Analysis of Typhoon-Induced Wave Overtopping Vulnerability Due to Sea Level Rise Using a Coastal–Seawall–Terrestrial Seamless Grid System

Abstract

The vulnerability to coastal disasters resulting from storm surges and wave overtopping (WOT) during typhoon intrusions is significantly escalating due to rising sea levels. In particular, coastal seawalls constructed along the coast through engineered assessments are experiencing an increase in the frequency of WOT and associated flooding in proportion to the reduction in freeboard due to rising sea levels. This study employed a unified modeling system that combines an empirical formula for estimating WOT volumes with a numerical model simulating tides, waves, and storm surges. The analysis was conducted across the Northwest Pacific (NWP) Ocean, encompassing coastal seawalls and terrestrial regions, using an integrated seamless grid system, which utilized ADCIRC + SWAN + EurOtop, for the present day, 2050, 2070, and 2100 to investigate how vulnerability to WOT changes with sea level rise. The maximum envelope of WOT inundation results for three historical and two 100-year return period synthetic typhoons confirms that vulnerability to WOT intensifies with rising sea levels. The single-process integrated model applied in this study can serve not only for long-term coastal seawall protection design but also for the short-term early warning system for storm surges and WOT, contributing to immediate preparedness efforts.

1. Introduction

During typhoons, high waves caused via low pressure and typhoon movement induce surges, resulting in storm surges along coastal lowlands. However, these storm surges primarily affect natural coastal lowlands, and most of the engineered seawalls constructed in front of these areas effectively control this natural storm surge flooding. Nevertheless, a recurring issue is WOT flooding, which differs from storm surge inundation. It is characterized by high waves that overtop the seawall, even when the crest level of the seawall is lower than the sea level plus the height of the incoming waves, providing sufficient freeboard [1,2]. In other words, wave overtopped flooding represents a unique manifestation of a storm surge. This phenomenon occurs when wave energy concentrates on artificially protective barriers such as coastal seawalls, causing waves to overflow beyond sea level due to the runup phenomenon. This contrasts with the conventional understanding of storm surges, which typically involves the potential energy difference of seawater flooding low-lying areas, as often illustrated in the bathtub analogy. In Korea, over 54% of the coastline has already been fortified with engineered seawalls for coastal disaster prevention [3]. Such seawalls are recognized as a representative method of coastal disaster prevention, and they are commonly constructed in front of coastal cities worldwide.

Reducing coastal flooding risk requires a combination of measures to be taken, identified by van Dongeren et al. and Stokes et al. as PMP (prevention, mitigation, preparedness) [4,5]. Prevention is regarded as long-term engineering of hard or soft sea defense, mitigation can be applied as preventing coastal development or relocating coastal communities, and preparedness is a short-term proactive action including a near-real- or real-time early warning system (EWS) of a storm surge or WOT event. The ability to forecast coastal overtopping several days in advance allows authorities to prepare for an event, for example, through informing the type and location of emergency services that should be mobilized, or to prevent flood damage through informing where temporary flood defense should be deployed, as demonstrated by Stokes et al. [5]. They have developed and tested an efficient forecasting system for providing operational warnings up to three days in advance for the entire 1000 km coastline of southwest England, called SWEEP-OWWL. It is capable of predicting wave runup elevation and overtopping volumes along the energetic and macro-tidal coastline, featuring embayed, sandy, gravel, and engineered regions. Machine learning (ML) and artificial neural networks (ANNs) have been increasingly studied in WOT using the database of CLASH [1,6,7,8,9,10]; it is necessary to operate an EWS giving the exact time and location of the storm surge and WOT inundation for the vulnerable areas during storm events [11,12,13]. After the study by van Gent [9], for the neural network modeling on the WOT, Zanutitigh et al. [8] suggested an advanced scheme. Recently, Bieman et al. [6,7] applied a gradient boosting decision tree technique in training the CLASH database for WOT.

With rising sea levels, the frequency of both nuisance and extreme coastal flooding of WOT events is expected to increase in most places globally. In addition, real- or near-real-time forecasting of a storm surge and/or WOT is very important because reliable forecasts of WOT could considerably enhance a coastal community’s ability to prepare and mitigate the risk to life, property, and infrastructure during coastal flooding events, as demonstrated by Stokes et al. [5].

Xie et al. [14] constructed an integrated atmosphere–ocean–coast and overtopping–drainage modeling framework based on the coupled tide, surge, and wave model, SWAN + ADCIRC, to assess the risk and facilitate coastal adaptation and resilience to flooding in a changing climate in the northeastern USA. They revealed the reason for the WOT difficulties is a lack of field data of WOT at the seawalls to validate the model predictions. They pointed to the importance of the integrated tide, surge, wave, and flooding modeling framework to accurately predict the flooding due to WOT. However, the literature on the integrated atmosphere–ocean–coast–overtopping model of flooding due to WOT at coastal structures is limited [15,16,17,18], as they showed.

