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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. [ABSTRACT FROM AUTHOR]