Multi-scale variability of beach profiles at Duck: A wavelet analysis

Beach profiles have been observed to change over a range of spatial and temporal scales; however techniques for quantifying this variability have not been fully established. In this paper, a wavelet technique is introduced as a method to study the multi-scale variability of beach profiles. The beach profile data comprising a 22-year time series surveyed at the US Army Corps of Civil Engineers Field Research Facility (FRF) at Duck are analysed using the adapted maximal overlap discrete wavelet transform (AMODWT). The analysis successfully identifies strong local features in the variability of beach profiles in time and space separately that cannot be isolated by traditional statistical methods. The analysis of spatial wavelet variances provides a new means of investigating the depth of closure. Analysis of variances by temporal scales shows that the combined effects of several temporal scales with one or two dominant scales can be seen at particular points across profiles whilst the dominant temporal scales are different at different portions of the profiles. The method allows for the extremely nonstationary behaviour of beach profile to be analysed into separate frequency bands that can facilitate the interpretation of morphological changes in terms of physical processes.

[1]  Relationship between beach profiles and waves at Duck, North Carolina, determined by canonical correlation analysis , 2000 .

[2]  Donald P. Percival,et al.  On estimation of the wavelet variance , 1995 .

[3]  Magnus Larson,et al.  Forced and self-organized shoreline response for a beach in the southern Baltic Sea determined through singular spectrum analysis , 2001 .

[4]  Praveen Kumar,et al.  Wavelets in Geophysics , 1994 .

[5]  R. M. Lark,et al.  Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform , 2001 .

[6]  Praveen Kumar,et al.  Wavelet Analysis in Geophysics: An Introduction , 1994 .

[7]  Peter Guttorp,et al.  Multiscale detection and location of multiple variance changes in the presence of long memory , 2000 .

[8]  Robert J. Nicholls,et al.  Evaluation of depth of closure using data from Duck, NC, USA , 1998 .

[9]  Michele Capobianco,et al.  Analysis of field data of coastal morphological evolution over yearly and decadal time scales. Part 2 Non-linear techniques , 2003 .

[10]  Peter Guttorp,et al.  Long-Memory Processes, the Allan Variance and Wavelets , 1994 .

[11]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[12]  David O. Smallwood,et al.  Characterization and simulation of gunfire with wavelets , 1998 .

[13]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  M. Merrifield,et al.  Detecting Propagating Signals with Complex Empirical Orthogonal Functions: A Cautionary Note , 1990 .

[15]  G. Różyński.  Long-term shoreline response of a nontidal, barred coast , 2005 .

[16]  Michele Capobianco,et al.  Variability of shore and shoreline evolution , 2002 .

[17]  Nathaniel G. Plant,et al.  Analysis of the scale of errors in nearshore bathymetric data , 2002 .

[18]  H. N. Southgate,et al.  Analysis and modeling of field data on coastal morphological evolution over yearly and decadal time scales. Part 1: Background and linear techniques , 2003 .

[19]  R. Nicholls,et al.  Storm-driven variability of the beach-nearshore profile at Duck, North Carolina, USA, 1981-1991 , 1998 .

[20]  J. Iyama,et al.  Application of wavelets to analysis and simulation of earthquake motions , 1999 .

[21]  D. Stauble,et al.  SEDIMENT DYNAMICS AND PROFILE INTERACTIONS: DUCK94 , 1997 .

[22]  Kathelijne Mariken Wijnberg,et al.  Intersite comparison of interannual nearshore bar behavior , 2003 .

[23]  I. Daubechies,et al.  Wavelets on the Interval and Fast Wavelet Transforms , 1993 .

[24]  R. Reese.  Geostatistics for Environmental Scientists , 2001 .

[25]  Dominic E. Reeve,et al.  Comments on “Forced and self-organized shoreline response for a beach in the southern Baltic Sea determined through singular spectrum analysis” [Coast. Eng. 43 (2001) 41–58] , 2002 .

[26]  H. N. Southgate,et al.  Fractal properties of coastal profile evolution at Duck, North Carolina , 2000 .

[27]  Nicholas C. Kraus,et al.  Temporal and spatial scales of beach profile change, Duck, North Carolina , 1994 .

[28]  R. Nicholls,et al.  A Conceptual Fairweather-Storm Model of Beach Nearshore Profile Evolution at Duck, North Carolina, U.S.A. , 1995 .

[29]  D. Inman,et al.  Description of seasonal beach changes using empirical eigenfunctions , 1975 .

[30]  W. Birkemeier.  Time Scales of Nearshore Profile Changes , 1984 .

[31]  R. Hallermeier,et al.  A PROFILE ZONATION FOR SEASONAL SAND BEACHES FROM WAVE CLIMATE , 1980 .