Abstract

Upwelling radiance measurements made with instruments designed to float at the sea surface are shaded both by the instrument housing and by the buoy that holds the instrument. The amount of shading is wavelength dependent and is affected by the local marine and atmospheric conditions. Radiance measurements made with such instruments should be corrected for this self-shading error before being applied to remote sensing calibrations or remote sensing algorithm validation. Here we use Monte Carlo simulations to compute the self-shading error of a commercially available buoyed radiometer so that measurements made with this instrument can be improved. This approach can be easily adapted to the dimensions of other instruments.

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References

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  1. H. R. Gordon and K. Ding, "Self-shading of in-water optical instruments," Limnol. Oceanogr. 37, 491-500 (1992).
    [CrossRef]
  2. D. R. Lyzenga, "Remote sensing of bottom reflectance and water attenuation parameters in shallow water using aircraft and Landsat data," Int. J. Remote Sensing 2, 71-82 (1981).
    [CrossRef]
  3. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytic radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
    [CrossRef]
  4. J. E. O'Reilley, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, "Ocean color chlorophyll algorithms for SeaWiFS," J. Geophys. Res. 103, 24937-24953 (1998).
    [CrossRef]
  5. D. R. Lyzenga, "Passive remote sensing techniques for mapping water depth and bottom features," Appl. Opt. 17, 379-383 (1978).
    [CrossRef] [PubMed]
  6. G. Zibordi and G. M. Ferrari, "Instrument self-shading in underwater optical measurements: experimental data," Appl. Opt. 34, 2750-2754 (1995).
    [CrossRef] [PubMed]
  7. E. Aas and B. Korsbo , "Self-shading effect by radiance meters on upward radiance observed in coastal waters," Limnol. Oceanogr. 42, 968-974 (1997).
    [CrossRef]
  8. J. Piskozub, A. R. Weeks, J. N. Schwarz, and I. S. Robinson, "Self-shading of upwelling irradiance for an instrument with sensors on a sidearm," Appl. Opt. 39, 1872-1878 (2000).
    [CrossRef]
  9. G. S. Fargion and J. L. Mueller, Ocean optics protocols for satellite ocean color sensor validation, revision 2 (NASA Tech. Memo. 209966, NASA Goddard Space Flight Center, Greenbelt, Maryland, 2000).
  10. Coastal Benthic Optical Properties, http://www.psicorp.com/cobop/cobop.html.
  11. H. R. Gordon, "Ship perturbation of irradiance measurements at sea. 1. Monte-Carlo simulations," Appl. Opt. 24, 4172-4182 (1985).
    [CrossRef] [PubMed]
  12. C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters, (Academic Press, New York, 1994).
  13. G. R. Fournier and J. L. Forand, "Analytic phase function for ocean water," in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194-201 (1994).
  14. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, "Comparison of numerical models for computing underwater light fields," Appl. Opt. 32, 7484-7504 (1993).
    [CrossRef] [PubMed]
  15. C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).
  16. S. Mc Lean, Satlantic Incorporated, Halifax, Nova Scotia, Canada. Personal correspondence.
  17. A. Ariew, "Are probabilities necessary for evolutionary explanations?," Biol. Phil. 13, 245-253 (1998).
    [CrossRef]
  18. A. W. Harrison and C. A. Coombes, "An opaque cloud cover model of sky short wavelength radiance," Solar Energy 41, 387-392 (1988).
    [CrossRef]
  19. C. S. Roesler, "Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique," Limnol. Oceanogr. 43, 1649-1660 (1998).
    [CrossRef]
  20. R. A. Leathers, T. V. Downes, and C. O. Davis, "Analysis of a point-source integrating-cavity absorption meter," Appl. Opt. 39, 6118-6127 (2000).
    [CrossRef]
  21. L. Prieur and 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]
  22. R. M. Pope and E. S. Fry, "Absorption spectrum (380-700nm) of pure water. II. Integrating cavity measurements," Appl. Opt. 36, 8710-8723, (1997).
    [CrossRef]
  23. R. C. Smith and K. S. Baker, "Optical properties of the clearest natural waters (200-800 nm)," Appl. Opt. 20, 177-184 (1981).
    [CrossRef] [PubMed]
  24. W. W. Gregg and K. L. Carder, "A simple spectral solar irradiance model for cloudless maritime atmospheres," Limnol. Oceanogr. 35, 1657-1675 (1990).
    [CrossRef]
  25. H. R. Gordon, "Dependence of the diffuse reflectance of natural waters on the sun angle," Limnol. Oceanogr. 34, 1484-1489 (1989).
    [CrossRef]
  26. K. S. Baker and R. C. Smith, "Irradiance transmittance through the air-water interface," in Ocean Optics X , R. W. Spinrad, ed., Proc. SPIE 1302, 556-565 (1990).

