Abstract

The remote-sensing reflectance R rs is not directly measurable, and various methodologies have been employed in its estimation. I review the radiative transfer foundations of several commonly used methods for estimating R rs, and errors associated with estimating R rs by removal of surface-reflected sky radiance are evaluated using the Hydrolight radiative transfer numerical model. The dependence of the sea surface reflectance factor ρ, which is not an inherent optical property of the surface, on sky conditions, wind speed, solar zenith angle, and viewing geometry is examined. If ρ is not estimated accurately, significant errors can occur in the estimated R rs for near-zenith Sun positions and for high wind speeds, both of which can give considerable Sun glitter effects. The numerical simulations suggest that a viewing direction of 40 deg from the nadir and 135 deg from the Sun is a reasonable compromise among conflicting requirements. For this viewing direction, a value of ρ ≈ 0.028 is acceptable only for wind speeds less than 5 m s-1. For higher wind speeds, curves are presented for the determination of ρ as a function of solar zenith angle and wind speed. If the sky is overcast, a value of ρ ≈ 0.028 is used at all wind speeds.

© 1999 Optical Society of America

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1999

1998

1997

1995

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100(C7), 13,143–13,150 (1995).
[CrossRef]

1993

1991

A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26, 263–306 (1991).
[CrossRef]

1989

J. R. V. Zaneveld, “An asymptotic closure theory of irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).

1988

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

1986

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

1985

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30(2), 286–298 (1985).

1981

Abreu, L. W.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Acharya, P. K.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Adler-Golden, S. M.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Anderson, G. P.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Arnone, R. A.

Austin, R. W.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, Vol. 25, , S. B. Hooker, E. R. Firestone, J. G. Acker, eds. (National Technical Information Service, Springfield, Va., 1995).

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

Berk, A.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Bernstein, L. S.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

Bukata, R. P.

R. P. Bukata, J. H. Jerome, K. Ya. Kondratyev, D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC Press, New York, 1995).

Carder, K. L.

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30(2), 286–298 (1985).

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Chetwynd, J. H.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Clark, D. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

Clough, S. A.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Coombes, C. A.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

Davis, C. O.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Deschamps, P.-Y.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

Fougnie, B.

Frouin, R.

Gallery, W. O.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Gentili, B.

Gordon, H. R.

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, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery, a review,” in Lecture Notes on Coastal and Estuarine Studies (Springer Verlag, New York, 1983), Vol. 4.
[CrossRef]

Gould, R. W.

Gurganus, E. A.

Harrison, A. W.

A. W. Harrison, C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

Houghton, W. M.

Jerome, J. H.

R. P. Bukata, J. H. Jerome, K. Ya. Kondratyev, D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC Press, New York, 1995).

Jin, Z.

Kattawar, G. W.

Kneizys, F. X.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Kondratyev, K. Ya.

R. P. Bukata, J. H. Jerome, K. Ya. Kondratyev, D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC Press, New York, 1995).

Ladner, S. D.

Lecomte, P.

Lee, Z. P.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Matthew, M. W.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Menzies, D. W.

D. A. Toole, D. A. Siegel, D. W. Menzies, J. J. Neumann, R. C. Smith, “Remote sensing reflectance determinations in coastal environments—impacts of instrumental characteristics and environmental variability,” Appl. Opt. (to be published).

Mobley, C. D.

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]

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

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

C. D. Mobley, Hydrolight 4.0 Users’ Guide, Second Printing (Sequoia Scientific, Inc., Redmond, Wash., 1998).

C. D. Mobley, D. Stramski, “Origins of variability in remote-sensing reflectances,” (Sequoia Scientific, Inc., Redmond, Wash., 1997).

Morel, A.

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100(C7), 13,143–13,150 (1995).
[CrossRef]

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]

A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26, 263–306 (1991).
[CrossRef]

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation of satellite visible imagery, a review,” in Lecture Notes on Coastal and Estuarine Studies (Springer Verlag, New York, 1983), Vol. 4.
[CrossRef]

Morris, W. D.

Mueller, J. L.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, Vol. 25, , S. B. Hooker, E. R. Firestone, J. G. Acker, eds. (National Technical Information Service, Springfield, Va., 1995).

Neumann, J. J.

D. A. Toole, D. A. Siegel, D. W. Menzies, J. J. Neumann, R. C. Smith, “Remote sensing reflectance determinations in coastal environments—impacts of instrumental characteristics and environmental variability,” Appl. Opt. (to be published).

Peacock, T. G.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Poole, L. R.

Pozdnyakov, D. V.

R. P. Bukata, J. H. Jerome, K. Ya. Kondratyev, D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC Press, New York, 1995).

Preisendorfer, R. W.

