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Intensities and widths of H2O lines between 1800 and 2100 cm-1
.I. Qaant. Spectrosc. Radiat. Trans/er, Vol. 18, pp. 491-499. Pergamon Press 1977. Printed in Great Britain
INTENSITIES AND WIDTHS BETWEEN 1800 A N D
OF H20 LINES 2 1 0 0 c m -~
Y. S. CHANG and J. H. StrAW Department of Physics, The Ohio State University,Columbus,OH 43210, U.S.A. (Received 15 March 1977)
Abstract--A n0n-linear, least-squares program was used to obtain the line intensities and widths of 91 air-broadened lines in the z,2rotation-vibrationband of water vapor in the region from 1800to 2100cm-1. The values obtained for the line intensities are, on the average, about 7% stronger than the Air Force Cambridge Research Laboratories(AFCRL) Atmospheric Absorption Line Parameters Compilation.The experimentalvaluesfor the half widths of the H20 lines are, on the average,4% higherthan the calculated AFCRL values. The measurementshave confirmedthe narrow widths of some high J transition lines measured by tunable diode laser spectroscopy. INTRODUCTION WATER vapor lines occur throughout the i.r. and information concerning their parameters is required in order to predict the transmittance of long air paths. There have been many observations of water vapor spectra and, in particular, measurements of line intensities and widths in the region from 1800 to 2100 cm -~ have been compiled t~) and reported by T o ~ and FARMER,t2) BEN-ARYEH,t3), PATEL,t4), BLUM et al., tS~ GUF_aP,A et ai., ~° and ENG et al. {7"s~ The reported accuracy of all these measurements is approx. 10-20%. In addition, calculated values for the intensities and widths of these lines have been given by BEN~.DICTand CALFE~,tg) and revised calculated values appear in the 1976 AFCRL atmospheric lines parameter compilation described by MCCLATCHEYet al. ") We have used a non-linear, least-squares program ~°) to obtaitl the line intensities and widths of 91 air-broadened lines in the 1,2 rotation-vibration band of H20 in the region from 1800 to 2100 cm -I. This method yields either the parameters of single isolated lines or else determines the parameters of several overlapping lines. The present study was undertaken both to study the application of the non-linear, least-squares program to obtain line parameters and to improve or confirm previous observations. EXPERIMENTAL The Ebert type grating spectrometer used in this study has been described previously. {11)A spectral resolution of about 0.06 cm -1 was obtained near 2000 cm -1 with a 26 x 13 cm replica grating with 300 lines/ram and a liquid-nitrogen-cooled PbSe detector. These spectra were displayed on paper charts 25 cm wide with a dispersion of about 0.1 cm-l/cm. A signal to noise ratio of about 50 was obtained by scanning at 20 cm-~/hr. Tests showed that the response of the instrument was directly proportional to the incoming radiant flux. The spectral dispersion varied slowly with spectral position and was determined by measuring the chart positions of water and CO lines of known frequency. The dispersion was assumed constant over the small interval occupied by each line or group of lines being measured. The physical slit widths varied between 100 and i40/zm; these widths gave values between 0.06 and 0.07 cm -~ for the full width at half height of the instrument-response function. The dependence of the width of the instrumentresponse function on the physical widths of the spectrometer slits was determined in subsidiary experiments, t~°) Three path lengths (1.55, 2.90 and 12.72 m) of laboratory air were used in this study. The lines showing peak absorptances greater than 20% were identified by comparison with the atmospheric absorption line-parameter compilation and spectra of each line were obtained on several occasions during a period of about a year. During this period, the room temperature varied between 21°C and 28°C, the dew point temperature varied between - I ° C and 15°C and small variations in the ground level atmospheric pressure were noted. The dew point temperature was measured with an EG & G model 880 dew point hygrometer with remote sensor mount, tm These dew point temperature readings agreed with those obtained from a standard 491
492
Y.S. CHANGand J. H. SHAW
sling psychrometer within _+0.1°C. The amount of water vapor (molecules/cm2) was then obtained from the partial pressure of water vapor (reduced to 0°C) derived from these temperature readings and the optical path length. It is estimated that the amount of H20 in the path could be determined within ±3%. The spectra were digitized with the aid of a Bendix Datagrid Digitizer. Usually data points were taken every 1.0 ram, in increments of AX + A Y rather than of AX alone. This procedure permitted more points to be collected near the center of a line, where most of the information is found on line parameters. For a single line, about 200 points were obtained within I cm -I of the line center. An example of a spectrum of a group of H20 lines near 1991 cm -I and the corresponding digitized point locations is shown in Fig. I. In this figure the pen deflection, and the digitized points are shown with an arbitrary wavenumber (cm -I) scale. Every other digitized point of the smoothed spectrum is shown, raised above the actual spectrum for clarity. The upper dashed line corresponds to the 100% transmittance line associated with the digitized points as found by the least squares program. The bottom dashed line corresponds to the zero transmittance line for the digitized points and the solid line is the zero line for the observed spectrum. The digitized data were stored on magnetic tape and then used to calculate the line parameters by using a non-linear least-squares program (13~with an IBM 370 computer. METHOD OF ANALYSIS C8^SG and S~Aw(l°) have described a non-linear least squares method of obtaining line intensities and widths from digitized spectra provided the line shape and the shape of the instrument response function are assumed. Near room temperature, and at pressures greater than a few torr, the Lorentz expression is often used to represent the shapes of lines belonging to vibration bands of gases. This can be written as Sa k(z,) = ~ ' [ 0 ' - z'o)2+ a2] '
(1)
where k(v) is the absorption coefficient at frequency z,, S is the line intensity, 2a is the separation between the frequencies at which the absorption coefficient is k~12, and ~,o is the position of the line center. The monochromatic transmittance T,. at some frequency 1, of a sample containing an amount u (mol/cm2) of absorber can then be written as
(2)
T,~(v) = exp [-k0,)u].
A typical spectrum of an isolated line of a homogeneous gas sample obtained with the grating spectrometer is shown in Fig. 2. The pen deflection is shown as a function of frequency.
ft.
2.5
2.O
115
IO
0.5
O
Wovenumber0
0.5
1.0
1.5
2,0
2.5
cm -I
Fig. !. The solid line is the observed spectrum of a group of H20 lines near 1991 cm -I with an arbitrary
wavenumberscale. The position at which digitizedvalues were obtainedare indicatedby the dots which have been raised above the actual spectrum for clarity.The upper and lower dashed lines represent the 100%and 0% transmittancelines for the digitizeddata.
Intensities and widths of H20 lines between 1800and 2100cm-m
Oil,)
I ..............
"i...............
f ..............
219.6o
1 ...............
