Appendix B: A practical model for the calculation of multiply scattered lidar returns

摘要

Lidar results are typically analyzed using an equation which assumes all photons contributing to the return have been singly scattered. Lidar pulses returned from clouds often encounter large optical depths within a short distance of the cloud boundary and many of the received photons are likely to result from multiple scattering. This paper presents an equation to predict the multiply scattered return. The equation is easy to solve on a small computer and allows specification of the scattering cross section and the scattering phase function as a function of penetration depth into the cloud. Atmospheric clouds are made of particles which are large compared to the wavelength of visible and near infrared lidars. Optical absorption by particles is typically negligible at these wavelengths. The solution derived in this paper applies to these conditions. The derivation is an approximation which considers only the contribution due to multiple small angle forward scatterings coupled with one large angle scattering which directs the photon back towards the receiver.