Skip to main content
SpringerLink
Log in

Light scattering in planetary atmospheres

  • Published:
Space Science Reviews Aims and scope Submit manuscript

Abstract

This paper reviews scattering theory required for analysis of light reflected by planetary atmospheres. Section 1 defines the radiative quantities which are observed. Section 2 demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers. Section 3 describes several methods to compute the effects of multiple scattering on the reflected light.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abhyankar, K. D. and Fymat, A. L.: 1971, Astrophys. J. Suppl. 23, 35.

    Google Scholar 

  • Allen, C. W.: 1963, Astrophysical Quantities, Athlone Press, London, 291 pp.

    Google Scholar 

  • Ambartsumian, V. A.: 1942, Astr. Zh. (Russ.) 19, 30.

    Google Scholar 

  • Ambartsumian, V. A.: 1958, Theoretical Astrophysics, Pergamon Press, New York, 645 pp.

    Google Scholar 

  • Appleby, J. F. and van Blerkom, D. J.: 1974, submitted to Icarus.

  • Bellman, R., Kagiwada, H., Kalaba, R., and Ueno, S.: 1967, Icarus 7, 365.

    Google Scholar 

  • Bellman, R. E., Kagiwada, H. H., Kalaba, R. E., and Ueno, S.: 1969, Icarus 11, 417.

    Google Scholar 

  • Bellman, R. E., Kalaba, R. E., and Prestrud, M. C.: 1963, Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness, American Elsevier, New York, 346 pp.

    Google Scholar 

  • Bellman, R., Kalaba, R., and Ueno, S.: 1963a, Icarus 1, 297.

    Google Scholar 

  • Bellman, R., Kalaba, R., and Ueno, S.: 1963b, J. Math. Anal. Appl. 7, 310.

    Google Scholar 

  • Bellman, R., Kalaba, R., and Wing, G. M.: 1960, J. Math. Phys. 1, 280.

    Google Scholar 

  • Belton, M. J. S., Hunten, D. M., and Goody, R. M.: 1968, in J. C. Brandt and M. B. McElroy (eds.), The Atmospheres of Venus and Mars, Gordon and Breach, New York, 288 pp.

    Google Scholar 

  • Bond, G. R. and Siewert, C. E.: 1971, Astrophys. J. 164, 97.

    Google Scholar 

  • Born, M. and Wolf, E.: 1959, Principles of Optics, Pergamon Press, New York, 803 pp.

    Google Scholar 

  • Bryant, H. C. and Cox, A. J.: 1966, J. Opt. Soc. Amer. 56, 1529.

    Google Scholar 

  • Bryant, H. C. and Jarmie, N.: 1974, Sci. Amer. 231, 60.

    Google Scholar 

  • Busbridge, I. W.: 1960, The Mathematics of Radiative Transfer, Cambridge Univ. Press, Cambridge, 143 pp.

    Google Scholar 

  • Busbridge, I. W.: 1967, Astrophys. J. 149, 195.

    Google Scholar 

  • Cabannes, J.: 1929, La Diffusion Moléculaire de la Lumière, Les Presses Universitaires de France, Paris, 326 pp.

    Google Scholar 

  • Carlstedt, J. L. and Mullikin, T. W.: 1966, Astrophys. J. Suppl. 12, 449.

    Google Scholar 

  • Case, K. M.: 1960, Ann. Phys. 9, 1.

    Google Scholar 

  • Case, K. M.: 1967, in E. Inönü and P. F. Zweifel (eds.), Developments in Transport Theory, Academic Press, New York, 381 pp.

    Google Scholar 

  • Case, K. M. and Zweifel, P. F.: 1967, Linear Transport Theory, Addison-Wesley, Reading, Mass., 342 pp.

    Google Scholar 

  • Cashwell, E. D. and Everett, C. J.: 1959, Monte Carlo Method, Pergamon Press, New York, 153 pp.

    Google Scholar 

  • Chandrasekhar, S.: 1944, Astrophys. J. 100, 76.