493
l ..........
zle'r.o
Is,
¢m -I
Fig. 2. Spectrumof an isolatedline of C0. The upper and lowerdashed lines representthe 100%and 0% transmittance lines obtainedfrom the non-linearleast squaresfit. The observed spectrum, I(v), is shown as the middle curve, the top curve, Io(v), corresponds to the spectrum which would be obtained if the absorption line were absent from the spectrum, and the bottom curve, 00,), corresponds to the spectrum of an opaque sample. Auxiliary experiments, information, or guesses are usually required to estimate both Io0') and O(v). Once these have been obtained the observed spectral transmittance T(v) and absorptance A(v) are given by I(v) - O(v)
(3)
T(v) = 1 - A(v) = Io(v)-O(v)"
Since spectra similar to that shown in Fig. 2 were obtained with an instrument of finite spectral resolution the observed transmittance is related to the corresponding monochromatic transmittance given by eqn (2) by the convolution with the appropriate instrument response function or(v, v'), 1~I)
f~or(v,
e -k<'~ dr'
T(v) =
,
(4)
®®or(v, V) dr' where the integrations were carried out over the spectral region where or(v, v') is greater than zero. It is difficult to measure the shapes of the response functions of grating spectrometers such as that used in this work and a variety of expressions has been proposed to represent them. W e have found that, under the experimental conditions used in this investigation, there is little difference in the values obtained for the line parameters when either a triangular or a Gaussian shape is assumed. °°) The results presented here were obtained by assuming or(l', v ' , : e x p
r-4ln2 L
(i'--'~v'~21ivfor
\
O
I
vol~<2.06
J
and or(v,V)=0 for
I~,-vo1>2.08
where 8 is the full width of the Gauss function at half its maximum value. Then, since • 821r.
!12
(5)
494
Y.S. CHANGand J. H. SHAW
Equations (3) and (4) can be written,
r
I(v)=O(v)+[lo(v)-O(v)] L4-'i~n 2J
j_® exp
(-~)2]exp[
k(v',u]dv'. (7)
Equation (7) shows that, for the case where the absorptance in a given spectral region is caused only by the presence of a single line, the pen deflection can be described analytically provided the values of S, vo, a, & Io(v), O(v) and the amount of absorber in the path are known. In this analysis it was assumed that Io(v) = a + b ( v - vo)+ c ( v - vo)2, and 0(v) = q, where a, b, c and q are constants to be determined in the analysis. For some of the single lines studied here, unambiguous values for all of these parameters could not be determined simultaneously and it was necessary to assign values obtained from subsidiary experiments to parameters such as 8 and q in order to determine the remaining parameters, Idv), Su, vo and a. Also, as discussed elsewhere,
Intensities and widths of H,O lines between 1800 and 2100 cm-'
495
Table 1. Comparison of calculated and observed intensities and widths of H20 lines. AFCRL Line Position (cm-z)
This Study Method
Intensity (cm-i/mol-cm-2 )
Half-Width (cm-i/atm~100
Intensity** (cm- l/mol-cm-e )
Half-Width (~m-l/atm~lOO
18o1.340 18o1,36o 1802.020 18o2.48o 18o5.15o
0.115E-19" O.385E-20 0.187E-21 0.174E-19 O.148E-20
2.2 2.2 6.1 5.4 8.4
o.o86±o.oo~ o.286±o.o13
4.26±0.15 4.26±0.15
o.148-~.008 o.144±o.oo4
6.91±0.58 8.96±0.25
1807.710 1808.680 1809.340 1810.620 1812.280
0.59OE-20 O.856E-22 0.285E-22 0.224E-19 o.~8~-2o
5.5 2.3 2.2 8.6 7.2
o.571±o.o21 2.1Ol±O.ogo 0.670±0.059 0.222±0.004 0.516±0.019
6.o6±0.23 2.29-+0.17 2.24_+0.17 8.99~o. 80 7.28~.52
1817.490 1817.490 1821.400 1822.77O 1825.200
0.155E-20 0.465E-20 O.191E-21 0.274E-20 O.401E-19
1.4 1.4 7.3 4.6 8.5
0.126±0.005 0.504±0,020
2.3o±o.io 2.3o±o.1o
0.276±0.021
3.98±o.2o
1825.430 1829.150 1830.150 1833.280 1833.28o
0.829E-20 0.196E-19 0.493E-19 O.566E-21 O.17OE-20
4.6 9.2 8.7 1.1 1.1
o.194±O.O07 0.540±O.015 O.525±o.021 0.158±0.oo6
1o.o8±o.8o 9.53±o.71 1.79±o.15 1.79±o.15
1834.770 1834.93o 1835.880 1837.200 1837.39O
O.151E-21 O.501E-22 O.21OE-21 0.759E-20 0.292E-21
7.5 7.3 7.9 8.4 9.0
0.200±0.029 0.677±0.048 o.19o±o.o13 0.794-+0.022 O.220_4-0.021
7.36-+0.30 7.24±o.42 7.91±o.76 8.46_+0.55 6.69±0.80
1842.140 1842.160 1843.44o 1844.200 1844.420
0.797E-21 0.346E-20 0.I16E-20 0.814E-19 0.269E-19
6.2 3.6 3.6 6.8 6.8
1845.400 18~5.57o 1846.030 1847.810 1848.820 1848.820 1852.400 1856.260 1858.550 1859.750
0.851E-21 0.717E-21 0.407E-21 O.12OE-19 0.564E-21 0.188E-21 0.35hE-21 0.166E-21 O.198E-20 0.245E-21
4.8 5.2 5.4 8.0 0.9 0.9 7.9 7.8 7.2 6.7
O.140±0.011 1.140-+0.320 o.382~.o95 o.3z5±o.o35 O. 190±O.O11 0.191-+O.008 0.266-+O.O2O
8.14_+o.23 o.63±o.15 o.63±o.15 8.35~.98 7.96-+o.6o 7.64-+o.30 6.65-+0.55
1859.864 186o.940 1861.560 1864.050 1864.o5o
0.876E-22 0.436E-21 0.131E-20 0.568E-22 0.170E-21
8.0 2.3 2.3 0.8 0.8
