3.1. Description and Domain with Model Set
XBeach is a two-dimensional, depth-averaged (i.e., 2DH) numerical model that integrates fluid dynamics and morphodynamic processes to simulate wave propagation and morphological changes under short-term storm wave conditions. The storm event in the study area was modeled using XBeach (1.23.5527) and the surfbeat mode (XBSB), specifically designed to simulate hydrodynamics and morphological changes in narrow areas, such as beaches, dunes, and barrier islands, during storm wave events. The XBSB model calculates the hydrodynamics (shortwave, longwave, and roller energy) with wave and water-level inputs as boundary conditions. Subsequently, it simulates the morphodynamics, including sediment transport and the resulting bed-level changes.
Figure 5a,b show the orthogonal grid and pre-depth data used for the XBeach modeling. Depth data were provided by an external agency and utilized in this study. The data surveyed on 23 August 2022, before the storm, underwent precise calibrations with an error margin of approximately 1 m. Depth measurements were conducted from 0 to 5 m using a single beam, whereas depths beyond this range were surveyed using a multibeam approach. Owing to the essential nature of data correction, a calibration was performed using DGNSS, a motion sensor, and a gyrocompass. Additionally, tidal and sound speed corrections were implemented to minimize the data errors. The grid resolution was configured to increase the density closer to the nearshore, thereby optimizing the simulation of the morphological changes within the surf and swash zones. Conversely, the grid size was proportionally enlarged seaward. Specifically, the cross-shore grid size ranged from 3 to 20 m, while the longshore grid maintained a consistent resolution of 10 m, resulting in a 201 × 201 grid configuration. The structures, including revetments, were designated as non-erodible layers. The wave boundary conditions were defined using the time-varying JONSWAP spectrum based on the observation data, incorporating the parameters (Hs, Tp, and Dp) outlined in
Section 2.2. Temporal variations in the water level were derived from the tide data in
Section 2.2, serving as the water level boundary conditions. The modeling period spanned from 29 August to 7 September, following the UAV observational data. For the computational efficiency, significant wave heights of less than 1 m were excluded. The morphological acceleration factor (morfac) was set at 10.
3.2. Parameter Calibration
The default parameter settings of XBeach were calibrated for North Sea wave conditions off the Dutch coast and were specifically designed to simulate the collapse of barrier islands during storms. Consequently, the offshore sediment transport and morphological changes were overestimated under typical beach conditions. To address this limitation, ongoing discussions focus on various parameter calibration methods [
3,
4,
12,
13]. In this study, a trial-and-error approach was employed based on the parameters proposed in previous studies [
5] along with additional parameters, with the aim of simulating overwash during storm events.
Various formulations were embedded in the XBeach model, allowing for an effective simulation of the morphological changes specific to the study area. Among these, the discussions on sediment transport equations are extensive. XBeach offers sediment transport formulations from Soulsby–Van Rijn [
14], van Thiel de Vries–Van Rijn [
9,
15,
16], and Van Rijn [
17]. A primary distinction between the widely used Soulsby and van Thiel de Vries–Van Rijn equations is that Soulsby employs a drag coefficient to determine the equilibrium sediment concentration, which is absent from van Thiel de Vries–Van Rijn. Additionally, the van Thiel de Vries–Van Rijn equation distinguishes between currents and waves in its calculation of critical velocity, whereas Soulsby does not. Although each formulation has its strengths, the effectiveness largely depends on the features of the coastal environment. For instance, De Vet et al. compared the Soulsby–Van Rijn and van Thiel de Vries–Van Rijn formulations, suggesting that the latter provided more credible results [
18]. The van Thiel de Vries–Van Rijn equation was noted to represent breaching more effectively and overwashing than the Soulsby equation, which overestimated the erosion rates. Conversely, Craig et al. [
19] favored Soulsby in modeling the microtidal, wave-dominated hydrodynamic environment of the Upper Texas Coast (UTC), effectively simulating phenomena, such as collision, overwash, and inundation. Similarly, Orzech et al. [
20] showed commendable Brier Skill Score results for Monterey Bay using the XBeach 2DH model. Monterey Bay, located in California, is characterized by its mild alongshore currents, rip channel bathymetry, and tidal range of approximately 1.6 m, features that resonate closely with the Songjeong Beach studied in this research. Consequently, this study aimed to simulate sediment transport by employing the Soulsby equation.
