OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 22 — Oct. 31, 2005
  • pp: 9052–9061

Theoretical derivation of the depth average of remotely sensed optical parameters

J. Ronald V. Zaneveld, Andrew H. Barnard, and Emmanuel Boss  »View Author Affiliations

Optics Express, Vol. 13, Issue 22, pp. 9052-9061 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (125 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The dependence of the reflectance at the surface on the vertical structure of optical parameters is derived from first principles. It is shown that the depth dependence is a function of the derivative of the round trip attenuation of the downwelling and backscattered light. Previously the depth dependence was usually modeled as being dependent on the round trip attenuation. Using the new relationship one can calculate the contribution of the mixed layer to the overall reflectance at the surface. This allows one to determine whether or not to ignore the vertical structure at greater depth. It is shown that the important parameter to average is the ratio of the backscattering and absorption coefficients. The surface reflectance is related to the weighted average of this parameter, not the ratio of the weighted average of the backscattering and the weighted average of the absorption. Only in the special case of “optical homogeneity” where the ratio of the backscattering and absorption coefficients does not vary with depth, can the vertical structure be ignored. Other special cases including constant backscattering and variable absorption are also investigated.

© 2005 Optical Society of America

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(280.0280) Remote sensing and sensors : Remote sensing and sensors

ToC Category:
Research Papers

Original Manuscript: September 15, 2005
Revised Manuscript: October 20, 2005
Published: October 31, 2005

J. Ronald Zaneveld, Andrew Barnard, and Emmanuel Boss, "Theoretical derivation of the depth average of remotely sensed optical parameters," Opt. Express 13, 9052-9061 (2005)

