Abstract

The penetration depth of light in the sea is defined for remote sensing purposes as the depth above which 90% of the diffusely reflected irradiance (excluding specular reflectance) originates. It is demonstrated that for a homogeneous ocean, this is the depth at which the downwelling in-water irradiance falls to 1/e of its value at the surface. Penetration depths as a function of wavelength are presented for a variety of water types, and a mean penetration depth z¯90 for a broadband sensor is defined and applied to the MSS on ERTS-1. The maximum z¯90 expected for ERTS-1 is found to be somewhat less than 20 m.

© 1975 Optical Society of America

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References

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  1. Proceedings of the Symposium on Significant Results Obtained from the Earth Resources Technology Satellite-1, 5–9 March 1973, NASA/Goddard Space Flight Center, Greenbelt, Md. 20771, publication NASA SP-327.
  2. V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
    [CrossRef]
  3. H. R. Gordon, Appl. Opt. 12, 2803 (1973); W. R. McCluney, Appl. Opt. 13, 2422 (1974).
    [CrossRef] [PubMed]
  4. If H(z, −) is the downwelling irradiance at a depth z beneath the sea surface, the downwelling irradiance attenuation coefficient K(z, −) is defined byK(z,−)=−[1/H(z,−)](d/dz)H(z,−).
  5. H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974). In this paper Rτ was referred to as R1.
    [CrossRef] [PubMed]
  6. O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 54, 318 (1973).
  7. Although only a few calculations have been carried out for inhomogeneous media [O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 55, 287 (1974)], it appears that for these media the more general value of z90 is correct.
  8. R. W. Preisendorfer, Monogr. U. G. G. I., No. 10, 11 (1961).
  9. N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), 194 pp.
  10. K. Kalle, Oceanogr. Mar. Biol. 4, 91 (1966).
  11. J. E. Tyler, R. C. Smith, Measurements of Spectral Irradiance Underwater (Gordon and Breach, New York, 1970), p. 41ff.
  12. R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
    [CrossRef]
  13. R. C. Smith, J. E. Tyler, J. Opt. Soc. Am. 57, 589 (1967).
    [CrossRef]

1974

H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974). In this paper Rτ was referred to as R1.
[CrossRef] [PubMed]

Although only a few calculations have been carried out for inhomogeneous media [O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 55, 287 (1974)], it appears that for these media the more general value of z90 is correct.

1973

R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
[CrossRef]

O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 54, 318 (1973).

V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
[CrossRef]

H. R. Gordon, Appl. Opt. 12, 2803 (1973); W. R. McCluney, Appl. Opt. 13, 2422 (1974).
[CrossRef] [PubMed]

1967

1966

K. Kalle, Oceanogr. Mar. Biol. 4, 91 (1966).

1961

R. W. Preisendorfer, Monogr. U. G. G. I., No. 10, 11 (1961).

Borchardt, J. F.

V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974). In this paper Rτ was referred to as R1.
[CrossRef] [PubMed]

Although only a few calculations have been carried out for inhomogeneous media [O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 55, 287 (1974)], it appears that for these media the more general value of z90 is correct.

O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 54, 318 (1973).

Goldman, C. R.

R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
[CrossRef]

Gordon, H. R.

H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974). In this paper Rτ was referred to as R1.
[CrossRef] [PubMed]

Although only a few calculations have been carried out for inhomogeneous media [O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 55, 287 (1974)], it appears that for these media the more general value of z90 is correct.

O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 54, 318 (1973).

H. R. Gordon, Appl. Opt. 12, 2803 (1973); W. R. McCluney, Appl. Opt. 13, 2422 (1974).
[CrossRef] [PubMed]

Jerlov, N. G.

N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), 194 pp.

Kalle, K.

K. Kalle, Oceanogr. Mar. Biol. 4, 91 (1966).

Klemas, V.

V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, Monogr. U. G. G. I., No. 10, 11 (1961).

Smith, R. C.

R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
[CrossRef]

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

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

Treasure, W. M.

V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
[CrossRef]

Tyler, J. E.

R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
[CrossRef]

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

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

Appl. Opt.

J. Opt. Soc. Am.

Limnol. Oceanogr.

R. C. Smith, J. E. Tyler, C. R. Goldman, Limnol. Oceanogr. 18, 189 (1973).
[CrossRef]

Monogr. U. G. G. I.

R. W. Preisendorfer, Monogr. U. G. G. I., No. 10, 11 (1961).

Oceanogr. Mar. Biol.

