Abstract

We describe a method by which the aerosol component of the radiance at the top of the atmosphere (TOA) can be synthesized from the radiances generated by individual components of the aerosol size–refractive-index distribution. The method is exact in the single-scattering approximation. For regimes in which the single-scattering approximation is not valid, the method usually reproduces the aerosol contribution with an error ≲2–3% (and only rarely >3–4%) for Sun and viewing angles as large as 80° and 70°, respectively, and for aerosol optical thicknesses as large as 0.50. In the blue, where molecular scattering makes a dominant contribution to the TOA radiance, the percent error in the synthesized total radiance is significantly less than in the synthesized aerosol component and typically will be less than the radiometric calibration uncertainties of Earth-orbiting sensors. When the aerosol is strongly absorbing, the method can fail; however, the potential for failure is easy to anticipate a priori. An obvious application of our technique is to provide a basis for the estimation of aerosol properties with Earth-orbiting sensors, e.g., the Multiangle Imaging Spectroradiometer.

© 1994 Optical Society of America

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References

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  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. 33, 443–452 (1994).
    [CrossRef] [PubMed]
  2. 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]
  3. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 Vol. 1 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).
  4. 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. KIaasen, 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]
  5. 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]
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  8. 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-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).
  9. 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).
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  10. 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]
  11. 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]
  12. M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
    [CrossRef]
  13. A. Jayaraman, P. Koepke, “Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere,” Appl. Opt. 31, 3473–3480 (1992).
    [CrossRef] [PubMed]
  14. G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climtaology and Radiative Characteristics (Deepak, Hampton, Va., 1991).
  15. S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 μm range,” Remote Sensing Environ. (to be published).

1994 (2)

1992 (1)

1991 (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]

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. KIaasen, 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)

1983 (3)

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-83-0187, NTIS AD A137796 (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. KIaasen, 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]

Biggar, S. F.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 μm range,” Remote Sensing Environ. (to be published).

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.

Brown, O.B.

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. KIaasen, 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]

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-83-0187, NTIS AD A137796 (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. KIaasen, 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,” Rep. AFGL-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols—Global Climtaology 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. KIaasen, 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. KIaasen, 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. KIaasen, 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]

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. KIaasen, 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]

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. KIaasen, 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. McClain, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 Vol. 1 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Evans, R. H.

Feldman, G. C.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 Vol. 1 of SeaWiFS Technical Report Series (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,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).

F. X. Kenizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the lowtran 6 model,” Rep. AFGL-83-0187, NTIS AD A137796 (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]

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-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

Gellman, D. I.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 μm range,” Remote Sensing Environ. (to be published).

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. KIaasen, 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.

Gregg, W. W.

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

Herman, M.

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA Tech. Memo. 104566 Vol. 1 of SeaWiFS Technical Report Series (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]

Jayaraman, A.

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]

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-83-0187, NTIS AD A137796 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1983).

KIaasen, 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. KIaasen, 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]

King, M. D.

M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
[CrossRef]

Koepke, P.

A. Jayaraman, P. Koepke, “Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere,” Appl. Opt. 31, 3473–3480 (1992).
[CrossRef] [PubMed]

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

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. KIaasen, 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]

McClain, C. R.

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

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. KIaasen, 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]

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. KIaasen, 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]

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. KIaasen, 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]

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-83-0187, NTIS AD A137796 (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. KIaasen, 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,” Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass., 1979).

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

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

Slater, P. N.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 μm range,” Remote Sensing Environ. (to be published).

Tanre, D.

Wang, M.

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]

Appl. Opt. (6)

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. KIaasen, 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]

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

M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
[CrossRef]

Other (6)

“Earth Observing System: science and mission requirements working group report,” NASA Tech. Memo. 86129 (NASA, Washington, D.C., 1984).

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

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

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

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 μm range,” Remote Sensing Environ. (to be published).

