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A new parameterization of the integral ozone transmission
Pergamon
PII: SOO38-092X(96) 00030-8
Solar Energy Vol. 56, No. 6, pp. 573-581, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003%092X/96 $15.00 f 0.00
A NEW PARAMETERIZATION OF THE INTEGRAL OZONE TRANSMISSION B. E. PSILOGLOU, * Laboratory
**** M. SANTAMOURIS, * C. VAROTSOS * and D. N. ASIMAKOPOULOS ****
of Meteorology, Department of Applied Physics, University of Athens, 33 Ippokratous Street, CR-106 80 Athens, Greece and ** Institute of Meteorology and Physics of the Atmospheric Environment, National Observatory of Athens, P.O. Box 20048, CR-118 10 Athens, Greece (Communicated
by AMOS ZEMEL)
Abstract-A new expression for the integral transmission of atmospheric ozone has been developed. This expression is based on the latest ozone spectral absorption data and on the Neckel and Labs model (1981, 1984), incorporating the most recent corrections on the extraterrestrial solar spectrum, introduced by Wehrli (1985) and VanHoosier et al. (1988). The proposed expression can be used to parameterize the integral ozone transmission and to estimate in conjunction with solar radiation models the direct, diffuse and global solar radiation on the Earth’s surface. Copyright 0 1996 Elsevier Science Ltd.
1. INTRODUCTION
Solar radiation is absorbed by the lower troposphere and by the Earth’s surface and is one of the major driving sources of tropospheric air motion. A reliable treatment of solar radiation in numerical models of atmospheric circulation is required for accurate long-range weather forecasts and for climatological studies. Accordingly, it is necessary to assess the incident solar radiation on the Earth’s surface. The assessment of solar radiation on the Earth’s surface, using physical meteorological models, requires knowledge of the transmission functions of all atmospheric constituents. Various methods for the determination of the principal absorbers, such as water vapor (H,O), atmospheric ozone (0,) and uniformly mixed minor gases (COZ, CO, CH4, N20, 0,) have already been proposed by several researchers (Bird and Hulstrom, 1980, 1981; Hoyt, 1978; Atwater and Ball, 1978; Lacis and Hansen, 1974; Watt, 1978; Santamouris et al., 1983, 1985; Santamouris and Rigopoulos, 1987; Psiloglou et al., 1994, 1995). Ozone contributes to the atmospheric absorption of solar radiation in the ultraviolet (h < 0.4 pm) and visible (0.4 pm
ozone absorption band (Hartley band) the absorption cross-section of the ozone molecule attains a maximum of 1.08 x lo-” cm2 at a wavelength of 2553 A. The ozone absorption cross-section multiplied by Loschmidt’s number (2.686763 x 102’mv3) provides the volume ozone absorption coefficient, at standard pressure and temperature conditions (STP), of 290.17 atm-cm-‘, which corresponds to the decadic ozone volume absorption coefficient of 126.02 atm-cm-’ (ozone volume absorption coefficient x log(e)). This means that a 0.3 atm-cm thick ozone layer at standard pressure attenuates a light beam passing through it, at a zenith angle of 30”, by 4.51 x 1O43or by a factor of about 1044. In this article, the Neckel and Labs (Neckel and Labs; 1981, 1984) extraterrestrial solar spectrum is used to derive the integral transmission function. This is the best recently available expression proposed by several studies on the assessment of the extraterrestrial solar irradiante (Hardrop, 1980; Frohlich, 1980). Further, new experimental data on atmospheric ozone spectral transmittance, have been incorporated into the latest version of the LOWTRAN code (Pierluissi and Maragoudakis, 1986), which allow for the recalculation of the atmospheric ozone integral transmission. The purpose of this article is to present a new accurate expression for the atmospheric ozone integral transmission function, based on improved spectral absorption data, and on the most recent solar radiation spectra1 values. The proposed expression can be easily incorporated
B. E. Psiloglou et al.
574
into solar radiation models in order to accurately estimate the direct, diffuse and global radiation intensity on the Earth’s surface. 2. CALCULATION
with (3) and
PROCEDURE
Ozone absorbs significant quantities of solar radiation at the Hartley (0.22-0.32 pm) and Huggins (0.30-0.345 pm) ultraviolet bands, as well as at the weak Chappuis band (0.44-0.75 pm) in the visible region, and at specific bands (4.75,9.6, 14.1 pm) in the infrared region (Kondratyev, 1969). To estimate the amount of solar radiation absorbed by atmospheric ozone, the following integral transmission function is used:
c = loC’
U =0.7732 x 1O-4 x M, x P, x Z
Eh x z x dh
where Eh is the extraterrestrial solar spectrum irradiance at wavelength h and r is the equivalent spectral infrared, ~~~, or ultraviolet-visible, uv_vIs, transmittance for the atmospheric ozone. The integral transmission function To, is evaluated by numerical integration between 0 and 57490 cm-‘, with a 5 cm-’ spectral interval using the Neckel and Labs (1981,1984) extraterrestrial solar spectrum and the most recent corrections introduced by Wehrli (1985), VanHoosier and Brueckner (1987), and VanHoosier et al. (1988). Previous studies on the calculation of extraterrestrial solar irradiante indicate that the Neckel and Labs (1981) spectrum is the best one recently available (Hardrop, 1980; Frohlich, 1980). Extensive comparisons between the Neckel and Labs spectrum and the Thekaekara reference work (Thekaekara, 1976) given by Bird et al. (1983), show that in the wavelength region 0.6-1.5 pm, the Thekaekara spectrum has an error of about 6-8%, while Mecherikunnel et al. (1983) reports errors of more than lo%, especially for the 0.5-0.8 pm spectral region. The spectral infrared transmittance, rIR, of the atmospheric ozone (0,) is calculated using the expression of the latest version of the LOWTRAN code, LOWTRAN 7 (Pierluissi and Maragoudakis, 1986). The band model is characterized by the use of the exponential transmission function defined as: rIR = exp[-(C
x W)“]
(2)
(5)
P, is the air density in gm-3, M, is the ozone volume mixing ratio in ppmv and 2 is the altitude in km. Equation (2) is used because it is based on the physical interpretation of the various phenomena and on the well established Curtiss-Godson approximation. It is analytically simple and asymptotic to one and zero, respectively, as the argument ranges from zero to infinity (Pierluissi and Maragoudakis, 1986). The rms transmittance difference over the entire spectrum, between FASCOD (Smith et al., 1978) and the band model in eqn (2), along a vertical path from sea level to the top of the U.S. Standard Atmosphere (100 km altitude), is 1.84% according to Pierluissi and Maragoudakis (1986). The parameters of the proposed band model have been determined and/or validated through a combination of synthetic and measured transmittance spectra. The synthetic spectra were generated through a series of line-by-line calculations using FASCODlC (Smith et al., 1978). FASCODlC uses the standard atmospheric profiles (Valley, 1956) and the AFGL line parameter compilation (Rothman, 1981). The measured spectra are consistant with laboratory measurements which are available in part as digitized tables on magnetic tapes, and in part as spectral curves or figures in open literature publications and technical reports. For a given band, the transmittance calculations generally consist of 10 monochromatic curves along homogeneous paths at 10 different pressure levels within the standard atmospheric profiles. These spectral data were then degraded at 5 cm-’ spectral intervals.
