Atlas of Computed Infrared Atmospheric Absorption Spectra

Transcription

1 NCAR-TN/STR-112 NCAR TECHNCAL NOTE November 1975 Atlas of Computed nfrared Atmospheric Absorption Spectra Atmospheric Transmissions in the Wave-Number Region from 1 to 2600 cm-' for Altitudes above 54, 45, 40, 30, 14, and 4 km Thomas G. Kyle, 'Upper Atmosphere Project, NCAR Ahron Goldman, University of Denver ATMOSPHERC QUALTY AND MODFCATON DVSON -s--,,,,,,,-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- NATONAL CENTER FOR ATMOSPHERC RESEARCH BOULDER, COLORADO

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3 PREFACE ABSTRACT The material in this publication is the result of a request for information concerning the transparency of the atmosphere to infrared radiation at different observing altitudes by Professor Rainer Weiss of the Massachusetts nstitute of Technology. Available data on the subject are only for short wave number intervals and usually for only a small altitude range. Thus, it was decided that this information could prove useful to others and should therefore be made available. The primary concern in the decision to produce the report was not whether it could be useful, but whether it might be misused. f it is assumed that the accuracy of the transmissions was as great as the accuracy of the computations (by concluding that the mixing ratios used were completely valid or by improper scaling of the results), misuse could occur. n the hope of forestalling such problems, the authors have attempted to emphasize the limitations of the results. An atlas of atmospheric absorption calculations is presented for a vertical path through the atmosphere above altitudes of 4, 14, 30, 40, 45, and 54 km. The calculations are made with spectral resolutions of 0, 5, and 20 cm-l for the spectral region from 1 to 2600 cm-l. A discussion of the accuracy of the results is presented. ACKNOWLEDGMENTS The authors thank Rainer Weiss of the Massachusetts nstitute of Technology, who suggested generating this atlas, and the NCAR Computing Facility for assistance in its preparation. Part of the computer programming was carried out by Michael Callan. iii

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5 CONTENTS LST OF TABLES Preface *.-..*..-..* * e. -.-*. iii Table - Atmospheric layers used in the computations... 5 Abstract Table - The number of lines and the sum of the line Acknowledgments.... *.l l...-.l.* iii intensities. * ****** ***** 6 List of Tables List of Figures......* vi 1. NTRODUCTON COMPUTATONAL PROCEDURES... 2 Table - The number of lines and the sum of the square roots of the line intensity-line halfwidth... Table V - The integral of the fractional absorption with respect to wavenumber is listed for different altitudes DESCRPTON OF THE SPECTRA ACCURACY AND UNCERTANTES Tables Figures References v

6 vi List of Figures Figure 1 Transmission through the atmosphere above 54, 45, and 40 km between 21 and 1250 cml at 20 cm-l resolution Transmission through the atmosphere above 30, 14, between 21 and 1250 cmc1 at 20 cm- resolution. 3 Transmission through the atmosphere above 54, 45, between 1250 and 2500 cm-l at 20 cm-1 resolution 4 Transmission through the atmosphere above 30, 14, between 1250 and 2500 cml-1 at 20 cm- 1 resolution 5 Transmission through the atmosphere above 54, 45, between 6 and 1250 cm-l at 5 cm-l resolution. 6 Transmission through the atmosphere above 30, 14, between 6 and 1250 cm"l at 5 cm~l resolution. 7 Transmission through the atmosphere above 54, 45, between 1250 and 2500 cm-1 at 5 cm-1 resolution. 8 Transmission through the atmosphere above 30, 14, between and 2500 cm"l at 5 cm-1 resolution. 9 Transmission through the atmosphere above 54, 45, between 1 and 200 cm-l at 0 cml-1 resolution. 10 Transmission through the atmosphere above 30, 14, between 1 and 200 cm- 1 at 0 cm-l resolution. 11 Transmi-ssin through the atmosphere above 54, 45, between 200 and 400 cm-l at 0 cm"l resolution. 12 Transmission through the' atmosphere above 30, 14, and 4 km between 200 and 400 cm-l at 0 cm-l resolution.... * Transmission through the atmosphere above 54, 45, between 400 and 600 cm-l at 0 cml resolution. 14 Transmission through the atmosphere above 30, 14, between 400 and 600 cm- 1 at 0 cm resolution. 15 Transmission through the atmosphere above 54, 45, between 600 and 800 cm-l at 0 cm-1 resolution. 16 Transmission through the atmosphere above 30, 14, between 600 and 800 cml- 1 at 0 cm- 1 resolution. and 4 km and 40 km and 4 km and 40 km and 4 km and 40 km and 4 km and 40 km. e and 4 km and 40 km and 40 km and 4 km and 40 km and 4 km Figure 17 Transmission through the atmosphere above 54, 45, and 40 km between 800 and 1000 cm- 1 at 0 cm- 1 resolution Transmission through the atmosphere above 30, 14, and 4 km 1 between 800 and 1000 cm-l at 0 cm resolution Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between Transmission between 2000 through the atmosphere above 54, 45, and 40 km and 1200 cm- 1 at 0 cm~ 1 resolution through the atmosphere above 30, 14, and 4 km and 1200 cm1 at 0 cm-1 resolution through the-atmosphere aove 54, 45, and 40 km and 1400 cm at 0 cm resolution through the atmosphere above 30, 14, and 4 km and 1400 cm- at 0 cm-l resolution through the atmosphere above 54, 45, and 40 km and 1600 cm-l at 0 cm-1 resolution through the atmosphere above 30, 14, and 4 km and 1600 cm-1 at 0 cm-l resolution through the atmosphere above 54, 45, and 40 km and 1800 cm-l at 0 cm-' resolution through the atmosphere above 30, 14, and 4 km and 1800 cm-l at 0 cml-1 resolution through the atmosphere above 54, 45, and 40 km and 2000 cml at 0 cm-l resolution through the atmosphere above 30, 14, and 4 km and 2000 cm-l at 0 cm-1 resolution through the atmosphere above 54, 45, and 40 km and 2200 cm-1 at 0 cm-1 resolution Transmission through the atmosphere above 30, 14, and 4 km between 2000 and 2200 cm- 1 l at 0 cm-1 resolution Transmission through the atmosphere above 54, 45, and 40 km between 2200 and 2400 cm- 1 at 0 cm resolution Transmission through the atmosphere above 30, 14, and 4 km between 2200 and 2400 cm-l at 0 cm-l resolution Transmission through the atmosphere above 54, 45, and 40 km between 2400 and 2600 cm-1 at 0 cm-l resolution Transmission through the atmopshere above 30, 14, and 4 km between 2400 and 2600 cm-1 at 0 cm- 1 resolution... 71

