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Applied Optics

Applied Optics


  • Vol. 42, Iss. 9 — Mar. 20, 2003
  • pp: 1564–1573

Irradiance inversion theory to retrieve volume scattering function of seawater

Takafumi Hirata  »View Author Affiliations

Applied Optics, Vol. 42, Issue 9, pp. 1564-1573 (2003)

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An attempt to retrieve the volume scattering function (VSF) of source-free and no-inelastic-scattering ocean water is made from the upwelling irradiance E u and downwelling irradiance E d . It will be shown, from the radiative transfer equation, that the VSF of seawater can be calculated by the planar irradiances when the scattering phase function of the suspended particles in the backward direction and the molecular VSF are known. On the derivation of the hydrosol VSF, several optical properties such as the absorption coefficient a; the scattering coefficients of hydrosol, b, b f , b b and those of the suspended particles, b p , b fp , b bp ; the beam attenuation coefficient c; the average cosines μ̅, μ̅ d , and μ̅ u ; and the backscattering shape factor for the downwelling light stream, r du , will also be obtained. On the derivation of those optical parameters, classical knowledge related to interrelationships between inherent optical properties and apparent optical properties and obtained with Monte Carlo numerical simulations is analytically verified. The present theory can be applied to surface waters and any wavelengths, except for waters and wavelengths with an extremely low b b /a ratio.

© 2003 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(030.5620) Coherence and statistical optics : Radiative transfer
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(290.1350) Scattering : Backscattering
(290.3200) Scattering : Inverse scattering

Original Manuscript: April 30, 2002
Revised Manuscript: October 11, 2002
Published: March 20, 2003

Takafumi Hirata, "Irradiance inversion theory to retrieve volume scattering function of seawater," Appl. Opt. 42, 1564-1573 (2003)

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  1. A. A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).
  2. J. R. V. Zaneveld, “New developments of the theory of radiance transfer in the ocean,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steenmann Nielsen, eds. (Academic, London, 1974), pp. 121–134.
  3. N. K. Højerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975). [CrossRef]
  4. R. W. Preisendorfer, C. D. Mobley, “Direct and inverse irradiance models in hydrologic optics,” Limnol. Oceanogr. 29, 903–929 (1984). [CrossRef]
  5. H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991). [CrossRef]
  6. J. T. O. Kirk, “Estimation of the absorption and the scattering coefficients of natural waters by use of underwater irradiance measurements,” Appl. Opt. 33, 3276–3278 (1994). [CrossRef] [PubMed]
  7. H. R. Gordon, G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997). [CrossRef] [PubMed]
  8. H. R. Gordon, G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998). [CrossRef]
  9. L. Hubert, D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]
  10. V. A. Timofeeva, “Optics of turbid waters,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steenmann Nielsen, eds. (Academic, London, 1974), pp. 177–219.
  11. N. K. Højerslev, J. R. V. Zaneveld, “A theoretical proof of the existence of the submarine asymptotic daylight field,” Rep. 34, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1977), pp. 1–16.
  12. J. T. O. Kirk, “Relationship between nephelometric turbidity and scattering coefficients in certain Australian waters,” Aust. J. Mar. Freshwater Res. 31, 1–12 (1980). [CrossRef]
  13. J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989). [CrossRef]
  14. J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989). [CrossRef]
  15. N. J. McCormick, G. E. Rinaldi, “Seawater optical property estimation from in situ irradiance measurements,” Appl. Opt. 28, 2605–2613 (1989). [CrossRef] [PubMed]
  16. Z. Tao, N. J. McCormick, R. Sanchez, “Ocean source and optical property estimation from explicit and implicit algorithms,” Appl. Opt. 33, 3265–3275 (1994). [CrossRef] [PubMed]
  17. R. A. Leathers, N. J. McCormick, “Ocean inherent optical property estimation from irradiances,” Appl. Opt. 36, 8685–8697 (1997). [CrossRef]
  18. E. Aas, “Two-stream irradiance model for deep waters,” Appl. Opt. 26, 2095–2101 (1987). [CrossRef] [PubMed]
  19. R. H. Stavn, A. D. Weidemann, “Shape factors, two-flow models, and the problem of irradiance inversion in estimating optical parameters,” Limnol. Oceanogr. 34, 1426–1441 (1989). [CrossRef]
  20. N. J. McCormick, P. W. Francisco, “Radiative transfer two-stream shape factors for ocean optics,” Appl. Opt. 34, 6248–6255 (1995). [CrossRef] [PubMed]
  21. S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36, 2620–2629 (1997). [CrossRef] [PubMed]
  22. H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989). [CrossRef]
  23. J. E. Tyler, R. C. Smith, W. H. Wilson, “Predicted optical properties for clear natural water,” J. Opt. Soc. Am. 62, 83–91 (1972). [CrossRef]
  24. N. K. Højerslev, “Daylight measurements for photosynthetic studies in the Western Mediterranean,” Rep. 26, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1974), pp. 1–38.
  25. J. H. Jerome, R. P. Bukata, J. E. Bruton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988). [CrossRef] [PubMed]
  26. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989). [CrossRef]
  27. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991). [CrossRef] [PubMed]
  28. 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, 417–427 (1975). [CrossRef] [PubMed]
  29. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steenmann Nielsen, eds. (Academic, New York, 1974), pp. 1–24.
  30. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jing, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7505 (1993). [CrossRef] [PubMed]
  31. T. J. Petzold, “Volume scattering function for selected ocean waters,” SIO Technical Report (Scripps Institution of Oceanography, La Jolla, California, 1972), Refs. 72–78.
  32. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

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