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Volume scattering function of natural waters: Backscattering extrapolation

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Extrapolation of the volume scattering function (VSF), β, to the vicinity of the backscattering direction (scattering angle θ = 180°) may be required, for example, in the calculation of the backscattering coefficient, b_b, if the nephelometer angle range is limited. Such is typically the case with polar nephelometers, although specialized nephelometers for measurement of the VSF in the vicinity of the backscattering directions have been developed (for example, Maffione RA and Honey 1992).

For natural waters, such as seawater, the VSF varies little in the vicinity of θ = 180° (for example, Mobley CD 1994, Maffione RA and Honey 1992). Voss KJ et al 1998 estimated that only as little as 1% of the backscattering coefficient is contributed by the scattering angle range of 170° to 180°. This is also due to the fact that the a contribution, dβ = β(θ)dθ, to b_b is weighed by sinθ. Hence, Voss et al used a constant-VSF approximation in order to determine b_b by numerical integration of the VSF data obtained for cultures of Emiliania huxleyi with a polar nephelometer of Petzold TJ 1972 in a scattering angle range of 10° to 170° at 1° intervals. Chami M et al 2005 also assumed a constant-VSF approximation in their calculation of the backscattering coefficient.

However, if such relatively detailed data are not available, other approaches to the extrapolation of the VSF data to θ = 180° may be needed. In studies aimed at the determination of the backscattering coefficients of phytoplankton species, Vaillancourt RD et al 2004, Balch WM et al 1999, and Voss KJ et al 1998 all perfomed such an extrapolation by fitting Beardsley-Zaneveld (BZ) approximation (Beardsley GF Jr and Zaneveld 1969) to their VSF data. Vaillancourt et al fitted the BZ approximation to data for 29 marine phytoplankton cultures obtained with a Dawn nephelometer (Wyatt Technol. Corp) for 15 scattering angles (an older instrument model) more or less evenly spaced in a range of ~35° to 145°. A Dawn nephelometer, operated at a wavelength of 633 nm was also used by Balch et al to obtain VSFs for 6 marine phytoplankton cultures. Voss et al fitted the BZ approximation to very coarsely spaced VSF data (at 45°, 90°, and 135°) obtained with a Brice-Phoenix nephelometer for E. huxleyi cultures and found that that the difference between b_b values obtained by the integration of the BZ approximation and those obtained by integration of the high-resolution VSF data and of the flat-back approximation (see above) were moderate (SD = 6%). The BZ approximation was also used by Hou W 1997 to fit the experimental VSF of the large marine particles (>~500 µm) measured at 60°, 90°, and 120°.

Cubic splines have also been used to both interpolate between the measured values of the VSF as well as extrapolate the VSF to the large scattering angle range (Oishi T 1990).

In contrast to the above, somewhat utilitary approximations, one should note a two-parameter (slope of the power law PSD and refractive index of the particles) Fournier-Forand approximation (FF; Forand GR and Fournier 1999, Fournier GR and Forand 1994) to the VSF of seawater. That approximation is based on the anomalous diffraction approximation (ADA; van de Hulst HC 1981) and realistic assumptions regarding the shape of the PSD, as well as the refractive index of the particles. It has been found to be one of the most accurate approximations for the VSF of seawater (Mobley CD et al 2002, Haltrin VI 1998). As pointed out by Mobley CD et al (2002), the backscattering coefficient can in that case be calculated analytically by using the values of the two fit parameters of the FF function.

See also: Relationships between the backscattering coefficient and scattering at an angle.

CITATION: Jonasz M. 2006. Volume scattering function of natural waters: Backscattering extrapolation (www.tpdsci.com/Tpc/VsfSwXplBck.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 15-May-2006 Modified: 20-Dec-2010 Peer-reviewed: 15-May-2006

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