BAD : It was heavy rain yesterday.
GOOD : It rained heavily yesterday.
GOOD : There was some heavy rain yesterday.
When you begin with it , use rain as a verb: 'It's raining again!' 'This month it's rained nearly every day.'
When you begin with there , use rain as a noun: 'There's been a lot of rain this month.'
BAD : Two minutes later it started pouring rain.
GOOD : Two minutes later it started pouring with rain.
BAD : The next day the sky poured heavily.
GOOD : The next day it poured with rain.
it + pour with rain : 'Whenever I forget my umbrella, it pours with rain.' 'We can't go out - it's pouring with rain.'