Abstract

In examining the dependence of the sea surface reflectance of skylight ρs on sky conditions, wind speed, solar zenith angle, and viewing geometry, Mobley [Appl. Opt. 38, 7442 (1999). [CrossRef]  ] assumed ρs is independent of wavelength. Lee et al. [Opt. Express 18, 26313 (2010). [CrossRef]  ] showed experimentally that ρs does vary spectrally due to the spectral difference of sky radiance coming from different directions, which was ignored in Mobley’s study. We simulated ρs from 350 nm to 1000 nm by explicitly accounting for spectral variations of skylight distribution and Fresnel reflectance. Furthermore, we separated sun glint from sky glint because of significant differences in magnitude, spectrum and polarization state between direct sun light and skylight light. The results confirm that spectral variation of ρs(λ) mainly arises from the spectral distribution of skylight and would vary from slightly blueish due to normal dispersion of the refractive index of water, to neutral and then to reddish with increasing wind speeds and decreasing solar zenith angles. Polarization moderately increases sky glint by 8 – 20% at 400 nm but only by 0 – 10% at 1000 nm. Sun glint is inherently reddish and becomes significant (>10% of sky glint) when the sun is at the zenith with moderate winds or when the sea is roughened (wind speeds > 10 m s-1) with solar zenith angles < 20°. We recommend a two-step procedure by first correcting the glint due to direct sun light, which is unpolarized, followed by removing the glint due to diffused and polarized skylight. The simulated ρs(λ) as a function of wind speeds, sun angles and aerosol concentrations for currently recommended sensor-sun geometry, i.e., zenith angle = 40° and azimuthal angle relative to the sun = 45°, is available upon request.

© 2017 Optical Society of America

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OSA Recommended Articles
Spectral variability of sea surface skylight reflectance and its effect on ocean color

Ting-Wei Cui, Qing-Jun Song, Jun-Wu Tang, and Jie Zhang
Opt. Express 21(21) 24929-24941 (2013)

Estimation of the remote-sensing reflectance from above-surface measurements

Curtis D. Mobley
Appl. Opt. 38(36) 7442-7455 (1999)

References

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2015 (1)

2013 (2)

2012 (2)

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Opt. 51(35), 8324–8340 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (2)

Z. Lee, Y.-H. Ahn, C. Mobley, and R. Arnone, “Removal of surface-reflected light for the measurement of remote-sensing reflectance from an above-surface platform,” Opt. Express 18(25), 26313–26324 (2010).
[Crossref] [PubMed]

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

2006 (3)

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

A. Tanaka, H. Sasaki, and J. Ishizaka, “Alternative measuring method for water-leaving radiance using a radiance sensor with a domed cover,” Opt. Express 14(8), 3099–3105 (2006).
[Crossref] [PubMed]

2002 (2)

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

2000 (1)

1999 (1)

1995 (1)

1988 (1)

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

1985 (1)

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida1,” Limnol. Oceanogr. 30(2), 286–298 (1985).
[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. Transf. 29(6), 521–537 (1983).
[Crossref]

1980 (1)

A. Morel, “In-water and remote measurements of ocean color,” Boundary-Layer Meteorol. 18(2), 177–201 (1980).
[Crossref]

1954 (1)

Acharya, P. K.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Adler-Golden, S. M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Ahmed, S.

Ahn, Y.-H.

Anderson, G. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Arnone, R.

Berk, A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Bernstein, L. S.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Berthon, J. F.

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

Bettenhausen, C.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Borel, C. C.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Carder, K. L.

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida1,” Limnol. Oceanogr. 30(2), 286–298 (1985).
[Crossref]

Chetwynd, J. J. H.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Chowdhary, J.

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Opt. 51(35), 8324–8340 (2012).
[Crossref] [PubMed]

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Cooley, T. W.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Coombes, C. A.

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

Cox, C.

Cui, T.-W.

D’Alimonte, D.

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

De Cauwer, V.

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

Fox, M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Fry, E. S.

Gardner, J. A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Gautam, R.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Gilerson, A.

Greb, S.

Harmel, T.

Harrison, A. W.

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

Hlaing, S.

Hoke, M. L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Holben, B. N.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Hooker, S. B.

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

Hsu, N. C.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Hu, Y.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Ishizaka, J.

Jeong, M. J.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Josset, D. B.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Lazin, G.

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

Lee, J.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Lee, Z.

Legbandt, T.

Lewis, P. E.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Li, C.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Lockwood, R. B.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Lucker, P. L.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

McLean, S.

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

Menzies, D. W.

Mobley, C.

Mobley, C. D.

Moore, G.

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

Morel, A.

A. Morel, “In-water and remote measurements of ocean color,” Boundary-Layer Meteorol. 18(2), 177–201 (1980).
[Crossref]

Munk, W.

Muratov, L.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Nakajima, T.

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. Transf. 29(6), 521–537 (1983).
[Crossref]

Neumann, M. J.

