What type of clause or phrase is the sentence “watching the tide roll in.”? ?

D-participial phrase. This is the  correct option.

Watching the tide roll in, Otis sat on the dock of the bay and found himself suddenly inspired. The underlined structure is headed by a participle because  its full form would be: While Otis was watching the ride roll in The words in bold  type show the full pattern: to be , in the past, plus the verb ,to watch, in the participle form. It is also called a phrase because it can be replaced by a phrase: During that time, Otis sat In fact, this is a prepositional phrase indicating time. As the speaker wants to give more details, she/ he  tells what Otis was doing during that time. Besides, the speaker is referring to Otis in this phrase, so he/ she does not need to mention him again; Otis is mentioned in the main clause.

These options are not right:

A-main clause. ( Example: Watching the tide roll in, Otis sat on the dock of the bay and found himself suddenly inspired. )

B-Gerund phrase (Example : Watching the tide is nice. This differs from a participle because watching is not part of  a continuous form. We cannot replace it by " Otis was watching the tide ..." Watching ,here, has a nominal function. It can be replaced by "This").

C-independent clause (Example: Watching the tide roll in, Otis sat on the dock of the bay and found himself suddenly inspired. )