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Applied Optics

Applied Optics


  • Vol. 17, Iss. 21 — Nov. 1, 1978
  • pp: 3431–3438

Single-scattering solution for radiative transfer through a turbid atmosphere

J. Otterman  »View Author Affiliations

Applied Optics, Vol. 17, Issue 21, pp. 3431-3438 (1978)

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A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, bounded by a Lambert surface, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on idealization of the scattering phase function of the aerosols. The equations developed here are subsequently applied to analyze quantitatively (1) the enhancement of the surface irradiation and (2) the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and subsequent atmospheric scattering. An order-of-magnitude error analysis is presented.

© 1978 Optical Society of America

Original Manuscript: July 30, 1977
Published: November 1, 1978

J. Otterman, "Single-scattering solution for radiative transfer through a turbid atmosphere," Appl. Opt. 17, 3431-3438 (1978)

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  1. J. Otterman, R. S. Fraser, “Adjacency Effects on Imaging by Surface Reflection and Atmospheric Scattering: Cross-Radiance to Zenith”, submitted, Applied Optics (1978).
  2. J. E. Hansen, L. D. Travis, Space Sci. Rev. 16, 527 (1974). [CrossRef]
  3. D. Deirmendjian, L. Sekera, Tellus 6, 382 (1954). [CrossRef]
  4. K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).
  5. K. L. Coulson, J. Atmos. Sci. 25, 759 (1968). [CrossRef]
  6. J. Otterman, R. S. Fraser, Remote Sensing Environ. 5, 247 (1976). [CrossRef]
  7. J. E. Colwell, Remote Sensing Environ. 3, 175 (1974). [CrossRef]
  8. J. Otterman, Geophys. Res. Lett. 4, 441 (1977). [CrossRef]
  9. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (U.S. Department of Commerce, Applied Mathematics Series 55, National Bureau of Standards, Washington, D.C., 1964).

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