Abstract

Radiative transfer across the water-air interface has important implications for optics and remote sensing of natural waters. The upward radiance emerging from the water suffers a critical change when it passes through the water-air interface. Upwelling radiance transmittance τw,a is an optical process occurring at the water-air interface that determines the in-water radiances propagating through the interface. In previous studies, τw,a was successfully derived for determining the water-leaving radiances in open ocean waters, despite being oversimplified with a constant value. The constant τw,a value becomes rapidly invalid in high scattering and absorbing waters within nearshore and inland environments. In this study, we attempt to quantitatively solve the upwelling radiance transmittance τw,a (i.e., the percentage of in-water photons that escape through the water-air interface) for varying coefficients of scattering and absorption within the range of natural waters. The two important optical phenomena which are ignored in the previous studies have been fully accounted: (i) the particulate contribution to the refractive index (RI) of seawater and (ii) the multiple interactions of the upwelling photons with the water-air interface. As a result, this study leads to a new theoretical formulation of the upwelling radiance transmittance applicable to all natural waters. The effect and variation of the new formulation on the water-leaving radiance and remote sensing reflectance is further studied for coastal and inland waters. Particular attention is also focused on the conversion of sub-surface remote sensing reflectance (rrs) to above-surface remote sensing reflectance (Rrs), which is important for calibration and validation of the remote sensing algorithms. The results show substantial improvement in the ocean color quantities (Lw and Rrs) by up to factor 33% for scattering waters and <5% for absorbing waters.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Radiance transmittance measured at the ocean surface

Jianwei Wei, Zhongping Lee, Marlon Lewis, Nima Pahlevan, Michael Ondrusek, and Roy Armstrong
Opt. Express 23(9) 11826-11837 (2015)

An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance

Zhong Ping Lee, Keping Du, Kenneth J. Voss, Giuseppe Zibordi, Bertrand Lubac, Robert Arnone, and Alan Weidemann
Appl. Opt. 50(19) 3155-3167 (2011)

References

  • View by:
  • |
  • |
  • |

  1. T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).
  2. J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).
  3. J. E. Tyler, Radiance Distribution as a Function of Depth in the Submarine Environment (University of California, 1960).
  4. J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
  5. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag New York Inc., 1983).
  6. B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).
  7. A. Gershun, “The light field,” J. Math. Phys. 18, 141–146 (1939).
  8. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Elsevier, 1965).
  9. C. L. Wyatt, Radiometric Calibration: Theory and Methods (Academic, 1978).
  10. C. D. Mobley, “Radiative Transfer: Across the surface,” in Light and Water: Radiative Transfer in the Natural Waters (Academic, 1994).
  11. F. E. Nicodemus, “Radiance,” Am. J. Phys. 31, 368–377 (1963).
  12. J. Dera, “Marine Physics,” in Elsevier Oceanography Series (Elsevier, 1992), Vol. 53.
  13. R. W. Austin, “Inherent spectral radiance signatures of the ocean surface,” in Ocean Color Analysis (Scripps Inst. Oceanogr., 1974), p. 2.1–2.20.
  14. P. J. Dev and P. Shanmugam, “A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters,” J. Quant. Spectrosc. Radiat. Transf. 142, 75–92 (2014).
  15. C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38(36), 7442–7455 (1999).
    [PubMed]
  16. M. L. Boas, Mathematical Methods in the Physical Sciences (Wiley India, 2006).
  17. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
    [PubMed]
  18. J. L. Mueller, A. Morel, R. Frouin, C. Davis, R. Arnone, K. Carder, R. G. Steward, S. Hooker, C. D. Mobley, S. Mclean, M. Miller, B. Holben, C. Pietras, G. S. Fargion, K. D. Knobelspiesse, J. Porter, and K. J. Voss, Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4, Volume III : Radiometric Measurements and Data Analysis Protocols. NASA/TM-2003–21621 (2003), Vol. III.
  19. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. II Bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993).
    [PubMed]
  20. E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
  21. D. Stramski, A. Morel, and A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplanktonic cells: a retrieval of the bulk refractive index,” Appl. Opt. 27(19), 3954–3956 (1988).
    [PubMed]
  22. H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).
  23. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).
  24. J. R. V. Zaneveld and H. Pak, “Method for the determination of the index of refraction of particles suspended in the ocean*,” J. Opt. Soc. Am. 63, 321 (1973).
  25. R. W. Austin and G. Halikas, The Index of Refraction of Seawater (University of California at San Diego, 1976).
  26. J. L. Mueller and R. W. Austin, Ocean Optics Protocols for SeaWiFS Validation, Revision 1, Volume 25 (1995).
  27. S. K. Sahu and P. Shanmugam, “Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles,” Opt. Express 23(17), 22291–22307 (2015).
    [PubMed]
  28. R. W. Austin, “Gulf of Mexico, Ocean-color surface-truth measurements,” Boundary-Layer Meteorol. 18, 269–285 (1980).
  29. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
  30. C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
  31. K. Voss and A. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13(11), 4250–4262 (2005).
    [PubMed]
  32. H. R. Gordon and D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20(24), 4175–4180 (1981).
    [PubMed]
  33. J. Wei, Z. Lee, M. Lewis, N. Pahlevan, M. Ondrusek, and R. Armstrong, “Radiance transmittance measured at the ocean surface,” Opt. Express 23(9), 11826–11837 (2015).
    [PubMed]
  34. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998).
    [PubMed]
  35. H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
  36. E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40(27), 4885–4893 (2001).
    [PubMed]
  37. C. S. Roesler and E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30, 1468 (2003).
  38. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1035–1050 (2002).
    [PubMed]

