On June 1 , the National Hurricane Center named the storm Tropical Storm Barry . Barry was now 235 miles ( 375 km ) to the west of Key West , Florida . Initially it maintained characteristics of both a tropical and subtropical cyclone , although deep convection continued to organize near the center ; based on the observations , the National Hurricane Center initiated advisories on Tropical Storm Barry at 2100 UTC on June 1 while the storm was centered about 235 miles ( 375 km ) west of Key West , Florida .