7 1. NTRODUCTON most of the relevant vibration-rotation and pure rotation transitions During the last decade extensive tabulations of infrared line parameters of a number of atmospheric gases have become available. During that time, efficient line-by-line computer programs have been developed which, with today's large computers, allow the calculations of atmospheric transmission spectra at altitudes up to ~50 km in the wavelength interval from 1 pm to 1 cm. Such spectra can be calculated for arbitrary atmospheric profiles of temperatures, pressures, and mixing ratios of minor constituents, with arbitrary optical paths and spectral resolutions. These techniques have been used extensively in the analysis of observed atmospheric infrared and microwave emission and absorption spectra and also in feasibility studies of remote sensing of atmospheric trace constituents by infrared and microwave spectroscopy. They have been verified by numerous studies, mostly in the infrared. These spectral calculations can reproduce the observed atmospheric absorption spectra within 10 to 15% in most cases. Such studies have many applications. For example, they can serve as a useful guide for planning atmospheric and astronomical observations from high altitudes. An extensive bibliography on the subject is beyond the scope of this work, but typical examples are given in Kyle (1969) and in Goldman, Williams, and Murcray (1974). of HO20, C02, 03, N,0, CH4, and 02, and the pure rotational transitions of H20 and 03. For this work the pure rotation 02 lines (Gebbie, Burroughs, and Bird, 1969) were added to the AFCRL tape, but the weak rotational lines of CO and N20 were not added. t should be noted that other atmospheric species (such as HNO3 and N02) were not included in these calculations. t is well known that for long-path solar spectra (such as those obtained during sunset or sunrise), the HN03 and N02 bands can contribute significantly to the observed atmospheric transmission. The HN03 molecule has important stratospheric vibration-rotation absorption bands near 5, 7.5, 11, and 21 pm, as well as a pure rotation spectrum from 10 to 40 cm-. N02 shows an important stratospheric vibration-rotation absorption band near 6 plm, near the center of the 6 pm HO20 band, as well as a pure rotation spectrum in the cm-l region. However, these effects are negligible for vertical paths (as in the present study). t should also be noted that the present calculations apply to clear atmospheres only, with no cloud effects. Furthermore, aerosol effects were not included. The calculations concern the atmosphere of the earth alone, so no solar lines are included. The solar lines would result in considerable differences in regions such as near the CO absorptions. We present new calculations of atmospheric transmission which cover the spectral region from 1 to 2600 cm-l. The calculations are for a vertical atmospheric path from altitudes of 4, 14, 30, 40, 45, and 54 km, corresponding to atmospheric and astronomical observations from high-altitude ground stations, aircraft, and balloons. Each of the spectra is presented at spectral resolutions of 0, 5, and 20 cm-'. corresponding to practical atmospheric and astronomical observational techniques. The atmospheric transmission spectra are calculated using the most recently available line parameters for the various molecular species. The line parameters are those generated by various researchers and compiled on magnetic tape by AFCRL (McClatchy et al., 1973). These cover 1