2015 (2)

2014 (2)

P. J. Dev and P. Shanmugam, “A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters,” J. Quant. Spectrosc. Radiat. Transf. 142, 75–92 (2014).

H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).

2013 (1)

B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).

2006 (1)

T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).

2005 (1)

2003 (1)

C. S. Roesler and E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30, 1468 (2003).

2002 (1)

2001 (3)

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40(27), 4885–4893 (2001).
[PubMed]

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

1999 (1)

1998 (2)

Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998).
[PubMed]

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).

1996 (2)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
[PubMed]

1993 (1)

1989 (2)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).

1988 (2)

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

D. Stramski, A. Morel, and A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplanktonic cells: a retrieval of the bulk refractive index,” Appl. Opt. 27(19), 3954–3956 (1988).
[PubMed]

1981 (1)

1980 (1)

R. W. Austin, “Gulf of Mexico, Ocean-color surface-truth measurements,” Boundary-Layer Meteorol. 18, 269–285 (1980).

1973 (1)

1963 (1)

F. E. Nicodemus, “Radiance,” Am. J. Phys. 31, 368–377 (1963).

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 141–146 (1939).

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).

Armstrong, R.

Austin, R. W.

R. W. Austin, “Gulf of Mexico, Ocean-color surface-truth measurements,” Boundary-Layer Meteorol. 18, 269–285 (1980).

J. L. Mueller and R. W. Austin, Ocean Optics Protocols for SeaWiFS Validation, Revision 1, Volume 25 (1995).

Baker, K. S.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

Boss, E.

C. S. Roesler and E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30, 1468 (2003).

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1035–1050 (2002).
[PubMed]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40(27), 4885–4893 (2001).
[PubMed]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

Bricaud, A.

Brown, J. W.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

Brown, O. B.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

Carder, K. L.

Chang, G.

T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).

Chapin, A.

Clark, D. K.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

H. R. Gordon and D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20(24), 4175–4180 (1981).
[PubMed]

Dev, P. J.

P. J. Dev and P. Shanmugam, “A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters,” J. Quant. Spectrosc. Radiat. Transf. 142, 75–92 (2014).

Dickey, T.

T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).

Evans, R. H.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

Gentili, B.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. 18, 141–146 (1939).

Gordon, H. R.

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

H. R. Gordon and D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20(24), 4175–4180 (1981).
[PubMed]

Hariharasudhan, V. G.

H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).

Herring, S.

Jaffe, J.

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

Kirk, J. T. O.

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).

Lee, Z.

Lewis, M.

J. Wei, Z. Lee, M. Lewis, N. Pahlevan, M. Ondrusek, and R. Armstrong, “Radiance transmittance measured at the ocean surface,” Opt. Express 23(9), 11826–11837 (2015).
[PubMed]

T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

Manjusha, S.

B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).

McLean, J.

