Sunday, 22 January 2012
An Intercomparison of Techniques Used to Fit Gamma Distributions to Cloud Particle Size Distributions
Hall E (New Orleans Convention Center )
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 an intercept (N0), slope (λ) and shape (μ) parameter. From model output, N0, λ and μ are determined from the predicted moments and, when fewer than three moments are prognosed, varying assumptions. These assumptions are commonly based on in-situ aircraft observations that characterize the dependence of N0, λ, and μ on properties such as the total ice water content and temperature. To account for the fact that in-situ observations do not always cover the complete range of particle sizes, an incomplete gamma fitting (IGF) method has been developed to minimize the differences between the fitted moments and those calculated by directly integrating the size distributions. In this study, the performance of the IGF is compared against the performance of other fitting algorithms, including a standard gamma fitting method which minimizes the square of the difference between the observed and fitted curves, a normalized gamma fit that weights the square of the difference by the inverse square of the observed value, and a discrete moment fitting method which is the same as the IGF except that fit moments are calculated by integrating the fit distribution at the diameters of the observed distributions rather than by using the incomplete gamma function. Using an idealized gamma function as input to the different fitting algorithms, it is found that the normalized gamma fit and the discrete moment fit best match the N0, λ and μ of the input distribution, whereas the IGF best matches the input moments. The fitting techniques are also tested using in-situ distributions measured during the Convection and Moisture Experiment (CAMEX-4) and the NASA African Monsoon Multidisciplinary Analyses (NAMMA) using two-dimensional cloud and precipitation probes. Implications on the uncertainty of derived fit parameters are discussed.