Abstract

Modeling of subsurface irradiance reflectance fields especially in turbid coastal, harbor and lagoon waters has important applications in ecology, engineering and optical remote sensing. The present study aims at exploring many possible causes of variation in the proportionality factor f and analyzing its effect on the subsurface irradiance reflectance in different waters. A new model is then developed to estimate this optical property as a function of the absorption coefficient (a), backscattering coefficient (bb), incident illumination condition, and other wavelength-depth dependent factors. Implementation of this new model is examined for five types of waters with varying turbidity and chlorophyll. Model results are verified with in situ measurements data and compared with the results from existing models. Formulas already proposed for estimating R in the previous studies and generally expressed by R = 0.33(bb/(a + bb)) or R = f (bb/(a + bb)) where f = 0.975-0.629μ0 (μ0 is the incident photons just below the sea surface) work fairly well in clear oceanic waters, but yield large errors in turbid coastal and lagoon waters due to the use of a constant value ~0.33 or the dimensionless parameter f which does not account for certain processes in the model (e.g., multiple scattering, depth-dependent changes in the diffuse components of solar radiation, and spectral variation in f). By contrast, the new model estimates the reflectances having good agreement with in situ data from just below the water surface and throughout the water column. The improved performance of the present model is because it includes a parameterization of the proportionality factor f which varies with wavelength and depends on the sun angle, inherent optical properties, and diffuse attenuation coefficients. Knowledge related to interrelationships between inherent optical properties and apparent optical properties can be used to study the variability of the subsurface reflectance in homogeneous and stratified coastal waters with respect to many possible causes of its variations.

© 2014 Optical Society of America

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References

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  1. K. J. Voss, A. Morel, “Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,” Limnol. Oceanogr. 50(2), 698–705 (2005).
    [CrossRef]
  2. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983), p. 114.
  3. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975).
    [CrossRef] [PubMed]
  4. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
    [CrossRef]
  5. V. I. Haltrin, “About nonlinear dependence of Remote Sensing and Diffuse reflection coefficients on Gordon’s Parameter,” in Current Problems in Optics of Natural Waters (2003), p. 382.
  6. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
    [CrossRef] [PubMed]
  7. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993).
    [CrossRef] [PubMed]
  8. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
    [CrossRef] [PubMed]
  9. A. Morel, D. Antoine, B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
    [CrossRef] [PubMed]
  10. J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29(2), 350–356 (1984).
    [CrossRef]
  11. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34(8), 1484–1489 (1989).
    [CrossRef]
  12. S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36(12), 2620–2629 (1997).
    [CrossRef] [PubMed]
  13. W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
    [CrossRef]
  14. W. S. Pegau, D. Gray, J. R. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36(24), 6035–6046 (1997).
    [CrossRef] [PubMed]
  15. J. R. V. Zaneveld, J. C. Kitchen, and C. Moore, “Scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII (International Society for Optics and Photonics, 1994), Vol. 26, pp. 44–55.
  16. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997).
    [CrossRef] [PubMed]
  17. R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20(2), 177–184 (1981).
    [CrossRef] [PubMed]
  18. A. Albert, C. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
    [CrossRef] [PubMed]
  19. T. Hirata, N. K. Højerslev, “Relationship between the irradiance reflectance and inherent optical properties of seawater,” J. Geophys. Res. 113(C3), C03030 (2008).
    [CrossRef]
  20. C. S. Roesler, E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30(9), 1468 (2003).
    [CrossRef]
  21. A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
    [CrossRef]
  22. S. P. Tiwari, P. Shanmugam, “An evaluation of models for the satellite-estimation of phytoplankton absorption coefficients in coastal / oceanic waters,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 364–371 (2014).
    [CrossRef]
  23. D. McKee, M. Chami, I. Brown, V. S. Calzado, D. Doxaran, A. Cunningham, “Role of measurement uncertainties in observed variability in the spectral backscattering ratio: a case study in mineral-rich coastal waters,” Appl. Opt. 48(24), 4663–4675 (2009).
    [CrossRef] [PubMed]
  24. V. I. Haltrin, “One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater,” Appl. Opt. 41(6), 1022–1028 (2002).
    [CrossRef] [PubMed]
  25. D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
    [CrossRef] [PubMed]
  26. D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
    [CrossRef]
  27. C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
    [CrossRef]
  28. D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
    [CrossRef]

