Physical model for multiple scattered space-borne lidar returns from clouds

A practical model for determining the time-dependent lidar attenuated backscattering coefficient β was developed for application to global lidar data. An analytical expression for the high-order phase function was introduced to reduce computational cost for simulating the angular distribution of the multiple scattering irradiance. The decay rate of the multiple scattering backscattered irradiance was expressed by incorporating the dependence on the scattering angle and the scattering order based on the path integral approach. The estimated β over time and the actual range showed good agreement with Monte Carlo simulations for vertically homogeneous and inhomogeneous cloud profiles, resulting in about 15% mean relative error corresponding to 4 times improved accuracy against the Ornstein- Förth Gaussian approximation method.