Verification and modification of empirical formulas for computing wave shoaling

During the past decades, various empirical formulas have been proposed for computing shoaling wave heights. There are no papers describing the applicability and accuracy of various empirical formulas, based on a wide range of wave conditions. The main objective of this study is to examine the accuracy of 10 empirical formulas, together with the often-used formulas (Shuto's and linear wave formulas), for computing regular wave shoaling. Seventy-one cases of measured shoaling wave heights from six sources of published experimental data were used to examine the formulas. It was found that the Shuto's formula gives the best predictions, while the linear wave formula gives reasonable overall predictions of shoaling wave heights. The best empirical formula has better accuracy than that of the linear wave formula, but has slightly less accuracy than that of Shuto's formula. However, the best empirical formula contains an implicit equation, which has to be solved by an iteration method and may not be convenient in practice. To simplify the calculation, the best empirical formula was modified to an explicit form. The new formula has slightly better accuracy than that of Shuto's formula.