2014 (1)

S. P. Tiwari, P. Shanmugam, “An evaluation of models for the satellite-estimation of phytoplankton absorption coefficients in coastal / oceanic waters,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 364–371 (2014).
[CrossRef]

2010 (1)

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

2009 (1)

2008 (1)

T. Hirata, N. K. Højerslev, “Relationship between the irradiance reflectance and inherent optical properties of seawater,” J. Geophys. Res. 113(C3), C03030 (2008).
[CrossRef]

2007 (1)

D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
[CrossRef]

2005 (2)

C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
[CrossRef]

K. J. Voss, A. Morel, “Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,” Limnol. Oceanogr. 50(2), 698–705 (2005).
[CrossRef]

2003 (2)

C. S. Roesler, E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30(9), 1468 (2003).
[CrossRef]

A. Albert, C. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

1997 (3)

1996 (1)

1995 (1)

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

1993 (2)

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[CrossRef]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34(8), 1484–1489 (1989).
[CrossRef]

1984 (1)

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29(2), 350–356 (1984).
[CrossRef]

1981 (1)

1977 (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[CrossRef]

1975 (1)

Albert, A.

Antoine, D.

Babin, M.

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

Baker, K. S.

Binding, C. E.

D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
[CrossRef]

C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
[CrossRef]

Boss, E.

C. S. Roesler, E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30(9), 1468 (2003).
[CrossRef]

Bowers, D. G.

D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
[CrossRef]

C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
[CrossRef]

Bricaud, A.

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[CrossRef] [PubMed]

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

Brown, I.

Brown, O. B.

Calzado, V. S.

Chami, M.

Claustre, H.

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

Cunningham, A.

Doxaran, D.

Ellis, K. M.

D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
[CrossRef]

Fry, E. S.

Gentili, B.

Gong, S.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Gordon, H. R.

Gray, D.

Haltrin, V. I.

Hirata, T.

T. Hirata, N. K. Højerslev, “Relationship between the irradiance reflectance and inherent optical properties of seawater,” J. Geophys. Res. 113(C3), C03030 (2008).
[CrossRef]

Højerslev, N. K.

T. Hirata, N. K. Højerslev, “Relationship between the irradiance reflectance and inherent optical properties of seawater,” J. Geophys. Res. 113(C3), C03030 (2008).
[CrossRef]

Huang, C.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Jacobs, M. M.

Kirk, J. T. O.

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29(2), 350–356 (1984).
[CrossRef]

Le, C.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Li, Y.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Lv, H.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

McKee, D.

Mitchelson-Jacob, E. G.

C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
[CrossRef]

Mobley, C.

Morel, A.

K. J. Voss, A. Morel, “Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,” Limnol. Oceanogr. 50(2), 698–705 (2005).
[CrossRef]

A. Morel, D. Antoine, B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[CrossRef] [PubMed]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[CrossRef] [PubMed]

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

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[CrossRef]

Pegau, W. S.

W. S. Pegau, D. Gray, J. R. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36(24), 6035–6046 (1997).
[CrossRef] [PubMed]

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[CrossRef]

Platt, T.

Pope, R. M.

Prieur, L.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[CrossRef]

Roesler, C. S.

C. S. Roesler, E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30(9), 1468 (2003).
[CrossRef]

Sathyendranath, S.

Shanmugam, P.

S. P. Tiwari, P. Shanmugam, “An evaluation of models for the satellite-estimation of phytoplankton absorption coefficients in coastal / oceanic waters,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 364–371 (2014).
[CrossRef]

Smith, R. C.

Stramski, D.

Sun, D.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Tiwari, S. P.