(1) where A, x dh
(4)
where pressure (P) is expressed in hPa, temperature (T) in Kelvin, U is the absorber amount of ozone and W is the equivalent absorber amount of ozone, respectively. The subscript “0” denotes standard atmospheric conditions, while a, n, m, and C’ ((atm-cm)-‘) respectively, are parameters defining rIR for the atmospheric ozone over a specific spectral region. For the atmospheric ozone, U is expressed in atm-cm and is calculated using the following expression:
Integral
ozone transmission
Table 1. Band model parameters for the calculation of 20 cm- ’average transmittance through atmospheric ozone, at 5 cm-’ intervals, using eqn (2). The rms errors indicate residual errors with respect to the FASCODIC values
575
. ,
transmisston, ruv_vIs, i.e. kv-vIs
=
expC-
Wx
hl
(6)
where W (atm/cm) is the equivalent absorber amount and kh are the spectral absorption a n m coefficients of ozone. In the ultraviolet bands O-200 0.8559 0.4200 .3909 1.34 (Hartley-Huggins bands), recent spectroscopic 515-1275 0.7593 0.422 1 0.7678 2.25 data (Bass and Paur, 1985; Molina and Molina, 1630-2295 0.7819 0.3739 0.1225 1.13 1986; Yoshino et al., 1988; Cacciani et al., 1989) 2670-2845 0.9175 0.1770 0.9827 0.32 2850-3260 0.7703 0.3921 0.1942 0.25 were smoothed to 5 cm-’ resolution for the region 27,370-54,054 cm-’ (or 0.185-0.365 pm). The basic absorption coefficients are valid at a The parameters a, n and m are listed in reference temperature of 273 K, and a temperature correction is applied, for 27,370 < Table 1 for each spectral region modeled, together with the rms error obtained, using h < 40,800 cm- ’ (or 0.245 < h < 0.365 pm), for eqn (2), relative to the original transmittance other temperatures, employing the Bass algodata. rithm (Bass and Paur, 1985). The estimated Although the spectral parameter C’ ozone absorption coefficients as a function of ((atm-cm)-‘) was obtained at 5 cm-’ intervals temperature are obtained using a weighted average of the concentration and temperature throughout the regions, the number of the corresponding values is too large for listing. Instead, profiles defined in the tabulated reference atmoa continuous plot of the spectral parameter is spheres (Anderson et al., 1986). This results in an average ozone temperature of 213-235.7 K. presented in Fig. 1. To approximate real conditions at our site, in Ozone absorption of solar radiation is strong in the ultraviolet spectrum and moderate in the the Athens area, the mean vertical structure of visible spectrum. For these spectral bands the the atmosphere up to 6 km, from radiosonde data, for the period 1983 to 1990, is considered. Bouguer law is used to describe the ozone Spectral region (cm-‘)
Model parameters
RMS error (6)
O3 -
IR
1 :-
ii
Fig. 1. Spectral
parameter
C’ ((atm-cm)-‘) for the calculation of 20 cm-’ average transmittance intervals with the atmospheric ozone (0,) band model.
at 5 cm-’
516
B. E. Psiloglou
In the visible (Chappuis band, 13,00&24,200 cm-i or 0.413-0.769 pm), the spectroscopic data were also smoothed to 5 cm-’ intervals while a temperature dependence is also assumed between 0.413 and 0.56 pm. The calculated ozone spectral transmittance values for different total equivalent absorber amounts W (atm-cm) are shown in Figs 2-4. For a path with zenith angle other than o”, the equivalent absorber amount W must be multiplied by the optical air mass, M, given by the Kasten and Young (1989) equation: M = [cos 9, + 0.50572
x (96.07995 - f3,)- 1.6364]- 1
(7)
where 8, is the apparent zenith angle (in degrees). This expression for the optical air mass is accurate to more than 0.5%. Near zenith, the resulting error from eqn (7) is less than half that obtained by using Kasten’s earlier expression (Kasten, 1966). Alternatively, instead of the optical air mass (eqn (7)), the relative ozone mass (p) can be used, which is implemented to derive the total ozone value from UV spectrometers measurements, employing the following
et al.
expression (Robinson, 1966): 1 + z/r, ‘= [cos’ 0, + 2(z/re)]“2
where r, is the mean curvature of the earth and z is the height of a thin layer where all the ozone is assumed to be concentrated. Appreciable differences between M and p occur only for zenith angles greater than 80”. However, the use of eqn (8) for solar modeling is not recommended, because of the higher uncertainty introduced by the estimation of the height of the ozone layer compared with the calculation for the optical air mass. In addition, the amount of solar energy incident to a horizontal surface, for a zenith angle greater than 80”, is relatively small. Thus, the differences between M and p values are not significant for most typical applications. Following the above mentioned analysis, arithmetic values of the integral transmission function of the atmospheric ozone for various optical air masses are obtained using eqn (1). Parameterization techniques were then employed to obtain an analytical expression for the broadband transmission of the atmospheric ozone. The proposed expression for the integral
1.0
WAVELENGTH (pm) Fig. 2. Ozone spectral
transmittance
(8)
values for different total equivalent in the 3-18 pm spectral region.
