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Self-shading correction for upwelling sea-surface radiance measurements made with buoyed instruments

Robert A. Leathers, T. Valerie Downes, and Curtis D. Mobley

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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.

©2001 Optical Society of America

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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.

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

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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.

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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.

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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).

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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°.

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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.

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Tables (1)

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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.

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Equations (10)

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

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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