A Gamma Parameterization for Precipitating Particle Size Distributions Containing Snowflake Aggregates Drawn from Five Field Experiments

Abstract

Abstract In this study, we investigate the tendencies of gamma parameters for particle size distributions (PSDs) containing snowflake aggregates in orographic, convective, and stratiform clouds, above snowstorms and above rainstorms, in temperatures ranging from 0° to −45°C. We find a strong relationship between μ and Λ but no dependence on temperature. Higher μ are observed during the experiments sampling winter snowstorms, and lower μ are observed during experiments sampling frozen clouds above convective and orographic storms. We find that a gamma function with a μ of −1.25 provides the best average representation of PSD shape and the most accurate representation of PSD moments related to mass and reflectivity. We also provide a lookup table of maximum particle size boundaries that can be used to parameterize incomplete gamma functions with negative μ values. Significance Statement In many weather models and satellite retrieval algorithms, frozen clouds and precipitation are governed by the same assumptions even though they develop through different growth processes. This paper provides recommendations for snowflake aggregate size distributions that reflect natural conditions, and these recommended assumptions are demonstrated to improve estimates of mass and radar reflectivity. We studied a variety of storms, such as thunderstorms, snow storms, and winter rainstorms, and we found that our model for snowflake aggregates was nearly identical in all observed conditions.