Abstract

The second generation of ocean-color-analyzing instruments requires more accurate atmospheric correction than does the Coastal Zone Color Scanner (CZCS), if one is to utilize fully their increased radiometric sensitivity. Unlike the CZCS, the new instruments possess bands in the near infrared (NIR) that are solely for aiding atmospheric correction. We show, using aerosol models, that certain assumptions regarding the spectral behavior of the aerosol reflectance employed in the standard CZCS correction algorithm are not valid over the spectral range encompassing both the visible and the NIR. Furthermore, we show that multiple-scattering effects on the algorithm depend significantly on the aerosol model. Following these observations, we propose an algorithm that utilizes the NIR bands for atmospheric correction to the required accuracy. Examples of the dependence of the error on the aerosol model, the turbidity of the atmosphere, and surface roughness (waves) are provided. The error in the retrieved phytoplankton-pigment concentration (the principal product of ocean-color sensors) induced by errors in the atmospheric correction are shown to be <20% in approximately 90% of the cases examined. Finally, the aerosol thickness (τa) is estimated through a simple extension of the correction algorithm. Simulations suggest that the error in the recovered value of τa should be ≲ 10%.

© 1994 Optical Society of America

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1993 (1)

1992 (4)

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: 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. 2: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

1991 (1)

J.-M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanologica Acta 14, 3–22 (1991).

1990 (1)

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 Biogeochemic. Cycles 4, 225–240 (1990).
[CrossRef]

1989 (3)

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]

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 3: Variability in angular scattering patterns,” Appl. Opt. 28, 3061–3073 (1989).
[CrossRef] [PubMed]

1988 (2)

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. 93D, 10909–10924 (1988).
[CrossRef]

1987 (3)

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanologica Acta 7, 33–50 (1987).

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo, and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

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]

1986 (2)

P. A. Durkee, D. R. Jensen, E. E. Hindman, T. H. V. Haar, “The relationship between marine aerosol particles and satellite-detected radiance,” J. Geophys. Res. 91D, 4063–4072 (1986).
[CrossRef]

E. C. Monahan, I. G. O’Muircheartaigh, “Whitecaps and the passive remote sensing of the ocean surface,” Int. J. Remote Sensing 7, 627–642 (1986).
[CrossRef]

1984 (1)

1983 (2)

1981 (2)

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum wavelength,” J. Geophys. Res. 86, 9801–9805 (1981).
[CrossRef]

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]

1980 (4)

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

M. Viollier, D. Tanre, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary-Layer Meteorol. 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]

1979 (1)

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum viewing geometry,” J. Geophys. Res. 84, 7847–7856 (1979).
[CrossRef]

1978 (1)

1977 (1)

Y. Mekler, H. Quenzel, G. Ohring, I. Marcus, “Relative atmospheric aerosol content from ERTS observations,” J. Geophys. Res. 82, 967–970 (1977).
[CrossRef]

1976 (2)

1975 (1)

M. Griggs, “Measurements of the aerosol optical thickness over water using ERTS-1 data,” J. Air Pollut. Control Assoc. 25, 622–626 (1975).
[CrossRef] [PubMed]

1958 (1)

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

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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

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, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanologica Acta 14, 3–22 (1991).

Andreae, M. O.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo, and climate,” Nature (London) 326, 655–661 (1987).
[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]

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. 93D, 10909–10924 (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 Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Bricaud, A.

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanologica Acta 7, 33–50 (1987).

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]

Castano, D. J.

Cess, R.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

Cess, R. D.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Charlson, R. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo, and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

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. 93D, 10909–10924 (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, “Clear water radiances for atmospheric correction of Coastal Zone Color Scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[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]

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

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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Coakley, J. A.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

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 Biogeochemic. Cycles 4, 225–240 (1990).
[CrossRef]

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 Meteorol. 18, 247–267 (1980).
[CrossRef]

Durkee, P. A.

P. A. Durkee, D. R. Jensen, E. E. Hindman, T. H. V. Haar, “The relationship between marine aerosol particles and satellite-detected radiance,” J. Geophys. Res. 91D, 4063–4072 (1986).
[CrossRef]

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, SeaWiFS Technical Report Series: Volume 1, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

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.