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

Mobley, C. D.

Moore, K.

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

Morel, A.

Mueller, J. L.

J. L. Mueller and R. W. Austin, Ocean Optics Protocols for SeaWiFS Validation, Revision 1, Volume 25 (1995).

Nasiha, H. J.

H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).

Nicodemus, F. E.

F. E. Nicodemus, “Radiance,” Am. J. Phys. 31, 368–377 (1963).

Ondrusek, M.

Pahlevan, N.

Pak, H.

Patch, J. S.

Pegau, W. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

Roesler, C. S.

C. S. Roesler and E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30, 1468 (2003).

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).

Sahu, S. K.

Shanmugam, P.

S. K. Sahu and P. Shanmugam, “Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles,” Opt. Express 23(17), 22291–22307 (2015).
[PubMed]

H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).

P. J. Dev and P. Shanmugam, “A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters,” J. Quant. Spectrosc. Radiat. Transf. 142, 75–92 (2014).

B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).

Smith, R. C.

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

Steward, R. G.

Stramski, D.

Strand, M.

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

Sundarabalan, B.

B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).

Sundman, L. K.

Twardowski, M. S.

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40(27), 4885–4893 (2001).
[PubMed]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

Voss, K.

Wei, J.

Zaneveld, J. R. V.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

J. R. V. Zaneveld and H. Pak, “Method for the determination of the index of refraction of particles suspended in the ocean*,” J. Opt. Soc. Am. 63, 321 (1973).

Am. J. Phys. (1)

F. E. Nicodemus, “Radiance,” Am. J. Phys. 31, 368–377 (1963).

Appl. Opt. (8)

Boundary-Layer Meteorol. (1)

R. W. Austin, “Gulf of Mexico, Ocean-color surface-truth measurements,” Boundary-Layer Meteorol. 18, 269–285 (1980).

Geophys. Res. Lett. (1)

C. S. Roesler and E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30, 1468 (2003).

IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. (1)

H. J. Nasiha, P. Shanmugam, and V. G. Hariharasudhan, “A New Inversion Model to Estimate Bulk Refractive Index of Particles in Coastal Oceanic Waters: Implications for Remote Sensing,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7, 3069–3083 (2014).

J. Geophys. Res. (2)

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129 (2001).

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 141–146 (1939).

J. Opt. Soc. Am. (1)

J. Plankton Res. (1)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).

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

P. J. Dev and P. Shanmugam, “A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters,” J. Quant. Spectrosc. Radiat. Transf. 142, 75–92 (2014).

B. Sundarabalan, P. Shanmugam, and S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transf. 121, 30–44 (2013).

Limnol. Oceanogr. (3)

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).

Oceanography (Wash. D.C.) (1)

J. Jaffe, K. Moore, J. McLean, and M. Strand, “Underwater Optical Imaging: Status and Prospects,” Oceanography (Wash. D.C.) 14, 64–75 (2001).

Opt. Express (3)

Rev. Geophys. (1)

T. Dickey, M. Lewis, and G. Chang, “Optical oceanography: Recent advances and future directions using global remote sensing and in situ observations,” Rev. Geophys. 44, RG1001 (2006).

Other (11)

J. Dera, “Marine Physics,” in Elsevier Oceanography Series (Elsevier, 1992), Vol. 53.

R. W. Austin, “Inherent spectral radiance signatures of the ocean surface,” in Ocean Color Analysis (Scripps Inst. Oceanogr., 1974), p. 2.1–2.20.

J. L. Mueller, A. Morel, R. Frouin, C. Davis, R. Arnone, K. Carder, R. G. Steward, S. Hooker, C. D. Mobley, S. Mclean, M. Miller, B. Holben, C. Pietras, G. S. Fargion, K. D. Knobelspiesse, J. Porter, and K. J. Voss, Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4, Volume III : Radiometric Measurements and Data Analysis Protocols. NASA/TM-2003–21621 (2003), Vol. III.

M. L. Boas, Mathematical Methods in the Physical Sciences (Wiley India, 2006).

J. E. Tyler, Radiance Distribution as a Function of Depth in the Submarine Environment (University of California, 1960).

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag New York Inc., 1983).

R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Elsevier, 1965).