    Google Scholar 

  • Chandrasekhar, S.: 1950, Radiative Transfer, Oxford Univ. Press, 393 pp.

  • Coffeen, D. L. and Gehrels, T.: 1969, Astron. J. 74, 433.

    Google Scholar 

  • Coffeen, D. L. and Hansen, J. E.: 1974, in T. Gehrels (ed.), Planets, Stars and Nebulae Studied With Photopolarimetry, Univ. Arizona Press, Tucson, p. 518.

    Google Scholar 

  • Collins, D. G. and Wells, M. B.: 1965, REP. RRA-T54 (Radiation Research Associates, Inc., Ft. Worth, Texas), Vols. 1 and 2.

  • Collins, D. G., Blattner, W. G., Wells, M. B., and Horak, H. G.: 1972, Appl. Opt. 11, 2684.

    Google Scholar 

  • Coulson, K. L., Dave, J. V., and Sekera, Z.: 1960, Tables Related to Radiation Emerging From a Planetary Atmosphere with Rayleigh Scattering, Univ. of Calif. Press, Berkeley, 584 pp.

    Google Scholar 

  • Danielson, R. E., Moore, D. R., and van de Hulst, H. C.: 1969, J. Atmospheric Sci. 26, 1078.

    Google Scholar 

  • Dave, J. V.: 1964, Astrophys. J. 140, 1292.

    Google Scholar 

  • Dave, J. V.: 1969, Appl. Opt. 8, 155.

    Google Scholar 

  • Dave, J. V.: 1970, Appl. Opt. 9, 2673.

    Google Scholar 

  • Dave, J. V. and Armstrong, B. H.: 1974, submitted to J. Atmospheric Sci.

  • Dave, J. V. and Canosa, J.: 1974, J. Atmospheric Sci. 31, 1089.

    Google Scholar 

  • Dave, J. V. and Gazdag, J.: 1970, Appl. Opt. 9, 1457.

    Google Scholar 

  • Davison, B.: 1958, Neutron Transport Theory, Oxford Univ. Press, London, 450 pp.

    Google Scholar 

  • Deirmendjian, D.: 1964, Appl. Opt. 3, 187.

    Google Scholar 

  • Deirmendjian, D.: 1969, Electromagnetic Scattering on Spherical Polydispersions, American Elsevier, New York, 290 pp.

    Google Scholar 

  • Deuze, J. L., Devaux, C., and Herman, M.: 1973, Nouv. Rev. Optique 4, 307.

    Google Scholar 

  • de Vaucouleurs, G.: 1951, Ann. Phys. 6, 211.

    Google Scholar 

  • Diem, M.: 1948, Meteor. Rund. 1, 261.

    Google Scholar 

  • Dollfus, A. and Coffeen, D. L.: 1970, Astron. Astrophys. 8, 251.

    Google Scholar 

  • Feinstein, D. L., Butler, F. E., Piech, K. R., and Leonard, A.: 1972, Phys. Fluids 15, 1641.

    Google Scholar 

  • Friend, J. P.: 1966, Tellus 18, 465.

    Google Scholar 

  • Grant, I. P. and Hunt, G. E.: 1969, Proc. Roy. Soc. London A 313, 183.

    Google Scholar 

  • Hammersley, J. M. and Handscomb, D. C.: 1964, Monte Carlo Methods, John Wiley, New York, 178 pp.

    Google Scholar 

  • Hamming, R. W.: 1973, Numerical Methods For Scientists and Engineers, McGraw-Hill, New York, 721 pp.

    Google Scholar 

  • Hansen, J. E.: 1969, J. Atmospheric Sci. 26, 478.

    Google Scholar 

  • Hansen, J. E.: 1971a, J. Atmospheric Sci. 28, 120.

    Google Scholar 

  • Hansen, J. E.: 1971b, J. Atmospheric Sci. 28, 1400.

    Google Scholar 

  • Hansen, J. E.: 1971c, J. Atmospheric Sci. 28, 1515.

