Abstract

The first step in the coastal zone color scanner (CZCS) atmospheric-correction algorithm is the computation of the Rayleigh-scattering contribution, Lr, to the radiance leaving the top of the atmosphere over the ocean. In the present algorithm Lr, is computed by assuming that the ocean surface is flat. Computations of the radiance leaving a Rayleigh-scattering atmosphere overlying a rough Fresnel-reflecting ocean are presented to assess the radiance error caused by the flat-ocean assumption. The surface-roughness model is described in detail for both scalar and vector (including polarization) radiative transfer theory. The computations utilizing the vector theory show that the magnitude of the error significantly depends on the assumptions made in regard to the shadowing of one wave by another. In the case of the coastal zone color scanner bands, we show that for moderate solar zenith angles the error is generally below the 1 digital count level, except near the edge of the scan for high wind speeds. For larger solar zenith angles, the error is generally larger and can exceed 1 digital count at some wavelengths over the entire scan, even for light winds. The error in Lr caused by ignoring surface roughness is shown to be the same order of magnitude as that caused by uncertainties of ± 15 mb in the surface atmospheric pressure or of ± 50 Dobson units in the ozone concentration. For future sensors, which will have greater radiometric sensitivity, the error caused by the flat-ocean assumption in the computation of Lr could be as much as an order of magnitude larger than the noise-equivalent spectral radiance in certain situations.

© 1992 Optical Society of America

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  1. W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
    [CrossRef] [PubMed]
  2. H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
    [CrossRef] [PubMed]
  3. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983), p. 114.
  4. National Aeronautics and Space Administration and the Earth Observations Satellite Company, System Concept for Wide-Field-of-View Observations of Ocean Phenomena from Space (National Aeronautics and Space Administration, Washington, D.C., 1987).
  5. National Aeronautics and Space Administration, MODIS (Moderate-Resolution Imaging Spectrometer), Earth Observing System (National Aeronautics and Space Administration, Washington, D.C., 1986), Vol. IIb.
  6. National Aeronautics and Space Administration, “Earth Observing System: Science and Mission Requirements Working Group report,” tech. memo 86129 (National Aeronautics and Space Administration, Washington, D.C., 1984).
  7. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison between ship determinations and coastal zone color scanner estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  8. H. R. Gordon, “Radiative transfer: a technique for simulating the ocean in satellite remote sensing calculations,” Appl. Opt. 15, 1974–1979 (1976).
    [CrossRef] [PubMed]
  9. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
    [CrossRef] [PubMed]
  10. H. R. Gordon, D. K. Clark, “Atmospheric efforts in the remote sensing of phytoplankton pigments,” Boundary Layer Meterol. 18, 299–313 (1980).
    [CrossRef]
  11. M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
    [CrossRef]
  12. H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
    [CrossRef] [PubMed]
  13. H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
    [CrossRef] [PubMed]
  14. H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27, 862–871 (1988).
    [CrossRef] [PubMed]
  15. P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
    [CrossRef] [PubMed]
  16. H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: influence of El Chichón,” Appl. Opt. 27, 3319–3321 (1988).
    [CrossRef] [PubMed]
  17. J. -M. André, A. Morel, “Simulated effects of barometric pressure and ozone content upon the estimate of marine phytoplankton from space,” J. Geophys. Res. 94C, 1029–1037 (1989).
    [CrossRef]
  18. S. Chandrasekhar, Radiative Transfer (Oxford, U. Press, Oxford, 1950), p. 393.
  19. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  20. H. C. van Hulst, Multiple Light Scattering (Academic, New York, 1980), 739.
  21. W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), 207.
  22. C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  23. T. Takashima, “Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface,” Earth Moon Planet 33, 59–97 (1985).
    [CrossRef]
  24. T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectros. Radiat. Transfer 29, 521–537 (1983).
    [CrossRef]
  25. B. G. Smith, “Geometrical Shadowing of a Random Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967).
    [CrossRef]
  26. R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Acoust. Soc. Am. 41, 138–148 (1967).
    [CrossRef]
  27. R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–626 (1966).
    [CrossRef]
  28. T. Nakajima, “Solar radiative transfer in the atmosphere and ocean system,” Ph.D. dissertation of (Tohoku University, Sendai, Japan, 1980).
  29. P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
    [CrossRef]
  30. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960), 584.
  31. Z. Ahmad, R. S. Fraser, “An iterative radiative transfer code for ocean atmosphere systems,” J. Atmos. Sci. 39, 656–665 (1982).
    [CrossRef]
  32. Z. Sekera, “The effect of sea surface reflection of the sky radiation,” Union Geodes. Geophys. Int. 10, 66–72 (1961).
  33. H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
    [CrossRef]
  34. J. Hsiung, “Mean surface energy fluxes over the global ocean,” J. Geophys. Res. 91C, 10,585–10,606 (1986).
  35. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 470.

