Abstract

For the atmospheric correction of ocean-color imagery obtained over Case I waters with the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) instrument the method currently used to relax the black-pixel assumption in the near infrared (NIR) relies on (1) an approximate model for the nadir NIR remote-sensing reflectance and (2) an assumption that the water-leaving radiance is isotropic over the upward hemisphere. Radiance simulations based on a comprehensive radiative-transfer model for the coupled atmosphere–ocean system and measurements of the nadir remote-sensing reflectance at 670 nm compiled in the SeaWiFS Bio-optical Algorithm Mini-Workshop (SeaBAM) database are used to assess the validity of this method. The results show that (1) it is important to improve the flexibility of the reflectance model to provide more realistic predictions of the nadir NIR water-leaving reflectance for different ocean regions and (2) the isotropic assumption should be avoided in the retrieval of ocean color, if the chlorophyll concentration is larger than approximately 6, 10, and 40 mg m-3 when the aerosol optical depth is approximately 0.05, 0.1, and 0.3, respectively. Finally, we extend our scope to Case II ocean waters to gain insight and enhance our understanding of the NIR aspects of ocean color. The results show that the isotropic assumption is invalid in a wider range than in Case I waters owing to the enhanced water-leaving reflectance resulting from oceanic sediments in the NIR wavelengths.

© 2002 Optical Society of America

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2002 (2)

2001 (2)

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

R. A. Reynolds, D. Stramski, B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res. 106, 7125–7138 (2001).
[CrossRef]

2000 (3)

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean-color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

H. M. Dierssen, R. C. Smith, “Bio-optical properties and remote-sensing ocean-color algorithms for Antarctic Peninsula waters,” J. Geophys. Res. 105, 26,301–26,312 (2000).
[CrossRef]

M. Wang, S. W. Bailey, C. M. Pietras, C. R. McClain, “SeaWiFS provides unique global aerosol optical property data,” Eos Trans. Am. Geophys. Union 81, 197–202 (2000).
[CrossRef]

1999 (2)

D. Antoine, A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensing ocean color (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sensing 20, 1875–1916 (1999).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104, 5403–5421 (1999).
[CrossRef]

1998 (6)

B. Chen, K. Stamnes, B. Yan, Ø. Frette, J. J. Stamnes, “Water-leaving radiance in the NIR spectral region and its effects on atmospheric correction of ocean-color imagery,” J. Adv. Mar. Sci. Tech. Soc. 4, 329–338 (1998).

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean-color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. Oceans 103, 24937–24953 (1998).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) water: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

J. Muller, C. McClain, R. Caddrey, G. Feldman, “The NASA SIMBIOS Program,” Backscatter, 29–32 (1998).

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

1997 (3)

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observation System era,” J. Geophys. Res. 102, 17081–17106 (1997).
[CrossRef]

S. A. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation: I. Time series from the Sargasso Sea,” J. Geophys. Res. 102, 18607–18625 (1997).
[CrossRef]

H. Yang, H. R. Gordon, “Remote sensing of ocean color: assessment of water-leaving radiance bidirectional effects on atmospheric diffuse transmittance,” Appl. Opt. 36, 7887–7897 (1997).
[CrossRef]

1995 (2)

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

1994 (3)

1993 (1)

1992 (1)

1991 (1)

1989 (1)

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean color and its application to remote sensing of phytoplankton pigments in coastal waters,” Int. J. Remote Sensing 10, 1373–1394 (1989).
[CrossRef]

1988 (2)

1987 (1)

A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton—a simplified theoretical approach,” Deep-Sea Res. Part A 34, 1093–1105 (1987).
[CrossRef]

1986 (1)

H. R. Gordon, “Ocean color remote sensing: influence of the particle phase function and the solar zenith angle,” Eos Trans. Am. Geophys. Union 14, 1055 (1986).

1982 (4)

J. R. V. Zaneveld, “Remotely sensed reflectance and its dependence on the vertical structure: a theoretical derivation,” Appl. Opt. 21, 4146–4150 (1982).
[CrossRef] [PubMed]

K. Stamnes, “On the computation of angular distributions of radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 28, 47–51 (1982).
[CrossRef]

K. Stamnes, “Reflection and transmission by a vertically inhomogeneous planetary atmosphere,” Planet. Space Sci. 30, 727–732 (1982).
[CrossRef]

K. Stamnes, P. Conklin, “A new multilayer discrete ordinate approach to radiative transfer in vertically inhomogeneous atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 31, 273–282 (1982).
[CrossRef]

1981 (5)

K. Stamnes, R. Swanson, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres,” J. Atmos. Sci. 38, 387–399 (1981).
[CrossRef]

