How to find a leak in the attic?

Any ideas on how to detect a leak in your attic that only happens when it rains heavily? I have a spot where the water gathers in my sunroom above the ceiling and eventually drips through when it's torrential rain. The problem is we can't find where it's coming in on the roof and running into the attic. None of us want to go on the roof in a severe thunderstorm to try and see it happening! It's only a drip just now and I want it fixed before it causes too much damage in the long term. There are no obvious missing shingles.

We can't find it from inside the attic either. How can we find where the rain's coming in without anyone risking life and limb out in a storm? The attic roof slants right to the floor and it's impossible to physically crawl into every corner of it to inspect it because it slopes so low.  Thanks!