1989 (1)

J. -M. André, A. Morel, “Simulated effects of barometric pressure and ozone content upon the estimate of marine phytoplankton from space,” J. Geophys. Res. 94C, 1029–1037 (1989).
[CrossRef]

1988 (2)

1987 (1)

1986 (1)

J. Hsiung, “Mean surface energy fluxes over the global ocean,” J. Geophys. Res. 91C, 10,585–10,606 (1986).

1985 (1)

T. Takashima, “Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface,” Earth Moon Planet 33, 59–97 (1985).
[CrossRef]

1984 (1)

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

1983 (3)

1982 (1)

Z. Ahmad, R. S. Fraser, “An iterative radiative transfer code for ocean atmosphere systems,” J. Atmos. Sci. 39, 656–665 (1982).
[CrossRef]

1981 (1)

1980 (4)

H. R. Gordon, D. K. Clark, “Atmospheric efforts in the remote sensing of phytoplankton pigments,” Boundary Layer Meterol. 18, 299–313 (1980).
[CrossRef]

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
[CrossRef]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

1978 (1)

1976 (1)

1974 (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1967 (3)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

B. G. Smith, “Geometrical Shadowing of a Random Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967).
[CrossRef]

R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Acoust. Soc. Am. 41, 138–148 (1967).
[CrossRef]

1966 (1)

R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–626 (1966).
[CrossRef]

1961 (1)

Z. Sekera, “The effect of sea surface reflection of the sky radiation,” Union Geodes. Geophys. Int. 10, 66–72 (1961).

1954 (1)

Ahmad, Z.

Z. Ahmad, R. S. Fraser, “An iterative radiative transfer code for ocean atmosphere systems,” J. Atmos. Sci. 39, 656–665 (1982).
[CrossRef]

Anderson, F.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

André, J. -M.

J. -M. André, A. Morel, “Simulated effects of barometric pressure and ozone content upon the estimate of marine phytoplankton from space,” J. Geophys. Res. 94C, 1029–1037 (1989).
[CrossRef]

Austin, R. W.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Baker, E. T.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Ball, D.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Brockelman, R. A.

R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–626 (1966).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Castano, D. J.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford, U. Press, Oxford, 1950), p. 393.

Clark, D. K.

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison between ship determinations and coastal zone color scanner estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Atmospheric efforts in the remote sensing of phytoplankton pigments,” Boundary Layer Meterol. 18, 299–313 (1980).
[CrossRef]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Coulson, K. L.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960), 584.

Cox, C.

Dave, J. V.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960), 584.

Deschamps, P. Y.

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
[CrossRef]

Evans, R. H.

Fraser, R. S.

Z. Ahmad, R. S. Fraser, “An iterative radiative transfer code for ocean atmosphere systems,” J. Atmos. Sci. 39, 656–665 (1982).
[CrossRef]

Gordon, H. R.

H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27, 862–871 (1988).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: influence of El Chichón,” Appl. Opt. 27, 3319–3321 (1988).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison between ship determinations and coastal zone color scanner estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Atmospheric efforts in the remote sensing of phytoplankton pigments,” Boundary Layer Meterol. 18, 299–313 (1980).
[CrossRef]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
[CrossRef] [PubMed]

H. R. Gordon, “Radiative transfer: a technique for simulating the ocean in satellite remote sensing calculations,” Appl. Opt. 15, 1974–1979 (1976).
[CrossRef] [PubMed]

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983), p. 114.

Hagfors, T.

R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–626 (1966).
[CrossRef]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Herman, M.

Hovis, W. A.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Hsiung, J.

