Abstract

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere–ocean system with a rough air–water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox–Munk surface roughness model is not sufficient for high wind conditions.

© 2006 Optical Society of America

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  1. C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954).
    [CrossRef]
  2. A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters. II: bidirectional aspects," Appl. Opt. 32, 6864-6879 (1993).
    [CrossRef] [PubMed]
  3. G. N. Plass and G. W. Kattawar, "Radiative transfer in the earth's atmosphere and ocean: influence of ocean waves," Appl. Opt. 14, 1924-1936 (1975).
    [CrossRef] [PubMed]
  4. J. T. O. Kirk, "The upwelling light stream in natural waters," Limnol. Oceanogr. 34, 1410-1425 (1989).
    [CrossRef]
  5. H. Gordon and M. Wang, "Surface-roughness considerations for atmospheric correction of ocean color sensors. I. The Rayleigh-scattering component," Appl. Opt. 31, 4247-4260 (1992).
    [CrossRef] [PubMed]
  6. R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
    [CrossRef]
  7. T. Nakajima and M. Tanaka, "Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 29, 521-537 (1983).
    [CrossRef]
  8. J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
    [CrossRef]
  9. Z. Jin and K. Stamnes, "Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system," Appl. Opt. 33, 431-442 (1994).
    [CrossRef] [PubMed]
  10. K. I. Gjerstad, J. Stamnes, B. Hamre, J. K. Lotsberg, B. Yan, and K. Stamnes, "Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system," Appl. Opt. 42, 2609-2622 (2003).
    [CrossRef] [PubMed]
  11. K. Stamnes, S. C. Tsay, W. Wiscombe, and K. Jayaweera, "Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media," Appl. Opt. 27, 2502-2509 (1988).
    [CrossRef] [PubMed]
  12. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Remote Sensing (Wiley, 1985).
  13. M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly-rough ocean surface," IEEE Trans. Antennas Propag. AP-17, 557-585 (1969).
  14. Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
    [CrossRef]
  15. Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
    [CrossRef]
  16. S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
    [CrossRef]
  17. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).
  18. A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106(C4), 7163-7180 (2001).
    [CrossRef]
  19. T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1977).
  20. B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
    [CrossRef]
  21. W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
    [CrossRef]
  22. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
    [CrossRef]
  23. O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
    [CrossRef]
  24. N. Ebuchi and S. Kizu, "Probability distribution of surface slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers," J. Oceanogr. 58, 477-486 (2002).
    [CrossRef]

2005 (2)

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

2003 (1)

2002 (2)

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

N. Ebuchi and S. Kizu, "Probability distribution of surface slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers," J. Oceanogr. 58, 477-486 (2002).
[CrossRef]

2001 (1)

A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106(C4), 7163-7180 (2001).
[CrossRef]

2000 (1)

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

1999 (1)

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

1998 (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

1996 (1)

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1989 (2)

J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
[CrossRef]

J. T. O. Kirk, "The upwelling light stream in natural waters," Limnol. Oceanogr. 34, 1410-1425 (1989).
[CrossRef]

1988 (1)

1986 (1)

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

1983 (1)

T. Nakajima and M. Tanaka, "Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 29, 521-537 (1983).
[CrossRef]

1975 (1)

1969 (1)

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly-rough ocean surface," IEEE Trans. Antennas Propag. AP-17, 557-585 (1969).

1954 (1)

Ackerman, T. P.

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

Barkstrom, B. R.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Charlock, T. P.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

Clothiaux, E. E.

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

Cooper, J. E.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Cota, G.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Cox, C.

Deuze, J. L.

J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
[CrossRef]

Dubovik, O.

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

Ebuchi, N.

N. Ebuchi and S. Kizu, "Probability distribution of surface slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers," J. Oceanogr. 58, 477-486 (2002).
[CrossRef]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

Gentili, B.

Gjerstad, K. I.

Gordon, H.

Hamre, B.

Harrison, E. F.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Herman, M.

J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
[CrossRef]

Hobbs, P. V.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Holben, B. N.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Jankowiak, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Jayaweera, K.

Jin, Z.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

Z. Jin and K. Stamnes, "Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system," Appl. Opt. 33, 431-442 (1994).
[CrossRef] [PubMed]

Kahn, R.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Kato, S.

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

Kattawar, G. W.

Kaufman, Y. J.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

King, M. D.

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, "The upwelling light stream in natural waters," Limnol. Oceanogr. 34, 1410-1425 (1989).
[CrossRef]

Kizu, S.

