Snow Size Spectra and Radar Reflectivity

Some general properties of exponential particle-size distributions are discussed. Especially significant are the corrections to calculated liquid water content, precipitation rate, radar reflectivity, and median volume diameter resulting from truncations of the exponential size spectrum at maximum diameters less than infinity. These properties are used to analyze available snow particle-size distribution data. It is concluded that the equation, ND = N0 exp (−ΛD), describes the size distribution data for snow adequately. In the equation NDΔD is the concentration of snow particles of melted diameter D to D + ΛD, N0 = 2.50 × 103 R−0.94 mm−1 m−3, and Λ = 22.9 R−0.45 cm−1, where R is the precipitation rate in mm hr−1. These expressions for N0 and Λ differ from those given by Gunn and Marshall, and have the advantage that analytical manipulation of the size distribution equation yields consistent results. The following equations have been found for the precipitation content W, the median volume diameter D0, and the radar reflectivity factor Z: W = 0.250 R0.86 gm m−3, D0 = 0.14 R0.45 cm and Z = 1780 R2.21 mm6 m−3. The large exponent in the Z-R equation is related to the fact that the “effective” size of the snow particle-size distribution increases rather rapidly with the precipitation rate.