J. Hsiung, “Mean surface energy fluxes over the global ocean,” J. Geophys. Res. 91C, 10,585–10,606 (1986).

Labs, D.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Morel, A.

J. -M. André, A. Morel, “Simulated effects of barometric pressure and ozone content upon the estimate of marine phytoplankton from space,” J. Geophys. Res. 94C, 1029–1037 (1989).
[CrossRef]

Morel, A. Y.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983), p. 114.

Mueller, J. L.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Munk, W.

Nakajima, T.

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectros. Radiat. Transfer 29, 521–537 (1983).
[CrossRef]

T. Nakajima, “Solar radiative transfer in the atmosphere and ocean system,” Ph.D. dissertation of (Tohoku University, Sendai, Japan, 1980).

Neckel, H.

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Saunders, P. M.

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

Sayed, S. Y. E.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Sekera, Z.

Z. Sekera, “The effect of sea surface reflection of the sky radiation,” Union Geodes. Geophys. Int. 10, 66–72 (1961).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960), 584.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), 207.

Smith, B. G.

B. G. Smith, “Geometrical Shadowing of a Random Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967).
[CrossRef]

Strum, B.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Takashima, T.

T. Takashima, “Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface,” Earth Moon Planet 33, 59–97 (1985).
[CrossRef]

Tanaka, M.

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectros. Radiat. Transfer 29, 521–537 (1983).
[CrossRef]

Tanre, D.

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
[CrossRef]

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 470.

van Hulst, H. C.

H. C. van Hulst, Multiple Light Scattering (Academic, New York, 1980), 739.

Viollier, M.

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
[CrossRef]

Wagner, R. J.

R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Acoust. Soc. Am. 41, 138–148 (1967).
[CrossRef]

Wilson, W. H.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Wrigley, R. C.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Yentsch, C. S.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Appl. Opt. (8)

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison between ship determinations and coastal zone color scanner estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, “Radiative transfer: a technique for simulating the ocean in satellite remote sensing calculations,” Appl. Opt. 15, 1974–1979 (1976).
[CrossRef] [PubMed]

H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27, 862–871 (1988).
[CrossRef] [PubMed]

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “The coastal zone color scanner atmospheric correction algorithm: influence of El Chichón,” Appl. Opt. 27, 3319–3321 (1988).
[CrossRef] [PubMed]

Boundary Layer Meterol. (1)

H. R. Gordon, D. K. Clark, “Atmospheric efforts in the remote sensing of phytoplankton pigments,” Boundary Layer Meterol. 18, 299–313 (1980).
[CrossRef]

Boundary Layer Meterolog. (1)

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary Layer Meterolog. 18, 247–267 (1980).
[CrossRef]

Earth Moon Planet (1)

T. Takashima, “Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface,” Earth Moon Planet 33, 59–97 (1985).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

B. G. Smith, “Geometrical Shadowing of a Random Rough Surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967).
[CrossRef]

R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–626 (1966).
[CrossRef]

J. Acoust. Soc. Am. (1)

R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Acoust. Soc. Am. 41, 138–148 (1967).
[CrossRef]

J. Atmos. Sci. (1)

Z. Ahmad, R. S. Fraser, “An iterative radiative transfer code for ocean atmosphere systems,” J. Atmos. Sci. 39, 656–665 (1982).
[CrossRef]

J. Geophys. Res. (3)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

J. Hsiung, “Mean surface energy fluxes over the global ocean,” J. Geophys. Res. 91C, 10,585–10,606 (1986).

J. -M. André, A. Morel, “Simulated effects of barometric pressure and ozone content upon the estimate of marine phytoplankton from space,” J. Geophys. Res. 94C, 1029–1037 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quant. Spectros. Radiat. Transfer (1)

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectros. Radiat. Transfer 29, 521–537 (1983).
[CrossRef]

Science (2)

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Sol. Phys. (1)

H. Neckel, D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
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Union Geodes. Geophys. Int. (1)

Z. Sekera, “The effect of sea surface reflection of the sky radiation,” Union Geodes. Geophys. Int. 10, 66–72 (1961).

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T. Nakajima, “Solar radiative transfer in the atmosphere and ocean system,” Ph.D. dissertation of (Tohoku University, Sendai, Japan, 1980).

