Abstract

This is the second part of the validation effort of the recently developed vector version of the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) radiative transfer code (6SV1), primarily used for the calculation of look-up tables in the Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric correction algorithm. The 6SV1 code was tested against a Monte Carlo code and Coulson's tabulated values for molecular and aerosol atmospheres bounded by different Lambertian and anisotropic surfaces. The code was also tested in scalar mode against the scalar code SHARM to resolve the previous 6S accuracy issues in the case of an anisotropic surface. All test cases were characterized by good agreement between the 6SV1 and the other codes: The overall relative error did not exceed 0.8%. The study also showed that ignoring the effects of radiation polarization in the atmosphere led to large errors in the simulated top-of-atmosphere reflectances: The maximum observed error was approximately 7.2% for both Lambertian and anisotropic surfaces.

© 2007 Optical Society of America

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2006 (2)

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).
[CrossRef]

S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. Klemm, "Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance," Appl. Opt. 45, 6762-6774 (2006).
[CrossRef] [PubMed]

2005 (1)

2002 (3)

A. Lyapustin, "Radiative transfer code SHARM-3D for radiance simulations over a non-Lambertian nonhomogeneous surface: intercomparison study," Appl. Opt. 41, 5607-5615 (2002).
[CrossRef] [PubMed]

E. F. Vermote, N. Z. El Saleous, and C. O. Justice, "Atmospheric correction of MODIS data in the visible to middle infrared: first results," Remote Sens. Environ. 83, 97-111 (2002).
[CrossRef]

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

2000 (2)

W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Trans. Geosci. Remote Sens. 38, 977-998 (2000).
[CrossRef]

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

1998 (1)

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

1997 (1)

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17013 (1997).
[CrossRef]

1995 (1)

1994 (2)

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, "Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres," J. Quant. Spectrosc. Radiat. Transfer 51, 491-510 (1994).
[CrossRef]

L. D. Talley and G. C. Johnson, "Deep, zonal subequatorial currents," Science 263, 1125-1128 (1994).
[CrossRef] [PubMed]

1993 (1)

H. Rahman, B. Pinty, and M. M. Verstraete, "Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA Advanced Very High Resolution Radiometer Data," J. Geophys. Res. 98, 20791-20801 (1993).
[CrossRef]

1992 (3)

F.-M. Bréon, "Reflectance of broken cloud fields: simulation and parameterization," J. Atmos. Sci. 49, 1221-1232 (1992).
[CrossRef]

J.-L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data," J. Geophys. Res. 97, 20455-20468 (1992).

E. Vermote and D. Tanré, "Analytical expressions for radiative properties of planar Rayleigh scattering media, including polarization contributions," J. Quant. Spectrosc. Radiat. Transfer 47, 305-314 (1992).
[CrossRef]

1991 (1)

F. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 5, 413-423 (1991).
[CrossRef]

1989 (1)

J. L. Deuzé, 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]

1984 (1)

1980 (1)

E. C. Monahan and I. O'Muircheartaigh, "Optimal power-law description of oceanic whitecap dependence on wind speed," J. Phys. Oceanogr. 10, 2094-2099 (1980).
[CrossRef]

1970 (2)

1955 (1)

C. Cox and W. Munk, "Some problems in optical oceanography," J. Mar. Res. 14, 63-78 (1955).

1954 (2)

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

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]

Bamsley, M.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Ben-David, A.

Bidigare, R. R.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Bréon, F.-M.

F.-M. Bréon, "Reflectance of broken cloud fields: simulation and parameterization," J. Atmos. Sci. 49, 1221-1232 (1992).
[CrossRef]

Cairns, B.

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

Caudill, T. R.

Chowdhary, J.

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

Clark, D. K.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Coulson, K. L.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, 1960).

Cox, C.

C. Cox and W. Munk, "Some problems in optical oceanography," J. Mar. Res. 14, 63-78 (1955).

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

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]

d'Almeida, G. A.

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Dave, J. V.

d'Entremont, R. P.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Deschamps, P. Y.

J.-L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data," J. Geophys. Res. 97, 20455-20468 (1992).

Deuzé, J. L.

J. L. Deuzé, 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]

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Disney, M.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Doll, C.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Dunderdale, M.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

El Saleous, N. Z.