0.84o±o.170 0.401±o.032 0.129±0.012 0.640±0.009 o.196±o.005
7.89-+0.93 2.42±0.45 2.52-+O.46 0.43±0.10 0.43±0 .IO
1866.37o 1867.86o 1868.040 1869.340 1870.830
0.636E-20 0.163E-19 0.248E-20 0.48OE-19 0.269E-20
8.6 7.3 8.9 7-3 6.4
1876.610 1879.010 1879.340 1879.6OO 188~. 570
0.165E-21 0.470E-22 0.444E-21 0.148E-21 0.216E-20
7.4 0.8 1.5 1.5 8.7
0.190-+O.O11
8.25_+o.51
0.532±0.042 0.177-+0.O14 0.233-+0.019
1.63±O.ll 1.63±o. ii 8.77-+o.41
1885.240 1889.580 1892.630 1893.780 1893.780
O.362E-21 0.264E-19 0.127E-21 0.hO3E-22 O.121E-21
5.4 7.7 4.6 4.1 4.1
0.377±0.048 0.264±0.009 0.124±0.004 O.548±O.O41 0.164±O.O13
5.9e±o.6o 8.49-+o.78 3.52±0.20 3.89-+0.31 3.89±o. 31
189h.640 1895.170 1897.39o 1897.490 19Ol.82o
0.910E-22 0.815E-20 0.457E-22 O. 137E-21 O. 392E-21
4.4 7-7 1.1 i.i 4.5
o.982-+o.o3o o.431±O.Oll o .13o_+o.004 o. 370±o.o17
8.24-+o.25 1.28±o.io 1.28+o .lO 4.o8±o.35
1904.350 1907.960 1909.950 1914.6OO 1918 .O20
0. IO2E-20 0.433E-20 O.540E-20 0.124E-21 O.980E-20
8.7 7-9 8.4 3.6 5.4
o. lO6±o.004 0.481±0.028 O.839±O.O67 0.i12±0.004 I.O45+O.O75
8.18±0.36 8.86-+O.78 8.99±O.71 2.59±O.21 6.60-+0.70
Y. S. CHANG and J. H. Sx^w
496
Table 1. (Contd) AFCRL Line Position (em-z )
This Study Method
Intensity (cm- Z/mol-cm -2 )
Half-Width (cm- i/atm)xlOO
Intensity** (cm-l/mol-am -~ )
1918.o50 19~2.330 i~3.160 1933.19O 1941.630
O.292E-19 O.563E-20 O.IO~E-I 9 0.821E-21
5.4 8.0 7.8 7.7 7.4
0.313±0,022 0.598-+0.037 0.115-+0.010 0.760±0.045 1.052±0.034
6.60-+0.70 8.52-+0.70 8.08±0.82 7.90±0.58 8.08 ±O. lO
1942.5oo
O.154E-19 0.513E-20
6.1 6.0 7.9 8.1 6.8
0.183-+0.011 0.609±0.037 0.234_+0.006 0.236±0.013 0.113±0.005
6.38-+0.53 6.38±0.53 8.03±0.20 8.51±o.40 6.67±0.40
7.8 7.8 6.2 7.8 6.6
0.166±0.011 0.161±0.005 0.113±0.007 0.889±0.O31
7.12±O.15 9.17±0.60
6.04±0.20
0.280±0.008
6.98±0.21
0.774-+0.059 0.130±0.005 0.354+0.028 0.285±0.065 0.855±0.150
6.89±0.36 9.18±O.68
1,353±O.O56
6.38±0.25 7.51±O.52 7.87+0.57 8.09±0.56 7.20±0.37
1942.750
19~5.340
0.969E-21
0.197E-20
1946.350 1949.19o
0.225E-20 0.I19E-21
1954.990 1956.27o 1957.69o 1961.19o
0.I12E-20 0.I16E-21 0.122E-21
1966.270
0.809E-21 0.244E-20
Half-Width (cm-Z/atm)xlOO
7.64-+0.48
1976.190
0.718E-20 0.125E-21
1991.900 199l. 9O0
O.312E-20 0.241E-20 0.723E-20
6.4 8.1 6.9 4.5 4.5
1992.390 1992.660 1993.26o 1998.93o 2007.740
O. 966E-21 O.8OOE-21 0.385E-21 0.637E-21 0.405E-21
6.7 7.7 7.3 8.0 7.1
0,436±0.030 0.651±0.052 O.424+O.030
2009.330 2016,79O 2016.820 2018.340
O.191E-21 O.I12E-20 O.337E-20 O.IO4E-20 0.539E-21
6.9 5.0 5.0 6.8 7.1
0.253±O.O15 O.117±O.OO6 O.350±O.016 0.115±0.OO2 O.599±O,016
7.50±0.25 5.77+0.30 5.77±0.30 6.21+O.30
O.436E-21 0.223E-21 0.767E-22 0.417E-22 0.140E-20 O.466E-21 O.454E-21 o.99eE-22 O.431E-21 0.408E-21
7.1 7.7 8.0 7.3 5.4 5.4 6.5 6.8 7.1 3.9
O.439±O,O16
7,82±0.30
O.173±O.006 0.577±0.019 0.528±0.037
5.58±0.25 5.58±0.25 7.56±0.60
0.439±0,030 0.512+0.008
7.72±0.60 4.19±O.10
3.9 5.6 6.0 6.7 5.8
0.154±0.002 0.632±0.o45
4.19±0.10 5.53±0.40
2078.57O 2087.4O0
0.122E-20 0.511E-21 0.156E-21 0.523E-22 0.178E-21
2090.09O 20£0.090
0.167E-21 0.502E-21
4.2 4.2
0.251±0.016 O.759+0.049
4.49~O.22 4.49+0.22
1967.440
1988.410
2019.070 2O23.O80 2026.610 2027.030 2037.5OO 2041.34O 2 O41. 560
2043.95o 2046. 520
2060.490 2064. 910 2064.910 2065.840 2O74.24O
1,702±O.067
7.37±0.33 5.O1±O.60 5.O1+O.60
8.00±0.27
*The numbers in this column should be read as e.g. 0.115 × iO-IO cm-i/mol-cm -2 **These numbers are multiplied by the same powers of ten as in column 2. (a) Well-separated double lines (b) Intensity ratio 3:1 assumed for these overlapping lines (c) Lines belonging to groups of more than two lines
pairs of lines strongly overlapped. Thus, although the measurements for these lines were reproducible to better than 20%, systematic errors may affect the absolute accuracies. TOTH and FARUFm~2) measured the intensities of about 70 H20 lines in this region with the Michelson interferometer having an apodized spectral resolution of 0.15 cm-' described by SCHXNDLER.°4> These data were analyzed by using a curve of growth method and by assuming the line widths given by BaNF_mCr and CALF~J m TOrHJ'5) and ENO et all m Toth and Farmer noted that their results were, on the average, 5.5% smaller than the calculated values of BENEDICTand CALVE.m>The quoted uncertainty in their measured line intensities is from 7 to
Intensities and widths of H20 lines between 1800 and 2100 cm-~
iO-m
Intensity
497
/ / /o
/
./
10-2c
_J n.~b_ I0 -21 <~
10-22
./ /
,/
"°
/ i
10-22
10-23
i
i
ill,,I
i
, ~ , , "1~0_21
,
i
,J,,Ji
10-20
10-19
This study~ cm-I/mol-cm-2 Fig. 3. Comparison of measured intensities of H20 lines between 1800 to 2100cm -~ with those in the AFCRL atmospheric absorption line parameter compilation.
