Does the relationship invoke supernatural forces driving the phenomena?
Not necessarily. And even if, that doesn't mean that those supernatural forces are considered to be real in the same sense that some Christians might consider prayer to have a physical effect.
Somewhere in some Asiatic mountains don't remember where there's a tribe which practices slash-and-burn agriculture. Western visitors were worried, telling the tribe "we've heard of many tribes doing slash-and-burn, it depletes the earth over time, there's other ways to do it". The tribefolk said: "We've been doing this for at least a thousand years in this small area and never had a problem, look around you, things are lush, our harvests are plentiful". They invited the westerners to look all over the place and see for themselves, but not enter some specific sacred place.
That sacred place? The whole reason why the scheme worked: It was left untouched, completely to itself, a refuge for nature, meaning that each time an area would be burned, it was very quickly re-populated from that very place. The site of the site didn't really matter, all that mattered was that it's there, and that it was taboo to disturb. Is it supernatural? You might say no, a Daoist might say yes -- I got that story from a commentary seminar on the Dao De Jing, as an example of what the text meant with the "eternal feminine". The physical representation might be physical, but without the supernatural principle, physics wouldn't exist in the first place.
And we have these kinds of places here in the west, too. Though we generally let the appropriate kind of priests (ecologists or adjacent folks) enter it to commune with the spirits there.