absorber
amounts
W (atm-cm),
Integral
ozone transmission
w
u 0.8
WAVELENGTH (pm) Fig. 3. Ozone
spectral
transmittance
values for different total equivalent in the 0.25-0.8 pm spectral region.
absorber
amounts
W (atm-cm),
0.020
0.5
5 0.015
atm-cm
E 0.010
z
0.21
WAVELENGTH Fig. 4. Ozone
spectral
transmittance
for total equivalent 0.18-0.22 pm spectral
absorber region.
0.2 12
(p-4 amount
W=O.5 atm-cm,
in the
B. E. Psiloglou et al.
578
transmission function is the following: AxMxW T,3=1-[(l+BxM~W)C+D~M~W]
(9) where the constants A = 0.2554, B = 6107.26, C = 0.20395 and D = 0.4707 are defined from a least-squares fit, yielding a residual sum of squares (RSS) for 62 data points of RSS = 7.54 x 10-4. A comparison of the proposed ozone integral transmission function (eqn (9)) with the calculated values using eqns (l), (2) and (6) for values of the W x M product, is presented in Fig. 5. It is worth noting that eqn (9) can be easily used to estimate the integral transmission of the atmospheric ozone for solar radiation modeling. 3. COMPARISON WITH KNOWN EXPRESSIONS AND CONCLUDING RESULTS
The proposed expression (eqn (9)), for the integral transmission of the atmospheric ozone,
has been compared with other well known expressions proposed by Lacis and Hansen (1974), Watt (1978), Hoyt (1978), as well as by Bird and Hulstrom (1980, 1981). The corresponding expressions are listed in Table 2. The calculations with all five models are performed for values of W x M between 0.1 and 15.0, where W is the equivalent ozone amount and M the optical air mass. The results of this comparison are illustrated in Fig. 6. As shown in this figure, the Hoyt expression, using data from Manabe and Strickler (1964) to derive an empirical formula, appears to overestimate the atmospheric ozone transmission, compared with the results of the other models. Manabe and Strickler based their calculations on experimental data from Vigroux (1953). Shaw (1979) found that the mean values of ozone deduced by Chappuis band spectrophotometry differed systematically and were 17.5% lower than those derived from Dobson spectrophotometry (Dobson spectrophotometers are the basic instruments in the world-wide ozone network) when Vigroux’s (1953) absorption coefficients were employed in the data analysis.
1.0 00000 Calculated New Model
Values (eqn 9)
Fig. 5. A comparison of the proposed ozone integral transmission function (eqn (9)) with the calculated values as a function of the W x M product (atm-cm), where W is the equivalent ozone amount (atm-cm) and M the optical air mass.
Integral Table 2. Ozone transmission
579
ozone transmission
equations compared in this work, where WM = W x M, W= the equivalent ozone amount and M = the optical air mass Ozone
Author
transmission
equation
To, = 1 - [(0.02118 x A, + 1.082 x A2 + 0.0658 x A,) x WM] A, = (1 + 0.042 x WM + 0.000323 x WM*] -I
Lacis and Hansen (1974)
A,=(1 + 138.6x WM)-“.805 A,=[1+(103.6x WM)3]-’ To,= 10-‘0.007’+0.01 xWM, To,= 1- [0.045x (WM+ 8.34x 10m4)o.38 - 3.1x 10m3] To,= 1 - [(0.1611x A, + 0.002715x A,) x WM] A, = (1 + 139.48x WM)~“.3035 wM+o.0003x(wM)Z1-’ A,=rl+o.O44x _ 0.2554x iVM ’ To3= ’- [( 1 x 6107.26x WM)0.2039* + 0.4707x WM]
Watt(1978) Hoyt (1978) Bird and Hulstrom (1981, 1982)
Proposedexpression (ew (9))
Q=++=LACIS-HANSEN Q-=-=WATT -HOYT @%%3-0BIRD-HULSTROM -NEW MODEL 0.6 1 0
1
I 2
I
I 4
I
I 6
I I W"x
I
I 10
I
I 12
I
I 14
I 33
M Fig. 6. Integral ozone transmittance estimated using the proposed Lacis and Hansen (1974), Watt (1978), Hoyt (1978), Bird and Hulstrom (1981) and the new model (eqn (9)X as a function of the W x M product (atm-cm), where W is the equivalent ozone amount (atm-cm) and M the optical air mass.