20% but the absolute value is dependent on the assumed half width. Since the intensities of the H20 lines given in the atmospheric absorption line parameter compilation are 8% larger than those of Benedict and Calfee, the results of this study are about 20% higher than Toth and Farmer's values. 0.10
/.
Holf width
•
o~1I
•
0.08 • /dP
•//.,., ..'-
•oOO
•
~eo
:4
0.06
/~,.. • //
0.04 /
/ /
0.02 / e
I
•
I
0.02
I
I
0.04
I
I
0.06
I
I
0.08
I
I
0.10
This .~tudy~ cm-I/otm.
Fig. 4. Comparison of measured air-broadened widths of H20 lines between 1800 to 2100cm -~ with those in the AFCRL atmospheric absorption line parameter compilation. QSRTVoL18,No.5--C
498
Y.S. CHANGand J. H. SHAW
ENO et al. (~) also measured the intensities and widths of approx. 17 H20 lines in this region with tunable CW PbSSe diode lasers. In general, the observed intensities were smaller than the calculated values with estimated uncertainties of from I0 to 20%. Thus the agreement between all the experimental data is within the estimated uncertainty of the measurements. (2) Line h a l / w i d t h s BENEDICTand C~2EE(9) obtained a lower limit of 0.0319cm-l/atm for the widths of H20 lines. This limit was imposed by choosing a minimum collision diameter equal to the kinetic theory diameter. The line width values in the atmospheric absorption line parameter compilation represent revised calculations in which the Anderson theory was modified by setting the minimum collision diameter equal to zero. This causes the calculated half widths, especially for higher J transitions, to be reduced. The observed half widths shown in Table 1, in general, have confirmed the revised calculated values for the higher J transition lines. In Fig. 4 observed and calculated linewidth values are compared. The experimental results are, on the average, 3.8% larger than the calculated values and the standard deviation is about 6% from the average. Many of the high J transition lines are close doublets and are expected to have an intensity ratio of 3 to 1. There were experimental difficulties in measuring the widths of most of these lines because of the small estimated line separation. EN6 et al. m) and BLUMet al. <5) measured the half widths of several higher J transition lines of the H20 ~ band by using tunable diode lasers. Their values are compared with the values of this study in Table 2. The results are in excellent agreement, except for one very narrow line at 1864.050 cm-I. The absolute accuracy of the width obtained in this study is uncertain. It is seen that the results of this study have confirmed the revised calculations by Benedict and others for several high J transition lines. The present measurements include some previously unmeasured line intensities and widths. Table 2. Comparisonof measuredwidthsof selectedH20 lines. Transition
AFCRL Value
This Study
Eng
et al. (a)
Blum et el. (b)
Line Position
(=-i)
181?.490
upper
lower
state
state
All Values (cm-Z/atm)×lOO
IP(O.12)-ll(l.ll) Z2(l.12)-u(O.ll)
1.4}
1817.h90 1833.280
13(I.13)-L2(0.12)
I.i}
1833.280
13(0.13)-12(1.12)
i.i
].848.82O
14(1.14)-13(0.13) 14(0.14)-13(1.13)
0.9} 0.9
0.63-+0.15 *
].848.82O 1860. 940
12(l.ll)-ll(l.lO)
2.3
2.42±0.45
2.4-+0.3
1861.560
12(2.11)-Ii(i.i0)
2.3
2.92±0.46
2.4-+0.3 .
1864.050
15(i.15)-14(0.14)
0.8}
0.43±0.10"
1864.050
15(0.15)-14(l.14)
0.8
1879.010
16(i.16)-15(0.15)
o.8I
1879.oi0
16(0.16)-15(1.15)
0.8
1879.340
13(1.13)-12(2.11)
1.5
i879.600
13(2.12)-12(1.11)
1.5
1897.390
14(i.13)-13(2.12)
i.i
1.28±0.10
1897.49o
14(2.13)-13(1.12)
i.i
1.28±0.I0
*These lines unresolved.
(a) See ref. (7) (b) See ref. (5)
Width is
2.30±0.10"
1.4
the combined
1.79±0.15"
I.i_+0.i*
0.8±0.08*
0.75"
1.63±0.11
1.7±O.2
1.55
1.63±0.i1
1.7±0.2
1.45
width of both lines.
Intensities and widths of HzO lines between 1800and 2100cm-~
499
The overall c o m p a r i s o n of different sets of data indicates the accuracy of the technique and confirms the estimated a c c u r a c y of the p r e s e n t m e a s u r e m e n t s . It can be concluded that models for H 2 0 intensities and widths are excellent over wide ranges of line intensities a n d widths. REFERENCES 1. R. A. McCLATCHEY,W. S. BEN~IC'r, S. A. CLOUGH,D. E. BURCH,R. F. CALFEE,K. FOX,L. S. ROm~L,~and J. S. G.~JNO, AFCRL Atmospheric Absorption Line Parameters Compilation, AFCRL-TR-73-0096, Environmental Research Paper No. 434, (1973). 2. R. A. TOTH and C. B. F~mr~, J. Molec. Spectrosc. $5, 182 (1975). 3. Y. BEN-A~YEH,IQSRT 7, 211 (1967). 4. C. K. N. PATEL,Phys. Rev. Lett. 28, 649 (1972). 5. F. A. BLUM,K. W. NILL,P. L. K~LLEY,A. R. CALAWAand T. C. H~Co, N, Science 177, 694 (1972). 6. M. A. GuElu~, M. KEr~l, A. S~CHEZ, M. S. ~ and A. JAV~, J. Chem. Phys. 63, 1317 (1975). 7. R. S. ENo, P. L. KELLEY,A. R. C~WA and T. C. H~ttt,~, Chem. Phys. Lett. 19, 524 (1973). 8. R. S. ENG,P. L. KELLEY,A. R. CALAW^,T. C. H ~ m ~ and K. W. NIl.L,Molec. Ph~fs.~g, 653 (1974). 9. W. S. BENEDICTand R. F. CALVE, Line Parameters for the 1.9 and 6.3/~ Water Vapor Bands, ESSA Professional Paper 2 (1967). 10. Y. S. CHANOand J. H. SHAW,Appl. Spectrosc. 13, 213 (1977). 11. D. J. McC/~ and J. H. SHAW,Appl. Opt. 2 581 (1963). 12. The Dew point Hygrometer Model 880 Instruction Manual, (EG & G International, Inc., Mass., 1975). 13. BMD Manual, Health Science Computing Facility, UCLA, 177 (1966). 14. R. A. SCHINDLF~,AppL Opt. 9, 301 (1970). 15. R. A. TOTH,JQSRT 13, 1127 (1971).
