Abstract

Single and multiple scattering by molecules or by atmospheric aerosols only (homogeneous scattering), and heterogeneous scattering by aerosols and molecules, are recorded in Monte Carlo simulations. It is shown that heterogeneous scattering (1) always contributes significantly to the path reflectance (ρpath), (2) is realized at the expense of homogeneous scattering, (3) decreases when aerosols are absorbing, and (4) introduces deviations in the spectral dependencies of reflectances compared with the Rayleigh exponent and the aerosol angstrom exponent. The ratio of ρpath to the Rayleigh reflectance for an aerosol-free atmosphere is linearly related to the aerosol optical thickness. This result provides a basis for a new scheme for atmospheric correction of remotely sensed ocean color observations.

© 1998 Optical Society of America

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References

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  1. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
    [CrossRef] [PubMed]
  2. M. Viollier, D. Tanré, P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary-Layer Meteorol. 18, 247–267 (1980).
    [CrossRef]
  3. 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]
  4. P. Y. Deschamps, M. Herman, D. Tanré, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
    [CrossRef] [PubMed]
  5. H. R. Gordon, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
    [CrossRef] [PubMed]
  6. H. R. Gordon, M. Wang, “Retrieval of water-leaving reflectance and aerosol optical thickness over the oceans with SeaWIFS: a preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
    [CrossRef] [PubMed]
  7. 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]
  8. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  9. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
    [CrossRef] [PubMed]
  10. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  11. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
    [CrossRef] [PubMed]
  12. H. R. Gordon, D. J. Castaño, “Coastal Zone Color Scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
    [CrossRef] [PubMed]
  13. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).
  14. L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” AFCRL-68-0153, environmental research paper 285 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1968).
  15. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL-TR-79-0214, environmental research paper 676 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  16. World Climate Research Program 112, “A preliminary cloudless standard atmosphere for radiation computation,” WMO/TD-24 (World Meteorological Organization, Geneva, Switzerland, 1986).
  17. H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth observing system era,” J. Geophys. Res. 102, 17,081–17,106 (1997).
    [CrossRef]
  18. P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
    [CrossRef]
  19. S. Saitoh, “OCTS on ADEOS,” in Oceanographic Application of Remote Sensing, M. Ikeda, F. W. Dobson, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 473–480.
  20. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWIFS and Ocean Color, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).
  21. M. Rast, J. L. Bézy, “The ESA medium resolution imaging spectrometer (MERIS): requirements to its mission and performance of its system,” in RSS95, Remote Sensing in Action, Proceedings of the 21st Annual Conference of the Remote Sensing Society, P. J. Curran, Y. C. Robertson , eds. (Taylor & Francis, London, 1995), pp. 125–132.
  22. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  23. K. Ding, H. R. Gordon, “Atmospheric correction of ocean-color sensors: effects of the Earth’s curvature,” Appl. Opt. 33, 7096–7106 (1994).
    [CrossRef] [PubMed]

1997 (1)

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

1994 (3)

1993 (2)

1992 (1)

1991 (1)

1989 (1)

1988 (1)

1987 (1)

1983 (2)

1980 (1)

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

1978 (1)

1977 (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Bézy, J. L.

M. Rast, J. L. Bézy, “The ESA medium resolution imaging spectrometer (MERIS): requirements to its mission and performance of its system,” in RSS95, Remote Sensing in Action, Proceedings of the 21st Annual Conference of the Remote Sensing Society, P. J. Curran, Y. C. Robertson , eds. (Taylor & Francis, London, 1995), pp. 125–132.

Bréon, F. M.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

Bricaud, A.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Buriez, J. C.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

Castaño, D. J.

Clark, D. K.

Deschamps, P. Y.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

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

Ding, K.

Elterman, L.

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” AFCRL-68-0153, environmental research paper 285 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1968).

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWIFS and Ocean Color, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

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, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL-TR-79-0214, environmental research paper 676 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

Gentili, B.

