A tropical depression strengthened into Tropical Storm Philippe as it dumped heavy rains over central and western Cuba, the U.S. National Hurricane Center said Saturday. It said the rainfall is spreading north across the Florida Keys and South Florida.

The storm's winds have increased to 40 mph and additional strengthening is expected over the next 48 hours, the center said.

Tropical storm warnings are in effect for the Cuban provinces of Isla de la Juventud, La Habana, Ciudad de la

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Habana, Matanzas, Cienfuegos and Villa Clara as well as the northwestern Bahamas, the center said. Watches are also in effect for Craig Key, Golden Beach and the central Bahamas.

This image shows the projected path of Tropical Storm Philippe on Oct. 28, 2017. NHC

Heavy rains were expected for the Cayman Islands, western and central Cuba and the northern Bahamas. The center forecast about 2 to 4 inches of rain with higher localized accumulations in South Florida.

A high wind watch is up for almost all of New England. Flash flooding and widespread 60 mph gusts are likely. The ground is saturated and can't handle much additional rain. Flash flood watches are up for almost the entire northeast, CBS News' David Parkinson reports.

As of Saturday afternoon, the storm is projected to travel inland west of New York City. Rain totals up to 6 inches are possible in localized areas.