Coastal flooding Tuesday morning could cause problems for residents on the South Shore in both Nassau and Suffolk, though North Shore communities may not go unscathed, forecasters said Monday.

The National Weather Service issued a coastal flood warning for southern Nassau and southwest Suffolk from 7 to 11 a.m. A coastal flood advisory is in place from 7 a.m. to 1 p.m. for southeastern and northeastern Suffolk and from 9 a.m. to 1 p.m. for Nassau’s North Shore and for northwestern Suffolk.

The weather service said Monday night tides could rise as much as 2 to 2 1⁄2 feet above regular tides. It said “widespread flooding of vulnerable shore roads and properties” is possible due to the height of the storm tide and incoming waves.

The flooding comes just a day after a snowstorm Monday that shut down schools and closed roadways. It also comes as forecasts call for light snowfall Tuesday morning, possibly in time for the morning commute, said Faye Barthold, a weather service meteorologist in Upton. The snowfall could continue into Thursday with on-and-off bouts of light snow, summed up as “a prolonged period of unsettled, wintry weather,” Barthold said.

As for snow turning from light to heavy, conditions are not really “well defined,” she said Monday, other than “a little more focusing mechanism” for possibly heavier amounts on Tuesday.

On the horizon is an Arctic front that is forecast to hit Friday night, “setting the stage for a frigid weekend,” the weather service said Monday. Highs Saturday could be in the mid-to-upper 20s, said John Murray, a weather service meteorologist in Upton.

Sunday, highs could reach just the teens.

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“It is February. It is New York,” Barthold said.

Monday’s heavy snow, falling at an inch an hour in some areas, prompted dozens of Suffolk school districts to cancel classes.

Suffolk County Executive Steve Bellone said the East End took much of the brunt Monday.

Among Monday’s snowfall totals in Suffolk were 6 inches recorded at Flanders, Old Field, Yaphank and Southampton; 5 8⁄10 inches at Mattituck; 3 inches in Smithtown; and 2 2⁄10 inches at Long Island MacArthur Airport in Ronkonkoma. In Nassau, 3 1⁄2 inches fell in Plainview; 3 inches in Merrick and Massapequa; and 2 8⁄10 inches in Old Bethpage.

The State Department of Transportation reported 210 trucks, 26 loaders and 343 employees were engaged in snow removal in Suffolk on Monday.

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Both Southampton Town and East Hampton Village closed public buildings on Monday.

With David M. Schwartz and Lisa Irizarry