K. Stamnes, H. Dale, “A new look at the discrete ordinate method for radiative-transfer calculations in anisotropically scattering atmospheres. II: Intensity computations,” J. Atmos. Sci. 38, 2696–2706 (1981).
[CrossRef]

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

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific absorption of plankton pigments, dissolved organic matter and particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

1975 (1)

1974 (2)

G. M. Hale, M. R. Query, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1974).
[CrossRef]

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

1962 (1)

T. Sasaki, S. Watanabe, G. Oshiba, N. Okami, M. Kajihara, “On the instrument for measuring angular distribution of underwater radiance,” Bull. Jpn. Soc. Sci. Fish. 28, 489–496 (1962).
[CrossRef]

1960 (2)

J. E. Tyler, “Radiance distribution as a function of depth in a underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–412 (1960).

N. G. Jerlov, M. Fukuda, “Radiance distribution in the upper layers of the sea,” Tellus 12, 348–355 (1960).
[CrossRef]

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) water: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Antoine, D.

D. Antoine, A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensing ocean color (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sensing 20, 1875–1916 (1999).
[CrossRef]

Arnone, R. A.

R. A. Arnone, P. Martinolich, R. W. Gould, M. Sydor, R. P. Stumpf, “Coastal optical properties using SeaWiFS,” presented at Ocean Optics XIV, Kailua-Kona, Hawaii, 10–13 November, 1998.

Austin, R. W.

R. W. Austin, G. Halikas, The Index of Refraction of Seawater (Scripps Institute of Oceanography, La Jolla, Calif., 1976).

Babin, M.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) water: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

Bailey, S. W.

M. Wang, S. W. Bailey, C. M. Pietras, C. R. McClain, “SeaWiFS provides unique global aerosol optical property data,” Eos Trans. Am. Geophys. Union 81, 197–202 (2000).
[CrossRef]

Baker, K. S.

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

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

R. C. Smith, K. S. Baker, “The analysis of ocean optical data II,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 95–107 (1986).

Bricaud, A.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, “Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) water: analysis and implications for bio-optical models,” J. Geophys. Res. 103, 31,033–31,044 (1998).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Brown, J. W.

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

Brown, O. B.

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

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, 417–427 (1975).
[CrossRef] [PubMed]

Caddrey, R.

J. Muller, C. McClain, R. Caddrey, G. Feldman, “The NASA SIMBIOS Program,” Backscatter, 29–32 (1998).

Carder, K. L.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104, 5403–5421 (1999).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean-color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. Oceans 103, 24937–24953 (1998).
[CrossRef]

Charlton, F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Chen, B.

Chen, F. R.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104, 5403–5421 (1999).
[CrossRef]

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B. Hamre, O. Frette, S. R. Erga, J. J. Stamnes, K. Stamnes, “Parameterization and analysis of the optical absorption and scattering coefficients in a Western Norwegian fjord—a case II water study,” Appl. Opt., submitted for publication.

Stavn, R.

Stramski, D.

R. A. Reynolds, D. Stramski, B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res. 106, 7125–7138 (2001).
[CrossRef]

Stumpf, R. P.

R. A. Arnone, P. Martinolich, R. W. Gould, M. Sydor, R. P. Stumpf, “Coastal optical properties using SeaWiFS,” presented at Ocean Optics XIV, Kailua-Kona, Hawaii, 10–13 November, 1998.

Swanson, R.

K. Stamnes, R. Swanson, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres,” J. Atmos. Sci. 38, 387–399 (1981).
[CrossRef]

Sydor, M.

R. A. Arnone, P. Martinolich, R. W. Gould, M. Sydor, R. P. Stumpf, “Coastal optical properties using SeaWiFS,” presented at Ocean Optics XIV, Kailua-Kona, Hawaii, 10–13 November, 1998.

Thomas, G. E.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University, New York, 1999).

Travis, L. D.

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

Tsay, S. C.

Tsay, S.-C.

Tyler, J. E.

J. E. Tyler, “Radiance distribution as a function of depth in a underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–412 (1960).

Vassen, W.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

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Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

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H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
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[CrossRef]

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Wouts, R.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

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[CrossRef] [PubMed]

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B. Yan, K. Stamnes, “Fast yet accurate computation of the complete radiance distribution in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

B. Yan, “Radiative transfer modeling in the coupled atmosphere–ocean system and its application to the remote sensing of ocean-color imagery,” Ph.D. dissertation (University of Alaska, Fairbanks, Alaska, 2001).

K. I. Gjerstad, J. J. Stamnes, B. Hamre, B. Yan, K. Stamnes, “Monte Carlo simulations of radiative transfer in the coupled atmosphere–ocean system,” submitted to Appl. Opt. (2002).

