I have read that tornadoes produce a large amount of noise across the AM band. The claim was an AM radio tuned to white noise between stations whines and sings when a tornado is in the area and it gets louder and more distinct as it gets closer.

I don't know. Sounds like a good experiment for one of the many storm chaser crews out there. They could carry a battery powered Am radio or simply use the AM function on their car radio.

It would be an interesting experiment to try. But in the mean time a standard weather radio may be your best bet.

Another option to look into would be to talk to the local police or emergency services departments. Some have reverse 911 operations and a few are said to include weather emergencies. The operation of these systems is that when an alert is issues and localized it cross references the location of the emergency with a reverse phone directory. The computer then dials the phone numbers associated with each house in the area and delivers a pre-recorded warning message.

In one case my local police had the system call everyone a half mile down-wind of a industrial fire. The local system dials a couple score numbers at a time. So it is pretty fast. It isn't perfect but it seems to have alerted most of the people and worked well enough that it has become a regularly used tool for emergency services.

Some of these systems require that you contact the emergency services or police department and register your address to the phone number that will be used. This is increasingly important as more people every day are using cell phones as their only tele-communications link. Couldn't hurt to ask if they have such a system. Maybe ask why not if they don't.

There are also several pager companies out here who claim to keep abreast of disasters in your area and for a fee they will send you a warning. Sounds good if they are as good as their advertising claims. One I looked at said they operated at the county level. I wasn't in the right area. They were a SW outfit.