OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 26, Iss. 19 — Oct. 1, 1987
  • pp: 4133–4148

Bio-optical model describing the distribution of irradiance at the sea surface resulting from a point source embedded in the ocean

Howard R. Gordon  »View Author Affiliations

Applied Optics, Vol. 26, Issue 19, pp. 4133-4148 (1987)

View Full Text Article

Enhanced HTML    Acrobat PDF (1892 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A model of the optical properties of the ocean, providing the absorption and scattering coefficients of the medium as nonlinear functions of the concentration of pigments associated with phytoplankton and their immediate detrital material, is presented. Monte Carlo computations of the attenuation coefficient of downwelling irradiance Kd for an ocean–atmosphere system illuminated by the sun at zenith, agree well with experimental data and demonstrate the validity of such a model for studying the influence of phytoplankton biomass on the propagation to the surface of light generated through bioluminescence. The radiative transfer equation for the irradiance at the sea surface resulting from illumination by a point source embedded in the water is solved by Monte Carlo techniques. The solution technique is validated through comparison with an asymptotic analytic solution for isotropic scattering. The computations show that the irradiance distribution just beneath the surface as a function of R, the distance measured along the surface from a point vertically above the source, is described by two regimes: (1) a regime in which the irradiance is governed mostly by absorption and geometry with scattering playing a negligible role—the near field; (2) a regime in which the light field at the surface is very diffuse and the irradiance decays approximately exponentially in R and is a very weak function of the source depth—the diffusion regime. The near field is of primary interest because it contains most of the power reaching the sea surface. An analytical model of the irradiance distribution just beneath the surface as a function of R, the source depth, and the pigment concentration for the near field is presented. This model is based on the observation that at most scattering events the change in the photon's direction is slight, and therefore, scattering is rather ineffective in attenuating the irradiance. An analytic solution for the irradiance from the point source, then, is first carried out ignoring scattering altogether; however, recognizing that backscattering will attenuate the irradiance, the absorption coefficient is replaced by an effective attenuation coefficient k. This effective attenuation coefficient is determined by fitting the total power just beneath the surface determined from the Monte Carlo computations to the analytical model. The resulting k is closely related to Kd, and the Monte Carlo irradiance as a function of R and source depth in the near-field regime can be approximated with high accuracy using the model. These results indicate Kd can be estimated at night by releasing a point source in the water, measuring the irradiance at the surface as it sinks, and fitting the measurements to the relationships developed here to determine k. The analytic model also enables estimation of the source depth and power from the irradiance distribution just beneath the surface.

© 1987 Optical Society of America

Original Manuscript: January 26, 1987
Published: October 1, 1987

Howard R. Gordon, "Bio-optical model describing the distribution of irradiance at the sea surface resulting from a point source embedded in the ocean," Appl. Opt. 26, 4133-4148 (1987)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. M. Case, “Transfer Problems and the Reciprocity Principle,” Rev. Mod. Phys. 29, 651 (1957). [CrossRef]
  2. A. Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. Oceanogr. 22, 709 (1977). [CrossRef]
  3. By the term chlorophyll a we mean the concentration (mg/m3) of chlorophyll a and all chlorophyll-like pigments which absorb in the same spectral bands as chlorophyll a, such as phaeophytin a, and are contained in phytoplankton or in their detrital materials. The sum of the concentrations of chlorophyll a and phaeophytin a is frequently used as an indicator of plankton biomass. It is usually referred to as the pigment concentration.
  4. K. S. Baker, R. C. Smith, “Bio-optical Classification and Model of Natural Waters. 2,” Limnol. Oceanogr. 27, 500 (1982). [CrossRef]
  5. A. Morel, “Optical Properties of Pure Water and Pure Sea Water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, Eds. (Academic, New York, 1974).
  6. A. Morel, “In-water and Remote Measurement of Ocean Color,” Boundary-Layer Meteorol. 18, 177 (1980). [CrossRef]
  7. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Visible Satellite Imagery: A Review (Springer-Verlag, New York, 1983).
  8. L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption of Phytoplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981). [CrossRef]
  9. R. C. Smith, K. S. Baker, “The Bio-optical State of Ocean Waters and Remote Sensing,” Limnol. Oceanogr. 23, 247 (1978). [CrossRef]
  10. R. C. Smith, K. S. Baker, “Optical Classification of Natural Waters,” Limnol. Oceanogr. 23, 260 (1978). [CrossRef]
  11. L. A. Hobson, D. W. Menzel, R. T. Barber, “Primary Productivity and the Sizes of Pools of Organic Carbon in the Mixed Layer of the Ocean,” Mar. Biol. 19, 298 (1973). [CrossRef]
  12. S. Sathyendranath, “Influence des Substances en Solution et en Suspension dans les Eaux de Mer sur L'absorption er La Reflectance. Modelisation et Applications a'la Teledetection,” Ph.D. Thesis, 3rd cycle, U. Pierre et Marie Curie, Paris (1981), 123 pp.
  13. A. Bricaud, A. Morel, L. Prieur, “Optical Efficiency Factors of Some Phytoplankters,” Limnol. Oceanogr. 28, 816 (1983). [CrossRef]
  14. In general phytoplankton scattering will not satisfy the law BC(λ) ∼ λ−n for a constant value of n over the entire visible spectrum. This law is used here only to provide an analytical representation of the possible spectral behavior over this very limited portion of the spectrum.
  15. T. J. Petzold, Volume Scattering Functions for Selected Natural Waters, Scripps Institute of Oceanography, Visibility Laboratory, San Diego, CA 92152, SIO Ref. 72–78 (1972).
  16. H. R. Gordon, “Ship Perturbation of Irradiance Measurements at Sea. 1: Monte Carlo Simulations,” Appl. Opt. 24, 4172 (1985). [CrossRef] [PubMed]
  17. By the term exact, we mean in the sense that the solutions are given in terms of functions which can be evaluated numerically, e.g., Chandrasekhar's18H function.
  18. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  19. J. P. Elliott, “Milne's Problems with a Point Source,” Proc. R. Soc. London Ser. A 228, 424 (1955). [CrossRef]
  20. C. Mark, “Neutron Density Near a Plane Surface,” Phys. Rev. 72, 558 (1947). [CrossRef]
  21. R. W. Preisendorfer, Hydrological Optics. Vol. III: Solutions., PB-259795/3ST (National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22161 (1976).
  22. R. W. Preisendorfer, “On the Existence of Characteristic Diffuse Light in Natural Waters,” J. Mar. Res. 18, 1 (1959).
  23. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  24. G. Beardsley, J. R. V. Zaneveld, “Theoretical Dependence of the Near-Asymptotic Apparent Optical Properties on the Inherent Optical Properties of Sea Water,” J. Opt. Soc. Am. 59, 373 (1969). [CrossRef]
  25. L. Prieur, “Transfert radiatif dans les eaux de mer. Application a la determination de parametres optiques caracterisant leur teneur en substances dissoutes et leur contenu en particules,” D.Sci Thesis, U. Pierre et Marie Curie (1976), 243 pp.

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