1 1854 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 On Rayleigh Optical Depth Calculation BARRY A. BODHAINE NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado NORMAN B. WOOD Cooperative Intitute for Reearch in Environmental Science, NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado ELLSWORTH G. DUTTON NOAA/Climate Monitoring and Diagnotic Laboratory, Boulder, Colorado JAMES R. SLUSSER Natural Reource Ecology Laboratory, Colorado State Univerity, Fort Collin, Colorado 1 January 1999 and 3 May 1999 ABSTRACT Many different technique are ued for the calculation of Rayleigh optical depth in the atmophere. In ome cae difference among thee technique can be important, epecially in the UV region of the pectrum and under clean atmopheric condition. The author recommend that the calculation of Rayleigh optical depth be approached by going back to the firt principle of Rayleigh cattering theory rather than the variety of curvefitting technique currently in ue. A urvey of the literature wa conducted in order to determine the latet value of the phyical contant neceary and to review the method available for the calculation of Rayleigh optical depth. The recommended approach require the accurate calculation of the refractive index of air baed on the latet publihed meaurement. Calculation etimating Rayleigh optical depth hould be done a accurately a poible becaue the inaccuracie that arie can equal or even exceed other quantitie being etimated, uch a aerool optical depth, particularly in the UV region of the pectrum. All of the calculation are imple enough to be done eaily in a preadheet. 1. Introduction Modern Rayleigh cattering calculation have traditionally been made by tarting with thoe preented by Penndorf (1957). In Penndorf paper, the refractive index of air wa calculated uing the equation of Edlén (1953): (n 1) , (1) where n i the refractive index of air and i the wavelength of light in micrometer. Thi equation i for tandard air, which i defined a dry air at 760 mm Hg ( mb), 15C (88.15 K), and containing 300 Correponding author addre: Barry A. Bodhaine, NOAA/ CMDL, R/E/CG1, 35 Broadway, Boulder, CO ppm CO. It i an empirical relationhip derived by fitting the bet available experimental data and i dependent on the compoition of air, particularly CO and water vapor. Next, Penndorf (1957) calculated the Rayleigh cattering coefficient for tandard air uing the claic equation that i preented in many textbook (e.g., van de Hult 1957; McCartney 1976): 3 4 (n 1) 6 3, () 4 N (n ) 6 7 where i the cattering cro ection per molecule; N i molecular denity; the term (6 3)/(6 7) i called the depolarization term, F(air), or the King factor; and i the depolarization factor or depolarization ratio, which decribe the effect of molecular aniotropy. The F(air) term i the leat known for purpoe of Rayleigh cattering calculation and i reponible for the mot uncertainty. The depolarization term doe not depend on temperature and preure, but doe depend on the ga mixture. Alo, N depend on temperature and pre American Meteorological Society
2 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1855 ure, but doe not depend on the ga mixture. The reulting value of, the cattering cro ection per molecule of the ga, calculated from Eq. (), i independent of temperature and preure, but doe depend on the compoition of the ga. Note that N depend on Avogadro number and the molar volume contant, and i expreed a molecule per cubic centimeter, and that value for n and N mut be expreed at the ame temperature and preure. However, ince ( n 1)/ ( n ) i proportional to N, the reulting expreion for i independent of temperature and preure (Mc- Cartney 1976; Bucholtz 1995). Note that the uual approximation n 3 wa not included in Eq. () in the interet of keeping all calculation a accurate a poible. Reult of uch calculation were preented by Penndorf (1957) in hi Table III. It i thi table of value that ha been ued by many worker in the field to etimate Rayleigh optical depth, uually by ome curve-fitting routine over a particular wavelength range of interet. Soon after Penndorf paper wa publihed, Edlén (1966) preented a new formula for etimating the refractive index of tandard air: (n 1) , (3) although the maximum deviation of n from the 1953 formula wa given a only Edlén (1953, 1966) alo dicued the variation of refractive index with temperature and preure, and alo with varying concentration of CO and water vapor. In light of the Edlén (1966) reviion, Owen (1967) preented an indepth treatment of the indexe of refraction