Abstract

We investigate the influence of the curvature of the Earth on a proposed atmospheric-correction scheme for the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) by simulating the radiance exiting the top of a spherical-shell atmosphere and inserting the result into the proposed correction algorithm. The error in the derived water-leaving reflectance suggests that the effects of the curvature are negligible for solar zenith angles (θ0) ≤ 70°. Furthermore, for θ0 > 70° the error in atmospheric correction can usually be reduced if the molecular-scattering component of the top of the atmosphere reflectance (ρr) is computed with a spherical-shell atmosphere radiative transfer code. Also, for θ0 > 70° the error in atmospheric correction in a spherical-shell atmosphere, when ρr is computed with a spherical-shell model, can be predicted reasonably well from computations made with plane-parallel atmosphere radiative transfer codes. This implies that studies aimed at improving atmospheric correction can be made assuming plane-parallel geometry and that the investigator can be confident when θ0 > 70° that any improvements will still be valid for a spherical-shell atmosphere as long as ρr is computed in spherical-shell geometry. Finally, a scheme for computing ρr in a spherical-shell atmosphere in a relatively simple manner is developed.

© 1994 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).
  4. T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
    [CrossRef] [PubMed]
  5. A. Morel, J. -M. André, “Pigment distribution and primary production in the western Mediterranean as derived and modeled from coastal zone color scanner observations,” J. Geophys. Res. 96, 12685–12698 (1991).
    [CrossRef]
  6. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
    [CrossRef] [PubMed]
  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 CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  8. G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
    [CrossRef]
  9. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).
  10. V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
    [CrossRef]
  11. H. R. Gordon, D. J. Castafio, “Coastal Zone Color Scanner atmopsheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
    [CrossRef] [PubMed]
  12. 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]
  13. H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I: The Rayleigh-scattering component,” Appl. Opt. 31, 4247–4260 (1992).
    [CrossRef] [PubMed]
  14. H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. II: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
    [CrossRef] [PubMed]
  15. H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo calculations of the polarization characteristics of the radiation emerging from spherical shell atmospheres,” Appl. Opt. 11, 2684–2696 (1972).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. K. Ding, “Radiative transfer in spherical shell atmospheres for correction of ocean color remote sensing,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1993).
  20. M. Wang, “Atmospheric correction of the second generation ocean color sensors,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1991).
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    [CrossRef]
  22. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).
  23. F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).
  24. P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
    [CrossRef]
  25. K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
    [CrossRef]

1994

1992

1991

A. Morel, J. -M. André, “Pigment distribution and primary production in the western Mediterranean as derived and modeled from coastal zone color scanner observations,” J. Geophys. Res. 96, 12685–12698 (1991).
[CrossRef]

1990

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

1989

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

1988

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]

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

1987

1985

1983

1980

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

C. N. Adams, G. W. Kattawar, “Radiative transfer in spherical shell atmospheres. I. Rayleigh scattering,” Icarus 35, 139–151 (1978).
[CrossRef]

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

1972

1957

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

1954

Abreu, L. W.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

Adams, C. N.

C. N. Adams, G. W. Kattawar, “Radiative transfer in spherical shell atmospheres. I. Rayleigh scattering,” Icarus 35, 139–151 (1978).
[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.

A. Morel, J. -M. André, “Pigment distribution and primary production in the western Mediterranean as derived and modeled from coastal zone color scanner observations,” J. Geophys. Res. 96, 12685–12698 (1991).
[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]

Barnes, W. L.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Blattner, W. G.

Broenkow, W. W.

Brown, J.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Brown, J. W.

Brown, O. B.

Carle, M.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Case, K. M.

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

Castafio, D. J.

Chetwynd, J. H.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

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 CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[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]

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]

Clough, S. A.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

Collins, D. G.

Cox, C.

Deluisi, J. J.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Ding, K.

K. Ding, “Radiative transfer in spherical shell atmospheres for correction of ocean color remote sensing,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1993).

Elrod, J.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Endres, D.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Esaias, W.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Evans, R.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Evans, R. H.

Feldman, G. C.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Fenn, R. W.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).

Gallery, W. O.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

Gordon, H. R.

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I: The Rayleigh-scattering component,” Appl. Opt. 31, 4247–4260 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. II: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[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]

H. R. Gordon, D. J. Castafio, “Coastal Zone Color Scanner atmopsheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. R. Gordon, “Ship perturbation of irradiance measurements at sea. 1: Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
[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 CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[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]

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

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Horak, H. G.

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]

Kattawar, G. W.

