A new look into the relation between cloud drop number concentration and depth for rain initiation in deep convective clouds
Clouds must grow to a minimum depth to start precipitating. Here we show a new simple parametric relationship that is based on first principles as well as results that support it.
Warm rain can not form without droplet coalescence, which rate is proportional to ~R5, where R is cloud drop radius. This steep relation implies the existence of nearly a threshold R above which efficient warm rain formation can occur in the absence of tail of much larger drops in the distribution. Pinsky and Khain (2002) found the droplet effective radius (Re) threshold to be ~15 μm based on model calculations; therefore the mean droplet radius by volume (Rv) is slightly smaller than that. Initially, the cloud droplets that ascend above cloud base grow mainly by diffusion of water vapour onto them as the air cools. The adiabatic water content (ADImix), which is determined by the cloud depth and cloud base temperature and pressure, increases almost linearly with depth for clouds with warm bases (>~15°C). As a result Rv3 is expected to grow almost linearly with cloud depth in an adiabatic cloud, or in cloud where extreme inhomogeneous mixing between cloudy and cloud free air occurs, at a rate that depends on the number of activated CCN (Na).
In this study we analyze data collected in deep convective clouds by airborne cloud and precipitation instrumentation in view of the theoretical considerations described above. The cloud data has been collected during various field campaigns in different parts of the world recently, and is accompanied by aerosol data measured below the cloud bases. First, we found that indeed the vertical profile of Rv follows the theoretical diffusional growth curve, i.e. Rv3 is proportional to ADImix, although most of the cloud samples are far from adiabatic. The small deviations from this relationship occur due to respective small departures from the extreme inhomogeneous mixing towards homogeneous mixing, which slightly decrease droplet sizes due to partial evaporation.
Our analysis shows that when Rv reaches ~11μm (Re≈12 μm) the probability for the appearance of precipitation sized particles increases rapidly. This value is somewhat smaller than the model results, probably due to wider droplet spectra in our measurements. Where a considerable number of giant CCN is measured the critical Rv drops even further to below 10 μm. We also find that Na is closely and linearly related to the required depth for precipitation-sized particles to be present (Dp). Increasing Na by 100 per mg of cloudy air leads on average to an increase of ~400 meters in Dp, so that in highly polluted cases or where strong cloud base updrafts occur, clouds have to grow well above the freezing level, even in tropical atmosphere, before precipitation sized particles form by either warm or mixed phase processes.
The simple yet strong relationship found between Dp and Na, which is determined by the CCN properties and updrafts at cloud base, and their sensitivity to cloud base properties, demonstrates the importance of better representing cloud droplet concentrations (and aerosol properties) in non-resolving prediction and climate models, due to their effect on warm precipitation.