Abstract

Factor analysis is applied to multispectral (seventeen wavelengths) radiances simulated by a radiative transfer model (matrix-operator method) in and above coastal and open ocean waters. The calculated radiances were compared with measured radiances before applying factor analysis. They agree well for different sun elevations and even for turbid coastal waters. The factor analysis technique allows us to extract the characteristic signatures of phytoplankton, suspended matter, and yellow substance. The fluorescence of chlorophyll at λ = 685 nm is found to be a clear signal for phytoplankton, also in the presence of other suspensions and yellow substance. A comparison of different algorithms for the extraction of the fluoresence peak favors the addition of chlorophyll absorption at λ = 670 nm. The blue-green ratio is found to be useless for chlorophyll detection in coastal waters. Suspended matter and yellow substance can also clearly be seen in the factor loading for all multispectral radiances analyzed. However, suspended matter is reflected more strongly than yellow substance.

© 1986 Optical Society of America

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References

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  1. H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
    [CrossRef] [PubMed]
  2. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Bromkow, “Phytoplankton Pigment Concentrations in the Middle Atlantic Bight: Comparison of Ship Determinations and CZCS Estimates,” Appl. Opt. 22, 20 (1983).
    [CrossRef] [PubMed]
  3. NASA Earth Observing System, NASA TM-86129, 55 (1984).
  4. J. F. R. Gower, “Observations of In Situ Fluorescence of Chlorophyll a in Saavich Inlet,” Boundary-Layer Meteorol. 18, 235 (1980).
    [CrossRef]
  5. J. F. R. Gower, G. A. Borstad, “Use of the In Vivo Fluorescence Line at 685 μm for Remote Sensing Surveys of Surface Chlorophyll a,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 329–338.
    [CrossRef]
  6. J. Fischer, “Remote Sensing of Suspended Matter, Phytoplankton and Yellow Substances over Coastal Waters; Part 1: Aircraft Measurements,” Mitt. Geol. Palaeontol. Inst. Univ. Hamburg 55, 85 (1983).
  7. R. Doerffer, “Remote Sensing of Exceptional Plankton Blooms,” Forschungszentrum Geesthacht GmbH (1984).
  8. U. Forstner, W. Salomons, “Trace Metal Analysis on Polluted Sediments, Part 1: Assessment of Sources and Intensities, and Part 2: Evaluation of Environmental Impact,” Environ. Technol. Lett. 1, 494 (1980).
    [CrossRef]
  9. R. Doerffer, “Factor Analysis in Ocean Color Interpretation,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 339–345.
    [CrossRef]
  10. J. F. R. Gower et al., “The Information Content of Different Optical Spectral Ranges for Remote Chlorophyll Estimation in Coastal Waters,” Int. J. Remote Sensing 5, 349 (1984).
    [CrossRef]
  11. J. Fischer, “On the Information Content of Multispectral Radiance Measurements over an Ocean,” Int. J. Remote Sensing 6, 773 (1985).
    [CrossRef]
  12. U. Uberla, Faktorenanalyse (Springer-Verlag, Berlin, 1971).
    [CrossRef]
  13. G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix Operator Theory of Radiative Transfer. 1: Rayleigh Scattering,” Appl. Opt. 12, 314 (1973).
    [CrossRef] [PubMed]
  14. H. R. Gordon, “Diffuse Reflectance of the Ocean: The Theory of Its Augmentation by Chlorophyll a Fluorescence at 685 nm,” Appl. Opt. 18, 1161 (1979).
    [CrossRef] [PubMed]
  15. J. Fischer, H. Grassl, “Radiative Transfer in an Atmosphere-Ocean System: An Azimuthally Dependent Matrix-Operator Approach,” Appl. Opt. 23, 1032 (1984).
    [CrossRef] [PubMed]
  16. P. Koepke, “Aerosol Optical Thickness in the German Bight during MARSEN,” Eurasep Secretariat Newsletter (IRC, Ispra) No. 4 (1981).
  17. E. P. Shettle, R. W. Fenn, “Models of the Atmospheric Aerosols and their Optical Properties,” AGARD Conf. Proc.183 (1976).
  18. H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 330 to 1250 μm,” Sol. Phys. 74, 231 (1981).
    [CrossRef]
  19. L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption Curves of Phyloplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981).
    [CrossRef]
  20. N. K. Hojerslev, “On the Origin of Yellow Substance in Marine Environment,” in Proceedings, Workshop on Eurasep OCS Experiment (1979), pp. 13–28.
  21. R. Doerffer, “The Distribution of Substances in the Elbe-Estuary Determined by Remote Sensing,” Arch. Hydrobiol. Suppl. 43, 119 (1979).
  22. A. Morel, “In-Water and Remote Measurements of Ocean Color,” Boundary-Layer Meteorol. 18, 177 (1980).
    [CrossRef]