    Google Scholar 

  • Hansen, J. E. and Hovenier, J. W.: 1971, J. Quant. Spectr. Radiat. Transfer 11, 809.

    Google Scholar 

  • Hansen, J. E. and Hovenier, J. W.: 1974, J. Atmospheric Sci. 31, 1137.

    Google Scholar 

  • Hansen, J. E. and Pollack, J. B.: 1970, J. Atmospheric Sci. 27, 265.

    Google Scholar 

  • Herman, B. M. and Browning, S. R.: 1965, J. Atmospheric Sci. 22, 559.

    Google Scholar 

  • Horak, H. G.: 1950, Astrophys. J. 112, 445.

    Google Scholar 

  • Horak, H. G. and Chandrasekhar, S.: 1961, Astrophys. J. 134, 45.

    Google Scholar 

  • House, L. L. and Avery, L. W.: 1969, J. Quant. Spectr. Radiat. Transfer 9, 1579.

    Google Scholar 

  • Hovenier, J. W.: 1969, J. Atmospheric Sci. 26, 488.

    Google Scholar 

  • Hovenier, J. W.: 1971, Astron. Astrophys. 13, 7.

    Google Scholar 

  • Irvine, W. M.: 1963, Bull. Astron. Inst. Neth. 17, 176.

    Google Scholar 

  • Irvine, W. M.: 1965, Astrophys. J. 142, 1563.

    Google Scholar 

  • Junge, C. E.: 1963, Air Chemistry and Radiochemistry, Academic Press, New York, 382 pp.

    Google Scholar 

  • Kaper, H. G., Shultis, J. K., and Veninga, J. G.: 1970, J. Comp. Phys. 6, 288.

    Google Scholar 

  • Kastner, S. O.: 1964, Goddard Space Flight Center rept. TMX-55062, 12 pp.

  • Kattawar, G. W. and Adams, C. N.: 1971, Astrophys. J. 167, 183.

    Google Scholar 

  • Kattawar, G. W. and Plass, G. N.: 1967, Appl. Opt. 6, 1377.

    Google Scholar 

  • Kattawar, G. W., Plass, G. N., and Guinn, J. A.: 1973, J. Phys. Ocean. 3, 353.

    Google Scholar 

  • Kemp, J. C.: 1974, in T. Gehrels (ed.), Planets, Stars and Nebulae Studied with Photopolarimetry, Univ. Arizona Press, Tucson, p. 607.

    Google Scholar 

  • Kemp, J. C., Swedlund, J. B., Murphy, R. E., and Wolstencroft, R. D.: 1971a, Nature 231, 169.

    Google Scholar 

  • Kemp, J. C., Wolstencroft, R. D., and Swedland, J. B.: 1971b, Nature 232 165.

    Google Scholar 

  • Kendall, M. G. and Stuart, A.: 1963, The Advanced Theory of Statistics, Vol. 1, Distribution Theory, Hafner Publ. Com., New York, 433 pp.

    Google Scholar 

  • Kerker, M.: 1969, The Scattering of Light, Academic Press, New York, 666 pp.

    Google Scholar 

  • Khrgian, A. Kh.: 1961, Cloud Physics, Israel Prog. Scien. Trans., Jerusalem, 392 pp.

    Google Scholar 

  • Kofink, W.: 1967, in E. Inönü and P. F. Zweifel (eds.), Developments in Transport Theory, Academic Press, New York, 381 pp.

  • Kolesov, A. K. and Smotkii, O. I.: 1972, Soviet Astron. A. J. 15, 802.

    Google Scholar 

  • Kuščer, I.: 1955, J. Math. Phys. 34, 256.

    Google Scholar 

  • Kuščer, I. and McCormick, N. J.: 1974, UCLA International Conference on Radiation and Remote Probing of the Atmosphere, Western Periodicals, North Hollywood, 506 pp.

    Google Scholar 

  • Lacis, A. A. and Hansen, J. E.: 1974, J. Atmospheric Sci. 31, 118.

