I know here in Greensboro, NC, for the Triad Skywarn net, there are three potential repeaters designated (primary, secondary, and backup) for "criteria weather" traffic.
The Skywarn operators are tied into the NWS and if need be, ham operators can contact adjacent Skywarn nets, should their local net go down, to pass traffic on to the NWS. There are also phone numbers, fax numbers, etc. The Skywarn net control is a great resource for the public and NWS because everyone can check in and report their information to a single repository and that repository can turn around and pass all of that, at once, to the NWS in an accruate and manageable fashion.
KI4GIC