A Equation for Size Distribution of Precipitation Elements Based on the Normal Distribution of Liquid Water Content

Abstract

A equation of precipitation-element size distribution will be proposed in this paper. It is represented by the normal distribution of liquid water content per unit volume of air with size. The conventional distributions (e.g. Marshall-Palmer (1948) and Best (1950)) and the characteristic distributions observed and computed as reported in the writer's previous paper (Shiotsuki, 1974) are fitted by this equation. Furthermore, the melted drop-size distributions for snowflakes and graupels are also represented by such normal distribution.
The most. usefulness of the proposed equation is that it is applicable to almost all kinds of size distribution of various types of precipitation. The new equation is determined by the space liquid water content (M) and the mean diameter (D) and the standard deviation of i t (a) of the normal distribution of liquid water content. Thus the present equation also needs some parameters which may be dependent on precipitation type, as well as the conventional equations. But those three parameters of the present equation can be easily determined by observing the data of radar reflectivity (Z), precipitation intensity (R) and number flux of precipitation particles (N).