1985 (1)

J. Fischer, “On the Information Content of Multispectral Radiance Measurements over an Ocean,” Int. J. Remote Sensing 6, 773 (1985).
[CrossRef]

1984 (4)

J. Fischer, H. Grassl, “Radiative Transfer in an Atmosphere-Ocean System: An Azimuthally Dependent Matrix-Operator Approach,” Appl. Opt. 23, 1032 (1984).
[CrossRef] [PubMed]

NASA Earth Observing System, NASA TM-86129, 55 (1984).

R. Doerffer, “Remote Sensing of Exceptional Plankton Blooms,” Forschungszentrum Geesthacht GmbH (1984).

J. F. R. Gower et al., “The Information Content of Different Optical Spectral Ranges for Remote Chlorophyll Estimation in Coastal Waters,” Int. J. Remote Sensing 5, 349 (1984).
[CrossRef]

1983 (2)

J. Fischer, “Remote Sensing of Suspended Matter, Phytoplankton and Yellow Substances over Coastal Waters; Part 1: Aircraft Measurements,” Mitt. Geol. Palaeontol. Inst. Univ. Hamburg 55, 85 (1983).

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Bromkow, “Phytoplankton Pigment Concentrations in the Middle Atlantic Bight: Comparison of Ship Determinations and CZCS Estimates,” Appl. Opt. 22, 20 (1983).
[CrossRef] [PubMed]

1981 (2)

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 330 to 1250 μm,” Sol. Phys. 74, 231 (1981).
[CrossRef]

L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption Curves of Phyloplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981).
[CrossRef]

1980 (4)

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
[CrossRef] [PubMed]

J. F. R. Gower, “Observations of In Situ Fluorescence of Chlorophyll a in Saavich Inlet,” Boundary-Layer Meteorol. 18, 235 (1980).
[CrossRef]

U. Forstner, W. Salomons, “Trace Metal Analysis on Polluted Sediments, Part 1: Assessment of Sources and Intensities, and Part 2: Evaluation of Environmental Impact,” Environ. Technol. Lett. 1, 494 (1980).
[CrossRef]

A. Morel, “In-Water and Remote Measurements of Ocean Color,” Boundary-Layer Meteorol. 18, 177 (1980).
[CrossRef]

1979 (3)

H. R. Gordon, “Diffuse Reflectance of the Ocean: The Theory of Its Augmentation by Chlorophyll a Fluorescence at 685 nm,” Appl. Opt. 18, 1161 (1979).
[CrossRef] [PubMed]

N. K. Hojerslev, “On the Origin of Yellow Substance in Marine Environment,” in Proceedings, Workshop on Eurasep OCS Experiment (1979), pp. 13–28.

R. Doerffer, “The Distribution of Substances in the Elbe-Estuary Determined by Remote Sensing,” Arch. Hydrobiol. Suppl. 43, 119 (1979).

1976 (1)

E. P. Shettle, R. W. Fenn, “Models of the Atmospheric Aerosols and their Optical Properties,” AGARD Conf. Proc.183 (1976).

1973 (1)

Borstad, G. A.

J. F. R. Gower, G. A. Borstad, “Use of the In Vivo Fluorescence Line at 685 μm for Remote Sensing Surveys of Surface Chlorophyll a,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 329–338.
[CrossRef]

Bromkow, W. W.

Brown, J. W.

Brown, O. B.

Catchings, F. E.

Clark, D. K.

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Bromkow, “Phytoplankton Pigment Concentrations in the Middle Atlantic Bight: Comparison of Ship Determinations and CZCS Estimates,” Appl. Opt. 22, 20 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
[CrossRef] [PubMed]

Doerffer, R.

R. Doerffer, “Remote Sensing of Exceptional Plankton Blooms,” Forschungszentrum Geesthacht GmbH (1984).

R. Doerffer, “The Distribution of Substances in the Elbe-Estuary Determined by Remote Sensing,” Arch. Hydrobiol. Suppl. 43, 119 (1979).

R. Doerffer, “Factor Analysis in Ocean Color Interpretation,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 339–345.
[CrossRef]

Evans, R. H.

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models of the Atmospheric Aerosols and their Optical Properties,” AGARD Conf. Proc.183 (1976).

Fischer, J.

