Abstract

We have implemented Raman scattering in a vector radiative transfer model for coupled atmosphere and ocean systems. A sensitivity study shows that the Raman scattering contribution is greatest in clear waters and at longer wavelengths. The Raman scattering contribution may surpass the elastic scattering contribution by several orders of magnitude at depth. The degree of linear polarization in water is smaller when Raman scattering is included. The orientation of the polarization ellipse shows similar patterns for both elastic and inelastic scattering contributions. As polarimeters and multipolarization-state lidars are planned for future Earth observing missions, our model can serve as a valuable tool for the simulation and interpretation of these planned observations.

© 2015 Optical Society of America

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References

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    [Crossref]
  31. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II Integrating measurements,” Appl Opt. 36, 8710–8723 (1997).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  37. Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
    [Crossref]
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    [Crossref]
  39. G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  44. G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
    [Crossref]
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  47. Note that Fresnel cone is also called Snell’s window in underwater photographer: http://en.wikipedia.org/wiki/Snell%27s_window
  48. A. Ibrahim, A. Gilerson, T. Harmel, A. Tonizzo, J. Chowdhary, and S. Ahmed, “The relationship between upwelling underwater polarization and attenuation/absorption ratio,” Opt. Express 20, 25662–25680 (2012).
    [Crossref] [PubMed]
  49. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
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    [Crossref]

2015 (2)

2013 (1)

2012 (1)

2010 (1)

P. 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. Transfer 111, 1025–1040 (2010).
[Crossref]

2009 (5)

R. Pincus and K. F. Evans, “Computational cost and accuracy in calculating three-dimensional radiative transfer: results for new implementations of Monte Carlo and SHDOM,” J. Atmos. Sci. 66, 3131–3146 (2009).
[Crossref]

A. Morel and B. Gentili, “A simple band ratio technique to quantify the colored dissolved and detrital organic material from ocean color remotely sensed data,” Rem. Sens. Environ. 113, 998–1011 (2009).
[Crossref]

P. Zhai, Y. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
[Crossref] [PubMed]

X. Zhang and L. Hu, “Scattering by pure seawater at high salinity,” Opt. Express,  1712685–12691 (2009).
[Crossref] [PubMed]

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
[Crossref]

2008 (2)

H. Loisel, L. Duforet, D. Dessailly, M. Chami, and P. Dubuisson, “Investigation of the variations in the water leaving polarized reflectance from the POLDER satellite data over two biogeochemical contrasted oceanic areas,” Opt. Express 16, 12905–12918 (2008).
[Crossref] [PubMed]

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

2006 (1)

T. H. Waterman, “Reviving a neglected celestial underwater polarization compass for aquatic animals,” Biol. Rev. 81, 111–115 (2006).
[Crossref]

2005 (1)

2003 (2)

A. A. Kokhanovsky, “Parameterization of the Mueller matrix of oceanic waters,” J. Geophys. Res. 108, 3175 (2003).
[Crossref]

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

2002 (1)

2001 (2)

2000 (1)

1999 (2)

H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38, 3166–3174 (1999).
[Crossref]

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

1998 (3)

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[Crossref]

S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37, 2216–2227 (1998).
[Crossref]

1997 (2)

C. M. Hu and K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
[Crossref]

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II Integrating measurements,” Appl Opt. 36, 8710–8723 (1997).
[Crossref]

1995 (2)

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[Crossref]

Y. Ge, K. J. Voss, and H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13227–13236 (1995).
[Crossref]

1994 (3)

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, Ocean Optics XII, 222–233 (1994)
[Crossref]

G. Fourier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[Crossref] [PubMed]

1993 (1)

1992 (1)

1990 (1)

1988 (1)

1984 (2)

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl Opt. 23, 4427–4439 (1984).
[Crossref] [PubMed]

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[Crossref]

1975 (1)

N. P. Romanov and V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR),  38646–648 (1975).

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1967 (1)

G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[Crossref]

1954 (1)

Ahmed, S.

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

Babin, M.

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

Bartlett, J. S.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boss, E.

Boynton, G. C.

Bricaud, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

Cacciari, A.

Carder, K. L.

Chaikovskaya, L. I.

Chami, M.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer, (Dover, 1960).

Chowdhary, J.

A. Ibrahim, A. Gilerson, T. Harmel, A. Tonizzo, J. Chowdhary, and S. Ahmed, “The relationship between upwelling underwater polarization and attenuation/absorption ratio,” Opt. Express 20, 25662–25680 (2012).
[Crossref] [PubMed]

P. 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. Transfer 111, 1025–1040 (2010).
[Crossref]

Claustre, H.

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

Cox, C.

Davis, C. O.

Dessailly, D.

Dubuisson, P.

Duforet, L.

Evans, K. F.