An event-triggered WOT model was developed via coupling ADCIRC + SWAN [17] and EurOtop [1]. Additionally, beach morphology prediction was carried out via coupling ADCIRC + SWAN and XBeach [19]. This modeling approach was applied when a typhoon approached a specific region of interest, such as the Ryukyu Islands, and was predicted to pose a significant threat to the target area, Busan, Korea [3,20]. The WOT model focused on engineered coastal seawalls along Marine City in Busan, while beach breaching and morphological changes were applied to Haeundae Beach, located near Marine City, as shown in Figure 1. In the previous studies conducted in 2016 and 2018, the reproducibility and predictive potential of wave overtopped flooding were analyzed using the combined ADCIRC + SWAN + EurOtop model. The model was implemented in an unstructured grid system, spanning from the NWP Ocean to the land hinterland of Marine City in Busan, which includes the front seawall. Marine City suffered severe wave damage during the invasion of Typhoon Chava in 2016. Since then, an EWS for typhoon-induced wave overtopped flooding was implemented and provided advanced warnings via YouTube (for typhoons Kong-rey in 2018, Haishen in 2020, and Hinnamnor in 2022 [21,22,23]).

This study was conducted not only for the purpose of the EWS but also to examine the vulnerability of WOT inundation to sea level rise (SLR) in the context of long-term protection concepts for 2050, 2070, and 2100, aiming to establish appropriate crest levels to prevent wave overtopped flooding. This approach was applied to Busan areas including Marine City and the adjacent Millak District, as shown in Figure 1. In this study, tide + surge + wave + WOT + inland were operated as a unified system, i.e., ADCIRC + SWAN + EurOtop, based on seamless unstructured grids from the regional NWP Ocean, where the typhoon genesis occurred to the subgrid scale of the inland regions of Marine City and Millak District in Busan, Republic of Korea.

2. Methods

In this study, based on the concept of protection, mitigation, and preparedness (PMP), long-term coastal flooding was simulated from a historical perspective.

2.1. SLR Scenarios and Interaction with Tide in WOT

To assess coastal flooding resulting from long-term SLRs in the Busan area, the target years of 2050, 2070, and 2100 were selected, and SLR values of 0.25, 0.44, and 0.82 m, respectively, were considered in accordance with Shared Socio-economic Pathways, SSP5-8.5 [24]. These SLR values not only increase the water depth in the offshore areas but also signify a relatively lower elevation of the coastal seawalls and the hinterland terrain at the land–sea boundary. In the numerical model ADCIRC used in this study, such changes in water depth and land elevation at various irregular grid points can be easily incorporated via applying the geoid offset option in the supplementary input files, allowing for straightforward consideration of the SLR effects. The SLR was added in the ADCIRC + SWAN model as geoid offset, thus not only adding the depth on the sea-side but also de-elevating the seawall crest level and land-side digital elevation model (DEM).

To simulate the ocean and land surface flows, the primary or modified partial differential shallow water equations were solved on a suitably discretized grid. Such numerical simulations have been widely applied in numerous studies and cases, and it is a common approach in recent years that simultaneously considers both ocean and land flooding, including rivers [25]. However, it is difficult to simulate tidal, storm surge, wave, and overtopping flooding simultaneously in a single numerical model due to the discontinuity in the grid system of the numerical model for protruding structures at the boundary of the sea and land, and the presence of mathematical singularities at harbor structures such as upright seawalls.

The WOT resulting from typhoon-induced storm surges is primarily influenced via the sea surface elevation at the front of the seawall. Therefore, it is essential to accurately replicate the tidal levels in fine detail, capturing the ever-changing sea surface. The coupling of tide and surge is meaningful in terms of the nonlinear interactions between two phenomena, not only in storm surge reproduction [26,27] but also in WOT [14,20]. According to the study by Xie et al. [14], the WOT discharge has five times the interaction between the tide–surge and waves; this increased the WOT rate fivefold, mainly due to the increased wave height at the toe of the seawall. Thus, it should be incorporated regardless of the magnitude of the tidal amplifications. In the case of the south coast of the Republic of Korea, to which the target area Busan belongs, categorized as meso- to micro-tidal areas, the tidal influence remains significant in tidal-surge simulations [27]. Hence, employing a detailed grid resolution that can faithfully represent tidal effects is imperative. This includes inputting the eight major tidal constituents at open boundaries. Moreover, the nonlinear interaction of tide and surge played an important role in surge height modeling [13,27] around the Korean coast. In this study, nodal factors at the target year accounting for the 18.6-year variation were incorporated.

2.2. Incorporating Empirical WOT Formulas

The integrated empirical formula for WOT, EurOtop, was initially published in 2007 [1], followed by a revised version in 2016 and a finalized version in 2018 [2]. Essentially, it describes wave behavior in relation to significant wave heights at the front of a structure. The improved version [2] is also based on empirical formulas derived from laboratory experiments. Since these experiments were conducted at a constant water level, they assume a fixed freeboard value, $R_c$, and calculate the total overtopped volume as an average WOT flow rate. However, the time-varying $R_c$ fails to account for the gradual decrease in freeboard during the storm’s impact time, especially when the sea level transitions from low to high tide, as observed during the storm surge in the case of Typhoon Chaba in 2016 [20]. This represents a fundamental limitation of EurOtop, which was tested in a laboratory under fixed water levels. In response, Pepi et al. [28] conducted laboratory WOT experiments with varying water levels, highlighting the existing limitations of EurOtop at fixed water levels and the need for corrections.

