TPDSci VSF at small angles

VSF at the small angles - a two-mode log-normal fit

Two-mode log-normal fit of small-angle VSF
Fig. 2. A two-component (two-mode) log-normal approximation (gray curve —) represents reasonably well this volume scattering function [VSF, β(θ), where θ is the scattering angle] with a complex shape for a seawater sample dominated by a quasi-monosized species of particles as represented by unpublished data of Reynolds R. A. and Stramski D. (gray diamonds ♦, Monterey Bay, CA, USA, depth of 3 m, autumn 2006, dominated in its size range by dinoflagellate A. sanguinea, approximate mean cell diameter of 50 ľm, see the data file for additional info).
Such a multi-component approximation is consistent with the additive effects of the various components of the particle size distribution (PSD) on the VSF. Two log-normal components (modes) of the approximation have been identified in the VSF data shown, each described by equation: lnβ = a_i0 + a_i1 lnθ + a_i2 (lnθ)², where i numbers the components (modes). The coefficients of the small-angle mode (dark orange curve —) are a₀₀ = 5.8114 (0.2392), a₀₁ = -3.9125 (0.2917), a₀₂ = -0.80716 (0.08170). The coefficients of the wide-angle mode (light orange curve —) coefficients are a₁₀ = 5.2367 (0.0814), a₁₁ = -1.0340 (0.0380), a₁₂ = -0.086856 (0.025157). Single SD values are given in the parentheses for each coefficient. We obtained this non-optimized fit in three steps by using an approach essentially identical to that developed by Jonasz M and Fournier (1996) for fitting multi-mode log-normal approximation to PSD data for natural waters: (1) the small-angle mode was fitted to VSF data from a range of 0.0792-0.415° where it seemed dominant (dark orange curve —), (2) the fit was subtracted from the VSF data retaining only the positive values (open light orange diamonds ◊), (3) a log-normal function was fitted to these data in a range of θ of 0.792 to 9.68° resulting in the wide-angle range fit component (light orange curve —). Interestingly, the latter is very similar in shape to the VSF obtained with a similar nephelometer by Agrawal YC (green diamonds ♦, as shown in Fig. 1), if one neglects minor oscillations in that VSF at the small angles.

CITATION:
Jonasz M., Boss E. 2006. Volume scattering function at the small angles (www.tpdsci.com/Tpc/VsfSmlAngNatDsp.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 27-Nov-2007
Modified: 27-Nov-2007
Reviewed: 30-Jan-2008

Topics in Particle and Dispersion Science