Hawaii residents on Sunday were urged to remain vigilant and be prepared as Hurricane Olivia swirled closer to the islands.

The Central Pacific Hurricane Center said the storm is likely to maintain its Category 1 strength for another day or so before passing over the islands Tuesday night and Wednesday as a tropical storm.

A tropical storm watch was issued Sunday for Oahu, Maui County and Hawaii County, with tropical storm-force winds expected as early as Tuesday night.

Forecasters said computerized forecasting models were in disagreement over the exact path of the storm, so it’s important not to focus on the exact track as Olivia moves across the islands.

“Anyone in the main Hawaiian Islands should prepare for the likelihood of direct impacts from the system,” forecasters warned Sunday night. “Those impacts could include intense flooding rainfall, damaging winds, large and dangerous surf and storm surge.”

Gov. David Ige signed an emergency proclamation Sunday that allows the state to respond to damage, losses and suffering related to Olivia and declares the counties of Hawaii, Maui, Kalawao, Kauai and the City and County of Honolulu disaster areas to help with deploying emergency management functions.

Ige warned that even if Olivia arrives as a tropical storm, the islands still face the likelihood of high winds, heavy rains, high surf, storm surge and flooding that could wreak havoc on public and private property across the state.

“A tropical storm could bring heavy rain and flooding, especially in places that are saturated from previous storms,” the governor said in a statement. “Now is the time to prepare.”

The National Weather Service said the storm could have hurricane-force winds of 74 mph or higher extending outward up to 25 miles from the center and tropical-storm-force winds of 73 mph or less extending outward up to 125 miles.

Forecasters said total rainfall amounts of 10 to 15 inches, with isolated amounts over 20 inches, are possible with Olivia.

Much of the rain will fall on windward areas, many of which already received significant amounts of rain from last month’s Hurricane Lane. That means flooding will be a real threat, especially in those areas, forecasters said.

Large swells generated by Olivia are also expected to build near the main Hawaiian Islands and may create problems for some east-facing shores Tuesday or Wednesday.

While Honolulu Mayor Kirk Caldwell urged residents and visitors to be prepared, he cautioned them not to overdo it by hoarding supplies.

“Leave enough for other people,” Caldwell said. “Think about your friends, family and neighbors. Take enough just for yourself (or) just use our water supply. We have some of the best water in the world.”

A “Hurricane Hunter” crew flying a C-130 plane through Hurricane Olivia reported Sunday morning that the eye of the hurricane was breaking apart, Caldwell said.

The crew made four passes through Olivia and reported that “the eye is not as formed,” Caldwell said. “It’s broken on one side, kind of the southwestern side, which means it’s getting a little destabilized. That’s good information and the winds have dropped, which is good.”

Also Sunday morning, a statewide video teleconference with Olivia updates from the Central Pacific Hurricane Center was attended by directors and staff of various city departments. Another briefing on Olivia will be held at the city’s Emergency Operations Center at 8 a.m. this morning.

The Hawaii Emergency Management Agency urged Hawaii residents to prepare for what could be a major natural disaster affecting the entire state.

“Two things that concern us at a time like this are emergency fatigue and the public underestimating the threat,” HI-EMA Administrator Tom Travis said in a news release. “Because Lane wasn’t a direct hit, and Miriam and Norman bypassed the islands, people may start to feel like we’re safe. The warnings start to mean less. But let’s be clear — in each of those cases, we were lucky. Don’t plan on being lucky. Plan on being prepared.”

Travis said that while Olivia is expected to weaken somewhat and hit as a tropical storm, it still represents a significant danger to life and property.

“Don’t be fooled by jargon. We encourage everyone to prepare appropriately and immediately,” Travis said.

National Weather Service forecasters cautioned that Hawaii’s mountainous terrain can focus localized areas of strong winds and rain even well away from the storm’s center.

Hurricane forecaster Robert Ballard suggested that people take some time today to do a general pre-Olivia cleanup, including securing loose objects or bringing them indoors.

At 8 p.m. Sunday the storm was 570 miles east-northeast of Hilo and 730 miles east of Honolulu. It was moving west toward the islands at approximately 11 mph.

Meanwhile, the latest cyclone to form in the waters off Mexico and move in our general direction, Tropical Storm Paul, is forecast to weaken and dissipate later this week, according to the National Hurricane Center.