RODANTHE, N.C. — North Carolina’s Outer Banks will likely be drenched as a tropical weather system blows by with up to 5 inches of heavy rain. But the depression had yet to reach tropical storm strength as it curved out to sea today.

Elsewhere, a hurricane threatened to pass “dangerously close” to Hawaii, and a tropical storm warning was issued for parts of Florida’s Gulf Coast because of a tropical depression in the Gulf of Mexico.

In the Atlantic, the tropical depression began moving away from North Carolina’s coast Tuesday night but National Weather Service meteorologist Tom Lonka said the Outer Banks will be lashed with rain and wind today.

“There’ll be rain showers coming on shore, rain bands and gusty winds,” he said by phone Tuesday.

Business owners on North Carolina’s Ocracoke and Hatteras Islands say they’ve experienced a drop in foot traffic. But by late Tuesday, many tourists had decided to stay and brave the impending storm.

“Well, the sun has been shining and we’ve been hearing about this storm for two days,” Jennifer Bange, 43, of Painted Post, N.Y., said Tuesday. She was about to drive onto the ferry from Hatteras Island to Ocracoke, determined to show her two sons the small island.