The study area is shown in Figure 1, which shows the location of the abnormal surge-induced sea dike erosion on August 2–3, 2019, at point P2. The study area experiences minimal impact from tropical storms and depressions but is significantly influenced by two monsoon seasons: the northeast monsoon (from November to March) and the southwest monsoon (from May to September). Wind speeds during the Southwest Monsoon are higher, averaging 4.6–4.8 m/s at the Phu Quoc station, while offshore wind speeds range from 3.5 to 7.8 m/s (Quyet, 2023). There are about 10–12 southwest monsoon phases annually in the study area. Wind speeds during the southwest monsoon increase when tropical low-pressure systems are active in the East Sea of Vietnam. The coastal sea experiences semi-diurnal tides. Although the tidal range is not high with a maximum of about 1.0 m, the shallow water and low-lying coastal land make it vulnerable to rising water levels during spring tides, especially when strong monsoon winds occur. On the west coast of the Camau Peninsula, there are two provinces (Camau and Kien Giang) with a coastline of more than 340 km. These provinces play an important role in the economic development of the southern part of Vietnam through fisheries, aquaculture, and marine tourism. However, in recent years, coastal erosion in the Mekong Delta has become more severe and complex, particularly along the western coast of Cape Ca Mau (Duyen et al., 2024).

There is no marine weather station on the west coast of the Ca Mau Peninsula. However, at Song Doc hydrological station, which is located about 1.5 km from the river mouth, the change in water level was recorded during the high tide (Quyet, 2023). In the ocean (called the southwestern Sea of Vietnam), there are two marine weather stations located at Phu Quoc and Tho Chu Islands. At the two stations, the wind data is observed at 1:00, 7:00, 13:00, and 19:00 (local time, GMT+7), the wave data is from 7:00, 13:00, and 19:00, while the tide is observed every hour at Phu Quoc station and four times (at 1:00, 7:00, 13:00 and 19:00) per day at Tho Chu station. However, since the wave data was estimated by eyes, these are not used for analysis due to the limitation in accuracy. Fortunately, there were two projects that conducted wave observations by an AWAC (Acoustic Wave and Current Profiler) sensor at the location near Phu Quoc (ST1 in Figure 1) and Tho Chu station (ST2 in Figure 1), and these observations will be used to validate the numerical results of wave simulation (Quyet, 2023). The points of P1, P2, P3, P4, and P5 are used to discuss the surge and swell heights. A reanalyzed dataset of wind and air pressure from the ERA5 at a resolution of 0.5° was used to assess the speed and direction of the wind and used as input for the simulation of wave and surge in the study area. All data was provided by the Viet Nam Meteorological and Hydrological Administration (VNMHA). The SuWAT model used the bathymetric data extracted from the General Bathymetry Chart of the Ocean (GEBCO) by the British Ocean Data Center, updated in 2024 with a resolution of 15 arc-seconds (https://www.gebco.net/data_and_products/gridded_bathymetry_data/) and the coastal topographic maps, scaled from 1:10,000 to 1:25,000 and published by the Department of Survey, Mapping and Geographic Information (DOSM) of Vietnam in 2023.

The SuWAT is an open-source code model - a coupled system for simulating surge, wave, and tide, developed by Kim et al. (2008), was employed to simulate storm surge, wave, and tidal conditions in the study area. SuWAT is capable of parallel processing across multiple domains using the Message Passing Interface (MPI). In this model, the astronomical tide is incorporated via the global ocean tide model by Matsumoto et al. (2000), which provides tidal predictions for 16 tidal constituents: M2, S2, K1, O1, N2, P1, K2, Q1, M1, J1, OO1, 2N2, Mu2, Nu2, L2, and T2. At each time step, the tidal level is applied to the open boundaries, limited to the outermost domain (Kim et al., 2008).