Further, La& and Hansen’s (1974) expression slightly overestimates the atmospheric ozone transmission. This can be explained by the fact that the work was based on their empirical formula for ozone which was in turn based on the same original data sources that Hoyt used. Their data for wavelengths above 0.34 pm were given for 291 K. They used the data at 229 K for shorter wavelengths and reduced the longer wavelength data by 25% to
compensate for the difference in temperature. They developed separate expressions for the ultraviolet and visible bands, respectively. As seen from Fig. 6, the proposed expression (eqn (9)) is close to the Lacis and Hansen model, although they used inaccurate ozone spectral data. Therefore, it is confirmed that the Lacis and Hansen model is more accurate than the data used to construct it. The Watt (1978) as well as the Bird and
580
B. E. Psiloglou
Hulstrom (1980, 1981) expressions appear to underestimate the atmospheric ozone transmission function. This was expected since Watt’s model is based on the ozone data used by Moon (1940). Moon, in turn, used data measured by Wulf (1931) in the Chappuis band (0.413-0.769 pm) and data measured by Lauchli (1929) in the Hartley-Huggings band below 0.365 pm. Watt integrated the spectral data given by Moon (1940) to obtain broadband ozone absorption, which was then modified to agree with broadband total transmittance data from other sources. The Bird and Hulstrom model (1980, 1981) is based on line-by-line transmittance calculations degraded in resolution to 20 cm-’ (McClatchey et al., 1962), also used in a previous version of LOWTRAN. Bird and Hulstrom performed a least-squares fit to the LOWTRAN data with the equations of Lacis and Hansen (1974). In accordance to all models presented above, the Thekaekara (1976) extraterrestrial solar spectrum was used to derive the integral transmission. The Thekaekara solar spectrum, has an error of 6-lo%, for the 0.5-1.5 pm spectral region (Bird et al., 1983; Mecherikunnel et al., 1983), compared with the revised Neckel and Labs spectrum. Following the above mentioned analysis, it is clear that the proposed expression in this article for the integral transmission of the atmospheric ozone provides more accurate results than the previous ones. This expression is based on updated spectral absorption data, and on the Neckel and Labs model (1981, 1984), incorporating the most recent corrections (Wehrli, 1985; VanHoosier and Brueckner, 1987; VanHoosier et al., 1988) of the extraterrestrial solar spectrum. This expression can be applied to parameterize the integral ozone transmission and can be used easily by solar radiation models in order to estimate the beam, diffuse and global solar radiation fluxes. 4. REFERENCES Anderson S. M., Clough S. A., Kneizys F. X., Chetwynd J. H. and Shettle E. P. (1986) AFGL atmospheric constituent profiles (O-120 km), AFGL-TR-86-0110, Air Force Geophysics Lab., Hanscom AFB, MA. Atwater M. A. and Ball J. T. (1978) A numeric solar radiation model based on standard meteorological observations. Solar Energy 21, 163-170. Bass A. M. and Paur R. J. (1985) The ultraviolet crosssections of ozone, I. Measurements. Atmospheric Ozone, Proc. Quadrennial Ozone Symp., Halkidiki, Greece, Zerefos C. and Ghazi A. (Eds). D. Reidel, Hingham, MA, pp. 606-616.
et al.
Bird R. E. and Hulstrom R. L. (1980) Direct isolation models. SERI/TR-335-344, Solar Energy Research Institute, Golden, Colorado. Bird R. E. and Hulstrom R. L. (1981) A simplified clear sky model for direct and diffuse insolation on horizontal surfaces. SERI/TR-642-761, Solar Energy Research Institute, Golden, Colorado. Bird R. E., Hulstrom R. L. and Lewis L. J. (1983) Terrestrial solar spectral data sets. S&r Energy 30, 563-573. Cacciani M., Sarra A., Fiocco G. and Amaruso A. (1989) Absolute determination of the cross-sections of ozone in the wavelength region 339-355 nm at temperatures 220-293 K. J. Geophys. Res. 94( D6), 8485-8490. Frohlich C. (1980) Photometry and solar radiation. Proc. Annual Meeting Schweiz, Gesellschaftfur Astrophysik und Astronomic, Bern. Hardrop J. (1980) The sun among the stars~II1. Energy distributions of 16 northern G-type stars and the solar flux calibration. Astronomy and Astrophysics 91, 221-232. Hoyt D. V. (1978) A model for the calculation of solar global insolation. Solar Energy 21, 7-35. Kasten F. and Young A. T. (1989) Revised optical air mass tables and approximation formula. Applied Optics 28, 4735-4738. Kasten F. (1966) A new table and approximation formula for the relative optical air mass. Arch. Meteorol. Geophys. and Bioklimatol. Ser. B14, 206-223. Kondratyev K. Ya. (1969) Radiation in the Atmosphere. Academic Press, New York, pp. 132-137. Lacis A. L. and Hansen J. E. (1974) A parameterization for the absorption of solar radiation in the Earth’s atmosphere. J. Atmos. Sci. 31, 118-133. Lauchli A. (1929) Zur absorption der Ultravioleten strahlung im ozon. Zs. F. Phys., 92. Manabe S. and Strickler R. F. (1964) Thermal equilibrium of the atmosphere with convective adjustment. J. Atmos. Sci. 21, 361-385. McClatchey R. A., Benedict W. S., Clough S. A., Burch D. E., Calfee R. F., Fox K., Rothman L. S. and Garing J. S. (1962) AFCRL atmospheric line parameter compilation, AFCRL, Research Contract AF19 (604)-2633, Ohio State University. Mecherikunnel A. T., Gatlin J. A. and Richmond J. C. (1983) Data on total and spectral solar irradiance. Applied Optics 22, 1354-1359. Molina L. T. and Molina M. J. (1986) Absolute absorption cross-sections of ozone in the 1855350nm wavelength range. J. Geophys. Res. 91, 14501-14508. Moon P. (1940) Proposed standard solar-radiation curves for engineering use. 1. Franklin Institute 230, 583-617. Neckel H. and Labs D. (1981) Improved data of solar spectral irradiances from 0.33 to 1225 pm. Solar Physics 74, 231-249. Neckel H. and Labs D. (1984) The solar radiation between 3300 and 12,500 A. Solar Physics 90, 205-258. Pierluissi J. H. and Maragoudakis C. E. (1986) Molecular transmission band models for LOWTRAN. AFGLTR-86-0272, Air Force Geophysics Laboratory, Hanscorn Air Force Base, MA. Psiloglou B. E., Santamouris M. and Asimakopoulos D. N. (1994) On the atmospheric water vapor transmission function, for solar radiation models. Solar Energy 53, 445-453. Psiloglou B. E. Santamouris M. and Asimakopoulos D. N. (1995) Predicting the broadband transmittance of the uniformly mixed gases (COr, CO, CH,, N,O, 0,) in the atmosphere, for solar radiation models. Renewable Energy 6, 63-70. Robinson N. (1966) Solar Radiation. Elsevier, New York, p. 52. Rothman L. S. (1981) AFGL atmospheric absorption line
