Abstract

When strongly absorbing aerosols are present in the atmosphere, the usual two-step procedure of processing ocean color data—(1) atmospheric correction to provide the water-leaving reflectance (ρw), followed by (2) relating ρw to the water constituents—fails and simultaneous estimation of the ocean and aerosol optical properties is necessary. We explore the efficacy of using a simple model of the aerosol—a Junge power-law size distribution consisting of homogeneous spheres with arbitrary refractive index—in a nonlinear optimization procedure for estimating the relevant oceanic and atmospheric parameters for case 1 waters. Using simulated test data generated from more realistic aerosol size distributions (sums of log-normally distributed components with different compositions), we show that the ocean’s pigment concentration (C) can be retrieved with good accuracy in the presence of weakly or strongly absorbing aerosols. However, because of significant differences in the scattering phase functions for the test and power-law distributions, large error is possible in the estimate of the aerosol optical thickness. The positive result for C suggests that the detailed shape of the aerosol-scattering phase function is not relevant to the atmospheric correction of ocean color sensors. The relevant parameters are the aerosol single-scattering albedo and the spectral variation of the aerosol optical depth. We argue that the assumption of aerosol sphericity should not restrict the validity of the algorithm and suggest an avenue for including colored aerosols, e.g., wind-blown dust, in the procedure. A significant advantage of the new approach is that realistic multicomponent aerosol models are not required for the retrieval of C.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
  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]
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  4. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.
  5. 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 Geosci. Remote Sensing 27, 145–152 (1989).
    [CrossRef]
  6. H. R. Gordon, “Radiative transfer: a technique for simulating the ocean in satellite remote sensing calculations,” Appl. Opt. 15, 1974–1979 (1976).
    [CrossRef] [PubMed]
  7. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
    [CrossRef] [PubMed]
  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]
  9. 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]
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    [CrossRef]
  12. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Airforce Base, Mass., 1979).
  13. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
    [CrossRef]
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    [CrossRef]
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  16. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  17. 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]
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    [CrossRef]
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    [CrossRef]
  25. M. J. D. Powell, “Some global convergence properties of a variable metric algorithm for minimization without exact line searches,” AERE Harwell Rep. CSS15 (Atomic Energy Research Establishment, Harwell, Oxfordshire, UK, 1975).
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    [CrossRef] [PubMed]
  28. H. R. Gordon, “In-orbit calibration strategy for ocean color sensors,” Remote Sensing Environ. 63, 265–278 (1998).
    [CrossRef]
  29. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]
  30. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
    [CrossRef]
  31. G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

1998 (1)

H. R. Gordon, “In-orbit calibration strategy for ocean color sensors,” Remote Sensing Environ. 63, 265–278 (1998).
[CrossRef]

1997 (4)

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
[CrossRef]

F. Zhao, T. Nakajima, “Simultaneous determination of water-leaving reflectance and aerosol optical thickness from Coastal Zone Color Scanner measurements,” Appl. Opt. 36, 6949–6956 (1997).
[CrossRef]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the earth observing system era,” J. Geophys. Res. D 102, 17,081–17,106 (1997).
[CrossRef]

H. R. Gordon, T. Du, T. Zhang, “Remote sensing of ocean color and aerosol properties: resolving the issue of aerosol absorption,” Appl. Opt. 36, 8670–8684 (1997).
[CrossRef]

1996 (1)

1995 (1)

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. C 100, 13,143–13,150 (1995).
[CrossRef]

1994 (3)

1993 (1)

1991 (1)

1989 (1)

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 Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

1988 (2)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
[CrossRef]

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]

1983 (1)

1980 (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]

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]

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]

1972 (1)

P. E. Gill, W. Murray, “Quasi-Newton methods for uncostrained optimization,” J. Inst. Maths. Its Appl. 9, 91–108 (1972).
[CrossRef]

1958 (1)

C. Junge, “Atmospheric chemistry,” Adv. Geophys. 4, 1–108 (1958).
[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]

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]

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
[CrossRef]

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 Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
[CrossRef]

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]

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]

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Du, T.

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.

Evans, R. H.

