Abstract

We present an experimental and numerical study of the effects of multiple scattering on the optical properties of reef-building corals. For this, we propose a simplified optical model of the coral and describe in some detail methods for characterizing the coral skeleton and the layer containing the symbiotic algae. The model is used to study the absorption of light by the layer of tissue containing the microalgae by means of Monte Carlo simulations. The results show that, through scattering, the skeleton homogenizes and enhances the light environment in which the symbionts live. We also present results that illustrate the modification of the internal light environment when the corals loose symbionts or pigmentation.

© 2010 Optical Society of America

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  1. L. Muscatine and V. Weis, “Productivity of zooxanthellae and biogeochemical cycles,” in Primary Productivity and Biogeochemical Cycles in the Sea, P.G.Falkowski and A. D. Woodhead, eds. (Plenum, 1992), pp. 257–271.
  2. T. F. Goreau and N. I. Goreau, “The physiology of skeleton formation in corals. II. Calcium deposition by hermatypic corals under various conditions in the reef,” Biol. Bull. 117, 239–250 (1959).
    [CrossRef]
  3. G. D. Stanley, “The evolution of modern corals and their early history,” Earth-Sci. Rev. 60, 195–225 (2003).
    [CrossRef]
  4. B. E. Brown, “Coral bleaching: causes and consequences,” Coral Reefs 16, S129–S138 (1997).
    [CrossRef]
  5. O. Hoegh-Guldberg, “Climate change, coral bleaching and the future of the world’s coral reefs,” Mar. Freshwater Res. 50, 839–866 (1999).
    [CrossRef]
  6. O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
    [CrossRef] [PubMed]
  7. R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
    [CrossRef] [PubMed]
  8. R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
    [CrossRef]
  9. M. E. Warner, W. K. Fitt, and G. W. Schmidt, “Damage to photosystem II in symbiotic dinoflagellates: a determinant of coral bleaching,” Proc. Natl. Acad. Sci. USA 96, 8007–8012 (1999).
    [CrossRef] [PubMed]
  10. M. P. Lesser, “Elevated temperatures and ultraviolet radiation cause oxidative stress and inhibit photosynthesis in symbiotic dinoflagellates,” Limnol. Oceanogr. 41, 271–283(1996).
    [CrossRef]
  11. S. Enríquez, E. R. Méndez, and R. Iglesias-Prieto, “Multiple scattering on coral skeletons enhances light absorption by symbiotic algae,” Limnol. Oceanogr. 50, 1025–1032 (2005).
    [CrossRef]
  12. L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef] [PubMed]
  13. L. Wang and S. L. Jacques, MCML: Monte Carlo software package, http://omlc.ogi.edu/software/mc/index.html.
  14. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981). p. 4.
  15. E. A. Drew, “The biology and physiology of algal-invertebrate symbioses. II. The density of symbiotic algal cells in a number of herrnatypic corals and alcyonarians from various depths,” J. Exp. Mar. Biol. Ecol. 9, 71–75 (1972).
    [CrossRef]
  16. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002), p. 74.
  17. A. Ishimaru, Wave Propagation and Scattering in Random Media. (Oxford, 1997).
  18. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32, 559–568 (1993).
    [CrossRef] [PubMed]
  19. J. A. Jacquez and H. F. Kuppenheim, “Theory of the integrating sphere,” J. Opt. Soc. Am. 45, 460–470 (1955).
    [CrossRef]
  20. J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, and M. J. C. van Gemert, “Two Integrating Spheres with an Intervening Scattering Sample,” J. Opt. Soc. Am. A 9, 621–631 (1992).
    [CrossRef]
  21. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992), Sect. 10.4.

2007

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

2005

S. Enríquez, E. R. Méndez, and R. Iglesias-Prieto, “Multiple scattering on coral skeletons enhances light absorption by symbiotic algae,” Limnol. Oceanogr. 50, 1025–1032 (2005).
[CrossRef]

2003

G. D. Stanley, “The evolution of modern corals and their early history,” Earth-Sci. Rev. 60, 195–225 (2003).
[CrossRef]

1999

O. Hoegh-Guldberg, “Climate change, coral bleaching and the future of the world’s coral reefs,” Mar. Freshwater Res. 50, 839–866 (1999).
[CrossRef]

M. E. Warner, W. K. Fitt, and G. W. Schmidt, “Damage to photosystem II in symbiotic dinoflagellates: a determinant of coral bleaching,” Proc. Natl. Acad. Sci. USA 96, 8007–8012 (1999).
[CrossRef] [PubMed]

1998

R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
[CrossRef]

1997

B. E. Brown, “Coral bleaching: causes and consequences,” Coral Reefs 16, S129–S138 (1997).
[CrossRef]

1996

M. P. Lesser, “Elevated temperatures and ultraviolet radiation cause oxidative stress and inhibit photosynthesis in symbiotic dinoflagellates,” Limnol. Oceanogr. 41, 271–283(1996).
[CrossRef]

1995

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

1993

1992

J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, and M. J. C. van Gemert, “Two Integrating Spheres with an Intervening Scattering Sample,” J. Opt. Soc. Am. A 9, 621–631 (1992).
[CrossRef]

R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
[CrossRef] [PubMed]

1972

E. A. Drew, “The biology and physiology of algal-invertebrate symbioses. II. The density of symbiotic algal cells in a number of herrnatypic corals and alcyonarians from various depths,” J. Exp. Mar. Biol. Ecol. 9, 71–75 (1972).
[CrossRef]

1959

T. F. Goreau and N. I. Goreau, “The physiology of skeleton formation in corals. II. Calcium deposition by hermatypic corals under various conditions in the reef,” Biol. Bull. 117, 239–250 (1959).
[CrossRef]

1955

Bradbury, R. H.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Brown, B. E.

B. E. Brown, “Coral bleaching: causes and consequences,” Coral Reefs 16, S129–S138 (1997).
[CrossRef]

Caldeira, K.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Drew, E. A.

E. A. Drew, “The biology and physiology of algal-invertebrate symbioses. II. The density of symbiotic algal cells in a number of herrnatypic corals and alcyonarians from various depths,” J. Exp. Mar. Biol. Ecol. 9, 71–75 (1972).
[CrossRef]

Dubi, A.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Eakin, C. M.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Edwards, A. J.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Enríquez, S.

S. Enríquez, E. R. Méndez, and R. Iglesias-Prieto, “Multiple scattering on coral skeletons enhances light absorption by symbiotic algae,” Limnol. Oceanogr. 50, 1025–1032 (2005).
[CrossRef]

Fitt, W. K.

M. E. Warner, W. K. Fitt, and G. W. Schmidt, “Damage to photosystem II in symbiotic dinoflagellates: a determinant of coral bleaching,” Proc. Natl. Acad. Sci. USA 96, 8007–8012 (1999).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992), Sect. 10.4.

Gomez, E.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Goreau, N. I.

T. F. Goreau and N. I. Goreau, “The physiology of skeleton formation in corals. II. Calcium deposition by hermatypic corals under various conditions in the reef,” Biol. Bull. 117, 239–250 (1959).
[CrossRef]

Goreau, T. F.

T. F. Goreau and N. I. Goreau, “The physiology of skeleton formation in corals. II. Calcium deposition by hermatypic corals under various conditions in the reef,” Biol. Bull. 117, 239–250 (1959).
[CrossRef]

Greenfield, P.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Harvell, C. D.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Hatziolos, M. E.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Hoegh-Guldberg, O.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

O. Hoegh-Guldberg, “Climate change, coral bleaching and the future of the world’s coral reefs,” Mar. Freshwater Res. 50, 839–866 (1999).
[CrossRef]

R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
[CrossRef]

Hooten, A. J.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Iglesias-Prieto, R.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

S. Enríquez, E. R. Méndez, and R. Iglesias-Prieto, “Multiple scattering on coral skeletons enhances light absorption by symbiotic algae,” Limnol. Oceanogr. 50, 1025–1032 (2005).
[CrossRef]

R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media. (Oxford, 1997).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Jacquez, J. A.

