When I was younger my Dad used to listen to the shipping forecast on the radio so he could plan his fishing and sailing trips. Given the limited vocabulary it should be possible to use a speech to text processor to convert this to a digital form. But there's also some other systems out there, that should be a bit easier.
If you are in the USA there is the National Weather Radio Specific Area Message Encoding.
NWR SAME provides in a digital form at specific, timely information on the nature and location of a threat to the safety of those most immediately at risk from severe weather or other hazards. Its greatest value is to significantly improve the automatic selection and distribution of messages about events that threaten people and/or property.
I've not seen anyone who's managed to read the weather off either of these systems so I'll unlikely be adding radio as a backup system if my internet goes down but it's interesting to know that these services are there.
Hey I'm British, I'm allowed to be obsessed by the weather!