Methods for Estimating 2D Cloud Size Distributions from 1D Observations

The two-dimensional (2D) size distribution of clouds in the horizontal plane plays a central role in the calculation of cloud cover, cloud radiative forcing, convective entrainment rates, and the likelihood of precipitation. Here, a simple method is proposed for calculating the area-weighted mean cloud size and for approximating the 2D size distribution from the 1D cloud-chord lengths measured by aircraft and vertically pointing lidar and radar. This simple method (which is exact for square clouds) compares favorably against the inverse Abel transform (which is exact for circular clouds) in the context of theoretical size distributions. Both methods also perform well when used to predict the size distribution of real clouds from a Landsat scene. When applied to a large number of Landsat scenes, the simple method is able to accurately estimate the mean cloud size. As a demonstration, the methods are applied to aircraft measurements of shallow cumuli during the Routine ARM Aerial Facility (AAF) Clouds with Low Optical Water Depths (CLOWD) Optical Radiative Observations (RACORO) campaign, which then allow for an estimate of the true area-weighted mean cloud size.