MinuteCast from AccuWeather does exactly this. It looks at your location, looks at radar data for storm systems approaching your location, and estimates when precipitation will start at your location and how intense it will be. It’s generally pretty accurate, with some limitations. It seems to be pretty good for consistent rainstorms but it can get tripped up by pop-up thunderstorms, where the radar track can go suddenly from no rain to downpour. It doesn’t make predictions more then 2-3 hours out because past that timeframe it’s not easy to predict if weather will continue on its current track or change direction. Even with the limitations, I use it all the time. Mostly to tell if I should take the dogs out right away, or if I should wait an hour or two.