Checking to see if these dates correspond to climatic events only makes sense if the texts imply that. However, this list does not mention climatic events for these kings records. The only climatic event it does mention is the great flood which in their chronology comes after these lists of kings. So why would these writers use dates to some past events and leave out that context? I don't see any scholarly articles suggesting this. Googling for it only brings up this article. It comes across to me as ploy for self promotion rather than anything of value to prehistory.
https://en.wikipedia.org/wiki/Sumerian_King_List#Lines_1%E2%...
For a real example of a possible ancient human record of an actual event aboriginal australians have oral histories of a volcanic eruption 37kya.
https://www.science.org/content/article/aboriginal-tale-anci...