of dry CO - free air, pure CO, and pure water vapor, and provided expreion for dependence on temperature, preure, and compoition. However, Owen (1967) main interet wa in temperature and preure variation, and hi analyi doe not ignificantly impact our preent work becaue our calculation are performed at the temperature and preure of tandard air. Peck and Reeder (197) further refined the currently available data for the refractive index of air and uggeted the formula (n 1) (4) for the mot accuracy over a wide range of wavelength. Equation (4) i pecified for tandard air but at the beginning of their paper, Peck and Reeder (197) pecify tandard air a having 330 ppm CO. Alo, they repeat Edlén (1966) formula, which had clearly defined tandard air a having 300 ppm CO, but tate that it applie to air having 330 ppm CO. Here we will ue the equation of Peck and Reeder (197) and aume that it hold for tandard air having 300 ppm CO. Poible error in the depolarization term were conidered by Hoyt (1977), Fröhlich and Shaw (1980), and Young (1980, 1981). The correction propoed by Young (1981) had been accepted for modern Rayleigh cattering calculation in atmopheric application. In brief, Young (1981) uggeted that the value F(air) (6 3)/(6 7) be ued rather than the value ued by Penndorf (1957). Thi effect alone reduced Rayleigh cattering value by 1.%; however, it cannot be applied over the entire pectrum becaue F(air) i dependent on wavelength. Furthermore, ince the depolarization ha been meaured for the contituent of air (at leat in a relative ene), it i poible in principle to etimate the depolarization of air a a function of compoition. Bate (1984) and Bucholtz (1995) dicued the depolarization in detail. It appear that currently the bet etimate for (6 3)/(6 7) ue the equation given by Bate (1984) for the depolarization of N,O, Ar, and CO a a function of wavelength. It i therefore poible to calculate the depolarization of air a a function of CO concentration. Bate (1984) gave a formula for the depolarization of N a a function of wavelength a 1 4 F(N ) , (5) and for the depolarization of O a 1 F(O ) (6) Furthermore, Bate (1984) recommended that F(air) be calculated uing Eq. (5) and (6), auming that F(Ar) 1.00, F(CO ) 1.15, and ignoring the other contituent of air.. Optical depth A quantity of fundamental importance in atmopheric tudie i the optical depth (or optical thickne). Thi quantity ha been dicued by numerou author (e.g., Dutton et al. 1994; Stephen 1994) and i derived from the exponential law of attenuation variouly known a Bouguer law, Lambert law, or Beer law. For purpoe of illutration only, Bouguer law may be imply written a I() I 0 () exp[()/co], (7) where I 0 () i the extraterretrial flux at wavelength, I() i the flux reaching the ground, i the olar zenith angle, and () i the optical depth. Clear-ky meaurement of I() a a function of, and plotted a lni() veru ec, hould yield a traight line with lope () and intercept I 0 (extrapolated back to ec 0). An excellent example, along with a dicuion of thi proce, i hown by Stephen (1994) in hi Fig
3 1856 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 An important point i that (), the total optical depth, may be compoed of everal component given by () R () a () g (), (8) where R () i the Rayleigh optical depth, a () i aerool optical depth, and g () i the optical depth due to aborption by gae uch a O 3,NO, and H O. In principle it i poible to meaure () and then derive aerool optical depth by ubtracting etimate of R () and g (). In practice, however, arriving at reaonable etimate of thee quantitie can be difficult, particularly during fairly clean atmopheric condition uch a thoe found at Mauna Loa, Hawaii. At thi point it hould be apparent that in order to iolate the individual component of optical depth it i neceary to provide accurate etimate of Rayleigh optical depth. Rayleigh optical depth i relatively eay to calculate once the cattering cro ection per molecule ha been determined for a given wavelength and compoition becaue it depend only on the atmopheric preure at the ite. That i, it i neceary to calculate only the total number of molecule per unit area in the column above the ite, and thi depend only on the preure, a hown in the formula PA R(), (9) mg a where P i the preure, A i Avogadro number, m a i the mean molecular weight of the air, and g i the acceleration of gravity. Note that m a depend on the compoition of the air, wherea A and g are contant of nature. Although g may be conidered a contant of nature, it doe vary ignificantly