What does the adverb "early" modify?

Early in the morning our house was surrounded by cars.

What does the adverb "early" modify here? Does it modify the phrase "in the morning", or the phrase "was surrounded", or is it a sentential adverb, thus, modifying the whole sentence?

It modifies in the morning meaning the early morning (perhaps 5:00-7:00) rather than the late morning.

I have no idea what surrounded modified with early would even mean (perhaps the cars came earlier than expected?).