    Google Scholar 

  • Lenoble, J.: 1956, Rev. Opt. 35, 1.

    Google Scholar 

  • Lenoble, J.: 1961, Compt. Rend. Acta. Sci. 252, 2087.

    Google Scholar 

  • Lenoble, J.: 1970, J. Quant. Spectr. Radiat. Transfer 10, 533.

    Google Scholar 

  • Liou, K. N.: 1973, J. Atmospheric Sci. 30, 1303.

    Google Scholar 

  • Liou, K. N.: 1974, J. Atmospheric Sci., 31, 1473.

    Google Scholar 

  • Liou, K. N. and Hansen, J. E.: 1971, J. Atmospheric Sci. 28, 995.

    Google Scholar 

  • Lorenz, L.: 1898, Oeuvres Scientifiques, Vol. 1, Lehman and Stage, Copenhagen, p. 405.

    Google Scholar 

  • Lyot, B.: 1929, Ann. Obs. Paris (Meudon) 8, 161.

    Google Scholar 

  • Marchuk, G. I. and Mikhailov, G. A.: 1967a, Izv. Atmospheric Ocean. Phys. 3, 258.

    Google Scholar 

  • Marchuk, G. I. and Mikhailov, G. A.: 1967b, Izv. Atmospheric Ocean. Phys. 3, 394.

    Google Scholar 

  • Mark, J. C.: 1944, Nat. Res. Coun. Canada, Atomic Energy Project report MT 92.

  • Marshak, R. E.: 1947, Phys. Rev. 71, 443.

    Google Scholar 

  • Mathews, D. R., Hansen, K. F., and Mason, E. A.: 1967, Nucl. Sci. Eng. 27, 263.

    Google Scholar 

  • McCormick, N. J. and Kuščer, I.: 1966, J. Math. Phys. 7, 2036.

    Google Scholar 

  • McCormick, N. J. and Kuščer, I.: 1973, in E. J. Henley and J. Lewins (eds.), Advances in Nuclear Science and Technology 7, pp. 181, Academic Press, New York, 379 pp.

    Google Scholar 

  • McKee, T. B. and Cox, S. K.: 1974, submitted to J. Atmospheric Sci.

  • Mie, G.: 1908, Ann. Phys. 25, 377.

    Google Scholar 

  • Mika, J. R.: 1961, Nucl. Sci. Eng. 11, 415.

    Google Scholar 

  • Mingle, J. D.: 1973, The Invariant Imbedding Theory of Nuclear Transport, American Elsevier, New York, 131 pp.

    Google Scholar 

  • Mossop, S. C.: 1965, Geochim. Cosmochim. Acta 29, 201.

    Google Scholar 

  • Pahor, S.: 1966, Nucl. Sci. Eng. 26, 192.

    Google Scholar 

  • Pahor, S.: 1967, Nucl. Sci. Eng. 29, 248.

    Google Scholar 

  • Pahor, S. and Kuščer, I.: 1966, Astrophys. J. 143, 888.

    Google Scholar 

  • Peebles, G. H. and Plesset, M. S.: 1951, Phys. Rev. 81, 430.

    Google Scholar 

  • Penndorf, R.: 1957, J. Opt. Soc. Amer. 47, 176.

    Google Scholar 

  • Plass, G. N. and Kattawar, G. W.: 1968, Appl. Opt. 7, 415.

    Google Scholar 

  • Plass, G. N. and Kattawar, G. W.: 1971, J. Atmospheric Sci. 28, 1187..

    Google Scholar 

  • Plass, G. N., Kattawar, G. W., and Catchings, F. E.: 1973, Appl. Opt. 12, 314.

    Google Scholar 

  • Pollack, J. B.: 1967, Icarus 7, 42.

    Google Scholar 

  • Porch, W. M., Ensor, D. S., Charlson, R. J., and Heintzenberg, J.: 1973, Appl. Opt. 12, 34.

