In this Wednesday, June 5, 2013 GOES satellite photo provided by NASA/NOAA, Andrea, the first named storm of the Atlantic season, forms over the Gulf of Mexico. The tropical storm is likely to bring wet weather to parts of Florida's west coast by the end of the week. MIAMI (AP) - Heavy rain poured down on much of Florida Thursday as the first tropical storm of the Atlantic hurricane season headed toward the state's western coast, while a new tropical storm warning was issued for a swath of the U.S. East Coast. Tropical storm warnings were in effect for a large section of Florida's west coast from Boca Grande to Indian Pass and for the East Coast from Flagler Beach, Fla., all the way to Cape Charles Light in Virginia. Tropical Storm Andrea's maximum sustained winds increased to near 60 mph (95 kph) and the storm was expected to make landfall in Florida's Big Bend area Thursday afternoon before moving across southeastern Georgia and the Carolinas. It was not expected to strengthen into a hurricane. "This one fortunately is a fast-moving storm," said Florida Gov. Rick Scott. Slower-moving storms can pose a greater flood risk because they have more time to linger and dump rain. Scott said the biggest risk associated with the storm was the chance of tornadoes. He noted that there has been confirmation of eight tornadoes so far across the state and he urged Floridians to remain vigilant about warnings. Even before its center hit Florida, the storm disrupted graduation ceremonies at Clearwater's Countryside High School, where the Class of 2013 was supposed to graduate Thursday morning at Brighthouse Field, the spring training home of the Philadelphia Phillies. Principal Gerald Schlereth decided to move the ceremony to the high school's gymnasium, but the gym wouldn't accommodate the nearly 500 graduates, friends, families and school officials so it was decided that the seniors would graduate in two sessions. "You have to have a Plan B when weather is involved," said Ocy Ertzberger, head bookkeeper at the school of 2,400 students. The split sessions would likely mean double-duty for the valedictorian, salutatorian and other graduation speakers. Meanwhile, south Georgia residents were bracing for heavy rains that could lead to flooding. Forecasters at the National Weather Service said heavy rains and flooding would be the main threats in Georgia, but isolated tornadoes also were possible. "It looks like it's picking up speed and that's a good thing because it won't sit and rain us so long," said Jan Chamberlain, whose family runs the Blue Heron Inn Bed & Breakfast near the Sapelo Island Ferry station on Georgia's coast Thursday morning. In Florida, storm surge was expected to be the biggest threat as Andrea comes onshore, said Eric Blake, a hurricane specialist at the U.S. National Hurricane Center in Miami. The hurricane center said coastal areas from Tampa Bay north to Apalachicola could see storm surge of 2 to 5 feet, depending on the storm's progress and timing of high tide. Blake added that flash flooding was a concern, with 3 to 6 inches of rain expected. Isolated areas in Florida, Georgia and South Carolina could get 10 inches of rain. The National Weather Service in Tampa confirmed two tornados touched down early Thursday - one in Myakka City and the other in Sun City Center. Meteorologist Rodney Wynn said there were reports of downed tree limbs and power lines and minor flooding. The city of St. Petersburg distributed sand bags to residents concerned about flooding from Andrea, and the Florida Highway Patrol closed the Sunshine Skyway Bridge over Tampa Bay due to wind speeds over 40 mph. The storm was expected to hug the coastline, bringing rain as far as southern New England through the weekend. As of 11 a.m. EDT Thursday, the storm was centered about 110 miles (180 kilometers) west of Tampa and moving northeast at around 15 mph (24 kph). In Florida, Gulf Islands National Seashore closed its campgrounds and the road that runs through the popular beach-front park Wednesday. The national seashore abuts Pensacola Beach and the park road frequently floods during heavy rains. To the west, authorities in Alabama said that 13 people had to be rescued from rough surf kicked up by the storm Wednesday at beaches in two coastal towns. In Cuba, heavy rains associated with the storm system have soaked the western part of the island for the last several days, overflowing rivers and damaging crops. At least 30 towns were cut off by flooding, and more than 2,600 people sought refuge from the rising waters at relatives' homes or state-run shelters, Communist Party newspaper Granma reported Thursday. Contributing to this report were Associated Press writers Jeff Martin in Atlanta, Russ Bynum in Savannah, Ga., Gary Fineout in Tallahassee, Peter Orsi in Havana and Jennifer Kay in Miami.