Deriving cloud droplet number concentration from surface-based remote sensors with an emphasis on lidar measurements.

Given the importance of constraining cloud droplet number concentrations (Nd) in low-level clouds, we explore two methods for retrieving Nd from surface-based remote sensing that emphasize the information content in lidar measurements. Because Nd is the zeroth moment of the droplet size distribution (DSD), and all remote sensing approaches respond to DSD moments that are at least 2 orders of magnitude greater than the zeroth moment, deriving Nd from remote sensing measurements has significant uncertainty. At minimum, such algorithms require the extrapolation of information from two other measurements that respond to different moments of the DSD. Lidar, for instance, is sensitive to the second moment (cross-sectional area) of the DSD, while other measures from microwave sensors respond to higher-order moments. We develop methods using a simple lidar forward model that demonstrates that the depth to the maximum in lidar-attenuated backscatter (Rmax⁡) is strongly sensitive to Nd when some measure of the liquid water content vertical profile is given or assumed. Knowledge of Rmax⁡ to within 5 m can constrain Nd to within several tens of percent. However, operational lidar networks provide vertical resolutions of > 15 m, making a direct calculation of Nd from Rmax⁡ very uncertain. Therefore, we develop a Bayesian optimal estimation algorithm that brings additional information to the inversion such as lidar-derived extinction and radar reflectivity near the cloud top. This statistical approach provides reasonable characterizations of Nd and effective radius (re) to within approximately a factor of 2 and 30 %, respectively. By comparing surface-derived cloud properties with MODIS satellite and aircraft data collected during the MARCUS and CAPRICORN II campaigns, we demonstrate the utility of the methodology. [ABSTRACT FROM AUTHOR]