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The Use of Gamma Distributions to Quantify the Dependence of Cloud Particle Size Distributions in Hurricanes on Environmental Conditions

Event Type
Department of Atmospheric Sciences
Room 218 of the Mechanical Engineering Building
Jul 2, 2013   3:00 pm  
Jeana Mascio, Graduate Student, DAS, University of Illinois
Shirley Palmisano

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


In this study, observations acquired in tropical storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses project with in-situ cloud probes installed on the NASA DC-8 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 then fit to gamma functions to determine how the intercept (No), shape (μ), and slope (λ) parameters vary with environmental conditions such as the total water content (TWC), vertical velocity (w), temperature (T), and TC stage of development. The No, μ, λ solution representing the best fit is determined by forcing three moments of the fit distributions to match as closely as possible the corresponding moments computed from the observed SDs that are truncated between some minimum and maximum dimension. This is done using a non-linear Levenberg-Marquardt algorithm that minimizes the c2 difference between the fit and observed SDs. A surface of equally plausible solutions in No-μ-λ phase space is defined as all solutions whose c2 difference is within some Δc2 of the minimum c2 for each SD, where Δc2 is determined by how well the gamma distribution fits the SD and the uncertainty in the measured SD due to statistical sampling. Families of SDs were determined for different environmental conditions (e.g. SDs found for updrafts, downdrafts and stratiform regions for w).


There are minor differences in the range of No-μ-λ that characterize SDs for environmental conditions. There was a wider range of plausible No, μ, and λ values for graupel SDs than for snow SDs because fewer graupel were present leading to greater uncertainty in the SDs, and hence larger Δc2. The snow SDs and their characterizations were very similar to those for the SDs for all particles because of the small contributions of graupel to the total. To test the significance of the variation of SDs for different environmental conditions, frequency distributions of mass-weighted terminal velocities (VT) were calculated.


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