Jones, R. J.

R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
[CrossRef]

Knowlton, N.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Kuppenheim, H. F.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002), p. 74.

Larkum, W. D.

R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
[CrossRef]

Lesser, M. P.

M. P. Lesser, “Elevated temperatures and ultraviolet radiation cause oxidative stress and inhibit photosynthesis in symbiotic dinoflagellates,” Limnol. Oceanogr. 41, 271–283(1996).
[CrossRef]

Matta, J. L.

R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
[CrossRef] [PubMed]

Méndez, E. R.

S. Enríquez, E. R. Méndez, and R. Iglesias-Prieto, “Multiple scattering on coral skeletons enhances light absorption by symbiotic algae,” Limnol. Oceanogr. 50, 1025–1032 (2005).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002), p. 74.

Moes, C. J. M.

Mumby, P. J.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Muscatine, L.

L. Muscatine and V. Weis, “Productivity of zooxanthellae and biogeochemical cycles,” in Primary Productivity and Biogeochemical Cycles in the Sea, P.G.Falkowski and A. D. Woodhead, eds. (Plenum, 1992), pp. 257–271.

Muthiga, N.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Pickering, J. W.

Prahl, S. A.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992), Sect. 10.4.

Robins, W. A.

R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
[CrossRef] [PubMed]

Sale, P. F.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Schmidt, G. W.

M. E. Warner, W. K. Fitt, and G. W. Schmidt, “Damage to photosystem II in symbiotic dinoflagellates: a determinant of coral bleaching,” Proc. Natl. Acad. Sci. USA 96, 8007–8012 (1999).
[CrossRef] [PubMed]

Schreiber, U.

R. J. Jones, O. Hoegh-Guldberg, W. D. Larkum, and U. Schreiber, “Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae,” Plant Cell Environ. 21, 1219–1230 (1998).
[CrossRef]

Stanley, G. D.

G. D. Stanley, “The evolution of modern corals and their early history,” Earth-Sci. Rev. 60, 195–225 (2003).
[CrossRef]

Steneck, R. S.

O. Hoegh-Guldberg, P. J. Mumby, A. J. Hooten, R. S. Steneck, P. Greenfield, E. Gomez, C. D. Harvell, P. F. Sale, A. J. Edwards, K. Caldeira, N. Knowlton, C. M. Eakin, R. Iglesias-Prieto, N. Muthiga, R. H. Bradbury, A. Dubi, and M. E. Hatziolos, “Coral reefs under rapid climate change and ocean acidification,” Science 318, 1737–1742 (2007).
[CrossRef] [PubMed]

Sterenborg, H. J. C.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992), Sect. 10.4.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002), p. 74.

Trench, R. K.

R. Iglesias-Prieto, J. L. Matta, W. A. Robins, and R. K. Trench, “Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture,” Proc. Natl. Acad. Sci. USA 89, 10302–10305 (1992).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981). p. 4.

van Gemert, M. J. C.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992), Sect. 10.4.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

L. Wang and S. L. Jacques, MCML: Monte Carlo software package, http://omlc.ogi.edu/software/mc/index.html.

Warner, M. E.

M. E. Warner, W. K. Fitt, and G. W. Schmidt, “Damage to photosystem II in symbiotic dinoflagellates: a determinant of coral bleaching,” Proc. Natl. Acad. Sci. USA 96, 8007–8012 (1999).
[CrossRef] [PubMed]

Weis, V.

L. Muscatine and V. Weis, “Productivity of zooxanthellae and biogeochemical cycles,” in Primary Productivity and Biogeochemical Cycles in the Sea, P.G.Falkowski and A. D. Woodhead, eds. (Plenum, 1992), pp. 257–271.

Welch, A. J.

Woodhead, A. D.