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National Aeronautics and Space Administration and the Earth Observations Satellite Company, System Concept for Wide-Field-of-View Observations of Ocean Phenomena from Space (National Aeronautics and Space Administration, Washington, D.C., 1987).

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Figures (13)

Fig. 1
Fig. 1

Geometry of reflection from a tilted facet.

Fig. 2
Fig. 2

CZCS scan-center error in Ir for θ0 = 40°, σ = 0.10, and σ = 0.15.

Fig. 3
Fig. 3

CZCS scan-center error in Ir for θ0 = 40°, σ = 0.20, and σ = 0.30.

Fig. 4
Fig. 4

CZCS scan-center error in Ir for θ0 = 60°, σ = 0.10, and σ = 0.15.

Fig. 5
Fig. 5

CZCS scan-center error in Ir for θ0 = 60°, σ = 0.20, and σ = 0.30.

Fig. 6
Fig. 6

CZCS scan-edge error in Ir for θ0 = 40°, σ = 0.10, and σ = 0.15.

Fig. 7
Fig. 7

CZCS scan-edge error in Ir for θ0 = 40°, σ = 0.20, and σ = 0.30.

Fig. 8
Fig. 8

CZCS scan-edge error in Ir for θ0 = 60°, σ = 0.10, and σ = 0.15.

Fig. 9
Fig. 9

CZCS scan-edge error in Ir for θ0 = 40°, σ = 0.20, and σ = 0.30.

Fig. 10
Fig. 10

CZCS scan-edge variation in Ir for θ0 = 40° and 60°, resulting from surface-pressure variations of ± 15 mb.

Fig. 11
Fig. 11

CZCS scan-center and scan-edge variation in Ir for θ0 = 40°, resulting from ozone variations of ± 50 DU.

Fig. 12
Fig. 12

CZCS scan-center error in Ir computed by using the scalar theory for θ0 = 60°, σ = 0.20, and σ = 0.30.

Fig. 13
Fig. 13

CZCS scan-edge error in Ir computed by using the scalar theory for θ0 = 60°, σ = 0.20, and σ = 0.30.

Tables (3)

Tables Icon

Table I Quantization Increment DC (mW/cm2 μm sr) for Various CZCS Gains

Tables Icon

Table II Rough-Surface Error (in CZCS DC) for θ0 = 40° at Gain 2

Tables Icon

Table III Rough-Surface Error (in CZCS DC) for θ0 = 60° at Gain 3

Equations (53)