8 2 2. COMPUTATONAL PROCEDURES For these calculations the atmosphere above sea level was divided into seven homogeneous layers, with effective pressures of 09, 1, 2.5, 8, 36, 106, and 390 mb. The effective pressure is the median of each pressure range listed in Table. Also given in Table are the effective temperature and the number of absorbing molecules of the different species for each layer. This table is based on the AFCRL midlatitude summer profile (McClatchey et al., 1972). The altitudes chosen correspond to infrared observations from observatory, aircraft, and balloon altitudes. The computational technique is similar to that described in Kyle (1969). Four parameters are used for each spectral line: the frequency Vo (in inverse centimeters), the intensity (in inverse centimeters per molecule per square centimeter), the lorentz half-width a (in inverse centimeters per atmosphere), and the lower state energy E (in inverse centimeters). The Voigt line shape, truncated 5 cm-l from the line center, was used for all lines. The computational procedures used here are more accurate than the line parameters or the atmospheric model, as verified by a number of sample calculations, which indicate that the computational errors are less than 4%. Two aspects of the computation will now be described. One is the choice of the frequency net at which the monochromatic transmission is calculated. The other is the method of approximation used for the values of the half-widths. The monochromatic absorption coefficient computation was always made at equally spaced points whenever the distance from the line center was greater than or equal to 0 cml. For layers 1, 2, and 3A (below 30 km), only one point was used within 0 cm-l from the line center (at all frequencies). However, for the other four layers (above 30 km), the computations were made at distances of 0, 0/2, 0/4, and 0/8 cm-l from the line center for frequencies greater than 500 cm~l, while for frequencies less than 500 cm~l the points were spaced 83 x 10-7 and 83 x /2n, with n = 1,..., 7 from the line center. Such a small computational net at the lower frequencies was required at the high altitudes because the doppler width is proportional to the frequency and thus becomes very small. Approximations were made for both the doppler and lorentz halfwidth. The doppler width was computed for a temperature of 250K and for molecular weights which are multiples of 16. This approximates the doppler width within -10% of the exact value. Here it might be pointed out that errors in the integrated absorption are not very sensitive to errors in either the doppler or lorentz width. The approximations used for the doppler width can be justified since the parameter of interest is the ratio of doppler to lorentz width; only in exceptional cases is the lorentz width known to 10% accuracy. Similarly, only selected values of the lorentz width were used. These were so chosen that the error in the half-width should not be more than 10%. The particular values used were given by a = 0(0)n n = 0,...,40. Thus, values as small as 13 x 10 5 cm l could be used. The value of a was selected by using a from the line parameter compilation and by assuming that the half-width proportional to the effective pressure in the layer and inversely proportional to the square root of the effective temperature in the layer. This value was then rounded to the nearest value allowed by the above equation for a. After the monochromatic absorption coefficients were calculated for each layer, the monochromatic transmission from the top of the atmosphere down to a given altitude was computed by summing the absorption coefficients for all the layers above that altitude. As stated above, sample calculations were carried out for a number of special cases; errors in the integrated absorption of single lines were always less than 4%.

9 3. DESCRPTON OF THE SPECTRA The resolution of the spectra has been degraded by convolving the monochromatic transmission with a triangular instrument function. The full width at half-amplitude of the triangle is 20, 5, or 0 cm. The degraded transmission spectra are presented in the figures following the text. The calculations are for a vertical path through the atmosphere above each of the six altitudes. n the figures, each page displays three altitudes for a given spectral interval. The 20 cm l resolution spectra are presented first, then the 5 cm l resolution. These cover approximately 1250 cm l per page. The 0 cm l resolution spectra cover only 200 cm l per page and, since the total interval is cm l, these constitute the bulk of this atlas. The atlas demonstrates the atmospheric "windows" as a function of the observational altitudes and the spectral bandpass of the instrument. t is apparent that the notion of a window is particularly dependent on the bandpass. With a very narrow bandpass, numerous windows can be defined even from low altitudes. However, with wide bandpass filters, windows will be realized only at much higher altitudes. The synthetic spectra presented in the atlas can be used to estimate the transmission for altitudes and resolutions intermediate to those given in the atlas. For this purpose, Tables and give the values of.si. and ZCi(S a. 1 2, where the Si are the line intensities 5 cm l of the computational point. The 5 cm l cutoff of some lines is obvious, such as the shoulders of lines near 262, 365, and 413 cm-l This cutoff was used, not because these wings may be unimportant but because the line shapes in the wings of these lines are not well known. The continuum absorptions can be estimated by using an assumed line shape in the far wings and by referring to Table or to other sources. A magnetic tape of the results presented in this atlas will be retained in the NCAR archives and will be available to non-ncar researchers. and the ai are the lorentz half-widths. The sum is taken over all lines within 10 cm intervals. Table V gives the value of the integral of the absorption from a starting wave number up to the listed wave number. The starting wave numbers are integral multiples of 200 cm l; i.e., the value is reset to zero each 200 cm l. By the use of sums or differences of the listed values, the average transmission or absorption over any desired spectral region can be derived; this is equivalent to using a square rather than triangular instrument function. n considering the atmospheric windows, it should be kept in mind that the computations considered only the contributions of lines within 3

