Comment: With a directional particle, the verb can apply to any established object, e.g. a tree, a fence, the back of a truck - so this is not the same as the regular Omitted Object alternation with climb, which implies 'climbing (up)' (e.g. 'climbing (up) a mountain').

Comment: This is a "covert valency" alternation, because (i) it is a near paraphase of climbed over the fence, unlike as of climbed the ladder, mountain, etc. (ii) semantically the NP denotes an obstacle (e.g. fence, gate, wall): the construction implies going from one side of this obstacle to the other, (iii) the same construction is found with verbs like swim and jump (e.g. swim the river, jump the puddle), but with these verbs it is more obvious because they are normally intransitive.