6.7.4 Atmospheres with clouds and aerosols
The atmosphere can be divided into layers whose individual optical depth is evaluated, according to its properties, from t Tcs Tca Taers Taera Tma + tr, (6.150)
where tcs is the cloud-scattering optical depth, Tca is the cloud-absorption optical depth, raers is the aerosol-scattering optical depth, Taera is the aerosol-absorption optical depth, Tma is that for molecular absorption, and tr is that for Rayleigh or molecular scattering. The single scattering albedo for each layer is
with gc and gaer being the cloud and aerosol asymmetry factors, respectively, with the Rayleigh asymmetry factor gR = 0.
To proceed, we need to divide the atmosphere into clear- and cloudy-sky components. The cloudy-sky component is subdivided into non-overlapping components covered by low-level, middle-level and high-level clouds. There are methods for taking into account cloud overlap (Chapter 8). The delta-Eddington method computes the fraction of the incoming solar flux that is reflected by the planet to space, Rp, the fraction absorbed by the atmosphere, apa, and that absorbed by the Earth's surface, apg, where the planetary absorptivity ap = apa + apg, and so Rp + apa + apg = 1. These fractions define the shortwave radiation budget of the planet.
The planetary absorptivity has a clear-sky component as and three cloudy-sky components aci and is expressed as ap = (1 - Ac)as + Aciaci, (6.156)
i where the cloud-cover fractions Aci correspond to each of the individual cloud-cover components.
Total and Net Fluxes Down Photolysis Enhancement Factor
Flg. 6.17. Variation of the Eddington radiation moments J\ and H\, and fluxes; diffuse up Fi, diffuse down F^, direct down FjA, net down F^x, total down FTx, and photolysis enhancement factor fx. The atmosphere has total extinction optical depth r\ = 10, single scattering albedo = 0.99, asymmetry factor g = 0.8, incoming solar flux Sq\ = 1, solar zenith angle ^q = 0.6, surface albedo Rs\ = 0, and no thermal emission.
Here, we present sample computations using the delta-Eddington method and solve numerically, via the Thomas algorithm, the radiation diffusion equation as a second-order ordinary differential equation, as described above, using 40 optical depth levels. We consider an atmosphere with total monochromatic extinction optical depth tx = 10, single scattering albedo = 0.99 and asymmetry factor gx = 0.8 at all levels, and no thermal emission. We set the incoming solar flux Sqx = 1 and the solar zenith angle by /i,q =0.6. The resulting Eddington radiation moments Jx(tx) and Hx(rx) are shown in Fig. 6.17. The various radiation fluxes are also shown together with the photolysis enhancement factor. The fraction of the radiation reflected to space, i.e. the planetary albedo at the top of the atmosphere (tx = 0) is 0.538, the fraction absorbed by the surface is 0.301 and the fraction absorbed by the atmosphere is 0.161 and sum up to unity.
For more details regarding the exponential-sumfit, k-distribution and correlated-k methods for solar radiation transfer see, for example, Kato et al., and for an application see Irwin et al.
For ISCCP cloud climatologies see Rossow et al. and Rossow and Schiffer.
For more details on scattering of light by particles see the text by van de Hulst.
For tables of refractive index for standard air and Rayleigh scattering coefficients see the early work of Penndorf.
For wavelength variation of the asymmetry factor for water clouds see the report by Stephens.
6.8.2 References and further reading
Allen, C. W. (1976). Astrophysical quantities. Athlone Press, London.
Angstrom, A. (1929). On the atmospheric transmission of sun radiation and on dust in the air. Geograf. Ann. Deut., 11, 156-166.
Burch, D. E. and Williams, D. (1962). Total absorptance of carbon monoxide and methane in the infrared. Appl. Opt., 1, 587-594.
Chandrasekhar, S. (1960). Radiative transfer. Dover Publications Inc., New York.
Debye, P. (1909). Der Lichtdruk auf Kugeln von beliebigem Material. Ann. Physik. (Leipzig), 30, 57-136.
Fotiadi, A., Drakakis, E., Hatzianastassiou, N., Matsoukas, C., Pavlakis, K. G., Hatzidimitriou, D., Gerasopoulos, E., Mihalopoulos, N., and Vardavas, I. M., (2006). Aerosol physical and optical properties in the eastern Mediterranean basin, Crete, from Aerosol Robotic Network data. Atmos. Chem. Phys., 6, 53995412.
France, W. L. and Williams, D. (1966). Total absorptance of ammonia in the infrared. J. Opt. Soc. Amer., 56, 70-74.
Hatzianastassiou, N., Katsoulis, B. and Vardavas, I. M. (2004). Global distribution of aerosol direct radiative forcing in the ultraviolet and visible arising under clear skies. Tellus, 56B, 51-71.
Henderson-Sellers, A. and Wilson, M. F. (1983). Surface albedo data for climate modelling. Rev. Geophys. Space Phys., 21, 1743-1778.
Irvine, W. M. (1968). Multiple scattering by large particles II. Optically thick layers, Astrophys. J., 152, 823-834.
Irwin, P.G., Calcutt, S. B., Taylor, F. W. and Weir, A. L. (1996). Calculated k distribution coefficients for hydrogen- and self-broadened methane in the range 2000-9500 cm-1 from exponential sum fitting to band-modelled spectra. J. Geo-phys. Res., 101, 26137-26154.
Joseph, J. H., Wiscombe, W. J. and Weinman, J. A. (1976). The delta-Eddington approximation for radiative flux transfer. J. Atmos. Sci., 33, 2452-2459.
