Combined Rayleigh and Mie Scattering

The model atmosphere will, in general, contain both Rayleigh and several different Mie scatterers. Under these circumstances, the effective phase matrix is then a weighted average of each scatterer's phase matrix with its extinction. In general, the atmosphere is inhomogeneous so the effective phase matrix is height dependent. For N_l different types of scatterers (Rayleigh or Mie),

$${\b Z}(\tau;\mu,\phi;\mu',\phi') = \frac{ \sum_{l=1}^{N_l} n_... ...mu,\phi;\mu',\phi') } { \sum_{l=1}^{N_l} n_l(z) \sigma_{s,l} }$$ (7.11)

where n_l(z) is the number density of the l^th scatterer having a scattering cross-section of $\sigma_{s,l}$ and phase matrix ${\b Z}_l$.