with height and location on the earth urface and may be calculated according to the formula (Lit 1968) g (cm ) g 0 ( co)z ( co)z ( co)z 3, (10) where i the latitude, z i the height above ea level in meter, and g 0 i the ea level acceleration of gravity given by g ( co co ). (11) 3. Approximation for Rayleigh optical depth Many author have imply taken Rayleigh cattering cro-ection data from Penndorf (1957) over a particular wavelength interval of interet and applied a curvefitting routine to approximate the data for their own purpoe. Some, but not all, of thee author have applied Young (1981) correction. Teillet (1990) compared the formulation of everal author and found ignificant difference among them. It i not the purpoe of thi paper to urvey all of the approximation in ue by variou author nor i it to compare accuracie of the variou method; however, a few example will erve to illutrate ome of the difficultie. The implet approach, taken by many author, i to fit an equation of the form () A B, (1) where A and B are contant to be determined from a power-law fit and the equation i normalized to mb preure. An example wa given by Dutton et al. (1994), who performed uch a fit over the viible range and provided the equation p 4.05 () , (13) R p 0 where p i the ite preure, p 0 i mb, and i in micrometer. Clearly, one problem with thi approximation i that it cannot be extrapolated to other part of the pectrum, particularly the UV, where the powerlaw exponent i ignificantly different. To account for the fact that the exponent change, ome author (e.g., Fröhlich and Shaw 1980; Nicolet 1984) ued equation of the form molecule (BCD 1) R() A, (14) cm where the term molecule cm i calculated from the urface preure, a explained above. Thi equation i likely to be more accurate over a greater range of the pectrum. A lightly different approach wa taken by Hanen and Travi (1974), who uggeted the equation R () ( ), (15) where R () i normalized to mb. A a final example Stephen (1994) uggeted the equation R () (4.150.) (0.1188z z e ), (16) where the expreion i given in term of altitude (km) above ea level uing the tandard atmophere. The point here i that all of thee equation were ueful for the particular author over a limited wavelength range and at limited accuracy. Comparing thee variou equation how ignificant difference, epecially in the UV (Teillet 1990). More importantly, the difference among thee equation can be ignificantly greater than typical aerool optical depth found in the atmophere. In the cae of clean condition at Mauna Loa, it i poible for aerool optical depth to be calculated a negative value becaue of thee error.
4 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1857 TABLE 1. Contituent and mean molecular weight of dry air. Ga % volume Molecular wt % vol mol wt N O Ar Ne He Kr H Xe CO Mean molecular weight with zero CO Mean molecular weight with 360 ppm CO gm mol gm mol 1 4. Suggeted method to calculate Rayleigh optical depth of air Here we ugget a method for calculation of Rayleigh optical depth that goe back to firt principle a uggeted by Penndorf (1957) rather than uing curve-fitting technique, although it i true that the refractive index of air i till derived from a curve fit to experimental data. We ugget uing all of the latet value of the phyical contant of nature, and we ugget including the variability in refractive index, and alo the mean molecular weight of air, due to CO even though thee effect are in the range of 0.1% 0.01%. It hould be noted that aerool optical depth are often a low a 0.01 at Mauna Loa. Since Rayleigh optical depth i of the order of 1 at 300 nm, it i een that a 0.1% error in Rayleigh optical depth tranlate into a 10% error in aerool optical depth. Furthermore, it imply make ene to perform the calculation a accurately a poible. We hould note that the effect of high concentration of water vapor on the refractive index of air may be of the ame order a CO (Edlén 1953, 1966). However, for practical atmopheric ituation the total water vapor in the vertical column i mall and doe not ignificantly affect the above calculation. Furthermore, the water vapor in the atmophere i uually confined to a thin layer near the urface, which ignificantly complicate the calculation, wherea CO i generally well mixed throughout the atmophere. To facilitate the following Rayleigh optical depth calculation, the latet value of Avogadro number ( molecule mol 1 ), and molar volume at K and mb (.4141 L mol 1 ) were taken from Cohen and Taylor (1995). In order to calculate the mean