Abstract

There has been a large effort to relate the apparent optical properties of ocean water to the inherent optical properties, which are the absorption coefficient a, the scattering coefficient b, and the scattering phase function ρ(θ). The diffuse attenuation coefficient k diff has most often been considered an apparent optical property. However, k diff can be considered a quasi-inherent property k diff′ when defined as a steady-state light distribution attenuation coefficient. The Honey–Wilson research empirically relates k diff to a and b. The Honey–Wilson relation most likely applies to a limited range of water types because it does not include dependence on ρ(θ). A series of Monte Carlo simulations were initiated to calculate k diff′ in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo ω0 and the mean forward-scattering angle θm for two analytic phase functions with different shapes. It was found that k diff′ is nearly independent of the shape of ρ(θ) and can be easily parameterized in terms of a, b, and θm for 0.11 ≤ θm ≤ 0.48 rad and 0.5 ≤ ω0 ≤ 0.95. k diff′ is an asymptotic quantity; that is, a steady-state distribution is reached only after many scattering lengths.

© 1999 Optical Society of America

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References

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  1. See, for example, R. W. Preisendorfer, Hydrologic Optics, U.S. Department of Commerce Pub. PB-259 793 (National Technical Information Service, Springfield, Va., 1976), Vol. 1, pp. 118–119.
  2. G. P. Sorenson, R. C. Honey, J. R. Payne, “Analysis of the use of airborne laser radar for submarine detection and ranging,” (Stanford Research Institute, Stanford, Calif., 1966).
  3. H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21, 2996–3001 (1982) and references therein.
    [CrossRef] [PubMed]
  4. 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]
  5. G. C. Guenther, “Airborne LASER hydrography,” NOAA Professional Paper Series (National Ocean Service, Rockville, Md., 1985), p. 167.
  6. G. Plass, G. W. Kattawar, “Radiative transfer in an atmosphere-ocean system,” Appl. Opt. 8, 455–466 (1969).
    [CrossRef] [PubMed]
  7. J. W. McLean, D. R. Crawford, C. L. Hindman, “Limits of small angle scattering theory,” Appl. Opt. 26, 2053–2054 (1987).
    [CrossRef] [PubMed]
  8. D. Arnush, “Underwater light-beam propagation in the small-angle-scattering approximation,” J. Opt. Soc. Am. 62, 1109–1111 (1972).
    [CrossRef]

1987 (1)

1982 (1)

1975 (1)

1972 (1)

1969 (1)

Arnush, D.

Brown, O. B.

Crawford, D. R.

Gordon, H. R.

Guenther, G. C.

G. C. Guenther, “Airborne LASER hydrography,” NOAA Professional Paper Series (National Ocean Service, Rockville, Md., 1985), p. 167.

Hindman, C. L.

Honey, R. C.

G. P. Sorenson, R. C. Honey, J. R. Payne, “Analysis of the use of airborne laser radar for submarine detection and ranging,” (Stanford Research Institute, Stanford, Calif., 1966).

Jacobs, M. M.

Kattawar, G. W.

McLean, J. W.

Payne, J. R.

G. P. Sorenson, R. C. Honey, J. R. Payne, “Analysis of the use of airborne laser radar for submarine detection and ranging,” (Stanford Research Institute, Stanford, Calif., 1966).

Plass, G.

Preisendorfer, R. W.

See, for example, R. W. Preisendorfer, Hydrologic Optics, U.S. Department of Commerce Pub. PB-259 793 (National Technical Information Service, Springfield, Va., 1976), Vol. 1, pp. 118–119.

Sorenson, G. P.

G. P. Sorenson, R. C. Honey, J. R. Payne, “Analysis of the use of airborne laser radar for submarine detection and ranging,” (Stanford Research Institute, Stanford, Calif., 1966).

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Other (3)

G. C. Guenther, “Airborne LASER hydrography,” NOAA Professional Paper Series (National Ocean Service, Rockville, Md., 1985), p. 167.

See, for example, R. W. Preisendorfer, Hydrologic Optics, U.S. Department of Commerce Pub. PB-259 793 (National Technical Information Service, Springfield, Va., 1976), Vol. 1, pp. 118–119.

G. P. Sorenson, R. C. Honey, J. R. Payne, “Analysis of the use of airborne laser radar for submarine detection and ranging,” (Stanford Research Institute, Stanford, Calif., 1966).

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Figures (7)

Fig. 1
Fig. 1

Merten–Wells and Arnush analytic phase functions.

Fig. 2
Fig. 2

A and PB measured phase functions.

Fig. 3
Fig. 3

(k diff - a) and a three parameter fit.

Fig. 4
Fig. 4

l/n versus θ m for two scattering albedos.

Fig. 5
Fig. 5

Results from analytic phase function data.

Fig. 6
Fig. 6

Results from measured phase function data.4

Fig. 7
Fig. 7

Comparison of Honey–Wilson relation to the calculated relation.

Equations (12)

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kdiff=a+b/n,
ω0=b/a+b.
kdiff=a+1.431.17ω0θmb.
L=-1/bln τ,
Ps=exp-aL.
ρθ=CMWθ0/2πθ02+θ23/2
ρθ=CAγ/2πθexp-γθ,
0π/2dθ sinθρθ=1,
θm=0π/2dθ sinθρθθ.
 Psdn/Psdn+1=exp-kdiffΔd,
kdiff=a+c01-exp-dnc1/1-c2 exp-dnc1,
kdiff=a+1.431.17ω0θmb,

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