The surge module addresses the depth-averaged nonlinear shallow water equations by utilizing a staggered Arakawa C grid for spatial resolution and a leapfrog scheme for temporal integration. This approach employs an explicit finite difference scheme combined with the upwind method. The equations also incorporate wave forces as gradients of wave-induced radiation stress, which are calculated using the SWAN model. A standard quadratic drag law is applied for the sea surface and bottom boundary layers. In the wind stress, the conventional drag coefficient C _D proposed by Honda and Mitsuyasu (1980) is employed: C D = 1.290 − 0.024 W × 10 − 3 W ≤ 8 m / s 0.58 + 0.063 W × 10 − 3 W > 8 m / s (1) where W is the wind speed (m/s) at 10 m height. In the decoupled run, Equation 1 is used. On the other hand, the wave-dependent C _D (Janssen, 1989; 1991; Mastenbroek et al., 1993) is applied in the coupled run with SWAN model; C D = u * 2   /   U z 2 = κ   /   ln z + z e − z 0 z e 2 (2) where z _e is the effective roughness, z ₀ is the roughness length, z is the height, and κ = 0.4 is the von Kármán constant. The wave radiation stresses are expressed by: S x x = ρ g ∬ C g C cos 2 ⁡ θ + C g C − 1 2 E d σ d θ (3) S x y = S y x = ρ g ∬ C g C cos θ ⁡ sin ⁡ θ E d σ d θ (4) S y y = ρ g ∬ C g C sin 2 ⁡ θ + C g C − 1 2 E d σ d θ (5) here, C and Cg represent the wave phase velocity and group velocity, respectively, while σ and θ denote the angular frequency and wave direction. E is the energy density spectrum. Additionally, a conventional quadratic drag law is applied to the bottom boundary layer. The current and the sea surface level in the coarse grid domain are transferred to the open boundaries in the nested fine grid domain at each time step of 4 s employed through the entire domain.

In this study, SuWAT employs the Simulating WAves Nearshore (SWAN; Booij et al., 1999) model to solve the spectral action balance equation and estimate the wave spectrum, which is then integrated into SuWAT’s wave module (Kim et al., 2008; 2010). The wave module estimates waves based on time-varying currents and sea surface levels obtained from the surge module. Updated parameters, such as the wave-dependent drag coefficient and wave-induced radiation stress, are fed back to the surge module to recalculate currents and sea surface levels. The SWAN version 40.41 is specifically integrated as the wave module in SuWAT (Kim et al., 2008). The wave spectrum in the coarse grid domain is transferred to the open boundaries in the fine grid domain at each time step of 900 s. The time step is 900 s for the wave model. SuWAT’s accuracy has been validated in several studies, including Kim et al. (2015), Chien (2015), Thai et al. (2017a), Thuy et al. (2017), and Thuy et al. (2020).

SuWAT offers the flexibility to use either wind and sea level pressure (SLP) fields as a surface forcing boundary, generated by its internal parametric wind and pressure model or externally supplied fields from a numerical weather prediction model, such as the ECMWF (European Centre for Medium-Range Weather Forecasts) or WRF (Weather Research and Forecasting) models. In this study, a reanalysis of wind and pressure data from ERA5 was used to simulate the surge and wave conditions. For numerical simulations, wind and pressure inputs from ERA5 were linearly interpolated to the outermost domain (D1, as shown in Figure 4a). At open boundaries, the tidal predictions were imposed, and no-flux conditions were applied for a land boundary. This study did not consider the effect of river conditions on surges.

In a series of numerical simulations, the three-level rectangular structured grid system, detailed in Table 1, incorporates the complexity of the region’s geophysical features. The outermost domain, D1 (Figure 4a), spans the entire East Vietnam Sea, while the intermediate domain, D2 (Figure 4b), focuses on the southern coast of Vietnam. The innermost domain, D3, covers the west coast of Ca Mau province (Figure 4c). The spatial resolutions for D1, D2, and D3 in the horizontal and vertical directions are 7400, 1850, and 925 m, respectively. Bathymetric data for D1 and D2 were extracted from the GEBCO. In contrast, coastal topographic maps from DOSM provided data for D3. SuWAT directly applies the wind and pressure fields at each grid node of D1, shown in Table 1, while for D2 and D3, it interpolates the hourly data from D1 into 10-min intervals for the nested domains.

The tidal levels and surges induced by wind, air pressure, and waves affect the total rise of coastal water levels. Therefore, it is necessary to simultaneously analyze and evaluate the factors of tides, surges, and waves (including swells) in the study area.

Figure 8 shows the astronomical tidal variations at the erosion point (P2). This is the calculated data from the SuWAT model. On 02–03 August 2019, the coastal area of Ca Mau province was in the high tide period. The time of highest tide was from 14:00 to 17:00, which was the time when the abnormal water level rise occurred.

