Practitioners often employ diverse, though not always thoroughly validated, numerical models to directly or indirectly estimate wave overtopping (q) at sloping structures. These models, broadly classified as either phase-resolving or phase-averaged, each have strengths and limitations owing to the physical schematization of processes within them. Models which resolve the vertical flow structure or the full wave spectrum (i.e. sea-swell (SS) and infragravity (IG) waves) are considered more accurate, but more computationally demanding than those with approximations. Here, we assess the speed-accuracy trade-off of six well-known models for estimating q, under shallow foreshore conditions. The results demonstrate that: i) q is underestimated by an order of magnitude when IG waves are neglected; ii) using more computationally-demanding models does not guarantee improved accuracy; and iii) with empirical corrections to incorporate IG waves, phase-averaged models like SWAN can perform on par, if not better than, phase-resolving models but with far less computational effort.

Most of the experience collected on wave overtopping is concentrated on emerged or zero-freeboard structures, and only few experiments are available on over-washed dikes. The experience on submerged crest conditions is principally related to rubble mound structures and limited to the wave reflection and transmission processes. The existing tools for the prediction of the average wave overtopping discharge (q) at dikes are therefore targeted to represent overtopped structures, leading to cautious estimates at over-washed dikes and unrealistic overestimations in case of catastrophic scenarios such as breached dikes. This paper proposes a new conceptual and practical method for the prediction of q that is valid for both over-washed and fully breached dikes. It consists of three physically-based formulae whose coefficients are fitted on a new numerical database of smooth structures under variable wave attack. The predictions are compared with the new numerical results and the data and the tools available from the literature, i.e. experimental data, formulae and neural network. The new method gives a more realistic representation of the overtopping and overflow processes, reducing significantly the overestimation in case of breaching and being at least as accurate as the existing tools in case of over-washing.