Can 続けて be used intransitively?

Question

From a definition of 降り続く：

雨や雪などが、何日も続けて降る。「—・く長雨にうんざりする」

If you boil this down to 雨が続けて降る it appears to make no sense if you consider 続ける as a transitive verb. What's going on?

Answer 1

This 続けて is "continuously" that modifies 降る.

This is a te-form used like an adverb to modify how the action described by the second verb is done. 続けて can be remembered almost as a distinct adverb, but you can read the following questions for grammatical explanations:

• How can verb て become an adverb?
• 立ってそばを食べる vs 立ちながらそばを食べる
• て form and adverbial meaning

Answer 2

I believe it is related to the construction

Stem+続ける which can be attached even to intransitive verbs.

I guess maybe it's just an inverted version of 降り続ける.