From MarineBiotech Infopages
Definition of Storm surge:
The rise in water-level on an open coast as a result of the combined impact of the wind stress on the water surface, the atmospheric pressure reduction, decreasing water depth and the horizontal boundaries of the adjacent water. The storm surge does not include the effect of the astronomical tide.
This is the common definition for Storm surge, other definitions can be discussed in the article
The storm surge height at a location is in first approximation inversely proportional with the water depth in the offshore area off the shoreline. This means that shores out to deep oceans will only be exposed to relatively small surge where as shores out to shallow seas can be exposed to high surge