Most SLR and associated WOT modeling assumed that the sea surface elevation would not alter the tide and surge in the simulation. As demonstrated by Xie et al. [14], the timing of the storm wave occurrence is important in the reproduction of WOT; since waves are modulated via the water level, and the WOT mainly occurs during the rising and high water, a slight phase difference between the predicted water level and the observed data may result in a shift in the predicted WOT results. The ambient sea level and incoming wave conditions are calculated and renewed in the ADCIRC + SWAN coupled storm surge model every 10 min. The information on the water surface elevation (ζ) from ADCIRC, significant wave height ($H_s$), period ($T_p$), and the directions (Dir) from SWAN are input to the EurOtop module. [3,29]. Then, the overtopped rate (q) is calculated at every 0.1 s based on the WOT formula derived from EurOtop. Subsequently, the volume is allowed to propagate overland following the ADCIRC model with the wet–dry option, as illustrated in Figure 2.

So, in the hindcasting of the WOT in a previous study [20], during the rising water level, WOT strongly occurred, even though the total water surface elevation, i.e., the summation of the tide, surge, and significant wave height, did not meet the crest level of the seawall, i.e., there was still freeboard. The validity for the ADCIRC + SWAN coupling was verified in the relevant previous research, with an emphasis on the grid resolution effect [13], open boundary conditions, and some important parameter sensitivities [27].

Until now, simulating WOT in a unified grid system that encompasses the ocean, seawalls, and overland has been explored very restrictively. However, the efficiency of modeling both storm surges and WOT within a single grid system has been demonstrated [3,20,29], incorporating seawalls as the internal boundary between the marine and terrestrial domains via applying the empirical formulas from EurOtop, as shown in Figure 2. This method underwent validation through hindcasting, confirming its viability. Subsequently, this modeling approach was utilized, and the simulated information was disseminated to the public via YouTube as an EWS to provide notifications of the WOT risk in the Marine City area of Busan, Korea [21,22,23].

Basically, EurOtop defines the wave overtopping volume as a function of the dimensionless overtopping discharge $q/\sqrt{{gH}_{m0}^3}$ and the relative crest freeboard $R_c/H_{m0}$ for positive freeboard, as shown in the principal formula in Equation (1).

$$\frac{q}{\sqrt{g{H}_{m0}^3}}=a\exp \left[-{\left(b\frac{R_c}{H_{m0}}\right)}^c\right],$$

(1)

where $q$ is the mean overtopping discharge per meter structure width [m³/s per m], $H_{m0}^{}$ is the significant wave height [m], $R_c$ is the crest freeboard of structure [m], and $g$ is the gravity acceleration [m/s²]. When considering the influence factors such as the berm of a sloped seawall (${\gamma }_b)$, permeability and roughness of the cover material (${\gamma }_f)$, oblique wave attack (${\gamma }_{\beta })$, and the characteristics of a vertical wall (${\gamma }_v)$, the exponential function in the EurOtop basic Equation (1) is modified to account for these effects as follows, resulting in changes in the relative freeboard values.

$$\frac{q}{\sqrt{g{H}_{m0}^3}}=a\exp \left[-{\left(b\frac{R_c}{H_{m0}·{\gamma }_b·{\gamma }_f·{\gamma }_{\beta }·{\gamma }_v}\right)}^c\right]$$

(2)

The initial version [1] applied an equation where these relationships were coupled as an exponential function, with an exponent c = 1. However, in the revised version [2], this relationship was slightly modified, with c = 1.3. However, as mentioned in [2], the difference in the WOT volume between these two versions is not significant, especially when the relative crest freeboard $R_c/H_{m0}>0.5$, where they are almost the same. Therefore, continuity was maintained via applying the method that included all of the empirical formulas from the initial version, as established in previous research [3,20].

The WOT calculations were conducted using an integrated model that combines the empirical formula of EurOtop, incorporating tide, surge, and wave effects, and adding additional functions to ADCIRC v53. In previous research [3,20], all of the empirical formulae from the Eurotop [1] were taken into account. The entire EurOtop empirical equations, which cover most typical overtopping cases, including sloped armored or upright seawalls, were included in ADCIRC version 53. This allows automatic overtopping calculations to be conducted at every second with external sea level conditions from ADCIRC and the temporal wave height, periods, and incoming angle of waves [29].

Although Xie et al. [14] applied an integrated modeling system, their approach was not performed in a single framework. That is, it consisted of four components: (i) a tide, surge, and wave coupled hydrodynamic model SWAN + ADCIRC [30] spanning from the oceanic to nearshore region; (ii) a surf zone model; (iii) a WOT model [2]; and (iv) a drainage model to estimate the discharge from the basin behind the seawall. They intentionally introduced a foreshore surf zone and inland flows. However, such a combination is more appropriate in the case of coupled hazard analyses, such as when rain induced overland flows [25] with WOT inundations.