Other (26)

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

D. R. Lyzenga, "Remote sensing of bottom reflectance and water attenuation parameters in shallow water using aircraft and Landsat data," Int. J. Remote Sensing 2, 71-82 (1981).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytic radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

J. E. O'Reilley, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, "Ocean color chlorophyll algorithms for SeaWiFS," J. Geophys. Res. 103, 24937-24953 (1998).
[CrossRef]

D. R. Lyzenga, "Passive remote sensing techniques for mapping water depth and bottom features," Appl. Opt. 17, 379-383 (1978).
[CrossRef] [PubMed]

G. Zibordi and G. M. Ferrari, "Instrument self-shading in underwater optical measurements: experimental data," Appl. Opt. 34, 2750-2754 (1995).
[CrossRef] [PubMed]

E. Aas and B. Korsbo , "Self-shading effect by radiance meters on upward radiance observed in coastal waters," Limnol. Oceanogr. 42, 968-974 (1997).
[CrossRef]

J. Piskozub, A. R. Weeks, J. N. Schwarz, and I. S. Robinson, "Self-shading of upwelling irradiance for an instrument with sensors on a sidearm," Appl. Opt. 39, 1872-1878 (2000).
[CrossRef]

G. S. Fargion and J. L. Mueller, Ocean optics protocols for satellite ocean color sensor validation, revision 2 (NASA Tech. Memo. 209966, NASA Goddard Space Flight Center, Greenbelt, Maryland, 2000).

Coastal Benthic Optical Properties, http://www.psicorp.com/cobop/cobop.html.

H. R. Gordon, "Ship perturbation of irradiance measurements at sea. 1. Monte-Carlo simulations," Appl. Opt. 24, 4172-4182 (1985).
[CrossRef] [PubMed]

C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters, (Academic Press, New York, 1994).

G. R. Fournier and J. L. Forand, "Analytic phase function for ocean water," in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE 2258, 194-201 (1994).

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, "Comparison of numerical models for computing underwater light fields," Appl. Opt. 32, 7484-7504 (1993).
[CrossRef] [PubMed]

C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Mar. Res. 13, 198-227 (1954).

S. Mc Lean, Satlantic Incorporated, Halifax, Nova Scotia, Canada. Personal correspondence.

A. Ariew, "Are probabilities necessary for evolutionary explanations?," Biol. Phil. 13, 245-253 (1998).
[CrossRef]

A. W. Harrison and C. A. Coombes, "An opaque cloud cover model of sky short wavelength radiance," Solar Energy 41, 387-392 (1988).
[CrossRef]

C. S. Roesler, "Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique," Limnol. Oceanogr. 43, 1649-1660 (1998).
[CrossRef]

R. A. Leathers, T. V. Downes, and C. O. Davis, "Analysis of a point-source integrating-cavity absorption meter," Appl. Opt. 39, 6118-6127 (2000).
[CrossRef]