Feldman, G. C.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.

Fenn, R. W.

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

Fletcher, R.

R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1980), Vols. 1 and 2.

Gentili, B.

Gill, P. E.

P. E. Gill, W. Murray, “Quasi-Newton methods for uncostrained optimization,” J. Inst. Maths. Its Appl. 9, 91–108 (1972).
[CrossRef]

Gordon, H. R.

H. R. Gordon, “In-orbit calibration strategy for ocean color sensors,” Remote Sensing Environ. 63, 265–278 (1998).
[CrossRef]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the earth observing system era,” J. Geophys. Res. D 102, 17,081–17,106 (1997).
[CrossRef]

H. R. Gordon, T. Du, T. Zhang, “Remote sensing of ocean color and aerosol properties: resolving the issue of aerosol absorption,” Appl. Opt. 36, 8670–8684 (1997).
[CrossRef]

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]

M. Wang, H. R. Gordon, “Estimating aerosol optical properties over the oceans with the multiangle imaging spectroradiometer: some preliminary studies,” Appl. Opt. 33, 4042–4057 (1994).
[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, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
[CrossRef]

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, 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).
[CrossRef]

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.

Hansen, J. E.

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

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.

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]

Junge, C.

C. Junge, “Atmospheric chemistry,” Adv. Geophys. 4, 1–108 (1958).
[CrossRef]

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
[CrossRef]

Koepke, P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

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 Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

McClain, C. R.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, “SeaWiFS Technical Report Series: an Overview of SeaWiFS and Ocean Color,” NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992), Vol. 1.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

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 Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Morel, A.

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).
[CrossRef]

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]

Murray, W.

P. E. Gill, W. Murray, “Quasi-Newton methods for uncostrained optimization,” J. Inst. Maths. Its Appl. 9, 91–108 (1972).
[CrossRef]

Nakajima, T.

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 Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Powell, M. J. D.

M. J. D. Powell, “Some global convergence properties of a variable metric algorithm for minimization without exact line searches,” AERE Harwell Rep. CSS15 (Atomic Energy Research Establishment, Harwell, Oxfordshire, UK, 1975).

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 Geosci. Remote Sensing 27, 145–152 (1989).
[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]

Shettle, E. P.

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

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semi-analytic radiance model of ocean color,” J. Geophys. Res. D 93, 10,909–10,924 (1988).
[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]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

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

Voss, K. J.

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. C 100, 13,143–13,150 (1995).
[CrossRef]

Wang, M.

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented spheroids,” J. Geophys. Res. D 102, 16,831–16,847 (1997).
[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).
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Figures (8)

Fig. 1
Fig. 1

Relationship between ε′(765, 865) and ν (solid curve) averaged over all combinations of four values of τ a (865) (0.1, 0.2, 0.3, and0.4), six values of m i (0, 0.001, 0.003, 0.01, 0.03, and 0.04), and two values of m r (1.333 and 1.50), with θ0 = 20° and θ = 45.9°. Dashed curves represent the upper and lower envelopes of the relationship, and the darker area represents the standard deviation of the various cases about the mean for the given value of ν.

Fig. 2
Fig. 2

Spectral variation of the aerosol optical thickness for the models used to generate the test pseudodata.

Fig. 3
Fig. 3

Comparison between the volume size distribution of the aerosol models used to generate the test pseudodata (solid curves) and the Junge power-law distribution (dotted curves).

Fig. 4
Fig. 4

Comparison between the given (curves) and the retrieved (symbols) reflectances by use of the Junge power-law size distribution for θ = 1.02° (i.e., near nadir): (a) M80 with θ0 = 20°, (b) U80 with θ0 = 20°, (c) M80 with θ0 = 60°, and (d) U80 with θ0 = 60°. Unprimed parameters are the true values; primed parameters are the retrieved values.

Fig. 5
Fig. 5

Comparison of the true (solid curve) and retrieved (dashed curve) phase functions at 865 nm. The retrieved phase function is used to derive the aerosol optical thickness in Figs. 4(c) and 4(d): (a) M80 and (b) U80.

