Hurricane Rafael was chugging past western Jamaica on Tuesday and was expected to strengthen into a hurricane before making landfall in Cuba and potentially impacting the Florida Keys. The storm was located 60 miles east-northeast of Grand Cayman as of late Tuesday evening. It had maximum sustained winds of 80 mph and was moving northwest at 13 mph, according to the National Hurricane Center in Miami.The NHC said it is expected to rapidly intensify during its approach to Cuba late Tuesday and into Wednesday."Rafael is forecast to be a hurricane when it passes near or over the Cayman Islands during the next 12 hours, where damaging hurricane-force winds, a dangerous storm surge, and destructive waves are expected. Additional strengthening is expected before Rafael reaches western Cuba and the Isle of Youth on Wednesday," the NHC said.After crossing Cuba, it will emerge in the Gulf of Mexico. What it does in the Gulf remains in question, but the NHC has not ruled out potential impacts to the U.S."It is too soon to determine what, if any, impacts Rafael could bring to portions of the northern Gulf Coast. Residents in this area should regularly monitor updates to the forecast," the NHC said. RELATED STORY | Why do some people choose to stay put during dangerous hurricanes?On Tuesday morning, Cuban Civil Defense called on Cubans on social media to prepare as soon as possible, because when the storm makes landfall "it's important to stay where you are." The day before, authorities said they had issued an evacuation order for 37,000 people far eastern Cuba, in the province of Guantanamo, due to bad weather.A hurricane warning was in effect for the Cayman Islands and the Cuban provinces of Pinar del Rio, Artemisa, La Habana, Mayabeque, Matanzas and the Isle of Youth.In the Cayman Islands, officials closed schools and government offices as they urged residents to prepare. Long lines were reported at grocery stores as the storm approached.Jamaica also closed down as a precaution, with the storm's outer winds battering the island late Monday. "We urge all Jamaicans to remain vigilant," said Minister of Local Government and Community Development Desmond McKenzie.RELATED STORY | Tropical Storm Oscar dumps heavy rain on Cuba as it heads toward the BahamasThe storm is bad news for Cuba, which is still struggling to recover from Hurricane Oscar, which battered the island about two weeks ago after making landfall in the eastern part of Cuba, killing at least six people. The storm also coincided with a large-scale blackout on the island.Forecasters warned Rafael would unleash heavy rains across the western Caribbean that could lead to flooding and mudslides, with totals of 3 to 6 inches and up to 10 inches expected locally in Jamaica and parts of Cuba.Heavy rainfall also was expected to spread north into Florida and nearby areas of the southeast U.S. during the middle to late part of the week. A few tornadoes and a storm surge up to two feet also were expected Wednesday over the Keys and southwesternmost Florida mainland.Rafael is the 17th named storm of the season.The National Oceanic and Atmospheric Administration predicted the 2024 hurricane season was likely to be well above average, with between 17 and 25 named storms. The forecast called for as many as 13 hurricanes and four major hurricanes.An average Atlantic hurricane season produces 14 named storms, seven of them hurricanes and three major hurricanes.