Optical depth and multiple scattering depolarization in liquid clouds

In this paper, we calculate multiply scattered lidar signals with Monte Carlo method for measuring optical depth (extinction coefficient), effective size of water droplets, and liquid water content of clouds, and present algorithms that implement our method. We calculated multiply scattered lidar signals for various water droplet sizes and liquid water contents using a Monte Carlo method. A simple correspondence between water droplet optical depth and the degree of polarization in a modified gamma size distribution (C₁ cloud) is found. We also calculated the degree of polarization of a lidar signal for a given liquid water content, finding that the degree of polarization is only dependent on optical depth. Since the Raman lidar signal of liquid water depends on the total volume of the water droplet, the effective radius of the water droplet can thus be recovered from the degree of polarization of the lidar signal and the Raman signal of the liquid water.