10 4 4. ACCURACY AND UNCERTANTES Previous studies have shown that the line-by-line absorption calculations agree with the atmospheric absorption spectra observed under clear sky conditions within 10-20%. However, it is important to recognize that the accuracy of these calculations is no.better than the input parameters. Several factors contribute to inaccuracies and limitations of the present calculations; the most relevant will be discussed in the following paragraphs. Unfortunately, the uncertainties involved do not allow a simple solution to the problems at this time and will require further laboratory and field studies. A bibliography for most of the problems to be discussed below can be found in Kuriyan (1973). The spectral line frequencies are known in most cases within cm 1. Line position shifts due to pressure are known to be on the order of 01 cm l, but these were neglected here. The Voigt line shape used here is a convolution of lorentz and doppler shpaes; in the atmosphere it reduces to lorentz shape at the lower altitudes and to doppler shape at the higher altitudes. At the far wings of a spectral line, the Voigt shape is essentially a lorentz shape, even at the higher altitudes. The use of Voigt line shape is subjected to several limitations due to various uncertainties in our knowledge of spectral line shape. t has been established that the effect of collisions on the doppler shape is to reduce the effective doppler half-width (collision narrowing); this effect can be significant above the tropopause. t is also known that the lorentz shape is quite poor in the distant wings of a line. Many lines show either sublorentzian (such as C02 in the 4 and 15 pm bands) or super-lorentzian (such as H20 in the 6 pm band) behavior. For the low wave number region, the symmetrical lorentz shape could have been replaced with the asymmetrical Van Vleck-Weisskopf shape. This shape differs considerably from the lorentz shape in the far wings, but these were neglected here. t should also be noted that evidence exists for deviations from the lorentz shape even near the line centers, as for the C02 4 pm band. The uncertainties in the far wings of the lines are a dominant factor in estimating the continuum absorption in the atmospheric windows, especially in the 8-10 pm region. n other regions, the line absorption is, in general, larger than the continuum absorptions. Weak semicontinuous absorptions due to pressure-induced transitions of N2 and 2 at 4 and 6.5 pm, respectively, are known to exist. n addition, semicontinuous absorptions due to the H20 dimer can be significant in the 20 cm l region as well as in the cm~l region and in the near-infrared bands of HO20. Neither the pressureinduced bands nor the dimerization effect have been included in the present calculations. The weak, pressure-induced pure rotation spectrum for CH4 has also been excluded. n our calculations the line intensities are determined from the Boltzmann factors for the population of the energy levels and the matrix elements of the transition probabilities. n most cases, absolute transition probabilities are known within 10-20% and are derived mostly from laboratory measurements. The temperature dependence of the line itensities is provided here by the Boltzmann factors; thus, a thermal equilibrium is assumed. t should be noted that for altitudes above 50 km, deviations from thermal equilibrium can be significant, especially for the vibration-rotation bands of H20 and C02. The lorentz half-width is known to vary from one spectral line to another. However, in the compilation of line parameters a mean halfwidth value was used in many cases. Furthermore, although the tempera-- ture dependence of the lorentz half-width can vary significantly from one line to another, in the present (and in most other line-by-line computations)it is approximated by an inverse square-root dependence. The lorentz half-widths were further approximated as discussed under computational procedures (Section 2 above). t should be noted that the inhomogeneity of the atmospheric path results in effects due to refraction and, to a lesser extent, to anomalous dispersion in the vicinity of the absorption lines. These effects are negligible for vertical paths such as used here, but can become significant in long-path sunset of sunrise spectra. The refraction effects

11 especially become quite prominent under such conditions (Snider and Goldman, 1975). The transmission calculated in this atlas depends on the particular choice of the mixing ratio profiles of the minor constituents. This is particularly significant for the variable minor constituents such as H20 and 03; it is less significant for N20, CH4, and CO for which the mixing ratios above the tropopause are not well known. n conclusion, this atlas can be used as a guide for various infrared and microwave studies, as long as the basic limitations discussed above are recognized. Under these limitations the atlas can be expected to predict the correct atmospheric absorption within 10-20%. Table Atmospheric Layers Used in the Computations Number of molecules in layer (molecules/cm ) Alt. Press. Range Temp Layer (km) (mb.) ( K) H O Co2 0 N O CO CH llxO xl xl0 8 27xlO xl xlO 9 21xl xl xl x xl x x x A* xlO0 33x10 40xlO0 29xlO0 74xlO 1.56x10 25xlO 3 3B* x xlO xlO xl xlO x xl x lOxlO xl x x xl x xl xl x x xl x xl l.oox xl x x xl x xl 2 1 *The mb pressure range was too large for a single layer approximation, so an additional layer was added at 59.4 mb. This altitude is not included in the figures. 5

