The use of gamma distributions to quantify the dependence of cloud particle size distributions in hurricanes on cloud and environmental conditions

Mesoscale models that predict the evolution of tropical cyclones (TCs) are sensitive to the representation of cloud microphysical processes. Bulk cloud parametrizations used in such models make assumptions about the particle size distributions (PSDs) of different ice species, and their representativeness for TCs is not well known. In situ cloud probe data acquired in tropical storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses (NAMMA) project are used to define PSDs of snow and graupel, and of all ice hydrometeors combined. These PSDs are fitted to gamma functions to determine how the intercept (N0), shape (μ), and slope (λ) vary with cloud and environmental conditions. Families of PSDs are determined for each condition (e.g. PSDs found in updraughts, downdraughts and stratiform regions, for different ranges of ice water content (IWC) and temperature (T), and for differing stages of TC development). A volume of equally plausible solutions in (N0‐μ‐λ) phase space is defined for each environmental condition sampled based on the goodness of the fits and the uncertainty in the measured PSDs due to statistical sampling. Per cent overlap between two families in each environmental and cloud condition was calculated, and results show that areas with sustained vertical velocity with a magnitude of at least 1 m·s−1 lie in a different phase space than stratiform regions, and PSDs corresponding to IWC 0.1 g·m−3. All other environmental and cloud conditions did not have significant impacts on either the location or uncertainty in the family of ellipsoids. Three‐dimensional volumes in N0‐μ‐λ phase space that characterize equally realizable fitted parameters for all PSDs found within the following temperature ranges: (a) 0 > T ≥ −10 °C, (b) −10 > T ≥ −20 °C, (c) −20 > T ≥ −30 °C, (d) −30 > T ≥ −40 °C, and (e) T