I frequently ride w/ an umbrella and also experience wet knees. Riding w/ umbrella's is very common outside of the US. If light rain and jeans I usually just let them get wet as they'll dry fairly quickly when I get inside. If heavier rain or I'm wearing nicer pants or a suit then I'll use either a cape or thin rain pants. The cape works well on omafiets or bakfiets but will sometimes slide back behind my knees on an opafiets because of the top bar.
Some people use gaiters over their knees and that seems to work quite well.
Videos:
Posts:
Good overview:
https://bicycledutch.wordpress.com/2...ve-cycle-gear/
Numerous riding in the rain posts:
https://bicycledutch.wordpress.com/tag/rain/
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