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The influence of domain size on boundary condition specification and on computed storm surge response is investigated. Storm surge response along the Florida shelf in the Gulf of Mexico due to Hurricane Kate is examined over three domains using two different open ocean boundary forcing functions, a still water (or zero elevation) condition and an inverted barometer condition which accounts for the atmospheric pressure component of the meteorological forcing. The first domain is relatively small and is situated primarily on the continental shelf in the region of intense storm surge generation. A second domain includes the entire Gulf of Mexico basin. The final domain covers the Gulf of Mexico, contiguous basins, and extends out into the deep Atlantic Ocean. The computed storm surge response indicates that the small domain is inadequate, since cross-shelf boundaries are in regions of significant storm surge generation where surge and therefore boundary conditions are not known a priori. Also, the behavior of resonant modes that are physically excited within the Gulf of Mexico due to the passage of the hurricane is unknown at the boundaries of this small domain. The domain that includes the entire Gulf of Mexico captures the primary storm surge well but may not correctly model resonant modes. In general, these resonant modes are difficult to accurately set up by boundary condition specification, since they may be dependent on interactions between the Gulf and contiguous basins. The primary storm surge response as well as resonant modes excited by the storm are best represented using a domain which encompasses the western North Atlantic Ocean, the Caribbean Sea, and the Gulf of Mexico. This domain with deep Atlantic Ocean boundaries facilitates simple boundary condition specification and minimizes the influence of boundary conditions on storm surge generation in coastal regions. Basin resonant modes and basin to basin interactions are also captured.