Drizzle rates versus cloud depths for marine stratocumuli

Marine stratocumuli make a major contribution to Earth's radiation budget. Drizzle in such clouds can greatly affect their albedo, lifetime and fractional coverage, so drizzle rate prediction is important. Here we examine a question: does a drizzle rate (R) depend on cloud depth (H) and/or drop number concentration n in a simple way? This question was raised empirically in several recent publications and an approximate H-3/n dependence was observed. Here we suggest a simple explanation for H-3 scaling from viewing the drizzle rate as a sedimenting volume fraction (f) of water drops (radius r) in air, i.e. R = f u(r), where u is the fall speed of droplets at the cloud base. Both R and u have units of speed. In our picture, drizzle drops begin from condensation growth on the way up and continue with accretion on the way down. The ascent contributes H (f alpha H) and the descent H-2 (u alpha r alpha f H) to the drizzle rate. A more precise scaling formula is also derived and may serve as a guide for parameterization in global climate models. The number concentration dependence is also discussed and a plausibility argument is given for the observed n(-1) dependence of the drizzle rate. Our results suggest that deeper stratocumuli have shorter washout times.