## 1 Introduction
### Technical Background  
Wave overtopping can strongly influence the overall response of coastal defenses. In the last few decades, several studies have been carried out with the aim to investigate the overtopping phenomenon, but, at the present, few of them have analyzed the strategies to reduce the wave overtopping for existing infrastructures or new ones designed to impede the sea level rise [28; 29]. Conventional crown wall geometries are shown in Figure 2. The vertical wall is frequently adopted to reduce the overtopping discharge rate (Figure 2a) [30; 31]. The vertical face is sometimes substituted by a sloping ramp to limit the impulsive wave forces (Figure 2b). However, this solution leads to a worse hydraulic performance in terms of overtopping volumes. Figure 2c shows a seaward curved wall, which allows us to contain the overtopping discharge rate, but, at the same time, its behavior is characterized by the occurrence of relevant uplift pressures weakening the overall structure stability. Upgrading an intuition from the past (see the carved Breakwater [31] introduced by Phoenicians) a composite seawall consisting in the realization of a reservoir between the seaward vertical wall and the sloping ramp (Figure 2d) has been proposed for some recent coastal defenses [32; 33]. These nonconventional structures were demonstrated to be characterized by a high hydraulic and structural performance and an economic viability. The reservoir is often equipped with a drainage system providing an uplift pressure saving. In some cases, a parquet on the upper crown wall [27] is conveniently installed. This parquet is aimed to decrease the wave overtopping at the rear side of the structure for very extreme wave conditions. The hydraulic and structural behavior of seawalls and breakwaters equipped with parapets have been not massively analyzed in the technical literature. Most experimental studies described specific case studies rather than generic investigations. [PERSON] et al. [34] considered different layouts of modified-typed vertical breakwaters, such as a shifted sloping parquet and a caisson  
Figure 2: Standard defense structures to reduce the wave overtopping: (**a**) vertical seawall; (**b**) sloping ramp seawall; (**c**) seaward curved wall; (**d**) vertical seawall equipped with a reservoir and a landward sloping ramp. with rubble mound protection. The best efficiency in the overtopping reduction was achieved by introducing a recurved parquet at the crest of the vertical front wall. In [35], the influence of a small deflector parquet installed on the top of a vertical wall was analyzed. It was demonstrated that the overtopping discharge rate was strictly related to the dimensionless freeboard. [PERSON] et al. [36] carried out a set of overtopping measurements on different types of composite walls at small and large scales, and the experimental results were elaborated to derive a generically valid method for the prediction of the overtopping reduction. This study also provided a prediction method in a \"decision chart\" taking into account the inclination of the parquet. In [37], the reduction of wave overtopping of a smooth dike was investigated by installing a wave return wall, and lately [PERSON] at al. [38] evaluated the overtopping effect of several crest layouts, as a storm wall with or without nose, a promenade and a combination of both solutions, all of which to be mounted at crest level of the dike. Various recurred parapets, with different recurred extensions and angles, were tested by [39]. The results of such investigation confirmed the expected reduction of the overtopping discharge rate by increasing the angle of recurve. Despite the various design solutions, none of the aforementioned studies could be straightforwardly applied to the OBREC because of its specific geometry and hydraulic behavior. For this reason, the optimization of the OBREC geometry required a preliminary analysis based on physical model tests at the Aalborg University (Denmark) in 2012 and 2014. In particular, [PERSON] et al.