Abstract

The radiative transfer equation is modified to include the effect of fluorescent substances and solved in the quasi-single scattering approximation for a homogeneous ocean containing fluorescent particles with wavelength independent quantum efficiency and a Gaussian shaped emission line. The results are applied to the in vivo fluorescence of chlorophyll a (in phytoplankton) in the ocean to determine if the observed quantum efficiencies are large enough to explain the enhancement of the ocean’s diffuse reflectance near 685 nm in chlorophyll rich waters without resorting to anomalous dispersion. The computations indicate that the required efficiencies are sufficiently low to account completely for the enhanced reflectance. The validity of the theory is further demonstrated by deriving values for the upwelling irradiance attenuation coefficient at 685 nm which are in close agreement with the observations.

© 1979 Optical Society of America

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References

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  1. A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
    [CrossRef]
  2. R. A. Neville, J. F. R. Gower, J. Geophys. Res. 82, 3487 (1977).
    [CrossRef]
  3. J. L. Mueller, “The Influence of Phytoplankton on Ocean Color Spectra,” Ph.D. Thesis, Oregon State U., Corvallis (1973).
  4. H. R. Gordon, J. Opt. Soc. Am. 64, 773 (1974).
    [CrossRef]
  5. M. Kerker, J. Colloid Interface Sci. 58, 100 (1977).
    [CrossRef]
  6. H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
    [CrossRef]
  7. H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
    [CrossRef]
  8. J. P. Kratohuil, M. P. Lee, M. Kerker, Appl. Opt. 17, 1978 (1978).
    [CrossRef]
  9. E. Lee, R. E. Benner, J. B. Fenn, R. K. Chang, Appl. Opt. 17, 1980 (1978).
    [CrossRef]
  10. E. D. Traganza, Bull. Mar. Sci. 19, 897 (1969).
  11. C. S. Yentsch, D. W. Menzel, Deep Sea Res. 10, 221 (1963).
  12. P. Pringsheim, Fluorescence and Phosphorescence (Interscience, New York, 1949).
  13. L. S. Forster, R. Livingston, J. Chem. Phys. 20, 1315 (1952).
    [CrossRef]
  14. R. W. Preisendorfer, Union Geod. Geophys. Inst. Mon. 10, 11 (1961).
  15. H. R. Gordon, Appl. Opt. 12, 2803 (1973).
    [CrossRef] [PubMed]
  16. H. R. Gordon, O. B. Brown, M. M. Jacobs, Appl. Opt. 14, 417 (1975).
    [CrossRef] [PubMed]
  17. A. Morel, L. Prieur, Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retro-diffusion pour diverses régions marines. Centre Rech. Oceanogr., Villefranche-sur-Mer Rapp17, 157 (1975).
  18. K. Ya. Kondratiev, Radiation Characteristics of the Atmosphere and Earth’s Surface (Amerind, New Delhi, 1973).
  19. P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
    [CrossRef]
  20. D. A. Kiefer, Mar. Biol. 22, 263 (1973).
    [CrossRef]
  21. D. A. Kiefer, Mar. Biol. 23, 39 (1973).
    [CrossRef]
  22. R. W. Austin, Scripps Institution of Oceanography; personal communication.

1978 (2)

1977 (3)

M. Kerker, J. Colloid Interface Sci. 58, 100 (1977).
[CrossRef]

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

R. A. Neville, J. F. R. Gower, J. Geophys. Res. 82, 3487 (1977).
[CrossRef]

1976 (2)

H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[CrossRef]

1975 (1)

1974 (1)

1973 (3)

H. R. Gordon, Appl. Opt. 12, 2803 (1973).
[CrossRef] [PubMed]

D. A. Kiefer, Mar. Biol. 22, 263 (1973).
[CrossRef]

D. A. Kiefer, Mar. Biol. 23, 39 (1973).
[CrossRef]

1969 (1)

E. D. Traganza, Bull. Mar. Sci. 19, 897 (1969).

1963 (1)

C. S. Yentsch, D. W. Menzel, Deep Sea Res. 10, 221 (1963).

1961 (1)

R. W. Preisendorfer, Union Geod. Geophys. Inst. Mon. 10, 11 (1961).

1956 (1)

P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
[CrossRef]

1952 (1)

L. S. Forster, R. Livingston, J. Chem. Phys. 20, 1315 (1952).
[CrossRef]

Austin, R. W.

R. W. Austin, Scripps Institution of Oceanography; personal communication.

Bannister, T. T.

P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
[CrossRef]

Benner, R. E.

Brown, O. B.

Chang, R. K.

Chew, H.

H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

Fenn, J. B.

Forster, L. S.

L. S. Forster, R. Livingston, J. Chem. Phys. 20, 1315 (1952).
[CrossRef]

Gordon, H. R.

Gower, J. F. R.