R. Pincus and K. F. Evans, “Computational cost and accuracy in calculating three-dimensional radiative transfer: results for new implementations of Monte Carlo and SHDOM,” J. Atmos. Sci. 66, 3131–3146 (2009).
[Crossref]

Forand, J. L.

G. Fourier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Foujols, T.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Fourier, G.

G. Fourier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

Fournier, G.

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Freeman, S. A.

Fry, E. S.

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II Integrating measurements,” Appl Opt. 36, 8710–8723 (1997).
[Crossref]

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl Opt. 23, 4427–4439 (1984).
[Crossref] [PubMed]

Ge, Y.

Y. Ge, K. J. Voss, and H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13227–13236 (1995).
[Crossref]

Ge, Y. T.

Gentili, B.

A. Morel and B. Gentili, “A simple band ratio technique to quantify the colored dissolved and detrital organic material from ocean color remotely sensed data,” Rem. Sens. Environ. 113, 998–1011 (2009).
[Crossref]

Gilerson, A.

Gillotay, D.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Gordon, H. R.

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Harmel, T.

Hawes, S. K.

Herse, M.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Hu, C. M.

Hu, L.

Hu, Y.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Huot, Y.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

Ibrahim, A.

Jonasz, M.

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Josset, D. B.

P. Zhai, Y. Hu, C. R. Trepte, D. M. Winker, P. L. Lucker, Z. Lee, and D. B. Josset, “Uncertainty in the bidirectional reflectance model for oceanic waters,” Appl. Opt. 54, 4061–4069 (2015).
[Crossref]

P. 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. Transfer 111, 1025–1040 (2010).
[Crossref]

Katsev, I. L.

Kattawar, G. W.

Kishino, M.

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[Crossref]

Kokhanovsky, A. A.

A. A. Kokhanovsky, “Parameterization of the Mueller matrix of oceanic waters,” J. Geophys. Res. 108, 3175 (2003).
[Crossref]

Labs, S.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Lee, Z.

Lee, Z. P.

Lee, Z.-P.

Lewis, M. R.

Loisel, H.

Lucker, P. L.

Lupi, A.

Mandel, H.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Maritorena, S.

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

Marshall, B. R.

McLean, S. D.

Mobley, C.

Mobley, C. D.

Morel, A.

A. Morel and B. Gentili, “A simple band ratio technique to quantify the colored dissolved and detrital organic material from ocean color remotely sensed data,” Rem. Sens. Environ. 113, 998–1011 (2009).
[Crossref]

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

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

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

Munk, W.

Okami, N.

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[Crossref]

Peacock, T. G.

Peetermans, W.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Petkov, B.

Pincus, R.

R. Pincus and K. F. Evans, “Computational cost and accuracy in calculating three-dimensional radiative transfer: results for new implementations of Monte Carlo and SHDOM,” J. Atmos. Sci. 66, 3131–3146 (2009).
[Crossref]

Platt, T.

Pope, R. M.

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II Integrating measurements,” Appl Opt. 36, 8710–8723 (1997).
[Crossref]

Prikhach, A. S.

Reynolds, R. A.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

Romanov, N. P.

N. P. Romanov and V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR),  38646–648 (1975).

Sathyendranath, S.

Shulkin, V. S.

N. P. Romanov and V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR),  38646–648 (1975).

Simon, P.C.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Smith, R. C.

Stavn, R. H.

Steward, R. G.

Stramski, D.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
[Crossref]

Sugihara, S.

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[Crossref]

Sundman, L. K.

Thuillier, G.

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Tomasi, C.

Tonizzo, A.

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Trepte, C. R.

Twardowski, M. S.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
[Crossref]

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

Tynes, H. H.

Vitale, V.

Vodacek, A.

Voss, K. J.

Walrafen, G. E.

G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[Crossref]

Waterman, T. H.

T. H. Waterman, “Reviving a neglected celestial underwater polarization compass for aquatic animals,” Biol. Rev. 81, 111–115 (2006).
[Crossref]

Waters, K. J.

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[Crossref]

Weidemann, A. D.

Westberry, T. K.

Winker, D. M.

Xu, X.

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, Ocean Optics XII, 222–233 (1994)
[Crossref]

G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31, 6491–6500 (1992).
[Crossref] [PubMed]

Zege, E. P.

Zhai, P.

Zhang, X.

