Some Effects of 8–12 µm Radiant Energy Transfer on the Mass and Heat Budgets of Cloud Droplets

Abstract

In standard treatments of the mass and energy budget of cloud droplets, radiant energy transfer is neglected on the grounds that the temperature difference between the droplet and its surroundings is small. This paper includes the effect of radiant heating and cooling of droplets by using the Eddington approximation for the solution of the radiative transfer equation. Although the calculation assumes that the cloud is isothermal and has a constant size spectrum with altitude, the heating or cooling of droplets by radiation changes the growth rate of the droplets very significantly. At the top of a cloud with a base at 2500 m and a top at 3000 m, a droplet will grow from 9.5 to 10.5 µm in about 4 min, assuming a supersaturation ratio of 1.0013. Such a growth rate is more than 20 times the growth rate for condensation alone, and may be expected to have a significant impact on estimates of precipitation formation, as well as droplet spectrum calculations.