Spatial Interpolation of Tidal Data in Irregularly-shaped Coastal Regions by Numerical Solution of Laplaceʹs Equation

A method was developed for spatially interpolating tidal constituent amplitude and phase data using the numerical solution of Laplaceʹs equation. The solution matches the input data values at ‘ internal boundaries ’, i.e., locations that represent observation stations. The boundary condition at land-water interfaces assumes that the normal derivative is proportional to the spatially-averaged value of the derivative in the normal direction. By adjusting the constant of proportionality at land boundaries, realistic distributions were obtained. An equivalent solution field can also be reconstructed by generating a set of weighting functions, thereby minimizing the number of solution fields needed. The method was tested in a simple basin and the solution was evaluated for a variety of parameters such as cell size, grid orientation, and boundary proportionality constant. The method was then applied to San Francisco Bay and distributions of tidal constituent amplitudes and epochs were compared with those generated by a numerical circulation model.