Appl Opt. (2)

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II Integrating measurements,” Appl Opt. 36, 8710–8723 (1997).
[Crossref]

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl Opt. 23, 4427–4439 (1984).
[Crossref] [PubMed]

Appl. Opt. (16)

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt.,  40, 400–412 (2001).
[Crossref]

C. Tomasi, V. Vitale, B. Petkov, A. Lupi, and A. Cacciari, “Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres,” Appl. Opt. 44, 3320–3341 (2005).
[Crossref] [PubMed]

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

P. Zhai, Y. Hu, C. R. Trepte, D. M. Winker, P. L. Lucker, Z. Lee, and D. B. Josset, “Uncertainty in the bidirectional reflectance model for oceanic waters,” Appl. Opt. 54, 4061–4069 (2015).
[Crossref]

B. R. Marshall and R. C. Smith, “Raman scattering and in- water ocean optical properties,” Appl. Opt. 29, 71–84 (1990).
[Crossref] [PubMed]

C. M. Hu and K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
[Crossref]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[Crossref]

R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
[Crossref] [PubMed]

G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31, 6491–6500 (1992).
[Crossref] [PubMed]

Y. T. Ge, H. R. Gordon, and K. J. Voss, “Simulation of inelastic scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
[Crossref] [PubMed]

H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38, 3166–3174 (1999).
[Crossref]

T. K. Westberry, E. Boss, and Z.-P. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52, 5552–5561 (2013).
[Crossref] [PubMed]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[Crossref] [PubMed]

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[Crossref] [PubMed]

S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37, 2216–2227 (1998).
[Crossref]

H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
[Crossref]

Biogeosciences (1)

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5, 495–507 (2008).
[Crossref]

Biol. Rev. (1)

T. H. Waterman, “Reviving a neglected celestial underwater polarization compass for aquatic animals,” Biol. Rev. 81, 111–115 (2006).
[Crossref]

J Geoph Res. (1)

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models,” J Geoph Res. 103, 31033–31044 (1998).
[Crossref]

J. Atmos. Sci. (1)

R. Pincus and K. F. Evans, “Computational cost and accuracy in calculating three-dimensional radiative transfer: results for new implementations of Monte Carlo and SHDOM,” J. Atmos. Sci. 66, 3131–3146 (2009).
[Crossref]

J. Chem. Phys. (1)

G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[Crossref]

J. Geophys. Res. (3)

Y. Ge, K. J. Voss, and H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13227–13236 (1995).
[Crossref]

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[Crossref]

A. A. Kokhanovsky, “Parameterization of the Mueller matrix of oceanic waters,” J. Geophys. Res. 108, 3175 (2003).
[Crossref]

J. Oceanogr. Soc. Jpn. (1)

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[Crossref]

J. of Geophys. Res. (1)

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

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

P. 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. Transfer 111, 1025–1040 (2010).
[Crossref]

Opt. Express (5)

Opt. Spectrosc. (USSR) (1)

N. P. Romanov and V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR),  38646–648 (1975).

Proc. SPIE (3)

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, Ocean Optics XII, 222–233 (1994)
[Crossref]

G. Fourier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[Crossref]

G. Fournier and M. Jonasz, “Computer-based underwater imaging analysis,” Proc. SPIE 3761, 62–70 (1999).
[Crossref]

Rem. Sens. Environ. (1)

A. Morel and B. Gentili, “A simple band ratio technique to quantify the colored dissolved and detrital organic material from ocean color remotely sensed data,” Rem. Sens. Environ. 113, 998–1011 (2009).
[Crossref]

Solar Physics (1)

G. Thuillier, M. Herse, S. Labs, T. Foujols, W. Peetermans, D. Gillotay, P.C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by SOLSPEC Spectrometer from the ATLAS 123 and EURECA missions,” Solar Physics,  2141–22 (2003).
[Crossref]

Space Sci. Rev. (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Other (8)

S. Chandrasekhar, Radiative Transfer, (Dover, 1960).

Committee on Extension to the Standard Atmosphere, U. S. Standard Atmosphere, (U.S. Government Printing Office, Washington D.C.1976).

Z. Lee, “Absorption coefficients for phytoplankton particles,” personal communication, (2015).

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

http://decadal.gsfc.nasa.gov/pace.html

T. K. Westberry, “Raman contribution ratio from Hydrolight 5.0,” personal communication, (2015).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Note that Fresnel cone is also called Snell’s window in underwater photographer: http://en.wikipedia.org/wiki/Snell%27s_window

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Figures (8)

