The prepositional phrase is used as an adverb indicating location. The deeper structure is a "that noun clause" (The frisbee that is on the roof is Jerod's).
The Frisbee on the roof is Jerod's.
A. adjective
'The Frisbee is on the roof' is treated just like 'The Frisbee is black.'
Terry is running up the hill.
B. adverb
The phrase 'up the hill' describes the running motion, not Terry.
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