Robust optical features of fine mode size distributions: Application to the Quebec smoke event of 2002

[ 1] Simple relationships involving the fundamental parameters of fine mode aerosol optical depth (tau(f)), Angstrom exponent (alpha(f)) and its derivative (alpha(f)') as near-monotonic functions of the effective van de Hulst parameter (rho(eff, f) = 2 (2 pi r(eff, f)/lambda) \m - 1\) were derived for the conceptual case of a log-translatable particle size distribution (LTPSD). This notion is useful in the interpretation of real sunphotometer data; the fine mode size distribution often approximates a LTPSD while departures from this behavior become more readily understood once one understands the first order optics. The near dependency of the fine mode optical parameters on rho(eff, f) was also exploited to obtain an explicit expression for rho(eff, f) as a function of alpha(f) and alpha(f)'. The relationships were applied to a representative case study to demonstrate their general applicability and then to the specific case of the July 2002 Quebec smoke event. A number of illustrations were given where the coherency of the derived relations indicated that the LTPSD concept was often a good approximation to reality. The analysis of the Quebec-smoke extinction data showed the existence of a weak but systematic dependence of the Angstrom exponents on smoke trajectory time and by inference a steady growth in particle size with time. The variation of r(eff, f) ( derived from AERONET inversions) was however observed to be inconsistent with this dependence unless one redefined this parameter in terms of the clearly delineated peak of the asymmetric fine mode particle size distribution (PSD). This definition led to a re-computed temporal rate of increase in reff, f which was coherent with the variation of the Angstrom parameters and which was coherent with a simple coagulative model based on conservation of volume. It was demonstrated that trajectory time was essentially a proxy variable for r(eff, f) and more fundamentally rho(eff, f) ( as predicted by the LTPSD relations). A similar proxy argument could be applied to the dependence of the Angstrom exponent on optical depth but such arguments are tempered by the relative variations of fine-mode abundance (A(f)) and particle size (by the value of the parameter gamma = dlogA(f)/dlogr(eff, f)).