Integral
ozone transmission
parameters compilation: 1980 Version. Applied Optics 20, 791. Santamouris M. J., Rigopoulos R. and Caouris Y. (1983) Estimating the atmospheric ozone transmission for solar radiation models. J. Pure and Applied Geophys. 21, 33-654. Santamouris M. J., Rigopoulos R. and Yiannoulis P. (1985) A note on an improved expression for the atmospheric CO,, N,O, CH, and Or integral transmission function. Atmosphere-Ocean 23, 313-316. Santamouris M. J. and Rigopoulos R. (1987) Estimating the atmospheric water vapor transmission for solar radiation models. Solar and Wind Technology 4, 211-214. Shaw G. E. (1979) Atmospheric ozone: Determination by Chappuis band absorption. J. Appl. Meteor. 18, 1335-1339. Smith H. J. P., Dube D. J., Gardner M. E., Clough S. A., Kneizys F. X. and Rothmans L. S. (1978) FASCODFast Atmospheric Signature Code. AFGL-TR-78-0081, Air Force Geophysical Laboratory, Hanscom A.F.B., MA. Thekaekara, M. P. (1976) Solar radiation measurements: Solar Energy 18, Techniques and instrumentation. 305-325. VanHoosier M. E. and Brueckner G. E. (1987) Solar Ultraviolet Spectral Irradiance Monitor (SUSIM): calibration
581
results from Spacelab 2. Proc. 8th Workshop on Vacuum Ultraviolet Radiometric Calibration of Space Experiments. VanHoosier M. E., Bartoe J. D., Brueckner G. E. and Prinz D. K. (1988) Absolute solar spectral irradiance 120 nm-400 nm (results from the Solar Ultraviolet Spectral Irradiance Monitor-SUSIM-experiment onboard Spacelab 2). Astro. Lett. and Communications 27, 1633168. Valley S. L. (Ed.) (1956) Handbook of Geophysics and Space Environments. McGraw-Hill, New York. Vigroux E. (1953) Contributions a l’etude experimentale de I’absorption de l’ozone. Ann. de Physique 8, 709-762. Watt D. (1978) On the nature and distribution of solar radiation, U.S. Dept of Energy, HCP/T2552-01. Wehrli Ch. (1985) Extra-terrestrial Solar Spectrum. Publication No. 615, Physikalisch Meteorologisches Observatorium and World Radiation Center, CH-7260, DavosDorf, Switzerland. Wulf 0. R. (1931) The determination of ozone by spectrobolometric measurements. Smithsonian Miscellaneous Collection 85, 9. Yoshino K., Freeman D. E., Esmond J. R. and Parkinson W. H. (1988) Absolute absorption cross-section coefficients in the wavelength region 238-335 nm and the temperature dependence. Planet. Space Sci. 36, 395-398.
PII: SOO38-092X(96) 00030-8
Solar Energy Vol. 56, No. 6, pp. 573-581, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003%092X/96 $15.00 f 0.00
A NEW PARAMETERIZATION OF THE INTEGRAL OZONE TRANSMISSION B. E. PSILOGLOU, * Laboratory
**** M. SANTAMOURIS, * C. VAROTSOS * and D. N. ASIMAKOPOULOS ****
of Meteorology, Department of Applied Physics, University of Athens, 33 Ippokratous Street, CR-106 80 Athens, Greece and ** Institute of Meteorology and Physics of the Atmospheric Environment, National Observatory of Athens, P.O. Box 20048, CR-118 10 Athens, Greece (Communicated
by AMOS ZEMEL)
Abstract-A new expression for the integral transmission of atmospheric ozone has been developed. This expression is based on the latest ozone spectral absorption data and on the Neckel and Labs model (1981, 1984), incorporating the most recent corrections on the extraterrestrial solar spectrum, introduced by Wehrli (1985) and VanHoosier et al. (1988). The proposed expression can be used to parameterize the integral ozone transmission and to estimate in conjunction with solar radiation models the direct, diffuse and global solar radiation on the Earth’s surface. Copyright 0 1996 Elsevier Science Ltd.
1. INTRODUCTION
Solar radiation is absorbed by the lower troposphere and by the Earth’s surface and is one of the major driving sources of tropospheric air motion. A reliable treatment of solar radiation in numerical models of atmospheric circulation is required for accurate long-range weather forecasts and for climatological studies. Accordingly, it is necessary to assess the incident solar radiation on the Earth’s surface. The assessment of solar radiation on the Earth’s surface, using physical meteorological models, requires knowledge of the transmission functions of all atmospheric constituents. Various methods for the determination of the principal absorbers, such as water vapor (H,O), atmospheric ozone (0,) and uniformly mixed minor gases (COZ, CO, CH4, N20, 0,) have already been proposed by several researchers (Bird and Hulstrom, 1980, 1981; Hoyt, 1978; Atwater and Ball, 1978; Lacis and Hansen, 1974; Watt, 1978; Santamouris et al., 1983, 1985; Santamouris and Rigopoulos, 1987; Psiloglou et al., 1994, 1995). Ozone contributes to the atmospheric absorption of solar radiation in the ultraviolet (h < 0.4 pm) and visible (0.4 pm
ozone absorption band (Hartley band) the absorption cross-section of the ozone molecule attains a maximum of 1.08 x lo-” cm2 at a wavelength of 2553 A. The ozone absorption cross-section multiplied by Loschmidt’s number (2.686763 x 102’mv3) provides the volume ozone absorption coefficient, at standard pressure and temperature conditions (STP), of 290.17 atm-cm-‘, which corresponds to the decadic ozone volume absorption coefficient of 126.02 atm-cm-’ (ozone volume absorption coefficient x log(e)). This means that a 0.3 atm-cm thick ozone layer at standard pressure attenuates a light beam passing through it, at a zenith angle of 30”, by 4.51 x 1O43or by a factor of about 1044. In this article, the Neckel and Labs (Neckel and Labs; 1981, 1984) extraterrestrial solar spectrum is used to derive the integral transmission function. This is the best recently available expression proposed by several studies on the assessment of the extraterrestrial solar irradiante (Hardrop, 1980; Frohlich, 1980). Further, new experimental data on atmospheric ozone spectral transmittance, have been incorporated into the latest version of the LOWTRAN code (Pierluissi and Maragoudakis, 1986), which allow for the recalculation of the atmospheric ozone integral transmission. The purpose of this article is to present a new accurate expression for the atmospheric ozone integral transmission function, based on improved spectral absorption data, and on the most recent solar radiation spectra1 values. The proposed expression can be easily incorporated
