Abstract

It is shown that measurements of the absorption coefficient and the volume-scattering function for scattering angles ≳ 15° of ocean water are sufficient for predicting the transport of irradiance in the ocean. Thus, difficult-to-measure small-angle scattering is not necessary in many applications. Furthermore, the irrelevance of small-angle scattering suggests the irrelevance of the scattering coefficient and of the routinely measured beam-attenuation coefficient in many radiative-transfer problems. Finally, these observations provide a method for determining the adequacy of instruments in which small sampling volumes (~ few cm3) are analyzed when predicting irradiance attenuation and diffuse reflection for large volumes (~ 10–104 m3).

© 1993 Optical Society of America

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References

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  1. H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. and Oceanogr. 36, 769–777 (1991).
    [CrossRef]
  2. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
    [CrossRef]
  3. H. R. Gordon, “Can the Lambert–Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
    [CrossRef]
  4. R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Int. 10, 11–30 (1961).
  5. T. J. Petzold, Volume Scattering Functions for Selected Natural Waters (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  6. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, New York, 1983).
  7. A. Morel, B. Gentilli, “Diffuse reflectance of oceanic waters: its dependence on sun angle as influenced by the molecular-scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
    [CrossRef] [PubMed]
  8. Y. Ge, H. R. Gordon, K. J. Voss, “Simulations of inelastic scattering contributions to the irradiance fields in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
    [PubMed]
  9. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).
  10. N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).
  11. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
    [CrossRef] [PubMed]
  12. D. M. DiToro, “Optics of turbid estuarine waters: approximations and applications,” Water Res. 12, 1059–1068 (1978).
    [CrossRef]
  13. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  14. J. R. V. Zaneveld, R. Bartz, J. C. Kitchen, “A reflective-tube absorption meter,” in Ocean Optics X, R. W. Spinrad, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1302, 124–136 (1990).

1993

1991

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

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. and Oceanogr. 36, 769–777 (1991).
[CrossRef]

1989

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

H. R. Gordon, “Can the Lambert–Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

1978

D. M. DiToro, “Optics of turbid estuarine waters: approximations and applications,” Water Res. 12, 1059–1068 (1978).
[CrossRef]

1973

1961

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Int. 10, 11–30 (1961).

Bartz, R.

J. R. V. Zaneveld, R. Bartz, J. C. Kitchen, “A reflective-tube absorption meter,” in Ocean Optics X, R. W. Spinrad, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1302, 124–136 (1990).

DiToro, D. M.

D. M. DiToro, “Optics of turbid estuarine waters: approximations and applications,” Water Res. 12, 1059–1068 (1978).
[CrossRef]

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

Feldman, G. C.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

Ge, Y.

Gentilli, B.

Gordon, H. R.

Y. Ge, H. R. Gordon, K. J. Voss, “Simulations of inelastic scattering contributions to the irradiance fields in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
[PubMed]

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. and Oceanogr. 36, 769–777 (1991).
[CrossRef]

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

H. R. Gordon, “Can the Lambert–Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
[CrossRef] [PubMed]

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

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

Kitchen, J. C.

J. R. V. Zaneveld, R. Bartz, J. C. Kitchen, “A reflective-tube absorption meter,” in Ocean Optics X, R. W. Spinrad, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1302, 124–136 (1990).

McClain, C. R.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

Morel, A.

Morel, A. Y.

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

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Natural Waters (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Preisendorfer, R. W.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Int. 10, 11–30 (1961).

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

Voss, K. J.

Zaneveld, J. R. V.

J. R. V. Zaneveld, R. Bartz, J. C. Kitchen, “A reflective-tube absorption meter,” in Ocean Optics X, R. W. Spinrad, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1302, 124–136 (1990).

Appl. Opt.

Limnol. and Oceanogr.

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. and Oceanogr. 36, 769–777 (1991).
[CrossRef]

Limnol. Oceanogr.

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

H. R. Gordon, “Can the Lambert–Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

Union Geod. Geophys. Int.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Int. 10, 11–30 (1961).

Water Res.

D. M. DiToro, “Optics of turbid estuarine waters: approximations and applications,” Water Res. 12, 1059–1068 (1978).
[CrossRef]

Other

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

J. R. V. Zaneveld, R. Bartz, J. C. Kitchen, “A reflective-tube absorption meter,” in Ocean Optics X, R. W. Spinrad, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1302, 124–136 (1990).

T. J. Petzold, Volume Scattering Functions for Selected Natural Waters (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1972).

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

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Vol. 1 of SeaWiFS Technical Report Series, NASA Tech. Memo. 104566 (NASA, Washington, D.C., 1992).

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

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Figures (6)

Fig. 1
Fig. 1

Plot of bt/b (a) and ct/c (b) as a function of αt. Curves in (b) correspond to ω0 = 0.50, 0.80, and 0.95 from top to bottom.

Fig. 2
Fig. 2

Kd/c as a function of optical depth for various αt. The curves without dots are for αt = 0, 10°, and 15°. The curves with dots are for αt = 25°, 35°, and 45°. αt increases from right to left. (a) ω0 = 0.5, (b) ω0 = 0.8, (c) ω0 = 0.95.

Fig. 3
Fig. 3

R as a function of optical depth for various αt The curves without dots are for αt = 0, 10°, and 15°. The curves with dots are for αt = 25°, 35°, and 45°. αt increases from right to left. (a) ω0 = 0.5, (b) ω0 = 0.8, (c) ω0 = 0.95.

Fig. 4
Fig. 4

Irradiances as a function of τ for ω0 = 0.8 and θ0 = 80°. The solid curves are the computations for αt = 0 and the dots are for αt > 0. (a) For Ed, Eu, and E0 the dots correspond to αt = 45°, and the irradiances are normalized to Ed = 1 just above the sea surface. (b) E2 is presented for αt = 15° and 45°. The plots for αt = 15° have been shifted to the left by one-half log unit to facilitate comparison.

Fig. 5
Fig. 5

Rt)/R(0) as a function of αt for (a) θ0 = 0° and (b) θ0 = 80°.

Fig. 6
Fig. 6

Lut)/Lu(0) as a function of αt for (a) θ0 = 0° and (b) θ0 = 80°.

Equations (13)

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b b = 2 π π / 2 π β ( α ) sin α d α .
b = 2 π 0 π β ( α ) sin α d α
cos θ d L ( z , θ , ϕ ) d z = - c ( z ) L ( z , θ , ϕ ) + Ξ β ( z , θ , ϕ θ , ϕ ) L ( z , θ , ϕ ) d Ω ,
cos α = cos θ cos θ + sin θ sin θ cos ( ϕ - ϕ ) .
E d ( z ) = Ξ d L ( z , θ , ϕ ) cos θ d Ω ,
E u ( z ) = - Ξ u L ( z , θ , ϕ ) cos θ d Ω ,
E 0 d ( z ) = Ξ d L ( z , θ , ϕ ) d Ω ,
E 0 u ( z ) = Ξ u L ( z , θ , ϕ ) d Ω ,
E 0 ( z ) = E 0 d ( z ) + E 0 u ( z ) ,
K x ( z , λ ) = - d { ln [ E x ( z , λ ) ] } d z ,
R ( z ) = E u ( z ) E d ( z )
β t ( α ) = { β ( α t ) , if α α t , β ( α ) , if α α t .
E l ( z ) = 0 2 π 0 π L ( z , θ , ϕ ) P l ( cos θ ) sin θ d θ d ϕ ,

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