Falkowski, P. G.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

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, SeaWiFS Technical Report Series: Volume 1, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 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, Hanscom Air Force Base, Mass., 1979).

Fraser, R. S.

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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Gordon, H. R.

M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. 2: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: Rayleigh scattering component,” Appl. Opt. 31, 4247–4260 (1992).
[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. 93D, 10909–10924 (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]

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]

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, “Atmospheric effects in the remote sensing of phytoplankton pigments,” Boundary-Layer Meteorol. 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]

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).

M. Wang, H. R. Gordon, “Remote sensing of environment,” a simple, moderately accurate, atmospheric correction algorithm for SeaWiFS, (submitted to Remote Sensing Environ.).

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, SeaWiFS Technical Report Series: Volume 1, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

Griggs, M.

M. Griggs, “Measurements of the aerosol optical thickness over water using ERTS-1 data,” J. Air Pollut. Control Assoc. 25, 622–626 (1975).
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M. Griggs, Satellite Measurements of Tropospheric Aerosols, NASA Contractor Rep. 3459 (NASA Langley Research Center, Hampton, Va., August1981).

M. Griggs, AVHRR Aerosol Ground Truth Experiment, Final Rep. contract NA–83–SAC–00106 (National Oceanic and Atmospheric Administration, National Environmental Satellite Service, Washington, D.C., January1984).

M. Griggs, AVHRR Measurements of Atmospheric Aerosols Over Oceans, NOAA Final Rep. contract M0–A01–78–00–4092 (National Oceanic and Atmospheric Administration, National Environmental Satellite Service, Washington, D.C., November1981).

Haar, T. H. V.

P. A. Durkee, D. R. Jensen, E. E. Hindman, T. H. V. Haar, “The relationship between marine aerosol particles and satellite-detected radiance,” J. Geophys. Res. 91D, 4063–4072 (1986).
[CrossRef]

Hales, J. M.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Hansen, J. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Herman, M.

Hindman, E. E.

P. A. Durkee, D. R. Jensen, E. E. Hindman, T. H. V. Haar, “The relationship between marine aerosol particles and satellite-detected radiance,” J. Geophys. Res. 91D, 4063–4072 (1986).
[CrossRef]

Hofmann, D. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, SeaWiFS Technical Report Series: Volume 1, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

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]

Jensen, D. R.

P. A. Durkee, D. R. Jensen, E. E. Hindman, T. H. V. Haar, “The relationship between marine aerosol particles and satellite-detected radiance,” J. Geophys. Res. 91D, 4063–4072 (1986).
[CrossRef]

Junge, C.

C. Junge, “Atmospheric chemistry,” Adv. Geophys. 4, 1–108 (1958).
[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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Kim, Y.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

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 Biogeochemic. Cycles 4, 225–240 (1990).
[CrossRef]

Koepke, P.

P. Koepke, “Effective reflectance of ocean whitecaps,” Appl. Opt. 23, 1816–1824 (1984).
[CrossRef] [PubMed]

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum wavelength,” J. Geophys. Res. 86, 9801–9805 (1981).
[CrossRef]

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum viewing geometry,” J. Geophys. Res. 84, 7847–7856 (1979).
[CrossRef]

Kolber, Z.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

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 Biogeochemic. 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]

Lovelock, J. E.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo, and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Marcus, I.

Y. Mekler, H. Quenzel, G. Ohring, I. Marcus, “Relative atmospheric aerosol content from ERTS observations,” J. Geophys. Res. 82, 967–970 (1977).
[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, SeaWiFS Technical Report Series: Volume 1, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

McClain, E. P.

C. R. N. Rao, L. L. Stowe, E. P. McClain, J. Sapper, “Development and application of aerosol remote sensing with AVHRR data from the NOAA satellites,” in Aerosols and Climate, P. Hobbs, M. P. McCormick, eds. (Deepak, Hampton, Va., 1988) pp. 69–80.

Mekler, Y.

Y. Mekler, H. Quenzel, G. Ohring, I. Marcus, “Relative atmospheric aerosol content from ERTS observations,” J. Geophys. Res. 82, 967–970 (1977).
[CrossRef]

Monahan, E. C.

