According to Rayleigh scattering theory for small spheres, back scattering is proportional to |K2Z where K is the dielectric factor and Z is the sum of the sixth powers of the diameter D. For small non-spherical particles of uncertain density, a similar quantity can be used: |K12ZS, where K1 is the dielectric factor for the material when reduced to unit density, and Z = ∑D16, where D1 is the diameter of the particle when reduced to a sphere of unit density; S is a shape factor which for snow remains between 1 and 1.5.
An analysis of Langille and Thain's (1951) radar observations on snow shows fairly good correlation between Z and the snowfall R, particularly when considered one day at a time. An overall Z = Z(R) relation for snow for all days of Langille's observations is found to agree with that previously established for rain (Marshall, Langille and Palmer, 1947). That is, equal precipitation rates R, whether rain or snow, give equal values of Z.
The transition at the melting level in the case of “continuous” rain is considered in the light of this finding. Rapid aggregation amongst the raindrops and wet snowflakes in the melting region could account for the necessary differences in size distribution between snow and rain of the same precipitation rate.
Marshall and Palmer (1949) have suggested that all size distributions for precipitation are exponential when plotted as number against diameter. Taking as a fair approximation for rain that the distribution curves belong to a single family, one may establish the particular distribution by a measurement of R. When this approximation is less valid, as it appears to be for snow, one may still establish the particular exponential distribution by measuring Z and R simultaneously.