The words out and there are both prepositions. In this particular instance the preposition out is taking the preposition there as its complement. For a modern account of prepositions see one of the following vetted grammar sources:
- The Cambridge Grammar of the English Language Huddleston & Pullum, 2002
- Oxford Modern English Grammar Aarts, 2011
Whereas before the great linguist Otto Jespersen, people had identified prepositions as a family of words that occurred before nouns, Jespersen had the insight to observe that this family was being misidentified, or rather misdescribed. He noted that words such as in, on, at, after, before, until have the same syntactic properties regardless of whether they occurred before nouns or not. In a blinding flash of what can surely only be described as common sense, he decided that these were actually always the same words. This radical idea follows on rather mundanely, but methodically, from the way that we treat other parts of speech such as nouns or verbs.
Modern grammars such as CaGEL have gone one step further than this, but this need not bother us here. One knock-on effect of realising that prepositions need not always precede nouns, is that some prepositions don't occur before nouns at all, in the same way that some verbs never take objects. Such words include items such as:
- abroad, here, there, away, back, out
Prepositions such as out and there have various syntactic properties in common with other prepositons:
- they are modifiable by the specialised adverbs straight and right.
- they occur as the complements of other prepositions.
- they occur as complements of the verb BE.
- they, and the phrases they head, can post-modify nouns.
- they aren't modifiable by very.
Notice that out there is a complement of BE in the OP's example. We could also have :
- He was right out there, in the middle of the storm.
The preposition phrase could be used to post-modify a noun:
- The man right out there in the middle of the storm.
The whole phrase could be the complement of another preposition:
All of this shows out there to be a preposition phrase. Notice that none of the tests above will work with adverbs. You can test this yourself with an adverb like locally, for example.
Hope this is helpful!