molecular weight of dry air with variou concentration of CO, the percent by volume of the contituent gae in air were taken from Seinfeld and Pandi (1998), and the molecular weight of thoe gae were taken from the Handbook of Phyic and Chemitry (CRC 1997). Thee reult are hown in Table 1. The mean molecular weight (m a ) for dry air were calculated from the formula (%Vol MolWt) ma. (17) (%Vol) Note that the error ariing from the fact that (%Vol) i not exactly 100 i negligible. Auming a imple linear relationhip between m a and CO concentration, m a may be etimated from the equation m a (CO ) gm mol 1, where CO concentration i expreed a part per volume (ue for 360 ppm). We recommend tarting with Peck and Reeder (197) formula for the refractive index of dry air with 300 ppm CO concentration: (n300 1) , (18) and caling for the deired CO concentration uing the formula (n 1) CO (CO ), (19) (n 1) 300 where the CO concentration i expreed a part per volume (Edlén 1966). Thu the refractive index for dry air with zero ppm CO i (n0 1) , (0) and the refractive index for dry air with 360 ppm CO i (n360 1) , (1) where it mut be emphaized that Eq. (18) (1) are given for K and mb, and in unit of micrometer. We recommend that the cattering cro ection (cm molecule 1 ) of air be calculated from the equation 3 4 (n 1) 6 3, () 4 N (n ) 6 7 where n i the refractive index of air at the deired CO concentration, i expreed in unit of centimeter, N molecule cm 3 at K and mb, and the depolarization ratio i calculated a follow. Uing the value for depolarization of the gae O,N, Ar, and CO provided by Bate (1984), we recommend that the depolarization of dry air be calculated uing Eq. (5) (6) and the following equation to take into account the compoition of air:
5 1858 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME F(N ) 0.946F(O ) CCO 1.15 F(air, CO ), (3) C CO where C CO i the concentration of CO expreed in part per volume by percent (e.g., ue for 360 ppm). The reult of Eq. (3) for tandard air (300 ppm CO ) are hown in Fig. 1. Note that the value of N in Eq. () wa calculated from Avogadro number and the molar volume, and then caled to K according to the formula 3 N (molecule cm ) molecule mol K L mol K 1L. (4) 1000 cm 3 Finally, we recommend that the Rayleigh optical depth be calculated from the formula PA R(), (5) mg a where P i the urface preure of the meaurement ite (dyn cm ), A i Avogadro number, and m a i the mean molecular weight of dry air calculated from the formula m a (CO ) , a in Eq. (17). The value for g need to be repreentative of the maweighted column of air molecule above the ite, and hould be calculated from Eq. (10) (11), modified by uing a value of z c determined from the U.S. Standard Atmophere, a provided by Lit (1968). To determine z c we ued Lit (1968, p. 67) table of the denity of air a a function of altitude and calculated a maweighted mean above each altitude value, uing an average altitude and average denity for each layer lited in the table. Next a leat quare traight line wa paed through the reulting z c value up to m, giving the following equation: z c z , (6) where z i the altitude of the oberving ite and z c i the effective ma-weighted altitude of the column. For example, an altitude of z 0 m yield an effective maweighted column altitude of z c m to ue in the calculation of g. The reulting value or R hould be conidered the bet currently available value for the mot accurate etimate of optical depth. 5. Optical depth of the contituent of air A a enitivity tudy, the contribution of CO to the Rayleigh optical depth of air may be etimated a a function of wavelength by uing the above formula expreed for CO. Owen (1967) give the refractive index of CO at 15C and mb a 8 (nco 1) , (7) where i expreed in unit of micrometer a before. Next the cattering cro ection of a CO molecule can be calculated from Eq. (), where N molecule cm 3 at K and mb a before, and the King factor F(CO ) taken to be 1.15, a uggeted by Bate (1984). Finally (CO, ) can be calculated uing Eq. (5), where m (the molecular weight of CO ), and multiplying by (for a CO concentration of 360 ppm) to etimate the number of CO molecule. Note that (H O, ) for 44 kg m column water vapor wa calculated in a imilar manner uing the refractive index of H O given by Harvey et al. (1998) and a depolarization ratio of 0.17 for H O given by Marhall and Smith (1990). The reult of thee calculation are hown in Table, where the change of optical depth (H O) i given for the cae where dry air molecule are replaced by H O molecule for 44 kg m column water vapor. Thu for a Rayleigh optical depth of 1.4 for air at 300 nm, a CO con- TABLE. Optical depth of the contituent of air (tandard preure mb and altitude 0 m). FIG. 1. Depolarization factor for dry air with 300 ppm CO. (nm) (N O Ar) (CO ) (H O) (H O)
