One way to do this with your existing phone is to use a PC that is always running some code that monitors NOAA and sends your phone a text message (email) based on whatever conditions you give it.
Before you think, "impossible for the 'regular' guy," check out Misterhouse (
www.misterhouse.net ). It's open source (i.e. free). It is a collection of Perl files that can handle something like this - or full home automation. You may have to tweak some code a little, but the email list is a wealth of help. I do know that there is a guy who wrote some code to do almost exactly what you want, and he'd likely share it with you.
Neat stuff, for sure.