Fig. 1
Fig. 1 The viewing geometry with the solar zenith, viewing zenith, and azimuth angles defined. The plane contains the x-axis and zenith is the principal plane, which also contains the sun.
Fig. 2
Fig. 2 The reduced Mueller matrices for elastic and inelastic scattering in ocean water.
Fig. 3
Fig. 3 (a)The radiance (Wm2µm1Sr1) in the nadir-viewing direction just below the ocean surface. The solar zenith angle is 45° and the wind speed is 5 m/s. The solid and dashed curves show the cases without and with Raman scattering, respectively. (b) The ratio of the inelastic scattering radiance to the total radiance as in Fig. 3(a). The subscript R and t stands for Raman scattering and total radiance, respectively. The same color code is used to denote the [Chla] values in Figs. 3(a) and Figs. 3(b)
Fig. 4
Fig. 4 The radiance (Wm2µm1Sr1) as a function of the viewing zenith angle at λ = 560nm in the principal plane. The solar zenith angle is 45°; and the wind speed is 5 m/s. The words ”w/o Raman” and ”w Raman” mean that the case is without or with Raman scattering, respectively.
Fig. 5
Fig. 5 The radiance (Wm2µm1Sr1) as a function of the viewing zenith angle at λ = 660nm in the principal plane for the same system as in Fig. 4.
Fig. 6
Fig. 6 The degree of linear polarization as a function of the viewing zenith angle at λ = 560nm in the principal plane for the system shown in Fig. 4
Fig. 7
Fig. 7 The degree of linear polarization as a function of the viewing zenith angle at λ = 660nm in the principal plane for the system shown in Fig. 5.
Fig. 8
Fig. 8 The Orientation of the Polarization Ellipse (OPE) as a function of the viewing angle at the detector depth of 40 m for the same case as in Fig. 7(a).

Equations (22)

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μ d L ( z , μ , ϕ , λ ) d z = c ( z , λ ) L ( z , μ , ϕ , λ ) + S ( z , μ , ϕ , λ ) + S R ( z , μ , ϕ , λ ) ,
S ( z , μ , ϕ , λ ) = b ( z , λ ) 0 2 π 1 1 P ( z , μ , ϕ , μ , ϕ , λ ) L ( z , μ , ϕ , λ ) d μ d ϕ ,
P ( z , μ , ϕ , μ , ϕ , λ ) = R ( π i 2 ) F ( z , Θ , λ ) R ( i 1 ) .
0 2 π 1 1 F 11 ( z , μ , ϕ , μ , ϕ , λ ) d μ d ϕ = 1.
S R ( z , μ , ϕ , λ ) = 0 λ 0 2 π 1 1 b R ( z , λ , λ e ) P R ( z , μ , ϕ , μ , ϕ , λ , λ e ) L ( z , μ , ϕ , λ e ) d μ d ϕ d λ e ,
c ( z , λ ) = a e ( z , λ ) + a R ( z , λ ) + b ( z , λ ) ,
a ( λ , [ Chla ] ) = a w ( λ ) + a y ( λ , [ C h l a ] ) + a p ( λ , [ Chla ] ) ,
a w ( λ ) = a w e ( λ ) + a R ( λ ) ,
a e ( λ , [ Chla ] ) = a w e ( λ ) + a y ( λ , [ Chla ] ) + a p ( λ , [ Chla ] ) .
a y ( λ , [ Chla ] ) = 0.0316 [ Chla ] 0.63 exp ( 0.014 ( λ 440 ) ) .
a p ( λ , [ Chla ] ) = A p ( λ ) [ Chla ] E p ( λ ) ,
b ( λ , [ Chla ] ) = b w ( λ ) + b p ( λ , [ Chla ] ) .
b w ( λ ) = 0.00193 ( 550 / λ ) 4.32
b p ( λ , [ Chla ] ) = 0.347 [ Chla ] 0.766 ( λ 660 ) v ,
v = 0.5 ( log 10 [ Chla ] 0.3 ) ,
B b p ( [ Chla ] ) = 0.002 + 0.01 ( 0.5 0.25 log 10 [ Chla ] ) ,
F 11 , w = 0.06225 ( 1 + 0.835 cos 2 Θ ) .
a R ( λ ) = 2.7 × 10 4 ( 488 λ ) 5.3 .
b R ( λ , λ ) = a R ( λ ) f R ( λ , λ ) ,
F 11 , R = 3 16 π ( 1 + 3 ρ 1 + 2 ρ ) ( 1 + 1 ρ 1 + 3 ρ cos 2 Θ ) .
F ¯ 11 , R = 1 , F ¯ 12 , R = ( 1 ρ ) ( cos 2 Θ 1 ) 1 + cos 2 Θ + ( 3 cos 2 Θ ) ρ , F ¯ 21 , R = F ¯ 12 , R , F ¯ 22 , R = ( 1 ρ ) ( cos 2 Θ + 1 ) 1 + cos 2 Θ + ( 3 cos 2 Θ ) ρ , F ¯ 33 , R = 2 ( 1 ρ ) cos Θ 1 + cos 2 Θ + ( 3 cos 2 Θ ) ρ , F ¯ 44 , R = 2 ( 1 3 ρ ) cos Θ 1 + cos 2 Θ + ( 3 cos 2 Θ ) ρ , F ¯ o t h e r , R = 0 ,
f R ( λ , λ e ) d λ = f R ( λ , λ e ) d λ e = 1.

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