INTENSITIES AND WIDTHS BETWEEN 1800 A N D
OF H20 LINES 2 1 0 0 c m -~
Y. S. CHANG and J. H. StrAW Department of Physics, The Ohio State University,Columbus,OH 43210, U.S.A. (Received 15 March 1977)
Abstract--A n0n-linear, least-squares program was used to obtain the line intensities and widths of 91 air-broadened lines in the z,2rotation-vibrationband of water vapor in the region from 1800to 2100cm-1. The values obtained for the line intensities are, on the average, about 7% stronger than the Air Force Cambridge Research Laboratories(AFCRL) Atmospheric Absorption Line Parameters Compilation.The experimentalvaluesfor the half widths of the H20 lines are, on the average,4% higherthan the calculated AFCRL values. The measurementshave confirmedthe narrow widths of some high J transition lines measured by tunable diode laser spectroscopy. INTRODUCTION WATER vapor lines occur throughout the i.r. and information concerning their parameters is required in order to predict the transmittance of long air paths. There have been many observations of water vapor spectra and, in particular, measurements of line intensities and widths in the region from 1800 to 2100 cm -~ have been compiled t~) and reported by T o ~ and FARMER,t2) BEN-ARYEH,t3), PATEL,t4), BLUM et al., tS~ GUF_aP,A et ai., ~° and ENG et al. {7"s~ The reported accuracy of all these measurements is approx. 10-20%. In addition, calculated values for the intensities and widths of these lines have been given by BEN~.DICTand CALFE~,tg) and revised calculated values appear in the 1976 AFCRL atmospheric lines parameter compilation described by MCCLATCHEYet al. ") We have used a non-linear, least-squares program ~°) to obtaitl the line intensities and widths of 91 air-broadened lines in the 1,2 rotation-vibration band of H20 in the region from 1800 to 2100 cm -I. This method yields either the parameters of single isolated lines or else determines the parameters of several overlapping lines. The present study was undertaken both to study the application of the non-linear, least-squares program to obtain line parameters and to improve or confirm previous observations. EXPERIMENTAL The Ebert type grating spectrometer used in this study has been described previously. {11)A spectral resolution of about 0.06 cm -1 was obtained near 2000 cm -1 with a 26 x 13 cm replica grating with 300 lines/ram and a liquid-nitrogen-cooled PbSe detector. These spectra were displayed on paper charts 25 cm wide with a dispersion of about 0.1 cm-l/cm. A signal to noise ratio of about 50 was obtained by scanning at 20 cm-~/hr. Tests showed that the response of the instrument was directly proportional to the incoming radiant flux. The spectral dispersion varied slowly with spectral position and was determined by measuring the chart positions of water and CO lines of known frequency. The dispersion was assumed constant over the small interval occupied by each line or group of lines being measured. The physical slit widths varied between 100 and i40/zm; these widths gave values between 0.06 and 0.07 cm -~ for the full width at half height of the instrument-response function. The dependence of the width of the instrumentresponse function on the physical widths of the spectrometer slits was determined in subsidiary experiments, t~°) Three path lengths (1.55, 2.90 and 12.72 m) of laboratory air were used in this study. The lines showing peak absorptances greater than 20% were identified by comparison with the atmospheric absorption line-parameter compilation and spectra of each line were obtained on several occasions during a period of about a year. During this period, the room temperature varied between 21°C and 28°C, the dew point temperature varied between - I ° C and 15°C and small variations in the ground level atmospheric pressure were noted. The dew point temperature was measured with an EG & G model 880 dew point hygrometer with remote sensor mount, tm These dew point temperature readings agreed with those obtained from a standard 491
492
Y.S. CHANGand J. H. SHAW
sling psychrometer within _+0.1°C. The amount of water vapor (molecules/cm2) was then obtained from the partial pressure of water vapor (reduced to 0°C) derived from these temperature readings and the optical path length. It is estimated that the amount of H20 in the path could be determined within ±3%. The spectra were digitized with the aid of a Bendix Datagrid Digitizer. Usually data points were taken every 1.0 ram, in increments of AX + A Y rather than of AX alone. This procedure permitted more points to be collected near the center of a line, where most of the information is found on line parameters. For a single line, about 200 points were obtained within I cm -I of the line center. An example of a spectrum of a group of H20 lines near 1991 cm -I and the corresponding digitized point locations is shown in Fig. I. In this figure the pen deflection, and the digitized points are shown with an arbitrary wavenumber (cm -I) scale. Every other digitized point of the smoothed spectrum is shown, raised above the actual spectrum for clarity. The upper dashed line corresponds to the 100% transmittance line associated with the digitized points as found by the least squares program. The bottom dashed line corresponds to the zero transmittance line for the digitized points and the solid line is the zero line for the observed spectrum. The digitized data were stored on magnetic tape and then used to calculate the line parameters by using a non-linear least-squares program (13~with an IBM 370 computer. METHOD OF ANALYSIS C8^SG and S~Aw(l°) have described a non-linear least squares method of obtaining line intensities and widths from digitized spectra provided the line shape and the shape of the instrument response function are assumed. Near room temperature, and at pressures greater than a few torr, the Lorentz expression is often used to represent the shapes of lines belonging to vibration bands of gases. This can be written as Sa k(z,) = ~ ' [ 0 ' - z'o)2+ a2] '
(1)
where k(v) is the absorption coefficient at frequency z,, S is the line intensity, 2a is the separation between the frequencies at which the absorption coefficient is k~12, and ~,o is the position of the line center. The monochromatic transmittance T,. at some frequency 1, of a sample containing an amount u (mol/cm2) of absorber can then be written as
(2)
T,~(v) = exp [-k0,)u].
A typical spectrum of an isolated line of a homogeneous gas sample obtained with the grating spectrometer is shown in Fig. 2. The pen deflection is shown as a function of frequency.
ft.
2.5
2.O
115
IO
0.5
O
Wovenumber0
0.5
1.0
1.5
2,0
2.5
cm -I
Fig. !. The solid line is the observed spectrum of a group of H20 lines near 1991 cm -I with an arbitrary
wavenumberscale. The position at which digitizedvalues were obtainedare indicatedby the dots which have been raised above the actual spectrum for clarity.The upper and lower dashed lines represent the 100%and 0% transmittancelines for the digitizeddata.
Intensities and widths of H20 lines between 1800and 2100cm-m
Oil,)
I ..............
"i...............
f ..............
219.6o
1 ...............