C. N. Adams, G. W. Kattawar, “Radiative transfer in spherical shell atmospheres. I. Rayleigh scattering,” Icarus 35, 139–151 (1978).
[CrossRef]

Kenizys, F. X.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

Kim, Y.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Kreiner, F. W.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Kuring, N.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Maymon, P. W.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Maynard, N.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

McClain, C. R.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Montgomery, H. E.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Morel, A.

A. Morel, J. -M. André, “Pigment distribution and primary production in the western Mediterranean as derived and modeled from coastal zone color scanner observations,” J. Geophys. Res. 96, 12685–12698 (1991).
[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).

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.

Ng, C.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Ostrow, H.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Platt, T.

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

Podesta, G.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Reddy, P. J.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Salomonson, V. V.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Sathyendranath, S.

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[CrossRef] [PubMed]

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]

Selby, J. E. A.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

Shettle, E. P.

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).

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]

Walsh, S.

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Wang, M.

Wells, M. B.

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.

D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo calculations of the polarization characteristics of the radiation emerging from spherical shell atmospheres,” Appl. Opt. 11, 2684–2696 (1972).
[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. 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 CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, “Ship perturbation of irradiance measurements at sea. 1: Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
[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]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I: The Rayleigh-scattering component,” Appl. Opt. 31, 4247–4260 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. II: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castafio, “Coastal Zone Color Scanner atmopsheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

EOS Trans. Am. Geophys. Union

G. C. Feldman, N. Kuring, C. Ng, W. Esaias, C. R. McClain, J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S. Walsh, M. Carle, G. Podesta, “Ocean color: availability of the global data set,” EOS Trans. Am. Geophys. Union 70, 634–641 (1989).
[CrossRef]

Global Biogeochem. Cycles

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Icarus

C. N. Adams, G. W. Kattawar, “Radiative transfer in spherical shell atmospheres. I. Rayleigh scattering,” Icarus 35, 139–151 (1978).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

J. Geophys. Res.

A. Morel, J. -M. André, “Pigment distribution and primary production in the western Mediterranean as derived and modeled from coastal zone color scanner observations,” J. Geophys. Res. 96, 12685–12698 (1991).
[CrossRef]

J. Opt. Soc. Am.

Rev. Mod. Phys.

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29, 651–663 (1957).
[CrossRef]

Science

T. Platt, S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241, 1613–1620 (1988).
[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, 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]

Other

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

K. Ding, “Radiative transfer in spherical shell atmospheres for correction of ocean color remote sensing,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1993).

M. Wang, “Atmospheric correction of the second generation ocean color sensors,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1991).

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-TR-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, 1983).

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

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Figures (9)

Fig. 1
Fig. 1

Geometry of the radiative transfer problem for the SSA model.

Fig. 2
Fig. 2

Example of the two contributions to the radiance in the presence of a Fresnel-reflecting sea surface.

Fig. 3
Fig. 3

Error in atmospheric correction at 443 nm with τa(865) = 0.2: (a) Maritime model at the scan center, (d) Maritime model at the scan edge, (b) Coastal model at the scan center, (e) Coastal model at the scan edge, (c) Tropospheric model at the scan center, (f) Tropospheric model the scan edge.

Fig. 4
Fig. 4

Quantity Mssa/Mppa changes very slowly with θ0 for different SeaWiFS bands. The curves from top to bottom refer to λ = 412, 550, 670, and 865 nm, ϕ = 90°, with (a) θ = 5°, (b) θ = 20°, (c) θ = 40°, and (d) θ = 60°.

Fig. 5
Fig. 5

α parameter as a function of θ (ϕ = 90°) at θ0 = 40° is shown for different SeaWiFS bands. The curves from top to bottom refer to λ = 412, 550, 670, and 865 nm.

Fig. 6
Fig. 6

Geometry in the absolute frame.

Fig. 7
Fig. 7

Geometry in the local frame.

Fig. 8
Fig. 8

Geometric quantities and definitions used in the calculation of the single-scattering radiance for the SSA-modeled atmosphere.

Fig. 9
Fig. 9

Definitions of the geometric quantities used in the determination of the specular direction.

Tables (3)

Tables Icon

Table 1 Comparison of the Radiometric Performance of SeaWiFS and CZCS for θ0 = 60° Near the Scan Edge

Tables Icon

Table 2 Errors in Estimating the SSA Total Rayleigh Radiance with λ = 412 nm and ϕ = 90°

Tables Icon

Table 3 Errors in Estimating the SSA Total Rayleigh Radiance with λ = 865nm and ϕ = 90°

Equations (32)

