OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 26, Iss. 11 — Jun. 1, 1987
  • pp: 2095–2101

Two-stream irradiance model for deep waters

Eyvind Aans  »View Author Affiliations

Applied Optics, Vol. 26, Issue 11, pp. 2095-2101 (1987)

View Full Text Article

Enhanced HTML    Acrobat PDF (765 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The two-stream model expresses the vertical attenuation coefficient K and the irradiance ratio R as functions of the absorption coefficient a, the backward scattering coefficient bb, the downward and upward average cosines μ ¯ d and μ ¯ u, and the normalized reflectance coefficients of downward and upward scalar irradiance, rd and ru. While K/a and R are almost linear functions of bb/a when bb/a is small, they will approach asymptotic values, which only depend on rd, ru, μ ¯ d, and μ ¯ u when bb/a becomes large. The results agree well with oceanic observations of K and R. They also agree with theoretical results derived by other methods. Still proper testing of the model in turbid waters remains.

© 1987 Optical Society of America

Original Manuscript: October 29, 1986
Published: June 1, 1987

Eyvind Aans, "Two-stream irradiance model for deep waters," Appl. Opt. 26, 2095-2101 (1987)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Gershun, “The Light Field,” J. Math. Phys. 18, 51 (1939).
  2. A. Morel, R. C. Smith “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335 (1981). [CrossRef]
  3. M. V. Kozlyaninov, V. N. Pelevin, “On the Application of a One-dimensional Approximation in the Investigation of the Propagation of Optical Radiation in the Sea,” Dept. Commerce, J. Publ. Res. Ser. Rep. 36, 54 (1966).
  4. J. Joseph, “Untersuchungen fiber Ober- and Unterlicht-messungen im Meere,” Dtsch. Hydrogr. Z. 3, 324 (1950). [CrossRef]
  5. R. W. Preisendorfer, Hydrologic Optics, Vol. 5: Properties (U.S. Department of Commerce National Oceanic and Atmospheric Administration, Environmental Research Laboratory, Honolulu, 1976).
  6. L. Prieur, “Transfert radiatif dans les eaux de mer. Application à la determination de parametres optiques caracterisant leur teneur en substances dissoutes et leur contenu en particules,” Thesis, U. P. et M. Curie, Paris (1976).
  7. R. W. Preisendorfer, C. D. Mobley, “Direct and Inverse Irradiance Models in Hydrologic Optics,” Limnol. Oceanogr. 29, 903 (1984). [CrossRef]
  8. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  9. K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).
  10. V. V. Sobolev, A Treatise on Radiative Transfer (Van Nostrand, New York, 1963).
  11. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, Oxford, 1975).
  12. E. Aas, “The Wavelength Selectivity of Light Scattering in the Barents Sea,” Inst. Rep. Ser., Inst. Geofysikk, U. Oslo54 (1984).
  13. C. H. Whitlock, L. R. Pool, J. W. Usry, W. M. Houghton, W. G. Witte, W. D. Morris, E. A. Gurganus, “Comparison of Reflectance with Backscatter and Absorption Parameters for Turbid Waters,” Appl. Opt. 20, 517 (1981). [CrossRef] [PubMed]
  14. D. Bauer, A. Morel, “Etyde aux petit angles de l’indicatrice de diffusion de la lumière par les eaux de mer,” Ann. Geophys. 23, 109 (1967).
  15. A. Morel, “Optical Properties of Pure Water and Pure Sea Water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, Eds. (Academic, London, 1974), p. 1.
  16. R. C. Smith, “Structure of Solar Radiation in the Upper Layers of the Sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, Eds. (Academic, London, 1974), p. 95.
  17. J. E. Tyler, “Radiance Distribution as a Function of Depth in an Underwater Environment,” Bull. Scripps Inst. Oceanogr. 7, 363 (1960).
  18. J. E. Tyler, R. C. Smith, W. H. Wilson, “Predicted Optical Properties for Clean Natural Water,” J. Opt. Soc. Am. 62, 83 (1972). [CrossRef]
  19. E. Aas, “The Vertical Attenuation Coefficient of Submarine Irradiance,” Inst. Rep. Ser., Inst. GeofysikkU. Oslo28 (1978).
  20. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  21. N. K. Højerslev, “Inherent and Apparent Optical Properties of the Western Mediterranean and the Hardangerfjord,” Rep. Inst. Fysisk Oceanografi, U. Copenhagen21 (1973).
  22. N. K. Højerslev, “Inherent and Apparent Optical Properties of the Baltic,” Rep. Inst. Fysisk Oceanografi, U. Copenhagen23 (1974).
  23. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed Relationships Between the Inherent and Apparent Optical Properties of a Flat Homogeneous Ocean,” Appl. Opt. 14, 417 (1975). [CrossRef] [PubMed]
  24. J.T.O. Kirk, “Monte Carlo Study of the Nature of Underwater Light Field in, and the Relationships Between Optical Properties of, Turbid Yellow Waters,” Aust. J. Mar. Freshwater Res. 32, 517 (1981). [CrossRef]
  25. J.T.O. Kirk, “Dependence of Relationship Between Inherent and Apparent Optical Properties of Water on Solar Altitude,” Limnol. Oceanogr. 29, 350 (1984). [CrossRef]
  26. A. Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. Oceanogr. 22, 709 (1977). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited