Analysis of the spatio-temporal behaviour of beach morphology at Duck using fractal methods

In this study, monthly beach elevation time series (between 1981 and 2003) at Duck, North Carolina are analysed using fractal methods. This work extends a fractal analysis carried out by Southgate and Moller [Southgate, H.N., Moller, I., 2000. Fractal properties of coastal profile evolution at Duck, North Carolina. J. Geophys. Res. 105 (C5), 11489–11507] using twice the amount of data (22.3 yr) with the aim of investigating the fractal properties at different profile locations over a larger range of timescales. Differences in fractal properties between the periods 1981–1992 and 1992–2003 are also examined. The results of this analysis are used to distinguish between the timescales on which the beach elevation responses at various cross-shore and alongshore locations are related (or unrelated) to external forcing. Two fractal analysis approaches, based on the calculation of global and local Hurst exponents, are used. The local Hurst exponent method identifies local fractal properties in the data over ranges of timescales and also accounts for nonstationarity in relation to the data mean. Hence, it is considered to be a more appropriate technique for identifying the fractal properties in such dynamic natural time series. The analysis of the entire 22.3-year long data set shows fractal properties over more varied timescales and beach locations than previously observed by Southgate and Moller [Southgate, H.N., Moller, I., 2000. Fractal properties of coastal profile evolution at Duck, North Carolina. J. Geophys. Res. 105 (C5), 11489–11507]. For the dune and upper shoreface, fractal properties are estimated at timescales between 1 and 50 months, while the inner and outer bar zones exhibit fewer fractal properties over varied timescales between 10 and 90 months. Cross-shore locations corresponding to the typical positions of the nearshore sand bars at Duck exhibit non-fractal properties, reflecting the dominant influences of wave forcing in these areas. Alongshore differences in the fractal properties (which were not previously studied) are also identified between the pairs of profile lines located north and south of the FRF pier. These observations demonstrate the importance of studying both alongshore and cross-shore morphological variability. The differences in the spatio-temporal patterns of the fractal properties identified for the 1981–1992 and 1992–2003 periods illustrate the variation of the beach morphology with time. This demonstrates the need for re-evaluating beach behaviour using extended data. The present work shows that the timescales on which fractal properties are estimated are consistent with the timescales on which previous studies found the influences of the external forcing conditions at Duck to be relatively weak.