So “according to” in polite ~ます form then.
I wasn’t sure what a weather front ( 前線 ) was so I looked it up:
A weather front is a transition zone between two different air masses at the Earth’s surface. Each air mass has unique temperature and humidity characteristics.
It doesn’t really tells me much more about what it is but it’s a bit more precise.
前線『が』is the subject of that sentence.
九州『を』is usually the direct object although here it’s different. More specifically:
ⓒ indicates an area traversed
日本『の』南 means the “south of Japan”.
通って: Is the ~て form of 通る.
I think it’s probably the following meaning in order to be in synch with を:
ⓐ to go by, to go past, to go along, to travel along, to pass through, to use (a road), to take (a route), to go via, to go by way of
『へ』is a particle which indicates a destination followed by 延び. What I don’t understand is how 延び works interaction with へ here since it’s a noun and not a verb. I’m used to an active movement verb being used with 『へ』.