When something happens in a way that amazes you, use the adverb surprisingly, like when you find the kids at your new school to be surprisingly friendly.
If a situation is surprising, it is completely unexpected — and you can say that it happens surprisingly. You might discover that the day is surprisingly warm, and you don't need your furry hat after all; or you may realize that college is surprisingly difficult after you breezed through high school. The French root word is surprise, "a taking unawares," which comes from surprendre, "to overtake." Surprisingly is surprisingly old, dating from the 1600's.