12 6 Table The number of lines and the sum of the line intensities are given for the lines of each molecule in the specified interval. The units of the line intensities are cm l/molecule cm7 2 and correspond to a temperature of 296K. WAVENUMBER (1/CM) H20 C02 NO. SUM NO. SUM 03 N20 CO CH4 WAVENUMBER NO. SUM NO*. SUM NO. SUM NO. SUM (1/CM) H20 C02 03 N20 CO NO. SUM NO, SUM NO. SUM NO, '-SUM NO. SUM NO. CH4 SUM * E E E-20 4o5E E-19 1E-18 4E E-18 1E-18 2E-18 2E-18 6E E-18 2E-18 1E-18 5E-18 3E-19 3E-18 9E-19 8E-19 5E-18 5E-19 3E-18 2E-19 1E-18 2E-18 2E-19 1E-18 1E-18 7E-20 2E-18 1E-19 1E-18 1E-19 4E-19 6E E-20 3E E-20 2E-19 2e2E-20 1E-19 3E-20 2E-20 3E-20 7E E E-20 1E E E-26 1E-25 8E-26 5E-25 4E-25 6E ,7E E ,7E OE ,3E *6E ,9E-20 '96 5,8E *4E *1E ,OE ,2E o4E o9E E *7E ? E E-20 1E-20 1E-21 6E E-21 6E-21 7E E-21 7E-21 2E-21 2E-21 2E E-21 7E-22 1E-21 7E-22 4E E E-21 1E-21 2E E-22 1E-22 7E E-22 3E-23 2o2E E-22 5E E E-23 3o4E-23 2E-23 4E-23 1E-22 21E-23 3E-23 4E-23 8E-24 4E-23 9E-24 3E-23 9E-25 2E-23 1*OE-23 4E-24 2E-23 2E-24 3E E-24 1E-23 3E-23 4E-23 2E-22 8E E-22 8E-22 3E E-20 1E E-20 3E-20 1.e9E-19 6E-19 9o9E-19 4E-18 9E-19 loe-18 4E E-19 5E-20 8E E-20 1E-20 3E-21 9E-22 2o5E-22 8E E-22 1E-22 5E-23 2E-23 4E-24 3E-24 2*1E-24 3E-24 9E E-24 3E-24 8E-24 1E-23 2E-23 7E E-22 9E E-23 1E-22 7E-23 6E ' *8E-22 2*5E-21 7,4E-21 1,3E-20 2*1E-20 3,1E-20 4*7E-20 6*8E-20 6*9E-20 4,9E-20 4o5E-20 7,7E-20 7*5E-20 4,5E-20 3o6E E E E-20 8*4E-21 5*OE-21 1*OE E E-23 1E-23 5E E E-20 8E-20 2E E E-21 2E-20 7E E-19 5E E E-19 6E-20 1E-20 2E-21 1E-22 4E-24 8E-23 2E-22 3E-22 1E-21 2E-22 2E-22 9E-23 4*OE-24 9*2E-23 2*8E-22 4o4E-22 2o2E-22 3*5E E-22 2*5E-22 2E-23