493
l ..........
zle'r.o
Is,
¢m -I
Fig. 2. Spectrumof an isolatedline of C0. The upper and lowerdashed lines representthe 100%and 0% transmittance lines obtainedfrom the non-linearleast squaresfit. The observed spectrum, I(v), is shown as the middle curve, the top curve, Io(v), corresponds to the spectrum which would be obtained if the absorption line were absent from the spectrum, and the bottom curve, 00,), corresponds to the spectrum of an opaque sample. Auxiliary experiments, information, or guesses are usually required to estimate both Io0') and O(v). Once these have been obtained the observed spectral transmittance T(v) and absorptance A(v) are given by I(v) - O(v)
(3)
T(v) = 1 - A(v) = Io(v)-O(v)"
Since spectra similar to that shown in Fig. 2 were obtained with an instrument of finite spectral resolution the observed transmittance is related to the corresponding monochromatic transmittance given by eqn (2) by the convolution with the appropriate instrument response function or(v, v'), 1~I)
f~or(v,
e -k<'~ dr'
T(v) =
,
(4)
®®or(v, V) dr' where the integrations were carried out over the spectral region where or(v, v') is greater than zero. It is difficult to measure the shapes of the response functions of grating spectrometers such as that used in this work and a variety of expressions has been proposed to represent them. W e have found that, under the experimental conditions used in this investigation, there is little difference in the values obtained for the line parameters when either a triangular or a Gaussian shape is assumed. °°) The results presented here were obtained by assuming or(l', v ' , : e x p
r-4ln2 L
(i'--'~v'~21ivfor
\
O
I
vol~<2.06
J
and or(v,V)=0 for
I~,-vo1>2.08
where 8 is the full width of the Gauss function at half its maximum value. Then, since • 821r.
!12
(5)
494
Y.S. CHANGand J. H. SHAW
Equations (3) and (4) can be written,
r
I(v)=O(v)+[lo(v)-O(v)] L4-'i~n 2J
j_® exp
(-~)2]exp[
k(v',u]dv'. (7)
Equation (7) shows that, for the case where the absorptance in a given spectral region is caused only by the presence of a single line, the pen deflection can be described analytically provided the values of S, vo, a, & Io(v), O(v) and the amount of absorber in the path are known. In this analysis it was assumed that Io(v) = a + b ( v - vo)+ c ( v - vo)2, and 0(v) = q, where a, b, c and q are constants to be determined in the analysis. For some of the single lines studied here, unambiguous values for all of these parameters could not be determined simultaneously and it was necessary to assign values obtained from subsidiary experiments to parameters such as 8 and q in order to determine the remaining parameters, Idv), Su, vo and a. Also, as discussed elsewhere,
Intensities and widths of H,O lines between 1800 and 2100 cm-'
495
Table 1. Comparison of calculated and observed intensities and widths of H20 lines. AFCRL Line Position (cm-z)
This Study Method
Intensity (cm-i/mol-cm-2 )
Half-Width (cm-i/atm~100
Intensity** (cm- l/mol-cm-e )
Half-Width (~m-l/atm~lOO
18o1.340 18o1,36o 1802.020 18o2.48o 18o5.15o
0.115E-19" O.385E-20 0.187E-21 0.174E-19 O.148E-20
2.2 2.2 6.1 5.4 8.4
o.o86±o.oo~ o.286±o.o13
4.26±0.15 4.26±0.15
o.148-~.008 o.144±o.oo4
6.91±0.58 8.96±0.25
1807.710 1808.680 1809.340 1810.620 1812.280
0.59OE-20 O.856E-22 0.285E-22 0.224E-19 o.~8~-2o
5.5 2.3 2.2 8.6 7.2
o.571±o.o21 2.1Ol±O.ogo 0.670±0.059 0.222±0.004 0.516±0.019
6.o6±0.23 2.29-+0.17 2.24_+0.17 8.99~o. 80 7.28~.52
1817.490 1817.490 1821.400 1822.77O 1825.200
0.155E-20 0.465E-20 O.191E-21 0.274E-20 O.401E-19
1.4 1.4 7.3 4.6 8.5
0.126±0.005 0.504±0,020
2.3o±o.io 2.3o±o.1o
0.276±0.021
3.98±o.2o
1825.430 1829.150 1830.150 1833.280 1833.28o
0.829E-20 0.196E-19 0.493E-19 O.566E-21 O.17OE-20
4.6 9.2 8.7 1.1 1.1
o.194±O.O07 0.540±O.015 O.525±o.021 0.158±0.oo6
1o.o8±o.8o 9.53±o.71 1.79±o.15 1.79±o.15
1834.770 1834.93o 1835.880 1837.200 1837.39O
O.151E-21 O.501E-22 O.21OE-21 0.759E-20 0.292E-21
7.5 7.3 7.9 8.4 9.0
0.200±0.029 0.677±0.048 o.19o±o.o13 0.794-+0.022 O.220_4-0.021
7.36-+0.30 7.24±o.42 7.91±o.76 8.46_+0.55 6.69±0.80
1842.140 1842.160 1843.44o 1844.200 1844.420
0.797E-21 0.346E-20 0.I16E-20 0.814E-19 0.269E-19
6.2 3.6 3.6 6.8 6.8
1845.400 18~5.57o 1846.030 1847.810 1848.820 1848.820 1852.400 1856.260 1858.550 1859.750
0.851E-21 0.717E-21 0.407E-21 O.12OE-19 0.564E-21 0.188E-21 0.35hE-21 0.166E-21 O.198E-20 0.245E-21
4.8 5.2 5.4 8.0 0.9 0.9 7.9 7.8 7.2 6.7
O.140±0.011 1.140-+0.320 o.382~.o95 o.3z5±o.o35 O. 190±O.O11 0.191-+O.008 0.266-+O.O2O
8.14_+o.23 o.63±o.15 o.63±o.15 8.35~.98 7.96-+o.6o 7.64-+o.30 6.65-+0.55
1859.864 186o.940 1861.560 1864.050 1864.o5o
0.876E-22 0.436E-21 0.131E-20 0.568E-22 0.170E-21
8.0 2.3 2.3 0.8 0.8