B. E. Psiloglou et al.
574
into solar radiation models in order to accurately estimate the direct, diffuse and global radiation intensity on the Earth’s surface. 2. CALCULATION
with (3) and
PROCEDURE
Ozone absorbs significant quantities of solar radiation at the Hartley (0.22-0.32 pm) and Huggins (0.30-0.345 pm) ultraviolet bands, as well as at the weak Chappuis band (0.44-0.75 pm) in the visible region, and at specific bands (4.75,9.6, 14.1 pm) in the infrared region (Kondratyev, 1969). To estimate the amount of solar radiation absorbed by atmospheric ozone, the following integral transmission function is used:
c = loC’
U =0.7732 x 1O-4 x M, x P, x Z
Eh x z x dh
where Eh is the extraterrestrial solar spectrum irradiance at wavelength h and r is the equivalent spectral infrared, ~~~, or ultraviolet-visible, uv_vIs, transmittance for the atmospheric ozone. The integral transmission function To, is evaluated by numerical integration between 0 and 57490 cm-‘, with a 5 cm-’ spectral interval using the Neckel and Labs (1981,1984) extraterrestrial solar spectrum and the most recent corrections introduced by Wehrli (1985), VanHoosier and Brueckner (1987), and VanHoosier et al. (1988). Previous studies on the calculation of extraterrestrial solar irradiante indicate that the Neckel and Labs (1981) spectrum is the best one recently available (Hardrop, 1980; Frohlich, 1980). Extensive comparisons between the Neckel and Labs spectrum and the Thekaekara reference work (Thekaekara, 1976) given by Bird et al. (1983), show that in the wavelength region 0.6-1.5 pm, the Thekaekara spectrum has an error of about 6-8%, while Mecherikunnel et al. (1983) reports errors of more than lo%, especially for the 0.5-0.8 pm spectral region. The spectral infrared transmittance, rIR, of the atmospheric ozone (0,) is calculated using the expression of the latest version of the LOWTRAN code, LOWTRAN 7 (Pierluissi and Maragoudakis, 1986). The band model is characterized by the use of the exponential transmission function defined as: rIR = exp[-(C
x W)“]
(2)
(5)
P, is the air density in gm-3, M, is the ozone volume mixing ratio in ppmv and 2 is the altitude in km. Equation (2) is used because it is based on the physical interpretation of the various phenomena and on the well established Curtiss-Godson approximation. It is analytically simple and asymptotic to one and zero, respectively, as the argument ranges from zero to infinity (Pierluissi and Maragoudakis, 1986). The rms transmittance difference over the entire spectrum, between FASCOD (Smith et al., 1978) and the band model in eqn (2), along a vertical path from sea level to the top of the U.S. Standard Atmosphere (100 km altitude), is 1.84% according to Pierluissi and Maragoudakis (1986). The parameters of the proposed band model have been determined and/or validated through a combination of synthetic and measured transmittance spectra. The synthetic spectra were generated through a series of line-by-line calculations using FASCODlC (Smith et al., 1978). FASCODlC uses the standard atmospheric profiles (Valley, 1956) and the AFGL line parameter compilation (Rothman, 1981). The measured spectra are consistant with laboratory measurements which are available in part as digitized tables on magnetic tapes, and in part as spectral curves or figures in open literature publications and technical reports. For a given band, the transmittance calculations generally consist of 10 monochromatic curves along homogeneous paths at 10 different pressure levels within the standard atmospheric profiles. These spectral data were then degraded at 5 cm-’ spectral intervals.
(1) where A, x dh
(4)
where pressure (P) is expressed in hPa, temperature (T) in Kelvin, U is the absorber amount of ozone and W is the equivalent absorber amount of ozone, respectively. The subscript “0” denotes standard atmospheric conditions, while a, n, m, and C’ ((atm-cm)-‘) respectively, are parameters defining rIR for the atmospheric ozone over a specific spectral region. For the atmospheric ozone, U is expressed in atm-cm and is calculated using the following expression:
Integral
ozone transmission
Table 1. Band model parameters for the calculation of 20 cm- ’average transmittance through atmospheric ozone, at 5 cm-’ intervals, using eqn (2). The rms errors indicate residual errors with respect to the FASCODIC values
575
. ,
transmisston, ruv_vIs, i.e. kv-vIs
=
expC-
Wx
hl
(6)
where W (atm/cm) is the equivalent absorber amount and kh are the spectral absorption a n m coefficients of ozone. In the ultraviolet bands O-200 0.8559 0.4200 .3909 1.34 (Hartley-Huggins bands), recent spectroscopic 515-1275 0.7593 0.422 1 0.7678 2.25 data (Bass and Paur, 1985; Molina and Molina, 1630-2295 0.7819 0.3739 0.1225 1.13 1986; Yoshino et al., 1988; Cacciani et al., 1989) 2670-2845 0.9175 0.1770 0.9827 0.32 2850-3260 0.7703 0.3921 0.1942 0.25 were smoothed to 5 cm-’ resolution for the region 27,370-54,054 cm-’ (or 0.185-0.365 pm). The basic absorption coefficients are valid at a The parameters a, n and m are listed in reference temperature of 273 K, and a temperature correction is applied, for 27,370 < Table 1 for each spectral region modeled, together with the rms error obtained, using h < 40,800 cm- ’ (or 0.245 < h < 0.365 pm), for eqn (2), relative to the original transmittance other temperatures, employing the Bass algodata. rithm (Bass and Paur, 1985). The estimated Although the spectral parameter C’ ozone absorption coefficients as a function of ((atm-cm)-‘) was obtained at 5 cm-’ intervals temperature are obtained using a weighted average of the concentration and temperature throughout the regions, the number of the corresponding values is too large for listing. Instead, profiles defined in the tabulated reference atmoa continuous plot of the spectral parameter is spheres (Anderson et al., 1986). This results in an average ozone temperature of 213-235.7 K. presented in Fig. 1. To approximate real conditions at our site, in Ozone absorption of solar radiation is strong in the ultraviolet spectrum and moderate in the the Athens area, the mean vertical structure of visible spectrum. For these spectral bands the the atmosphere up to 6 km, from radiosonde data, for the period 1983 to 1990, is considered. Bouguer law is used to describe the ozone Spectral region (cm-‘)
Model parameters
RMS error (6)
O3 -
IR
1 :-
ii
Fig. 1. Spectral
parameter
C’ ((atm-cm)-‘) for the calculation of 20 cm-’ average transmittance intervals with the atmospheric ozone (0,) band model.
