The Use of Gamma Functions to Quantify the Dependence of Hurricane Size Distributions on Total Water Content, Vertical Velocity, Temperature and Tropical Cyclone Development Stage

Mesoscale models that predict the temporal evolution of tropical cyclones (TCs) are sensitive to the representation of cloud microphysical processes through their effect on latent heat release. The cloud parameterizations used in such models make assumptions about the size distributions of different ice species, such as cloud ice, graupel, and snow, which are typically based on observations obtained in mid-latitude cloud systems. The representativeness of these parameterizations for TCs is not well known.

In this study, in-situ observations of ice hydrometeors acquired in TCs, storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses project, the Convection and Moisture Experiment-4, and in Hurricanes Norbert (1984) and Emily (1987) are fit to gamma distributions to determine how the intercept (No), slope (l) and shape (m) parameter vary with cloud and meteorological parameters such as the total water content (TWC), vertical velocity (w), temperature (T), and TC stage of development. The derived relationships of No, l and m with TWC, w and T are compared against relationships found using data collected in other tropical and mid-latitude locations. Implications for the representation of cloud microphysics in hurricane models are discussed.