Simulating storm waves in the nearshore area using spectral model: Current issues and a pragmatic solution
Introduction
As storm waves contribute to extreme water levels (Dodet et al., 2019) and drive large morphological changes (Wright and Short, 1984, Coco et al., 2014, Castelle et al., 2015), they are of paramount importance for coastal hazards. In a context of sea-level rise associated with climate change and a continuous increase of coastal populations (Neumann et al., 2015), it is essential to model accurately the propagation, transformation and dissipation of wind-generated surface gravity waves (hereafter short waves) in the nearshore area, in particular during storms.
Regional applications of fully-coupled ocean circulation and spectral wave numerical models have become widespread for all types of applications, ranging from operational predictions to engineering or research purposes (e.g. Bidlot et al., 2002, Boudière et al., 2013, Guérin et al., 2018). However, the ability of these models to accurately simulate wave-induced hydrodynamics during storms in the nearshore area remains uncertain, which is partly explained by the scarcity of field observations required to verify numerical models, especially in the surf zone. In deep water, the parameterizations of the physical processes contributing to wave generation by the wind and its subsequent propagation and transformation have benefited from decades of theoretical and practical developments (e.g. Hasselmann, 1962, Hasselmann and Hasselmann, 1985, The Wamdi Group, 1988, Cavaleri et al., 2007, Ardhuin et al., 2010 and many others). In the nearshore area, dominant processes such as the adiabatic triad interactions and the dissipation due to depth-induced wave breaking remain heavily parameterized in such models, to the point that the current solutions are sometimes referred to as “engineering solutions” (e.g., see Cavaleri et al., 2007 for a relatively recent review on spectral wave models and the parameterization of the different physical processes involved). Alternatively, modelling chains that combine phase-averaged model forcing local phase-resolving models over a specific area (e.g., see Postacchini et al., 2019) permit to describe the key processes associated with wave transformation in the nearshore while requiring little parameterizations. However, such application remains possible only locally as it is quite computationally expensive, which prohibits this approach for operational applications at the regional scale.
Close to shore, short waves undergo complex transformations and dissipate their energy mostly through depth-induced breaking. In the absence of universal consensus on the criteria for wave breaking and on the spectral distribution of energy dissipation, it is more convenient to model the macroscale effects in terms of the averaged loss of energy. Several formulations have been proposed in the literature to compute the average energy dissipation rate in a Rayleigh-distributed wave field, based on the cross-shore conservation of the bulk wave energy flux. Many of these formulations have subsequently been adapted to compute a corresponding source term for spectral modelling purposes. The underlying approach of depth-induced breaking models follows the seminal work of Le Mehauté (1962), in which the dissipation rate of a breaking (or broken) wave (hereafter referred to as a breaker) is approximated by that of a hydraulic jump of equivalent height (bore-based model). The average energy dissipation rate is obtained by applying the dissipation rate of a breaker to the fraction of breaking (or broken) waves in the original wave field. Therefore, the average energy dissipation rate is controlled by the computation of the fraction of breaking waves (hereinafter ) and a breaking coefficient, which is related to the degree of saturation of the breaker and hence controls its energy dissipation rate. Mostly, the different models differ in the formulation of and numerous studies further aimed at improving the parameterization of through ad hoc scalings with the local bed slope and/or local wave characteristics (e.g., see Salmon et al., 2015). However, the performance of these scalings remain uncertain at other sites (especially under storm waves) and admittedly lack physical grounds. In contrast, the breaking coefficient has received much less attention in such modelling approach; it is generally kept constant in both time and space, and is seen as a calibration factor. In contrast with these class of depth-induced breaking models, it is worth noting that an alternative approach was proposed by Filipot and Ardhuin (2012). These authors introduced a unified formulation for wave breaking from deep ocean up to the inner surf zone in which a dissipation term is computed for each wave scale based on the decomposition of the frequency spectrum introduced by Filipot et al. (2010). Although this formulation brought interesting insights and showed comparable predictive skills to those specific to deep or shallow water environments, it remains scarcely used especially in studies related to coastal applications.