J. Fischer, “On the Information Content of Multispectral Radiance Measurements over an Ocean,” Int. J. Remote Sensing 6, 773 (1985).
[CrossRef]

J. Fischer, H. Grassl, “Radiative Transfer in an Atmosphere-Ocean System: An Azimuthally Dependent Matrix-Operator Approach,” Appl. Opt. 23, 1032 (1984).
[CrossRef] [PubMed]

J. Fischer, “Remote Sensing of Suspended Matter, Phytoplankton and Yellow Substances over Coastal Waters; Part 1: Aircraft Measurements,” Mitt. Geol. Palaeontol. Inst. Univ. Hamburg 55, 85 (1983).

Forstner, U.

U. Forstner, W. Salomons, “Trace Metal Analysis on Polluted Sediments, Part 1: Assessment of Sources and Intensities, and Part 2: Evaluation of Environmental Impact,” Environ. Technol. Lett. 1, 494 (1980).
[CrossRef]

Gordon, H. R.

Gower, J. F. R.

J. F. R. Gower et al., “The Information Content of Different Optical Spectral Ranges for Remote Chlorophyll Estimation in Coastal Waters,” Int. J. Remote Sensing 5, 349 (1984).
[CrossRef]

J. F. R. Gower, “Observations of In Situ Fluorescence of Chlorophyll a in Saavich Inlet,” Boundary-Layer Meteorol. 18, 235 (1980).
[CrossRef]

J. F. R. Gower, G. A. Borstad, “Use of the In Vivo Fluorescence Line at 685 μm for Remote Sensing Surveys of Surface Chlorophyll a,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 329–338.
[CrossRef]

Grassl, H.

Hojerslev, N. K.

N. K. Hojerslev, “On the Origin of Yellow Substance in Marine Environment,” in Proceedings, Workshop on Eurasep OCS Experiment (1979), pp. 13–28.

Howis, W. A.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
[CrossRef] [PubMed]

Kattawar, G. W.

Koepke, P.

P. Koepke, “Aerosol Optical Thickness in the German Bight during MARSEN,” Eurasep Secretariat Newsletter (IRC, Ispra) No. 4 (1981).

Labs, D.

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 330 to 1250 μm,” Sol. Phys. 74, 231 (1981).
[CrossRef]

Morel, A.

A. Morel, “In-Water and Remote Measurements of Ocean Color,” Boundary-Layer Meteorol. 18, 177 (1980).
[CrossRef]

Mueller, J. L.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
[CrossRef] [PubMed]

Neckel, H.

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 330 to 1250 μm,” Sol. Phys. 74, 231 (1981).
[CrossRef]

Plass, G. N.

Prieur, L.

L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption Curves of Phyloplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981).
[CrossRef]

Salomons, W.

U. Forstner, W. Salomons, “Trace Metal Analysis on Polluted Sediments, Part 1: Assessment of Sources and Intensities, and Part 2: Evaluation of Environmental Impact,” Environ. Technol. Lett. 1, 494 (1980).
[CrossRef]

Sathyendranath, S.

L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption Curves of Phyloplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981).
[CrossRef]

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models of the Atmospheric Aerosols and their Optical Properties,” AGARD Conf. Proc.183 (1976).

Uberla, U.

U. Uberla, Faktorenanalyse (Springer-Verlag, Berlin, 1971).
[CrossRef]

AGARD Conf. Proc. (1)

E. P. Shettle, R. W. Fenn, “Models of the Atmospheric Aerosols and their Optical Properties,” AGARD Conf. Proc.183 (1976).

Appl. Opt. (4)

Arch. Hydrobiol. Suppl. (1)

R. Doerffer, “The Distribution of Substances in the Elbe-Estuary Determined by Remote Sensing,” Arch. Hydrobiol. Suppl. 43, 119 (1979).

Boundary-Layer Meteorol. (2)

A. Morel, “In-Water and Remote Measurements of Ocean Color,” Boundary-Layer Meteorol. 18, 177 (1980).
[CrossRef]

J. F. R. Gower, “Observations of In Situ Fluorescence of Chlorophyll a in Saavich Inlet,” Boundary-Layer Meteorol. 18, 235 (1980).
[CrossRef]

Environ. Technol. Lett. (1)

U. Forstner, W. Salomons, “Trace Metal Analysis on Polluted Sediments, Part 1: Assessment of Sources and Intensities, and Part 2: Evaluation of Environmental Impact,” Environ. Technol. Lett. 1, 494 (1980).
[CrossRef]

Forschungszentrum Geesthacht GmbH (1)

R. Doerffer, “Remote Sensing of Exceptional Plankton Blooms,” Forschungszentrum Geesthacht GmbH (1984).

Int. J. Remote Sensing (2)

