Time scale of warm precipitation in simple models

The time that it takes for precipitation to form in warm clouds is an important parameter in cloud physics. An interesting question is whether rainfall occurs faster over warmer regions of the planet or in a warmer climate. As temperature increases, the cloud liquid water content increases in accordance to the saturation along a moist adiabatic temperature gradient. For simple models is possible to estimate the variation of the time scale of precipitation formation with temperature, assuming that the cloud liquid water behaves adiabatically. Here we compare the behavior of simple collision-coalescence models (such as the simple Bowen-model), stochastic models and parameterizations used in mesoscale numerical models to estimate the time that takes for precipitation to form in warm clouds. We will compare our results with available observations from the literature.