The variable G (dimension-less) defines the asymmetry parameter of the phase function, thus controling the shape of the aerosol phase function, which has an influence on the scattering effects caused by aerosols. For values between -1 (backward scattering) to +1 (forward scattering), the phase function is modelled through the spectrally-independent Henyey-Greenstein empirical approximation (Henyey and Greenstein, 1941): $$Φ(θ)_{HG} = {1}/{4π}{1-g^2}/{(1+g^2-2g\cosθ)^{3/2}}$$
where Φ is the aerosol phase function as function of the scattering angle θ and g is the Heyney-Greenstein asymmetry parameter.
For typical aerosols, G values range from 0.6 to 1 (Holben et al., 1998, Hess et al., 1998, Dubovik et al., 2002).
If G=10 (default value), MODTRAN will use instead the Mie approximation of spherical particles (Mie, 1908) to model the phase function. In this case, the spectrally-dependent asymmetry parameter will be automatically taken from the aerosol model selected in IHAZE.
Henyey, L., & Greenstein, J., (1941), "Diffuse radiation in the galaxy." Astrophysical Journal, Vol. 93, pp. 70-83.
Mie, G., (1908), "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen." Annal. Phys., Vol. 330, pp. 377-445.
Holben, B., Eck, T., Slutsker, I., Tanré, D., Buis, J., Setzer, A., Vermote, E., Reagan, J., Kaufman, Y., Nakajima, T., et al., (1998), "AERONET—A Federated Instrument Network and Data Archive for Aerosol Characterization." Remote Sensing of Environment, Vol. 66, No. 1, pp. 1-16.
Hess, M., Koepke, P., & Schult, I. (1998), "Optical properties of aerosols and clous: the software package OPAC." Bulletin of the Americal Meteorologic Soctiety. Vol. 79, No. 5, pp. 831‒ 844.
Dubovik, O.; Holben, B., Eck, T., Smirnov, A., Kaufman, Y., King, M., Tanré, D., Slutsker, I., (2002), "Variability of absorption and optical properties of key aerosol types observed in worldwide locations." Journal of the Atmospheric Sciences, Vol. 59, pp. 590-608.