The linearized hydrodynamic equations for storm surges are solved in analytic form for a very simple model basin and an arbitrary field of wind and pressure to show that a solution can be obtained as an integral of the product of the atmospheric forcing function and an influence function whose value tends to zero with increasing time lags. In practical cases this solution can be computed as a weighted sum of the meteorological observations during a short period before the storm surge observation.
A finite difference scheme for a slightly more general basin is then developed and the solution given formally in terms of a polynomial involving both vectors and matrices. It is shown that this solution is equivalent to the analytic solution and that both are equivalent to a linear function of the meteorological measurements of wind and pressure which must be used to obtain a description of any actual forcing function for storm surges. The technique can be generalized to provide the solution for basins of almost any shape.
The difficulties and uncertainties involved in the hydrodynamic solution are discussed, and the advantages of using a statistical method to determine the solution of the problem when sufficient data are available are shown.