2.3. Typhoon Tracks Affecting WOT

In this simulation, typhoons that have affected the Busan area since the year 2000 and synthesized tracks for future wave overtopped flooding were considered. Typhoon wind fields, including historical typhoons like Maemi in 2003, Chaba in 2016, and Hinnamnor in 2022, as well as synthetic typhoons with a 100-year return period, which have been drawn from over 177,244 synthesized typhoons [31], as shown in Figure 3, were generated using the Tropical Cyclone Risk Model (TCRM [32]) [20,31]. These typhoons were considered in light of the significant impact they had on the respective locations. These factors were applied to simulate storm surges and wave overtopped flooding.

2.4. Discretization and Details in Computation

In this study, tide + surge + wave + WOT + inland were operated as a unified system, i.e., ADCIRC + SWAN + EurOtop, based on seamless unstructured grids from the Northwestern Pacific Ocean, where the typhoon genesis has occurred to the subgrid scale of the inland regions of Marine City and Millak District in Busan, Korea, as shown in Figure 4. A seamless grid, which covers from the NWP basin to the local overland area, has resolution ranges from 100 km in the deep basin to less than 5 m at the overland. The very fine DEM data of Marine City enable the representation of the high-rise modern coastal city area. In addition to the finely resolved coastal and overland unstructured grids, the seawalls were represented as a thin and long weir with paring nodes from the sea and land sides within a seamless grid system, as shown in Figure 5.

The numerical modeling grid was built based on the NWP−116k grid, established for calculations in the EWS [13]. To this grid, Marine City and Millak District were added in a patch form, expanding upon previous research [20] which had only considered the core area of Marine City along the coast. Consequently, this grid system includes the entire hinterland, with an elevation of up to 5 m, encompassing the entire Millak District to the left, Haeundae to the right of Suyeong Bay, and adjacent to Marine City. The eight major tidal constituents extracted from FES2014 [33] were applied at the offshore boundaries. To accommodate tidal variations within the domain, the nodal factor was considered, adjusting it from the current state in 2023 to the corresponding target years of 2050, 2070, and 2100. Nonetheless, morphological variations and associated tidal alterations were not accounted for and were assumed simplistically.

The seawalls, which serve as internal boundaries between the marine and terrestrial domains, are crucial factors that influence the WOT. Ensuring the seawall specifications (shape, crest elevation, armor layer, etc.) and representing them appropriately is of utmost importance. In the ADCIRC model, seawalls are discretized to resemble a thin strip shape, as shown in Figure 5, with nodes corresponding to both the marine and terrestrial areas. These pairing seawall nodes are located in the marine area, allowing them to dynamically adapt to the changing water depths and incoming significant wave heights ($H_s$) at the front of the seawall. The optimal EurOtop formula was automatically selected based on this information, and the WOT rates were calculated. These WOT volumes were then transmitted to the terrestrial counterpart pairing nodes, where overland flow was simulated on the gridded land surface. In other words, the simulated flow from the WOT crosses the seawall and is transferred to the terrestrial area. If the amount of flow is very small and challenging to model in terms of overland flow, a mechanism is designed to store the WOT flow for a certain period and then propagate it afterward [3]. The storm-induced WOT mean discharge, even if there was enough freeboard, was calculated at the sea-side nodes from the time-variant appropriate empirical equations of EurOtop, conveyed at every computational time span, to the land-side paring nodes. Then, the overland flow was also simulated within the ADCIRC model with different surface roughness, with a Manning’s coefficient of 0.016 accounting for paved road, as compared to the coastal bottom condition of 0.023 [20].

During storm intrusions, the incoming wind-induced wave period typically falls within the range of 10 to 20 s. The WOT occurs only from the peak wave crests and is therefore discontinuous, often referred to as white water overtopping [2], in contrast to the continuous flooding caused via general storm surges. In the Supplementary Materials, Videos S1 and S2 show video footage from the 2016 typhoon Chaba, vividly demonstrating the discontinuous nature of actual WOT events. Furthermore, through this footage and the previous study [20], it becomes possible to estimate the wave period responsible for generating WOT and gain an intuitive understanding of these discontinuous WOT events. Consequently, due to the relatively smaller volume of WOT compared to storm surges and its discontinuous characteristics, it is challenging to generalize the modeling of WOT using a continuous overland flow concept. In cases where WOT inundation occurs sporadically, especially when the wave height is not at its maximum peak, which typically occurs during the initial or final stage of WOT events, small WOT volumes are accumulated when they do not reach the wet–dry criteria of a specific value of 0.1 m within a local finite element containing the corresponding node, allowing for overland flow and preventing overestimation. Therefore, in this study, a method was devised where the calculated WOT volume, computed every 0.1 s, accumulated at each grid node paired with the terrestrial domain of the thin weir until the total head reached or exceeded the dry–wet limit value in the ADCIRC model. Once the WOT volume exceeded the wet threshold, it propagated inland as natural overland flow.