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[CrossRef]

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[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
[CrossRef]

A. Morel, K. J. Voss, B. Gentili, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143–13150 (1995).
[CrossRef]

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

S. A. Garver, D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation: I. Time series from the Sargasso Sea,” J. Geophys. Res. 102, 18607–18625 (1997).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, D. Kamykowski, “Semianalytic moderate-resolution imaging spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104, 5403–5421 (1999).
[CrossRef]

R. A. Reynolds, D. Stramski, B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res. 106, 7125–7138 (2001).
[CrossRef]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observation System era,” J. Geophys. Res. 102, 17081–17106 (1997).
[CrossRef]

J. Geophys. Res. Oceans (1)

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. McClain, “Ocean-color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. Oceans 103, 24937–24953 (1998).
[CrossRef]

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

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[CrossRef]

K. Stamnes, P. Conklin, “A new multilayer discrete ordinate approach to radiative transfer in vertically inhomogeneous atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 31, 273–282 (1982).
[CrossRef]

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H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific absorption of plankton pigments, dissolved organic matter and particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
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Planet. Space Sci. (1)

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R. A. Arnone, P. Martinolich, R. W. Gould, M. Sydor, R. P. Stumpf, “Coastal optical properties using SeaWiFS,” presented at Ocean Optics XIV, Kailua-Kona, Hawaii, 10–13 November, 1998.

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

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University, New York, 1999).

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

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D. Roland, H. Schiller, “Algorithm theoretical basis document (ATBD) 2.12: pigment index, sediment and gelbstoff retrieval from directional water leaving radiance reflectances using an inverse modeling technique,” PO-TN-MEL-GS-0005 (GKSS Research Center, 21502 Geesthacht, Germany, 1997).

B. Hamre, O. Frette, S. R. Erga, J. J. Stamnes, K. Stamnes, “Parameterization and analysis of the optical absorption and scattering coefficients in a Western Norwegian fjord—a case II water study,” Appl. Opt., submitted for publication.

B. Yan, “Radiative transfer modeling in the coupled atmosphere–ocean system and its application to the remote sensing of ocean-color imagery,” Ph.D. dissertation (University of Alaska, Fairbanks, Alaska, 2001).

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K. I. Gjerstad, J. J. Stamnes, B. Hamre, B. Yan, K. Stamnes, “Monte Carlo simulations of radiative transfer in the coupled atmosphere–ocean system,” submitted to Appl. Opt. (2002).

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Figures (12)

Fig. 1
Fig. 1

(a) R rs (0-, λ) computed from the simple reflectance model [Eq. (4)] as a function of the chlorophyll concentration [Chl]; (b) extinction coefficient; (c) scattering coefficient; (d) backscattering coefficient.

Fig. 2
Fig. 2

Comparison of the nadir R rs (0+, 670 nm) values based on Eq. (4) with those adopted from the SeaBAM database: Model denotes the simple reflectance model given by Eq. (4). The case with [YS] = [SS] = 0.0 m-1 is for the case when only chlorophyll particles are included in calculations of a and b b in Eq. (4). The other cases are for waters in which yellow substance and sediment particles in addition to chlorophyll particles are accounted for in the computations of a and b b (i.e., the expressions in Section 4 are used). Here [YS] represents the absorption coefficient of the yellow substance at 440 nm and [SS] the scattering coefficient of sediments at 550 nm (see Section 4 for details).

Fig. 3
Fig. 3

Dependence of the Q factor at [Chl] = 10.0 mg m-3 on the polar angle at several azimuthal angles (5°, 60°, 120°, and 175°). The HG phase function with the g values shown in Table 1 is used to mimic scattering by chlorophyll particles. The solar zenith angle is 45°: (a) 670 nm; (b) 765 nm.

Fig. 4
Fig. 4

Seven phase functions and their associated Q factors. The simulations of the Q factor is for a chlorophyll concentration of [Chl] = 10.0 mg m-3, an aerosol optical depth of τ865 = 0.1, and a relative azimuthal angle of Δϕ = 30°: (a) Q factor at 670 nm, (b) Q factor at 765 nm, (c) comparisons of the seven phase functions.

Fig. 5
Fig. 5

Variation of the Q factor at nadir with the solar zenith angle at 670, 765, and 865 nm where the relative azimuthal angle Δϕ = 180°.

Fig. 6
Fig. 6

TOA reflectance deviations at a polar angle of θ = 5.3° as a function of oceanic chlorophyll concentration [Chl] for aerosol optical depths of τ865 = 0.05, 0.1, and 0.3. The coastal aerosol model at relative humidity, RH = 90%, is used: (a) τ865 = 0.05, (b) τ865 = 0.1, (c) τ865 = 0.3.

Fig. 7
Fig. 7

Same as in Figs. 6(a)6(c) but for the deviation of ∊ ms (765, 865) and γ(765): (a) τ865 = 0.05, (b) τ865 = 0.1, (c) τ865 = 0.3.

