Partitioning the distribution function of radar reflectivity in convective storms using maximum likelihood method

A method to estimate the parameters of radar reflectivity distribution functions of convective storm systems is presented. To carry out this estimation, the probability density distribution of the radar reflectivity, P(Z), is computed using data collected on continental convective storm systems with the radar of Little Rock in central Arkansas. We show that P(Z) can be modeled as a mixture of Gaussian components, each of them corresponding to a type of precipitation. The EM (Expectation Maximization) algorithm is used to decompose P(Z) in these merged components. In the precipitation associated with intense continental convective storms, four main populations are considered: shallow precipitation, stratiform precipitation, convective precipitation, and hail. Each component is described by the fraction of area occupied inside P(Z) and by the Gaussian parameters, mean and variance. The retrieval of the mixed distribution by a linear combination of the Gaussian components gives a very satisfactory P(Z) fitting. It is shown that this method enables to follow the evolution with time of the various precipitation components of a convective system crossing the radar observed area.