S. P. Tiwari, P. Shanmugam, “An evaluation of models for the satellite-estimation of phytoplankton absorption coefficients in coastal / oceanic waters,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 364–371 (2014).
[CrossRef]

Voss, K. J.

K. J. Voss, A. Morel, “Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,” Limnol. Oceanogr. 50(2), 698–705 (2005).
[CrossRef]

Wang, Q.

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

Zaneveld, J. R.

Zaneveld, J. R. V.

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[CrossRef]

Appl. Opt. (12)

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975).
[CrossRef] [PubMed]

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20(2), 177–184 (1981).
[CrossRef] [PubMed]

S. Sathyendranath, T. Platt, “Analytic model of ocean color,” Appl. Opt. 36(12), 2620–2629 (1997).
[CrossRef] [PubMed]

W. S. Pegau, D. Gray, J. R. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity,” Appl. Opt. 36(24), 6035–6046 (1997).
[CrossRef] [PubMed]

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

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993).
[CrossRef] [PubMed]

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997).
[CrossRef] [PubMed]

D. Stramski, A. Bricaud, A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[CrossRef] [PubMed]

V. I. Haltrin, “One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater,” Appl. Opt. 41(6), 1022–1028 (2002).
[CrossRef] [PubMed]

A. Morel, D. Antoine, B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[CrossRef] [PubMed]

D. McKee, M. Chami, I. Brown, V. S. Calzado, D. Doxaran, A. Cunningham, “Role of measurement uncertainties in observed variability in the spectral backscattering ratio: a case study in mineral-rich coastal waters,” Appl. Opt. 48(24), 4663–4675 (2009).
[CrossRef] [PubMed]

Estuar. Coast. Shelf Sci. (1)

D. G. Bowers, C. E. Binding, K. M. Ellis, “Satellite remote sensing of the geographical distribution of suspended particle size in an energetic shelf sea,” Estuar. Coast. Shelf Sci. 73(3-4), 457–466 (2007).
[CrossRef]

Geophys. Res. Lett. (1)

C. S. Roesler, E. Boss, “Spectral beam attenuation coefficient retrieved from ocean color inversion,” Geophys. Res. Lett. 30(9), 1468 (2003).
[CrossRef]

Hydrobiologia (1)

D. Sun, Y. Li, Q. Wang, H. Lv, C. Le, C. Huang, S. Gong, “Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China),” Hydrobiologia 644(1), 337–349 (2010).
[CrossRef]

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

S. P. Tiwari, P. Shanmugam, “An evaluation of models for the satellite-estimation of phytoplankton absorption coefficients in coastal / oceanic waters,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 364–371 (2014).
[CrossRef]

J. Geophys. Res. (2)

T. Hirata, N. K. Højerslev, “Relationship between the irradiance reflectance and inherent optical properties of seawater,” J. Geophys. Res. 113(C3), C03030 (2008).
[CrossRef]

A. Bricaud, M. Babin, A. Morel, H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[CrossRef]

Limnol. Oceanogr. (5)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[CrossRef]

K. J. Voss, A. Morel, “Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions,” Limnol. Oceanogr. 50(2), 698–705 (2005).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29(2), 350–356 (1984).
[CrossRef]

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34(8), 1484–1489 (1989).
[CrossRef]

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[CrossRef]

Opt. Express (1)

Remote Sens. Environ. (1)

C. E. Binding, D. G. Bowers, E. G. Mitchelson-Jacob, “Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties,” Remote Sens. Environ. 94(3), 373–383 (2005).
[CrossRef]

Other (3)

J. R. V. Zaneveld, J. C. Kitchen, and C. Moore, “Scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII (International Society for Optics and Photonics, 1994), Vol. 26, pp. 44–55.

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983), p. 114.

V. I. Haltrin, “About nonlinear dependence of Remote Sensing and Diffuse reflection coefficients on Gordon’s Parameter,” in Current Problems in Optics of Natural Waters (2003), p. 382.

