Empirical Expression of Phase Function for Non-Spherical Particles

In electromagnetic radiative transfer calculations, the accuracy and the computation time are usually determined by the representation of scattering phase function. Accurate calculations are time consuming even for non-spherical particles. In order to get a better fit to exact calculations and simulate the backward-scattering peak of non-spherical particles, we developed a new empirical expression of non-spherical based on the fundamental theory of electromagnetic scattering and radiation transmission. This empirical expression of phase function is an algebraic expression with one single free parameter(asymmetry factor), and can be expanded into Legendre polynomials. We compared the Henyey-Greenstein* phase function and the new empirical expression with the T-matrix method for dustlike aerosol with different geometric shape, and found the new empirical expression provided a more realistic description for the scattering of non-spherical particles. Furthermore, the calculated value for ratio of scattering intensity at 90 degree to the scattered intensity in the backward direction is more reasonable when the ratio of the horizontal to rotational axes and the diameter-to-length ratio is larger than 0.5. We also investigated the effectiveness in approximating scattering from polydispersed particles by comparison between the new empirical expression, the Henyey-Greenstein* phase function and the T-matrix method for four of the log normal distribution polydispersions. The results show that the new empirical expression fits the T-matrix method much better than the Henyey-Greenstein* phase function. For the new empirical expression, the RMSE is small for 100% data except for the ellipsoidal oceanic aerosol at the wavelength of 633 nm. Similarly, the effectiveness of the new empirical expression is significant when we calculate the ratio of scattered intensity at 90 degree to the scattered intensity in the backward direction of non-spherical aerosol. In summary, the new empirical expression provides more accurate calculation for scattered intensity of non-spherical particles in the backward direction, and is helpful in electromagnetic radiative transfer calculations, and the reformatting radiative transfer models in terms of the new empirical expression should require relatively less effort.