mean average rainfall

I dropped in on Sanjoy Mahajan's course 6.055/2.038 Art of approximation in science and engineering at MIT yesterday. We learned about mean average rainfall; you can estimate it pretty well by considering the mean Solar flux, the specific heat of vaporization of water, and the density of water. If you assume all of the Solar flux goes into evaporating the oceans you get 5 m/yr of rainfall, but the true average on the earth is about 1 m/yr; the factor of 5 comes from things like the fact that much of the earth is land, much is covered by clouds, light is reflected, light is absorbed by other processes, and other messy details of the energy budget.

After class, Mahajan and I discussed the size of raindrops, which has a similarly simple calculation: They break up when the stresses exceed the surface tension stress; the main stress is air resistance, which, at terminal velocity, is balancing gravity. I haven't checked the calculation, but Mahajan says this gives you a few mm.