Abstract

The multiangle imaging spectroradiometer (MISR) scheduled to be flown on the first platform of the Earth Observing System in 1998 provides an opportunity to enhance considerably the accuracy with which aerosol properties over the ocean can be retrieved through passive sensing from Earth orbit. As opposed to most radiometers in space that scan the earth in a plane normal to the subsatellite path, the MISR will scan the earth simultaneously in nine planes and thus provide the radiance exiting the atmosphere over a given pixel in nine different directions and at four wavelengths. We examine the problem of extracting the aerosol optical thickness (τa) over the oceans from MISR data, and we produce two algorithms, a single-band algorithm and a spectral or two-band algorithm, for deriving τa. The algorithms are based on the use of realistic aerosol models as candidates on which to base an estimation of the aerosol optical properties. They take into account all orders of multiple scattering. Simulations suggest that for nonabsorbing or mildly absorbing aerosol (single-scattering albedo ωa > 0.90) the error in the recovered τa is ≲10%, as long as the candidate models adequately cover the size refractive index distribution range of the expected aerosols. In the special case of a strongly absorbing aerosol (ωa = 0.75), the error in τa becomes large; however, the combination ωaτa (the scattering optical thickness) can still be recovered with an error of ≲20%, although it is always underestimated. The reason for this decrease in accuracy is that multiple-scattering effects are a strong function of ωa. A simple extension of the two-band algorithm permits the retrieval of the aerosol scattering phase function with surprising accuracy.

© 1994 Optical Society of America

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1993 (1)

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 32, 443–452 (1993).

1992 (4)

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

H. R. Gordon, M. Wahg, “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 (2)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

1989 (1)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

1988 (1)

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, 10,909–10,924 (1988).

1987 (1)

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]

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)

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]

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

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]

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 (1)

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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Ackerman, T. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Ackleson, S. G.

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

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]

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, 10,909–10,924 (1988).

Balch, W. M.

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

Bothwell, G. W.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

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, 10,909–10,924 (1988).

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]

Brown, O. B.

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, 10,909–10,924 (1988).

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]

Bruegge, C. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Clark, D. K.

Clark, J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb 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]

d’Almeida, G. A.

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

Daniels, J. A.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Danielson, E. D.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Davies, R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 290.

Deschamps, P. Y.

Diner, D. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[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]

Duval, V. G.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McCIain, “SeaWiFS Technical Report Series: volume 1, an overview of SeaWiFS and ocean color,” Tech. Mem. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Evans, R. H.

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, 10,909–10,924 (1988).

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]

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.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McCIain, “SeaWiFS Technical Report Series: volume 1, an overview of SeaWiFS and ocean color,” Tech. Mem. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

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,” Tech. 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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Floyd, E. L.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

Ford, V. G.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Gerstl, S. A. W.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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. 32, 443–452 (1993).

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

H. R. Gordon, M. Wahg, “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]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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, 10,909–10,924 (1988).

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

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

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

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McCIain, “SeaWiFS Technical Report Series: volume 1, an overview of SeaWiFS and ocean color,” Tech. Mem. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

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).
[CrossRef] [PubMed]

M. Griggs, “AVHRR measurements of atmospheric aerosols over oceans,” Final Rep. M0-A01-78-00-4092 (National Oceanic and Atmospheric Administration National Environmental Satellite Service, Washington, D.C., 1981).

M. Griggs, “Satellite measurements of tropospheric aerosols,” Cont. Rep. 3459 (NASA, Washington, D.C., 1981).

M. Griggs, “AVHRR aerosol ground truth experiment,” Final Rep. NA-83-SAC-00106 (National Oceanic and Atmospheric Administration National Environmental Satellite Service, Washington, D.C., 1984).

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]

Holligan, P. M.

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McCIain, “SeaWiFS Technical Report Series: volume 1, an overview of SeaWiFS and ocean color,” Tech. Mem. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Hovland, L. E.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

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]

Jones, K. L.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb 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]

Klaasen, K. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Koepke, P.

P. Koepke, “Effective reflectance of oceanic 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]

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

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]

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]

Martonchik, J. V.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

McCIain, C. R.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McCIain, “SeaWiFS Technical Report Series: volume 1, an overview of SeaWiFS and ocean color,” Tech. Mem. 104566 (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

McCIain, E. P.

C. R. N. Rao, L. L. Stowe, E. P. McCIain, 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]

Middleton, D.

D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hill, New York, 1960).

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]

Morel, A. Y.

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

Nakamoto, G. W. L. A. D. I.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (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]

Pagano, R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (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. McCIain, 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.

Reilly, T. H.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Sapper, J.

C. R. N. Rao, L. L. Stowe, E. P. McCIain, 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.

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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Sellers, P. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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,” Tech. 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,” Tech. Rep. AFGL-TR-83-0187 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

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. 93D, 10,909–10,924 (1988).