N. Ebuchi and S. Kizu, "Probability distribution of surface slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers," J. Oceanogr. 58, 477-486 (2002).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Remote Sensing (Wiley, 1985).

Lavenu, F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Lee, R. B.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Lotsberg, J. K.

Maritorena, S.

A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106(C4), 7163-7180 (2001).
[CrossRef]

Martins, J. V.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Mather, J. H.

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

Mobley, C. D.

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

Morel, A.

A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106(C4), 7163-7180 (2001).
[CrossRef]

A. Morel and B. Gentili, "Diffuse reflectance of oceanic waters. II: bidirectional aspects," Appl. Opt. 32, 6864-6879 (1993).
[CrossRef] [PubMed]

Munk, W.

Nakajima, T.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

T. Nakajima and M. Tanaka, "Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 29, 521-537 (1983).
[CrossRef]

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1977).

Plass, G. N.

Preisendorfer, R. W.

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

Reagan, J. A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Redemann, J.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Remer, L. A.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Rose, F.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Rutan, D. A.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Rutledge, C. K.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Rutledge, K.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

Sancer, M. I.

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly-rough ocean surface," IEEE Trans. Antennas Propag. AP-17, 557-585 (1969).

Santer, R.

J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
[CrossRef]

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

Setzer, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Remote Sensing (Wiley, 1985).

Slutsker, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Smith, G. L.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Smith, W. L.

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

Stamnes, J.

Stamnes, K.

Tanaka, M.

T. Nakajima and M. Tanaka, "Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 29, 521-537 (1983).
[CrossRef]

Tanre, D.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Remote Sensing (Wiley, 1985).

Tsay, S. C.

Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

Wang, M.

Wielicki, B. A.

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

Wiscombe, W.

Yan, B.

Zhang, T.

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

Appl. Opt. (6)

Bull. Am. Meteorol. Soc. (1)

B. A. Wielicki, B. R. Barkstrom, E. F. Harrison, R. B. Lee, G. L. Smith, and J. E. Cooper, "Clouds and the Earth's radiant energy system (CERES): an Earth observing system experiment," Bull. Am. Meteorol. Soc. 77, 853-868 (1996).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly-rough ocean surface," IEEE Trans. Antennas Propag. AP-17, 557-585 (1969).

J. Atmos. Ocean. Technol. (1)

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

J. Atmos. Sci. (2)

Z. Jin, T. P. Charlock, K. Rutledge, G. Cota, R. Kahn, J. RedemannT. Zhang, D. A. Rutan, and F. Rose, "Radiative transfer modeling for the CLAMS experiment," J. Atmos. Sci. 62, 1052-1070 (2005).
[CrossRef]

W. L. Smith, Jr., T. P. Charlock, R. Kahn, J. V. Martins, L. A. Remer, P. V. Hobbs, J. Redemann, and C. K. Rutledge, "EOS TERRA aerosol and radiative flux validation: an overview of the Chesapeake lighthouse and aircraft measurements for satellites (CLAMS) experiment," J. Atmos. Sci. 62, 903-918 (2005).
[CrossRef]

J. Geophys. Res. (2)

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106(C4), 7163-7180 (2001).
[CrossRef]

J. Oceanogr. (1)

N. Ebuchi and S. Kizu, "Probability distribution of surface slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers," J. Oceanogr. 58, 477-486 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (3)

T. Nakajima and M. Tanaka, "Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 29, 521-537 (1983).
[CrossRef]

J. L. Deuze, M. Herman, and R. Santer, "Fourier series expansion of the transfer equation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 41, 483-494 (1989).
[CrossRef]

S. Kato, T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, "The K-distribution method and correlated-k approximation for a shortwave radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 62, 109-121 (1999).
[CrossRef]

Limnol. Oceanogr. (1)

J. T. O. Kirk, "The upwelling light stream in natural waters," Limnol. Oceanogr. 34, 1410-1425 (1989).
[CrossRef]

Remote Sens. Environ. (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-16 (1998).
[CrossRef]

Other (3)

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1977).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, Optical Properties of the Atmosphere, AFCRL Rep. AFCRL-72-0497 (Air Force Cambridge Research Laboratories, Bedford, Mass. A, 1972).

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Remote Sensing (Wiley, 1985).

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Figures (7)

Fig. 1
Fig. 1

Model-simulated upwelling radiance field at the TOA and the downwelling radiance field at depths of 0, 10, 100, and 200   m in the ocean for three different wind speeds and for three wavelength sets (broadband, narrowband at 531   nm , and narrowband at 865   nm ). The SZA is 40°.

