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Volume scattering functions (VSF) of natural dispersions such as seawater are very asymmetric (Fig. 1), with the forward scattered light power (scattering angle, θ = 0°) being typically greater than that of the backward scattered light (θ = 180°) by a factor on the order of 105 (extrapolated) and more (for example, Petzold TJ 1972). Numerous measurements of the VSF of natural dispersions have been made (for example, see Jonasz M and Fournier 2007, p. 208-225, Mobley CD 1994, p. 100-114, Kullenberg G 1974, Smith RC et al 1971, for reviews and Jonasz M 1996b for a representative data collection).
Given the asymmetry of the VSF of natural dispersions, the small-angle VSF data are important in many applications, including imaging in turbid waters, and retrieval of the slope of the particle size distribution (for example, Forand L and Fournier 1999, Fournier GR and Forand 1994).
Agrawal YC 2005 presents small-angle (θ = 0.1 to 20°) VSF data obtained with a LISST-100 instrument (Sequoia Scientific, Inc., Bellevue, WA, USA) off the New Jersey coast at the Long Term Ecological Observatory LEO-15 during the summer of 2001. He found that the VSF form rarely agrees with that of the widely used data of Petzold (Petzold TJ 1972). Agrawal observed a systematic variability in the normalized VSF with time and water depth and gives coefficients of the polynomial (log-normal) fit:
| lnβ(θ) = a0 + a1 lnθ + a2 (lnθ )2 | (1) |
where θ is the scattering angle [rad], to the time-averaged normalized VSFs as functions of water depth [the use of logβ in the Agrawal YC 2005 is a typographical error]. See also an evaluation by Mobley CD et al 2002 of the various approximations for oceanic VSF in the scattering angle range of 0 to 180° and of the effect of choosing an approximation on the modeling of underwater light field. Examples of log-normal fits for marine VSF data are shown in Fig. 1 and Fig. 2 in VSF at the small angles for natural dispersions.
A number of other approximating functions have been used to represent VSFs of natural waters, including the Fournier-Forand appproximation (FF, for example, Forand L and Fournier 1999, Fournier GR and Forand 1994). Jonasz M and Fournier 2007 (p. 250-264) and Mobley CD 1994 (p. 114-117) review the various approximations of the VSF. The FF approximation implies, in the small-angle range, a power-law dependency of the VSF on the scattering angle, θ, i.e. lnβ(θ) = a0 + a1 lnθ, with a slope, a1, related to the slope of a power-law approximation of the particle size distribution (see VSF at the small angles for natural dispersions and power-laws).
See also: Volume scattering function: Small-angle measurement techniques, Significance of the VSF at the small angles.
| CITATION: Jonasz M. 2006. Volume scattering function of natural waters (www.tpdsci.com/Tpc/VsfSw.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 17-Jan-2006 Modified: 31-Jan-2008 Reviewed: 29-Nov-2007 |
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