The Distribution With Size of Aggregate Snowflakes

Average-size distributions for aggregate snowflakes are well represented above D = 1 mm by ND = Noe−AD where D is the diameter of the water drop to which the aggregate would melt. This is the same equation that Marshall and Palmer (1948) reported for rain, but for rain No = 8.0 × 103 m−3 mm−1 and A = 41 R−0.21 while for snow No = 3.8 × 103 R−0.87 m−3 mm−1 and A = 25.5 R−0.48 where R is in millimeters of water per hour. The sum of the sixth powers of the (melted) particle diameters in unit volume (Z), the mass of snow in unit volume (M), and the precipitation rate (R) are found to be related by Z = 2000 R−2.0 and M = 250 R−0.90; combining these two gives Z = 9.57 × 10−3 M−2.2, with Z in mm6 m−3, M in mgm m−3 and R in mm hr−1 of water. The relation Z = 2000 R−2.0 is in good agreement with Z = 2150 R−1.8, an average locus through recently reported Japanese data for aggregate flakes. The relation Z = 200 R−1.6 for snow, published earlier by the present authors, is thought to be in error due to the method of sampling used at that time. Comparing standard rain and melted-snow distributions of the same R requires that there be considerable break-up of the larger particles when snow turns to rain at the melting level. Further, to explain the observed radar-signal increase from the rain over that from the snow, a considerable increase in R at or below the melting level is required.