13 Table - Continued WAVENUMBER (1/CM) H20 NO 0 SUM C02 NO, SUM 03 N20 CO NO. SUM NO, SUM NO, SUM CH4 NO, SUM WAVENUMBER (1/CM) H20 C02 03 N20 CO NO. SUM NO. SUM NO. SUM NO* SUM NO, SUM CH4 NO. SUM 6*0E-24 2E-23 1*6E-23 7,7E-24 7E-24 9E-24 4E-23 1*9E-23 4*5E-24 3E-23 6*9E-23 4E-23 5E-23 1*9E-22 4E-23 4*6E-23 6E-23 4E-22 2E-22 1*6E-22 1*2E-23 6E-22 4E-22 8E-23 5E-22 lo8e-22 3E-21 1*7E-21 2E-21 1.o3E E-21 1E E-21 2*5E-20 1*7E-20 5*0E-21 6*3E-20 4E E-20 1*4E-19 2E-20 1E-19 6E-20 1*6E E-20 3E-19 9*7E-20 2*6E-19 1*2E-19 2o6E-19 lo(o « ? , *5E E-24 2e5E-23 7,8E-23 1*5E-22 1*9E-22 8o6E-23 2*8E-22 1*7E-22 3*5E-23 11E *2E E-18 2*2E-18 2*2E-18 1*5E-18 3,7E E E-20 3o7E-20 3,OE-20-2*4E-20 3*2E-20 4,7E-20 4,OE-20 2*3E E-20 1,2E-20 7*9E-21 12E *0E-19 1E-19 4E-19 3E-19 4E-19 5*7E-19 3*7E-19 2E-19 2*5E-21 1E-20 3*2E-20 2*4E-19 1*4E-19 2E-19 2E-19 6*4E-19 2*4E-19 2E-19 4E-19 5E-19 3E-19 4E-19 2E-20 4E-19 1E-19 1*9E-19 1*6E-19 2*3E-19 6*6E-20 1E-19 4E-20 3*4E-20 7E-20 6*0E-20 1E-19 3*0E-21 7E-20 3E-21 2E-20 8E-21 lole E-20 1E-20 l*oe-21 2*6E E-21 1*OE E-22 3*2E-21 1E ? O E E E-20 1*1E-20 5o2E-23 2e1E-22 1*5E E-21 2*3E-21 3*7E-21 4*6E-21 5 OE E-21 9*4E-24 9*5E-23 1*9E E E-21 2*5E-22 2*3E-22 2*2E E-22 3*OE E E-20 8*OE E E-20 7*9E-20 3o7E-20 1 *1E-20 2o7E E-21 3*5E-20 17E-19 6*2E-19 1*5E-18 1*9E-18 89OE-19 2*OE E-18 6*6E-19 1 OE-19 5*7E-21 5*6E *7E-22 5*4E-21 9*4E E-20 5E-20 1*lE E-19 2E-19 4.OE E-19 4E-19 4E-19 1E-18 1E-19 4E-19 6E-19 8E-19 4E-19 1*9E-19 4E-20 6E-21 12E-21 8E-24 1E-22 2*1E-22 6E-22 5*4E E-22 1E E-23 3*4E-23 2*2E-22 7*9E-22 1*4E-21 4*OE-21 5*9E-21 2*1E-21 11E-21 2*OE E E E-25 1*6E-24 3*9E-24 5*8E-24 5*1E-24 1,3E-23 5*4E-23 1*6E E-22 9*9E-23 2*2E-22 3o7E-24 1*5E-23 1*8E E-24 1*7E-24 1 OE *8E-21 7o4E-21 2*9E E-21 3*5E-21 1*3E-21 6*6E E-23 3*6E-23 2E-22 4E-23 8E *1E E E-22 7

14 8 Table - Continued WAVFNUMBER (1/CM) H20 C02 03 N20 NO. SUM NO, SuM NO, SUM NO. SUM CO NO* SUM CH4 NO. SUM WAVENUMPER (/CM) H20 C02 03 N20 CO NO. SUM NO. SUM NO, SUM NO, SUM NO. SUM CH4 NO, SUM ) C r rr rr 1 ) ) - Cc r rr rr rr rr rr rr rr rr ' E-22 6E E-22 1E E E-23 2E E-22 2E E-22 1E-22 3E-22 7E-23 3E-22 1*OE-22 6E-23 9E-23 2E-23 6E-23 1E-23 5.*3E-2 3 3E-23 8E-24 2E-23 2E-23 3E-23 4E- 24 1E E-24 1E-23 5.o3E-24 5E-24 3E-24 2E-24 1E-24 1E-24 9,0E-25 1E-24 5E-25 5E E-25 2E E-25 3E-25 6E-26 2E E-25 1E-25 3E-25 2.OE E-24 8E-24 1E-23 7E-23 2E-22 7E-22 6E-22 13E-21 1E E-22 1a1E-22 1E-22 1E-22 1E-23 8E-24 2E-24 1E E-24 4E E-23 7E-23 3E-22 2E-21 1E-20 4*1E-20 1E-19 lo9e-19 2E-19 1E-19 6E-19-1E-18 5E-18 1E-17 2*1E-17 1E-17 1E-17 2E-17 9E-18 4E-19 *OE-21 1E-23 2E-23 1E-23 1E-23 2E-23 1*OE-23 1E-24 9E-25 2E E-22 2*1E-21 6E E-20 2E E E-19 2*CE-19 3E-19 7E-19 6*6E-19 1F E-19 5E-19 9E-20 7E-19 1E-18 1*2E-18 6E-19 8E-19 2E-19 1E-19 4E-20 1E-20 1E-21 1E , E E-25 3E-25 1*2E-24 1*7E-24 9E-25 3E-24 4E-24 4E-24 7E E-21 9E E-20 1E-19 2E-19 2E-19 1E-19 3E E-19 6*7E E-22 8E E-22 2E-22 5E-22 5E-22 5E E-22 1*8E E E-22 9,2E-21 3*1E-20 7*6E E-19 2*1E E-19 1,7E-19 4,2E-19 5*2E E-22 1E-21 5E-21 2E-20 7E E-19 7E-19 2E-18 5E-18 9E E-18 5E E-17 9E-18 1E E-20 1E-22 9E-22 2E-21 4E E-21 2E-21 5E-21 3E-21 1E-21 3E-22 2E o3E-22 1*6E-21 9*8E-21 3 *3E-20 6*2E-20 5*OE E-20 8*OE E E E-22