K. Kalle, Oceanogr. Mar. Biol. 4, 91 (1966).

Rem. Sens. Environ.

V. Klemas, J. F. Borchardt, W. M. Treasure, Rem. Sens. Environ. 2, 205 (1973).
[CrossRef]

Trans. Am. Geophys. Union

O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 54, 318 (1973).

Although only a few calculations have been carried out for inhomogeneous media [O. B. Brown, H. R. Gordon, Trans. Am. Geophys. Union 55, 287 (1974)], it appears that for these media the more general value of z90 is correct.

Other

N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), 194 pp.

Proceedings of the Symposium on Significant Results Obtained from the Earth Resources Technology Satellite-1, 5–9 March 1973, NASA/Goddard Space Flight Center, Greenbelt, Md. 20771, publication NASA SP-327.

If H(z, −) is the downwelling irradiance at a depth z beneath the sea surface, the downwelling irradiance attenuation coefficient K(z, −) is defined byK(z,−)=−[1/H(z,−)](d/dz)H(z,−).

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

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Figures (4)

Fig. 1
Fig. 1

Rτ/R for layers of optical thickness τ. The parameter next to each curve is ω0. τ90 is the value of τ for which Rτ/R = 0.9.

Fig. 2
Fig. 2

Comparison of K(0,−)z90 with unity as a function of ω0 for the three phase functions for the case of collimated incident irradiance from the zenith and for perfectly diffuse incident irradiance [phase B (diffuse)].

Fig. 3
Fig. 3

z90 as a function of b/a for phase functions A and C, for collimated incident irradiance from the zenith, and an incident field of perfectly diffuse irradiance (identified by the subscript d).

Fig. 4
Fig. 4

Variation of z90 with wavelength for various water types given by Jerlov in Ref. 9.

Tables (1)

Tables Icon

Table I Mean Penetration Depths in Meters for ERTS-1 MSS Bands

Equations (19)

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N z ( μ ) = 4 H 0 n ( n + 1 ) 2 T ( μ , μ ) 1 + μ P ( μ ) ω 0 1 ω 0 F × { 1 exp [ z c ( 1 ω 0 F ) ( 1 + μ ) / μ ] } ,
[ N z 90 ( μ ) ] / [ N ( μ ) ] = 0.9 = 1 exp [ c z 90 ( μ ) ( 1 ω 0 F ) ( 1 + μ ) / μ ]
z 90 ( μ ) c ( 1 ω 0 F ) = 2.30 μ / ( 1 + μ ) .
z 90 ( μ ) K ( 0 , ) = 2.30 μ / ( 1 + μ ) .
z 90 ( μ ) K ( 0 , ) 1.
R z 90 / R = 0.9 ,
R z = 2 π 0 1 N z ( μ ) μ d μ / H 0
z 90 K ( 0 , ) 1.
τ 90 [ K ( 0 , ) / c ] = z 90 K ( 0 , )
a ( z ) K ( z , ) ,
z 90 1 / a ,
R z 90 / R = 0.90 ,
0 1 λ 1 λ 2 G ( μ , μ , λ ) { 1 exp [ z K λ ( 0 , ) ( 1 + μ ) / μ ] } μ d λ d μ = 0.9 0 1 λ 1 λ 2 G ( μ , μ , λ ) μ d λ d μ ,
G ( μ , μ , λ ) = 4 H 0 n ( n + 1 ) 2 T ( μ , μ ) 1 + μ P ( μ ) ω 0 1 ω 0 F ,
0 1 λ 1 λ 2 G ( μ , μ , λ ) exp [ z K λ ( 0 , ) ( 1 + μ ) / μ ] μ d λ d μ = 0.1 0 1 λ 1 λ 2 G ( μ , μ , λ ) μ d λ d μ .
λ 1 λ 2 R ( λ ) exp [ z K λ ( 0 , ) 2.26 ] d λ = 0.1 λ 1 λ 2 R ( λ ) d λ ,
z ¯ 90 λ 1 λ 2 z 90 ( λ ) R ( λ ) H 0 ( λ ) d λ / λ 1 λ 2 R ( λ ) H 0 ( λ ) d λ
z ¯ 90 = λ 1 λ 2 z 90 ( λ ) R ( λ ) d λ / λ 1 λ 2 R ( λ ) d λ .
K(z,)=[1/H(z,)](d/dz)H(z,).

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