Fig. 2
Fig. 2

Effects of surface roughness on radiance distributions at 531   nm in the components of the principal plane containing most of the reflected solar beam in the atmosphere (top row), and most of the refracted solar beam in the ocean (rows 2–4). The SZA is 40°.

Fig. 3
Fig. 3

Comparison of modeled and measured broadband radiances as a function of sunglint angle. The nine numbers are the mean model-observation biases for the nine glint-angle intervals (10° each) from 0° to 90°, respectively.

Fig. 4
Fig. 4

Modeled irradiances versus cos(SZA) with upwelling irradiance in the atmosphere and downwelling irradiance in the ocean, for different wind speeds and different wavelengths.

Fig. 5
Fig. 5

Effects of wind speed on ocean surface albedo at 670   nm . The left panel shows the modeled and measured surface albedo during three afternoons. The right panel shows the observed wind speed for each afternoon. Different colors are for different days.

Fig. 6
Fig. 6

Effects of multiple scattering (reflection) and shadowing among surface wave facets on ocean albedo simulation. The three panels are for the three selected days as in Fig. 5. The long dashed curve is the albedo computed without multireflection but with shadowing; the short dashed curve is the albedo computed without shadowing but with multireflection; the dotted curve is the albedo calculated with a flat surface. The error bar represents the measured albedo range to within 3° of the SZA.

Fig. 7
Fig. 7

Effect of multiple scattering between surface facets on the albedo. The upper two panels show the direct albedo (beam incidence) and the lower two panels show the diffuse albedo (isotropic incidence). The left panels are for incidence from air and the right panels are for incidence from water. The numbers by each pair of curves on the right of panels (a) and (b) represent the incident angles in degrees. For each pair of curves, the solid curve is for single scattering and the dashed curve is for multiple scattering.

Equations (34)