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L t = L r + L a + L g + t L w ,
L ( θ r , ϕ r ) = ρ + ( θ i ) L ( θ i , ϕ i ) ,
L ( θ r , ϕ r ) = 2 π r ( θ i , ϕ i θ r , ϕ r ) L ( θ i , ϕ i ) d Ω i ,
r ( θ 1 , ϕ 1 θ 2 , ϕ 2 ) = ρ + ( χ ) p ( θ 1 , ϕ 1 θ 2 , ϕ 2 ) S ( θ 1 , ϕ 1 θ 2 , ϕ 2 ) ,
p ( μ 1 , ϕ 1 μ 2 , ϕ 2 ) = 1 μ 2 a 2 exp ( 1 - 2 a σ 2 ) π σ 2 ,
μ 1 = cos θ 1 , μ 2 = cos θ 2 , cos 2 χ = - μ 1 μ 2 - [ ( 1 - μ 1 2 ) ( 1 - μ 2 2 ) ] 1 / 2 × cos ( ϕ 2 - ϕ 1 ) , a = ( 1 + cos 2 χ ) ( μ 1 - μ 2 ) 2 ,
σ 2 = 0.00534 W .
S ( μ 1 , ϕ 1 μ 2 , ϕ 2 ) = U ( v 1 ) ,
U ( v i ) = 1 1 + F ( v i ) ,
F ( v i ) = 1 2 [ exp ( - v i 2 ) π v i - 2 π v i exp ( - t 2 ) d t ] , v i = μ i σ 1 - μ i 2 ,
S ( μ 1 , ϕ 1 μ 2 , ϕ 2 ) = U ( v 1 ) U ( v 2 ) .
r ( μ i , ϕ i μ r , ϕ r ) = r ( 0 ) ( μ i μ r ) + 2 m = 1 r ( m ) ( μ i μ r ) cos m ( ϕ r - ϕ i ) ,
r ( m ) ( μ i μ r ) = 1 2 π 0 2 π r ( μ i , ϕ i μ r , ϕ r ) × cos m ( ϕ r - ϕ i ) d ϕ i .
L ( θ , ϕ ) = L ( 0 ) ( θ ) + 2 m = 1 L ( m ) ( θ ) cos m ( ϕ - ϕ 0 ) .
L ( m ) ( μ r ) = 2 π 0 1 r ( m ) ( μ i μ r ) L ( m ) ( μ i ) d μ i .
I r = FI i ,
F = [ ρ + ρ - 0 0 ρ - ρ + 0 0 0 0 ρ 33 0 0 0 0 ρ 33 ] , ρ ± ( θ i ) = 1 2 [ tan 2 ( θ i - θ t ) tan 2 ( θ i + θ t ) ± sin 2 ( θ i - θ t ) sin 2 ( θ i + θ t ) ] , ρ 33 ( θ i ) = - tan ( θ i - θ t ) tan ( θ i + θ t ) sin ( θ i - θ t ) sin ( θ i + θ t ) sin θ t = 1 n sin θ i .
I ( θ r , ϕ r ) = 2 π R ( θ i , ϕ i θ r , ϕ r ) I ( θ i , ϕ i ) d Ω i ,
I = L ( α ) I ,
L ( α ) = [ 1 0 0 0 0 cos 2 α sin 2 α 0 0 - sin 2 α cos 2 α 0 0 0 0 1 ] .
I r = L ( - α r ) FL ( α i ) I i .
R f = L ( - α r ) FL ( α i ) ,
I r = R f I i
R ( μ i , ϕ i μ r , ϕ r ) = p ( μ i , ϕ i μ r ϕ r ) × S ( μ i , ϕ i μ r , ϕ r ) × R f ( μ i , ϕ i μ r , ϕ r ) .
R = [ p + p - C i p - S i 0 C r p - C r p + C i + S r p 33 S i C r p + S i - S r p 33 C i 0 S r p - S r p + C i - C r p 33 S i S r p + S i + C r p 33 C i 0 0 0 0 p 33 ] ,
R i j ( μ i , ϕ i μ r , ϕ r ) = R i j ( 0 ) ( μ i , μ r ) + 2 m = 1 R i j ( m ) ( μ i , μ r ) cos m ( ϕ r - ϕ i ) ,
R ˜ i j ( μ i , ϕ i μ r , ϕ r ) = 2 m = 1 R ˜ i j ( m ) ( μ i , μ r ) × sin m ( ϕ r - ϕ i ) .
I = [ I ( θ , ϕ ) Q ( θ , ϕ ) U ˜ ( θ , ϕ ) V ˜ ( θ , ϕ ) ] = [ I ( 0 ) ( θ ) + 2 m = 1 I ( m ) ( θ ) cos m ( ϕ - ϕ 0 ) Q ( 0 ) ( θ ) + 2 m = 1 Q ( m ) ( θ ) cos m ( ϕ - ϕ 0 ) 2 m = 1 U ˜ ( m ) ( θ ) sin m ( ϕ - ϕ 0 ) 2 m = 1 V ˜ ( m ) ( θ ) sin m ( ϕ - ϕ 0 ) ] .