E. F. Vermote, N. Z. El Saleous, and C. O. Justice, "Atmospheric correction of MODIS data in the visible to middle infrared: first results," Remote Sens. Environ. 83, 97-111 (2002).
[CrossRef]

Engelsen, O.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, Parametric Bidirectional Reflectance Factor Models: Evaluation, Improvements and Applications, Eur. Rep. 16426 EN (Space Appl. Inst., Ispra, Italy, 1996).

Evans, F. F.

F. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 5, 413-423 (1991).
[CrossRef]

Flittner, D. E.

Gao, F.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Gazdag, J.

Herman, B. M.

Herman, M.

J. L. Deuzé, 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]

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Hobson, P.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Hu, B.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Jin, Y.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Johnson, G. C.

L. D. Talley and G. C. Johnson, "Deep, zonal subequatorial currents," Science 263, 1125-1128 (1994).
[CrossRef] [PubMed]

Justice, C. O.

E. F. Vermote, N. Z. El Saleous, and C. O. Justice, "Atmospheric correction of MODIS data in the visible to middle infrared: first results," Remote Sens. Environ. 83, 97-111 (2002).
[CrossRef]

Kimes, D. S.

D. S. Kimes, W. W. Newcomb, R. F. Nelson, and J. B. Schutt, "Directional reflectance distributions of a hardwood and a pine forest canopy," IEEE Trans. Geosci. Remote Sens. 24, 281-293 (1986).

Klemm, F.

Koepke, P.

P. Koepke, "Effective reflectance of oceanic whitecaps," Appl. Opt. 23, 1816-1824 (1984).
[CrossRef] [PubMed]

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Kotchenova, S. Y.

S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. Klemm, "Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance," Appl. Opt. 45, 6762-6774 (2006).
[CrossRef] [PubMed]

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Lacis, A. A.

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, "Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres," J. Quant. Spectrosc. Radiat. Transfer 51, 491-510 (1994).
[CrossRef]

Leroy, M.

J.-L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data," J. Geophys. Res. 97, 20455-20468 (1992).

Lewis, P.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Li, X.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Liang, S.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Liou, K.-N.

K.-N. Liou, An Introduction to Atmospheric Radiation (Academic, 1980).

Lucht, W.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Trans. Geosci. Remote Sens. 38, 977-998 (2000).
[CrossRef]

Lyapustin, A.

Lyapustin, A. I.

Martonchik, J. V.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, Parametric Bidirectional Reflectance Factor Models: Evaluation, Improvements and Applications, Eur. Rep. 16426 EN (Space Appl. Inst., Ispra, Italy, 1996).

Masuda, K.

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).
[CrossRef]

Matarrese, R.

Mishchenko, M. I.

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17013 (1997).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, "Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres," J. Quant. Spectrosc. Radiat. Transfer 51, 491-510 (1994).
[CrossRef]

Miura, T.

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Monahan, E. C.

E. C. Monahan and I. O'Muircheartaigh, "Optimal power-law description of oceanic whitecap dependence on wind speed," J. Phys. Oceanogr. 10, 2094-2099 (1980).
[CrossRef]

Morcrette, J. J.

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Morel, A.

A. Morel, "Optical modeling of the upper ocean in relation to its biogenous matter content (Case I Waters)," J. Geophys. Res. 93, 10479-10768 (1988).

Mueller, J. L.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Muller, J.-P.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Munk, W.

C. Cox and W. Munk, "Some problems in optical oceanography," J. Mar. Res. 14, 63-78 (1955).

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

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]

Nelson, R. F.

D. S. Kimes, W. W. Newcomb, R. F. Nelson, and J. B. Schutt, "Directional reflectance distributions of a hardwood and a pine forest canopy," IEEE Trans. Geosci. Remote Sens. 24, 281-293 (1986).

Newcomb, W. W.

D. S. Kimes, W. W. Newcomb, R. F. Nelson, and J. B. Schutt, "Directional reflectance distributions of a hardwood and a pine forest canopy," IEEE Trans. Geosci. Remote Sens. 24, 281-293 (1986).

O'Muircheartaigh, I.

E. C. Monahan and I. O'Muircheartaigh, "Optimal power-law description of oceanic whitecap dependence on wind speed," J. Phys. Oceanogr. 10, 2094-2099 (1980).
[CrossRef]

Ondrusek, M. E.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Pinty, B.

H. Rahman, B. Pinty, and M. M. Verstraete, "Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA Advanced Very High Resolution Radiometer Data," J. Geophys. Res. 98, 20791-20801 (1993).
[CrossRef]

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, Parametric Bidirectional Reflectance Factor Models: Evaluation, Improvements and Applications, Eur. Rep. 16426 EN (Space Appl. Inst., Ispra, Italy, 1996).

