"Kenneth G. Wilson (1923–). The Columbia Guide to Standard American English. 1993.
upward (adv., adj.), upwards (adv.)
Upward is the adjective, as in He took an upward swing with the bat. Upwards is the more common adverb, but upward too is an adverb, as in We climbed upwards [upward] along the ridge. All three are Standard."