Something isn't right there. 'appears to be' and 'turns out to be' are entirely different things; there's no implication of confirmation in the word 'appears' (nor of appearance in 'turns out to be').
So does 'blijkt' mean only the former, only the latter, or sometimes one and sometimes the other? Or does it mean something different still, like 'you can tell he's nice'?
- Hij schijnt gezond te zijn - Appears (but not certain), often used when you doubt it is true.
- Hij blijkt gezond te zijn - Appears (confirmed)
- Hij lijkt gezond te zijn - Appears (not confirmed, but kind of certain)
In combination with to rain it might be clearer: - Het schijnt te regenen - It appears (seems) to rain, perhaps someone told you but you are not sure - Het lijkt te regenen - It appears (looks like) to rain, you look outside and it looks like it might be raining, though you are not 100% sure - Het blijkt te regenen - It appears to rain, you know for certain that it is raining.
I have a problem here, coming from German, in which "scheinbar" (schijnbaar) means that someone or -thing appears to have a trait but really doesn't, and "anscheinend" (according to van Dale: naar het schijnt, kennelijk) means more presumedly. Even Germans have difficulties differentiating. Does this difference exist between "schijnen" and "blijken" or "lijken"? Er ist scheinbar gesund = He appears to be healthy (but he isn't really). Would that be: Hij blijkt (of schijnt of lijkt?) gezond te zijn (maar hij is erg ziek). ?
Blijken has very specific connotations -- I would say that it's best to use blijken when something is evident/obvious.
Whereas both lijken and schijnen leave room for doubt.
- Het blijkt nu dat hij het gedaan heeft. -- "It now seems/appears that he did it."
The evidence might be against him; there may now be little room for doubt, etc.)
- Het lijkt alsof hij het gedaan heeft. -- "It seems/appears/looks as if he did it."
Here there is much more room for doubt. It might be assumed that 'he did it', but the ultimate conclusion is not (yet) concrete.
- Het schijnt dat hij het gedaan heeft. -- "It seems/people say that he did it."
Schijnen can be very similar in meaning to lijken -- a primary note to consider here is the differences in syntax.
Er uitzien is a potential alternative to both lijken and schijnen.
- Het ziet ernaar uit dat hij het gedaan heeft. -- "It seems/looks like he did it."