The Earth was flooded for about a year, including the 40 days of rain. Sediments were deposited which were later eroded, metamorphosed and lithified as the waters subsided.
Scientists disguise the evidence of a worldwide flood by using jargon which is something other than a worldwide flood, but this one is a dead giveaway. "Heavy rainfall." How heavy? 40 days and nights to be exact.
"Trend from temperate climate to subtropical". That sounds suspiciously like a way to say that it started raining a lot. Some seasonal variations? No kidding? It started raining, then it stopped raining.
We're already seen the descriptions of the Cambrian and Ordovician start with a statement on climate. It's a subtle way to pay homage to the fact that a vast amount of water moved a vast amount of sediment.