Abstract

The quasi-single-scattering approximation in which a δ function replaces the forward portion of the volume scattering function is applied to radiative transfer in the ocean. Immediately beneath the surface, the product of the reflectance R and the downwelling irradiance-attenuation coefficient K(−) is equal to an integral of the volume scattering function in the backward direction weighted by a geometrical factor. Spectral variations of the volume scattering function are revealed in K(−)R; this is used to examine the wavelength dependence of scattering in two very different natural waters. In the clear water of Crater Lake, the backscattering is proportional to λ−3 (λ = wavelength), whereas the turbid, productive waters of San Vicente Reservoir show a complex dependence of backscattering on wavelength, which is associated with anomalous dispersion due to the 670-nm absorption band of the chlorophyll that is contained in the suspended phytoplankton.

© 1974 Optical Society of America

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References

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  1. J. E. Tyler and R. C. Smith, Measurements of Spectral Irradiance Underwater (Gordon and Breach, New York, 1970), p. 41ff.
  2. H. R. Gordon, Appl. Opt. 12, 2803 (1973).
    [Crossref] [PubMed]
  3. For experimental conditions in which this model is a valid approximation, the upwelling radiance just beneath the water surface is related to β(δ) and the incident irradiance in the water H0 by N(μ)/H0=β(δ)[c(1-ω0F)(μ+μ0)]-1,which shows that experimental measurement of N(μ) can be inverted to yield the shape of β(δ) in the angular range (π/2−θ0)< δ<π.
  4. R. C. Smith and J. E. Tyler, J. Opt. Soc. Am. 57, 589 (1967).
    [Crossref]
  5. G. Kullenberg, Deep Sea Res. 15, 423 (1968).
  6. T. J. Petzold, Volume Scattering Functions for Selected Waters (Scripps Institution of Oceanography, Univ. of Calif., San Diego, 1972), SIO Ref. 72–78.
  7. R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
    [Crossref]

1973 (2)

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

R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
[Crossref]

1968 (1)

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

1967 (1)

Goldman, C. R.

R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
[Crossref]

Gordon, H. R.

Kullenberg, G.

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Waters (Scripps Institution of Oceanography, Univ. of Calif., San Diego, 1972), SIO Ref. 72–78.

Smith, R. C.

R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
[Crossref]

R. C. Smith and J. E. Tyler, J. Opt. Soc. Am. 57, 589 (1967).
[Crossref]

J. E. Tyler and R. C. Smith, Measurements of Spectral Irradiance Underwater (Gordon and Breach, New York, 1970), p. 41ff.

Tyler, J. E.

R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
[Crossref]

R. C. Smith and J. E. Tyler, J. Opt. Soc. Am. 57, 589 (1967).
[Crossref]

J. E. Tyler and R. C. Smith, Measurements of Spectral Irradiance Underwater (Gordon and Breach, New York, 1970), p. 41ff.

Appl. Opt. (1)

Deep Sea Res. (1)

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

J. Opt. Soc. Am. (1)

Limn. Oceanogr. (1)

R. C. Smith, J. E. Tyler, and C. R. Goldman, Limn. Oceanogr. 18, 189 (1973).
[Crossref]

Other (3)

T. J. Petzold, Volume Scattering Functions for Selected Waters (Scripps Institution of Oceanography, Univ. of Calif., San Diego, 1972), SIO Ref. 72–78.

J. E. Tyler and R. C. Smith, Measurements of Spectral Irradiance Underwater (Gordon and Breach, New York, 1970), p. 41ff.

For experimental conditions in which this model is a valid approximation, the upwelling radiance just beneath the water surface is related to β(δ) and the incident irradiance in the water H0 by N(μ)/H0=β(δ)[c(1-ω0F)(μ+μ0)]-1,which shows that experimental measurement of N(μ) can be inverted to yield the shape of β(δ) in the angular range (π/2−θ0)< δ<π.

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Figures (1)

Fig. 1
Fig. 1

K(−)R as a function of wavelength for San Vicente Reservoir (SVR) and Crater Lake (CL). Note that the Crater Lake data have been multiplied by 10, as indicated on the curve.

Equations (6)

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R = 1 c 0 2 π 0 1 β ( δ ) μ d μ μ + μ 0 d ϕ ,
cos δ = - μ μ 0 + ( 1 - μ 0 2 ) 1 2 ( 1 - μ 2 ) 1 2 cos ( ϕ - ϕ 0 ) ,
F = 1 - { 0 2 π 0 1 β ( δ ) d μ d ϕ / 2 π - 1 1 β ( μ ) d μ } .
K ( - ) = c ( 1 - ω 0 F ) / μ 0 .
K ( - ) R = 1 μ 0 0 2 π 0 1 β ( δ ) μ μ 0 + μ d μ d ϕ .
N(μ)/H0=β(δ)[c(1-ω0F)(μ+μ0)]-1,