Privette, J. L.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Rahman, H.

H. Rahman, B. Pinty, and M. M. Verstraete, "Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA Advanced Very High Resolution Radiometer Data," J. Geophys. Res. 98, 20791-20801 (1993).
[CrossRef]

Roberts, G.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Roujean, J.-L.

J.-L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data," J. Geophys. Res. 97, 20455-20468 (1992).

Roy, D.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Santer, R.

J. L. Deuzé, 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]

Schaaf, C. B.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Trans. Geosci. Remote Sens. 38, 977-998 (2000).
[CrossRef]

Schutt, J. B.

D. S. Kimes, W. W. Newcomb, R. F. Nelson, and J. B. Schutt, "Directional reflectance distributions of a hardwood and a pine forest canopy," IEEE Trans. Geosci. Remote Sens. 24, 281-293 (1986).

Sekera, Z.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, 1960).

Shettle, E. P.

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Stephens, G. L.

F. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 5, 413-423 (1991).
[CrossRef]

Strahler, A. H.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Trans. Geosci. Remote Sens. 38, 977-998 (2000).
[CrossRef]

Strugnell, N. C.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Talley, L. D.

L. D. Talley and G. C. Johnson, "Deep, zonal subequatorial currents," Science 263, 1125-1128 (1994).
[CrossRef] [PubMed]

Tanré, D.

E. Vermote and D. Tanré, "Analytical expressions for radiative properties of planar Rayleigh scattering media, including polarization contributions," J. Quant. Spectrosc. Radiat. Transfer 47, 305-314 (1992).
[CrossRef]

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Thome, K. J.

Travis, L. D.

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17013 (1997).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, "Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres," J. Quant. Spectrosc. Radiat. Transfer 51, 491-510 (1994).
[CrossRef]

Trees, C. C.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Tsang, T.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Vermote, E.

E. Vermote and D. Tanré, "Analytical expressions for radiative properties of planar Rayleigh scattering media, including polarization contributions," J. Quant. Spectrosc. Radiat. Transfer 47, 305-314 (1992).
[CrossRef]

Vermote, E. F.

S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. Klemm, "Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance," Appl. Opt. 45, 6762-6774 (2006).
[CrossRef] [PubMed]

E. F. Vermote, N. Z. El Saleous, and C. O. Justice, "Atmospheric correction of MODIS data in the visible to middle infrared: first results," Remote Sens. Environ. 83, 97-111 (2002).
[CrossRef]

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

Verstraete, M. M.

H. Rahman, B. Pinty, and M. M. Verstraete, "Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA Advanced Very High Resolution Radiometer Data," J. Geophys. Res. 98, 20791-20801 (1993).
[CrossRef]

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, Parametric Bidirectional Reflectance Factor Models: Evaluation, Improvements and Applications, Eur. Rep. 16426 EN (Space Appl. Inst., Ispra, Italy, 1996).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Zhang, X.

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Geosci. Remote Sens. (2)

D. S. Kimes, W. W. Newcomb, R. F. Nelson, and J. B. Schutt, "Directional reflectance distributions of a hardwood and a pine forest canopy," IEEE Trans. Geosci. Remote Sens. 24, 281-293 (1986).

W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Trans. Geosci. Remote Sens. 38, 977-998 (2000).
[CrossRef]

J. Atmos. Sci. (1)

F.-M. Bréon, "Reflectance of broken cloud fields: simulation and parameterization," J. Atmos. Sci. 49, 1221-1232 (1992).
[CrossRef]

J. Geophys. Res. (5)

J.-L. Roujean, M. Leroy, and P. Y. Deschamps, "A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data," J. Geophys. Res. 97, 20455-20468 (1992).

H. Rahman, B. Pinty, and M. M. Verstraete, "Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA Advanced Very High Resolution Radiometer Data," J. Geophys. Res. 98, 20791-20801 (1993).
[CrossRef]

A. Morel, "Optical modeling of the upper ocean in relation to its biogenous matter content (Case I Waters)," J. Geophys. Res. 93, 10479-10768 (1988).

A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, "Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment," J. Geophys. Res. 25, 135-138 (1998).