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Figures (10)

Fig. 1
Fig. 1

Systematic diagram showing the different types (water types) of in situ data used in this study [also see Table 1]. Green arrows indicate Chl and brown arrows indicate SS. The arrows pointing upwards and downwards represent high and low levels of these constituents.

Fig. 2
Fig. 2

In situ R versus bb/(a + bb) showing the variations in slope ‘f’ for different types of waters.

Fig. 3
Fig. 3

The relationship between f(400) and (1/a). It explains the magnitude of the f component which strongly depends on the inverse of absorption coefficient (1/a) [plotted for 400nm]. The straight line y = 0.0699x is the minimal value for f when the sun is at nadir position.

Fig. 4
Fig. 4

Spectral plots of the in situ IOPs such as the particulate beam attenuation, particulate absorption and particulate backscattering coefficients used in this study.

Fig. 5
Fig. 5

Comparison of the model reflectance (R) with the in situ R spectra in five types of waters. Note that for Type V waters, the brown, red and pink lines (Morel and Prieur [4], Morel and Gentili [7] and Kirk [10] models) follow the R values in the secondary Y-axis.

Fig. 6
Fig. 6

Comparison of the present model with in situ R and the Hirata and Højerslev [19] model for the four types of waters. Due to the absence of in situ data for different depths in lagoon waters, the model results are not shown for Type V waters.

Fig. 7
Fig. 7

Spectral comparison of the model and in situ reflectances at just below the water surface ‘R(0-)’ and at depths ‘R(z)’ for four different stations in five different water types with varying levels of Chl and SS concentrations.

Fig. 8
Fig. 8

Comparison of the vertical profiles of the model and in situ R in Type I-IV waters (top to bottom, row-wise) at four different stations (column-wise).

Fig. 9
Fig. 9

Scatterplots of the model and in situ R for five different types of waters (at eight key wavelengths 412, 448, 488, 531, 555, 670, 685, 710nm).

Fig. 10
Fig. 10

Plots showing (a) decreasing, (b) increasing, (c) decreasing/increasing reflectance patterns for the wavelength 448nm.

Tables (6)

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Table 1 Classification of water types for this study

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Table 2 Spectral coefficients of kChl and kSS at three nanometer intervals.

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Table 3 Statistical comparison of the model and in situ R for the selected wavelengths

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Table 4 The variation of Ku and Kd for the decreasing subsurface reflectance [Fig. 10(a)]

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Table 5 The variation of Ku and Kd for the increasing subsurface reflectance [Fig. 10(b)]

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Table 6 The variation of Ku and Kd for the decreasing/increasing subsurface reflectance [Fig. 10(c)]

Equations (15)

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K u,d (λ, z 1 z 2 )=( 1 z 2 z 1 )[ ln( E u,d ( z 1 ) E u,d ( z 2 ) ) ]
R( 0 ,λ)= E u ( 0 ,λ) E d ( 0 ,λ)
R( 0 ,λ)=f( b b a+ b b )
a(λ)= a w (λ)+ a p (λ)+ a CDOM (λ)
b b (λ)= b bw (λ)+ b bp (λ)
R( 0 ,λ)=0.33( b b a+ b b )
f=0.9750.629cos μ 0
R( 0 ,λ)=( 0.9750.629cos μ 0 )( b b a+ b b )
f ( 0 , λ ) = f ( 400 ) { 1 + ( k C h l ( λ ) × [ C h l ] 2 ) + ( k s s ( λ ) × S S ) } .
f(400)=0.0699×( 1 a(400) )[ 1+0.039 ( θ s ) 0.3 ]
f(λ,z)=f( 0 ,λ)× e K u z × e + K d z
=f( 0 ,λ)× e K u z+ K d z
f(λ,z)=f( 0 ,λ)× e ( K u K d )z
R(λ,z)=f(λ,z)( b b a+ b b )
R(λ,z)=f(400)[ 1+[ k Chl (λ)× ( Chl ) 2 ]+[ k ss (λ)×SS] ]×( b b a+ b b ) e ( K u K d )z

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