Abstract

A model that relates the coefficients of absorption (a) and backscattering (b b) to diffuse attenuation (K d), radiance reflectance (R L), and the mean cosine for downward irradiance (μd) is presented. Radiance transfer simulations are used to verify the physical validity of the model for a wide range of water column conditions. Analysis of these radiance transfer simulations suggests that absorption and backscattering can be estimated with average errors of 1% and 3%, respectively, if the value of μd is known with depth. If the input data set is restricted to variables that can be derived from measurements of upward radiance (L u) and downward irradiance (E d), it is necessary to use approximate values of μd. Examination of three different approximation schemes for μd shows that the average error for estimating a and b b increases to ∼13%. We tested the model by using measurements of L u and E d collected from case II waters off the west coast of Scotland. The resulting estimates of a and b b were compared with independent in situ measurements of these parameters. Average errors for the data set were of the order of 10% for both absorption and backscattering.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
    [CrossRef]
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    [CrossRef]
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2000 (2)

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[CrossRef]

H. Loisel, D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
[CrossRef]

1999 (1)

1998 (1)

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

1997 (2)

1996 (2)

1993 (2)

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38, 188–192 (1993).
[CrossRef]

1990 (1)

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

1989 (1)

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]

1981 (1)

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Austin, R. W.

R. W. Austin, T. J. Petzold, “The determination of the diffuse attenuation coefficient of seawater using the Coastal Zone Color Scanner,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 239–256.
[CrossRef]

Carder, K. L.

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, J. L. Mueller, “Method to derive ocean absorption coefficients from remote-sensing reflectance,” Appl. Opt. 35, 453–462 (1996).
[CrossRef] [PubMed]

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

Cunningham, A.

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

Davis, C. O.

Forand, J. L.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Fournier, G. R.

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

Fry, E. S.

Gentili, B.

Gordon, H. R.

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]

Gregg, W. W.

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

Griffiths, C. R.

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

Jones, K. J.

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

Kitchen, J. C.

J. R. V. Zaneveld, J. C. Kitchen, C. C. Moore, “Scattering error correction of reflection-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Leathers, R. A.

Lee, Z. P.

Loisel, H.

McCormick, N. J.

McKee, D.

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

Mitchell, B. G.

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[CrossRef]

Mobley, C. D.

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[CrossRef]

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

Moore, C. C.

J. R. V. Zaneveld, J. C. Kitchen, C. C. Moore, “Scattering error correction of reflection-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Morel, A.

Mueller, J. L.

Peacock, T. G.

Pegau, W. S.

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38, 188–192 (1993).
[CrossRef]

Petzold, T. J.

R. W. Austin, T. J. Petzold, “The determination of the diffuse attenuation coefficient of seawater using the Coastal Zone Color Scanner,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 239–256.
[CrossRef]

Pope, R. M.

Prieur, L.

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Roesler, C. S.

Sathyendranath, S.

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Slater, J.

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

Stramska, M.

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[CrossRef]

Stramski, D.

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[CrossRef]

H. Loisel, D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000).
[CrossRef]

Zaneveld, J. R. V.

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38, 188–192 (1993).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, C. C. Moore, “Scattering error correction of reflection-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Appl. Opt. (7)

Limnol. Oceanogr. (6)

M. Stramska, D. Stramski, B. G. Mitchell, C. D. Mobley, “Estimation of the absorption and backscattering coefficients from in-water radiometric measurements,” Limnol. Oceanogr. 45, 628–641 (2000).
[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]

W. S. Pegau, J. R. V. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38, 188–192 (1993).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

H. Loisel, A. Morel, “Light scattering and chlorophyll concentration in Case 1 waters: a reexamination,” Limnol. Oceanogr. 43, 847–858 (1998).
[CrossRef]

W. W. Gregg, K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

Other (5)

R. W. Austin, T. J. Petzold, “The determination of the diffuse attenuation coefficient of seawater using the Coastal Zone Color Scanner,” in Oceanography from Space, J. F. R. Gower, ed. (Plenum, New York, 1981), pp. 239–256.
[CrossRef]

G. R. Fournier, J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 194–201 (1994).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, C. C. Moore, “Scattering error correction of reflection-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

D. McKee, A. Cunningham, J. Slater, K. J. Jones, C. R. Griffiths, “Inherent and apparent optical properties in coastal waters: a study of the Clyde Sea in early summer,” Estuarine Coastal Shelf Sci. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Linear relationship between the cosine of the solar zenith angle measured underwater and the mean cosine for downward irradiance immediately beneath the sea surface. Data from Table 3 in Ref. 6.

Fig. 2
Fig. 2

Distributions of (a) the best-fit parameter g and (b) the ratio of f/Q. The data in these plots are for depths to 10 m, for five wavelengths in the blue-green part of the spectrum, and were derived from radiance transfer simulations that cover an extensive range of water column conditions.

Fig. 3
Fig. 3

Distributions of errors in estimations of (a) absorption and (b) backscattering obtained by use of Eqs. (3) and (4). Data were taken from radiance transfer simulations performed to a depth of 10 m for five wavelengths in the blue-green part of the spectrum. The mean cosine for downward irradiance is known exactly in this case.

Fig. 4
Fig. 4

IOPs estimated by use of Eqs. (3) and (4) plotted against independent in situ measurements taken of (a) absorption and (b) backscattering off the west coast of Scotland. Estimates are based on the approximation K d (z d (z) = K d (z d (0).

Fig. 5
Fig. 5

Distributions of the error in estimation of (a) absorption and (b) backscattering for field data from the west coast of Scotland. These estimates are based on the approximation K d (z d (z) = K d (z d (0).

Tables (2)

Tables Icon

Table 1 Average Wavelength-Specific Values of g and f/Q from Radiance Transfer Simulations

Tables Icon

Table 2 Errors in IOP Retrieval Associated with Different Approximations for Kd (z d (z)

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Kd=ga+bbμd,
RL=fQbba,
a=Kdμdg1+RLf/Q,
bb=Kdμdg1+f/QRL.
μd0=0.827 cosθsw+0.144,
θsw=sin-1sinθanw,

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