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Applied Optics

Applied Optics


  • Vol. 37, Iss. 18 — Jun. 20, 1998
  • pp: 3886–3896

Radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies

Howard R. Gordon and G. Chris Boynton  »View Author Affiliations

Applied Optics, Vol. 37, Issue 18, pp. 3886-3896 (1998)

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A full multiple-scattering algorithm for inverting profiles of the upwelling and downwelling irradiances to yield profiles of the absorption and backscattering coefficients in a vertically stratified water body is described and tested with simulated data. The algorithm does not require knowledge of the scattering phase function of the medium. The results are better the closer the phase function assumed in the retrievals is to the true phase function, although excellent retrievals of the absorption coefficient can still be obtained with an inaccurate phase function. Simulations show that the algorithm is capable of determining the vertical structure of a stratified water body and usually provides the absorption coefficient profile with an error ≲2% and the backscattering coefficient profile with an error ≲10%, as long as the spacing between pseudodata samples is sufficiently small that the necessary derivatives of the irradiances can be accurately computed. The performance is only slightly degraded when the upwelling radiance (nadir viewing) is substituted for the upwelling irradiance.

© 1998 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(290.0290) Scattering : Scattering
(290.1350) Scattering : Backscattering
(290.4210) Scattering : Multiple scattering

Original Manuscript: November 3, 1997
Revised Manuscript: March 6, 1998
Published: June 20, 1998

Howard R. Gordon and G. Chris 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)

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  1. 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]
  2. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, New York, 1994).
  3. 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]
  4. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977). [CrossRef]
  5. H. R. Gordon, W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14, 413–416 (1975). [CrossRef] [PubMed]
  6. H. R. Gordon, “Remote sensing of optical properties in continuously stratified waters,” Appl. Opt. 17, 1893–1897 (1978). [CrossRef] [PubMed]
  7. H. R. Gordon, D. K. Clark, “Remote sensing optical properties of a stratified ocean: an improved interpretation,” Appl. Opt. 19, 3428–3430 (1980). [CrossRef] [PubMed]
  8. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in FORTRAN (Cambridge University, Cambridge, England, 1992).
  9. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993). [CrossRef] [PubMed]
  10. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975). [CrossRef]
  11. J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968). [CrossRef]
  12. D. A. Siegal, M. C. O’Brien, J. C. Sorensen, D. A. Konnoff, E. A. Brody, J. L. Mueller, C. O. Davis, W. G. Rhea, S. B. Hooker, “Results of the SeaWiFS Data Analysis Round-Robin (DARR-94),” Vol. 26 of SeaWiFS Technical Report Series NASA Tech. Memor. 104566 (July1994).
  13. H. R. Gordon, “The sensitivity of radiative transfer to small-angle scattering in the ocean: a quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993). [CrossRef] [PubMed]
  14. G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sensing Environ. 27, 343–358 (1989). [CrossRef]
  15. 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]
  16. Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995). [CrossRef]

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