Tampa, Fla. ? Most of Florida’s west coast was under a tropical storm watch Sunday as the first named storm of the 2006 Atlantic hurricane season spun over the Gulf of Mexico, threatening to bring heavy rain in the next few days.

In the evening, Tropical Storm Alberto had maximum sustained wind near 45 mph, up 10 mph from early in the morning, but it was not likely to grow into a hurricane, the National Hurricane Center said.

“We do not have any significant changes,” said Lixion Avila, a senior hurricane specialist. “The system remains poorly organized.”

Alberto is a lopsided tropical storm with the most intense wind and rains massed on the eastern edge of the system, Avila said. The first of the storm’s rains swept across the Florida peninsula Sunday with no major reports of damage.

Forecasters said 30 inches of rain could fall over the western half of Cuba, creating a threat of flash floods and mudslides, while 5 to 10 inches were possible over the Florida peninsula and 3 to 5 inches could fall over the Keys through Tuesday.

An unidentified family takes cover as they make their way through a mall parking lot Sunday in Orlando, Fla., as Tropical Storm Alberto caused rains in the area. Alberto is the first named storm of the 2006 hurricane season.

The prospect of a wet storm without hurricane-force wind was welcomed by firefighters who have been battling wildfires for six weeks on Florida’s east coast.

“A good soaking rain would do a lot to help stop the fires in our area,” said Pat Kuehn, a spokeswoman for Volusia County Fire Services. “It has been a hard fire season. We’ve had several fires a week here.”

Residents of the state’s Gulf Coast were watching the storm, including Patricia Haberland, whose back porch was flooded by 12 inches of rain in March. She put a few valuables in plastic bins this weekend just to be on the safe side.

“Other than that, we’re carrying on as usual, going to work, going to church,” said Haberland, 52. “It doesn’t look like it’s going to have a major impact on our area.”

The storm was not expected to cross the Keys, but some tourists were not taking any chances on the low-lying islands.

“I had a bunch of people check out this morning,” said Nikki LaMarca, front desk manager at Courtney’s Place in Key West. “It’s amazing. People are actually leaving.”

At 11 p.m. EDT, Alberto was centered about 345 miles south-southwest of the Florida Panhandle, forecasters said.