Use of collocated sensors to measure coastal wave reflection

Two different methods for estimating frequency-dependent reflection coeffic ients for waves incident on a coastline using collocated measurements of el evation (or pressure) and horizontal current are investigated by simulating time series with known true reflection coefficients and added uncorrelated noise. The methods are applicable to measurements made in the nearshore zo ne where waves propagate essentially shore-normally. A time domain method i s shown to introduce a significant positive bias in the estimated reflectio n coefficient. A contour plot is calculated giving the bias as a function o f the estimated reflection coefficient and the coherence between the estima ted incoming and outgoing wave time series, which can be used to provide co rrections for the bias. A new principal component analysis (PCA) technique is found to be essentially bias-free. For this method, 95% confidence level s on zero reflection coefficient are computed for a range of numbers of deg rees of freedom. Spatial separation between the sensors equivalent to a tim e delay, at the wave phase velocity, of tau(x) produces a spurious peak wit h a reflection coefficient of one at frequency 1/(4 tau(x)). The peak is ve ry sensitive to small errors in estimating the time delay, which result in apparent reflection coefficients even higher than one. The conclusion is th at the time delay must be made as small as possible in order to push the sp urious peak to a high frequency. Application of these results is demonstrat ed using field data taken on a natural beach.