0.84o±o.170 0.401±o.032 0.129±0.012 0.640±0.009 o.196±o.005
7.89-+0.93 2.42±0.45 2.52-+O.46 0.43±0.10 0.43±0 .IO
1866.37o 1867.86o 1868.040 1869.340 1870.830
0.636E-20 0.163E-19 0.248E-20 0.48OE-19 0.269E-20
8.6 7.3 8.9 7-3 6.4
1876.610 1879.010 1879.340 1879.6OO 188~. 570
0.165E-21 0.470E-22 0.444E-21 0.148E-21 0.216E-20
7.4 0.8 1.5 1.5 8.7
0.190-+O.O11
8.25_+o.51
0.532±0.042 0.177-+0.O14 0.233-+0.019
1.63±O.ll 1.63±o. ii 8.77-+o.41
1885.240 1889.580 1892.630 1893.780 1893.780
O.362E-21 0.264E-19 0.127E-21 0.hO3E-22 O.121E-21
5.4 7.7 4.6 4.1 4.1
0.377±0.048 0.264±0.009 0.124±0.004 O.548±O.O41 0.164±O.O13
5.9e±o.6o 8.49-+o.78 3.52±0.20 3.89-+0.31 3.89±o. 31
189h.640 1895.170 1897.39o 1897.490 19Ol.82o
0.910E-22 0.815E-20 0.457E-22 O. 137E-21 O. 392E-21
4.4 7-7 1.1 i.i 4.5
o.982-+o.o3o o.431±O.Oll o .13o_+o.004 o. 370±o.o17
8.24-+o.25 1.28±o.io 1.28+o .lO 4.o8±o.35
1904.350 1907.960 1909.950 1914.6OO 1918 .O20
0. IO2E-20 0.433E-20 O.540E-20 0.124E-21 O.980E-20
8.7 7-9 8.4 3.6 5.4
o. lO6±o.004 0.481±0.028 O.839±O.O67 0.i12±0.004 I.O45+O.O75
8.18±0.36 8.86-+O.78 8.99±O.71 2.59±O.21 6.60-+0.70
Y. S. CHANG and J. H. Sx^w
496
Table 1. (Contd) AFCRL Line Position (em-z )
This Study Method
Intensity (cm- Z/mol-cm -2 )
Half-Width (cm- i/atm)xlOO
Intensity** (cm-l/mol-am -~ )
1918.o50 19~2.330 i~3.160 1933.19O 1941.630
O.292E-19 O.563E-20 O.IO~E-I 9 0.821E-21
5.4 8.0 7.8 7.7 7.4
0.313±0,022 0.598-+0.037 0.115-+0.010 0.760±0.045 1.052±0.034
6.60-+0.70 8.52-+0.70 8.08±0.82 7.90±0.58 8.08 ±O. lO
1942.5oo
O.154E-19 0.513E-20
6.1 6.0 7.9 8.1 6.8
0.183-+0.011 0.609±0.037 0.234_+0.006 0.236±0.013 0.113±0.005
6.38-+0.53 6.38±0.53 8.03±0.20 8.51±o.40 6.67±0.40
7.8 7.8 6.2 7.8 6.6
0.166±0.011 0.161±0.005 0.113±0.007 0.889±0.O31
7.12±O.15 9.17±0.60
6.04±0.20
0.280±0.008
6.98±0.21
0.774-+0.059 0.130±0.005 0.354+0.028 0.285±0.065 0.855±0.150
6.89±0.36 9.18±O.68
1,353±O.O56
6.38±0.25 7.51±O.52 7.87+0.57 8.09±0.56 7.20±0.37
1942.750
19~5.340
0.969E-21
0.197E-20
1946.350 1949.19o
0.225E-20 0.I19E-21
1954.990 1956.27o 1957.69o 1961.19o
0.I12E-20 0.I16E-21 0.122E-21
1966.270
0.809E-21 0.244E-20
Half-Width (cm-Z/atm)xlOO
7.64-+0.48
1976.190
0.718E-20 0.125E-21
1991.900 199l. 9O0
O.312E-20 0.241E-20 0.723E-20
6.4 8.1 6.9 4.5 4.5
1992.390 1992.660 1993.26o 1998.93o 2007.740
O. 966E-21 O.8OOE-21 0.385E-21 0.637E-21 0.405E-21
6.7 7.7 7.3 8.0 7.1
0,436±0.030 0.651±0.052 O.424+O.030
2009.330 2016,79O 2016.820 2018.340
O.191E-21 O.I12E-20 O.337E-20 O.IO4E-20 0.539E-21
6.9 5.0 5.0 6.8 7.1
0.253±O.O15 O.117±O.OO6 O.350±O.016 0.115±0.OO2 O.599±O,016
7.50±0.25 5.77+0.30 5.77±0.30 6.21+O.30
O.436E-21 0.223E-21 0.767E-22 0.417E-22 0.140E-20 O.466E-21 O.454E-21 o.99eE-22 O.431E-21 0.408E-21
7.1 7.7 8.0 7.3 5.4 5.4 6.5 6.8 7.1 3.9
O.439±O,O16
7,82±0.30
O.173±O.006 0.577±0.019 0.528±0.037
5.58±0.25 5.58±0.25 7.56±0.60
0.439±0,030 0.512+0.008
7.72±0.60 4.19±O.10
3.9 5.6 6.0 6.7 5.8
0.154±0.002 0.632±0.o45
4.19±0.10 5.53±0.40
2078.57O 2087.4O0
0.122E-20 0.511E-21 0.156E-21 0.523E-22 0.178E-21
2090.09O 20£0.090
0.167E-21 0.502E-21
4.2 4.2
0.251±0.016 O.759+0.049
4.49~O.22 4.49+0.22
1967.440
1988.410
2019.070 2O23.O80 2026.610 2027.030 2037.5OO 2041.34O 2 O41. 560
2043.95o 2046. 520
2060.490 2064. 910 2064.910 2065.840 2O74.24O
1,702±O.067
7.37±0.33 5.O1±O.60 5.O1+O.60
8.00±0.27
*The numbers in this column should be read as e.g. 0.115 × iO-IO cm-i/mol-cm -2 **These numbers are multiplied by the same powers of ten as in column 2. (a) Well-separated double lines (b) Intensity ratio 3:1 assumed for these overlapping lines (c) Lines belonging to groups of more than two lines
pairs of lines strongly overlapped. Thus, although the measurements for these lines were reproducible to better than 20%, systematic errors may affect the absolute accuracies. TOTH and FARUFm~2) measured the intensities of about 70 H20 lines in this region with the Michelson interferometer having an apodized spectral resolution of 0.15 cm-' described by SCHXNDLER.°4> These data were analyzed by using a curve of growth method and by assuming the line widths given by BaNF_mCr and CALF~J m TOrHJ'5) and ENO et all m Toth and Farmer noted that their results were, on the average, 5.5% smaller than the calculated values of BENEDICTand CALVE.m>The quoted uncertainty in their measured line intensities is from 7 to
Intensities and widths of H20 lines between 1800 and 2100 cm-~
iO-m
Intensity
497
/ / /o
/
./
10-2c
_J n.~b_ I0 -21 <~
10-22
./ /
,/
"°
/ i
10-22
10-23
i
i
ill,,I
i
, ~ , , "1~0_21
,
i
,J,,Ji
10-20
10-19
This study~ cm-I/mol-cm-2 Fig. 3. Comparison of measured intensities of H20 lines between 1800 to 2100cm -~ with those in the AFCRL atmospheric absorption line parameter compilation.
