Looking on the internet deeply has found these results:

heavy rain is the most popular phrase on the web.

hard rain 11,100,000 results on the web	heavy rain 126,800,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Even a hard rain... would take more than a day or two to kill a man. After a hard rain, that river is deep. Cold, hard rain. And when it rains hard rain, I scream and I run in circles. Maybe after one more hard rain. It's going to rain hard tonight. Only the hard wind and rain. Cold, hard rain.	And heavy rain, two months later, on the other side of the world. The application approved during today's vote was made by Ireland, and it concerns the heavy rain that caused severe flooding in November 2009. Because the weather report calls for heavy rain. Hurricane force winds and heavy rain. The game was canceled because of the heavy rain. We had a heavy rain last night. When a heavy rain hatches them in large numbers... they crowd together. Ireland applied for assistance from the Fund following heavy rain leading to severe flooding in November 2009.

hard rain

11,100,000 results on the web

heavy rain

126,800,000 results on the web

More popular!

And heavy rain, two months later, on the other side of the world.
The application approved during today's vote was made by Ireland, and it concerns the heavy rain that caused severe flooding in November 2009.
Because the weather report calls for heavy rain.
Hurricane force winds and heavy rain.
The game was canceled because of the heavy rain.
We had a heavy rain last night.
When a heavy rain hatches them in large numbers... they crowd together.
Ireland applied for assistance from the Fund following heavy rain leading to severe flooding in November 2009.