Simulating storm waves in the nearshore area using spectral model: Current issues and a pragmatic solution

Highlights

• Spectral wave models are likely to underestimate storm wave heights in the nearshore.

• Wave energy dissipation by depth-induced breaking is overestimated.

• An alternative parameterization of depth-induced breaking models is proposed.

• Wave setup can be underestimated by 100% with inadequate breaking parameterizations.

Abstract

Short waves are of key importance for nearshore dynamics, particularly under storms, where they contribute to extreme water levels and drive large morphological changes. Therefore, it is crucial to model accurately the propagation and dissipation of storm waves in the nearshore area. In this paper, field observations collected in contrasted environments and conditions are combined with predictions from a third-generation spectral wave model to evaluate four formulations of wave energy dissipation by depth-induced breaking. The results reveal a substantial over-dissipation of incident wave energy occurring over the continental shelf, resulting in a negative bias on significant wave height reaching up to 50%. To overcome this problem, a breaking coefficient dependent of the local bottom slope is introduced within depth-induced breaking models in order to account for the varying degrees of saturation naturally found in breaking and broken waves. This approach strongly reduces the negative bias observed in the shoreface compared to default parameterizations, yielding significant improvements in the prediction of storm waves. Among the implications of this study, our new parameterization of the breaking coefficient results in systematically increased predictions of the wave setup near the shoreline compared to the default parameterization. This increase reaches a factor 2 for gently sloping beaches.

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 $Q_b$) 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 $Q_b$ and numerous studies further aimed at improving the parameterization of $Q_b$ 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.