Salmon fly hatch

I've always wanted to be there when the salmon flies started to hatch in Montana. These big stone flies (Pteronarcys californica) crawl out along the streamside vegetation and rocks after a 3 year nymphal period around late May to early July. The hatch continues for about 3 weeks.

Now here's the problem: how to predict when the hatch begins? Especially how to plan a trip with the salmon hatch as your main goal? Pretty impossible since it's usually when the run off is just coming down from full swing. If you arrive too soon, your fishing is limited to small tributaries or spring creeks. If you arrive too late, well… you're too late.