Locative expressions as adverbial complements — not as adverbial modifiers
The problem is that your understanding of an adverb as a word that modifies a verb isn’t inclusive enough. Yes, manner adverbs can modify verbs. But many adverb types can modify things other than verbs, while some adverb types cannot even modify verbs at all.
And in some sentences, the adverbs aren’t even modifiers of anything: they’re complements. That’s exactly what’s happening here, but you need to see through to the clause that’s been deleted for it to make sense to see these as complements not modifiers.
So what then is an adverb after all? It’s a whole bunch of distinct though sometimes partly overlapping word classes all clumped together under one label.
Part of the confusion here is that historically, the “adverb” lexical category has been used as an umbrella term covering a broad collection of word classes that differ from each other not merely in their semantic properties but also in their syntactic properties. Some of these word classes are so different from each other that tossing them into a single same-named bucket can hide critical differences. You seem to have done this, provoking your confusion.
At the phrase level, adverbial phrases and clauses are multi-word syntactic constituents that can be swapped out for a single adverb. But because not all words classified as “adverbs” are identical in their semantic and syntactic properties, adverbials are likewise diversified.
Probably the easiest way to resolve your particular case is by classifying this particular use of below as a place adverb acting in the role of adverbial complement to a clause whose principal parts were “whiz-deleted”. (Whiz-deletion is the removal from a clause of a wh- word and an inflection of be, leaving just the tail end behind.)
That way, because it is now a complement instead of a modifier, it has no need to find a verb to modify, nor anything else to modify either.
Adverbial complements are mainly found as complements to linking verbs, prototypically copular be but also verbs like seem, become, appear, remain, and all the sense verbs. I’ll use be in these examples of locative expressions all used as place-adverbial complements.
- The milkman will be here soon.
- The cat is upstairs.
- The crew were ashore.
- The dog has been in the garage all night long.
- The kelp was below.
- Finally we were home!
Notice that although place adverbials can be adverbial complements, manner adverbials cannot be:
- The song was *quietly. [UNGRAMMATICAL]
- The song was *in a quiet manner. [UNGRAMMATICAL]
The same applies when the adverbial complement is used as a required but non-object complement of a transitive verb like put. You can use place adverbials for these sorts of complements, but you still cannot use manner adverbials for them:
- Put the dog outside.
- Put the dog in the garage.
- Put the dog *quietly. [UNGRAMMATICAL]
This proves that locative expressions have syntactic properties that cannot be explained if your only word classes are the classical seven of noun, verb, adjective, adverb, preposition, conjunction, and interjection. There are more classes of word than just those seven, and locatives are one such.
When it comes to using below as an adverb, the OED gives for one sense:
In a lower place, at a lesser elevation; in or on the lower part, lowermost surface, etc., of something.
And then, rather tellingly, they provide this recent citation for that sense, one that’s very like your own:
2012 The Independent 18 July 40/4 — We peered over the edge of the boats at vast forests of kelp and the ghost white wisps of moon jellyfish below.
If you read below as the adverbial complement to a whiz-deleted “peer at the kelp and jellyfish
which were below” clause, or in your case “gazed at the water which was below”, then that these are adverbs used as complements to a now-“missing” be verb here makes perfect syntactic sense.
You’re describing the position of something, and “where” questions can be easily answered with place adverbials. But that doesn’t mean they are somehow “not adverbs” when used with linking verbs. They still are. They’re just complements, though, not modifiers.