C. L. Wyatt, Radiometric Calibration: Theory and Methods (Academic, 1978).

C. D. Mobley, “Radiative Transfer: Across the surface,” in Light and Water: Radiative Transfer in the Natural Waters (Academic, 1994).

R. W. Austin and G. Halikas, The Index of Refraction of Seawater (University of California at San Diego, 1976).

J. L. Mueller and R. W. Austin, Ocean Optics Protocols for SeaWiFS Validation, Revision 1, Volume 25 (1995).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Systematic geometrical representation of the transfer of radiance from one medium to another n1 and n2 respectively. P is the layer of separation (interface) between the two media, θ1, θ2 and θ3 are the incident, refracted and reflected angles with respect to normal, and θc is the critical angle.
Fig. 2
Fig. 2 In situ measured data of single scattering albedo ω ( = b / c   ) for 14 different environments representing the clear oceanic waters (deep blue) to highly turbid scattering waters (red). This plot clearly shows the effects of absorption and scattering with respect to the wavelength. The lowest and highest values of ω measured being near zero for clear open oceanic waters (at a wavelength 750 nm) and 0.97 for mineral rich turbid waters (at a wavelength 715 nm).
Fig. 3
Fig. 3 (a) Plot of the additional term ( 1 μ u ω ) / r f 2 + μ u ω n w 2 / ( 1 ρ w , a ) representing the ratio of new theoretical upwelling radiance transmittance τw,a relative to the pure water geometrical upwelling radiance transmittance τw,a (The black dots in ‘a’ represent τw,a:τpw,a = 1). (b) The new theoretical upwelling radiance transmittance τw,a is applied for the natural water types with measured ω values ranging from 0 to 1 (The black dots in ‘b’ represent τ p w , a = ( 1 ρ w , a ) / n w 2 0.541 line). The legends of these spectra are given in Fig. 2.
Fig. 4
Fig. 4 Spectral relative percentage of improvement in the ocean color quantities, Lw and Rrs.
Fig. 5
Fig. 5 Water-leaving radiance (L w ) determined using the conventional radiance transmittance (grey line) and new theoretical radiance transmittance (dark line) values for four different water types (clear oceanic water – (a), harbour water – (b), turbid coastal water (mineral) – (c), and turbid productive inland water – (d)). Water-leaving radiance (Lw) determined using the conventional radiance transmittance (grey line) and new theoretical radiance transmittance (dark line) values for four different water types (clear oceanic water, harbour water, turbid coastal water (mineral), and turbid productive inland water).
Fig. 6
Fig. 6 Remote sensing reflectances (R rs ) determined using the conventional radiance transmittance (grey line) and new theoretical radiance transmittance (dark line) values for four different water types (clear oceanic water – (a), harbour water – (b), turbid coastal water (mineral) – (c), and turbid productive inland water – (d)).
Fig. 7
Fig. 7 Comparison of the conversion of sub-surface remote sensing reflectance, rrs(0-,λ), to above-surface remote sensing reflectance, Rrs(0+,λ), using the present formulation [Eq. (18)] (derived as a function of ω and rf) and the model of Lee et al. [34] (shown in red line). The lowest line represents the transmission factor for a sub-surface remote sensing signal, τw,a(1-ρa,w) = 0.40, and the highest line represents the τw,a(1-ρa,w) = 0.75. The blue and orange shaded regions depict the waters inclined toward absorption and scattering respectively.

Tables (2)

Tables Icon

Table 1 Successive interactions of the photons escaping the water-air interface for a non-absorbing medium.

Tables Icon

Table 2 Coefficients for the determination of rf.

Equations (36)