Gordon, H. R.

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

K. Ding, H. R. Gordon, “Atmospheric correction of ocean-color sensors: effects of the Earth’s curvature,” Appl. Opt. 33, 7096–7106 (1994).
[CrossRef] [PubMed]

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

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862–871 (1988).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “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 of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

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

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWIFS and Ocean Color, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

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, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

Jayaraman, A.

Jin, Z.

Kattawar, G. W.

Koepke, P.

Leroy, M.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[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, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

Mobley, C. D.

Morel, A.

Podaire, A.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

Prieur, L.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Rast, M.

M. Rast, J. L. Bézy, “The ESA medium resolution imaging spectrometer (MERIS): requirements to its mission and performance of its system,” in RSS95, Remote Sensing in Action, Proceedings of the 21st Annual Conference of the Remote Sensing Society, P. J. Curran, Y. C. Robertson , eds. (Taylor & Francis, London, 1995), pp. 125–132.

Reinersman, P.

Saitoh, S.

S. Saitoh, “OCTS on ADEOS,” in Oceanographic Application of Remote Sensing, M. Ikeda, F. W. Dobson, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 473–480.

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

Sèze, G.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[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,” AFGL-TR-79-0214, environmental research paper 676 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Stamnes, K.

Stavn, R. H.

Tanré, D.

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

Voltz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

Wang, M.

Appl. Opt. (12)

H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862–871 (1988).
[CrossRef] [PubMed]

P. Y. Deschamps, M. Herman, D. Tanré, “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, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

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

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]

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 of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

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

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

K. Ding, H. R. Gordon, “Atmospheric correction of ocean-color sensors: effects of the Earth’s curvature,” Appl. Opt. 33, 7096–7106 (1994).
[CrossRef] [PubMed]

Boundary-Layer Meteorol. (1)

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

IEEE Trans. Geosci. Remote Sens. (1)

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[CrossRef]

J. Geophys. Res. (1)

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

Limnol. Oceanogr. (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Other (7)

S. Saitoh, “OCTS on ADEOS,” in Oceanographic Application of Remote Sensing, M. Ikeda, F. W. Dobson, eds. (CRC Press, Boca Raton, Fla., 1995), pp. 473–480.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWIFS and Ocean Color, Vol. 1 of tech. rep. series NASA Tech. Memo. 104566 (NASA Greenbelt Space Flight Center, Greenbelt, Md., July1992).

M. Rast, J. L. Bézy, “The ESA medium resolution imaging spectrometer (MERIS): requirements to its mission and performance of its system,” in RSS95, Remote Sensing in Action, Proceedings of the 21st Annual Conference of the Remote Sensing Society, P. J. Curran, Y. C. Robertson , eds. (Taylor & Francis, London, 1995), pp. 125–132.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical properties of the atmosphere,” AFCRL 71-0279, environmental research paper 354 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1971).

L. Elterman, “UV, visible, and IR attenuation for altitudes to 50 km,” AFCRL-68-0153, environmental research paper 285 (U.S. Air Force Cambridge Research Laboratories, Bedford, Mass., 1968).

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL-TR-79-0214, environmental research paper 676 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

World Climate Research Program 112, “A preliminary cloudless standard atmosphere for radiation computation,” WMO/TD-24 (World Meteorological Organization, Geneva, Switzerland, 1986).

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Figures (11)

Fig. 1
Fig. 1

Vertical profiles that we used for molecules, ozone, and aerosol. (a) Vertical repartition of the attenuation coefficients at 550 nm, taken from Elterman.14 The four solid curves correspond to τ a = 0.05, 0.1, 0.3, 0.5. For the last three values, only the bottom layer aerosol contents (<5 km) are changed while the whole profile is shifted to yield an optical thickness of 0.05. The profile with steps at 2 and 12 km is used for sensitivity studies (see text). (b) For molecules and ozone the optical thicknesses over the 0–2- and 2–50-km layers, computed from the vertical profiles shown in (a), are homogeneously distributed in the same layers to construct an equivalent simplified atmosphere. For aerosols, their whole content [0–50 km in (a)] has been confined within the 0–2-km boundary layer.