L. Prieur and 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]

R. M. Pope and E. S. Fry, "Absorption spectrum (380-700nm) of pure water. II. Integrating cavity measurements," Appl. Opt. 36, 8710-8723, (1997).
[CrossRef]

R. C. Smith and K. S. Baker, "Optical properties of the clearest natural waters (200-800 nm)," Appl. Opt. 20, 177-184 (1981).
[CrossRef] [PubMed]

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

H. R. Gordon, "Dependence of the diffuse reflectance of natural waters on the sun angle," Limnol. Oceanogr. 34, 1484-1489 (1989).
[CrossRef]

K. S. Baker and R. C. Smith, "Irradiance transmittance through the air-water interface," in Ocean Optics X , R. W. Spinrad, ed., Proc. SPIE 1302, 556-565 (1990).

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Figures (7)

Fig. 1.
Fig. 1.

Self-shading error of the TSRB (solid line) in deep water for b/a=2 compared with that computed with Eqs. (1) and (2) for radii 0.044 m and 0.15 m. The TSRB error was computed for an empirical sky model at 480 nm with the sun zenith angle θ 0=30 degrees.

Fig. 2.
Fig. 2.

Self-shading error of the TSRB in deep water for b/a=2, five solar zenith angles, and no skylight.

Fig. 3.
Fig. 3.

Shaded and unshaded normalized radiance and percent shading error of the TSRB and of the TSRB cylindrical body without the buoy compared with Eq. (1) for radii 0.044 m and 0.15 m. The computations are for a sun in a black sky, deep water, and a=b=0.2 m-1.

Fig. 4.
Fig. 4.

Percent shading error of the TSRB in deep water versus solar zenith angle θ 0 for a sun in a black sky, six values of a, and b/a=2.

Fig. 5.
Fig. 5.

Percent shading error of the TSRB in deep water for a=0.02 m-1 (dashed), 0.05 m-1 (solid), and 1.0 m-1 (dotted) and θ 0=0° (top, blue), 10° (middle, green), and 20° (bottom, red).

Fig. 6.
Fig. 6.

TSRB self-shading error as a function of water depth for absorption coefficient a=0.2 m-1, scattering coefficient b=0.4 m-1, and bottom albedo Rb =0.2. The dashed lines show the shading error in optically deep waters for solar zenith angles θ 0=0°, 10°, and 20°.

Fig. 7.
Fig. 7.

Example TSRB shading correction. The upper plot shows the water absorption spectrum a(λ), the ratio f(λ) of skylight to sunlight, and the corresponding shading error ε(λ). The lower plot shows the measured and corrected upwelling radiance spectra.

Tables (1)

Tables Icon

Table 1. Percent shading error (100×ε) of a TSRB for given values of absorption coefficient a, scattering coefficient b, and solar zenith angle θ 0.

Equations (10)

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ε = [ 1 exp ( kar ) ] ,
ε = ε sun + ε sky f 1 + f ,
ε = ( L u true L u m ) L u true ,
[ x y z ] = [ x 1 y 1 z 1 ] + [ α β γ ] s , 0 s L ,
[ x y z ] = [ x 0 y 0 z 0 ] + [ ρ cos ( θ ) ρ sin ( θ ) u ] , 0 ρ r 0 θ 2 π , 0 u h ,
( x 1 x 0 + α s ) 2 + ( y 1 y 0 + β s ) 2 = r 2 .
s = B ± B 2 4 AC 2 A , A = α 2 + β 2 , B = 2 α ( x 1 x 0 ) + 2 β ( y 1 y 0 ) , C = ( x 1 x 0 ) 2 + ( y 1 y 0 ) 2 r 2 .
u = z 1 z 0 + γ s .
a ( λ ) = K d ( λ ) [ 1 R ( λ ) ] cos θ 0 0.6 + [ 0.47 + 2.5 R ( λ ) ] cos θ 0 ,
L u true ( λ ) = L u m ( λ ) ( 1 ε ( λ ) ) .

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