Analysis of the spatio-temporal behaviour of beach morphology at Duck using fractal methods Y. Gunawardena a, ⁎, S. Ilic b, 1 , H.N. Southgate c , H. Pinkerton d,2 a Departments of Geography and Environmental Science, Lancaster University, Lancaster, LA1 4YQ, United Kingdom b Department of Geography, Lancaster University, LA1 4YQ, United Kingdom c Faculty of Civil Engineering and Geosciences, Technical University of Delft, PO Box 5048, 2600, GA Delft, The Netherlands d Department of Environmental Science, Lancaster University, LA1 4YQ, United Kingdom ABSTRACT ARTICLE INFO Article history: Received 8 October 2007 Received in revised form 12 March 2008 Accepted 20 March 2008 Keywords: beach elevations Duck cross-shore alongshore fractals 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. © 2008 Elsevier B.V. All rights reserved. 1. Introduction It is recognised that morphological changes within the coastal environment are the result of complex processes and interactions operating over a wide range of spatial and temporal scales. Changes in the beach profile that are strongly correlated with external forcing variables, such as waves, tides and currents, can be considered as ‘forced’ responses. Examples of this type of beach response include: seasonal changes in the beach profile that are correlated with seasonal variations in the wave climate (Winant et al., 1975; Aubrey, 1979, 1983; Birkemeier, 1985) and the strong direct response of the beach profile to individual or groups of high-energy storms (Lippmann et al., 1993; Lee et al., 1998). Linear force–response relationships between different beach morphological and external wave forcing variables at Duck have also been derived by Larson et al. (2000). Yet, studies have also shown that, on certain spatio-temporal scales, the beach response is not Marine Geology 252 (2008) 38–49 ⁎ Corresponding author. Tel.: +44 1524 510246, +44 1524 510248; fax: +44 1524 510269. E-mail addresses: y.gunawardena@lancaster.ac.uk (Y. Gunawardena), s.ilic@lancaster.ac.uk (S. Ilic), h.n.southgate@tudelft.nl (H.N. Southgate), h.pinkerton@lancaster.ac.uk (H. Pinkerton). 1 Tel.: +441524 510246, +44 1524 510248; fax: +44 1524 510269. 2 Tel.: +44 1524 593912; fax: +44 1524 593985. 0025-3227/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2008.03.013 Contents lists available at ScienceDirect Marine Geology journal homepage: www.elsevier.com/locate/margeo