Stowe, L. L.

C. R. N. Rao, L. L. Stowe, E. P. McCIain, 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.

Tanre, D.

Voss, K. J.

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

Wahg, M.

Wang, M.

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 32, 443–452 (1993).

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

M. Wang, “Atmospheric correction of the second generation ocean color sensors,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1991), p. 135.

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]

White, M. L.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[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]

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]

Adv. Geophys. (1)

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

Appl. Opt. (8)

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

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

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 32, 443–452 (1993).

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

H. R. Gordon, M. Wahg, “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. S. Fraser, “Satellite measurement of mass of Sahara dust in the atmosphere,” Appl. Opt. 15, 2471–2479 (1976).
[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]

IEEE Trans. Geosci. Remote Sensing (1)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a multi-angle imaging spectroradiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, G. W. Bothwell, E. D. Danielson, E. L. Floyd, V. G. Ford, L. E. Hovland, K. L. Jones, M. L. White, “A multi-angle imaging spectroradiometer for terrestrial remote sensing from the Earth Observing System,” Int. J. Imaging Syst. Technol. 3, 92–107 (1991).
[CrossRef]

Int. J. Remote Sensing (1)

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]

J. Air Pollut. Control Assoc. (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]

J. Geophys. Res. (5)

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

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

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]

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, 10,909–10,924 (1988).

Limnol. Oceanogr. (1)

W. M. Balch, P. M. Holligan, S. G. Ackleson, K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 34, 629–643 (1991).
[CrossRef]

Nature (London) (1)

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

ρa(λ) + ρra(λ) as a function of ρas(λ) for (a) λ = 443 nm and θ0 = 60° and (b) λ = 865 nm and θ0 = 60° at the center of the MISR scan. The lower solid curve is for the Tropospheric model with RH = 70%, the upper solid curve is for the Maritime model with RH = 98%, and the dotted curve is the single-scattering result. Points correspond to τa = 0.05, 0.1, 0.3, 0.5.

Fig. 2
Fig. 2

σi/〈τai for the nine aerosol models for (a) the June 21 case and (b) the December 21 case; τa(865) = 0.2.

Fig. 3
Fig. 3

ɛ(λ, 865) as a function of λ for the three aerosol models with (a) θ0 = 20°, θ = 0°, and ϕ = 90, and (b) θ0 = 60°, θ = 0°, and ϕ = 90°. The solid, chained, dashed, and dotted curves refer to 70%, 80%, 90%, and 98% RH, respectively.

Fig. 4
Fig. 4

Phase functions for the four aerosol models at 865 nm with RH = 80%.

Fig. 5
Fig. 5

ρt − ρrtρw versus ρas relationship as a function of ωa for Ө0 = 60°.

Fig. 6
Fig. 6

σi/〈τai, for the nine aerosol models for the June 21 case and a Haze C aerosol with (a) m = 1.333 − oi and (b) m = 1.50 − 0i; τa(865) = 0.2.

Fig. 7
Fig. 7

Retrieved Pa(Ө, λ) as a function of scattering angle for the (a) case 1 Maritime aerosol, (b) case 1 Coastal aerosol, (c) case 1 Tropospheric aerosol, (d) case 2 Maritime aerosol, (e) case 2 Coastal aerosol, (f ) case 2 Tropospheric aerosol, all with 80% humidity at λ = 865 nm.

Fig. 8
Fig. 8

Retrieved Pa(Ө, λ) as a function of scattering angle for the (a) case 1 and (b) case 2 Urban aerosol with 80% humidity at λ = 865 nm.

Fig. 9
Fig. 9

Retrieved Pa(Ө, λ) as a function of scattering angle for the Haze C aerosol with (a) m = 1.333 − 0i and ν = 2, (b) m = 1.333 − 0i and ν = 3, (c) m = 1.333 − 0i and ν = 4, (d) m = 1.50 − 0i and ν = 2, (e) m = 1.50 − 0i and ν = 3, (f ) m = 1.50 − 0i and ν = 4.

Fig. 10
Fig. 10

Percent error in the retrieved value of τa(865) for 20 realizations of cy with α0 = 0. The solid curve is for the 21 June case and the dashed curve is for the 21 December case. If there were no calibration error, the retrieval error would be 4.50% and 5.07% for June and December, respectively.