O’Donnell, D.

Pahlevan, N.

Park, Y.-J.

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

Quan, X.

Ruddick, K. G.

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

Sasaki, H.

Sayer, A. M.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Shettle, E. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

Siegel, D. A.

Smith, R. C.

Song, Q.-J.

Steward, R. G.

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida1,” Limnol. Oceanogr. 30(2), 286–298 (1985).
[Crossref]

Tanaka, A.

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. Transf. 29(6), 521–537 (1983).
[Crossref]

Tang, J.-W.

Tonizzo, A.

Toole, D. A.

Trepte, C. R.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Tsay, S. C.

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Weidemann, A.

Zhai, P.-W.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Zhang, J.

Zibordi, G.

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

Appl. Opt. (7)

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38(36), 7442–7455 (1999).
[Crossref] [PubMed]

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Opt. 51(35), 8324–8340 (2012).
[Crossref] [PubMed]

C. D. Mobley, “Polarized reflectance and transmittance properties of windblown sea surfaces,” Appl. Opt. 54(15), 4828–4849 (2015).
[Crossref] [PubMed]

T. Harmel, A. Gilerson, S. Hlaing, A. Tonizzo, T. Legbandt, A. Weidemann, R. Arnone, and S. Ahmed, “Long Island Sound Coastal Observatory: assessment of above-water radiometric measurement uncertainties using collocated multi and hyperspectral systems,” Appl. Opt. 50(30), 5842–5860 (2011).
[Crossref] [PubMed]

D. A. Toole, D. A. Siegel, D. W. Menzies, M. J. Neumann, and R. C. Smith, “Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability,” Appl. Opt. 39(3), 456–469 (2000).
[Crossref] [PubMed]

X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34(18), 3477–3480 (1995).
[Crossref] [PubMed]

Z. Lee, N. Pahlevan, Y.-H. Ahn, S. Greb, and D. O’Donnell, “Robust approach to directly measuring water-leaving radiance in the field,” Appl. Opt. 52(8), 1693–1701 (2013).
[Crossref] [PubMed]

Atmos. Chem. Phys. (1)

N. C. Hsu, R. Gautam, A. M. Sayer, C. Bettenhausen, C. Li, M. J. Jeong, S. C. Tsay, and B. N. Holben, “Global and regional trends of aerosol optical depth over land and ocean using SeaWiFS measurements from 1997 to 2010,” Atmos. Chem. Phys. 12(17), 8037–8053 (2012).
[Crossref]

Boundary-Layer Meteorol. (1)

A. Morel, “In-water and remote measurements of ocean color,” Boundary-Layer Meteorol. 18(2), 177–201 (1980).
[Crossref]

Hyperspectral, and Ultraspectral Imagery (1)

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Golden, J. J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, ““MODTRAN5: 2006 update,” in Algorithms and Technologies for Multispectral,” Hyperspectral, and Ultraspectral Imagery XII, 62331F (2006).

J. Atmos. Ocean. Technol. (2)

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol. 19(4), 486–515 (2002).
[Crossref]

G. Zibordi, S. B. Hooker, J. F. Berthon, and D. D’Alimonte, “Autonomous above-water radiance measurements from an offshore platform: A field assessment experiment,” J. Atmos. Ocean. Technol. 19(5), 808–819 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transf. (2)

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. Transf. 29(6), 521–537 (1983).
[Crossref]

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Limnol. Oceanogr. (2)

K. G. Ruddick, V. De Cauwer, Y.-J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr. 51(2), 1167–1179 (2006).
[Crossref]

K. L. Carder and R. G. Steward, “A remote-sensing reflectance model of a red-tide dinoflagellate off west Florida1,” Limnol. Oceanogr. 30(2), 286–298 (1985).
[Crossref]

Opt. Express (3)

Sol. Energy (1)

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

Other (3)

R. W. Austin, “Inherent spectral radiance signatures of the ocean surface,” in Ocean Color Analysis SIO S. Q. Duntley, R. W. Austin, W. H. Wilson, C. F. Edgerton, and S. E. Moran, eds. (Scripps Institution of oceanography, 1974), pp. 2-1–2-20, Ref. 74–10.

J. L. Mueller, G. S. Fargion, and C. R. McClain, “Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 4, Vol. III: Radiometric Measurements and Data Analysis Protocols,” NASA/TM-2003–21621, NASA Goddard Space Flight Center, 2003).

S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public. 8, 13058 (2013).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram showing the typical experimental setup for above-water water-leaving radiance measurements. As a convention, the sun is always placed in the X-Z plane.

Fig. 2
Fig. 2

The contours of logarithmic probability density p (sr−1) as a function of skylight direction (θ, φ) at wind speeds of 0, 5, 10 and 15 m s−1. In each polar plot, the center represents the sensor’s FOV, zenith angles (θ) vary from 0 to 90° in radial direction, and azimuth angles (φ) are defined relative to the sun. The star, □ and + symbols denote the directions of the sun (θsun, φsun) = (30°, 0), the sensor (θv, φv) = (40°, 45°) and specular point of the sensor (θ’, φ’) = (40°, 225°), respectively.

