Parametric modelling of nearshore wave reflection

Abstract The importance of wave reflection on nearshore hydrodynamics has recently been acknowledged by an increasing number of studies, yet it is difficult to simulate by the conventional parametric wave transformation models widely used in coastal engineering practice. Here, we propose a simple and efficient semi-empirical method to deal with this issue. The proposed method considers wave reflections resulted from both the underwater sloping bottom and the shoreline. The former is represented by a local underwater reflection-induced energy transfer term, based on a similarity analysis of the bulk wave reflection from equivalent sloping steps. The latter is calculated as the shoreline boundary condition by utilizing a simple empirical formula of wave reflection coefficient for an emerged coastal structure. Model verifications against the previous theoretical/empirical formulas, experimental data and numerical results suggest a promising predictability of the proposed method for the cross-shore reflected wave height transformation with various bathymetry configurations. Three different formulas of the bulk reflection coefficient for an underwater sloping step are tested and compared, indicating the importance of considering slope effects in these formulas. Model results also suggest that wave reflection along a steep beach profile can be quantitatively comparable to the shoreline reflection, and it is important to include reflections of both sources in numerical modelling. The simple method can be extended and incorporated into the existing operational parametric wave models. It serves as a possible approach to simulate wave reflection with low computational demand and reasonable accuracy, and to include wave reflection influences in studying coastal processes on a broad range of time and spatial scales.