The outer bands of what’s left of Hurricane Jeanne began wafting over South Carolina Sunday — an early signal of the possibly heavy rains and strong wind gusts expected in the Midlands by mid-day.

Already Sunday, the effects of the storm had been blamed for one death on the S.C. coast and suspected in a second.

After drilling Florida and parts of Georgia early Sunday, the bulk of the remnants of Hurricane Jeanne are expected to cross the western edge of the Midlands late this morning and dump 2 to 5 inches of rain, plus deliver a one-two punch of potential flooding and tornadoes.

Expect the rain to start by mid-morning and become quite heavy by noon, said Tony Petrolito, a meteorologist with the National Weather Service in Columbia. By the afternoon and early evening, the easterly winds will have reached 15 to 25 mph, with occasional gusts near 40 mph.

Nearly the entire state, save a few lucky Pee Dee counties, is under a flood watch, meaning small streams, creaks and drainage areas could overflow.

Particularly vulnerable to flooding is the northwestern part of the state, including the Greenville area, which is already saturated from encounters with other storms.

The latest forecast from the National Hurricane Center showed Jeanne’s center crossing South Carolina along Interstate 85 in the Upstate.

In the Lowcountry, the Beaufort County School District said Sunday that all its schools would be closed today in anticipation of heavy rains and winds and the potential of tornadoes.

Of particular concern to the Midlands, however, is the threat of tornadoes. The area of Columbia east to the Pee Dee holds “the best potential for tornadoes during the afternoon and evening,” Petrolito said. “Pretty much the whole eastern side of the Midlands.”

The state’s emergency operations center remains closed, but state officials are on alert to changes in the forecast, said John Legare, spokesman for the S.C. Emergency Management Division.

Authorities say a Kentucky man who drowned near Garden City Beach on Saturday became the first S.C. victim of Jeanne and a missing Georgetown County man, who encountered rough water and fell overboard during a fishing trip Saturday on the South Santee River, might be the second..

Small craft advisories and rip current warnings had been issued along the S.C. coast on Saturday, but no evacuations — mandatory or voluntary — are expected there, said Chris Drummond, communications director for Gov. Mark Sanford.

“It’s just going to be messy,” Drummond said.

Jeanne would be the fourth tropical system to pass through the state this busy hurricane season. Two named tropical systems — Charley and Gaston — made landfall on the South Carolina coast, while the remnants of Bonnie tracked into the state after that storm made landfall in the Gulf of Mexico.

The fringes of Hurricanes Frances and Ivan also brought heavy rain, tornadoes and damage, though the center of those storms did not track through the state.

Knight Ridder Newspapers and The Associated Press contributed to this report.Reach Gould Sheinin at (803) 771-8658 or asheinin@thestate.com