From WordNet (r) 3.0 (2006) [wn]:
climb up
v 1: go upward with gradual or continuous progress; "Did you
ever climb up the hill behind your house?" [syn: climb,
climb up, mount, go up]
2: appear to be moving upward, as by means of tendrils; "the
vine climbed up the side of the house" [syn: ascend, {climb
up}]
3: rise in rank or status; "Her new novel jumped high on the
bestseller list" [syn: rise, jump, climb up]