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Acceptance angle effects on the beam attenuation in the ocean

Emmanuel Boss, Wayne H. Slade, M. Behrenfeld, and G. Dall’Olmo

Open Access Open Access

Abstract

The beam attenuation serves as a proxy for particulate matter and is a key parameter in visibility algorithms for the aquatic environment. It is well known, however, that the beam attenuation is a function of the acceptance angle of the transmissometer used to measure it. Here we compare eight different transmissometers with four different acceptance angles using four different deployment strategies and sites, and find that their mean attenuation values differ markedly and in a consistent way with instrument acceptance angle: smaller acceptance angles provide higher beam attenuation values. This difference is due to variations in scattered light collected with different acceptance angles and is neither constant nor easy to parameterize. Variability (in space or time) in the ratios of beam attenuations measured by two different instruments correlates, in most cases, with the particle size parameter (as expected from Mie theory), but this correlation is often weak and can be the opposite of expectations based on particle size changes. We recommended careful consideration of acceptance angle in applications of beam transmission data especially when comparing data from different instruments.

©2009 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Normalized volume scattering function as function of angles from Petzold’s average phase function ([11], blue curve) and measurements from MVCO (for 9/5/2005, see methods) [11]. The area under the curves to the left of the red lines represent the fraction of total scattering that does NOT contribute to attenuation for instruments with acceptance angles at the horizontal position of the red line (0.0269, 0.93 and 1.2°) corresponding to instruments whose measurements we analyze here (Table 1).

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Fig. 2.
Fig. 2. Ratio of scattering coefficients based on integrating the VSF (β) from π to the acceptance angle to the total scattering coefficient for homogeneous spheres with three different indices of refraction (n=1.05+i0.005 (+), n=1.05+i0.0001 (o), 1.15+i0.0001 (x)) and four different acceptance angles matching those of the instruments we compare in this paper (1.2°-black, 0.93°-red, 0.026°-green, and 0.006°- blue, Table 1) as function of size.

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Fig. 3.
Fig. 3. Measurements taken 10m off the Darling Marine Center pier. Top panels: time series of the beam attenuation (660nm) measured with a 10cm pathlength c-star (top), measured with a 25cm ac-9 at 676nm (2nd from top) and measured with a 670nm LISST-B (3rd from top). Time series of the spectral slope of the beam attenuation coefficient (γ) based on the spectral measurements of the ac-9. Note: The color scale varies between the panels and that the LISST was not deployed at the same time or with the same package as the two other instruments (see text). Bottom panel: histograms of the frequency of occurrence of the ratios among the measured beam attenuations.

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Fig. 4.
Fig. 4. Top panel: time series of 1-min averages of the beam attenuation measured with a 10cm pathlength ac-9 (blue), LISST-100X-B (green) and LISST-100X-Floc (red). Second panel: time series of the ratios of 1-min averages cp,ac-9/cpg,LISST-B (blue), cp,ac-9/ cpg,LISST-FLOC (green), and cpg,LISST-B/ cpg,LISST-FLOC (red). Third panel: time series of the spectral slope of the particulate beam attenuation (γ). Bottom panel: histograms of the frequency of occurrence of the ratios depicted in the second panel.

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Fig. 5.
Fig. 5. Top panel: spatial distribution of 1-min averages of the beam attenuation measured with a 25cm path-length ac-s (red) and a C-Star (blue) measured across equatorial Pacific at 140°W at 650nm (N=2397). Middle panel: spatial distribution of the ratios of 1-min averages cC-Star/ cac S. Bottom panel: spatial distribution of the spectral slope of the particulate beam attenuation, γ, a size-related parameter, where smaller γ implies larger mean particle size [24].

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Fig. 6.
Fig. 6. Aggregate size as function of time (blue line) and the corresponding ratio of the beam attenuation measured by the LISST-B at 670nm to that of the ac-9 at 676nm as function of time as measured during a laboratory clay aggregation experiment. Oscillations in the ratio are due to decrease of signal to noise ratio as the water clarifies of settling particles (cpg,LISST-B decreased from 12m-1 to 3m-1 during the experiment).

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Fig. 7.
Fig. 7. Top panel: time series of 1-min averages of the beam attenuation measured with a 10cm pathlength ac-9 corrected for acceptance angle difference as in Eq. (5) (blue), LISST-B (green). Bottom panel: histograms of the frequency of occurrence of the ratio of the two time series depicted in the top panel.

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Fig. 8.
Fig. 8. Top panel: time series of the ratio of 1-min averages of the beam attenuation measured with a 10cm pathlength ac-9 corrected for acceptance angle difference as in Eq. (5). Middle panel: Median diameter based on the LISST inversion of VSF to particulate size distribution. Bottom panel: slope of the spectral particulate beam attenuation of the ac-9.

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Tables (1)

Tables Icon

Table 1. Collimated commercial beam transmissometers whose measurements we compare in this study. For the ac meters we only display information for the wavelength used here. For reference the common Sea Tech transmissometer had an acceptance angle of 1.03° [4], a 660nm wavelength and a pathlength of 25cm.

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Equations (5)

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c = − 1 L ln ( T ) .
b theory = 2 π ∫ o π β sin ⁡ θ d θ .
c measured = a + 2 π ∫ θ acceptance π β sin ⁡ θ d θ .
θ acceptance = sin ⁡ − 1 { 1 n sin ⁡ [ tan ⁡ − 1 ( r f ) ] } .
c p , ac 9 corrected = c p , ac 9 + 2 π ∫ θ LISST − B θ ac − 9 β sin ⁡ θ d θ .
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