This work focuses on the multi-scale variability of beach profiles. This includes the spatial variability over a range of scales of surveyed beach profiles and the complex temporal variability of beach elevation at given positions along the profile. The aims of this work are to characterize the variability of beach profiles in both time and space, to identify the predominant spatial and temporal patterns of beach profile changes, to identify the extreme profile changes due to infrequent storms/storm groups, to understand the nature of beach profile change in depth, to quantify the non-stationarity of beach profile and to provide insight into the prediction of beach profiles. This thesis includes a critical literature review of the existing profile models, such as numerical and data-driven models, to predict beach profiles. Particular focus is on the data-driven models since they characterize the beach in a site-dependent manner. The main weakness of the existing data-driven approaches is that many of the techniques assume stationarity and yet the processes in question are non-stationary, which necessitates more advanced techniques for investigating the variability of beach profiles. Hence in this thesis the wavelet technique is introduced, which is a relatively new technique. It is also shown how the use of a wavelet basis for decomposing the profile signals spatially allows a more satisfactory value for the depth of closure associated with a data set to be defined. Particular interests are in the beach profile data from the Field Research Facility (FRF) at Duck, North Carolina, USA. The field data and previous works by other researchers are introduced and preliminary studies are conducted including the interpolation of data and the empirical orthogonal function (EOF) analysis. A connection is established between EOF and wavelet analysis. In addition to the identification of basic patterns of beach profile changes, emphasis is given to the non-stationary investigation of beach profile changes in both time and space locally. In this way, the infrequent events are identified at different temporal scales. The responses of beach profile changes to different wave/storm conditions are discussed. The intermittent character of beach profile change is displayed in both time and space, providing much insight to the argument by Southgate and Moller (2000). Also, the depth of closure is presented by analysing the local components of wavelet variance in space, which is scale-dependent. The results agree with Larson and Kraus(1994). The wavelet analysis is validated on the beach profile data at the Coastal Research Station (CRS), Lubiatowo, Poland. Focus is on the spatial variability across the beach profile. Due to the multi-bar system, the spatial scale contents of beach profile changes at Lubiatowo are more complicated than Duck. The predominant spatial scales indicate that wave breaking may be the major factor of bar formation at this site. This is consistent with Pruszak et al. (1997).

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