The correct estimation of set-up is very important to evaluate coastal hazard and to design coastal structures. In this paper, we derived a mathematical expression for wave set-up in the context of random waves. The solution to this expression assumes straight, parallel depth contours and constant average flow parameters in the longshore direction. We then investigated the effect of different types of sea state taking account of different frequency spectrum and spreading function assumed in the expression on estimates of wave set-up. We found the set-up was highly influenced by the frequency spectrum used. Finally, we applied this expression to estimate set-up values at locations in Italy and in the United States using buoy data provided by ISPRA (Istituto Superiore per la Protezione e la Ricerca Ambientale) and NDBC (National Data Buoy Centre).
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