The grid system used in this modeling experiment was based on a relatively lightweight grid for the oceanic domain, aiming for fast calculations. From this oceanic grid, patches for the seawall and terrestrial areas were added. For the majority of typhoons that generate WOT in Busan, the area of interest, the time, and the wind field properties of typhoon intrusions can be known in advance through pre-forecasting, typically 2–3 days prior [13]. Therefore, starting from that period, simulations of typhoon-induced storm surges and WOT were conducted for 4 days. The time step for calculations (${∆}_t$) was set to 0.1 s. However, when the entire computational domain was partitioned and processed on a parallel computer with 138 CPU cores, the total computation took approximately 6–7 h on a computer with the following specifications: (CPU: E5620 (4C, 3.0 GHz)*2EA with Mellanox’s Infiniband of 19 Gbps bandwidth). This computation time allowed for efficient real-time forecasting and early warning of typhoon-induced storm surges and WOT, with forecasts available at least two days in advance, including estimates of typhoon paths and wind field properties.

3. Results

Here, the validity of simulating the typhoon-induced storm surges and WOT in a unified grid system encompassing the coastal area, seawall, and terrestrial domain, as described earlier, is first examined. Subsequently, the vulnerability of the terrestrial inundation due to SLRs for the target years is analyzed. In addition, the hardware specifications used in the calculations, along with computation time evaluation, are discussed. The challenges related to applying the current WOT empirical formulas to various seawall types and parameters constraints are also addressed.

3.1. Validity Tests of WOT Simulation

Even though there are many studies on WOT, as demonstrated by Lashley et al. [34], many empirical overtopping formulae were developed and validated using physical model tests and numerical simulations—without actual verification in the field. Thus, it is necessary to verify the applied formulae in real situations.

To validate the adequacy of WOT modeling, as outlined in the previous methodology, the first step is to conduct hindcasting using a unified seamless unstructured grid that encompasses the coastal area, seawalls, and terrestrial region, incorporating thin hydraulic weirs at the borders of the sea and land. This approach aims to reproduce the recorded inundation traces or known inundation extents through broadcast media during historical typhoon events, such as when WOT occurred.

WOT, as previously explained, lacks an analytical solution and can vary significantly depending on the diverse types of seawalls and external dynamic factors. Although machine learning techniques for WOT have some advantages of rapid and computationally economical approaches, compared to applying complicated numerical models with empirical formulae such as EurOtop, the accuracy of the overtopped discharge still remains a problem. Because most empirical formulae are based on a laboratory scale or pilot in situ scale, the external forcing conditions such as the sea level and wave characteristics are fixed and tested. However, in real WOT situations, the rapid time-variant external conditions behave somewhat differently to the laboratory scale; thus, they should be precisely measured and compared to the empirical formulae. In a previous study [20], WOT videos on the local broadcasts were used to determine the importance of the external wave characteristics including the wave period and incoming direction.

For model validation, quantitative WOT was verified for Typhoon Chaba in 2016, as described in the previous research [20], where only Marine City was focused on, and thus, the local grid was patched with seawall representation. Subsequently, the cases of WOT induced by typhoons Kong-Rey in 2018, Haishen in 2020, and Hinnamnor in 2022 were predicted as EWS [21,22,23] for Marine City. In this research, the model grid, as applied in [20], was expanded to include not only Marine City but also the hinterland of Millak District, up to 5 m of ground level, and revalidated for the case of Hinnamnor in 2022. The results, as seen in Figure 6, depict the maximum inundation areas and depths for Marine City and Millak District during the typhoon Hinnamnor. When comparing these modeling results with inundation traces [35], it is evident that qualitatively, the areas inundated by WOT were accurately reproduced. Therefore, the performance and applicability of the integrated numerical model ADCIRC + SWAN + EurOtop, which is constructed in a unified unstructured grid system from the marine to terrestrial areas, were revalidated in this study for simulating WOT, following the previous research [20] that successfully reproduced the WOT during the typhoon Chaba in 2016.

Even under identical laboratory conditions, the WOT results can exhibit variations. The regression fitting equations used to model these diverse WOT characteristics are based on EurOtop’s empirical formulas. However, due to the notable differences in the estimated WOT rates under various conditions, assessing the reliability of WOT in real-world scenarios remains a challenging task. Recently, Lashley et al. [34] applied an efficient field measuring apparatus using wired mesh and abundant social media for WOT at Crosby, UK. The wired wall system incorporates a three-dimensional grid of vertical capacitance wires that records the length of the wires in contact with water and the speed of the water passing through the grid [34]. Thus, these kinds of approaches can enhance the reliability of WOT simulations and forecasting, regardless of the analyzed approaches of WOT. Therefore, until quantified comparisons of real-world WOT are introduced, as in this study, using numerical models to estimate WOT extents and quantities in the inundation simulation in Busan is considered a highly valid approach for evaluating WOT reproduction.

3.2. WOT Inundation Considering SLR

In the methodology, SLRs corresponding to the target years of 2050, 2070, and 2100, with SLRs of 0.25 m, 0.44 m, and 0.82 m, respectively, were considered to be in line with the projected rise of the SSP5-8.5 [24]. The modeling results for the WOT due to reduced freeboard, ignoring other effects such as the coastal morphology caused via sea level changes, are shown in Figure 7. It is numerically demonstrated that the WOT for Marine City, the target area, and Millak District, located at the entrance of Suyeong Bay, increases compared to the current year,2023. It is clear that the SLR will increase the overtopping discharge even for small SLR rates. The frequency of a current extreme overtopping discharge will increase with the SLR, as suggested by Chini and Stansby [36] and Xie et al. [14].

