The storm was moving north at about 8mph (13km/h), the National Hurricane Center said.
The National Weather Service has issued a flash flood watch for Wake, Chatham, Nash and Johnston counties and points south through 8 a.m. Tuesday.
Earlier Monday, Alberto rolled up big waves and tides along beaches of the northern Gulf Coast. And, it said, heavy rains are also expected in many areas.
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A storm surge warning was in place from the Suwannee River to Navarre, Florida, and a tropical storm warning covered the area from the Suwannee River to the border of Florida and Alabama.
To the north, Alberto lumbered ashore in the Panhandle, pelting white sand beaches with blustery winds and stinging rain.
Strong storms possible Thursday and Friday: As Alberto moves away, a different type of summertime weather pattern kicks in; that could deliver some intense summertime storms on Thursday and Friday.
Alberto also disrupted Memorial Day plans in Alabama, Florida and MS as it moved into the Southeast. Isolated deluges of 12 inches (30 centimeters) were possible.
The mayor of Orange Beach, on Alabama's Gulf Coast, says Subtropical Storm Alberto is bringing rain and aggravation but isn't causing any serious problems in his community.
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The storm forced some Memorial Day tributes to be cancelled across Florida's Panhandle.
The risk of flash flooding was only marginal -5 percent- in the Lowcountry as of Monday morning. Storm watches and warnings were discontinued for coastal regions, but those inland remained in effect.
"We want to make sure we can move a little bit of water downstream to create a little bit of extra storage just in case we do get some of the heavy rains that Alberto promises the area over the next several days", said Jim Hopson, a spokesperson with TVA. Monday will see a few afternoon showers or storms and Tuesday will be dry with highs in the mid 80's both days.
The storm's approach also triggered mandatory evacuations of some small, sparsely populated Gulf Coast barrier islands in one Florida county.
However, the NHC said the season is likely to be "near or above normal". An average hurricane season produces 12 named storms, of which six become hurricanes, including three major hurricanes.
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