Determination of Semi-Empirical Models for Mean Wave Overtopping Using an Evolutionary Polynomial Paradigm

Corrado Altomare,Daniele B Laucelli,Xavi Gironella,Hajime Mase

doi:10.3390/jmse8080570

Abstract

The present work employs the so-called Evolutionary Polynomial Regression (EPR) algorithm to build up a formula for the assessment of mean wave overtopping discharge for smooth sea dikes and vertical walls. EPR is a data-mining tool that combines and integrates numerical regression and genetic programming. This technique is here employed to dig into the relationship between the mean discharge and main hydraulic and structural parameters that characterize the problem under study. The parameters are chosen based on the existing and most used semi-empirical formulas for wave overtopping assessment. Besides the structural freeboard or local wave height, the unified models highlight the importance of local water depth and wave period in combination with foreshore slope and dike slope on the overtopping phenomena, which are combined in a unique parameter that is defined either as equivalent or imaginary slope. The obtained models aim to represent a trade-off between accuracy and parsimony. The final formula is simple but can be employed for a preliminary assessment of overtopping rates, covering the full range of dike slopes, from mild to vertical walls, and of water depths from the shoreline to deep water, including structures with emergent toes.

Highlights

Wave overtopping occurs when sea waves run up coastal defenses, reach their crest, and flow over it
The mean overtopping discharge depends on local wave conditions and on the layout and main features of the coastal defense, such as slope of the seaward face ([12]), slope of the foreshore before the defense ([13]), structural crest freeboard ([12,14]), presence of storm walls ([15]), presence of a berm ([16]), blocks or any artificial element on the surface of the structure that might increase its roughness to the wave run-up ([17]), etc
The search for a unified formula for wave overtopping assessment for smooth sea dikes and vertical walls, including cases with zero freeboard and emergent toe, is facilitated by employing a data-driven approach, namely Evolutionary Polynomial Regression (EPR), which can be freely downloaded on http://www.idea-rt.com/products-our-job/epr-moga-xl

Summary

Introduction

Wave overtopping occurs when sea waves run up coastal defenses, reach their crest, and flow over it. Overtopping can be characterized in terms of individual discharges and volumes or flow properties, such as velocities and depth, of each wave that will eventually overtop the coastal structures. The crest level of any coastal structure is usually defined to limit the mean or average overtopping discharge below certain thresholds. The mean overtopping discharge depends on local wave conditions (wave height, wave period, water depth) and on the layout and main features of the coastal defense, such as slope of the seaward face ([12]), slope of the foreshore before the defense ([13]), structural crest freeboard ([12,14]), presence of storm walls ([15]), presence of a berm ([16]), blocks or any artificial element on the surface of the structure that might increase its roughness to the wave run-up ([17]), etc. Both deep-water wave height and period (Hm0,o and Tm−1,0,o) and local wave characteristics (Hm0,t and Tm−1,0,t) are indicated. Maasr.pSrcoi.vEendg. t2o02s0h, 8o,wx FbOeRttPeErEpReRrfEoVrImEWance for wave overtopping predictions for a different kind of3woaf 2v4e spectra (e.g., single or double peak spectrum), as detailed in [18]

Methods

Findings

Discussion

Conclusion