Fig. 6
Fig. 6

Comparison between the given (curves) and the retrieved (symbols) reflectances by use of the Junge power-law size distribution for θ = 1.02° (i.e., near nadir): (a) T80 with θ0 = 20° and (b) T80 with θ0 = 60°. Unprimed parameters are the true values; primed parameters are the retrieved values.

Fig. 7
Fig. 7

Comparison between the given (curves) and the retrieved (symbols) reflectances by use of the Junge power-law size distribution for θ = 1.02° (i.e., near nadir) in the presence of the calibration errors in Table 7: (a) M80 with θ0 = 60° and positive calibration error, (b) M80 with θ0 = 60° and negative calibration error, (c) U80 with θ0 = 60° and positive calibration error, and (d) U80 with θ0 = 60° and negative calibration error. Unprimed parameters are the true values, primed parameters are the retrieved values, and ρ c represents the calibration error.

Fig. 8
Fig. 8

Comparison between the given (curves) and the retrieved (symbols) reflectances by use of the Junge power-law size distribution for θ0 = 20° and θ = 1.02° (i.e., near nadir) for cases in which the aerosol is uniformly mixed with air from the surface to an altitude h: (a) U80 aerosol with h = 2 km (U280) and (b) U80 aerosol with h = 4 km (U480). Unprimed parameters are the true values; primed parameters are the retrieved values.

Tables (10)

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Table 1 Characteristics of the Test Aerosol Models used in the Study

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Table 2 Values of Single-Scattering Albedo at λ = 412 and 865 nm for the Test Aerosol Models used in the Study

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Table 3 Retrieval of Aerosol’s Single-Scattering Albedoa

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Table 4 Retrieval of Ocean’s Pigment Concentrationa

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Table 5 Retrieval of Water Scattering Parametera

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Table 6 Mean SLSQ and its Standard Deviation σS (both in %), over all Values of τa(865), C, and Sun-Viewing Geometries

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Table 7 Values of the Residual Radiometric Calibration Uncertainty after Effecting an In-Orbit Calibration Adjustmenta

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Table 8 Retrieval of Ocean’s Pigment Concentration with Negative Calibration Errora

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Table 9 Retrieval of Ocean’s Pigment Concentration with Positive Calibration Errora

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Table 10 Retrieval of Ocean’s Pigment Concentrationa

Equations (10)

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

ρ t λ = ρ r λ + ρ a λ + ρ ra λ + t λ ρ w λ ,
ρ t λ - ρ r λ = ρ a λ + ρ ra λ + t λ ρ w λ .
d N d D = K ,   D 0 < D D 1 , = K D 1 D ν + 1 ,   D 1 < D D 2 , = 0 ,   D > D 2 ,
ε λ s ,   λ = ρ a λ s + ρ ra λ s ρ a λ + ρ ra λ ,
ρ A λ j ;   m i ,   m r ρ a λ j ;   m i ,   m r + ρ ra λ j ,   m i ,   m r , ρ W λ j ;   C ,   b 0 t λ j ρ w λ j ;   C ,   b 0 ,
ρ A λ 1 ;   m i ,   m r + ρ W λ 1 ;   C ,   b 0 = ρ t λ 1 - ρ r λ 1 , ρ A λ 2 ;   m i ,   m r + ρ W λ 2 ;   C ,   b 0 = ρ t λ 2 - ρ r λ 2 , …………… ρ A λ N ν ;   m i ,   m r + ρ W λ N ν ;   C ,   b 0 = ρ t λ N ν - ρ r λ N ν .
0 m i min m i m i max , 0 < m r min m r m r max , 0 < C min C C max , 0 < b 0 min b 0 b 0 max .
S LSQ 2 m i ,   m r ,   C ,   b 0 = 1 N ν - 1 × i = 1 N ν ρ A λ j ;   m i ,   m r + ρ W λ j ;   C ,   b 0 ρ t λ j - ρ r λ j - 1 2 .
d N d D = i = 1 M d N i d D ,
d N i d D = N i log e 10 2 π σ i D exp - 1 2 log 10 D / D i σ i ,

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