Fig. 2
Fig. 2

TOA reflectances for λ = 445 nm, θ s = 60°, and four values of τ a (550) (0.05, 0.1, 0.3, and 0.5). The aerosol is the maritime model with a relative humidity of 70%. Reflectances are displayed as a function of viewing angle θ v throughout the Sun and anti-Sun half-vertical planes (Δϕ = 0 and Δϕ = π, respectively) and in the perpendicular half-plane (Δϕ = π/2). Viewing angle θ v is limited to 70°. Solid curves, results for the 50-layer structured atmosphere; dotted curves, results for the simplified two-layer atmosphere. (a) Global path reflectances, ρpath; (b) reflectances that are due only to multiple Rayleigh scattering, ρ r *; (c) reflectances that are due to multiple scattering by aerosols only, ρ a *; (d) reflectances that are due to heterogeneous scattering, ρra*.

Fig. 3
Fig. 3

TOA reflectances for a vertically structured (50-layer) atmosphere as a function of wavelength when θ s = 40°, θ v = 30°, and Δϕ = π/2. The aerosol is the maritime model with a relative humidity of 70% and an optical thickness of 0.3 at 550 nm. The various reflectances as indicated are described in the text.

Fig. 4
Fig. 4

TOA reflectances as a function of θ v and in the vertical planes as in Fig. 2, when λ = 445 nm and θ s = 40°, for a vertically structured (50-layer) atmosphere containing either both aerosols and molecules (dotted and dashed curves) or only one of these two scatterers (solid curves). The aerosol is the maritime model with a relative humidity of 70% and τ a (550) = 0.3. (a) The path reflectance and the reflectances that are due to multiple scattering by aerosols (ρ a * and ρ a ) or molecules (ρ r * and ρ r ). (b) The reflectances that are due to heterogeneous scattering, ρra*, and the correction term, C ra.

Fig. 5
Fig. 5

Reflectances as a function of τ a for the wavelengths indicated and when θ s = 40°, θ v = 30°, and Δϕ = π/2 (the aerosol is the maritime model with a relative humidity of 70%). (a) Reflectances that are due to multiple scattering by aerosols only: The dotted curve is for ρ a and is therefore unique and the solid curves are for ρ a *. (b) Reflectances that are due only to multiple Rayleigh scattering, ρ r *. (c) Reflectance that is due to heterogeneous scattering, ρra*. (d) Path reflectance, ρpath. Filled diamonds, simulations carried out for τ a (550) = 0.05, 0.1, 0.3, 0.5.

Fig. 6
Fig. 6

Relative proportions 〈ρ̅ r *〉, 〈ρ̅ a *〉, 〈ρ̅ra*〉, and 〈 ra〉 (in percent) displayed as a function of η a (see text) (a) when τ a is changed (from 0 to 2) and τ r is kept fixed and (c) when τ r is changed (from 0.02 to 0.35) and τ a is kept fixed (the aerosol phase function is that of the maritime model, with a relative humidity of 70% and the Sun at its zenith). Filled diamonds, points of the computations, namely, τ a = 0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 2.0 when τ r = 0.05; and τ r = 0, 0.02, 0.05, 0.1, 0.2, 0.3, 0.35 when τ a is 0.05. The corresponding variations of ρ̅path, ρ̅ r *, ρ̅ a *, ρ̅ra* are displayed in (b) and (d).

Fig. 7
Fig. 7

Isolines of the relative proportions (a) 〈ρ̅ r *〉, (b) 〈ρ̅ a *〉, and (c) 〈ρ̅ra*〉 (in percent of ρ̅path) within the η a –τ a plane. The hyperbolic envelopes correspond to the extrema of η a for a given τ a value and delimit the domain inside which τ r varies from 0.02 to 0.35 (i.e., near infrared to ultraviolet). The aerosol is the maritime model, with a relative humidity of 70% and the sun at its zenith.

