iMapWeather Radio is an iOS app ($9.99) that uses location-based services to deliver pertinent emergency weather warnings to the user, while avoiding unnecessary ones (i.e. there's a tornado elsewhere in your state). You can also tailor which warnings you want to receive, in case you don't care about minor thunderstorms etc.
The 1.1 update has improved the location-based services, as well as the 'follow me' feature. 'Follow me' allows the app to constantly update the pertinent emergency area, so you can get weather warnings no matter where you go. Their info page says that the GPS feature uses as little power as possible.
In addition to monitoring your current position, the iMapWeather Radio app will track up to 5 stationary locations, so you can keep an eye on your home, relatives, child's school, etc.
source: iTunes via PR Newswire