Fig. 8
Fig. 8

Phase function at 765 nm for two types of sediment particles calculated with a Mie code assuming a gamma size distribution.65 Sediment (1) represents the inputs: r eff = 1.95 and v eff = 0.50, a size range from 3 to 5 µm, a refractive index n = 1.1–i0.0, which is the best fit with measurements of the phase function sediments shown in Fig. 9(a) of Volten et al.52 Sediment (2) represents the inputs: r eff = 5.93 and v eff = 0.00 and a size range from 5 to 12 µm, n = 1.1–i1.05, which is the best fit with measurements of the phase function of sediments shown in Figs. 9(b) of Volten et al.52

Fig. 9
Fig. 9

(a) Variation of the asymmetry factor with the chlorophyll concentration at 670, 765, and 865 nm where [SS] = 0.5 m-1, and the phase function, Sediment (1), is used for sediments. (b) Comparison of the asymmetry factor s at 765 nm with the chlorophyll concentration for two different sediment phase functions with two values of [SS].

Fig. 10
Fig. 10

Same as Fig. 9 but as a function of the sediment concentration. In (a) [Chl] = 5.0 mg · m-3.

Fig. 11
Fig. 11

Variation of the Q factors at 765 nm at five chlorophyll concentrations: 1.0, 5.0, 10.0, 20.0, 50.0 mg m-3. Here [YS] = 0.1 m-1, the phase function, Sediment (1), is used for sediments: (a) [SS] = 0.5 m-1; (b) [SS] = 3.0 m-1.

Fig. 12
Fig. 12

(a) TOA reflectance deviations as a function of oceanic chlorophyll concentration when [SS] = 0.5 m-1. (b) TOA reflectance deviations as a function of oceanic sediment concentration when [Chl] = 10.0 mg m-3. The plots are based on the coastal aerosol model at RH = 90% with τ865 = 0.05, the Sediment (1) phase function for sediment particles, and the Petzold phase function for chlorophyll particles.

Tables (1)

Tables Icon

Table 1 Asymmetry Factors that Yield Rrs(0-, λ) Values Computed with the CAO-DISORT Model Identical to Those Estimated from the Simple Reflectance Model [Eq. (4)] When the Absorption Coefficient is the Same

Equations (37)

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

Rrs0+, θ, ϕ, λ=Lu0+, θ, ϕ, λEd0+, λ,
Rrs0+, θ, ϕ, λ=trλRrs0-, θ, ϕ, λ
trλ=1-ρFλ, θnw2λtd.
Rrs0-, λ=m1bba+bb+m2bba+bb2,
a=aw+ac,
bb=1/2bw+bbp,
bbp=bp5500.002+0.020.5-0.25 log10×Chl550λ,
bw=0.00288λ500-4.32, bp550=0.416Chl0.766.
b=bw+bp, bp=bp550550/λ.
Pwcos Θ=33+xw1+xw cos2 Θ,
Ppcos Θ=1-g21+g2-2g cos Θ3/2.
PocnΘ=PwΘbw+PpΘbpbw+bp.
Qθ, ϕ, λ=Eu0-, λ/Lu0-, θ, ϕ, λ.
PpΘ=PocnΘ-PwΘb-bw
ρtotλ=ρpathλ+tρwλ,
tρwλ=ρtotλ-ρpathλ.
ρwTOAλtρwλ.
Lw0-, θ, λ=Lw0-, λ.
ρwIso,TOAλ=ρtotIsoλ-ρpathλ,
ρwTrue,TOAλ=ρtotTrueλ-ρpathλ,
ΔρtotTOAλ=100×ρtotIsoλ-ρtotTrueλ/ρtotTrueλ=100×ρwIso,TOAλ-ρwTrue,TOAλ/ρtotTrueλ.
msλ, 865=ρmsλ/ρms865,
γλ=ρpathλ/ρrλ
Δms765, 865100×msIso765, 865-msTrue765, 865msTrue765, 865,
msIso765, 865=ρms765+Δρtot765ρms865+Δρtot865,
msTrue765, 865=ρms765ρms865,
Δρtotλ=ρtotTrueλ-ρtotIsoλ.
Δγ765100×γIso765-γTrue765γTrue765,
γIso765=ρpath765+Δρtot765ρr765,
γTrue765=ρpath765ρr765.
a=aw+ap+ay,
ac=acsChl0.818,
ay=ay440 exp-0.014λ-440.
b=bw+bp+bs,
bs=SS550.0/λn,
PocnΘ=PwΘbw+PpΘbp+PsΘbsbw+bp+bs,
gλ=gwλbw+gpλbp+gsλbsbw+bp+bs.

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