Linear relation between convective cloud drop number concentration and depth for rain initiation

Coalescence of cloud droplets is essential for the production of small raindrops at a given vertical distance above the cloud base (Dp). The rate of droplet coalescence is determined mainly by droplet size, spectrum width and concentrations. The droplet condensational growth is determined by the number of activated CCN (Na) and height above cloud base. Here we show that when the droplet mean volume radius, rv, exceeds ∼13 μm, or when droplet effective radius (re) exceeds ∼14 μm, considerable precipitation mass (>0.03 g kg−1) is likely to be present in growing convective clouds. This is because the rate of droplet coalescence is proportional to ∼rv5 which practically implies the existence of a threshold rv above which efficient warm rain formation can occur, and also because the vertical profile of rv, even in diluted clouds, nearly follows the theoretical adiabatic condensational growth curve. The small observed deviations are mainly caused by deviations from purely inhomogeneous mixing which cause partial droplet evaporation. Consequently, Dp must theoretically change nearly linearly with Na. This is confirmed here observationally, where increasing Na by 100 per milligram (≈cm3 at cloud base) of air, resulted in an increase of ∼280 m in Dpfor both Israeli and Indian deep convective clouds. This means that in highly polluted clouds or where strong cloud‐base updrafts occur, clouds have to grow well above the freezing level, even in tropical atmosphere, before precipitation forms either by warm or by mixed‐phase processes. Key Points Cloud depth for precipitation onset changes linearly with drop concentration Droplet effective radius of ~13 micron indicates onset of precipitation in Cu Entrainment‐mixing in deep Cu tends toward the inhomogeneous extreme