I disagree with the deadeye stormfather/endless weeping theory, mainly because there are five more books and endless rain seems like a great setting for another full series. It would make sense if it was the end of Roshar, but unless this copies HoA and someone ascends and fixes the world, It feels like a weird direction for the second half to go.
alternative explanations to the death rattles
Kaladin in book five, once again at honor chasm and depressed during a highstorm.
I like Aredor's idea that this is a lift backstory reference.
This seems like kaladin in RoW; there is a storm and it's also figurative for the constant inner-conflict. Teft is dead, as far as he knows, the tower is about to be corrupted and Odium has defeated him.
I think this might be the shattering of the shattered plains.
This reminds of a quote at the end of WoR where Aladar is talking to Dalinar about how they've won the war of vengance but it feels like they've lost.
Just becuase this has a negative connotation doesn't mean Dalinar loses. the only thing affected by the contest is Dalinars soul. this is referring to something else.