Fractal properties of coastal profile evolution at Duck, North Carolina

Observed variations in coastal morphology on monthly to decadal timescales are often difficult to explain in terms of physical processes operating on shorter timescales. One reason could be that the morphology evolves to high-dimensional, self-organized states. Circumstantial evidence for this would be indicated by fractal distributions of the dynamical variables. Fractal analysis techniques are applied to beach level time series collected at Duck, North Carolina, United States. After processing for this study, the data set consists of time series of monthly beach and nearshore levels at up to 86 locations, at 10 m spacing, along each of four shore-normal profile lines, over a period of 10.5 years. Time series of shoreline positions are also analyzed. Several fractal analysis techniques are used based on the Burst exponent H, and various sources of error are considered and quantified. Results indicate different fractal behavior in different cross-shore zones. H values of around 0.5 are found in the nearshore bar zones and are thus consistent with a random Gaussian process, while values around 0.8 are found farther offshore and on upper parts of the beach, indicating long-range persistency. Further analyses are done to determine time spans over which fractal behavior occurs. Generally, fractal responses are found at locations and timescales where the temporal variations of wave forcing are relatively weak. Suggestions are made to interpret these findings in terms of forced and self-organized morphodynamic change in different cross-shore zones and over different timescales. Some possible implications for predicting future coastal morphology are discussed.