R. A. Neville, J. F. R. Gower, J. Geophys. Res. 82, 3487 (1977).
[CrossRef]

Jacobs, M. M.

Kerker, M.

J. P. Kratohuil, M. P. Lee, M. Kerker, Appl. Opt. 17, 1978 (1978).
[CrossRef]

M. Kerker, J. Colloid Interface Sci. 58, 100 (1977).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

Kiefer, D. A.

D. A. Kiefer, Mar. Biol. 22, 263 (1973).
[CrossRef]

D. A. Kiefer, Mar. Biol. 23, 39 (1973).
[CrossRef]

Kondratiev, K. Ya.

K. Ya. Kondratiev, Radiation Characteristics of the Atmosphere and Earth’s Surface (Amerind, New Delhi, 1973).

Kratohuil, J. P.

Latimer, P.

P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
[CrossRef]

Lee, E.

Lee, M. P.

Livingston, R.

L. S. Forster, R. Livingston, J. Chem. Phys. 20, 1315 (1952).
[CrossRef]

McNulty, P. J.

H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[CrossRef]

Menzel, D. W.

C. S. Yentsch, D. W. Menzel, Deep Sea Res. 10, 221 (1963).

Morel, A.

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

A. Morel, L. Prieur, Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retro-diffusion pour diverses régions marines. Centre Rech. Oceanogr., Villefranche-sur-Mer Rapp17, 157 (1975).

Mueller, J. L.

J. L. Mueller, “The Influence of Phytoplankton on Ocean Color Spectra,” Ph.D. Thesis, Oregon State U., Corvallis (1973).

Neville, R. A.

R. A. Neville, J. F. R. Gower, J. Geophys. Res. 82, 3487 (1977).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, Union Geod. Geophys. Inst. Mon. 10, 11 (1961).

Prieur, L.

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

A. Morel, L. Prieur, Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retro-diffusion pour diverses régions marines. Centre Rech. Oceanogr., Villefranche-sur-Mer Rapp17, 157 (1975).

Pringsheim, P.

P. Pringsheim, Fluorescence and Phosphorescence (Interscience, New York, 1949).

Rabinowitch, E. I.

P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
[CrossRef]

Traganza, E. D.

E. D. Traganza, Bull. Mar. Sci. 19, 897 (1969).

Yentsch, C. S.

C. S. Yentsch, D. W. Menzel, Deep Sea Res. 10, 221 (1963).

Appl. Opt. (4)

Bull. Mar. Sci. (1)

E. D. Traganza, Bull. Mar. Sci. 19, 897 (1969).

Deep Sea Res. (1)

C. S. Yentsch, D. W. Menzel, Deep Sea Res. 10, 221 (1963).

J. Chem. Phys. (1)

L. S. Forster, R. Livingston, J. Chem. Phys. 20, 1315 (1952).
[CrossRef]

J. Colloid Interface Sci. (1)

M. Kerker, J. Colloid Interface Sci. 58, 100 (1977).
[CrossRef]

J. Geophys. Res. (1)

R. A. Neville, J. F. R. Gower, J. Geophys. Res. 82, 3487 (1977).
[CrossRef]

J. Opt. Soc. Am. (2)

Limnol. Oceanogr. (1)

A. Morel, L. Prieur, Limnol. Oceanogr. 22, 709 (1977).
[CrossRef]

Mar. Biol. (2)

D. A. Kiefer, Mar. Biol. 22, 263 (1973).
[CrossRef]

D. A. Kiefer, Mar. Biol. 23, 39 (1973).
[CrossRef]

Phys. Rev. A (1)

H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

Science (1)

P. Latimer, T. T. Bannister, E. I. Rabinowitch, Science 124, 1585 (1956).
[CrossRef]

Union Geod. Geophys. Inst. Mon. (1)

R. W. Preisendorfer, Union Geod. Geophys. Inst. Mon. 10, 11 (1961).

Other (5)

A. Morel, L. Prieur, Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retro-diffusion pour diverses régions marines. Centre Rech. Oceanogr., Villefranche-sur-Mer Rapp17, 157 (1975).

K. Ya. Kondratiev, Radiation Characteristics of the Atmosphere and Earth’s Surface (Amerind, New Delhi, 1973).

J. L. Mueller, “The Influence of Phytoplankton on Ocean Color Spectra,” Ph.D. Thesis, Oregon State U., Corvallis (1973).

P. Pringsheim, Fluorescence and Phosphorescence (Interscience, New York, 1949).

R. W. Austin, Scripps Institution of Oceanography; personal communication.

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Figures (7)

Fig. 1
Fig. 1

Irradiance reflectivity R(λ) just beneath the surface from Morel and Prieur.16

Fig. 2
Fig. 2

Attenuation coefficient for downwelling irradiance from Ref. 16 for the stations in Fig. 1.

Fig. 3
Fig. 3

Spectra of solar irradiance H0(λ) from Ref. 17 and phytoplankton ac(λ) from Ref. 1.

