The close call happened during extremely poor weather around 1 p.m. on Saturday, March 23.
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The FAA says Southwest Airlines Flight 147, which had veered off course due to inclement weather, was instructed by an air traffic controller to perform a go-around at LaGuardia.
They say the incident happened on the flight's second attempt to land. During that attempt, Southwest Airlines says the flight ended up diverting to Baltimore after encountering turbulence and low visibility.
The aircraft later returned to LaGuardia after a brief layover in Baltimore.
It's unclear if a strong gust of wind shear pushed them off course during the landing.
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The FAA is investigating and will determine if the plane flew over the tower at LaGuardia.
The airline also said it's "reviewing the event as part of its safety systems."