How warm and moist do environments have to be to produce rain?

Rainfall is a spiky, noisy field with non-unique relationships to its environment. However, certain statistical moments of rainfall exhibit tractable properties. A clean separation between raining and non-raining environments can emerge when the statistics are arranged sensibly. These statistics can then be mined to quantify controls on tropical rainfall.

How does the tropical wind field react to rain?

A particularly simple class of wind-rain interactions emerge when rainfall acts like a relief valve to release instability built up in the environment. In this class of interactions, clouds can be thought to "adjust" their environment to a more stable state.

However, clouds must also compete with atmospheric gravity waves in the adjustment process. Any horizontal differences in temperature tend to be erased by gravity waves. As instabilities constantly crop in space, this competition between rain and gravity waves is playing out continuously. The quantitive details of this competition decide many aspects of transient tropical weather and mean climate.