From the perspective of protection for an entire city facing SLR hazards, it is essential to identify the expected WOT areas and maximum possible inundation depths for the presented Maximum Envelope of Overtopped Water Elevation (MEOWE) for the WOT areas, following the intrusion of five typhoons. The final results are visualized in Figure 7. Additionally, for the convenience of policymakers, in the Supplementary Materials, Figures S1−S4, in the form of HTML files using Python’s Folium functionality, have been included, which can be viewed in a web browser. This allows for an easy understanding of the expected maximum inundation extent and depth due to the SLR for each target year.

Furthermore, for quantitative comparison, the maximum inundation area, inundation width, and depth from the seawall to the inland were calculated and are presented in

Table 1. Quantitative comparison of the WOT inundation depth, width, and landward length for the respective target years: present, 2050, 2070, and 2100.

Target Year	Sea Level Rise (m)	$\mathbf{Maximum}\mathbf{Inundation}\mathbf{Area}\left({\mathbf{k}\mathbf{m}}^2\right)$		$\mathbf{Inundation}\mathbf{Width}\left(\mathbf{Length}\right)\mathbf{in}\mathbf{k}\mathbf{m}$
		Marine City	Millak District	Marine City	Millak District
Present	-	0.48	0.51	1.35 (0.58)	3.14 (0.38)
2050	0.25	0.54	0.56	1.39 (0.60)	3.35 (0.43)
2070	0.44	0.60	0.61	1.40 (0.61)	3.36 (0.44)
2100	0.82	0.81	0.75	2.35 (0.85)	3.42 (0.46)

for Marine City and the adjacent Millak District. These two areas are characterized by the occurrence of inundation, as seawater accumulates in Suyeong Bay due to its topographical features, depending on the typhoon’s path.

The quantitative analysis reveals an expansion in the WOT inundation area due to SLR. In Millak District, the inundation area is projected to increase by over 1.10 times, compared to the current year, by 2050, while in Marine City, a 1.13-fold increase is anticipated. However, by 2070, when the SLR is 0.44 m, it is expected that the expansion in inundation areas will be relatively similar to that of 2050, which saw a SLR of 0.25 m. Nonetheless, in 2100, with a sharp SLR of 0.82 m, the Marine City area is forecasted to experience a 1.69-fold increase in inundation area compared to the current year. Similarly, in Millak District, a 1.47-fold expansion is expected. This highlights a clear increase in the possibility of WOT as a consequence of reduced freeboard, assuming the current seawall conditions remain unchanged.

However, it is important to note that WOT, based on its nature, occurs under specific conditions due to high waves, even when there is a seawall freeboard. In other words, it is unlikely that the inundation area due to WOT will significantly expand unless it reaches the threshold of nearly zero freeboard. Furthermore, the WOT inundation results obtained through predictions based on SLR scenarios, considering the SLR values used in this study, show an expansion in the hinterland’s inundation depth and area compared to the current conditions. The assumption of increasing sea levels of 0.25, 0.44, and 0.82 m for the years 2050, 2070, and 2100, compared to the present, as seen in Equation (1) of the WOT basic formula, implies a relative reduction in freeboard. This results in an exponential increase in WOT. In other words, the vulnerability to WOT does not change linearly with SLR. Therefore, as attempted in this study, an evaluation of WOT vulnerability in the target area can be achieved by considering the coastal topography and seawall characteristics, along with a comprehensive numerical model that adequately accounts for SLRs.

The findings in this study are limited to the specific study area and may vary under different circumstances, such as changes in hinterland buildings or topography. Therefore, it is crucial to exercise caution when dealing with grid resolution, especially when detailed seawall information and hinterland characteristics are considered, as the results may differ accordingly. Moreover, the impact of climate change on typhoon intensity and elevated storm surge levels may be significant factors contributing to inundation and should be further studied in detail.

4. Discussion

In coastal seawalls, especially in areas prone to significant wave action, engineering considerations typically involve designing and constructing seawalls with a minimum design frequency of 50 to 100 years, depending on the location. These seawalls are commonly designed with typical cross sections that include seawall slopes, berm installations, and crest parapets, tailored to suit the site conditions. WOT for such conventional seawall configurations is typically addressed using the EurOtop empirical models.

However, as seen in Figure 8, some coastal areas feature stepped embankments constructed with a focus on user convenience, such as tourists. In such cases, engineering considerations may take a back seat to social and economic factors, and these structures are often built to address high tides or waves. In these scenarios, suitable empirical formulas for estimating WOT rates may be lacking. Therefore, the most approximate parameters are often applied to similar-shaped formulas, and modeling WOT during typhoon events becomes challenging, as it relies on whether WOT occurred and the associated discharge at the time of the typhoon invasion.