20% but the absolute value is dependent on the assumed half width. Since the intensities of the H20 lines given in the atmospheric absorption line parameter compilation are 8% larger than those of Benedict and Calfee, the results of this study are about 20% higher than Toth and Farmer's values. 0.10
/.
Holf width
•
o~1I
•
0.08 • /dP
•//.,., ..'-
•oOO
•
~eo
:4
0.06
/~,.. • //
0.04 /
/ /
0.02 / e
I
•
I
0.02
I
I
0.04
I
I
0.06
I
I
0.08
I
I
0.10
This .~tudy~ cm-I/otm.
Fig. 4. Comparison of measured air-broadened widths of H20 lines between 1800 to 2100cm -~ with those in the AFCRL atmospheric absorption line parameter compilation. QSRTVoL18,No.5--C
498
Y.S. CHANGand J. H. SHAW
ENO et al. (~) also measured the intensities and widths of approx. 17 H20 lines in this region with tunable CW PbSSe diode lasers. In general, the observed intensities were smaller than the calculated values with estimated uncertainties of from I0 to 20%. Thus the agreement between all the experimental data is within the estimated uncertainty of the measurements. (2) Line h a l / w i d t h s BENEDICTand C~2EE(9) obtained a lower limit of 0.0319cm-l/atm for the widths of H20 lines. This limit was imposed by choosing a minimum collision diameter equal to the kinetic theory diameter. The line width values in the atmospheric absorption line parameter compilation represent revised calculations in which the Anderson theory was modified by setting the minimum collision diameter equal to zero. This causes the calculated half widths, especially for higher J transitions, to be reduced. The observed half widths shown in Table 1, in general, have confirmed the revised calculated values for the higher J transition lines. In Fig. 4 observed and calculated linewidth values are compared. The experimental results are, on the average, 3.8% larger than the calculated values and the standard deviation is about 6% from the average. Many of the high J transition lines are close doublets and are expected to have an intensity ratio of 3 to 1. There were experimental difficulties in measuring the widths of most of these lines because of the small estimated line separation. EN6 et al. m) and BLUMet al. <5) measured the half widths of several higher J transition lines of the H20 ~ band by using tunable diode lasers. Their values are compared with the values of this study in Table 2. The results are in excellent agreement, except for one very narrow line at 1864.050 cm-I. The absolute accuracy of the width obtained in this study is uncertain. It is seen that the results of this study have confirmed the revised calculations by Benedict and others for several high J transition lines. The present measurements include some previously unmeasured line intensities and widths. Table 2. Comparisonof measuredwidthsof selectedH20 lines. Transition
AFCRL Value
This Study
Eng
et al. (a)
Blum et el. (b)
Line Position
(=-i)
181?.490
upper
lower
state
state
All Values (cm-Z/atm)×lOO
IP(O.12)-ll(l.ll) Z2(l.12)-u(O.ll)
1.4}
1817.h90 1833.280
13(I.13)-L2(0.12)
I.i}
1833.280
13(0.13)-12(1.12)
i.i
].848.82O
14(1.14)-13(0.13) 14(0.14)-13(1.13)
0.9} 0.9
0.63-+0.15 *
].848.82O 1860. 940
12(l.ll)-ll(l.lO)
2.3
2.42±0.45
2.4-+0.3
1861.560
12(2.11)-Ii(i.i0)
2.3
2.92±0.46
2.4-+0.3 .
1864.050
15(i.15)-14(0.14)
0.8}
0.43±0.10"
1864.050
15(0.15)-14(l.14)
0.8
1879.010
16(i.16)-15(0.15)
o.8I
1879.oi0
16(0.16)-15(1.15)
0.8
1879.340
13(1.13)-12(2.11)
1.5
i879.600
13(2.12)-12(1.11)
1.5
1897.390
14(i.13)-13(2.12)
i.i
1.28±0.10
1897.49o
14(2.13)-13(1.12)
i.i
1.28±0.I0
*These lines unresolved.
(a) See ref. (7) (b) See ref. (5)
Width is
2.30±0.10"
1.4
the combined
1.79±0.15"
I.i_+0.i*
0.8±0.08*
0.75"
1.63±0.11
1.7±O.2
1.55
1.63±0.i1
1.7±0.2
1.45
width of both lines.
Intensities and widths of HzO lines between 1800and 2100cm-~
499
The overall c o m p a r i s o n of different sets of data indicates the accuracy of the technique and confirms the estimated a c c u r a c y of the p r e s e n t m e a s u r e m e n t s . It can be concluded that models for H 2 0 intensities and widths are excellent over wide ranges of line intensities a n d widths. REFERENCES 1. R. A. McCLATCHEY,W. S. BEN~IC'r, S. A. CLOUGH,D. E. BURCH,R. F. CALFEE,K. FOX,L. S. ROm~L,~and J. S. G.~JNO, AFCRL Atmospheric Absorption Line Parameters Compilation, AFCRL-TR-73-0096, Environmental Research Paper No. 434, (1973). 2. R. A. TOTH and C. B. F~mr~, J. Molec. Spectrosc. $5, 182 (1975). 3. Y. BEN-A~YEH,IQSRT 7, 211 (1967). 4. C. K. N. PATEL,Phys. Rev. Lett. 28, 649 (1972). 5. F. A. BLUM,K. W. NILL,P. L. K~LLEY,A. R. CALAWAand T. C. H~Co, N, Science 177, 694 (1972). 6. M. A. GuElu~, M. KEr~l, A. S~CHEZ, M. S. ~ and A. JAV~, J. Chem. Phys. 63, 1317 (1975). 7. R. S. ENo, P. L. KELLEY,A. R. C~WA and T. C. H~ttt,~, Chem. Phys. Lett. 19, 524 (1973). 8. R. S. ENG,P. L. KELLEY,A. R. CALAW^,T. C. H ~ m ~ and K. W. NIl.L,Molec. Ph~fs.~g, 653 (1974). 9. W. S. BENEDICTand R. F. CALVE, Line Parameters for the 1.9 and 6.3/~ Water Vapor Bands, ESSA Professional Paper 2 (1967). 10. Y. S. CHANOand J. H. SHAW,Appl. Spectrosc. 13, 213 (1977). 11. D. J. McC/~ and J. H. SHAW,Appl. Opt. 2 581 (1963). 12. The Dew point Hygrometer Model 880 Instruction Manual, (EG & G International, Inc., Mass., 1975). 13. BMD Manual, Health Science Computing Facility, UCLA, 177 (1966). 14. R. A. SCHINDLF~,AppL Opt. 9, 301 (1970). 15. R. A. TOTH,JQSRT 13, 1127 (1971).