Use of collocated sensors to measure coastal wave reflection

Two different methods for estimating frequency-dependent reflection coefficients for waves incident on a coastline using collocated measurements of elevation (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 zone where waves propagate essentially shore-normally. A time domain method is shown to introduce a significant positive bias in the estimated reflection coefficient. A contour plot is calculated giving the bias as a function of the estimated reflection coefficient and the coherence between the estimated incoming and outgoing wave time series, which can be used to provide corrections for the bias. A new principal component analysis (PCA) technique is found to be essentially bias-free. For this method, 95% confidence levels on zero reflection coefficient are computed for a range of numbers of degrees of freedom. Spatial separation between the sensors equivalent to a time delay, at the wave phase velocity, of tau(x) produces a spurious peak with a reflection coefficient of one at frequency 1/(4 tau(x)). The peak is very sensitive to small errors in estimating the time delay, which result in apparent reflection coefficients even higher than one. The conclusion is that the time delay must be made as small as possible in order to push the spurious peak to a high frequency. Application of these results is demonstrated using field data taken on a natural beach.