Abstract
Field observations and theoretical studies have found that the volume scattering functions (VSFs) of oceanic particles exhibit minimum variability at angles near 120°. However, its physical interpretation is still unknown. We find this minimum variability angle represents the intersection of two backscattering-normalized VSFs, one representing particles of sizes smaller than the wavelength of light and the other larger than the wavelength of light. This also suggests that the VSFs of oceanic particles at angles between 90° and 180°, which play a critical role in ocean color study, can be modeled by linear mixing of these two end members. We further validate this mixing model using measured VSFs in coastal and oceanic waters around the US and develop a two-component model predicting the backward shapes of the VSFs.
Highlights
The volume scattering function (VSF, m−1 sr−1; β(θ)) in the backward direction (i.e., 90 ≤ θ ≤180°) largely dictates the magnitude and shape of reflected solar radiation from the ocean [1] that is amenable to above-water observation
Most of the variability in the shape of backward scattering α(θ) by particles can be explained by the linear mixing of just two groups of end members, one representing backscattering by very small particles and the other large particles
Because the backward angular scattering within each group are very similar to each other, we further showed that applying linear mixing by using just one end member from each group can adequately reproduce the measured α(θ) with an uncertainty < 10% for angles from 90 – ~170° (Figs. 3 and 4)
Summary
The volume scattering function (VSF, m−1 sr−1; β(θ)) in the backward direction (i.e., 90 ≤ θ ≤180°) largely dictates the magnitude and shape of reflected solar radiation from the ocean [1] that is amenable to above-water observation. Zhang et al [11] could not find the physical root for this intriguing behavior of χ and concluded with an open statement: “It remains to be investigated as to what physical connotation the classic mean value of β(θ) in the backward angles carries that leads to such a constrained variability.”. Attempting to answer this question leads to the objectives of this study: (i) to offer a physical interpretation on why backward scattering exhibits constrained variability at angles around 120°; and (ii) to explore its application for better interpreting ocean color observations Zhang et al [11] could not find the physical root for this intriguing behavior of χ and concluded with an open statement: “It remains to be investigated as to what physical connotation the classic mean value of β(θ) in the backward angles carries that leads to such a constrained variability.” Attempting to answer this question leads to the objectives of this study: (i) to offer a physical interpretation on why backward scattering exhibits constrained variability at angles around 120°; and (ii) to explore its application for better interpreting ocean color observations
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