'Widespread rain' is correct and usable in written English.
You can use it to describe a lot of rain occurring over a wide area. For example: "We are expecting widespread rain over the weekend."
A depression moving across southern England on 24th July provided widespread rain with daily totals reaching 38mm in west London.
Two storms that moved through the region last week and brought widespread rain have raised hopes that a five-year drought could begin to ease.
One is that equipment and construction troops sent from the site to help repair widespread rain damage last year may still be at other posts.
Raindrops could be falling by 10 to 11 p.m. or so, but the steady, widespread rain should generally hold off until after midnight.
By George Packer The Burmese military government, which hides from its people in the splendid isolation of a jungle capital newly manufactured in the center of the country, told the public, on April 29th, to expect widespread rain and forty-five-mile-an-hour winds on the southern coast.
Tomorrow morning will see widespread rain, which could be heavy at times.
Widespread rains sent soy beans futures prices soaring yesterday on the Chicago Board of Trade with prices pushing through seasonal highs in six of the seven deliveries.
The rest of state reported widespread rains of 1-7 inches.
This system brought widespread rains to a wide swathe of India during its existence.
The depression brought widespread rains to southern Maharashtra and Karnataka states, with 40 mm (1.5 in) of rain recorded in Karwar.
Starting in late December, widespread rains produced by the precursor to Helen prompted the issuance of flood warnings throughout the Top End region.
