We are investigating the feasibility of deducing the surf zone topography (and longshore currents) from offshore measurements of infragravity edge wave wavenumber-frequency (k-f) spectra using an alongshore-aligned linear array of current meters (5 to 7 elements with a maximum lag less than 250m). In our initial effort, we consider the simpler problem in which longshore currents are absent and assume that the total depth profile can be divided into two parts: a mean plane beach plus perturbations about the plane beach.
Several methods can be used to determine the mean beach slope of a depth profile from edge wave k-f spectra. The technique that we have investigated in detail is a Template-Matching Technique (TMT). This technique is a pattern-matching technique that matches a library of modeled k-f spectra of edge waves on planar beaches as observed at different offshore locations against a measured k-f spectrum. Testing of the TMT for simulated (including stochastic noise) k-f edge wave measurements on both planar and nonplanar depth profiles has indicated that this method can provide good estimates of the mean beach slopes. Earlier work suggested that good estimates were possible from measurements near the shoreline. However, the present study indicates that reasonable mean beach slope estimates can be obtained from edge wave measurement locations in depths as great as 8m.
To extract non-planar features, we are investigating the application of an inverse model of a perturbation expansion to the edge wave equations. A study of the forward model (where the lowest order solution is the plane beach approximation) shows that 1] at a given wavenumber, the k-f relationship and the cross-shore structure of the higher mode edge waves are influenced more by shoreline features than are the lower mode edge waves, and 2] the spatial structure of the edge wave is influenced more by shoreline features than is the k-f dispersion relationship
These points and others indicate that while the inverse model may be able to pick up features like foreshore steepening using only the observed k-f dispersion relationship, it is necessary to incorporate information about the cross-shore structure of the edge waves in the model to be able to deduce the presence of features like sand bars. How such information is obtained and incorporated in a inverse model is presently under investigation and will also be discussed in this presentation.