" The ground was approximated as a Lambert surface"
Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view.[1] More technically, the surface's luminance is isotropic, and the luminous intensity obeys Lambert's cosine law. Lambertian reflectance is named after Johann Heinrich Lambert, who introduced the concept of perfect diffusion in his 1760 book Photometria.
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Comments

"The phase functions can be fit by modifications of Mie phase functions for equal-volume spheres in a systematic way as outlined in Appendix A. Similar extrapolations can be made for the scattering and absorption cross-sections and the degree of linear polarization up to large values of N. "
Our model does not fit the phase functions by systematically modifying mie phase functions for equal volume sphere. Rather it fits phase functions by systematically modifying the coherent superposition of the scattering of the spherical monomers of the aggregate particle. I need to think about it! What I say is definitely correct for absorption cross section, but how about the phase function?
For polarization, it is systematically correcting monomer polarization.