15 Table The number of lines and the sum of the square roots of the line intensity-line halfwidth product are given in the indicated intervals in units of (cm- 1 /atmosphere) 1 / 2 of 296K and one atmosphere was used. (cm-'/molecule cm" 2 ) 1 / 2. A temperature WAVENUMBER (/CM) H20 C02 03 N20 CO NO. SUM NO, SUM NO, SUM NO, SUM NO. SUM NO, CH4 SUM WAVENUMBER H20 C02 03 (/CM) NO SUM NO. SUM NO. SUM N20 CO NO. SUM NO, SUM NO, CH4 SUM n 10?o l(o E-12 1E-10 7E-11 4E E-10 8E-10 5E-10 1E-09 9E-10 looe-09 1E-09 4*6E-10 1E-09 1E E-10 1E E-10 1E-09 5E-10 5E E-09 5E-10 1E-09 2E-10 7E-10 7E-10 2E-10 6E-10 7E E-10 7E E-10 6E-10 1E-10 3E-10 5E-10 9E-11 2E-10 1E-10 3E-10 6E E-10 looe E-11 1E-10 1E-10 6E-11 l.oe-10 5E-11 3E E E-13 1E-13 1E-12 7E-13 1E E E E-10 8E-10 1,OE-09 9E-10 8E-10 8E-10 7E-10 5,8E-10 4E-10 3E-10 2E-10 1E-10 7E-11 2E-11 5no ) O i rr i rr 3 r. * E E-11 4E-11 2E-11 4E-11 3E-11 3E E-11 3E-11 3E-11 1E-11 2E-11 2E-11 2E-11 1*OE E-11 l.oe-11 l.oe-11 l*oe-11 19E E-11 7E-12 4E-12 3E-12 1*1E-11 5E-12 2o3E-12 6*6E-12 3o3E-12 e1.e E-12 2E-12 2E-12 1E-12 3E-12 5E-12 1E-12 2E-12 3E E-12 2E-12 1E-12 2E-12 6E-13 2E-12 1E-12 1E-12 3E-12 6E-13 1E E-12 3E-12 4E-12 6E-12 2E E-11 3E-11 5E-11 2E E-10 6E-10 3l.5E-10 6E E E-09 5E E-09 1*4E-09 8o8E-10 5E-10 4E E-10 2E-10 2*2E-10 l*oe-10 5*3E-11 2*8E-11 1*4E E E-12 6*6E-12 9E-12 3E-12 2E-12 2E-12 3E-12 15E-12 2E E-12 3E E-12 6E-12 8E-12 1E-11 8E E-12 o11e-11 6E-12 2E E-12 9E-11 2E E-10 4E-10 6E-10 8E-10 1E-09 l.oe E-10 6E-10 1E-09 1E-09 8E-10 6E-10 5E-10 4E-10 4E-10 2E E-10 4E E E ,5E *3E o1E *3E E *OE E E OE E E E E E E E E E E E E E E E E E E-13 8E E-11 2E E-11 1E E-11 1E-11 2E-12 9

16 10 Table - Continued WAVENUMBER (1/CM) 10O ? , O H20 C02 03 N20 CO CH4 WAVENUMBER H20 C02 03 N20 CO CH4 NOo SUM NO* SUM NO, SUM NO, SUM NO, SUM NO, SUM (/CM) NO* SUM NO. SUM NO, SUM NO. SUM NO. SUM NO, SUM E E E E OE E E E E E E E E E E E E E E E E E E E E E E E E *0E E E E E E E E l.5e E *5E E E E E E E E E E E E-13 1E-12 3E-12 7E-12 1*OE E-11 1*OE-11 1,7E E-11 8E E E E E ,5E E O*OE E E E E E *9E E *9E E E E E E ' *3E-11 1E-10 2*5E-10 3E-10 4E-10 3E-10 4E-10 4,OE-10 2E-10 1E-10 7.*3E-l1 1E-10 3E-10 6E-10 1E-09 2E E-09 2eOE-09 2*6E-09 2E-09 1E-09 7E-10 1E-10 5E *OE-11 5E-11 7E E-10 2E-10 2E-10 4,2E E E-10 4E E-10 7E-10 2E-09 1E E-10 5E-10 8E-10 6E-10 5E-10 2*5E-10 4E E-11 8E-11 9E-11 3E-11 3E-11 3E-11 1E-11 le ! O E E E E E E E E E ,8E E E E E E E E E E E E E l.oe E E E o1E E E E E E E E E E E E E E E E E E E E E E E E E-14 3,OE-13 5*5E-13 9*1E-13 1*6E-12 3*5E E-12 7*6E-12 1*2E-11 1*7E-11 1*9E-11 9e8E-12 2o2E-11 2*4E-12 4*OE-12 3*3E-12 2*2E-12 1*3E E E E-12 1E-11 2E-11 6E-11 le-11 1E-11 2o5E-12 11E-12 l.oe-1 1.5E-11 3E-11 3E E-1 aole-11 1E E E-11 3*OE E-11 1*4E-10 1*9E-10 6*8E-11 59OE-11 1*5E-11 3E-12 5E-12 2E E-12 1*1E E-13 3o8E-12 1*2E E E *5E E E E E E E E E E E-11

