lightbrite,
Tornadoes form from thunderstorms, particularly supercell thunderstorms, which are discrete, small in size (compared to hurricanes and snowstorms, for example), and have a short warning time. It can be sunny and warm just a few miles from a violent tornado.
Large tornado outbreaks can be predicted, sometimes days in advance, but it is impossible to predict the exact path of any tornado until the severe thunderstorms have actually developed. Therefore, I’m not sure closing a shul on a day with an enhanced tornado threat makes sense. Obviously if one hears thunder or sees a storm approaching, he should take shelter and wait for it to pass before venturing outside. Note that in the eastern U.S., most thunderstorms produce very heavy rainfall, and the rain shield may obscure a tornado from view.
Some communities in areas where tornado outbreaks are more likely have warning sirens that sound when a tornado warning is issued. Most communities in the eastern U.S. do not have these sirens. There are weather radios that can be purchased, and set up to sound an alarm if a tornado warning is issued for your local area.
One other thing – if you rely on an eruv and severe weather has struck your area, it is possible that the eruv may be damaged and down.