Variational data-analysis method for combining laboratory-measured light-scattering phase functions and forward-scattering computations

A method is developed based on the variational data-analysis formalism to combine laboratory-measured scattering phase functions with forward-scattering phase function computations based on independent size distribution (SD) measurements. The algorithm yields an optimal estimate of the true phase function of the system that is not only based on the measurements and the computational results but also on all available information of the error variances and, if applicable, error covariances of the measured and computed phase functions. The high flexibility of the method is demonstrated by applying it to phase functions of feldspar and fly ash aerosols. Further, the algorithm is employed to determine the asymmetry parameter g of nine different mineral aerosol samples at two different optical wavelengths, and to assess the relative importance of different error sources in the determination of g. It is found that the use of spherical model particles in simulations of g can result in errors on the same order of magnitude as the uncertainty of the refractive index. The use of spherical model particles in computations of forward scattering, however, is found to be only a minor error source.