JPL 2006 : Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies Evaluation Number 15. NASA Panel for Data Evaluation: S. P. Sander, R. R. Friedl, A. R. Ravishankara, D. M. Golden, C. E. Kolb, M. J. Kurylo, J. Molina, G. K. Moortgat, H. Keller-Rudek, B. J.Finlayson-Pitts, P.H. Wine, R. E. Huie, and V. L. Orkin. Jet Propulsion Laboratory Publication 06-2, California Institute of Technology, Pasadena.
Kato, S., Ackerman, T. P., Mather, J. H., Clothiaux, E. E. (1999). The kdistrib-ution method and correlated-k approximation for a shortwave radiative transfer model. J. Quant. Spectrosc. Radiat. Trans., 62, 109-121.
Koepke, P., Hess, M., Schult, I. and Shettle, E. P. (1997). Global Aerosol Data Set. Report No 243, Max-Planck Institut für Meteorologie, Hamburg.
Kontratyev, K. Ya. (1973). Radiation characteristics of the atmosphere and the Earth's surface. Amerind. Pub. Co., New Delhi.
Kuhn, M. H. (1989). The role of land ice and snow in climate. In Understanding climate change, eds. A. Berger, R.E. Dickinson, and J.W. Kidson, Geophys. Monogr., 52, IUGG 7, AGU, Washington, DC.
Lavvas, P., Coustenis, A. and Vardavas, I. M. (2007). Coupling photochemistry with haze formation in Titan's atmosphere. Part I. Model description. Planet. Space Sci., in press.
Mie, G. (1908). Contributions to the optics of turpid media, especially colloidal metal solutions. Ann. Physik. (Leipzig), 25, 377-445.
Penndorf, R. (1957). Tables of refractive index for standard air and the Rayleigh scattering coefficient for the spectral region between 0.2 and 20.0 ¡m and their application to atmospheric optics. J. Opt. Soc. Am., 47, 176-182.
Rossow, W. B., Walker, A. W., Beuschel, D. E. and Roiter, M. D. (1996). International Satellite Cloud Climatology Project (ISCCP). Documentation of new cloud datasets, 115 pp., World Meteorological Organisation, Geneva.
Rossow, W. B. and Schiffer, R. A. (1999). Advances in understanding clouds from ISCCP. Bull. Am. Meteorol. Soc., 80, 2261-2287.
Sagan, C. and Pollack, J. B. (1967). Anisotropic non-conservative scattering and the clouds of Venus. J. Geophys. Res., 72, 469-477.
Sellers, W. D. (1965). Physical climatology. University of Chicago Press, Chicago.
Shettle, E. P. and Weinmann, J. A. (1970). The transfer of solar irradiance through inhomogeneous turbid atmospheres evaluated by Eddington's approximation. J. Atmos. Sci., 27, 1048-1055.
Stull, V. R., Wyatt, P. and Plass, G. N. (1964). The infrared transmittance of carbon dioxide. Appl. Opt., 3, 241-254.
Stephens, G. L. (1979). Optical properties of eight water cloud types. CSIRO Div. of Atmos. Phys. Tech. Pap. 36, Melbourne.
Valley, S. L. (ed.) (1965). Handbook of geophysics and space environments. Air Force Cambridge Research Laboratories. McGraw-Hill, New York.
van de Hulst, H. C. (1981). Light scattering by small particles. Dover, New York.
Vardavas, I. M. and Carver, J. H. (1984). Solar and terrestrial parameterizations for radiative-convective models. Planet. Space Sc., 32, 1307-1325.
Vardavas, I. M. (1989). A Fibonacci search technique for model parameter selection. Ecol. Model., 48, 65-81.
Williams, P. W. (1972). Numerical computation. Nelson, London.
Wyatt, P. J., Stull, V. R. and Plass, G. N. (1964). The infrared transmittance of water vapour. Appl. Opt., 3, 229-241.
Solar ultraviolet radiation plays a key role in the determination of a planet's climate through photolysis reactions involving the molecules that constitute their atmospheres. In the Earth's atmosphere, radiation below about 300 nm plays a key role as important molecules such as H2O, CO2, O2 and O3, are easily photolyzed in this spectral region. Most of the photolysis occurs in the upper atmosphere, and via diffusion turbulence and advection the photolysis products are transferred to the lower atmosphere where they take part in the chemistry of the atmospheric constituents. The atmospheric composition in turn controls both the solar and terrestrial radiation fields and the thermal structure. There is thus a strong coupling between atmospheric photochemistry, composition and climate.
The Earth's surface also plays a crucial role in the control of species concentrations via emission (both anthropogenic and natural) and deposition processes (both dry and wet removal), representing species sources and sinks. Loss to space via diffusion and thermal (Jeans) escape is important for the lighter species, such as H and H2. Inflow from space of molecules, such as H2O and CO2, via meteorites can also be important to the long-term evolution of planetary atmospheres. Thus whatever species is emitted into the atmosphere of a planet, there must be ultimately a loss mechanism to the surface or space, otherwise there will be an accumulation of the emitted species or its photochemical products.
The concentration of molecular species at some level within the atmosphere is controlled by a number of physico-chemical processes that include
1. Emission from the Earth's surface
2. Ejection and infall into the atmosphere
3. Dry deposition at the Earth's surface
4. Wet deposition or rainout within the troposphere
5. Transport by turbulence, diffusion, and advection
6. Collisionally driven chemical production and destruction
7. Radiation-driven production and destruction.
The number density, n, of species i, is determined at each atmospheric level by the continuity equation that describes the rate of change of the number density due to production and loss mechanisms arising from photochemical reactions, emission, surface deposition and transport. The general form of the continuity equation for a molecular species i is
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