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The sky is dark blue.

Source:

http://www.bbc.co.uk/learningenglish/english/course/intermediate/unit-8/session-2/activity-3

Catherine: The sky is dark blue. The sky is dark blue.

Finn: So, is blue an adjective or adverb?

Catherine: It’s an adjective. Blue is describing the noun sky. Now number two: it's actually the same sentence but this time, think about the word dark. Is dark an adjective or an adverb?

Finn: The sky is dark blue.

Catherine: Right. So, is dark an adjective or adverb?

Finn: Dark here is an adverb.

Adjectives are used to describe nouns, i.e. the car is red.

Adverbs are most commonly used to describe verbs, i.e he fought valiantly

But adverbs can also describe adjectives. How is the car red? Is it blazingly red? Is it cheesily red? Cheekily red maybe?

That is the case for your sentence. The sky is blue. How is it blue? Darkly. It is not being blue lightly, it is being blue darkly.

BUT

It doesn't always need to be this way. One can also have adjective combinations, which would be what most would assume the sentence in question is employing. An adjective combination is where two conceptually separate adjectives join to describe one concept. Dark blue is an adjective, built by two, working in a combination. The sentence in question is ambigious in that sense, as we can't know whether it's an adverb describing an adjective, or an adjective combination. The only person that can really decide that, is the author. But in this case, it doesn't really matter which one it is, as the meaning remains the same either way.

The answer to the question “Why is dark an adverb in this sentence?” is that it is not one; that source is wrong. That’s because dark cannot ever be an adverb, let alone here. It’s just that color-words can behave somewhat curiously.

The OED says that dark is an adjective when it has this color-related sense:

3c. Prefixed, as a qualification, to adjectives of colour: Deep in shade, absorbing more light than it reflects; the opposite of light. (Usually hyphened with the adj. when the latter is used attributively.)

And here are two citations provided of this:

• 
  1859 J. Ruskin Two Paths v. 202
  That lovely dark purple colour of our Welsh and Highland hills is owing, not to their distance merely, but to their rocks.


• 
  1863 M. L. Whately Ragged Life Egypt xvii. 163
  Clad in the ordinary dark-blue drapery.

Why do they say this is an adjective? If you think it through, you’ll see why dark cannot be an adverb here, only an adjective.

The proof is that if we construe blue to be an adjective, it should be gradable:

1. This sky is bluer than yesterday’s.

That works just fine, and even works attributively: a bluer sky. So blue is a fine adjective there. You can even apply an intensifier and call it very blue, something impossible for nouns, which do not admit very.

But when using blue along with dark, a funny thing happens: you can no longer grade it as an adjective. This is ungrammatical:

2. The sky is dark *bluer than yesterday’s was. [WRONG]

Therefore you must either consider blue to be a noun so that it can be modified by a gradable adjective:

3. The sky is darker blue than yesterday’s was.

Or else you must call dark blue a compound word of some sort, either a compound adjective or a compound noun. Because it admits articles, it seems more like a noun phrase being used as a predicate complement:

4. Today’s sky is a darker blue than yesterday’s was.

Just because you have darker blue sky doesn’t mean that darker is an adverb. It is only ever an adjective. Not even the darkest blues use adverbs. :)

Color-words are curious critters.