Normal mode decomposition for identification of storm tide and tsunami hazard

Normal mode decomposition is shown to be a useful analysis methodology in the evaluation of storm tide and tsunami hazard at a coastal site. The prediction of the normal modes, the basin eigenmodes, is formulated as a Sturm-Liouville problem. Numerical solution follows transformation to a matrix eigenvalue problem. Numerical implementation issues are identified and resolved, and typical eigenmode solutions for spatially varied basins in one and two spatial dimensions are given. A spectral line plot is demonstrated as a suitable analysis summary for an historical storm tide or tsunami event. Prediction of the response amplitudes at the discrete eigenmodes is formulated and solved as a problem in multi-dimensional optimization.