Variability of Multibar Profiles in Terms of Random Sine Functions

A new concept of statistical analysis of multibar profiles is presented in the study; vertical residuals about a reference Dean curve are treated as sine functions with random amplitude (envelope), bar wave number and phase. The data set consists of 71 transects, collected from 1964 to 1994 by the Polish Academy of Science, Institute of Hydro-Engineering, Coastal Research Facility at Lubiatowo (CRF), situated some 80 km northwest of Gdańsk. The morphology of the nearshore zone there is typical of the south Baltic Sea and is characterized by a mild slope (m= tan α≈ 1.0) and fine sand sediment D₅₀= 0.22 mm). Because the Baltic Sea is semiisolated from the Atlantic, no tides can be observed, and beach profiles are mostly subject to wave attack and storm surges. The envelope of random sine functions (RSF) describes mean deviation about a Dean reference profile with respect to its location on the profile. Thus, it depicts vertical cross-shore variability, which may be useful for determination of wave breaking zones where the profile variability is especially intensive (envelope peaks). Bar wave numbers characterize bar lengths and distances between bars along the profile. Multibar cross-shore profiles can thus be analysed by means of only two parameters, based on very simple RSF methodology. The random sine function method poses an alternative in multibar beach profile description with respect to empirical orthogonal functions, because it seems to be less ambiguous in many cases. The results of the study contain empirical relationships, which depict bar lengths on a multibar profile, and vertical deviations about the reference profile, which can be regarded as assessment of bar height.