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. The phenomenon of wave set-up may substantiallycontribute to the formation of devastating coastal flooding in certaincoastal areas. We study the appearance and properties of empiricalprobability density distributions of the occurrence of different set-upheights on an approximately 80 km long section of coastline near Tallinn inthe Gulf of Finland, eastern Baltic Sea. The study area is oftenattacked by high waves propagating from various directions, and the typicalapproach angle of high waves varies considerably along the shore. Thedistributions in question are approximated by an exponential distributionwith a quadratic polynomial as the exponent. Even though different segmentsof the study area have substantially different wave regimes, the leadingterm of this polynomial is usually small (between −0.005 and 0.005) andvaries insignificantly along the study area. Consequently, the distributionof wave set-up heights substantially deviates from a Rayleigh or Weibulldistribution (that usually reflect the distribution of different waveheights). In about three-quarters of the occasions, it is fairly wellapproximated by a standard exponential distribution. In about 25 % of thecoastal segments, it qualitatively matches a Wald (inverse Gaussian)distribution. The Kolmogorov–Smirnov test (D value) indicates that theinverse Gaussian distribution systematically better matches the empiricalprobability distributions of set-up heights than the Weibull, exponential, orGaussian distributions.

Variability of distributions of wave set-up heights along a shoreline with complicated geometry