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  μ d I ( τ , μ , ϕ ) d τ = I ( τ , μ , ϕ ) ω ( τ ) 4 π 0 2 π d ϕ × 1 1 p ( τ , μ , ϕ , μ , ϕ ) I ( τ , μ , ϕ ) × + Q ( τ , μ , ϕ ) ,
Q ( τ , μ , ϕ ) = { ω ( τ ) / 4 π F 0 p ( τ , μ , ϕ , μ 0 , ϕ 0 ) exp ( τ / μ 0 ) , τ τ a , 0 , τ > τ a ,
μ i a d I ( τ , μ i a ) d τ = I ( τ , μ i a ) - j = - N 1 j 0 N 1 ω j a D ( τ , μ i a , μ j a ) × I ( τ , μ j a ) + X 0 ( τ , μ i a ) exp ( - τ / μ 0 ) , i = ±1 , ±2 ,   …   , ± N 1 ; τ τ a
μ i o d I ( τ , μ i o ) d τ = I ( τ , μ i o ) - j = - N 2 j 0 N 2 ω j o D ( τ , μ i o , μ j o ) × I ( τ , μ j o ) , i = ± 1 , ± 2 ,   …   , ± N 2 ; τ > τ a .
μ i o = 1 1 ( μ i a ) 2 / ( n w / n a ) 2 , i = 1 , 2 ,   …   , N 1 ,
ω i o = n a 2 μ i a n w 2 μ i o ω i a , i = 1 , 2 ,   …   , N 1 .
I ( τ , μ i a ) = j = 1 N 1 [ C j G j ( μ i a ) exp ( k j a τ ) + C j G j ( μ i a ) × exp ( k j a τ ) ] + Z 0 ( μ i a ) exp ( τ / μ 0 ) , i = ± 1 , ± 2 ,   …   , ± N 1 ; τ τ a ,
I ( τ , μ i o ) = j = 1 N 2 [ C j G j ( μ i o ) exp ( k j o τ ) + C j G j ( μ i o ) × exp ( k j o τ ) ] , i = ± 1 , ± 2 ,   …   , ± N 2 ; τ > τ a ,
I ( τ a , μ i a ) = j = 1 N 1 I ( τ a , μ j a ) R ( μ i a , μ j a , n w / n a ) + j = 1 N 2 I ( τ a + , μ j o ) T ( μ i a , μ j o , n a / n w ) + 1 π μ 0 F 0 exp ( τ a / μ 0 ) R ( μ i a , μ 0 , n w / n a ) , i = 1 , 2 ,   …   , N 1 ,
I ( τ a + , μ i o ) = j = 1 N 1 I ( τ a , μ j a ) T ( μ i o , μ j a , n w / n a ) + j = 1 N 2 I ( τ a + , μ j o ) R ( μ i o , μ j o , n a / n w ) + 1 π μ 0 F 0 exp ( τ a / μ 0 ) T ( μ i o , μ 0 , n w / n a ) , i = 1 , 2 ,   …   , N 2 ,
R ( μ , μ , n ) = 2 δ m 0 2 π 0 2 π R ˜ ( μ , ϕ , μ , ϕ , n ) × cos m ( ϕ ϕ ) d ( ϕ ϕ ) ,
T ( μ , μ , n ) = 2 δ m 0 2 π 0 2 π T ˜ ( μ , ϕ , μ , ϕ , n ) × cos m ( ϕ ϕ ) d ( ϕ ϕ ) , δ m 0 = { 1 , if   m = 0 , 0, otherwise .
P ( μ n ) = 1 π σ 2 exp ( 1 μ n 2 σ 2 μ n 2 ) ,
σ 2 = 0.003 + 0.00512 U .
ARF ( θ , ϕ ) = π I ( θ , ϕ ) E ,
R 0 ( μ , ϕ , μ , ϕ , n ) = r ( cos α r , n ) × p ( μ , ϕ μ , ϕ , μ n r , σ ) × s ( μ , μ , σ ) ,
p ( μ , ϕ μ , ϕ , μ n r , σ ) = 1 4 μ ( μ n r ) 4 P ( μ n r ) ,
cos α = μμ + 1 μ 2 1 μ 2 cos ( ϕ ϕ ) ,
cos α r = ( 1 cos α ) / 2 ,
μ n r = μ + μ 2 ( 1 cos α ) .
T 0 ( μ , ϕ , μ , ϕ , n ) = t ( cos α t , n ) × p ( μ , ϕ μ , ϕ , μ n t , σ ) × s ( μ , μ , σ ) ,
p ( μ , ϕ μ , ϕ , μ n t , σ ) = n n 2 + cos 2 α t 1 4 μ ( μ n t ) 4 cos α t P ( μ n t ) .
cos α t = | n cos α 1 | n 2 2 n cos α + 1 ,
μ n t = μ   cos   α t + sin α t 1 μ 2 × 1 ( 1 μ 2 ) sin 2 ( ϕ ϕ ) / sin α .
R 1 ( μ , ϕ , μ , ϕ , n ) = 1 1 1 0 2 π d ( ϕ 1 ϕ ) × R 0 ( μ 1 , ϕ 1 , μ , ϕ , n ) × R 0 ( μ , ϕ , μ 1 , ϕ 1 , n ) ,
R 2 ( μ , ϕ , μ , ϕ , n ) = 1 1 2 0 2 π d ( ϕ 2 ϕ ) × R 1 ( μ 2 , ϕ 2 , μ , ϕ , n ) × R 0 ( μ , ϕ , μ 2 , ϕ 2 , n ) ,
R 3 ( μ , ϕ , μ , ϕ , n ) = 1 1 3 0 2 π d ( ϕ 3 ϕ ) × R 2 ( μ 3 , ϕ 3 , μ , ϕ , n ) × R 0 ( μ , ϕ , μ 3 , ϕ 3 , n ) ,
    R ˜ ( μ , ϕ , μ , ϕ , n ) = i = 0 N R i ( μ , ϕ , μ , ϕ , n ) .
T 1 ( μ , ϕ , μ , ϕ , n ) = 1 1 1 0 2 π d ( ϕ 1 ϕ ) × R 0 ( μ 1 , ϕ 1 , μ , ϕ , n ) × T 0 ( μ , ϕ , μ 1 , ϕ 1 , n ) ,
T 2 ( μ , ϕ , μ , ϕ , n ) = 1 1 2 0 2 π d ( ϕ 2 ϕ ) × R 1 ( μ 2 , ϕ 2 , μ , ϕ , n ) × T 0 ( μ , ϕ , μ 2 , ϕ 2 , n ) ,
T 3 ( μ , ϕ , μ , ϕ , n ) = 1 1 3 0 2 π d ( ϕ 3 ϕ ) × R 2 ( μ 3 , ϕ 3 , μ , ϕ , n ) × T 0 ( μ , ϕ , μ 3 , ϕ 3 , n ) ,
    T ˜ ( μ , ϕ , μ , ϕ , n ) = i = 0 N T i ( μ , ϕ , μ , ϕ , n ) .
R R ( μ 0 ) = 1 μ 0 0 1 0 2 π d ( ϕ ϕ 0 ) × μ R ˜ ( μ , ϕ , μ 0 , ϕ 0 , n ) .
R d f = 2 0 1 μ R R ( μ ) d μ .

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