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17013 (1997).
[CrossRef]

J. Mar. Res. (2)

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

C. Cox and W. Munk, "Some problems in optical oceanography," J. Mar. Res. 14, 63-78 (1955).

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

E. C. Monahan and I. O'Muircheartaigh, "Optimal power-law description of oceanic whitecap dependence on wind speed," J. Phys. Oceanogr. 10, 2094-2099 (1980).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (4)

E. Vermote and D. Tanré, "Analytical expressions for radiative properties of planar Rayleigh scattering media, including polarization contributions," J. Quant. Spectrosc. Radiat. Transfer 47, 305-314 (1992).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, "Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres," J. Quant. Spectrosc. Radiat. Transfer 51, 491-510 (1994).
[CrossRef]

J. L. Deuzé, 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]

F. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 5, 413-423 (1991).
[CrossRef]

Limnol. Oceanogr. (1)

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, "Accessory pigments versus chlorophyll a concentrations within the Euphotic Zone: A ubiquitous relationship," Limnol. Oceanogr. 45, 1130-1143 (2000).
[CrossRef]

Remote Sens. Environ. (3)

K. Masuda, "Infrared sea surface emissivity including multiple reflection effect for isotropic Gaussian slope distribution model," Remote Sens. Environ. 103, 488-496 (2006).
[CrossRef]

E. F. Vermote, N. Z. El Saleous, and C. O. Justice, "Atmospheric correction of MODIS data in the visible to middle infrared: first results," Remote Sens. Environ. 83, 97-111 (2002).
[CrossRef]

C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Bamsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sens. Environ. 83, 135-148 (2002).
[CrossRef]

Science (1)

L. D. Talley and G. C. Johnson, "Deep, zonal subequatorial currents," Science 263, 1125-1128 (1994).
[CrossRef] [PubMed]

Other (8)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

K.-N. Liou, An Introduction to Atmospheric Radiation (Academic, 1980).

E. F. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, S. Y. Kotchenova, and T. Miura, Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide Version 3 (November, 2006), http://www.6s.ltdri.org.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, 1960).

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, Parametric Bidirectional Reflectance Factor Models: Evaluation, Improvements and Applications, Eur. Rep. 16426 EN (Space Appl. Inst., Ispra, Italy, 1996).

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Midway Islands, https://www.cia.gov/cia/publications/factbook/geos/um.html.

Salt Concentration, www.nas.nasa.gov/News/Archive/2006/08-30-06.html.

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Figures (5)

Fig. 1
Fig. 1

Part II validation scheme.

Fig. 2
Fig. 2

Validation of 6SV1 in scalar mode against SHARM for Lambertian and anisotropic surfaces. For all three plots the aerosol atmosphere is presented by the standard continental model, τ a e r = { 0.2 ; 0.8 } , λ = 750 n m , SZA = {0.0°, 10.0°, 23.07°, 45.0°, 58.67°, 75.0°}, AZ = {0°, 90°, 180°}, and VZA = {0°–79°}. (a) Lambertian surface with the ground reflectance ρ = 0.25 , (b) RPV grass model incorporated into the code through the approximate formulas, and (c) the same model incorporated directly.

Fig. 3
Fig. 3

Validation of 6SV1 against Coulson's tabulated values for a molecular atmosphere bounded by a Lambertian surface. The validation was performed for four different cases: (1) τ m o l = 0.1 , ρ = 0.25 , SZA = {0.0°, 36.87°, 66.42°}; (2) τ m o l = 0.1 , ρ = 0.8 , SZA = {23.07°, 53.13°, 78.46°}; (3) τ mol = 0.25 , ρ = 0.25, SZA = {23.07°, 53.13°, 78.46°}; and (4) τ m o l = 0.25 , ρ = 0.8 , SZA = {0.0°, 36.87°, 66.42°}.

Fig. 4
Fig. 4

(a) Validation of 6SV1 against Monte Carlo for a molecular atmosphere ( τ mol = 0.25 ) bounded by a Lambertian surface ( ρ = 0.25 ) . The specified angular coordinates designate the boundary VZA values for the Monte Carlo output solid angles. The radius coordinate designates the relative difference between the TOA reflectances of both codes. SZA = {0.0°; 23.0°; 50.0°}. (b) Validation of 6SV1 against Monte Carlo for a clean maritime aerosol atmosphere ( τ a e r = 0.7 ) bounded by a Lambertian surface ( ρ = 0.15 ) . The geometrical conditions are the same as in (a). The simulations were performed at λ = 0.550 μ m . (c) Validation of 6SV1 against Monte Carlo for a molecular atmosphere with τ m o l = 0.093 bounded by shrubs (the RPV BRDF model [14], filled circles) and for a molecular atmosphere with τ m o l = 0.054 bounded by pine forest (the Roujean et al. BRDF model [17], open circles). The geometrical conditions are the same as in (a). (d) TOA reflectances calculated by 6SV1 for a molecular atmosphere with τ m o l = 0.093 bounded by shrubs (the RPV BRDF model, filled circles) and for a molecular atmosphere with τ m o l = 0.054 bounded by pine forest (the Roujean et al. BRDF model, open circles). The geometrical conditions are the same as in (a).

