Raindrops from one Place are Different from Another Place

Marshall and Palmer (1948) [1], in a highly cited article, present their exponential general relation of;

Λ = 41 R- 0.21 cm-1 where R is the rate of rainfall

ND = N0 e- ΛD where D is diameter of raindrops.

When D = 0, ND = N0 and in this MP model, they find that N0 = 0.08 cm-1. However, Jennings, for this paper, worked up the exact raindrop data in MP Fig. 2 and got.

Λ = 41.1 R- 0.212 cm-1 (Jennings)

This is undersetandably very close to the MP result, but in an extended discussion in Pruppacher and Klett (1997) [2] pp. 30-38, it is remarked that N0 can depend on R in the following way where (Sekhorn and Srivastava (1971)) [3] find.

N0 = 7 x 103 R0.37 m- 3mm- 1 and Λ = 3.8 R- 0.14 mm-1

Jennings got N0 = 0.0847 cm- 4 for Fig. 2 and keeps the accuracy because the data in MP Fig. 2 is linear above D = 1.5 mm raindrop size. Marshall and Palmer also note that the mass of rainwater can be calculated and correlated with the rate of rainfall R by the MP equation at the top here. At small raindrop size, there is devation from linearity of ln ND versus D, which has a negative slope. In the MP paper, in Fig. 1, we note that the N0 is not constant and applying Jennings formula above does not work.