Eta could get stronger, and forecasters warned it could be a hurricane by the time it reaches the Florida Keys tonight.
A tropical storm warning was in effect for South Florida, from the Brevard and Volusia County line to Englewood, including Florida Bay and Lake Okeechobee.
Tropical storm Eta pounded central Cuba with torrential rain on Sunday, bursting the banks of rivers and causing flash flooding in some towns before exiting via the island's northern coast and churning on track to the Florida keys.
Eta was on track to cross central Cuba on Saturday night, approach South Florida and the Florida Keys on Sunday, pass near or over South Florida and the Florida Keys Sunday night and Monday and be over the southeastern Gulf of Mexico on Tuesday.
Heavy rainfall could also spark flash flooding there, it said.
The peak of the storm winds for Miami will likely be felt around 6 a.m. Monday, the National Weather Service predicted, although the wind might not slow down until late Monday night.
It's unclear where Eta would go after Thursday, but it's believed the tropical storm will remain at that strength level the entire path.
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A storm surge of 2 to 4 feet is possible in the Storm Surge Watch from Golden Beach to Bonita Beach, which includes the Florida Keys and Biscayne Bay.
Packing maximum sustained winds of 95 kilometers (59 miles) per hour, Eta dumped up to 328 millimeters (12.9 inches) of rain on central Cuba, Cuba's meteorology office said, warning the ground would struggle to absorb this as it was already saturated due to recent heavy rains. Several shelters also opened in Miami and the Florida Keys for residents in mobile homes and low lying areas.
Rains over the past few days have triggered landslides, including 13 that blocked roads, and the overflow of five rivers, the Chiapas civil protection agency said.
Through the day Saturday, we can expect scattered shower activity, and isolated thunderstorms.
Eta had winds of 65 miles per hour.
It had been raining hard since Monday even though Eta's center didn't reach Honduras until Wednesday. Kelly said the effects from Eta will be felt far from the center of the storm's circulation.
A few tornadoes can't be ruled out to the right of Eta's center, particularly in the spiral rain bands that will pivot onshore in southeast Florida and the Keys during most of Sunday and Monday.