Cumulative versus transient shoreline change: Dependencies on temporal and spatial scale

Using shoreline change measurements of two oceanside reaches of the North Carolina Outer Banks, USA, we explore an existing premise that shoreline change on a sandy coast is a self-affine signal, wherein patterns of change are scale invariant. Wavelet analysis confirms that the mean variance (spectral power) of shoreline change can be approximated by a power law at alongshore scales from tens of meters up to similar to 4-8 km. However, the possibility of a power law relationship does not necessarily reveal a unifying, scale-free, dominant process, and deviations from power law scaling at scales of kilometers to tens of kilometers may suggest further insights into shoreline change processes. Specifically, the maximum of the variance in shoreline change and the scale at which that maximum occurs both increase when shoreline change is measured over longer time scales. This suggests a temporal control on the magnitude of change possible at a given spatial scale and, by extension, that aggregation of shoreline change over time is an important component of large-scale shifts in shoreline position. We also find a consistent difference in variance magnitude between the two survey reaches at large spatial scales, which may be related to differences in oceanographic forcing conditions or may involve hydrodynamic interactions with nearshore geologic bathymetric structures. Overall, the findings suggest that shoreline change at small spatial scales (less than kilometers) does not represent a peak in the shoreline change signal and that change at larger spatial scales dominates the signal, emphasizing the need for studies that target long-term, large-scale shoreline change.