Fig. 4
Fig. 4

Integrand of the integral in Eq. (9) as a function of depth.

Fig. 5
Fig. 5

Integrand of the integral in Eq. (10) for several stations showing the effect of fEF).

Fig. 6
Fig. 6

Fit of RF) − RsF) to Eq. (10) using the values oft from Table I.

Fig. 7
Fig. 7

Variation of the integral in Eq. (9) with depth for C67 and C91.

Tables (2)

Tables Icon

Table I Values of η Required to Explain R(685) − Rs(685) and the Associated Chorophyll a (Chi a) Values

Tables Icon

Table II Comparison of Computed Values of Ku(685) from Eq. (9) and Observed Values of Ku(685) and K(685)

Equations (18)

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β Φ ( θ , λ F , λ E ) J ( θ , λ F ) Δ V Δ λ E H ( λ E ) d λ E ,
Φ ( λ F , λ E ) Ω β Φ ( θ , λ F , λ E ) d Ω ,
η ( λ F , λ E ) = λ F λ E Φ ( λ F , λ E ) Δ λ F a ( λ E ) ,
d L d l ( l , ξ ^ , λ F ) = - c ( l , λ F ) L ( l , ξ ^ , λ F ) + Ω β ( l , α , λ F ) L ( l , ξ ^ , λ F ) d Ω + λ E 1 λ E 2 Ω β Φ ( l , α , λ F , λ E ) L ( l , ξ ^ , λ E ) d Ω d λ E ,
b ( l , λ F ) = 2 π 0 π β ( l , θ , λ F ) sin θ d θ .
β Φ ( l , θ , λ F , λ E ) = Φ ( l , λ F , λ E , ) / 4 π .
η ( l , λ E ) = line λ F Φ ( l , λ F , λ E ) d λ F / λ E a ( l , λ E ) .
Φ ( l , λ F , λ E ) = η ( l , λ E ) λ E a ( l , λ E ) λ O F 1 ( 2 π σ 2 ) 1 / 2 exp - ( λ F - λ O F ) 2 2 σ 2 ,
d L ( l , ξ ^ , λ F ) c ( l , λ F ) d l = - L ( l , ξ ^ , λ F ) + ω 0 ( l , λ F ) 4 π Ω P ( l , α , λ F ) L ( l , ξ ^ , λ F ) d Ω + η ( l ) ( 2 π σ 2 ) - 1 / 2 c ( l , λ F ) 4 π λ O F exp [ - ( λ F - λ O F ) 2 2 σ 2 ] × λ E 1 λ E 2 λ E a ( l , λ E ) h ( l , λ E ) d λ E ,
h ( l , λ E ) = Ω L ( l , ξ ^ , λ E ) d Ω .
μ d L ( Z , μ , λ F ) c ( λ F ) d Z = L ( Z , μ , λ F ) - ω 0 ( λ F ) 2 × - 1 1 P ( cos α , λ F ) L ( Z , μ , λ F ) d Ω - δ 0 4 π λ E 1 λ E 2 λ E a ( λ E ) h ( l , λ E ) d λ E ,
F ( λ ) = 2 π 0 π / 2 P ( α , λ ) sin α d α .
L ( z , μ , λ F ) = ω 0 ( λ F ) H 0 ( λ F ) P ( - μ , λ F ) exp [ - K ( λ F ) Z ] ( 1 + μ ) [ 1 - ω 0 ( λ F ) F ( λ F ) ] + δ 0 4 π λ E 1 λ E 2 λ E a ( Ω E ) H 0 ( λ E ) exp [ - K ( λ E ) Z ] [ 1 + μ K ( λ E ) / K ( λ F ) ] d λ E ,
H u ( z , λ F ) 2 π 0 1 L ( z , μ , λ F ) μ d μ
H u ( z , λ F ) = R S ( λ F ) H 0 ( λ F ) exp [ - K ( λ F ) Z ] + δ 0 2 λ E 1 λ E 2 a ( λ E ) λ E H 0 ( λ E ) × exp [ - K ( λ E ) Z f ( λ E , λ F ) d λ E ,
f ( λ E , λ F ) = K ( λ F ) K ( λ E ) { 1 + K ( λ F ) K ( λ E ) ln [ 1 + K ( λ E ) K ( λ F ) ] } ,
R ( λ O F ) - R s ( λ O F ) = η ( 2 π σ 2 ) - 1 / 2 2 K ( λ O F ) μ 0 H 0 ( λ O F ) λ O F × λ E 1 λ E 2 λ E a ( λ E ) H 0 ( λ E ) f ( λ E , λ O F ) d λ E .
ln [ H u ( Z 2 , λ ) / H u ( Z 1 , λ ) ] = - K u ( Z 1 , Z 2 , λ ) ( Z 2 - Z 1 ) .

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