L. Muscatine and V. Weis, “Productivity of zooxanthellae and biogeochemical cycles,” in Primary Productivity and Biogeochemical Cycles in the Sea, P.G.Falkowski and A. D. Woodhead, eds. (Plenum, 1992), pp. 257–271.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Appl. Opt.

Biol. Bull.

T. F. Goreau and N. I. Goreau, “The physiology of skeleton formation in corals. II. Calcium deposition by hermatypic corals under various conditions in the reef,” Biol. Bull. 117, 239–250 (1959).
[CrossRef]

Comput. Methods Programs Biomed.

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Figures (10)

Fig. 1
Fig. 1

Illustration of the basic nature of corals. (a) Coral with retracted tentacles. (b) Coral with extended tentacles. (c) Coral skeleton. (d) Symbiotic algae S. kawagutii. The length of the marker is 10 μm .

Fig. 2
Fig. 2

Schematic diagram of the coral model considered.

Fig. 3
Fig. 3

Schematic diagrams of the arrangements used for the characterization of the photosynthetic cells. Setup for the measurement of (a) extinction and (b) absorption.

Fig. 4
Fig. 4

Extinction and absorption cross sections of S. kawagutii cells grown in a low light environment as functions of the wavelength in the visible region of the spectrum. The curve with a continuous line represents the extinction cross section, the curve with the dashed line represents the absorption cross section, and the curve with the dashed-dot line represents the scattering cross section.

Fig. 5
Fig. 5

Schematic diagram of the setup for the measurement of the reflection and transmission coefficients of a slab of skeleton. An integrating sphere with three beams is used for these measurements.

Fig. 6
Fig. 6

Reflection and transmission coefficients of a coral skeleton slab of thickness d = 3 mm . The curve with the continuous line represents the absorption, the curve with the dashed line is the reflectance, and the curve with the dashed-dot line is the transmittance.

Fig. 7
Fig. 7

Absorption as a function of depth in the animal tissue. The dashed line is for the “flat layer model” (flat layer of animal tissue with symbionts) and the continuous line is for a “flat coral” (layer of animal tissue with symbionts in front of a flat skeleton). The parameters employed for the flat coral model are given in Table 1.

Fig. 8
Fig. 8

Reflectance of a coral as a function of the surface density of cells η.

Fig. 9
Fig. 9

Enhancement factor ε as a function of the number of cells per projected area η for different structures.

Fig. 10
Fig. 10

Enhancement factor as a function of the absorption coefficient of the skeleton μ a . (a) Pigmented coral with η = 10 6   cells / cm 2 , and (b) bleached coral with η = 10 5   cells / cm 2 . The continuous curve is for the coral model, and the dashed curve is for the flat coral model. The dashed-dot curve in (a) is the reflectance of a flat skeleton as a function of μ a . The thin vertical line is at μ a = 0.5 cm 1 .

Tables (2)

Tables Icon

Table 1 Parameters Employed for Calculations with the “Flat Coral Model”

Tables Icon

Table 2 Absorption Results for the Models Studied

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

μ a = ρ C a ,
μ s = ρ C s .
P m = P o exp ( ρ 0 C e L ) ,
P m = P o exp ( ρ 0 C a L ) .
P dr = A δ A is m 1 [ m α + R d A s / A is + r d A δ / A is ] P 01 .
P cr = A δ A is R T 1 [ m α + R d A s / A is + r d A δ / A is ] P 02 ,
P ct = A δ A is T T 1 [ m α + R d A s / A is + r d A δ / A is ] P 03 .
R T = m P cr P dr P 01 P 02 ,
T T = m P ct P dr P 01 P 03 .
P a = Σ a I 0 ,
P a ( 0 ) = C a I 0 ,
ε = P a N P a ( 0 ) = Σ a N C a .
ε = Q a η C a ,
Q a = P a I 0 Σ V ,
A = 1 T = 1 e μ a d / cos θ 0 ,
ε = 1 e μ a d / cos θ 0 μ a d / cos θ 0 .

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