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

Reinersman, P.

Robertson, D. C.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Selby, J. E. A.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Shettle, E. P.

P. K. Acharya, A. Berk, L. S. Bernstein, M. W. Matthew, S. M. Adler-Golden, D. C. Robertson, G. P. Anderson, J. H. Chetwynd, F. X. Kneizys, E. P. Shettle, L. W. Abreu, W. O. Gallery, J. E. A. Selby, S. A. Clough, “MODTRAN user’s manual versions 3.7 and 4.0” (Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Mass., 1998).

Siegel, D. A.

D. A. Toole, D. A. Siegel, D. W. Menzies, J. J. Neumann, R. C. Smith, “Remote sensing reflectance determinations in coastal environments—impacts of instrumental characteristics and environmental variability,” Appl. Opt. (to be published).

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

D. A. Toole, D. A. Siegel, D. W. Menzies, J. J. Neumann, R. C. Smith, “Remote sensing reflectance determinations in coastal environments—impacts of instrumental characteristics and environmental variability,” Appl. Opt. (to be published).

Stamnes, K.

Stavn, R. H.

Steward, R. G.

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida,” Limnol. Oceanogr. 30(2), 286–298 (1985).

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote-sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, ed., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Stramski, D.

C. D. Mobley, D. Stramski, “Origins of variability in remote-sensing reflectances,” (Sequoia Scientific, Inc., Redmond, Wash., 1997).

Sydor, M.

Terrie, G. E.

Toole, D. A.

D. A. Toole, D. A. Siegel, D. W. Menzies, J. J. Neumann, R. C. Smith, “Remote sensing reflectance determinations in coastal environments—impacts of instrumental characteristics and environmental variability,” Appl. Opt. (to be published).

Usry, J. W.

Voss, K. J.

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100(C7), 13,143–13,150 (1995).
[CrossRef]

Whitlock, C. H.

Witte, W. G.

Wood, C. G.

Zaneveld, J. R. V.

J. R. V. Zaneveld, “An asymptotic closure theory of irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).

Appl. Opt.

J. Geophys. Res.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. C. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93(D9), 10,909–10,924 (1988).
[CrossRef]

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R. W. Austin, “Inherent spectral radiance signatures of the ocean surface,” in S. Q. Duntley, R. W. Austin, W. H. Wilson, C. F. Edgerton, S. E. Moran, “Ocean color analysis,” (Scripps Institution of Oceanography, La Jolla, Calif., 1974).

C. D. Mobley, Hydrolight 4.0 Users’ Guide, Second Printing (Sequoia Scientific, Inc., Redmond, Wash., 1998).

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Figures (15)

Fig. 1
Fig. 1

Illustration of concepts for a wind-blown sea surface. L r is the surface-reflected part of the incident sky radiance L s . L w is the transmitted part of the upwelling underwater radiance L u . The downward-looking radiometer has a FOV with solid angle ΩFOV.

Fig. 2
Fig. 2

Illustration of the sky regions seen by a detector looking at the sea surface. U is the wind speed. The detector and specular point are centered at θ = 40° from the zenith. One hundred points are plotted for U = 0, and 5,000 points are plotted for the other cases.

Fig. 3
Fig. 3

Sun and sensor geometry as often used in field measurements.

Fig. 4
Fig. 4

Comparison of ρ as computed by Hydrolight (solid curve) and by Austin12 (dashed curve). The wind speed is 10 m s-1 and the Sun is at θ s = 60° in a uniform background sky.

Fig. 5
Fig. 5

Illustration of the sky region seen by a detector for U = 15 m s-1, as in Fig. 2; 10,000 points are plotted. The solid lines are contours of the relative sky radiance computed by the formulas of Harrison and Coombes11 for θ s = 30° in a clear sky.

Fig. 6
Fig. 6

Effects of Sun glitter and nonuniform sky radiance on ρ. The wind speed is U = 10 m s-1 and the sky has a radiance distribution characteristic of a clear sky (as in Fig. 5); θ s is the solar zenith angle. The dotted curves are different Monte Carlo simulations for the θ s = 30° case. The dashed curve is Austin’s curve from Fig. 4.

Fig. 7
Fig. 7

Contour plots of ρ (solid lines) as a function of viewing direction (θ v , ϕ v ) for θ s = 30 deg and two wind speeds. Contour values are 0.03 to 0.12 by 0.01. The ✴ symbols show the specular direction of the Sun, and the θ v contours (dotted lines) are labeled along the ϕ v = 135-deg direction.

Fig. 8
Fig. 8

Effect of wind speed and viewing direction on ρ for a Sun zenith angle of θ s = 30 deg and a clear-sky radiance distribution. The solid curves are for an azimuthal viewing direction of ϕ v = 135 deg, and the dotted curves are for ϕ v = 90 deg.

