Wiscombe and Grams (1976) and Remizovich and Radkevich (1996) showed an interesting relation between backscatter fraction, β, i.e. integral of the azimuth integrated phase function over forward hemisphere with respect to the zenith angle of the direction of incidence and over backward hemisphere with respect to the zenith angle of the scattering direction, and mean scattering angle <γ>: β = <γ>/π. Those papers also showed that <γ> can be presented as a weighted sum of all Legendre moments of odd orders of the phase function. This is because only Legendre polynomials of odd orders are responsible for disbalance in probability of scattering between forward and backward hemispheres. Thus, <γ> can be used as alternative characteristic of anisotropy of single scattering: greater <γ> indicates less anisotropic scattering.
Mean scattering angle was calculated in this work for a set of mono- and poly- disperse particles as well as for some aerosol models used in the MODIS aerosol retrieval algorithm (Levi et al. 2009) and some ice cloud bulk models described by Baum et al. (2014). It was shown that mean scattering angle allows to distinguish different phase functions better than asymmetry parameter g. For example, in the above mentioned case of ice spheres <γ> = 16.7° at 0.5 μm and <γ> = 17.0° at 1.0 μm, i.e. the difference of <γ> between these wavelengths is 1.6% while the difference of g is only 0.2%.
Baum, B. A., P. Yang, A. J. Heymsfield, A. Bansemer, A. Merrelli, C. Schmitt, and C. Wang, (2014), Submitted to J. Quant. Spectrosc. Radiant. Transfer, Special Issue ELS-XIV.
Levy, R.C., L.A. Remer, D. Tanre, S. Mattoo, and Y.J. Kaufman, (2009), "Algorithm for Remote Sensing of Tropospheric Aerosol from MODIS for Collection 005: Revision 2", available at http://modis-atmos.gsfc.nasa.gov/_docs/ATBD_MOD04_C005_rev2.pdf
Remizovich, V.S. and A.V. Radkevich, (1996), Laser Physics, vol. 6, No. 4, pp. 679694.
Wiscombe, W.J. and G.W. Grams, (1976), J. Atmos. Sci., vol. 33, pp. 2440 - 2451.