For WOT during typhoon Chaba in 2016, the previous study [20] had already thoroughly demonstrated the reproducibility of the numerical model, which combined ADCIRC + SWAN + EurOtop and the processes involved. Additionally, the previous study examined whether the roughness coefficient ${\gamma }_f$, which considers the characteristics of the seawall armor material, tetrapod, should be applied with smoother values of 0.63 than the default values of 0.4 provided by the EurOtop empirical formula from [1] when the freeboard decreases over time. Lashley et al. [34] showed that correcting the wave periods at the toe of the structure calculated via SWAN using an empirical formula, as recommended by EurOtop [2], increased the estimated q by a factor of 10. Moreover, they found the adjusted roughness coefficient ${\gamma }_f$ on the stepped revetment might be applicable, although EurOtop [2] recommends the minimum and maximum friction factors (${\gamma }_f$) of 0.75 and 0.9.

In particular, ongoing research is essential for developing appropriate empirical formulas to apply to various nonstandard types of seawalls that are not covered in the existing EurOtop manual. Additionally, as suggested in previous research [20], further investigation is needed to determine the appropriate value for the ${\gamma }_f$ coefficient in cases where the water level varies rapidly with water depth. The importance of choosing the value of ${\gamma }_f$ should also be addressed, because this parameter directly affects WOT rates. In the research focusing on the preparation of new equations to enhance the WOT rate and improve accuracy in recent years [37], even the ${\gamma }_f$ and ${\gamma }_{\beta }$ expressions of the latest version of the EurOtop [2] were fitted with the first version [1]; those parameters should be obtained for the new predictions based on the newest tests.

In studies that apply the EurOtop empirical formula to estimate WOT, there is ongoing consideration regarding the accurate application of the significant wave height ($H_{m0}$), which is a key factor directly influencing WOT. Assuming the right-hand side of the basic Equation (1) is constant, the rate of change in WOT ($∆q/q$) increases by 1.5 times, based on the relationship with the observed or estimated significant wave height variation (${∆H}_{m0}/H_{m0}$). However, when applied to actual sloped seawalls, as shown in Equation (2), the variability in the modified WOT due to the normalized relative freeboard, considering the characteristics relating to the gamma parameters, becomes even more significant. Nevertheless, determining suitable values for these parameters when applied to real seawalls can be challenging, and their values may vary with rapidly changing water levels, potentially imposing limitations on the accurate calculation of WOT. This is because most of the empirical WOT equations are derived from results obtained under fixed water level conditions in laboratory experiments. Therefore, adjustments should be considered to account for rapidly varying water levels in real-world environments. Thus, in the real application of WOT, the appropriate time-variant external forcing and parameters should be moderately chosen and applied.

The results of simulating WOT, considering the SLRs for the years 2050, 2070, and 2100, compared to the current conditions, show that in the case of the SLR ranging from 0.25 to 0.44 m, the inundation extent and depth generally remain consistent. In other words, in the target areas of Busan Marine City and Millak District, even with the existing front seawall crest elevation and wave height added to the sea level, which resulted in positive freeboard values, WOT still occurred. However, the extent of the WOT was slightly increased compared to the current conditions but remained almost identical in terms of the affected areas.

However, even in the case of 2100 when the SLR is 0.82 m, compared to the current conditions, the inundation depth remained nearly the same, particularly in the immediate vicinity of the seawall. However, the inundation extent expanded in this scenario. This outcome is attributed to the peculiar nature of WOT in contrast to typical storm surge flooding. In WOT, when the total head, obtained via adding the significant wave height to the sea level, is lower than the crest level, even when there is a positive freeboard, it results in WOT. Unlike the bathtub effect seen in conventional storm surge flooding, where water flows over the land due to a total head exceeding the crest level, WOT occurs due to the unique flooding characteristics where water accumulates just behind the seawall. The WOT discharge is greatly affected via the significant wave height and relative freeboard at the toe of the structure [2]. In addition, the gamma parameters also affect the rate more than the significant wave height. Additionally, as the duration of WOT corresponds to the decreasing freeboard, the inundation extent expands, while the inundation depth behind the seawall remains relatively constant.

The importance of the water depth, sea level elevation, and incident wave conditions in front of the seawalls in reproducing WOT has been emphasized by many researchers in the context of WOT reproduction. For example, Chini and Stansby [36] applied the first version of EurOtop [1] to a vertical barrier at the toe of the seawall and a sloped seawall with berm and showed some importance of the incoming wave height on WOT. For a given significant wave height, the overtopping discharge rate increases with the increasing water level. In terms of return periods of wave overtopped flooding, Chini and Stansby [36] demonstrated that the frequency of flooding of a given magnitude would increase with time, dependent on future climate projections and SLRs, and, correspondingly, how the magnitude of flooding with a given return period would increase.

Through the simulated results, it can be indirectly inferred that guidance for coastal seawall construction and the appropriate crest height considering future SLRs may be provided to face SLRs in vulnerable coastal cities. Maintaining a minimum freeboard, which is the difference between the crest height and sea level, plus the wave height, appears to be effective in preventing WOT due to future SLRs. In other words, considering the approach of this study in the design of WOT protection can scientifically determine the appropriate crest height to address the SLR and can be applied effectively in engineering practices.

