voigt optical depth. l y

~

y K(o, y)

l y

~

y K(o, y)

l y

~

y K(o, y)

1.8

1.12521

3.6

1.03606

6.0

1.01353

2.0

1.10454

3.8

1.03256

6.5

1.01157

2.2

1.08853

4.0

1.02955

7.0

1.01001

2.4

1.07588

4.2

1.02693

7.5

1.00874

2.6

1.06573

4.4

1.02464

8.0

1.00769

2.8

1.05745

4.6

1.02263

8.5

1.00683

3.0

1.05063

4.8

1.02085

9.0

l.D0610

3.2

1.04493

5.0

1.01928

9.5

1.00548

3.4

1.04014

5.5

1.01603

I0.0

1.00495

330

T.D. WILKERSONet al.

cm-~/(mol/cm:), yi are the half-widths at half-maximum in cm -~, v is the frequency in cm -~, and vo is the line center frequency in cm -~. At the line center, "tic = SAi/TryE

(3)

Using Eq. (3) and the Lorentz half-width relation 3'2/Yl =

PJP1,

(4)

where P~ are broadening gas pressures, then (5)

r~c = r,cPIA2IP2AI.

Combining Eqs. (5) and (2), we obtain an expression for the optical depth of one profile in terms of the measured optical depth and the experimental parameters P~ and Ai; viz., (6)

tic = rmcP2AI/(P2AI + PjA2).

We then proceed to extract the halfwidth of the absorption profile in the gas cell by using Eqs. (1-4) to find all other contributions to the measured halfwidth. From Eqs. (1) and (2), r~ = SA,(y,l~r)l(v- vo)~+ 3'121-' + SA2(3"J~r)f(v- roy + 3'2:1-'-

(7)

r,.c = (SAd~ry,) + (SA2hry2).

(8)

Ym~- v - Uo.

(9)

At the line center,

Defining the measured half width

such that T,.(V

-

vo) = ~',.d2,

SA~(y,l~r)(3"J ÷ y,2)-, ÷ S A 2 ( y d I ~ ) ( y J ÷ y22)-'

( 1o) =

½(SI¢)[(A,ly,) + (Ady2)].

(11)

Using Eq. (4) to eliminate y2, one obtains AIyJ(Y,.2+ Yl2)- j + A2yI(P2/PI)[Y,. 2+ Yl2(P2/Pl)2]-1 = ~[(AI/Yl)+ (A2PI/ylP2)].

(12)

This expression can be solved as a quadratic in 3'2 (taking the positive real root to give the halfwidth 3', of the profile due to gas in the cell alone) in terms of the measured halfwidth 3',. and the experimental pressures and abundances: 4+ 2[Ym2(PI2-P22)(AIP2-AzPI)] yra4pI2 0' YJ Yl L P22(AIP2+A2PO ] - ~ P2

(13)

Thus, using Eq. (5) and the solution to Eq. (13), we were able to unfold the desired line parameters from measured line parameters. APPENDIX C Weighting [unction In order to give more weight to the data that were the least susceptible to error, we studied the strip chart recordings to estimate which data were more accurate and to express this result quantitatively. At low transmissions, the measurements were generally limited by the recorder penwidth, which corresponded to an error in intensity, of approx. AI = 0.003 on a 1,0

.8

.4

.2 0

f I

I

I

I

~

I

I

I

I

P

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0,8

0.9

1.0

OBSERVED CENTRAL INTENSITY, Ic

Fig. 7. Weighting function used in averaging multiple measurements of each absorption line.

Intensities and N2 collision-broadening coefficients

331

scale of 0-1. At higher intensity the signals were limited by random fluctuations on the order of 1%, or AI = 0.01I. Solving simultaneously for the two AI equations, the changeover from one limiting error to the other occurs at I = 0.3; therefore, AI = 0.003 for I ~ 0.3 (penwidth), and 41 = 0.01I for 1 I> 0.3 (1% noise). One would also like the weighting function, w, to have a broad maximum around the optical depth unity. The product Ir satisfies this requirement. Since we want the weight to decrease as the errors increase, w should be inversely dependent on, or contain a subtractive term proportional to, the error AL The term we chose which satisfies this requirement is e ~ (Alll)(lr) ~. Then

e

= ~0.003/I2r [ 0.01/It

for I < 0.3, for I>0.3.

For zero error, 1.0 was chosen as the maximum weight, and w = t . O - ce, where the error term was scaled by a constant c, depending on how rapidly the weighting function should decrease with increasing errors. We chose a value of 2.0 for c, gMng less weight to data from lines near saturation and also from weak, noisy lines. In practice we used the observed central intensity lc of the line in this weighting function. The final weighting function used was then

w

=[l-(O.O06/Ic2r) [ 1-(0.021I¢r)

for for

/,<0.3, Ic>0.3.

This equation gave a maximum weight of 0.9456 at ~"= 1 and reached zero at I~ = 0.98 and I~ = 0.042. Very few measurements were made at such extremely small and large absorptions. Figure 6 is a graph of this weighting function.