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

Abstract

Abstract. The phenomenon of wave set-up may substantially contribute to the formation of devastating coastal flooding in certain coastal areas. We study the appearance and properties of empirical probability density distributions of the occurrence of different set-up heights on an approximately 80 km long section of coastline near Tallinn in the Gulf of Finland, eastern Baltic Sea. The study area is often attacked by high waves propagating from various directions, and the typical approach angle of high waves varies considerably along the shore. The distributions in question are approximated by an exponential distribution with a quadratic polynomial as the exponent. Even though different segments of the study area have substantially different wave regimes, the leading term of this polynomial is usually small (between −0.005 and 0.005) and varies insignificantly along the study area. Consequently, the distribution of wave set-up heights substantially deviates from a Rayleigh or Weibull distribution (that usually reflect the distribution of different wave heights). In about three-quarters of the occasions, it is fairly well approximated by a standard exponential distribution. In about 25 % of the coastal segments, it qualitatively matches a Wald (inverse Gaussian) distribution. The Kolmogorov–Smirnov test (D value) indicates that the inverse Gaussian distribution systematically better matches the empirical probability distributions of set-up heights than the Weibull, exponential, or Gaussian distributions.

Sea Level Dynamics and Coastal Erosion in the Baltic Sea Region

“…Wave set-up refers to a wave-induced increase in the mean water level caused by the release of momentum from the dissipation of a long sequence of breaking waves and swash is caused by the run-up of single waves on the beach (Melet et al, 2018). For example, for some coasts in the Gulf of Finland (Soomere et al, 2013;Soomere et al, 2020) and along the shores of the western Estonian archipelago (Eelsalu et al, 2014) potential wave set-up may reach values of up to 70-80 cm. Moreover, the shape of the shoreline and irregular bottom topography may strongly modify local wave conditions (Tuomi et al, 2012;Tuomi et al, 2014), and wave set-up and run-up may both have a strong influence on the level of the flooding and erosion at the shore (Dean and Bender, 2006).…”

“…This also applies to the modeling of wave properties as spatial resolutions of wave fields of about 500 m and even finer are necessary to account adequately for contributions of coastal processes such as wave set-up on total nearshore water levels (Pindsoo and Soomere, 2015;Pindsoo and Soomere, 2020). Moreover, there are indications that the empirical distribution of set-up heights in some coastal sections follows an inverse Gaussian distribution that substantially complicates the construction of joint probability distributions of different components of extreme water levels (Soomere et al, 2020). There is also a need to better understanding the mechanisms and the long-term changes (mean, frequency, variability) of seiches and meteotsunamis.…”

Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry

“…This was also shown by comparing the DT TG@SA cycle and DT SA@TG trends over a decadal time frame. Also, TGs are located at the coast, so they may also be influenced by other processes, such as wave set-up and set-down [81], which may not always be captured by the SA. This may suggest that TG may not be the ideal dataset to represent sea-level variation, especially with trend estimates.…”

“…For instance, at stations like Dirhami (#1) and Pori (#13), the TG trends are higher compared to the SA measurements, whereas at stations like Kolobrzeg (#5), they are lower. These variations may be attributed to persistent marine dynamics influencing coastal areas, such as surface waves causing wave set-up and set-down [81]. However, further investigation is required to fully understand and address these discrepancies in future studies.…”

Diverse erosional indicators along a rapidly retreating Holocene strandplain margin, leeward Hiiumaa Island, Estonia

“…The coastline of Estonia, especially along its northern margin, represents ideal field sites for such a study due to the combination of: 1) the functionally non-tidal basin; 2) the recent isostatic uplift, and 3) the abundant sediment supply resulting in prograded strandplains of various orientations (Orviku et al 2003;Kont et al 2007;Tõnisson et al 2011;Rosentau et al 2013;Muru et al 2018;Tõnisson et al 2018;Suursaar et al 2019Suursaar et al , 2022Rosentau et al 2020;Soomere et al 2020). The latter contain a rich archive of erosional signatures due to the net accretionary mode facilitated by uplift, which is often termed "forced regression".…”