A method to obtain scattering phase function based on particle size distribution and refractive index retrieved from Aurora 4000 multi-angle scattering measurements: A numerical study

Scattering phase function of aerosol particles is crucial to the accurate estimation of aerosol direct radiative forcing, and is also of great interest in the field of remote sensing. One feasible and promising way to obtain scattering phase function on a long-term scale with satisfying temporal resolution is based upon the particle size distribution (PSD) and the refractive index (m = n + ik) simultaneously retrieved from multi-wavelength multi-angle scattering detected by Aurora 4000, a commercially available and easily operated, as well as lab- and field-deployable instrument. In this study, a retrieval algorithm was specifically developed according to the characteristics of Aurora 4000 measurements, using the regularization method. The algorithm was systematically evaluated for its applicability, capability and limitation by a series of designed numerical experiments, considering both monomodal and bimodal log-normal distributions with various settings of parameters and different m, in order to be prepared for its application in field studies. The retrieval algorithm has exhibited a successful performance in deriving the PSDs and the real part of the refractive index (n) without a priori assumptions about the shape of the PSDs and the value of n, and consequently in obtaining scattering phase function, for aerosol particles from purely scattering to slightly absorbing (the imaginary part of the refractive index k <= 0.01) both without and with assumed measurement errors (when +/-psi(s)<=+/- 3%). Under such circumstances, relative errors in retrieved effective diameter (D-e), total surface area concentration (S-a), total volume concentration (V-a) are almost within +/- 20%, relative errors in retrieved total number concentration (N-a) stay roughly within +/- 50%, and absolute errors of n are well within +/- 0.02. Moreover, relative errors in backscattering ratio (BSR) and the defined parameter to describe relative errors in scattering phase function (delta P), as good indicators for demonstrating how well scattering phase function can be captured, averagely locate within +/- 20% and +/- 10%, respectively. In contrast, relative errors in the widely used parameters of the asymmetry parameter (g) and hemispheric backscattering ratio (HBSR) remain still quite small even when considerable deviations can be observed in the forward and backward scattering regimes. Hopefully, when applied in field studies in the next step, the retrieval algorithm established in this study will improve our knowledge and understanding on angular scattering properties of ambient aerosol particles, as well as the associated impacts on aerosol direct radiative forcing.