6 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1859 centration of 360 ppm would contribute an optical depth about Some example calculation Uing the above equation we now preent example calculation to how new value for the cattering cro ection (a a function of wavelength) of dry air containing 360 ppm CO, imilar to the preentation of Penndorf (1957) and Bucholtz (1995). In addition we preent new value for Rayleigh optical depth for dry air containing 360 ppm CO at ea level, mb, and a latitude of 45; and at Mauna Loa Obervatory (MLO) (altitude 3400 m, preure 680 mb, and a latitude of ). The reult of thee calculation are hown in Table 3. For thoe reader who wih to ue curve-fitting technique, we have invetigated everal different equation imilar to thoe ued by other author, a dicued earlier in thi paper. We found that the accuracie of thoe equation were not ufficient for our purpoe, and therefore we looked for a more accurate approach. We find that the equation a b c y (8) 1 d e give excellent accuracy. Thi five-parameter equation fall in the cla of ratio of polynomial commonly ued in curve-fitting application. It give an excellent FIG.. Percent error for Eq. (9) fit to the cattering cro-ection data in Table 3. fit in thi cae becaue the general form of the data being fit by the equation i alo a ratio of polynomial. For the cattering cro-ection data in Table 3 the bet-fit equation i 8 (10 cm ) (9) Equation (9) i accurate to better than 0.01% over the nm range, and till better than 0.05% out to 1000 nm when fitting the cattering cro-ection data in Table 3. In fact, thi equation i accurate to better than 0.00% over the range nm (ee Fig. ). Bet fit for the other two example provided in Table 3 are R(ea level, 45N) and (30) R(MLO, 3.4 km, 680 mb) (31) It hould be noted that only the leading coefficient in Eq. (30) (31) are different from thoe in Eq. (9). Thee numerical value repreent the value of the PA/ m a g term (molecule in the column) given in Eq. (5) for the two cae (taking into account the 10 8 factor that wa removed from the cattering cro ection data to facilitate curve fitting calculation). 7. Concluion We have preented the latet value of the phyical contant neceary for the calculation of Rayleigh optical depth. For the mot accurate calculation of thi quantity it i recommended that uer go directly to firt principle and that Peck and Reeder (197) formula be ued to etimate the refractive index of tandard air. Next, we recommend that Penndorf (1957) method be ued to calculate the cattering cro ection per molecule of air, taking into account the concentration of CO. In mot cae the effect of water vapor may be neglected. The recommendation of Bate (1984) were ued for the depolarization of air a a function of wavelength. Next the Rayleigh optical depth hould be calculated uing the atmopheric preure at the ite of interet. Note the importance of taking into account variation of g. We do not necearily recommend the ue of curve-fitting technique to generate an equation for etimating Rayleigh optical depth becaue the inaccuracie that arie can equal or even exceed other quantitie being etimated, uch a aerool optical depth. Furthermore, all of the above calculation are imple enough to be done in a preadheet if deired, or can eaily be programmed in virtually any computer language. However, for thoe who wih to ue a imple
7 1860 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 TABLE 3. Scattering cro ection (per molecule) and Rayleigh optical depth ( R ) for dry air containing 360 ppm CO. Rayleigh optical depth are given for a location at ea level, mb, 45 latitude, and at MLO at altitude 3400 m, preure 680 mb, and latitude WV (m) (cm ) E E E E E6 8.55E6 7.68E E E E E E E E E E E E E E6.989E6.7589E6.6011E6.4546E6.3183E6.1915E6.0733E E E E E E E E E E E E E E E E E E E7 8.31E E E E E E E E E E E E E E E E E7 R (ea level, 45N).7137E00.488E00.766E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E01.941E E E E01.461E E01.111E01.116E E E E E E E E E E E E E E E E E E E E E0 R (MLO, 680 mb) King factor 1.864E E E E E E E E E E E E E E E E E E E E E E E E E E E01.843E E E01.443E01.30E E E E E E E E E E E E E E E E E E E E0 9.64E E E E E E E E E E E WV (m) (cm ) E E E E E E E E E E7.9583E7.8618E7.7691E7.680E7.5948E7.518E7.4341E7.3584E7.856E7.157E7.1484E7.0836E7.013E E E E E E E E E E E E7 1.48E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E8 TABLE 3. (Continued ) R (ea level, 45N) E E E E E E0 7.91E E E E E E E E E E E E E E E E E0 4.07E E E E E E E E E E E E0.9898E0.9089E0.8308E0.755E0.68E0.6116E0.5433E0.477E0.413E0.3514E0.914E0.334E0.177E0.18E0.0701E0.0190E E E E E E E0 1.70E E E E E E E E0 R (MLO, 680 mb) King factor E E E E E E E E E E E E E E E E E E E E E E0.975E0.8406E0.7569E0.676E0.5985E0.536E0.4514E0.3818E0.3146E0.498E0.187E0.168E0.0685E0.01E E E E E E E E E E0 1.54E E E E E E E E E E E E E E E E E E E E
