|Abstract or Summary
- The characterization of bathymetry and its time evolution is very important for both oceanographic science applications, and for societal reasons relating to coastal engineering
and development. Historically, the process of depth surveying has been costly and labor-intensive.
This is especially true in nearshore regions, hence a method that is both economic and reliable is of great interest. In this regard, depth inversion techniques take advantage of the interaction between the surface wave field and the underlying bathymetry such that observations of surface wave propagation can be coupled with a dispersion relation to infer bathymetry. Using field measurements, several different types of wave observation data have been tested in inversion methods, e.g. arrays of pressure sensors (Holland, 2001), marine radar (Bell, 1999), aerial photogrammetry (Dugan et al., 2001) and video imagery (Stockdon and Holman, 2000). Typically, these studies use the linear wave dispersion relation and measured wave phase speeds (c) to perform the inversion, and agreement is generally good in intermediate water depths in the absence of currents; errors increase as waves enter shallow water, increase in nonlinearity, and
eventually break. In addition, numerical techniques exist that account for some nonlinear processes (e.g. Kennedy et al., 2000b; Misra et al., 2003) but they require more input data, usually in the form of high resolution free surface measurements. These nonlinear methods can potentially make improved depth estimates, however, they have only been tested with synthetic data. In this study, we undertake a novel approach for investigating phase speeds of nonlinear waves and the potential for using them for depth inversions. The approach is novel in the sense that our observational data set consists of both in situ and remotely sensed data and also high resolution numerical data for interpolating between the in situ measurements. Our observations were made from a set of laboratory experiments conducted in large scale wave flume. Laboratory wave conditions included both regular and random waves and a range of wave heights and periods were considered. The final data set used for the depth inversion algorithm was reduced to regular cases only. The wave height profile H(x) is simulated with high spatial resolution using a combined refraction/difraction model REF/DIF1 (Kirby and Dairymple, 1994), where the in situ data is used for calibration. Next, wave parameters such as phase speed, wavenumber and frequency are estimated based on the remote video measurements. The resulting hybrid data set is used as input for performing depth inversion including nonlinearity using the composite dispersion relation of Kirby and Dalrymple (1986). Results indicate that inclusion of nonlinearity significantly improves the retrieved depths, especially in shallow water. The resulting degree of accuracy is comparable with previous observations for intermediate water. Analysis of the error suggests that the main source of error can be attributed to the phase speed estimation, thus it is apparent that the composite dispersion equation is capable of explaining the principal physical process well.