Fig. 8
Fig. 8

Exponents that depict the variations of the various partial reflectances from λ = 445 to λ = 865 nm plotted as a function of θ s and for two aerosol types [see text and Eq. (9)] and τ a (550) = 0.3. Note that the vertical axes are interrupted and the scales are different for the upper and lower parts of both (a) and (b).

Fig. 9
Fig. 9

Relative importances (in percent) in the total signal (integrated over all azimuths and over 0°–70° for θ v ) of various scattering events, grouped as a function of their order and type of scattering. Computations are carried out for a 50-layer atmosphere and an aerosol of the maritime type with a relative humidity of 70%. The Sun’s zenith angle is 40°. Top, λ = 445; bottom, λ = 865 nm. Results are shown for the single-component atmospheres and the corresponding compound atmospheres, with τ a = 0.33 and τ = 0.25 at 445 and 865 nm, respectively, corresponding to τ a (550) = 0.30. Columns and rows are numbered according to the number of scattering events: 0, 1, 2, 3, and 4 or more scattering events, of either molecular or aerosol type. The parallelepipeds are proportional in height to the percentages of the scattering order and type in question. They are replaced by gray shades for the compound atmosphere.

Fig. 10
Fig. 10

Reflectances as a function of τ a and when θ s = 40°, θ v = 30°, Δϕ = π/2, and τ r = 0.2 (i.e., λ ∼ 460 nm); the phase function is that of the maritime model for a relative humidity of 70%. (a)–(d) As in Fig. 5; each curve is for one value of ω a , as indicated.

Fig. 11
Fig. 11

Relative variation of the path reflectance at 865 and 775 nm for the maritime aerosol model displayed as a function of τ a and expressed as the ratio ρpath r , when θ s = 40°, θ v = 30°, and Δϕ = π/2. The four curves are for four values of relative humidity, as indicated. Arrows symbolize a possible way to identify a couple of aerosol models enclosing the actual aerosol. The circled numbers identify the successive steps of this scheme, as discussed in the text.

Tables (2)

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Table 1 Symbols and Definitions

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Table 2 Parameters Defining the 64 cases Used for Comparison of Atmospheres Made of 2 or 50 Layers

Equations (16)

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ρ λ ,   θ v ,   θ s ,   Δ ϕ = π L λ ,   θ v ,   θ s ,   Δ ϕ / E s λ cos θ s .
ρ path = ρ rs + ρ as ,
ρ as rs λ ,   θ s ,   θ ν ,   Δ ϕ = τ a r λ ω a r λ p a r λ ,   θ s ,   θ ν ,   Δ ϕ / 4 μ s μ v ,
p a r λ ,   θ s ,   θ v ,   Δ ϕ = P a r λ ,   γ - + ρ F θ s + ρ F θ v P a r λ ,   γ + ,
cos γ ± = ± cos θ s cos θ ν - sin θ s sin θ ν cos Δ ϕ ,
ρ path = ρ r + ρ a + C ra ,
ρ path = ρ s + CT .
ρ path = ρ r * + ρ a * + ρ ra * ,
C ra = ρ ra * + ρ r * - ρ r + ρ a * - ρ a ,
ρ ¯ = 0 2 π 0 70   ρ θ v ,   Δ ϕ cos θ v sin θ v d θ v d ϕ .
η a = τ a / τ a + τ r ,
η r = 1 - η a .
n = ln ρ λ i / ρ λ j ln λ i / λ j ,
ρ path - ρ r = ρ a * + ρ ra * + ρ r * - ρ r = f ρ as .
ρ path / ρ r = ρ a * + ρ ra * + ρ r * / ρ r = f τ a .
τ a 775 = τ a 865 c 775 / c 865 .

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