The characterization of ice hydrometeor gamma size distributions as volumes in N₀-λ-μ phase space: Implications for microphysical process modeling

Gamma distributions represent particle size distributions (SDs) in mesoscale and cloud-resolving models that predict one, two, or three moments of hydrometeor species. They are characterized by intercept (N₀), slope (λ), and shape (μ) parameters prognosed by such schemes or diagnosed based on fits to SDs measured in situ in clouds. Here, ice crystal SDs acquired in arctic cirrus during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) and in hurricanes during the National Aeronautic and Space Administration (NASA) African Monsoon Multidisciplinary Analyses (NAMMA) are fit to gamma distributions using multiple algorithms. It is shown that N₀, λ, and μ are not independent parameters but rather exhibit mutual dependence. Although N₀, λ, and μ are not highly dependent on choice of fitting routine, they are sensitive to the tolerance permitted by fitting algorithms, meaning a three-dimensional volume in N₀-λ-μ phase space is required to represent a single SD. Depending on the uncertainty in the measured SD and on how well a gamma distribution matches the SD, parameters within this volume of equally realizable solutions can vary substantially, with N₀, in particular, spanning several orders of magnitude. A method to characterize a family of SDs as an ellipsoid in N₀-λ-μ phase space is described, with the associated scatter in N₀-λ-μ for such families comparable to scatter in N₀, λ and μ observed in prior field campaigns conducted in different conditions. Ramifications for the development of cloud parameterization schemes and associated calculations of microphysical process rates are discussed.