J. F. R. Gower et al., “The Information Content of Different Optical Spectral Ranges for Remote Chlorophyll Estimation in Coastal Waters,” Int. J. Remote Sensing 5, 349 (1984).
[CrossRef]

J. Fischer, “On the Information Content of Multispectral Radiance Measurements over an Ocean,” Int. J. Remote Sensing 6, 773 (1985).
[CrossRef]

Limnol. Oceanogr. (1)

L. Prieur, S. Sathyendranath, “An Optical Classification of Coastal and Oceanic Waters Based on the Specific Absorption Curves of Phyloplankton Pigments, Dissolved Organic Matter, and Other Particulate Materials,” Limnol. Oceanogr. 26, 671 (1981).
[CrossRef]

Mitt. Geol. Palaeontol. Inst. Univ. Hamburg (1)

J. Fischer, “Remote Sensing of Suspended Matter, Phytoplankton and Yellow Substances over Coastal Waters; Part 1: Aircraft Measurements,” Mitt. Geol. Palaeontol. Inst. Univ. Hamburg 55, 85 (1983).

NASA Earth Observing System, NASA TM-86129 (1)

NASA Earth Observing System, NASA TM-86129, 55 (1984).

Proceedings, Workshop on Eurasep OCS Experiment (1)

N. K. Hojerslev, “On the Origin of Yellow Substance in Marine Environment,” in Proceedings, Workshop on Eurasep OCS Experiment (1979), pp. 13–28.

Science (1)

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Howis, “Phytoplankton Pigments from Nimbus 7 Coastal Zone Color Scanner: Comparisons with Surface Measurements,” Science 210, 63 (1980).
[CrossRef] [PubMed]

Sol. Phys. (1)

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 330 to 1250 μm,” Sol. Phys. 74, 231 (1981).
[CrossRef]

Other (4)

R. Doerffer, “Factor Analysis in Ocean Color Interpretation,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 339–345.
[CrossRef]

J. F. R. Gower, G. A. Borstad, “Use of the In Vivo Fluorescence Line at 685 μm for Remote Sensing Surveys of Surface Chlorophyll a,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 329–338.
[CrossRef]

U. Uberla, Faktorenanalyse (Springer-Verlag, Berlin, 1971).
[CrossRef]

P. Koepke, “Aerosol Optical Thickness in the German Bight during MARSEN,” Eurasep Secretariat Newsletter (IRC, Ispra) No. 4 (1981).

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Figures (14)

Fig. 1
Fig. 1

Normalized absorption coefficient for chlorophyll (—), and yellow substance (…) as well as normalized extinction for suspended matter (---) depending on wavelength λ. The reference wavelength is λ = 440 nm. The wavelengths of the radiative transfer model are also indicated (●).

Fig. 2
Fig. 2

Measured (---) and calculated (—) multispectral upward radiances just above the ocean surface for (I) chlorophyll density ρp = 16 μg/liter, suspended matter density ρs = 11.8 mg/liter, yellow substance ρys = 9.4 mg/liter, and solar zenith angle θ0 = 60° (●); (II) ρp = 8 μg/liter, ρs = 2.5 mg/liter, ρys = 7.1 mg/liter, and θ0 = 45° (■); (III) ρp = 7 μg/liter, ρs = 1.9 mg/liter, ρys = 9.2 mg/liter, and θ0 = 45° (▲); the measured substance densities and sun elevations are the input parameters for the model calculations.

Fig. 3
Fig. 3

(a) Chlorophyll plus pheophytin density in μg/liter for a mean concentration ρp = 5.6 μg/liter and standard deviation σp = 10.2 μg/liter. (b) Suspended matter density in mg/liter; mean density ρs = 3.2 mg/liter and σs= 6.4 mg/liter. (c) Yellow substance concentration in mg/liter; mean density ρys = 1.8 mg/liter and σys = 1.8 mg/liter.

Fig. 4
Fig. 4

(a) Multispectral upward radiance just below the ocean surface for coastal water (case I as given in Table I) according to substance variations as given in Figs. 3(a)–(c). (b) As in (a), but without yellow substance, for coastal water (case IV) as given in Table I.

Fig. 5
Fig. 5

(a) Factor loadings of the dominating eigenvalues of the analyzed multispectral radiances according to Fig. 4(a). (b) As in (a) but according to Fig. 4(b).

Fig. 6
Fig. 6

Normalized factor score P2 (—) and normalized color ratios (---) via all analyzed families of radiances from Fig. 4(a); the correlation coefficient between both quantities is −0.72.

Fig. 7
Fig. 7

Normalized factor score P4 (—) and normalized fluorescence line height (---) derived from F3 [Eq. (10)], for details see Fig. 6.

