Abstract

The influence of the bottom albedo on the diffuse reflectance of a flat, homogeneous ocean is computed as a function of bottom depth and albedo for three oceanic scattering phase functions and several values of ω0. The results show that the bottom can have a large effect on the reflectivity, especially for small optical depths. When combined with the observed optical properties of clear natural water, the calculations are shown to be in good agreement with the observed dependence of in-water nadir radiance spectra, with depth. The apparent independence of the reflectance on the mode of illumination observed earlier for the infinitely deep ocean is found to be invalid for a shallow ocean. The effect of departures of the bottom law of diffuse reflectance from Lambertian is investigated and shown to be considerable in some cases.

© 1974 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, Appl. Opt. 12, 1549 (1973).
    [CrossRef] [PubMed]
  2. S. C. Freden, E. P. Mercanti, M. A. Beckek, Eds., Symposium on Significant Results Obtained from the Earth Resources Technology Satellite (National Aeronautics and Space Administration SP-327, 1973), Vol. 1, Sec. B.
  3. H. R. Gordon, Appl. Opt. 12, 2803 (1973).
    [CrossRef] [PubMed]
  4. G. Kullenberg, Deep Sea Res. 15, 423 (1968).
  5. G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
    [CrossRef] [PubMed]
  6. G. N. Plass, G. W. Kattawar, J. Phys. Oceanog. 2, 139 (1972).
    [CrossRef]
  7. Calculations have been carried out for ω0 = 0.4, 0.6, 0.7, 0.75, 0.85, and 0.9, as well as those listed, and also for τB = 5. The results of these calculations are available in tabular form on request.
  8. J. E. Tyler, R. C. Smith, W. H. Wilson, J. Opt. Soc. Am. 62, 83 (1972).
    [CrossRef]
  9. S. Q. Duntley, J. Opt. Soc. Am. 53, 214 (1963).
    [CrossRef]
  10. These are discussed in Ref. 8.

1973 (2)

1972 (2)

G. N. Plass, G. W. Kattawar, J. Phys. Oceanog. 2, 139 (1972).
[CrossRef]

J. E. Tyler, R. C. Smith, W. H. Wilson, J. Opt. Soc. Am. 62, 83 (1972).
[CrossRef]

1969 (1)

1968 (1)

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

1963 (1)

Appl. Opt. (3)

Deep Sea Res. (1)

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

J. Opt. Soc. Am. (2)

J. Phys. Oceanog. (1)

G. N. Plass, G. W. Kattawar, J. Phys. Oceanog. 2, 139 (1972).
[CrossRef]

Other (3)

Calculations have been carried out for ω0 = 0.4, 0.6, 0.7, 0.75, 0.85, and 0.9, as well as those listed, and also for τB = 5. The results of these calculations are available in tabular form on request.

These are discussed in Ref. 8.

S. C. Freden, E. P. Mercanti, M. A. Beckek, Eds., Symposium on Significant Results Obtained from the Earth Resources Technology Satellite (National Aeronautics and Space Administration SP-327, 1973), Vol. 1, Sec. B.

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Figures (6)

Fig. 1
Fig. 1

Variation of diffuse reflectance with bottom depth and albedo (A) for phase function C and ω0 = 0.55. Parameter A from bottom to top is 0 (0.1) 1.

Fig. 2
Fig. 2

Comparison between observed and computed nadir radiance ratio over a sand bottom (and reef). Data are from Duntley.

Fig. 3
Fig. 3

Example of the ratio of diffuse reflectance at two wavelengths for which the optical properties of the water differ but the optical properties of the bottom are the same.

Fig. 4
Fig. 4

Comparison between the sun and sky cases of the values of R1 and R2. R1′ = (R1DR1C)/R1C and R2′ = (R2DR2C)/R2C where D and C refer to the sky and sun cases, respectively.

Fig. 5
Fig. 5

Comparison between n0 from Eq. (7)(lines) and the “exact” values determined from the Monte Carlo simulation (solid circles).

Fig. 6
Fig. 6

Influence of the law of diffuse reflectance of the bottom on the diffuse reflectance of the ocean. = 0 implies a Lambertian bottom.

Tables (4)

Tables Icon

Table I R1, R2, r, and f for Phase Function A

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Table II R1, R2, r, and f for Phase Function B

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Table III R1, R2, r, and f for Phase Function C

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Table IV Optical Properties of the Ocean Used in Preparation of Fig. 2

Equations (17)

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T = l n ( ρ 1 ) ,
ρ 3 = 2 π 0 θ p ( θ ) sin θ d θ ,
μ = cos θ = ( 1 ρ 5 ) 1 / 2
Q = Q 1 + [ A Q 2 / ( 1 r A ) ] ,
H ( + ) = H 1 ( + ) + [ A H 2 ( + ) / ( 1 r A ) ] .
R d = H ( + ) / H inc ,
R d = R 1 + [ A R 2 / ( 1 r A ) ] ,
τ B = 0 z B c ( z ) d z ,
f R 2 / n 0
H ( τ B ) = ( 1 γ ) H inc exp [ τ B ( 1 ω 0 F ) / μ 0 ] ,
n 0 = ( m 2 / H inc ) μ c 1 0 2 π [ 1 γ ( μ , μ ) ] I inc ( μ , ϕ ) μ × exp [ τ B ( 1 ω 0 F ) / μ ] d μ d ϕ ,
2 π 0 1 I ( μ ) μ d μ = A H .
N + = i = 0 N i + ,
n i + = A n i 1 = A h n i 1 + = A 2 h n i 2 = A 2 h 2 n i 2 + = = A i h i 1 n 0 ,
N + = N 0 + + g i = 1 n i + = N 0 + + g A i = 0 ( A h ) i n 0 = N 0 + + g A n 0 1 A h .
g A n 0 = A [ ( N 1 + / n 1 + ) n 0 ]
N + = N 0 + + { A [ N 1 + ( n 0 / n 1 + ) ] / [ 1 A ( n 1 / n 1 + ) ] } .

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