Therefore, if it is possible to minimize WOT and gauge its discharge, it would enable the development of structural measures capable of immediately diverting or pumping excessive wave discharge into the hinterland, even with the economic construction of seawalls designed to allow WOT. With appropriate overtopping mitigation measures in place, it would be possible to minimize storm-induced WOT, thus reducing the risk of disasters in vulnerable coastal cities exposed to storm surges and SLRs.

Due to the significant impact of the terrain and water depth in front of the seawalls on WOT, it is essential to conduct a detailed assessment that considers the specific characteristics of the target area. Thus, the specific geometry in front of the seawall has been treated as part of the seawall structure represented in EurOtop.

The proposed numerical model accounting for the tide, wave, surge, WOT, and overland flow, using the seamless grids from the regional sea to overland via a hydraulic structure, can be successfully applied and generate the storm-induced WOT inundation. However, several limitations should be noted and further analyzed in future research endeavors: 1. Issues arising from the consistent application of the attenuation coefficient for seawall covers, as observed in previous research [20]. This includes reduced porosity due to gap filling (caused via wave setup during typhoons) and the smoothing effect on seawall slopes that may occur during such events; 2. the proper selection of coefficients in terms of Manning’s roughness due to spatial variations in the characteristics of terrestrial areas; 3. inherent limitations of the model itself, with particular attention to aspects related to the wave characteristics, such as the significant wave height; 4. the constraints and limitations of applying the EurOtop formula. Thus, in future research, there is a need to upgrade the integrated EurOtop version in ADCIRC v53 to the latest version, v55 or higher, and incorporate the newest EurOtop empirical formulas and any improved formulas to generalize the coupling WOT in seamless grid modeling.

Despite several limitations, the WOT simulations conducted using the newly introduced seamless grid system in this study can be valuable for quantitatively assessing the vulnerability of coastal cities and their infrastructure in the face of future SLRs and for formulating countermeasures. This approach differs from conventional storm surge models in which WOT and onshore flooding propagation are considered independently, making it challenging to simultaneously model the dynamic external force changes at the front shore of the seawalls and the inundation depth and area of overtopped waves over the seawalls. Consequently, the interactions between the external water level changes and WOT’s onshore propagation were challenging to comprehend, as they were treated as separate phenomena. The research approach to WOT risk due to SLRs, as pursued in this study, is expected to provide solutions for adapting to future climate change in other coastal areas as well. Similar to the research conducted by Bonaldo et al. [38], which studied the modulation of wave energy in coastal areas based on the climate change scenario, it is anticipated that some regions may experience a local increase in the severity of sea states impacting the coast.

However, through this study, it is possible that even in cases where natural storm surge seawalls are established, significant portions of the hinterland could be inundated due to WOT in the worst-case scenarios. This understanding can provide substantial assistance in formulating both short-term preparedness and long-term protection. In particular, this integrated model, apart from protection approaches such as raising seawall heights or installing submerged breakwater structures at the seawall front in the long term, can also serve as a robust tool. It enables us to automatically erect the deployment of protective barriers and other preparedness measures in advance for short-term perspectives, such as early warning for WOT.

5. Conclusions

In this study, a simulation of future WOT risks was conducted for Marine City and Millak District, adjacent to Suyeong Bay, Busan, Korea, which frequently experiences WOT during typhoon events, considering the target years up to 2100 and the projected SLR. The integrated model, comprising ADCIRC + SWAN + EurOtop, was applied using a seamless unstructured grid system from the NWP Ocean to coastal seawalls and land areas. Three historical typhoons that caused WOT and two typhoons generated randomly, representing the 100-year return period, were selected to simulate WOT. The experimental results indicate an increasing vulnerability to WOT with rising sea levels, but the extent of onshore damage due to WOT, resulting from the reduction in coastal seawall freeboard corresponding to SLRs, is not expected to be as severe as anticipated when overlapped with general storm surge-induced flooding.

However, in situations where sea levels continue to rise, there is a significant likelihood of extensive inundation in the coastal hinterland. Although this study did not consider compound disasters, in cases where a substantial increase in inland water levels occurs due to heavy rainfall during typhoon events, combined with the slow recession of WOT into offshore areas, there is a considerable concern for potential disasters and associated damages. The final results for WOT due to five target typhoons were used to identify areas and inundation depths prone to flooding based on the MEOWE concept. The findings of this study can be effectively integrated into long-term structural disaster mitigation strategies to minimize vulnerability to wave-induced inundation hazards in the coastal hinterland behind the seawall systems. They can also contribute to immediate response measures and preparedness in the event of a disaster.

However, in future research, continuous efforts will be required to enhance the development of empirical formulas that can be effectively applied to various types of seawall structures, going beyond the typical seawall forms considered in existing WOT empirical formulas. The development of integrated formulas that can adapt to various seawall forms, armoring materials, or porosity changes should be prioritized. Additionally, the development of numerical models capable of accurately representing seawalls and inundation-prone areas within a minimum grid spacing of 1–2 m, along with efficient simulation techniques, is deemed necessary.