Fig. 8
Fig. 8

Normalized factor score P4 (—) and normalized phytoplankton density (---), for details see Fig. 6.

Fig. 9
Fig. 9

Normalized factor score P1 (—) and normalized suspended matter density (---), for details see Fig. 6.

Fig. 10
Fig. 10

Normalized factor score P2 (—) and normalized yellow substance density (---), for details see Fig. 6.

Fig. 11
Fig. 11

Multispectral radiance just below the ocean surface for open ocean water (case V as given in Table I).

Fig. 12
Fig. 12

Factor loadings P1–P4 of the dominating eigenvalues of the analyzed radiance according to Fig. 11.

Fig. 13
Fig. 13

Multispectral upward radiance at 1-km height with varying aerosol extinction (σA = 5%); the optical properties of the ocean water as in Fig. 3.

Fig. 14
Fig. 14

Factor loadings P1–P4 of the dominating eigenvalues of the analyzed radiance from Fig. 13.

Tables (7)

Tables Icon

Table I Mean Density of Phytoplankton (Chlorophyll + Pheophytin) ρp in μg/liter, Suspended Matter ρs in mg/liter, Yellow Substance ρys in mg/liter, and Their Corresponding Standard Deviations σp, σs, σys; the Star Indicates that Part of ρs Correlated with ρp

Tables Icon

Table II Correlation Coefficients Between Factor Scores P1–P4 or Phytoplankton and Color Ratio, Fluorescence Algorithms or Water Substances; Water Type, Case I in Table I

Tables Icon

Table III Correlation Coefficients as in Table II but for Coastal Water Case II According to Table I

Tables Icon

Table IV Correlation Coefficients as in Table II but for Coastal Water Case III According to Table I

Tables Icon

Table V Correlation Coefficients as in Table II but for Coastal Water Case IV According to Table I

Tables Icon

Table VI Correlation Coefficients as in Table II but for Open Ocean Water (Case V According to Table I)

Tables Icon

Table VII Correlation Coefficients as in Table II but for Radiances at 1-km Height

Equations (13)

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U C = A ,
a i j = u i j λ j / u 1 j 2 + + u k j 2 .
z i j = a i 1 p 1 j + + a i k p k j ,
z i j = L ( λ i , x j ) L ( λ i ) ¯ S i ,
L ( λ i ) ¯ = 1 l j = 1 l L ( λ i , x j ) , S i = 1 l 1 j = 1 l [ L ( λ i , x j ) L ( λ i ) ] 2 ¯ .
1 l j = 1 1 z i j = 0 , for i = 1 , , K , 1 l 1 j 1 1 z i j 2 = 1 , for i = 1 , , K .
P = A 1 Z .
( μ d d τ + 1 ) L ( τ , μ , ϕ , λ ) = ω 0 ( τ , λ ) 0 2 π 1 1 L ( τ , μ , ϕ , λ ) × P ( τ , μ , ϕ , , μ , ϕ , λ ) d μ d ϕ + ω 0 ( τ , λ ) π F 0 ( λ ) P ( τ , μ , ϕ , μ 0 , ϕ 0 , λ ) × exp ( τ / μ 0 ) + η ( 2 π σ 2 ) 1 / 2 c ( τ , λ F ) 4 π λ F × exp [ ( λ λ F ) 2 2 σ 2 ] λ E 1 λ E 2 λ E a ( P ) ( τ , λ E ) × h ( τ , μ 0 , λ E ) d λ E .
C 1 = L ( λ 550 ) / L ( λ 445 ) .
F 1 = L ( λ F ) L ( λ 1 ) ( λ F λ 2 ) + L ( λ 2 ) ( λ 1 λ F ) λ 2 λ 1 ,
F 2 = L ( λ F ) [ L ( λ 1 ) ( λ F λ 2 ) + L ( λ 2 ) ( λ 1 λ F ) λ 2 λ 1 ] .
F 3 = L ( λ 685 ) L ( λ 665 ) ,
phytoplankton density ρ p = α a ( p ) = 0.04545 g m 2 a ( p ) ( λ = 440 nm ) ρ p in g m 3 or mg / liter if a ( p ) in m 1 , suspended matter density ρ s = β c ( s ) = 8.00 g m 2 c ( s ) ρ s in g m 3 or mg / liter for c in m 1 , yellow substance density ρ y s = 4.72 g m 2 a ( y s ) ( λ = 450 nm ) exp ( 0.0014 Δ λ with Δ λ = 380 450 nm = 70 nm ρ y s in g m 3 or mg / liter for a ( y s ) in m 1 .

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