Hurricane Ian is heading toward Florida after raking western Cuba on Tuesday - and officials in the Sunshine State are pleading with people to flee the peninsula's west coast ahead of what could be life-threatening storm surge in the Tampa and Fort Myers areas and flooding rains.

Ian, a Category 3 storm packing sustained winds of 115 mph, was over the southeastern Gulf of Mexico around 11 a.m. ET, having made landfall in Cuba early Tuesday as a Category 3, the US National Hurricane Center said.

Cuba's tobacco-rich Pinar del Rio province lost power because of the storm, according to Cuban state television. Floodwater covered fields and fallen trees lay in front of buildings in San Juan y Martinez, a town in the province, images from state media outlet Cubadebate show.

Up to 16 inches of rain and mudslides and flash flooding were possible in western Cuba, the hurricane center said. Mayelin Suarez, a resident of Pinar del Rio city, told Reuters that storm made for the darkest night of her life.

"We almost lost the roof off our house," Suarez told Reuters. "My daughter, my husband and I tied it down with a rope to keep it from flying away."

Ian's forecast course is for western Florida next, where rains and tropical storm-strength winds will begin Tuesday, with the system poised to deliver life-threatening storm surge - ocean water pushed onshore - and flooding rain Wednesday into Thursday morning as it first crawls along off the coast and then heads inland.

The storm could make landfall near Venice - roughly a 20-mile drive southeast of Sarasota - on Wednesday evening as at least a Category 3 hurricane - sustained winds of at least 111 mph.

And officials are warning: Leave the coast now.

"Today is really going to be your last day to ... actually move out (of) the storm surge warning area," Michael Brennan, acting deputy director of the National Oceanic and Atmospheric Administration, told CNN on Tuesday morning.

The storm poses numerous perils for west-central Florida:

- Storm surge: A storm surge warning - meaning the surge could threaten life - is in effect for much of Florida's west coast, from Suwanee in the Big Bend region to the peninsula's tip in the Everglades.

A warning also is in effect for far northeastern Florida's coast, from near the Georgia state line down to Marineland, as well as for St. John's River further inland.

The worst - 8 to 12 feet - is forecast Florida's west coast from just south of Bradenton down to Bonita Beach south of Fort Myers, the hurricane center said.

Large storm surge also is possible in areas outside that zone, including Tampa Bay, which could see a surge of 5 to 8 feet, the hurricane center said.

If that happens, that would surpass the highest surge recorded in the Tampa Bay area - around 4 feet from 1985's Hurricane Elena and March 1993's "Storm of the Century."

- Rain: Totals could be 12-24 inches around Tampa and west-central Florida through Thursday night, posing numerous flooding threats. That's two or more months' worth of rain for that area, as the average September brings about 6 inches of rain there.

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