"falls of rain" is correct and usable in written English.
It is generally used to refer to a significant amount of rainfall. For example, "The falls of rain were so heavy that pools of water gathered on the ground."
August was a wet month in southern areas with several quite intense, but often localised, falls of rain.
There is the plain data: four of the five wettest years in recorded weather history have occurred since 2000, and, according to the BBC, days when there are especially heavy falls of rain have become more common since 1960.
However, the future is not clear, but typhoons at Nikkō might show only a very slight increase [15] perhaps 0.2 per season (September December). Nevertheless it is likely that there will be more heavy falls of rain, with the frequency of days where precipitation exceeds 200 mm perhaps some 50% higher [16] (Fig. 3).
Flooding occurs once the catchment is saturated; heavy falls of rain later in the season generate more widespread flooding.
From the flowing of rivers to the falling of rain, this movement keeps us all alive.
Sulphur dioxide, fluoride and chloride emissions would have generated intense falls of acid rain.
They concluded smaller size impedes the formation of rain clouds, and the falling of light rain is beneficial for agriculture.
Often called "splash cups", the fruiting bodies are adapted for spore dispersal by using the kinetic energy of falling drops of rain.
It too would be black were it not for a recent fall of rain.
Of the 1876 flurry, The Times observed, "There was a slight fall of rain, sleet and snow in the early hours of Sunday morning, making it exceedingly disagreeable for the few persons who were obliged to be on the streets".
My father was the sunny type, able to discern patches of incipient blue in the most leaden skies and who would describe each fall of rain, however prolonged or torrential, as "a clearing-up shower".