Fig. 3
Fig. 3

The reflectance angle (a) and Fresnel reflectance at 532 nm (b) estimated for each quad. The polar axes and symbols are the same as in Fig. 2.

Fig. 4
Fig. 4

The normalized sky light distribution, Lsky(θ,φ) / Lsky(θ’,φ’), as a function of θsun (10, 30 and 50°) and wavelengths (400 and 700 nm). The yellow contour line, if shown, has a value of 16. The polar axes and symbols are the same as in Fig. 2. The star indicates the direction in the sky with the lowest radiance.

Fig. 5
Fig. 5

Variations of rsky, Rsky and ρsky with wind speeds (U = 0, 5, 10 and 15 m s−1) and solar zenith angles (θsun = 0 and 30°). Note that the blue solid line (U = 0 m s−1, θsun = 0°) and blue dotted line (U = 0 m s−1, θsun = 30°) overlap each other in (b) and (c). The dotted line in (a) represents Fresnel reflectance for reflectance angle of 40° and the dashed line in (b) and (c) represents the values computed if the skylight distribution is assumed to be spectral-invariant and simulated using the Harrison and Coombes [19] model U = 10 m s−1 and θsun = 30°.

Fig. 6
Fig. 6

Variations of rsun (a), Rsun (b) and ρsun (c) with wind speeds (U = 0, 5, 10 and 15 m s−1) and solar zenith angles (θsun = 0 and 30°). Open, grey and black circles in (d) indicate those conditions under which average ρsun(λ)/ρsky(λ) < 1%, 1-10%, and > 10%.

Fig. 7
Fig. 7

Simulated ρs(λ) for various wind speeds and solar zenith angles are grouped depending on the importance of the sun glint. (a), (b) and (c) correspond to cases denoted by open, grey and black circles in Fig. 6(d). For the same wind speed (i.e., curves of same color), ρs(λ) have higher values for smaller solar zenith angle. The y-scale in (c) is different from (a) and (b).

Fig. 8
Fig. 8

ρs(λ) simulated for U = 10 m s−1 and θsun = 30° and for different sensor viewing geometry as indicated in the legend. The dashed lines are ρsun(λ), dotted lines ρsky(λ) and solid lines ρs(λ).

Fig. 9
Fig. 9

Ratios of ρsky(λ) to ρsky(λ; U = 10; τa = 0.05) simulated for θsun = 30° and various wind speeds and aerosol optical depths. From bottom to top, the blue lines are for U = 0, 5, 8, 10, 12 and 15 m s−1 and τa = 0.05; the red dotted lines are for U = 10 m s−1 and τa = 0, 0.05, 0.1 and 0.3.

Fig. 10
Fig. 10

Ratios of ρs(λ) simulated with and without polarization for various solar zenith angles (θsun), wind speeds (U) and aerosol optical depth (τa). The mean of the ratios is shown as black dotted line in each panel.

Equations (12)

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L w (λ; Ω v )= L t (λ; Ω v ) 2π p(Ω Ω v )r(λ;Ω Ω v ) L s (λ;Ω)dΩ.
L w (λ; Ω v )= L t (λ; Ω v ) ρ s (λ) L s (λ;θ',φ'),
ρ s (λ)= 2π p(Ω Ω v )r(λ;Ω Ω v ) L s (λ;Ω)dΩ L s (λ;θ',φ',) .
ρ s (λ)= ρ sky (λ)+ ρ sun (λ),
ρ sky (λ)= 2πΩs p(Ω Ω v )r(λ;Ω Ω v ) L sky (λ;Ω)dΩ L sky (λ;θ',φ',) ,
ρ sun (λ)= Ωs p(Ω Ω v )r(λ;Ω Ω v ) L sun (λ;Ω)dΩ L sky (λ;θ',φ') ,
ρ sky (λ)= L sky (λ; θ m , φ m ) L sky (λ;θ',φ',) 2πΩs p(Ω'Ω)r(λ;Ω'Ω)dΩ' = R sky (λ) r sky (λ),
ρ sun (λ)= L sun (λ; θ sun , φ sun ) L sky (λ;θ',φ') Ωs p(Ω Ω v )r(λ;Ω Ω v )dΩ = R sun (λ) r sun (λ),
p i = p θ × p φ 2π p i ,
p θ =exp( tan 2 θ ni,min 2 σ 2 )exp( tan 2 θ ni,max 2 σ 2 ),
p φ = φ ni,max φ ni,min 2π ,
[ cos θ sun sin α 0.5 cosβsin θ sun cos α 0.5 sin α 0.5 sinβ sin θ sun sin α 0.5 cosβcos θ sun cos α 0.5 ],

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