Debbie Arita, an office manager at a supermarket in Hilo on the Big Island of Hawaii, took stock of the conditions. Tropical Storm Hone was approaching the region, but the scene on Friday was far from chaotic — no frantic rush for supplies, no desperate boarding up of windows.

To Ms. Arita, who said she has been through her fair share of hurricanes and tsunamis, the prevailing mood seemed to be alertness without anxiousness.

“There’s no sense of panic here,” she said.

Hone (pronounced ho-NAY) is expected to deliver a glancing blow to Hawaii as it passes near or south of the Big Island late Saturday into early Sunday. Forecasters have warned of the potential for damaging winds, life-threatening surf and flash floods.

Officials and residents largely said they were preparing, but not yet with alarm. While a landfall of a named storm on Hawaii is rare, storms frequently come close enough to affect the islands’ weather.

Mitch Roth, the mayor of Hawaii County, which covers the Big Island, wants residents to remain watchful. “We want people to be prepared for any kind of hazard,” Mr. Roth said.

In August 2018, Hurricane Lane drenched the Big Island with 58 inches of rainfall, damaged over 100 buildings and killed one person — despite the eye of the storm passing over 100 miles south of the state.

The Big Island, the largest and southernmost island in the Hawaiian archipelago, is expected to bear the brunt of Hone’s impact. Forecasters predict excessive rainfall and flash flooding could begin Saturday afternoon and continue through Sunday, with some areas receiving up to 10 inches of rain. A tropical storm warning remains in effect for the island.

The rest of the islands could also feel the storm’s effects. Forecasters warn of dangerous swells that could produce life-threatening surf and rip currents across the state.

As of Saturday morning, the storm had maximum sustained winds of nearly 65 miles per hour and was expected to strengthen into a hurricane southwest of the Big Island by Sunday. After Hone passes, the islands could face another threat as Hurricane Gilma, a Category 1 hurricane in the North Pacific Ocean, looms behind.

Mr. Roth described the Big Island as the “tip of the spear” for storms, as it is often the first island in the state to feel the impact. Storms typically weaken as they pass over the island before reaching the rest of Hawaii, he added.

Mr. Roth said that state and local officials, emergency workers, utilities and other stakeholders have been meeting daily to discuss storm preparations. As the storm approaches, these meetings have grown larger; on Friday morning, Mr. Roth said about 60 to 70 people gathered in the island’s emergency operations center, with more joining via video.

By Friday, Mr. Roth said, officials had identified potential shelter sites, dispatched road crews to clear debris from streams and distributed sandbags to homes and businesses at risk of flooding.

Hawaiian Electric, the main electricity utility in the state, warned on Friday that customers should anticipate outages. The utility said it was also preparing for the possibility that strong winds in areas of high wildfire risk could lead to power shutoffs.

Forecasters also have warned that Hone could heighten the risk of fires in some parts of the state. Much of Hawaii is currently experiencing a drought, and some areas may receive little rain but encounter strong winds during the storm. Last August, a devastating fire in Lahaina on Maui, fueled by strong winds, killed more than 100 people.

Still, Sam Ingram, 46, who lives on the Big Island, said he was not too concerned about the storm. Mr. Ingram, who runs a tour company, said he has not sensed unease from others, either.

Mr. Ingram said he was accustomed to wet weather. He lives in a community a short drive away from Hilo, which is sometimes described as the rainiest city in the country.

“It’s like hot weather in Phoenix,” he said. “It’s what we expect.”

Elsewhere on the island, some residents were taking more precautionary measures.

Zane Monteleone, 42, relocated his family to the Big Island after surviving the Lahaina wildfire last year — which killed more than 100 people and devastated the island of Maui — because of a shortage of affordable housing in the aftermath. Mr. Monteleone, who now operates a restaurant in Naalehu, one of the southernmost communities on the Big Island, said that a key lesson he learned from Lahaina is that the worst can happen without warning, which is why he’s preparing for Hone.

At his Hana Hou Restaurant, Mr. Monteleone closed the windows and brought in items like chairs and umbrellas from outside. At home, he ran through his disaster checklist, making sure that important documents and keepsakes were all in one place. He also reminded his children not to open the fridge if the power goes out so the cool air stays in and protects the food longer. On Friday, his wife purchased extra flashlights, candles and lanterns.

“It’s better to be safe than sorry,” he said. “If something happens, at least we know that we did everything we could.”