E. C. Monahan, I. G. O’Muircheartaigh, “Whitecaps and the passive remote sensing of the ocean surface,” Int. J. Remote Sensing 7, 627–642 (1986).
[CrossRef]

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.

J.-M. André, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery, revisited,” Oceanologica Acta 14, 3–22 (1991).

A. Bricaud, A. Morel, “Atmospheric corrections and interpretation of marine radiances in CZCS imagery: use of a reflectance model,” Oceanologica Acta 7, 33–50 (1987).

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.

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]

Mugnai, A.

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]

O’Muircheartaigh, I. G.

E. C. Monahan, I. G. O’Muircheartaigh, “Whitecaps and the passive remote sensing of the ocean surface,” Int. J. Remote Sensing 7, 627–642 (1986).
[CrossRef]

Ohring, G.

Y. Mekler, H. Quenzel, G. Ohring, I. Marcus, “Relative atmospheric aerosol content from ERTS observations,” J. Geophys. Res. 82, 967–970 (1977).
[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]

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]

Quenzel, H.

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum wavelength,” J. Geophys. Res. 86, 9801–9805 (1981).
[CrossRef]

P. Koepke, H. Quenzel, “Turbidity of the atmosphere determined from satellite: calculation of optimum viewing geometry,” J. Geophys. Res. 84, 7847–7856 (1979).
[CrossRef]

Y. Mekler, H. Quenzel, G. Ohring, I. Marcus, “Relative atmospheric aerosol content from ERTS observations,” J. Geophys. Res. 82, 967–970 (1977).
[CrossRef]

Rao, C. R. N.

C. R. N. Rao, L. L. Stowe, E. P. McClain, J. Sapper, “Development and application of aerosol remote sensing with AVHRR data from the NOAA satellites,” in Aerosols and Climate, P. Hobbs, M. P. McCormick, eds. (Deepak, Hampton, Va., 1988) pp. 69–80.

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 Biogeochemic. 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]

Sapper, J.

C. R. N. Rao, L. L. Stowe, E. P. McClain, J. Sapper, “Development and application of aerosol remote sensing with AVHRR data from the NOAA satellites,” in Aerosols and Climate, P. Hobbs, M. P. McCormick, eds. (Deepak, Hampton, Va., 1988) pp. 69–80.

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]

Schwartz, S. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 255, 423–430 (1992).
[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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 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 A 137796 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 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, Hanscom Air Force Base, Mass., 1979).

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. 93D, 10909–10924 (1988).
[CrossRef]

Stowe, L. L.

C. R. N. Rao, L. L. Stowe, E. P. McClain, J. Sapper, “Development and application of aerosol remote sensing with AVHRR data from the NOAA satellites,” in Aerosols and Climate, P. Hobbs, M. P. McCormick, eds. (Deepak, Hampton, Va., 1988) pp. 69–80.

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]

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 Meteorol. 18, 247–267 (1980).
[CrossRef]

Viollier, M.

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

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.

Warren, S. G.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo, and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Wilson, C.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

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]

Wirick, C.

P. G. Falkowski, Y. Kim, Z. Kolber, C. Wilson, C. Wirick, R. Cess, “Natural versus anthropogenic factors affecting low-level cloud albedo over the North Atlantic,” Science 256, 1311–1313 (1992).
[CrossRef] [PubMed]

Wiscombe, W. J.

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]

Adv. Geophys. (1)

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

Appl. Opt. (13)

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

R. S. Fraser, “Satellite measurement of mass of Sahara dust in the atmosphere,” Appl. Opt. 15, 2471–2479 (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. 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, 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]

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]

P. Koepke, “Effective reflectance of ocean whitecaps,” Appl. Opt. 23, 1816–1824 (1984).
[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]

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Figures (4)

Fig. 1
Fig. 1

ɛ(λ, 865) as a function of λ for viewing at the edge and the center of the SeaWiFS scan with θ0 = 60° for the maritime, coastal, and tropospheric aerosol models. For each model, the RH values are 70%, 90%, and 98% from the upper to the lower curves. (b) Same as (a) but plotted in log–log format.

