Abstract

Self-shading error of in-water optical measurements has been experimentally estimated for upwelling radiance and irradiance measurements taken just below the water surface. Radiance and irradiance data have been collected with fiber optics that terminated with 1°, 18°, and 2π optics housed in the center of a disk that simulated the size of the instrument. Analysis of measurements taken at 500, 600, and 640 nm in lake waters have shown errors ranging from a few percent up to several tens of percent as a function of the size of the radiometer, the absorption coefficient of the medium, the Sun zenith, and the atmospheric turbidity. Comparisons between experimental and theoretical errors, the latter computed according to a scheme suggested by other authors, have shown absolute differences generally lower than 5% for radiances and lower than 3% for irradiances. Analysis of radiance measurements taken with 1° and 18° fields of view have not shown appreciable differences in the self-shading error. This finding suggests that correction schemes for self-shading error developed for narrow-field-of-view radiance measurements could also be applied to measurements taken with relatively larger fields of view.

© 1995 Optical Society of America

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References

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  1. H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
    [CrossRef]
  2. R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters,” Appl. Opt. 20, 177–184 (1981).
    [CrossRef] [PubMed]
  3. S. Tassan, G. M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. (to be published).
  4. G. M. Ferrari, S. Tassan, “On the accuracy of determining light absorption by ‘yellow substance’ through measurements of induced fluorescence,” Limnol. Oceanogr. 36, 777–786 (1991).
    [CrossRef]
  5. D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
    [CrossRef]
  6. A. Angstrom, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
    [CrossRef]

1992 (1)

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

1991 (1)

G. M. Ferrari, S. Tassan, “On the accuracy of determining light absorption by ‘yellow substance’ through measurements of induced fluorescence,” Limnol. Oceanogr. 36, 777–786 (1991).
[CrossRef]

1990 (1)

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

1981 (1)

1961 (1)

A. Angstrom, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
[CrossRef]

Angstrom, A.

A. Angstrom, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
[CrossRef]

Baker, K. S.

Deroo, C.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Deschamps, P. Y.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Ding, K.

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Duhaut, P.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Ferrari, G. M.

G. M. Ferrari, S. Tassan, “On the accuracy of determining light absorption by ‘yellow substance’ through measurements of induced fluorescence,” Limnol. Oceanogr. 36, 777–786 (1991).
[CrossRef]

S. Tassan, G. M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. (to be published).

Gordon, H. R.

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Herman, M.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Morcrette, J. J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Perbos, J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Smith, R. C.

Tanré, D.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Tassan, S.

G. M. Ferrari, S. Tassan, “On the accuracy of determining light absorption by ‘yellow substance’ through measurements of induced fluorescence,” Limnol. Oceanogr. 36, 777–786 (1991).
[CrossRef]

S. Tassan, G. M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. (to be published).

Appl. Opt. (1)

Int. J. Remote Sensing (1)

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, P. Y. Deschamps, “Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code,” Int. J. Remote Sensing 11, 659–668 (1990).
[CrossRef]

Limnol. Oceanogr. (2)

G. M. Ferrari, S. Tassan, “On the accuracy of determining light absorption by ‘yellow substance’ through measurements of induced fluorescence,” Limnol. Oceanogr. 36, 777–786 (1991).
[CrossRef]

H. R. Gordon, K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37, 491–500 (1992).
[CrossRef]

Tellus (1)

A. Angstrom, “Techniques of determining the turbidity of the atmosphere,” Tellus 13, 214–223 (1961).
[CrossRef]

Other (1)

S. Tassan, G. M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Radiance (1° field of view) percentage errors as a function of aR for different Sun zenith angles: (a) 29.4°, (b) 40.9°, (c) 46.7°, (d) 51.1° [experimental data at 550 nm (◇), 600 nm (△), and 640 nm (□)]. The curves show the best fit of the experimental data (——), the theoretical error computed according to G&D (- - - - - - -), and the relative percentage difference between the theoretical and the experimentally fitted data (–⋯–⋯–).

Fig. 2
Fig. 2

Irradiance percentage errors as a function of aR for different Sun zenith angles: (a) 25.7°, (b) 30.4°, (c) 38.3°, (d) 43.8° [experimental data at 550 nm (◇), 600 nm (△), and 640 nm (□)]. The curves show the best fit of the experimental data (——), the theoretical error computed according to G&D (- - - - - - -), and the relative percentage difference between the theoretical and the experimentally fitted data (–⋯–⋯–).

Fig. 3
Fig. 3

Radiance (18° field of view) percentage errors as a function of aR at 30.7° Sun zenith [experimental data at 550 nm (◇), 600 nm (△), and 640 nm (□)]. The curves show the best fit of the experimental data (——), the theoretical error computed according to G&D (- - - - - - -), and the relative percentage difference between the theoretical and the experimentally fitted data (–⋯–⋯–).

Tables (3)

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Table 1 Absorption Coefficient of Water Particles a p and Yellow Substance a y Retrieved from Water Samples for Different Measuring Days

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Table 2 Chlorophyll-a and Sediment Concentrations

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Table 3 Angstrom Exponent α and Factor β for Different Measuring Days

Equations (3)

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ɛ = ( L u true - L u measured ) / L u true ,
ɛ = ( ɛ sun + ɛ sky r ) / ( 1 + r ) ,
r ~ E sky / E sun , ɛ sun = 1 - exp ( - k sun a R ) , ɛ sky = 1 - exp ( - k sky a R ) ,

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