Analysis of the scale of errors in nearshore bathymetric data

Most studies of nearshore hydrodynamics, sediment transport, and morphology focus on bathymetric variability within a narrow band of spatial and temporal scales. Typically, these studies rely on bathymetry estimates derived from field observations consisting of discrete samples in space and time with varying degrees of measurement error. Sampling limitations, which result in aliasing, and measurement errors can significantly contaminate variability at resolved scales, and may lead to large errors in the representation of the scales of interest. Using a spectral analysis, interpolation errors were analyzed for three different nearshore bathymetric data sets, each of which targeted a different range of spatial scales. Bathymetric features that were unresolved or poorly resolved (e.g. beach cusps) introduced the potential for contamination in two of the data sets. This contamination was significantly reduced using an appropriate scale-controlled interpolation method, leading to more accurate representations of the actual bathymetry. An additional benefit of using scale-controlled interpolation is that interpolation errors may be estimated independently of actual observations, which allows one to design bathymetric sampling strategies that ensure that dominant scales are either resolved or largely removed. Finally, interpolation errors corresponding to a particular sample design can be used to determine which interpolated values contribute usefully to a band-limited analysis of bathymetric variability.