Tropospheric humidity is likely to be a very important factor in the production of precipitation, with moist environments raining more. The saturation deficit is a convenient way of representing the degree of moistness of the environment. We define the saturation deficit as the saturated equivalent potential temperature minus the actual equivalent potential temperature. Variations in the latter variable are responsible for most variations in saturation deficit, since the profile of saturated equivalent potential temperature is essentially fixed in the deep tropics. The convection itself is primarily responsible for the second and fourth factors.
Convection can produce local winds which enhance surface fluxes.
However, aside from this, large-scale processes are primarily responsible for the first and third factors. If the above picture is correct, then external forcing of convection is caused primarily by enhanced surface fluxes resulting from high SSTs or strong surface winds. However, the time lag between enhanced fluxes and increased precipitation can be many days, since it takes a significant amount of time for such fluxes to moisten the atmospheric column. In this time a moistening column can be advected thousands of kilometers from the region of strongest surface fluxes. The effect of upper-level stratiform cloudiness on radiation is to suppress radiative cooling.