Within the XBeach model, two formulations related to shortwave breaking exist: the Roelvink et al. and Daly formulas. The Roelvink equation was used by default for all the statistical analyses. This equation is based on an empirical formula that incorporates the breaking coefficient (gamma) and the ratio of the wave height to the water depth. However, Daly et al. observed that this equation tended to underestimate the wave energy dissipation when the water depth increases rapidly. In response to this result, Daly introduced the parameter gamma2, which allowed for a more precise determination of wave breaking, even in areas with sharp changes in the water depth. Furthermore, when dealing with depths that have a plane slope instead of steep inclines, the differences in the results generated by the two formulas are negligible. In this study, based on the previous research, specific parameters and their associated formulas were adopted, and the Daly equation was used for the model setup.
Based on this, the gamma and gamma2 parameters were employed, and the waveform parameters related to the wave skewness and asymmetry, which were closely related to sediment transport, were calibrated. XBeach offered the two waveform equations provided by Ruessink et al. [
21] and van Thiel [
9]. Both computed skewness and asymmetry. The formula of Ruessink et al. suggests the Ursell number parameter, which is based on over 30,000 field observations of orbital skewness and asymmetry collected under non-breaking and breaking conditions. Based on the significant wave height, wave period, and water depth, they reported that the skewness and asymmetry were efficiently represented. Another approach involved the equation proposed by van Thiel et al., which was an extension of the wave-shaped model presented by Rienecker et al. [
22]. This model describes the shortwave shape as a weighted sum of eight sine and cosine functions. Skewness and asymmetry were then represented based on the computed near-bed shortwave flow velocity using this model. However, it remains unclear which of the two equations is more accurate [
11]. In this study, the default equation provided by van Thiel was used.
Several studies discuss the effects of skewness and asymmetry on sediment transport [
11,
13,
23]. According to van Thiel et al. [
9], Stokes waves exhibit higher onshore flow velocities than offshore waves. This implies that the sediment movement is more pronounced during the wave crest than during the wave trough. Consequently, skewness and asymmetry influence the Eulerian velocities through an additional onshore sediment advection velocity, denoted as
. Using skewness and asymmetry,
can be represented as:
where
is a coefficient related to the phase shift of the intrawave sediment concentration, flow, and skewness.
is the coefficient pertaining to the phase shift between the flow and the suspended sediment for asymmetry. Assuming that
and
are equivalent, they can be expressed as
, and the equation can be summarized as:
In XBeach, facua is denoted as a coefficient associated with the phase shift between intrawave sediment suspensions and orbital flow. In previous studies [
5], facua was used. A comparison with the sets of facSk and facAs was conducted in this study. Based on these observations, it was suggested that the profile shapes in the shoaling and breaker zones were significantly influenced by facSk. An increase in fasSk was linked to an increase in wave skewness, which was associated with an increase in offshore sediment fluxes, whereas [
24] the cross-shore profiles in the surf and swash zones were believed to be affected by facAs. As facAs increases, the asymmetry in the waves is enhanced, leading to an increase in onshore sediment transport. Based on this, the set parameter values and their ranges have been summarized in
Table 3.
Observational UAV data were used to calibrate the parameters. Comparisons between the observational and model values were only performed in overlapping areas, which, owing to the characteristics of the UAV, were confined to the subaerial region [
7,
19]. Based on this, the simulation skill proposed by Gallagher et al. (1998) [
25] could be employed to assess the accuracy of the elevation difference obtained from the UAV and model output. This skill is defined as follows:
where
N is the number of data points (i.e., the number of grids) in the overlapping section between the UAV’s pre- and post-data and the output of the model.
denotes the observed bed-level change in
, whereas
is the modeled bed-level change at point
. A skill value of 1 indicated a perfect match between the model predictions and observed data, indicating optimal accuracy. A skill of 0 suggested that the model’s accuracy was equivalent to random or base-level predictions, whereas a negative skill indicated that the model’s predictions were less accurate and that it performed poorly (
Table 4). Furthermore, the determination of the mean error allowed us to distinguish between biases resulting from systematic differences in the model outcomes and random variations. The equations for this are as follows:
Where
is the post-elevation of the model in cell
and
is the post-elevation of the observation data. A positive bias indicated that the model predicted higher elevations than those observed, whereas a negative bias signified that the model predicted lower elevations than those observed (
Table 4).