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

Abstract. Given the importance of constraining cloud droplet number concentrations (N_d) in low-level clouds, we explore two methods for retrieving N_d from surface-based remote sensing that emphasize the information content in lidar measurements. Because N_d is the zeroth moment of the droplet size distribution (DSD), and all remote sensing approaches respond to DSD moments are at least two orders greater than the zeroth moment, deriving N_d from remote sensing measurements has significant uncertainty. At minimum, such algorithms require 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 (r_max) is strongly sensitive to N_d when some measure of the liquid water content vertical profile is given or assumed. Knowledge of r_max to within 5 m can constrain N_d to within several 10’s of percent. However, operational lidar networks provide vertical resolutions or >15 m, making a direct calculation of N_d from r_max prohibitively 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 cloud top. This statistical approach provides reasonable characterizations of N_d and effective radius (r_e) 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 2 campaigns, we demonstrate the utility of the methodology.