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Relationships between the backscattering coefficient and VSF at an angle

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Significant relationships between the volume scattering function (VSF), β, at a small scattering angle and the scattering coefficient, b, (for example, Morel 1973a, Kopelevich and Burenkov 1971) have their counterparts in similarly significant linear relationships between VSF at an angle and the backscattering coefficient, b_b. Such a relationship for seawater has been proposed at an angle of 120° by Oishi (1990), based on numerical integration of the VSF calculated according to Mie theory by using power law, Gaussian, and log-normal PSD, and confirmed by Oishi through an analysis of experimental data:

bb = 2π χ β(120°)

(1)

where χ = 1.13 with an SD = 0.08, which corresponds to a ~14% error in the evaluation of b_b from β(120°). The backscattering coefficient is that of the whole seawater. Oishi cautions that the maximum of the correlation coefficient for b_b = 2π χ β(120°) is a weak one.

Maffione and Dana (1997) re-analyzed that problem by using a specific backscattering sensor geometry and proposed that the backscattering coefficient of seawater be calculated by using the value of β(140°) at a wavelength of 440 nm (in air). The value of the proportionality factor, χ, was changed to 1.08. Maffione and Dana report an arror of ~9% for b_b determined from β(140°). Chami et al (2005) obtained a similar value of χ for the backscattering coefficient, b_bp, contributed by the particles in the coastal waters of Black Sea.

The distinction between the total and particulate backscattering contribution proves suprisingly to be of a relatively minor importance at the scattering angle of ~120°, although seawater can contribute over 80% of b_b in the blue part of the visible spectrum for samples taken in clear natural waters, as pointed out by Boss and Pegau (2001). However, the role of seawater in the relationship b_b ~ β(θ), may be quite substantial at other angles θ. Hence, Boss and Pegau expand the χ factor as follows:

χ(θ) = χw(θ) y + χp(θ) ( 1 - y )

(2)

where y = β_w(θ) / β(θ). This parameter for seawater assumes, in practice, values ≤ 0.8. Clearly, if there exists a scattering angle, θ, such that χ_w(θ) = χ_p(θ), then also χ_w(θ) = χ_p(θ) = χ(θ), which simplifies the analysis. By using new, high-resolution VSF data for the coastal North Atlantic waters, Boss and Pegau found that such angle equals approximately 117°, i.e. it is close to 120°, originally proposed by Oishi (1990) as the optimal scattering angle for the determination of the backscattering coefficient, b_b, from VSF at a fixed angle as discussed above.

Thus, Boss and Pegau (2001) propose that either b_b be determined by using Eq. 1 with β(117°) substituting β(120°), i.e. at an angle where the χ factors for water, χ_w = b_w / [2π β_w(θ)], and particles, χ_p = b_p / [2π β_p(θ)], assume the same value (1.1; SD = 4%) or (at other angles) be determined by using the following relationship:

bb = 2π χp(θ) [ β(θ) - βw(θ) ] + bbw

(3)

 

CITATION: Jonasz M. 2006. Relationships between the backscattering coefficient and VSF at an angle (www.tpdsci.com/Tpc/VsfSwBbAngSca.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 15-May-2006 Modified: 29-Jul-2006 Peer-reviewed: 15-May-2006

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