It’s easy to miss the answer to progressing through the Royum: Summit map in Atelier Sophie 2. This guide will teach you how to get to the other side of Royum: Summit with the door in Atelier Sophie 2: The Alchemist of the Mysterious Dream.
Go to the area of the Royum Summit map highlighted in the screenshot below:
It should be raining. There aren’t any weather devices to stop the rain, but you should find two valves in the area highlighted in the screenshot above. Interact with only one of them once and the water preventing your passage should dry up.
Now go to the area highlighted in the screenshot below:
You should be able to cross fine since there’s no water blocking your passage. It should be smooth sailing as long as you follow the path to the blue door icon. It should bring you to the next area: Searing Maw.