The use of gamma distributions to quantify the dependence of cloud particle size distributions in tropical cyclones on cloud and environmental parameters

Mesoscale models that predict the temporal evolution of tropical cyclones (TCs) are sensitive to the representation of cloud microphysical processes. The cloud parameterizations used in such models make assumptions about the size distributions (SDs) of different ice species, and the representativeness of these parameterizations for TCs is not well known.

Observations acquired in tropical storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses project with in-situ cloud probes are used to identify snow and graupel particles through measures of particle morphology, and then to define SDs of snow and graupel, and of all ice hydrometeors combined. These SDs are fit to gamma functions to determine how the intercept (N0), shape (μ), and slope (λ) parameters vary with cloud and environmental conditions. Families of SDs are determined for each condition (e.g. SDs found in updrafts, downdrafts and stratiform regions for vertical velocity (w), for different ranges of ice water content (IWC) and temperature (T), and for the differing stages of TC development). The largest difference between elements of families was found for the T families. A volume of equally plausible solutions in N0-μ-λ phase space is defined as all solutions whose Χ² difference from the observed moments is within some ΔΧ² of the minimum Χ² for each SD, where ΔΧ² is determined as the largest of the minimum Χ² for the best fit and the uncertainty in the measured SD due to statistical sampling. There is a wider range of plausible N0, μ, and λ values for graupel SDs than for snow SDs because fewer graupel than snow were detected, leading to greater uncertainty in the graupel SDs, and hence larger ΔΧ².