The Application of Doubly-truncated Hydrometeor Distributions to Numerical Cloud Models

Book excerpt: A number of meteorological applications involving clouds require being able to determine a reasonable hydrometeor particle size distribution when given the mean hydrometeor mass density ('liquid-' or 'ice-water content') over a region of space. Such applications include numerical cloud model with 'parameterized' or 'bulk' microphysics, which have often assumed exponential size distributions. This study proposes a parameterization scheme based on a doubly-truncated exponential particle size distribution, i.e. a distribution that is truncated at both the large and small diameter ends. The necessary inputs to the scheme are the liquid or ice water content and the temperature of the sample, and, in some circumstances, and estimate of the lower truncation limit. Outputs include the parameters of the exponential distribution, including the upper truncation limit. A special set of relationships is used for rain when the largest particles exceed the assumed breakup diameter of 6 mm. The scheme relies on theoretical relationships derived from the equation for the double-truncated distribution, and on empirically-derived relationships. The empirical expressions include relationship between M and Z (where M is the liquid or ice water content and Z is the radar reflectivity) and values for the product Lambda D sum M (where Lambda is the parameter of the exponential distribution and D sub M is the upper truncation limit).