This study provides a critical and objective assessment of four specialized depth-induced breaking models, which rely on state-of-the-art formulations of the fraction of breaking waves. These models are implemented within the spectral model WWM-III (Roland et al., 2012) fully coupled with a 2DH configuration of the circulation model SCHISM (Zhang et al., 2016). The model performances are assessed at two contrasting sites under high-energy conditions. The results with the default parameterizations show a systematic over-dissipation of the incident wave energy over the inner continental shelf, especially in high-energy conditions. In order to address the inherent limitations of the default parameterizations of these models, which typically consider breakers as fully saturated bores, a new parameterization of the breaking coefficient is introduced based on Le Méhauté’s original work (Le Mehauté, 1962).
The manuscript is organized as follows. The theoretical background on depth-induced breaking modelling in parametric models and its application to phase-averaged models is reviewed in Section 2. The two study cases and the model implementation are presented in Section 3. In Section 4, the different depth-induced breaking formulations with their default parameterizations are firstly tested, highlighting their poor predictive skills under high-energy conditions. Then, the performances of the adaptive parameterization of the breaking coefficient within the four models are assessed at the two sites considered here. The results of this study and their implications are discussed in Section 5 before the concluding remarks are provided in Section 6.
Section snippets
Energy dissipation rate of a broken wave
The analogy between turbulent bores (hydraulic jumps) and individual breakers is often used to compute the associated energy dissipation rate per unit span () (e.g., see Lubin and Chanson, 2017 for a recent review on these non-linear processes and their similitude). The expression for the energy dissipation rate per unit span by a bore is given by Stoker (1957): where is the water density, is the gravitational acceleration, is the
Methods
The present study is supported with field measurements from two study areas: the Oléron Island, France, and Duck, North Carolina. This section presents the two study cases, underlying their contrasting features. The model implementation and the result assessment methodology are subsequently described.
Wave forcing assessment
In nearshore application with barely no local wave growth due to weak local winds as during the two study cases considered here, wave transformation processes are mostly dissipative as the dominant source terms induce the dissipation of wave energy. Therefore it is essential to assess the wave forcing originating from WW3 application as it accounts for most of the energy income. For the case O10, WW3 results are assessed with offshore Biscay Buoy measurements (see Fig. 1a for its location). For
The origin of the over-dissipation obtained with default parameterizations
The results show an almost systematic over-dissipation of wave energy when using the default parameterizations of the four formulations for depth-induced breaking source terms. For both study cases, the relative importance of the energy dissipation rates due to wave breaking over all source terms was computed in order to get insight into the spatial variations and the local dominance of breaking processes. Variation rates corresponding to the source terms associated with the energy input from
Conclusions
In this study, the third generation spectral model WWM fully coupled with a 2DH configuration of the circulation model SCHISM was used to simulate nearshore dynamics under storm waves at two contrasting sites. The results show a substantial over-dissipation of wave energy by depth-induced breaking using four state-of-the-art formulations of the corresponding source terms. These results highlight the limitations of the default parameterization of the depth-induced breaking formulations.
CRediT authorship contribution statement
M. Pezerat: Conceptualization, Methodology, Software, Writing - original draft. X. Bertin: Conceptualization, Writing - review & editing, Supervision. K. Martins: Conceptualization, Software, Writing - review & editing. B. Mengual: Software, Writing - review & editing. L. Hamm: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
M. Pezerat is supported by a PhD fellowship from CDA La Rochelle and from the FEDER project DURALIT. The study of extreme sea states and wave setup is a contribution to the Chair Regional Project EVEX. K. Martins acknowledges the financial support from the University of Bordeaux, through an International Postdoctoral Grant (Idex, nb. 1024R-5030). Authors greatly acknowledge the Hydrographic and Oceanographic French Office (SHOM) for providing field observations acquired during the projects
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