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

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Figures (5)

Fig. 1
Fig. 1

Phase functions for the four aerosol components at 865 nm with RH = 70%. Dotted curve, Urban1; dotted–dashed curve, Urban2; dashed curve, Oceanic; solid curve, Tropospheric.

Fig. 2
Fig. 2

Nadir-viewing relationship between [ρt − ρrtρw]i and τa for (a) λ = 443 nm and θ0 = 60° and (b) λ = 865 and θ0 = 60° for the individual components of the aerosol size distribution. The dotted lines are the least-squares fits.

Fig. 3
Fig. 3

Error in Eq. (9) as a function of θ0 for a nadir-viewing sensor at (a) 443 nm and (b) 865 nm when the Oceanic (O) and the Tropospheric (T) components are combined to form the Maritime (M) and Coastal (C) aerosol models. Results are for θ0 = 20°, 40°, 60°, and 80°. To avoid confusion, the points for τa = 0.3 and 0.5 are plotted at θ0 + 4° and θ0 + 8°, respectively.

Fig. 4
Fig. 4

Error in Eq. (9) as a function of θ0 for a nadir-viewing sensor at (a) 443 nm and (b) 865 nm when the Urban1 (U1) and the Urban2 (U2) components are combined to form the Urban (U) aerosol model. Results are for θ0 = 20°, 40°, 60°, and 80°. To avoid confusion, the points for τa = 0.3 and 0.5 are plotted at θ0 + 4° and θ0 + 8°, respectively.

Fig. 5
Fig. 5

Error in Eq. (9) as a function of θ0 for a nadir-viewing sensor at 865 nm when the Urban1 (U1) and the Urban2 (U2) components in the proportion 99 to 1 are combined to form the Urban (U) aerosol model. Results are for θ0 = 20°, 40°, 60°, and 80°. To avoid confusion, the points for τa = 0.3 and 0.5 are plotted at θ0 + 4° and θ0 + 8°, respectively.

Tables (3)

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Table 1 Number of Cases in which |Δ| Falls within the Indicated Range for the MISR Winter Geometry with the Urban Aerosola

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Table 2 Number of Cases in which |Δ| Falls within the Indicated Range for the MISR Winter Geometry with the Coastal Aerosola

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Table 3 Number of Cases in which |Δ| Falls within the Indicated Range at 865 nm for the Urban Aerosol with N1/(N1 + N2) = 0.99

Equations (12)

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n ( D ) = i = 1 2 n i ( D ) ,
n i ( D ) = d N i ( D ) d D = N i log e ( 10 ) 2 π σ i D exp [ - 1 2 ( log 10 ( D / D i ) σ i ) 2 ] ,
ρ t = ρ r + ρ as + t ρ w ,
ρ as = ω a τ a p a ( θ v , θ 0 ) / 4 cos θ v cos θ 0 ,
p a ( θ v , θ 0 , λ ) = P a ( θ - , λ ) + [ r ( θ v ) + r ( θ 0 ) ] P a ( θ + , λ ) , cos θ ± = ± cos θ 0 cos θ v - sin θ 0 sin θ v cos ( ϕ v - ϕ 0 ) ,
[ ρ as ( τ i ) ] i ( ω a p a ) i 4 cos θ v cos θ 0 τ i .
ρ as ( τ a ) = i = 1 2 [ ρ as ( τ i ) ] i .
τ i = c i * N i i = 1 2 c i * N i τ a r i τ a ,
ρ as ( τ a ) = i = 1 2 r i [ ρ as ( τ a ) ] i ,
ρ t ( τ a ) - ρ r - t ρ w = i = 1 2 r i [ ρ t ( τ a ) - ρ r - t ρ w ] i ,
ρ t = ρ r + ρ a + ρ r a + t ρ w ,
Δ ( i = 1 2 r i [ ρ t ( τ a ) - ρ r - t ρ w ] i ) - [ ρ t ( τ a ) - ρ r - t ρ w ]

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