Resolving heterogeneous structure and finite scattering in clouds and precipitation with ultra-high-resolution lidar

Abstract. Lidar is as a key observational tool for cloud profiling, enabling measurements near and within clouds at finer spatiotemporal resolutions than many other remote sensors. However, most atmospheric lidar retrievals rely on the volume backscatter lidar equation, which treats the received signal as a volumetric average over the sampled particle field. This approximation assumes that the average particle-backscatter behavior within the sample volume is representative of the underlying ensemble mean. This study shows that this condition is well satisfied only in locally homogeneous, high particle-occupancy regimes, which are not always present in clouds. Ultra-high-resolution lidar observations at 11 cm x 70 μs in range and time reveal sparsely populated and inhomogeneous cloud regions that violate these assumptions. These observations motivate a statistical formulation of volume scattering, showing that the classical volume-average interpretation emerges as the homogeneous, high-occupancy limit of finite-particle scattering. The formulation enables an analytic investigation of how cloud microphysical properties and instrument parameters contribute to measurement variability, demonstrating how sparse scattering within the sample volume can weaken the volumetric interpretation. Finally, two retrieval approaches are demonstrated that leverage ultra-high-resolution lidar data to estimate cloud-relevant parameters, including hydrometeor kinematics and photon flux, at the single-hydrometeor scale. This work clarifies the conditional limits of the volumetric approximation in cloud lidar and motivates new lidar designs and retrieval strategies that exploit individual particle-scattering contributions and their statistical nature.