Huddleston and Pullum analyze the final word in each of these as a preposition, where traditional grammar would define them as adverbs. How can we tell which is the correct analysis?
the sky above
the weather outside
the room downstairs
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Like many things in syntax, parts of speech are an abstraction—they don't necessarily correspond to any physical fact about reality. Instead, they're invented by theorists in order to explain the data they've observed.
In this case, I'm assuming Huddleston and Pullum call them prepositions because they can (usually) attach to nouns:
the sky above the field
the weather outside the house
And because in other environments, English prepositions can elide their arguments:
he went up [the stairs]
she walked past [the building]
So they chose to treat "above [the field]" and "up [the stairs]" as the same category of thing, in their theory.
But there's nothing inherently wrong about grouping "above [the field]" with "yesterday" instead, calling them both adverbs, and coming up with rules about when "above" is a preposition and when it's an adverb and how you can tell them apart.
The question is just, which theory explains the data more completely and elegantly? This is a somewhat subjective question, without a single definitive correct answer. (Though, if you're a student, the more important question is—which theory is your instructor using?)