Fig. 5
Fig. 5

(a) Average volume size distribution of aerosol particles measured by AERONET over Midway Islands (28.12 °N, 177.22 °W) on 31 January 2002. (b)–(c) Effects of polarization for a mixed (molecular + aerosol) atmosphere bounded by a Lambertian surface with (b) the ground reflectance ρ = 0.3 (b) and (c) an ocean surface. The aerosol constituent is modeled using the Midway Islands size distribution shown in (a). SZA = {0.0°, 10.0°, 23.07°, 45.0°, 58.67°, 75.0°}; AZ = {0°, 90°, 180°}; VZA = {0°–79°}. The ocean surface model parameters are specified in Table 1. The optical thickness values are listed in Table 2. (d) 6SV1 TOA reflectances for the mixed atmosphere bounded by the ocean surface. SZA (designated by θ S ) = {0.0°, 10.0°, 23.07°, 45.0°, 58.67°}; AZ = 90°; VZA = {0°–79°}. The ocean surface model parameters are specified in Table 1. The optical thickness values are listed in Table 2.

Tables (3)

Tables Icon

Table 1 Parameters of the 6SV1 BRDF Models used in the Part II Validation Study

Tables Icon

Table 2 Optical Thicknesses of Molecular, Aerosol, and Mixed (Molecular + Aerosol) Atmospheres a

Tables Icon

Table 3 Example of Time Estimates a for Scalar and Vector Calculations Depending on the Number of Legendre Coefficients b

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

ρ s ( θ s , ϕ s , θ v , ϕ v ) = ρ 0 cos k 1 θ s cos k 1 θ v ( cos   θ s + cos   θ v ) 1 k F ( ξ ) [ 1 + R ( G ) ] ,
G = [ tan 2 θ s + tan 2 θ v 2   tan   θ s   tan   θ v   cos ( ϕ s ϕ v ) ] 1 / 2 ,
F ( ξ ) = 1 Θ 2 [ 1 + Θ 2 2 Θ   cos ( π - ξ ) ] 1.5 ,
cos   ξ = cos   θ s   cos   θ v + sin   θ s   sin   θ v   cos ( ϕ s ϕ v ) ,
R ( G ) = 1 ρ 0 1 + G .
ρ ( θ s , θ v , ϕ ) = k 0 + k 1 f 1 ( θ s , θ v , ϕ ) + k 2 f 2 ( θ s , θ v , ϕ ) ,
f 1 ( θ s , θ v , ϕ ) = 1 2 π { ( π ϕ ) cos ( ϕ ) + sin ( ϕ ) } tan ( θ s ) tan ( θ v ) 1 π { tan ( θ s ) + tan ( θ v ) + tan 2 ( θ s ) + tan 2 ( θ v ) 2   tan ( θ s ) tan ( θ v ) cos ( ϕ ) } ,
f 2 ( θ s , θ v , ϕ ) = 4 3 π 1 cos ( θ s ) + cos ( θ v ) { ( π 2 ξ ) × cos ( ξ ) + sin ( ξ ) } 1 3 ,
cos ( ξ ) = cos ( θ s ) cos ( θ v ) + sin ( θ s ) sin ( θ v ) cos ( ϕ ) .
ρ os ( θ s , θ v , ϕ , λ ) = ρ wc ( λ ) + { 1 W } · ρ gl ( θ s , θ v , ϕ , λ ) + { 1 ρ wc ( λ ) } · ρ sw ( θ s , θ v , ϕ , λ ) ,
ρ wc ( λ ) = W · f ef · ρ f ( λ ) ,
ρ gl ( θ s , θ v , ϕ , λ ) = π P ( Z x , Z y ) R ( n , θ s , θ v , ϕ , λ ) 4   cos ( θ s ) cos ( θ v ) cos 4 ( β ) ,
ρ sw ( θ s , θ v , ϕ , λ ) = 1 n 2 R w ( λ ) · t d ( θ s ) · t u ( θ v ) 1 a · R w ( λ ) ,

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