17 Table - continued WAVENUMBER (1/CM) ? j H20 NO, SuM E E E E E E E le E E E o1.e E E E E E E E E *3E E E E E E E E E E E E E E E E E E E E E E E E *1E E E E E E-13 C02 03 N20 CO NO, SUM NO, SUM NO. SUM NO, SUM 32 1E E-12 2'8 3E E E E E E E E E E E E E E *6E E E E E E E E E E E E E E E E E E E E E E E E *6E E E E E E E E *1E E E-10 5E E-10 1E E-09 2E E-09 3,3E-09 8E E E E E E *5E E E E *6E E E E E E E *5E E E E E E E E E E E *5E E-11 4E-11 5E-11 9E E-10 1*9E-10 2*0E E-10 4E E-10 5*3E-10 3E-10 4*3E E-10 4F-10 5E-10 5E-10 3o0E E-10 2*2E E-10 7E-11 4E-11 17E-11 4o3E-12 NO. CH4 SUM 9E-12 5E-11 1*7E-10 3E-10 4E-10 3E-10 3E-10 5E E-10 1E-10 4 *1.E-11 WAVENUMBER (1/CM) H20 NO SUM 5E-13 9E E-13 1E-12 1E-12 1E-12 le-12 2E-12 2E E-12 C02 03 N20 CO NO. SUM NO. SUM NO. SUM NO, SUM 61 1E E E E E E E E E E-10 NO. CH4 SUM 4 6E E E E E E E E o2E E-11 11

18 12 Thus, the actual contribution of the absorption in an interval was included even though the table lists the same value of the integral for consecutive frequencies. NTEGRATED ABSORPTON (/CM) Table V The integral of the fractional absorption with respect to wave number is listed for different altitudes. The integrals were calculated to a greater number of significant figures than listed in the table. NTEGRATED ABSORPTON (/CM) FREQUENCY (1/CM) ALTTUDE , , , , , , , , , * ' s *000 *001 e003, e e * e *015 FRFQUENCY (/CM) ALTTUDE * , a , , , ,919 7,157 7, , , , , , o c 246 o246 * e *

19 Table V - Continued NTEGRATED ABSORPTON, (1/CM) NTEGRATED ABSORPTON (/CM) FREQUENCY (/CM) ALTTUDE FREQUENCY (/CM) ALTTUDE * * * * * , , ,497 3* * * * *382 4.* o * *681 4,765 4*944 4* * * X o 627.* * *720 * * e 803 * * ' * (0 39 * * * 986.* *288 o288 00» * o * * * *082 * *087 * * *096 * * *104 07, * * 123 * *, * , , * * * * * * * * * * 642 * * *656 * * ,

20 14 Table V - Continued NTEGRATED ABSORPTON (/CM) NTEGRATED ABSORPTON (1/CM) FRFQUENCY (/CM) ALTTUDE FREQUENCY (1/CM) ALTTUDE *998 19*998 20e o ,998 28, * e i e o o * ,810 1, ,789 2* *320 3*595 3* ,731 3* ,720 4, * * * e ,417 8*489.*022 *031 * * *806 * * * * *678 * 005 * * * * * o * *003 *043 * 044 * 044 * *061 * *079 * o o loo * l r * 140 e * X *174 o001 *012 * e 016 *017»021 oo * *037, o040 o * a oO47 47 * * X e o X * X *073 79* o X * o * , o , o o o * * * * e o o , * * *401 * * ,420 * *468 * * o e o 536 o * o204 * o o207,207 *207 *208 *208 o208 15,217, * o ,224 e225 o 243.* 243 *249,253 *263 *263 o 264 * *276 * o53 53 * , * o *063 * *065 s065 0oO65 * *065 *065,066,067 *067, *075 * o80, *082,083 *083 * *083,083 *083 83,