Sort:  Journal  |  Reset  


  1. Gordon, H.R., O.B. Brown and M.M. Jacobs, �??Computed relationships between the Inherent and Apparent Optical Properties,�?? Appl. Optics 14, 417- 427 (1975). [CrossRef]
  2. Morel, A. and L. Prieur, �??Analysis of variations in ocean color,�?? Limn. and Oceanog. 22, 709-722 (1977). [CrossRef]
  3. Gordon, H.R., O.B. Brown, R.H. Evans, J.W. Brown, R.C. Smith, K.S. Baker, and D.K. Clark, �??A semianalytical radiance model of ocean color,�?? J. Geophys. Res. 93, 10, 909-10,924 (1988). [CrossRef]
  4. Morel, A. and B. Gentili, �??Diffuse reflectance of oceanic waters. II. Bidirectional aspects,�?? Appl. Opt. 32, 6864-6879 (1993). [CrossRef] [PubMed]
  5. Lee, Z.P, K.L. Carder, and R. Arnone, �??Deriving inherent optical properties from water color: A multi-band quasi-analytical algorithm for optically deep waters,�?? Appl. Opt. 41, 5755-5772 (2002). [CrossRef] [PubMed]
  6. Gould, R. W., R. A. Arnone, and M. Sydor, "Absorption, scattering, and remote-sensing reflectance relationships in coastal waters: testing a new inversion algorithm," J. Coastal Res. 17, 328-341 (2001).
  7. Loisel, H., D. Stramski, B. G. Mitchell, F. Fell, V. Fournier-Sicre, B. Lemasle, and M. Babin, "Comparison of the ocean inherent optical properties obtained from measurements and inverse modeling," Appl. Opt. 40, 2384-2397 (2001). [CrossRef]
  8. Hoge, F.E. and P.E. Lyon, �??Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: An analysis of model and radiance measurements errors,�?? J. Geophys. Res. 101 16, 631-6, 648 (1996) [CrossRef]
  9. Roesler, C.S. and M. J. Perry, "In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance," J. Geophys. Res., 100, 13,279-13,294 (1995).
  10. Garver, S.A. and D. Siegel, �??Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,�?? J. Geophys. Res. 102, 18,607-18,625 (1997). [CrossRef]
  11. Barnard, A.H., J.R.V. Zaneveld, and W. S. Pegau, "In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion," Appl. Opt. 38, 5108-5117 (1999). [CrossRef]
  12. S. A. Garver, D. Siegel, �??Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation 1. Time series from the Sargasso Sea,�?? J. Geophys. Res. 102, 18, 607-18, 625 (1997). [CrossRef]
  13. Gordon, H.R. and D.K. Clark, "Remote sensing optical properties of a stratified ocean: an improved interpretation," Appl. Opt. 19, 3428-3430 (1980). [CrossRef] [PubMed]
  14. Gordon, H.R. "Diffuse reflectance of the ocean: influence of nonuniform phytoplankton pigment profile," Appl. Opt. 31, 2116-2129 (1992). [CrossRef] [PubMed]
  15. Voss, K.J. and A. Morel, �??Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,�?? Limnol. Oceanogr. 50, 698�??705 (2005). [CrossRef]
  16. Stramska, M. and D. Stramski, �??Effects of nonuniform vertical profile of chlorophyll concentration on remote-sensing reflectance of the ocean,�?? Appl. Opt. 44, 1735-1747 (2005). [CrossRef] [PubMed]
  17. Zaneveld, J. R.V., �??Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation,�?? Appl. Opt. 21, 4146-4150 (1982). [CrossRef] [PubMed]
  18. Twardowski, M.J., M.R. Lewis, A. Barnard and J.R.V. Zaneveld, �??In-water instrumentation and platforms for ocean color remote sensing applications,�?? (2005) In: Remote sensing of Coastal Aquatic Environments, Remote Sensing and Digital Image Processing, Vol. 7. R.L. Miller, C.E.del Castillo, and B.A.McKee, Eds. Springer, Dordrecht. 347 pp.
  19. Kitchen, J.C. and J.R.V. Zaneveld, �??On the non-correlation of the vertical structure of light scattering and chlorophyll a in Case I waters,�?? J. Geophys. Res., 95, 20237-20246 (1990). [CrossRef]
  20. Philpot, W.D. and S.Ackleson, �??Remote sensing of optically shallow, vertically inhomogeneous waters: A mathematical model,�?? in Proceedings: Symposium on results of 1980 Chesapeake Bay Plume study, College of Marine Sciences, Univ. of Delaware, Newark, Delaware (1981).
  21. Philpot, W.D. �??Radiative transfer in stratified waters: a single-scattering approximation for irradiance,�?? Appl. Opt. 26, 4123-4132 (1987). [CrossRef] [PubMed]
  22. Maritorena, S., More l, A., and B. Gentili, �??Diffuse reflectance of oceanic shallow waters: Influence of water depth and albedo,�?? Limnol. Oceanogr. 39, 1689-1703 (1994). [CrossRef]
  23. Preisendorfer, R.W., Hydrologic Optics (in 6 volumes), Dept. of Commerce, NOAA. (1976).
  24. Zaneveld, J.R.V. and W.S. Pegau, "A model for the reflectance of thin layers, fronts, and internal waves and its inversion," Oceanography 11, 44-47 (1998). [CrossRef]
  25. Berwald, J., D. Stramski, C. D. Mobley, and D. A. Kiefer, "Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field," Limnol. Oceanogr. 40, 1347-1357 (1995) [CrossRef]
  26. Zaneveld, J. R.V., M. J. Twardowski, A. Barnard, and M. R. Lewis, �??Introduction to radiative transfer,�?? (2005) In: Remote sensing of Coastal Aquatic Environments, Remote Sensing and Digital Image Processing, Vol. 7. R.L. Miller, C.E. del Castillo, and B.A. McKee, Eds. Springer, Dordrecht. 347 pp.
  27. Fennel, K. and E. Boss, "Subsurface maxima of phytoplankton and chlorophyll- Steady state solutions from a simple model," Limnol. Oceanogr. 48, 1521-1534 (2003). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited