Methods for Estimating 2D Cloud Size Distributions

A simple method for estimating the cloud sizes from aircraft or vertically pointing instruments.

The Science

The distribution of horizontal cloud sizes plays a central role in the calculation of cloud cover, cloud radiative forcing, convective entrainment rates, and the likelihood of precipitation. These variables are all important in understanding the role of clouds in the Earth’s energy and water cycles. While satellites can provide 2-dimensional (2D) cloud size distributions, they may not have high enough spatial resolution to resolve small clouds or the temporal sampling to study clouds across the daily cycle. In this study scientists propose a new method for approximating the 2-dimensional (2D) size distribution that can be applied to data from aircraft or from continuously operating vertically pointing ground-based instruments.

The Impact

Detailed observations of cloud properties are needed to evaluate simulations of clouds by weather and earth system models.  In this study, a simple method is proposed for approximating the 2D size distribution from sampled 1D cloud chord lengths. This simple method compares favorably against a more complicated mathematical formulation, known as the Abel transform, which has been used in previous studies. This work will allow researchers to more easily calculate the cloud size distribution from observational datasets, such as those at the Atmospheric Radiation Measurement (ARM) Facility sites, for studies of cloud processes and evaluation of numerical model simulations.


For a given patch of sky, the distribution of horizontal cloud sizes plays an important role in setting the total cloud cover, the cloud radiative forcing, convective entrainment rates, and the likelihood of precipitation. Despite the importance of the cloud-size distribution, it is not often measured directly. Instead, during field campaigns and at meteorological stations, cloud sizes are usually inferred indirectly from linear sampling by aircraft, radar, lidar, or radiometer. Unfortunately, the distribution of cloud-chord lengths measured in this way is not the same as the distribution of cloud sizes. This mismatch is caused by two effects: (1) an off-center sampling of a cloud will tend to yield a chord that is smaller than the true diameter, biasing the distribution to smaller sizes, and (2) large clouds are more likely to be sampled than small clouds, biasing the distribution to larger sizes. This study addresses how to map from the observed distribution of cloud-chord lengths to the actual distribution of cloud sizes.

DOE researchers propose a simple method 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 satellite scene. As a demonstration, the methods are applied to aircraft measurements of shallow cumuli during an ARM aircraft research campaign, which then allow for an estimate of the true area-weighted mean cloud size.

Principal Investigator(s)

David Romps
Lawrence Berkeley National Laboratory and UC Berkeley


This work was supported by the U.S. Department of Energy’s Climate Model Development and Validation (CMDV), an Office of Science, Office of Biological and Environmental Research activity, under contract DE-AC02-05CH11231.


D.M. Romps and A.M. Vogelmann, “Methods for estimating 2D cloud size distributions from 1D observations,” Journal of the Atmospheric Science, 74:3405-3417. 2017, DOI: 10.1175/JAS-D-17-0105.1