Cross-shore beach profiles along Estonian coasts of the Baltic Sea are analysed from the viewpoint of the frequency of occurrence of convex sections that may support non-reflecting wave propagation and unexpectedly high run-up events. In total 194 beach profiles, measured in 2006–2011 at 16 locations, are examined by means of their approximation with the power function h(x) = Axb. About half of the profiles can be adequately approximated using a single power function. These profiles are almost all concave. The relevant exponents are clustered around b = 2/3 that is characteristic to the Dean’s Equilibrium Profile. The rest of the profiles can be divided into two sections, each of which is approximated by a power function. The underwater sections of such profiles predominantly match the Dean’s Equilibrium Profile. About 10% of the subaerial sections (about 7% of all examples) have the exponent close to b = 4/3, for which high run-up events are likely.
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