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Applied Optics

Applied Optics


  • Vol. 41, Iss. 24 — Aug. 20, 2002
  • pp: 4962–4974

Fast and Accurate Model of Underwater Scalar Irradiance

Cheng-Chien Liu, Kendall L. Carder, Richard L. Miller, and James E. Ivey  »View Author Affiliations

Applied Optics, Vol. 41, Issue 24, pp. 4962-4974 (2002)

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A spectral model of scalar irradiance with depth is applied to calculations of photosynthetically available radiation for a vertically homogeneous water column. The model runs more than 14, 000 times faster than the full Hydrolight code, while it limits the percentage error to 2.20% and the maximum error to less than 4.78%. The distribution of incident sky radiance and the effects of a wind-roughened surface are integrated into this model. It can be applied to case 1 waters as well as to case 2 waters that happen to be gelbstoff rich, and the volume-scattering phase function can be generated dynamically based on the backscatter fraction. This new model is both fast and accurate and is, therefore, suitable for use interactively in models of the oceanic system, such as biogeochemical models or the heat budget part of global circulation models. It can also be applied by use of remote-sensing data to improve light-field calculations as a function of depth, which is needed for the estimation of global ocean carbon production and the ocean heat budget.

© 2002 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics

Cheng-Chien Liu, Kendall L. Carder, Richard L. Miller, and James E. Ivey, "Fast and Accurate Model of Underwater Scalar Irradiance," Appl. Opt. 41, 4962-4974 (2002)

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  1. T. R. Anderson, “A spectrally averaged model of light penetration and photosynthesis,” Limnol. Oceanogr. 38, 1403–1419 (1993).
  2. A. Morel and D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr. 24, 1652–1665 (1994).
  3. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
  4. C. D. Mobley and L. K. Sundman, Hydrolight 4.2 Users Guide (Sequoia Scientific, Inc., Redmond, Wash., 2001).
  5. C.-C. Liu, J. D. Woods, and C. D. Mobley, “Optical model for use in oceanic ecosystem models,” Appl. Opt. 38, 4475–4485 (1999).
  6. G. L. Mellor, Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model (Princeton University, Princeton, N.J., 1998).
  7. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), p. 231.
  8. M. J. R. Fasham, H. W. Ducklow, and S. M. McKelvie, “A nitrogen-based model of plankton dynamics in the oceanic mixed layer,” J. Mar. Res. 48, 591–639 (1990).
  9. J. L. Sarmiento, “Atmospheric CO2 stalled,” Nature 365, 697–698 (1993).
  10. A. Morel, “Optical modelling of the upper ocean in relation to its biogenous matter content (case 1 water),” J. Geophys. Res. 93(C9), 10749–10768 (1988).
  11. E.-N. Yeh, R. A. Barnes, M. Darzi, L. Kumar, E. A. Early, B. C. Johnson, J. L. Mueller, and C. C. Trees, “Case studies for SeaWiFS calibration and validation, Part 4,” in SeaWiFS Project Technical Report Series, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1997), p. 35.
  12. N. G. Jerlov, Optical Oceanography, Elsevier Oceanography Series (Elsevier, Amsterdam, 1968), p. 194.
  13. 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).
  14. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: a Review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983), Vol. 4, p. 114.
  15. J. J. Simpson and T. D. Dickey, “Alternative parameterizations of downward irradiance and their dynamical significance,” J. Phys. Oceanogr. 11, 876–882 (1981).
  16. J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, 2nd ed. (Cambridge University, Cambridge, England, 1994), p. 509.
  17. W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35(8), 1657–1675 (1990).
  18. F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24, 177–189 (1980).
  19. A. W. Harrison and C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41, 387–392 (1988).
  20. C. Cox and W. Munk, “The measurement of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
  21. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194–201 (1994).
  22. L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
  23. A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26, 263–306 (1991).
  24. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
  25. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994), p. 592.
  26. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
  27. R. C. Smith and K. Baker, “Optical properties of the clearest natural waters,” Appl. Opt. 20, 177–184 (1981).
  28. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
  29. A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).
  30. J. Berwald, 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).
  31. T. T. Bannister, “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr. 37, 773–780 (1992).
  32. N. J. McCormick, “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr. 40, 1013–1018 (1995).
  33. N. J. McCormick, “Asymptotic optical attenuation,” Limnol. Oceanogr. 37, 1570–1578 (1992).
  34. P. W. Francisco and N. J. McCormick, “Chlorophyll concentration effects on asymptotic optical attenuation,” Limnol. Oceanogr. 39, 1195–1205 (1994).
  35. J. P. Doyle and G. Zibordi, “Correction of oceanographic tower-shading effects on in-water radiance and irradiance measurements,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).
  36. A. Y. Morel, H. H. Loisel, and B. B. Gentili, “A database of in-water light fields,” in Ocean Optics XIV, proceedings on CD (U.S.N. Office of Naval Research, Ocean, Atmospheric, and Space Science and Technology Department, Arlington, Va., 1998).
  37. Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38, 3831–3843 (1999).
  38. K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
  39. J. L. Mueller and R. E. Lange, “Bio-optical provinces of the northeast Pacific Ocean: a provisional analysis,” Limnol. Oceanogr. 34, 1572–1586 (1989).
  40. T. Platt, S. Sathyendranath, C. M. Caverhill, and M. R. Lewis, “Ocean primary production and available light: further algorithms for remote sensing,” Deep-Sea Res. 35, 855–879 (1988).
  41. V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Appl. Opt. 38, 6826–6832 (1999).
  42. Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, and J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res. 103(C12), 27967–27978 (1998).

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