Dark sky is an interesting short-term (<60 minutes) weather app. The creators interpolate weather radar information and present it based on your GPS location in the form of a smooth animation, along with a precipitation estimate. So instead of knowing that there’s a 50% chance of rain in your region that afternoon (typical weather forecast), you’d know if there was a very likely chance of rain falling on your head in the next 15 minutes. The app is currently in development, and there’s a Kickstarter campaign if you want to contribute to the cause.  There’s also a blog post that explains in more detail how they are using the standard NOAA data.