at 5 cm-’
516
B. E. Psiloglou
In the visible (Chappuis band, 13,00&24,200 cm-i or 0.413-0.769 pm), the spectroscopic data were also smoothed to 5 cm-’ intervals while a temperature dependence is also assumed between 0.413 and 0.56 pm. The calculated ozone spectral transmittance values for different total equivalent absorber amounts W (atm-cm) are shown in Figs 2-4. For a path with zenith angle other than o”, the equivalent absorber amount W must be multiplied by the optical air mass, M, given by the Kasten and Young (1989) equation: M = [cos 9, + 0.50572
x (96.07995 - f3,)- 1.6364]- 1
(7)
where 8, is the apparent zenith angle (in degrees). This expression for the optical air mass is accurate to more than 0.5%. Near zenith, the resulting error from eqn (7) is less than half that obtained by using Kasten’s earlier expression (Kasten, 1966). Alternatively, instead of the optical air mass (eqn (7)), the relative ozone mass (p) can be used, which is implemented to derive the total ozone value from UV spectrometers measurements, employing the following
et al.
expression (Robinson, 1966): 1 + z/r, ‘= [cos’ 0, + 2(z/re)]“2
where r, is the mean curvature of the earth and z is the height of a thin layer where all the ozone is assumed to be concentrated. Appreciable differences between M and p occur only for zenith angles greater than 80”. However, the use of eqn (8) for solar modeling is not recommended, because of the higher uncertainty introduced by the estimation of the height of the ozone layer compared with the calculation for the optical air mass. In addition, the amount of solar energy incident to a horizontal surface, for a zenith angle greater than 80”, is relatively small. Thus, the differences between M and p values are not significant for most typical applications. Following the above mentioned analysis, arithmetic values of the integral transmission function of the atmospheric ozone for various optical air masses are obtained using eqn (1). Parameterization techniques were then employed to obtain an analytical expression for the broadband transmission of the atmospheric ozone. The proposed expression for the integral
1.0
WAVELENGTH (pm) Fig. 2. Ozone spectral
transmittance
(8)
values for different total equivalent in the 3-18 pm spectral region.
absorber
amounts
W (atm-cm),
Integral
ozone transmission
w
u 0.8
WAVELENGTH (pm) Fig. 3. Ozone
spectral
transmittance
values for different total equivalent in the 0.25-0.8 pm spectral region.
absorber
amounts
W (atm-cm),
0.020
0.5
5 0.015
atm-cm
E 0.010
z
0.21
WAVELENGTH Fig. 4. Ozone
spectral
transmittance
for total equivalent 0.18-0.22 pm spectral
absorber region.
0.2 12
(p-4 amount
W=O.5 atm-cm,
in the
B. E. Psiloglou et al.
578
transmission function is the following: AxMxW T,3=1-[(l+BxM~W)C+D~M~W]
(9) where the constants A = 0.2554, B = 6107.26, C = 0.20395 and D = 0.4707 are defined from a least-squares fit, yielding a residual sum of squares (RSS) for 62 data points of RSS = 7.54 x 10-4. A comparison of the proposed ozone integral transmission function (eqn (9)) with the calculated values using eqns (l), (2) and (6) for values of the W x M product, is presented in Fig. 5. It is worth noting that eqn (9) can be easily used to estimate the integral transmission of the atmospheric ozone for solar radiation modeling. 3. COMPARISON WITH KNOWN EXPRESSIONS AND CONCLUDING RESULTS
The proposed expression (eqn (9)), for the integral transmission of the atmospheric ozone,
has been compared with other well known expressions proposed by Lacis and Hansen (1974), Watt (1978), Hoyt (1978), as well as by Bird and Hulstrom (1980, 1981). The corresponding expressions are listed in Table 2. The calculations with all five models are performed for values of W x M between 0.1 and 15.0, where W is the equivalent ozone amount and M the optical air mass. The results of this comparison are illustrated in Fig. 6. As shown in this figure, the Hoyt expression, using data from Manabe and Strickler (1964) to derive an empirical formula, appears to overestimate the atmospheric ozone transmission, compared with the results of the other models. Manabe and Strickler based their calculations on experimental data from Vigroux (1953). Shaw (1979) found that the mean values of ozone deduced by Chappuis band spectrophotometry differed systematically and were 17.5% lower than those derived from Dobson spectrophotometry (Dobson spectrophotometers are the basic instruments in the world-wide ozone network) when Vigroux’s (1953) absorption coefficients were employed in the data analysis.
1.0 00000 Calculated New Model
Values (eqn 9)
Fig. 5. A comparison of the proposed ozone integral transmission function (eqn (9)) with the calculated values as a function of the W x M product (atm-cm), where W is the equivalent ozone amount (atm-cm) and M the optical air mass.
