Two years before Al Gore’s Oscar-winning An Inconvenient Truth elevated the conversation around global warming, Roland Emmerich unleashed The Day After Tomorrow, the 2004 blockbuster that brought the dangers of climate change to the popcorn crowd.

Emmerich was already known as the master of disaster, blowing up the White House in Independence Day (1996) and leveling part of New York in Godzilla (1998). While directing 2000’s The Patriot in hurricane-stricken North Carolina, the German filmmaker became intrigued with extreme weather. At his hotel’s bookstore, he stumbled upon the 1999 novel The Coming of the Global Superstorm, co-written by the conspiracy-enthused radio icon Art Bell and author Whitley Strieber.

The novel inspired Emmerich to dig into the idea that climate change could spark a new ice age over a period of days — not years or centuries. He enlisted Patriot producer Mark Gordon, who paired him with screenwriter Jeffrey Nachmanoff for a package that...