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Due to the angular asymmetry of the VSF for natural dispersions (see VSF at the small angles for natural dispersions), the probability of light scattering at an angle from the vicinity of θ = 0° is much greater than that for the larger angles. In the calculation of the scattering coefficients, b, the integrand β(θ)sinθ (see Scattering coefficient) may increase as tθ -s, where t is a magnitude factor and the slope s may range from about ~0.5 to 1.5 (see VSF at the small angles for natural dispersions). Hence, the small-angle values of the VSF are of significant importance. Indeed, the VSF typical of seawater within the scattering angle range of 0 to 1° may contribute as much as ~0.36b and as much as ~0.7b for the angle range of 0 to 10° (for example, Petzold 1972; Atlantic at Bahamas, station 7, Morel 1973a).
The small-angle VSF data are also important in models of imaging in moderately turbid media. Unpublished results of one of the authors (MJ) obtained by calculating the PSF (for example, Mertens and Replogle 1977) typical of seawater, with the use of the small-angle scattering theory (for example, Wells 1969), indicate that the VSF at a scattering angle as small as 0.0001 rad (~0.006°) may be of importance here.
Interestingly, it has been shown by Mobley et al (2002), who considered several approximations to the VSF of seawater, that the shape of the VSF in the small-angle range (0 to ~5°) is relatively unimportant for the calculation of certain parameters of the underwater light field, such as radiance distributions, irradiance, and irradiance reflectances in the radiative transfer (RT) theory. That work narrows the insignificance range of the VSF as compared to a range of 0 to 15° previously estimated by Gordon (1993). A reason for that narrowing may be a significant effect of the small-angle VSF on the backscattering ratio (backscattering coefficient / scattering coefficient) through a strong influence of the small-angle VSF on the scattering coefficient. A correct value of that ratio was found by Mobley et al to significantly improve the radiative transfer modeling provided that the phase function has a realistic shape. Note that an impact of the small-angle range on the radiative transfer was evaluated by Mobley et al at an angular resolution of 5°, typical of numerical RT models in the ocean and atmosphere (Mobley et al 1993). However, this does not mean that numerical RT models with a higher angular-resolution would not benefit from the availability of the small-angle VSF data.
| CITATION: Jonasz M., Boss E. 2006. Significance of the VSF at the small angles (www.tpdsci.com/Tpc/VsfSmlAngSgnf.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 07-Sep-2006 Modified: 07-Sep-2006 Reviewed: 05-Sep-2006 |
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