Hurricane Hone passed within 60 miles of Hawaii’s Big Island early Sunday, bringing heavy rain, knocking out power to thousands of customers and snapping native ohia trees like twigs.

More than 20,000 customers were without electricity on Sunday afternoon on the island, which has a population of about 206,000. But Mitch Roth, the mayor of Hawaii County, which covers the Big Island, said there were no reports of injuries or major damage.

Kazuo Todd, the fire chief for Hawaii County, said that nearly 18 inches of rain had fallen around the volcanoes in the southern part the island. But so far, neither the winds nor the flooding had been dramatic.

“We do live on an island in the Pacific where the water can drain off into the ocean relatively quickly,” Chief Todd said.

Forecasters predicted that Hone, which was a Category 1 storm as it was spinning westward below the islands on Sunday, could still bring up to 20 inches of rain to some areas. As the storm moves, it will slow down and push moisture over all the islands, increasing the potential for heavy rainfall statewide and the threat of flash flooding in some areas.

By midday Sunday, the Central Pacific Hurricane Center forecast that wind and rainfall would gradually diminish through the evening. The storm was producing life-threatening surf and rip currents in some areas. Many of the island’s beach parks were closed due to the conditions, Mr. Roth said.

For most residents, Hone was no cause for alarm. On Saturday evening at Kamehameha Park in Kapaau, on the northern tip of the island, one local baseball league made up of older residents still held its banquet, setting up wind screens to shield attendees from the gusts.

Some other residents were nervously watching the rain. Kumiko Mattison drove farther east from her home in Kaumana to Keaukaha, which is right on the water. Ms. Mattison and her husband run a nonprofit, Aina Hoola, that does wetland restoration there. As she drove, she noticed swollen bodies of water and rising tides. When she arrived, she found no apparent damage to the fish ponds or other wetland areas.

About 20 miles south in Nanawale Estates, Sean O’Phelan, 43, was hoping that the rain and wind lashing his small cabin would not uproot the surrounding trees.

Mr. O’Phelan, a handyman, event organizer and harmonica instructor, is not connected to the electrical grid or water system, relying on solar power and a rainwater storage tank. Less than a year ago, a different storm brought down a tree that crushed his carport.

Mr. O’Phelan was worried that his neighbors, some of whom also live off the grid and in tents, could suffer much more. But he said people were accustomed to helping one another during disasters.

“We’re all pretty confident that we’ll be able to share aloha with our neighbors and make sure that everybody’s safe,” he said.

On Friday, Hawaii Electric, the state’s main electricity utility, said it was preparing to possibly shut off power in areas with high wildfire risk, where strong winds could potentially fuel a devastating blaze. But by late Saturday, the National Weather Service had canceled the red-flag wildfire warning in the state, and the utility announced that shutoffs were no longer under consideration.

Residents were also keeping an eye on Hurricane Gilma, a Category 3 storm east of Hawaii. Forecasters expected it to weaken to a tropical depression before it reaches the state. Ian Morrison, a meteorologist at the National Weather Service in Honolulu, said forecasters hoped that rainfall from the storm would be spread over a day or two, rather than in a quick burst.