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ξ ^ · L ( r , ξ ^ ) = - c ( r ) L ( r , ξ ^ ) + β ( r , ξ ^ ξ ^ ) × L ( r , ξ ^ ) d Ω ( ξ ^ ) + J ( r , ξ ^ ) ,
b ( r ) = β ( r , ξ ^ ξ ^ ) d Ω ( ξ ^ )
L = F 0 i ( ω 0 P T ) i N ,
ρ t ( λ ) = ρ r ( λ ) + ρ a ( λ ) + ρ r a ( λ ) + t ρ w ( λ ) ,
S SSA T SSA S PPA T PPA
α M SSA M PPA
β M SSA T SSA = α M PPA T SSA
β α M PPA T PPA .
T SSA = S SSA 1 - β ,
s ^ = ( sin θ 0 , 0 , cos θ 0 ) .
v ^ = ( sin θ cos ϕ , sin θ sin ϕ , cos θ ) .
cos ω = ( R E + h ) + l cos θ R ,
l = - ( R E + h ) cos θ - [ R 2 + ( R E + h ) 2 ( cos 2 θ - 1 ) ] 1 / 2 .
z ^ = ( sin ω cos ϕ , sin ω sin ϕ , cos ω ) .
cos θ 0 = s ^ · z ^ = sin θ 0 sin ω cos ϕ + cos θ 0 cos ω .
y ^ = z ^ × s ^ z ^ × s ^ ,
y ^ = 1 sin θ 0 [ ( cos θ 0 sin ω sin ϕ ) x ^ + ( sin θ 0 cos ω - cos θ 0 sin ω cos ϕ ) y ^ + ( - sin θ 0 sin ω sin ϕ ) z ^ ] .
x ^ = y ^ × z ^ = 1 sin θ 0 { [ cos ω ( sin θ 0 cos ω - cos θ 0 sin ω cos ϕ ) + sin θ 0 sin 2 ω sin 2 ϕ ] x ^ + ( - sin θ 0 sin 2 ω × sin ϕ cos ϕ - cos θ 0 sin ω cos ω sin ϕ ) y ^ + [ cos θ 0 sin 2 ω sin 2 ϕ - sin ω cos ϕ ( sin θ 0 cos ω - cos θ 0 sin ω cos ϕ ) ] z ^ } .
cos θ = v ^ · z ^ = cos ( θ - ω ) .
v ^ · x ^ = sin θ cos ϕ v ^ · y ^ = sin θ sin ϕ .
sin ϕ = sin θ 0 sin ϕ sin ( θ - ω ) sin θ 0 sin θ cos ϕ = 1 sin θ 0 sin θ [ sin θ cos ω ( cos ω sin θ 0 cos ϕ - sin ω cos θ 0 ) + cos θ sin ω ( cos θ 0 sin ω - sin θ 0 cos ω cos ϕ ) ] .
cos θ 0 = cos θ 0 cos ω - sin θ 0 sin ω cos ϕ cos θ = cos ( θ + ω ) sin ϕ = sin θ 0 sin ϕ sin ( θ + ω ) sin θ 0 sin θ cos ϕ = 1 sin θ 0 sin θ [ sin θ cos ω ( cos ω sin θ 0 cos ϕ + sin ω cos θ 0 ) + cos θ sin ω ( cos θ 0 sin ω + sin θ 0 cos ω cos ϕ ) ] ,
cos ω = ( R E + h ) - l cos θ R
l = ( R E + h ) cos θ - [ R 2 + ( R E + h ) 2 ( cos θ 2 - 1 ) ] 1 / 2 .
cos θ 0 = cos θ 0 cos ω cos θ = cos ( θ + ω ) sin ϕ = sin θ 0 sin ( θ + ω ) sin θ 0 sin θ cos ϕ = sin ω cos θ 0 sin ( θ + ω ) sin θ 0 sin θ .
L = L 1 + L 2 + L 3 .
L 1 = F 0 P ( Θ 1 ) AB exp [ - ( c l AE ) ] exp [ - ( c l EF ) ] c d l ,
L 2 = F 0 P ( Θ 2 ) R F ( α ) exp [ - AB c d l ] BC × exp [ - ( c l BG ) ] exp [ - ( c l GH ) ] c d l ,
θ t = sin - 1 ( r 0 r 0 + h ) ,
L 3 = F 0 AB P ( Θ 3 ) R F ( β ) exp [ - ( c l AE ) exp [ - ( c l EP ) ] × exp [ - ( c l PQ ) c d l ,
cos ( ω s - ω ) = R sin 2 ω + cos ω ( 1 - R 2 sin 2 ω ) 1 / 2 ,
α α d + β β d + γ γ d = cos ( 180 - 2 ω + ω s ) , α s α d + β s β d + γ s γ d = cos ( 180 - 2 ω ) , ( β γ s - γ β s ) α d + ( γ α s - α γ s ) β d + ( α β s - β α s ) γ d = 0 ,

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