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

L ( θ , φ , λ ) = Δ 3 Φ Δ A Δ Ω Δ λ .
L w ( a i r , λ ) = τ w , a ( λ ) L u ( 0 , λ ) .
τ w , a ( λ ) = t ( λ ) n 2 ( λ ) = 1 ρ w , a ( λ , θ v ) n 2 ( λ ) .
τ w , a = τ p w , a + τ p w , a ( 1 τ p w , a ) + τ p w , a ( 1 τ p w , a ) 2 + τ p w , a ( 1 τ p w , a ) 3 + .   = τ p w , a { 1 + ( 1 τ p w , a ) + ( 1 τ p w , a ) 2 + ( 1 τ p w , a ) 3 + } .
= τ p w , a { 1 τ p w , a } . τ w , a = 1.
τ w , a = τ p w , a + μ u ω τ p w , a ( 1 τ p w , a ) + μ u ω τ p w , a ( 1 τ p w , a ) 2 + μ u ω τ p w , a ( 1 τ p w , a ) 3 + . = τ p w , a + μ u ω τ p w , a ( 1 τ p w , a ) { 1 + ( 1 τ p w , a ) + ( 1 τ p w , a ) 2 + ( 1 τ p w , a ) 3 + } .
= τ p w , a + μ u ω τ p w , a ( 1 τ p w , a ) × { 1 τ p w , a } . = τ p w , a + μ u ω ( 1 τ p w , a ) . τ w , a = τ p w , a ( 1 μ u ω ) + μ u ω .
n ( λ ) = n w ( λ ) × r f .
n w ( λ ) = 1.325147 + 6.6096   λ 137.1924 .
τ w , a = ( ( 1 ρ w , a ) n w 2 × ( 1 μ u ω ) r f 2 ) + μ u ω .
τ w , a = ( 1 ρ w , a ) n w 2 [ ( 1 μ u ω ) r f 2 + μ u ω n w 2 ( 1 ρ w , a ) ] .
L w ( a i r , λ ) = ( 1 ρ w , a ) n w 2 [ ( 1 μ u ω ) r f 2 + μ u ω n w 2 ( 1 ρ w , a ) ] L u ( 0 , λ ) .
μ u = cos θ ¯ = 0 π cos θ d ω 0 π d ω = 0.5.
τ w , a τ p w , a = ( 1 μ u ω ) r f 2 + μ u ω n w 2 ( 1 ρ w , a ) .
R r s ( 0 + , λ ) = L w ( a i r , λ ) E d ( 0 + , λ ) .
r r s ( 0 , λ ) = L u ( 0 , λ ) E d ( 0 , λ ) .
R r s ( 0 + , λ ) r r s ( 0 , λ ) = L w ( a i r , λ ) E d ( 0 + , λ ) × E d ( 0 , λ ) L u ( 0 , λ ) .
E d ( 0 , λ ) = ( 1 ρ a , w ) E d ( 0 + , λ ) .
R r s ( 0 + , λ ) = ( 1 ρ a , w ) ( 1 ρ w , a ) n w 2 [ ( 1 μ u ω ) r f 2 + μ u ω n w 2 ( 1 ρ w , a ) ] r r s ( 0 , λ ) .
R r s ( 0 + , λ ) = τ w , a ( 1 ρ a , w ) × r r s ( 0 , λ ) .
n 1 sin θ 1 = n 2 sin θ 2 .
n 1 2 sin 2 θ 1 = n 2 2 sin 2 θ 2 .
2 n 1 2 sin θ 1 cos θ 1 Δ θ 1 = 2 n 2 2 sin θ 2 cos θ 2 Δ θ 2 .
n 1 2 sin θ 1 cos θ 1 Δ θ 1 Δ ϕ = n 2 2 sin θ 2 cos θ 2 Δ θ 2 Δ ϕ .
ΔΩ 1 = sin θ 1 Δ θ 1 Δ ϕ .
ΔΩ 2 = sin θ 2 Δ θ 2 Δ ϕ .
n 1 2 cos θ 1 ΔΩ 1 = n 2 2 cos θ 2 ΔΩ 2 .
L 1 = ΔΦ 1 Δ A 1 ΔΩ 1 Δ λ .
L 2 = ΔΦ 2 Δ A 2 ΔΩ 2 Δ λ .
t = ΔΦ 2 ΔΦ 1 .
Δ A 1 = Δ A cos θ 1 .
Δ A 2 = Δ A cos θ 2 .  
L 2 L 1 = ΔΦ 2   Δ A 1   ΔΩ 1 ΔΦ 1   Δ A 2   ΔΩ 2 . L 2 L 1 = t cos θ 1 ΔΩ 1 cos θ 2 ΔΩ 2 .
L 2 L 1 = t n 2 2 n 1 2 .
L w = t n 2 L u .
r f = 1 + ( P 1 b ˜ b p ) 1 2 P 2 .

Metrics