Don't make the Internet website mistake of the early century.
Back around 2001 the "thing to do" was to establish a jurisdictional and organizational website. It was the wild, wild West of the Internet. People established a page that quickly went static with no new content, stale, stale, stale.
Now the question for you is, Should You Establish a Facebook Group?
GovGirl suggests the concept is good for notifications. Does that include disaster warnings? That is a choice you will need to make. Certainly the ability of Facebook to deliver content quickly is not to be challenged. And, many a person is much more wedded to Facebook than any warning app that you may be using.
I'd go back to the lesson from the early stages of Web pages. Be sure you are using the tool and it doesn't go cold from no use.