I ( m ) ( μ r ) = 2 π 0 1 d μ i [ R 11 ( m ) ( μ i , μ r ) I ( m ) ( μ i ) + R 12 ( m ) ( μ i , μ r ) Q ( m ) ( μ i ) - R ˜ 13 ( m ) ( μ i , μ r ) U ˜ ( m ) ( μ i ) ] , Q ( m ) ( μ r ) = 2 π 0 1 d μ i [ R 21 ( m ) ( μ i , μ r ) I ( m ) ( μ i ) + R 22 ( m ) ( μ i , μ r ) Q ( m ) ( μ i ) - R ˜ 23 ( m ) ( μ i , μ r ) U ˜ ( m ) ( μ i ) ] , U ˜ ( m ) ( μ r ) = 2 π 0 1 d μ i [ R ˜ 31 ( m ) ( μ i , μ r ) I ( m ) ( μ i ) + R ˜ 32 ( m ) ( μ i , μ r ) Q ( m ) ( μ i ) + R 33 ( m ) ( μ i , μ r ) U ˜ ( m ) ( μ i ) ] , V ˜ ( m ) ( μ r ) = 2 π 0 1 d μ i [ R 44 ( m ) ( μ i , μ r ) V ˜ ( m ) ( μ i ) ] .
I t = I r + I g ,
I g ( μ , ϕ ) = R ( μ 0 , ϕ 0 μ , ϕ ) I 0 exp ( - τ r μ - τ r μ 0 ) ,
I 0 = ( F 0 0 0 0 ) ,
τ r ( P + Δ P ) = P + Δ P P τ r ( P ) .
I r ( τ r ) = I r ( τ r ) [ 1 - exp ( - τ r / μ ) 1 - exp ( - τ r / μ ) ] ,
τ o 3 ( λ ) = a o 3 ( λ ) C o 3 ,
I r ( C o 3 + Δ C o 3 ) = I r ( C o 3 ) exp - [ Δ τ o 3 ( 1 μ + 1 μ 0 ) ] ,
cos θ d L ( τ ; θ , ϕ ) d r = - L ( τ ; θ ; ϕ ) + J ( τ ; θ , ϕ ) .
J ( τ ; θ , ϕ ) = 1 4 π 0 π d θ 0 2 π d ϕ sin θ × p ( τ ; θ , ϕ θ , ϕ ) L ( τ ; θ , ϕ ) ,
L ( 0 ; θ , ϕ ) = F 0 δ ( cos θ - cos θ 0 ) δ ( ϕ - ϕ 0 ) ,             θ 0 < π / 2.
cos θ d L ( m ) ( τ ; θ ) d τ = - L ( m ) ( τ ; θ ) + J ( m ) ( τ ; θ ) ,
J ( m ) ( τ ; θ ) = 1 2 0 π d θ sin θ × p ( m ) ( τ ; θ θ ) L ( m ) ( τ ; θ ) .
p ( τ ; θ , ϕ θ , ϕ ) = p ( 0 ) ( τ ; θ θ ) + 2 × m = 1 p ( m ) ( τ ; θ θ ) cos m ( ϕ - ϕ ) ,
p ( m ) ( τ ; θ θ ) = 1 2 π 0 2 π p ( τ ; θ , ϕ θ , ϕ ) × cos m ( ϕ - ϕ ) d ϕ ,
I = ( I Q U V ) ,
P = ( Q 2 + U 2 + V 2 ) 1 / 2 I ,
cos θ d I ( τ ; θ , ϕ ) d τ = - I ( τ ; θ , ϕ ) + J ( τ ; θ , ϕ ) .
J ( τ ; θ , ϕ ) = 1 4 π 0 π d θ 0 2 π d ϕ sin θ × Z ( τ ; θ , ϕ θ , ϕ ) I ( τ ; θ , ϕ ) ,
p ( τ ; θ , ϕ θ , ϕ ) = Z 11 ( τ ; θ , ϕ θ , ϕ ) .
Z = [ Z 11 Z 12 Z ˜ 13 Z ˜ 14 Z 21 Z 22 Z ˜ 23 Z ˜ 24 Z ˜ 31 Z ˜ 32 Z 33 Z 34 Z ˜ 41 Z ˜ 42 Z 43 Z 44 ] ,
I = [ I ( θ , ϕ ) Q ( θ , ϕ ) U ˜ ( θ , ϕ ) V ˜ ( θ , ϕ ) ] '
cos θ d I ( m ) ( τ ; θ ) d τ = - I ( m ) ( τ ; θ ) + J ( m ) ( τ ; θ ) ,
J 1 ( m ) = 1 2 0 π sin θ d θ × [ Z 11 ( m ) I ( m ) + Z 12 ( m ) Q ( m ) - Z ˜ 13 ( m ) U ˜ ( m ) - Z ˜ 14 ( m ) V ˜ ( m ) ] ,
I ( 0 ; θ , ϕ ) = ( F 0 0 0 0 ) δ ( cos θ - cos θ 0 ) δ ( ϕ - ϕ 0 ) ,             θ 0 < π / 2.

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