Integral Table 2. Ozone transmission
579
ozone transmission
equations compared in this work, where WM = W x M, W= the equivalent ozone amount and M = the optical air mass Ozone
Author
transmission
equation
To, = 1 - [(0.02118 x A, + 1.082 x A2 + 0.0658 x A,) x WM] A, = (1 + 0.042 x WM + 0.000323 x WM*] -I
Lacis and Hansen (1974)
A,=(1 + 138.6x WM)-“.805 A,=[1+(103.6x WM)3]-’ To,= 10-‘0.007’+0.01 xWM, To,= 1- [0.045x (WM+ 8.34x 10m4)o.38 - 3.1x 10m3] To,= 1 - [(0.1611x A, + 0.002715x A,) x WM] A, = (1 + 139.48x WM)~“.3035 wM+o.0003x(wM)Z1-’ A,=rl+o.O44x _ 0.2554x iVM ’ To3= ’- [( 1 x 6107.26x WM)0.2039* + 0.4707x WM]
Watt(1978) Hoyt (1978) Bird and Hulstrom (1981, 1982)
Proposedexpression (ew (9))
Q=++=LACIS-HANSEN Q-=-=WATT -HOYT @%%3-0BIRD-HULSTROM -NEW MODEL 0.6 1 0
1
I 2
I
I 4
I
I 6
I I W"x
I
I 10
I
I 12
I
I 14
I 33
M Fig. 6. Integral ozone transmittance estimated using the proposed Lacis and Hansen (1974), Watt (1978), Hoyt (1978), Bird and Hulstrom (1981) and the new model (eqn (9)X as a function of the W x M product (atm-cm), where W is the equivalent ozone amount (atm-cm) and M the optical air mass.
Further, La& and Hansen’s (1974) expression slightly overestimates the atmospheric ozone transmission. This can be explained by the fact that the work was based on their empirical formula for ozone which was in turn based on the same original data sources that Hoyt used. Their data for wavelengths above 0.34 pm were given for 291 K. They used the data at 229 K for shorter wavelengths and reduced the longer wavelength data by 25% to
compensate for the difference in temperature. They developed separate expressions for the ultraviolet and visible bands, respectively. As seen from Fig. 6, the proposed expression (eqn (9)) is close to the Lacis and Hansen model, although they used inaccurate ozone spectral data. Therefore, it is confirmed that the Lacis and Hansen model is more accurate than the data used to construct it. The Watt (1978) as well as the Bird and
580
B. E. Psiloglou
Hulstrom (1980, 1981) expressions appear to underestimate the atmospheric ozone transmission function. This was expected since Watt’s model is based on the ozone data used by Moon (1940). Moon, in turn, used data measured by Wulf (1931) in the Chappuis band (0.413-0.769 pm) and data measured by Lauchli (1929) in the Hartley-Huggings band below 0.365 pm. Watt integrated the spectral data given by Moon (1940) to obtain broadband ozone absorption, which was then modified to agree with broadband total transmittance data from other sources. The Bird and Hulstrom model (1980, 1981) is based on line-by-line transmittance calculations degraded in resolution to 20 cm-’ (McClatchey et al., 1962), also used in a previous version of LOWTRAN. Bird and Hulstrom performed a least-squares fit to the LOWTRAN data with the equations of Lacis and Hansen (1974). In accordance to all models presented above, the Thekaekara (1976) extraterrestrial solar spectrum was used to derive the integral transmission. The Thekaekara solar spectrum, has an error of 6-lo%, for the 0.5-1.5 pm spectral region (Bird et al., 1983; Mecherikunnel et al., 1983), compared with the revised Neckel and Labs spectrum. Following the above mentioned analysis, it is clear that the proposed expression in this article for the integral transmission of the atmospheric ozone provides more accurate results than the previous ones. This expression is based on updated spectral absorption data, and on the Neckel and Labs model (1981, 1984), incorporating the most recent corrections (Wehrli, 1985; VanHoosier and Brueckner, 1987; VanHoosier et al., 1988) of the extraterrestrial solar spectrum. This expression can be applied to parameterize the integral ozone transmission and can be used easily by solar radiation models in order to estimate the beam, diffuse and global solar radiation fluxes. 4. REFERENCES Anderson S. M., Clough S. A., Kneizys F. X., Chetwynd J. H. and Shettle E. P. (1986) AFGL atmospheric constituent profiles (O-120 km), AFGL-TR-86-0110, Air Force Geophysics Lab., Hanscom AFB, MA. Atwater M. A. and Ball J. T. (1978) A numeric solar radiation model based on standard meteorological observations. Solar Energy 21, 163-170. Bass A. M. and Paur R. J. (1985) The ultraviolet crosssections of ozone, I. Measurements. Atmospheric Ozone, Proc. Quadrennial Ozone Symp., Halkidiki, Greece, Zerefos C. and Ghazi A. (Eds). D. Reidel, Hingham, MA, pp. 606-616.
et al.
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parameters compilation: 1980 Version. Applied Optics 20, 791. Santamouris M. J., Rigopoulos R. and Caouris Y. (1983) Estimating the atmospheric ozone transmission for solar radiation models. J. Pure and Applied Geophys. 21, 33-654. Santamouris M. J., Rigopoulos R. and Yiannoulis P. (1985) A note on an improved expression for the atmospheric CO,, N,O, CH, and Or integral transmission function. Atmosphere-Ocean 23, 313-316. Santamouris M. J. and Rigopoulos R. (1987) Estimating the atmospheric water vapor transmission for solar radiation models. Solar and Wind Technology 4, 211-214. Shaw G. E. (1979) Atmospheric ozone: Determination by Chappuis band absorption. J. Appl. Meteor. 18, 1335-1339. Smith H. J. P., Dube D. J., Gardner M. E., Clough S. A., Kneizys F. X. and Rothmans L. S. (1978) FASCODFast Atmospheric Signature Code. AFGL-TR-78-0081, Air Force Geophysical Laboratory, Hanscom A.F.B., MA. Thekaekara, M. P. (1976) Solar radiation measurements: Solar Energy 18, Techniques and instrumentation. 305-325. VanHoosier M. E. and Brueckner G. E. (1987) Solar Ultraviolet Spectral Irradiance Monitor (SUSIM): calibration
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