Multiple-scattering lidar from both sides of the clouds: Addressing internal structure

[1] Multiple-scattering ( a. k. a. `` off- beam'') lidar is an emerging technology in cloud remote sensing. It delivers, as in classic lidar ceilometry, cloud base altitude but also the cloud's physical thickness H as well as its optical depth t ( averaged over horizontal scales on the order of H). The value of t in fact must lie beyond the range accessible by standard ( i. e., single- scattering/ on- beam) lidar profiling, namely, up to 3 - 4. A refined diffusion- theoretical model is presented here for signals from multiple- scattering lidar and applied, on the one hand, to retrieval algorithm development and, on the other hand, signal- to- noise ratio ( SNR) estimation. SNRs are computed for LANL's ground- based Wide- Angle Imaging Lidar ( WAIL) system and NASA's space- based Lidar- In- space Technology Experiment ( LITE). The refinements are threefold and all about internal structure. First, the laser source is modeled as a collimated anisotropic exponentially distributed internal source rather than an isotropic point source at the cloud boundary; this opens the possibility of using d- Eddington rescaling to capture the forward peaked phase function more effectively within the diffusion framework. Second, stratification of the scattering coefficient is modeled as an increasing function of distance to cloud base; this strongly differentiates the signals when observed from above or from below. Finally, Cairns' rescaling is applied to this conservative scattering problem to account for the systematic effects of random ( turbulence- driven) internal variability at scales up to a few mean free paths.