Fig. 9
Fig. 9

Effect of wind speed and Sun zenith angle on ρ for a viewing direction of θ v = 40 deg and a clear-sky radiance distribution. The solid curves are for an azimuthal viewing direction of ϕ v = 135 deg and the dotted curves are for ϕ v = 90 deg.

Fig. 10
Fig. 10

Representations of clouds. The shaded areas in panels 1, 2, and 3 show the locations of clouds in an otherwise clear sky (sky radiance contours as in Fig. 5); panel 4 shows the sky radiance distribution for a cloud parameter value of C = 0.5 in the Harrison and Coombes11 formulas. The Sun is at θ s = 30 deg and the viewing direction is (θ v , ϕ v ) = (40°, 135°). As in Figs. 2 and 5, the small rectangle shows the region of the sky that would be seen by a detector for zero wind speed, and the dots illustrate the region of the sky seen for a 10-m s-1 wind (2,000 points plotted).

Fig. 11
Fig. 11

modtran-simulated blue-sky (L s ) and cumulus cloud (L c ) radiances for the viewing geometry of Fig. 10. The dashed curve shows the ratio C L = L c /L s .

Fig. 12
Fig. 12

Relative contribution of the water-leaving radiance L w to the total upward radiance L t as a function of wind speed U and wavelength for a case 1 water body with 2 mg m-3 of chlorophyll and for θ s = 30 deg in a clear sky. The left panel is for a viewing direction of (θ v , ϕ v ) = (30°, 90°) and the right panel is for (θ v , ϕ v ) = (40°, 135°).

Fig. 13
Fig. 13

Exact and estimated R rs for a wind speed of U = 10 m s-1 and for θ s = 30 deg in a clear sky. The left panel is for a viewing direction of (θ v , ϕ v ) = (30°, 90°) and the right panel is for (θ v , ϕ v ) = (40°, 135°). The water body is the same as for Fig. 12. The curve patterns denote the exact R rs (solid curves); R rs is estimated by use of ρ = 0.0222 (dashed curves), ρ = 0.06 in Eq. (6) (left panel, dash–dot curve), or ρ = 0.034 in Eq. (6) (right panel, dash–dot curve); and the SeaWiFS estimate is based on Eq. (7) (dotted curves).

Fig. 14
Fig. 14

Exact and estimated R rs for a wind speed of U = 10 m s-1 and for θ s = 30 deg in a sky with clouds arranged as in the cloud 3 case of Fig. 10. Both panels have (θ v , ϕ v ) = (40°, 135°). The left panel is for case 1 water and the right panel is for case 2 water, as described in the text. In both panels the curves denote the exact R rs (solid curves), estimates made with ρ = 0.0332 (dashed curves and ρ = 0.0595 (dash–dot curves) and the SeaWiFS estimate (dotted curves).

Fig. 15
Fig. 15

Exact and estimated R rs for a wind speeds of U = 0 and 10 m s-1 for θ s = 30 deg in a clear sky. The water body is the case 2 water described in the text. The curve patterns denote the exact R rs (solid curves) the estimate made with Eq. (6) and the appropriate ρ value from Fig. 9 (dashed curves) and the SeaWiFS estimate (dotted curves). The bars at the bottom of the left panel show the nominal SeaWiFS bands.

Tables (1)

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Table 1 Simulations of Cloud Effects on ρa

Equations (12)

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Rrsθ, ϕ, λ  Lwθ, ϕ, λEdλ.
Ltθ, ϕ=Lrθ, ϕ+Lwθ, ϕ.
Ltθ, ϕΩFOV=1ΩFOVΩFOV2πd Lsθ, ϕ×rθ, ϕθ, ϕdΩθ, ϕdΩθ, ϕ+1ΩFOVΩFOV2πu Luθ, ϕ×tθ, ϕθ, ϕdΩθ, ϕdΩθ, ϕLrθ, ϕΩFOV+Lwθ, ϕΩFOV.
Lrθ, ϕΩFOV  ρLsθ, ϕΩFOV.
Lg=Rg/πEd.
Rrs=Lt-ρLsπRg Lg.
Rrsλ; final=Rrsλ; by Eq. 6-Rrs750 nm; by Eq. 6.
Lwa; θ, ϕΩFOV  τLuw; θ, ϕΩu.
τ=1-rFθ, θn2,
Rrsθ, ϕ=τ Luw; θ, ϕEda,
Edw=EuwRu+Eda1-Rs.
Rrsθ, ϕ=1-rFθ, θ1-Rsn21-RRu×Luw; θ, ϕEdw  T RQθ, ϕ,

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