The use of gamma distributions for characterizing cloud hydrometeor size distributions in hurricane models: Uncertainties and implications

Gamma distributions are commonly used to represent cloud particle size distributions in mesoscale and cloud resolving models that predict one, two or three bulk moments of different hydrometeor species. A gamma distribution is characterized by intercept (N₀), slope (λ) and shape (μ) parameters. From model output, N₀, λ and μ are determined from the predicted moments or, from various assumptions when fewer than three moments are prognosed. These needed assumptions about N₀, λ and μ are commonly obtained from fits to size distributions measured by suitably instrumented aircraft flying through tropical cyclones (TCs) and other cloud systems. In this presentation, uncertainties in gamma distribution parameters induced by use of alternate fitting techniques and uncertainties in size distributions measured by two-dimensional cloud and precipitation probes during the Convection and Moisture Experiment (CAMEX-4) and the NASA African Monsoon Multidisciplinary Analyses (NAMMA) are discussed. It is shown that N₀, λ and μ exhibit significant sensitivity to the tolerance allowed in fit parameters and on the uncertainties assumed to characterize size distributions. Therefore, N₀, λ and μ parameters can be selected randomly from a three-dimensional volume in N₀-λ-μ phase space to represent size distributions and for the development of cloud parameterization schemes. The rates of microphysical processes in such schemes exhibit significant differences to the nature of the assumptions about N₀, λ and μ. Implications for the modeling of TCs are discussed.