8 NOVEMBER 1999 NOTES AND CORRESPONDENCE 1861 WV (m) (cm ) E E E E E E E E E E E E E E E E E E E E E E8 TABLE 3. (Continued ) R (ea level, 45N) 1.416E E E0 1.66E E0 1.08E E E E E E E E E E E E E E E E E03 R (MLO, 680 mb) King factor E E E E E E E E E E E E E E E E E E E E E E equation and are atified with le accuracy, the technique ued to produce Eq. (9) (31) may be of interet. A more accurate etimate of the variou parameter dicued above become available, the equation of interet may eaily be modified. In ome calculation of optical depth it may be deired to take into account the vertical ditribution of the compoition of air, particularly CO. In thi cae a layerby-layer calculation may be done uing the etimated compoition for each layer, and then the total optical depth may be etimated by umming the optical depth for all of the layer. Acknowledgment. We thank Gail Anderon for her helpful comment concerning curve-fitting technique. APPENDIX Summary of Contant Value for the contant of nature that have been ued in thi paper are lited below. Avogadro number molecule mol 1 Molar volume at K and mb.4141 L mol 1 Molecular denity of a ga at K and mb molecule cm 3 Mean molecular weight of dry air (zero CO ) gm mol 1 Mean molecular weight of dry air (360 ppm CO ) gm mol 1 Acceleration of gravity (ea level and 45 latitude) g 0 (45) cm Ma-weighted air column altitude z c z REFERENCES Bate, D. R., 1984: Rayleigh cattering by air. Planet. Space Sci., 3, Bucholtz, A., 1995: Rayleigh-cattering calculation for the terretrial atmophere. Appl. Opt., 34, Cohen, E. R., and B. N. Taylor, 1995: The fundamental phyical contant. Phy. Today, 48, CRC, 1997: Handbook of Chemitry and Phyic. D. R. Lide and H. P. R. Frederike, Ed., CRC Pre, 447 pp. Dutton, E. G., P. Reddy, S. Ryan, and J. J. DeLuii, 1994: Feature and effect of aerool optical depth oberved at Mauna Loa, Hawaii: J. Geophy. Re., 99, Edlén, B., 1953: The diperion of tandard air. J. Opt. Soc. Amer., 43, , 1966: The refractive index of air. Metrologia,, Fröhlich, C., and G. E. Shaw, 1980: New determination of Rayleigh cattering in the terretrial atmophere. Appl. Opt., 19, Hanen, J. E., and L. D. Travi, 1974: Light cattering in planetary atmophere. Space Sci. Rev., 16, Harvey, A. H., J. S. Gallagher, and J. M. H. Levelt Senger, 1998: Revied formulation for the refractive index of water and team a a function of wavelength, temperature and denity. J. Phy. Chem. Ref. Data, 7, Hoyt, D. V., 1977: A redetermination of the Rayleigh optical depth and it application to elected olar radiation problem. J. Appl. Meteor., 16, Lit, R. J., 1968: Smithonian Meteorological Table. Smithonian, 57 pp. Marhall, B. R., and R. C. Smith, 1990: Raman cattering and inwater ocean optical propertie. Appl. Opt., 9, McCartney, E. J., 1976: Optic of the Atmophere. Wiley, 408 pp. Nicolet, M., 1984: On the molecular cattering in the terretrial atmophere: An empirical formula for it calculation in the homophere. Planet. Space Sci., 3, Owen, J. C., 1967: Optical refractive index of air: Dependence on preure, temperature and compoition. Appl. Opt., 6, Peck, E. R., and K. Reeder, 197: Diperion of air. J. Opt. Soc. Amer., 6, Penndorf, R., 1957: Table of the refractive index for tandard air and the Rayleigh cattering coefficient for the pectral region between 0. and 0.0 and their application to atmopheric optic. J. Opt. Soc. Amer., 47, Seinfeld, J. H., and S. N. Pandi, 1998: Atmopheric Chemitry and Phyic, from Air Pollution to Climate Change. Wiley, 136 pp. Stephen, G. L., 1994: Remote Sening of the Lower Atmophere. Oxford Univerity Pre, 53 pp. Teillet, P. M., 1990: Rayleigh optical depth comparion from variou ource. Appl. Opt., 9, van de Hult, H. C., 1957: Light Scattering by Small Particle. Wiley, 470 pp. Young, A. T., 1980: Revied depolarization correction for atmopheric extinction. Appl. Opt., 19, , 1981: On the Rayleigh-cattering optical depth of the atmophere. J. Appl. Meteor., 0,