Considering the fact that a lot of people today think first to tweet about an earthquake than drop, cover, and hold on; alerting people through Twitter on critical information may be very effective. Launched today, September 25th, Twitter Alerts will notify you directly on your phone (SMS or push notification) about tweets marked as alerts from accounts you signed up for.
In order to sign up, all you have to do is go to an account's setup page (twitter.com/[username]/alerts) and subscribe. Back in April when the bombings happened in Boston, the Boston Police Department communicated with the residents through Twitter, about the status of lockdown and manhunt. This is a perfect example of the idea behind this system.
These alerts, however, will not be replacing the cellular Wireless Emergency Alerts (WEAs) that the Federal Communications Commission has been sending out already.
Among the organizations that will implement this system are the American Red Cross as well the Federal Emergency Management Agency. See the full list here.