    Google Scholar 

  • Potter, J. F.: 1970, J. Atmospheric Sci. 27, 943.

    Google Scholar 

  • Rayleigh, Lord (J. W. Strutt): 1871, Phil. Mag. 41, 107, 274 and 477.

    Google Scholar 

  • Rayleigh, Lord (J. W. Strutt): 1918, Phil. Mag. 35, 373.

    Google Scholar 

  • Samuelson, R. E.: 1969, Icarus 10, 258.

    Google Scholar 

  • Schuster, A.: 1905, Astrophys. J. 21, 1.

    Google Scholar 

  • Schwarzschild, K.: 1906, Göttinger Nachrichten, 41.

  • Sekera, Z.: 1966, Memorandums RM-4951-PR and RM-5056-PR, Rand Corporation, Santa Monica.

    Google Scholar 

  • Sekera, Z. and Kahle, A. B.: 1966, Memorandum R-452-PR, Rand Corporation, Santa Monica.

    Google Scholar 

  • Shreider, Y. A.: 1966, The Monte Carlo Method, Pergamon Press, New York, 381 pp.

    Google Scholar 

  • Shurcliff, W. A.: 1962, Polarized Light, Harvard Univ. Press, Cambridge, 207 pp.

    Google Scholar 

  • Sobolev, V. V.: 1974, Light Scattering in Planetary Atmospheres, Pergamon Press, New York (in press).

    Google Scholar 

  • Spanier, J. and Gelbard, E. M.: 1969, Monte Carlo Principles and Neutron Transport Problems, Addison-Wesley, Reading, Mass., 234 pp.

    Google Scholar 

  • Stibbs, D. W. N. and Weir, R. E.: 1959, Monthly Notices Roy. Astron. Soc. 119, 512.

    Google Scholar 

  • Stokes, G. G.: 1862, Proc. Roy. Soc. (London) 11, 545.

    Google Scholar 

  • Sweigart, A. V.: 1970, Astrophys. J. Suppl. 22, 1.

    Google Scholar 

  • Travis, L. D.: 1974, in preparation.

  • Twomey, S., Jacobowitz, H., and Howell, H. B.: 1966, J. Atmospheric Sci. 23, 289.

    Google Scholar 

  • Uesugi, A. and Irvine, W. M.: 1970, Astrophys. J. 159, 127.

    Google Scholar 

  • van Blerkom, D. J.: 1971, Astrophys. J. 166, 235.

    Google Scholar 

  • van de Hulst, H. C.: 1948, Astrophys. J. 107, 220.

    Google Scholar 

  • van de Hulst, H. C.: 1957, Light Scattering by Small Particles, Wiley, New York, 470 pp.

    Google Scholar 

  • van de Hulst, H. C.: 1963, Tech. Rept., Inst. Space Studies, NASA, New York, 81 pp.

    Google Scholar 

  • van de Hulst, H. C.: 1970, Astron. Astrophys. 9, 359.

    Google Scholar 

  • van de Hulst, H. C. and Irvine, W. M.: 1962, La Physique des planètes (11th Liège International Astrophysical Symposium), p. 78.

  • Weickmann, H. K. and aufm Kampe, H. J.: 1953, J. Meteor. 10, 204.

    Google Scholar 

  • Weinman, J. A. and Guetter, P. J.: 1972, J. Appl. Meteor. 11, 136.

    Google Scholar 

  • Wick, G. C.: 1943, Z. Phys. 120, 702.

    Google Scholar 

  • Wing, G. M.: 1962, An Introduction to Transport Theory, John Wiley, New York, 169 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Goddard Institute for Space Studies, 10025, New York, N.Y., USA

    James E. Hansen & Larry D. Travis

Authors
  1. James E. Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Larry D. Travis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hansen, J.E., Travis, L.D. Light scattering in planetary atmospheres. Space Sci Rev 16, 527–610 (1974). https://doi.org/10.1007/BF00168069

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00168069

Keywords

Search

Navigation