An abnormal local rise in sea level accompanying a tropical cyclone and whose height is the difference between the observed level of the sea surface and the level that would have occurred in the absence of the storm.
The storm surge is due to two effects: (a) a (minor ~ 5 feet or so) barometric storm surge due to the lower pressures at the center of the tropical cyclone; and (b) a (major ~ 15-20 feet) wind related storm surge that is highest in the right front quadrant of the moving cyclone.
With respect to the right half of the moving storm, in that region the motion of the air relative to the storm (which is determined by the local pressure difference) is augmented by the motion of the storm itself. Conversely, winds are weakened in the left half of the moving storm.
The combination of effects usually makes the right front quadrant the most dangerous part of the storm from the standpoint of wind strength and storm surge.