A nor’easter could dump more than a half a foot of snow throughout the state this coming week, adding to what has been above-normal snowfall this season, according to the National Weather Service in Gray.

The storm would come on the heels of recording-setting low high temperatures in Portland and Augusta on Saturday.

Meteorologist John Jensenius said the storm will likely gain strength as it moves up the coast and through the Gulf of Maine. It could hit by midday Tuesday and continue into Wednesday, with the heaviest snowfall occurring overnight Tuesday. Strong winds and blowing snow are also possible, he said.

Since the storm is still a few days away, Jensenius said Saturday it was difficult to predict with much accuracy how much snow could fall during the nor’easter. But the weather service has already issued a winter storm watch for the southern half of the state, stretching from the coast to the western mountains. That storm watch will likely be extended Sunday to cover the entire state, he said.

“It is still very early and things could change based on the timing and track of the storm,” Jensenius said. “It’s too early to know who will get the most snow.”

Based on its current track, the storm could produce more than 6 inches of snow and heavy winds. If the storm moves out to sea, snow totals and wind speeds would be less. But if it tracks farther inland, coastal areas could see a mix of snow and rain, Jensenius said.

Any additional snowfall would add to an already above-normal season. To date, Portland has received nearly 16 inches more snow this winter than normal, Jensenius said. The normal snowfall by March 11 is 51.8 inches, but so far this season, Maine’s largest city has seen 67.4 inches.

The same is true in Bangor and Caribou, he said. Bangor has received 63.3 inches, compared to a normal of 55.7 inches, while Caribou has received 98.3 inches, compared to a normal of 90.4 inches.

Jensenius said that both Portland and Augusta set records for the lowest high temperatures for March 11. In Portland, the high temperature of 17 degrees was reached shortly after midnight Friday, beating a previous record low high of 23 degrees set in 1960. Augusta’s high reached only 14 degrees on Saturday, beating a record of 22 degrees, also set in 1960.

As of 9 p.m. Saturday, it was minus 7 degrees in Greenville, with a wind chill of minus 25. Elsewhere, the temperature and wind-chill factor were minus 3 in Millinocket (minus 24 wind chill); minus 5 in Caribou (minus 22); 1 degree in Augusta and Bangor (minus 17); and 6 degrees in Portland, (minus 7).

Jensenius said wind-chill advisories for much of the state would remain in effect until 8 a.m. Sunday, while the wind-chill warnings for the mountains would likely be scaled back to wind-chill advisories.