rain lasting at least ten days
霪 centers on a long, unbroken spell of rain, specifically one that lasts at least ten days. It describes a persistent, soaking downpour rather than a brief shower.
霪 combines 雨 (rain) with 淫, which likely contributes both sound and the idea of excess or prolonged duration. The character thus suggests rain that continues excessively.
The rain radical 雨 sits above 淫, which suggests excess. Picture rain that just won't stop, soaking everything for days on end.
For イン, imagine an inn where travelers are trapped by ten days of nonstop rain: inn -> イン, and the rain keeps falling.