The function of the prepositional phrase/particle in such clauses is to show the relationship between the action (walked, opened, looked) and the relative positioning, action or state of the subject. Even when such prepositions appear alone and are hence adverbs/particles, they have a retrievable prepositional object. Thus, He walked across clearly shows that the "walking" is "across" a given area. In the case of He walked across the square, across the square is a prepositional phrase (with across as its head word). In both cases, the single-word/multi-word expression (across and across the square) is independent of the verb. The action of the subject (walking) is being portrayed as having happened in/at/on/over a certain location (across the square). Similarly in She opened the shutters and looked outside and When he heard the crash, he looked up, outside is logically outside (of) the house, andup is similarly an adjunct (= upwards, in an upwards direction, he is looking in a direction that is higher than where his eyes were previously directed).