Tables (11)

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Table 1 Index i for Individual Aerosol Models

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Table 2 Percentage of Error in Retrieved τa at 865 nm for the Two MISR Cases Examineda

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Table 3 Percentage of Error in Retrieved τa(λ) at 670 and 865 nm for the MISR 21 June Case

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Table 4 Percentage of Error in Retrieved τa(λ) at 670 and 865 nm for the MISR 21 December Case

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Table 5 Percentage of Error in Retrieved τa and ωaτa at 865 nm for the Two MISR Cases Examined with an Urban Aerosola

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Table 6 Percentage of Error in Retrieved τa and ωaτa at 865 nm for the Two MISR Cases Examined with an Urban Aerosol Using the Spectral Algorithm

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Table 7 Percentage of Error In the Retrieved τa and the Value of σi/(τa)ia for the Haze C Aerosol at 865 nm for the Two MISR Cases Examinedb

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Table 8 Percentage of Error in Retrieved τa at 865 ran Using the Two-Band Algorithm for the Two MISR Cases Examineda

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Table 9 Percentage of Error in Retrieved ωa(865) for the MISR 21 June and 21 December Cases

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Table 10 Percentage of Error in Retrieved τa, ωa and ωaτa at 865 nm for the Two MISR Cases Examined with an Urban Aerosl Using the Spectral Algorithm

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Table 11 Percentage of Error in the Retrieved ωa for the Haze C Aerosol at 865 nm for the MISR 21 June Case

Equations (27)

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ρ as = ω a τ a 4 cos θ cos θ 0 P a ( Ө ) , cos Ө = cos θ cos θ 0 sin θ sin θ 0 cos ( ϕ ϕ 0 ) ,
0 π 2 π P ( Ө ) sin Ө d Ө = 4 π .
ω a τ a = 1 2 0 π ω a τ a P a ( Ө ) sin Ө d Ө .
ρ t = ρ r + ρ as + t ρ w ,
ρ as = ω a τ a 4 cos θ cos θ 0 × { P a ( Ө ) + P a ( Ө + ) [ r ( θ ) + r ( θ 0 ) ] } , cos Ө ± = ± cos θ cos θ 0 sin θ sin θ 0 cos ( ϕ ϕ 0 ) ,
ω a τ a { P a ( Ө ) + P a ( Ө + ) [ r ( θ ) + r ( θ 0 ) ] } .
τ a i = 1 9 j = 1 9 ( τ a ) i j ,
σ i { 1 8 j = 1 9 [ τ a i j τ a i ] 2 } 1 / 2 ,
ρ t = ρ r + ρ a + ρ ra + t ρ w ,
ρ t ρ r t ρ w = ρ a + ρ ra single scattering ρ as .
n ( D ) = i = 1 2 n i ( D ) ,
n i ( D ) = d N i ( D ) d D = N i log e ( 10 ) 2 π s i D × exp { 1 2 [ log 10 ( D / D i ) s i ] 2 } ,
ε ( λ , λ 0 ) = ρ as ( λ ) / ρ as ( λ 0 ) ,
ε ( λ , λ 0 ) = τ a ( λ ) ω a ( λ ) { P a ( Ө , λ ) + P a ( Ө + , λ ) [ r ( θ ) + r ( θ 0 ) ] } τ a ( λ 0 ) ω a ( λ 0 ) { P a ( Ө , λ 0 ) + P a ( Ө + , λ 0 ) [ r ( θ ) + r ( θ 0 ) ] } .
ε ( λ , 865 ) < ε m ( λ , 865 ) < ε + ( λ , 865 ) ,
τ a ( θ j , ϕ j ) = τ a ( θ j , ϕ j ) + ε m ε ε + ε × [ τ a ( θ j , ϕ j ) + τ a ( θ j , ϕ j ) ] .
τ a ( ave ) = 1 9 j = 1 9 τ a ( θ j , ϕ j ) .
ε ave ( λ , 865 ) = 1 N i = 1 N ε i ( λ , 865 ) .
n ( D ) = d N ( D ) d D = K , D 0 < D D 1 , = K ( D 1 D ) ν + 1 , D 1 < D D 2 , = 0 , D > D 2 ,
P a ( Ө ) = P a ( Ө ) + ε ave ε ε + ε [ P a ( Ө ) + P a ( Ө ) ] ,
ω a ( θ j , ϕ j ) = ω a ( θ j , ϕ j ) + ε m ε ε + ε × [ ω a ( θ j , ϕ j ) + ω a ( θ j , ϕ j ) ] .
ω a ( ave ) = 1 9 j = 1 9 ω a ( θ j , ϕ j ) .
( Δ ρ t ) j = ( ρ t ) j ( α 0 + α j ) ,
τ a i = τ a i + 1 9 j ( τ a ) i j ( α 0 + α j ) τ a i ( 1 + α 0 ) + τ a α i ,
( σ ) i 2 = { ( σ ) i 2 + 1 8 j [ ( τ a ) i j α j τ a α i ] 2 + 1 4 j [ ( τ a ) i j τ a i ] [ ( τ a ) i j α j τ a α i ] } × ( 1 + α 0 ) 2 ,
τ a i τ a i ( 1 + α 0 ) ,
σ i τ a i [ σ i 2 τ a i 2 + ( σ ατ a ) i 2 τ a i 2 + 2 c i σ i ( σ ατ a ) i τ a i 2 ] 1 / 2 ,

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