Fig. 2
Fig. 2

ρ a (λ) + ρ ra (λ) as a function of ρ as (λ) at the edge of the SeaWiFS. Upper solid curve is for the tropospheric model with RH = 70%; lower solid curve is for the maritime model with RH = 98%; and the dotted curve is the single-scattering result: (a) is for λ = 443 nm and θ0 = 60°; (b) is for λ = 865 nm and θ0 = 60°.

Fig. 3
Fig. 3

Error in retrieved t(443)ρ w (443) as a function of the solar zenith angle; RH = 80%; τ a (865) = 0.2: maritime aerosol with viewing at (a) the center and (b) the edge of the scan; coastal aerosol with viewing at (c) the center and (d) the edge of the scan; and tropospheric aerosol with (e) the center and (f) the edge of the scan.

Fig. 4
Fig. 4

Examples of the performance of the proposed algorithm at (a) the scan center and (b) the scan edge for a maritime aerosol when τ a (865) is increased from 0.2 (circles) to 0.4 (squares), and when τ a (865) = 0.2 but the surface is roughened by a 7.5 m/s wind (triangles), which is ignored in the operation of the algorithm.

Tables (5)

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Table 1 SeaWiFS Performance for θ0 = 60° at the Scan Edge

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Table 2 [L w (⊑)] N for Two Pigment Concentrations

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Table 3 Error in Retrieved τ a (865)a

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Table 4 Error in Retrieved τ a (865)a

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Table 5 Value of τ a (865) Required for Saturation of SeaWIFS at 865 nm

Equations (15)

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ρ = π L / F 0 cos θ 0 ,
ρ t ( λ ) = ρ r ( λ ) + ρ a ( λ ) + ρ r a ( λ ) + ρ g ( λ ) + t ρ w ( λ ) ,
ρ t ( λ ) = ρ r ( λ ) + ρ a s ( λ ) + t ρ w ( λ ) ,
ρ a s ( λ ) = ω a ( λ ) τ a ( λ ) p a ( θ , θ 0 , λ ) / 4 cos θ cos θ 0 , p a ( θ , θ 0 , λ ) = P a ( θ - , λ ) + [ r ( θ ) + r ( θ 0 ) ] P a ( θ + , λ ) , cos θ ± = ± cos θ 0 cos θ - sin θ 0 sin θ cos ( ϕ - ϕ 0 ) ,
ɛ ( λ i , λ j ) ρ a s ( λ i ) ρ a s ( λ j ) = ω a ( λ i ) τ a ( λ i ) p a ( θ , θ 0 , λ i ) ω a ( λ j ) τ a ( λ j ) p a ( θ , θ 0 , λ j ) .
ɛ ( λ , λ 4 ) = ( λ 4 λ ) n .
t = exp [ - τ r / 2 + τ Oz ) / cos θ ] ,
Δ ɛ ( λ , 865 ) ρ a s ( 865 ) = t ( λ ) Δ ρ w ( λ ) .
Δ ɛ ( 443 , 865 ) ± 0.001 ρ a s ( 865 ) .
Δ ɛ ( 443 , 865 ) ± 0.015 τ a ( 865 )
ɛ ( 765 , 865 ) = 1 N i = 1 N ɛ i ( 765 , 865 ) .
t ρ w ( λ ) = ρ t ( λ ) - ρ r ( λ ) - [ ρ a ( λ ) + ρ r a ( λ ) ] , ρ t ( 765 ) - ρ r ( 765 ) and ρ t ( 865 ) - ρ r ( 865 ) N Models ɛ ( 765 , 865 ) 2 Models , ɛ ( 765 , 865 ) 2 Models ɛ ( λ , 865 ) , ρ a s ( 865 ) ɛ ( λ , 865 ) ρ a s ( λ ) , ρ a s ( λ ) 2 Models ρ a ( λ ) + ρ r a ( λ ) .
log 10 3.33 C = - 1.2 log 10 r L + 0.5 ( log 10 r L ) 2 - 2.8 ( log 10 r L ) 3 ,
r L = 1 2 [ L w ( 443 ) ] N [ L w ( 550 ) ] N ,
t L w ( λ ) = [ L w ( λ ) ] N cos θ 0 × exp [ - ( τ r 2 + τ O z ) ( 1 cos θ 0 + 1 cos θ ) ] .

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