The regional wind field distributions at 15:00 on the dates of 1–4 August 2019 are shown in Figure 9, which is derived from the ECMWF reanalysis data. It can be seen that the prevailing wind direction was west in the northern part and southwest in the southern part of the study area. In the coastal area of Ca Mau and K. Giang provinces, wind direction prevails from the west and southwest. The strongest winds were found in the northern part of the area, and weaker ones were found in the southern part of the study area. At Phu Quoc station, the wind speed was regularly sustained above 8,0–10,7 m/s (level 5 on the Beaufort scale) in the afternoon and evening of August 2 and 3, 2019, and the wind speed reached a maximum of 12 m/s (level 7) at 13:00 on 3 August 2019. These wind speed values are rarely observed at Phu Quoc station. Meanwhile, at Tho Chu station (in the Southwest Sea), the wind speed increased from 2 August 2019, with a maximum of up to 5 m/s (level 3) at 13:00 on 3 August 2019, lower than those at Phu Quoc station (Quyet et al., 2023). The combination of high wind speeds and prolonged duration resulted in significant and sustained increases in water levels and wave heights during this high tide period. During this period, the wind field was active in the area due to the interaction with typhoon WIPHA, occurring in the East Vietnam Sea and making landfall in north Vietnam on the morning of 3 August 2019 (Figure 10).

The distribution of the maximum surge induced by wind stress and wave setup on the coastal area of Ca Mau and K. Giang provinces during the strong monsoon phase from August 1 to 5 August 2019, is shown in Figure 11. This result was calculated from the SuWAT model for the coupled surge with wave case. It can be seen that the highest surge is at point P4 (belonging to the coastal area of K. Giang Province), about 0.6m, and the surge height gradually decreases towards Ca Mau province. Thus, although coinciding with the high astronomical tide in the area, the surge at P4 is higher than at P2, but there was no report on the abnormal water level change at K. Giang province, such as recorded at point P2.

Figure 12 shows the time series of surge height at point P2 for two simulation cases, with and without considering the effect of wave setup (coupled and uncoupled model of surge and wave). The surge induced by wave setup (Z _{wave setup} ) was extracted as follows: Z w a v e   s e t u p = Z c o u p l e d   m o d e l − Z u n c o u p l e d   m o d e l (6)

The results show that the surge due to wind stress (the uncoupled case- Z _{uncoupled model} ) is about 0.33m, while the highest combined surge induced by winds and wave setup (Z _{coupled model} ) is about 0.46 m. Although the surge induced by wave setup is only about 0.13m, that contribution makes up about 25% of the total surge.

The calculated results of astronomical tide, surge, and total water levels (tide + surge) at P2 are shown in Figure 13. Although the surge peak was not at the same time as the highest of the astronomical tide (As. Tide), the surge contribution of about 0.42 m increased the total water level. It can be seen that the highest peak of total water level is at 15:00 on 2 and 3 August 2019, although the difference is not much in comparison to 31 July and 1 and 4 August 2019. However, the abnormal water level change occurred only on 2–3 August. Therefore, it is necessary to consider other factors, such as waves, in the following section.

In this study, swells were considered as long waves that propagated from the offshore of the southwestern Sea of Vietnam into the study area. The significant wave height was estimated from the incoming waves, taking into account the characteristics of both swell and local wind waves, with the estimation based on their respective heights (Holthuijsen, 2010). The distribution of the simulated significant wave height and swell height at 15:00 on 2 and 3 August 2019 are shown in Figures 14, 15, respectively. Note that in this case, the swell height was selected for the longer periods, i.e., higher than 10 s, while the period of significant waves was around 4–5 s. It can be seen from the figures that the prevailing wave direction is perpendicular to the shoreline. Compared to the south and the coast of K. Giang province, the height of significant waves and swells at the center of Ca Mau province is higher. It also can be confirmed by the extracted results of the swell height data at some representative locations (points P1–P5) along the southwest coast in Figure 16.

Figure 17 presents a comparison of significant wave height and swell height at point 2 for the period from August 1 to 6 August 2019. It can be seen that the trend of significant wave height is not exactly the same as the swell height, although both decreased after August 4. However, the highest significant wave height, on 2 August 2019, is about 1.6m, not much higher than other days. Meanwhile, there were two peaks of swell height on the afternoon of August 2 and 3, 2019 are 0.51 m and 0.52 m, respectively. The reanalysis data from ERA5 also showed two swell peaks; however, they were not at the same time as the highest of the astronomical tide (Quyet et al., 2023). The swell height is smaller than the significant wind wave height, but the period is longer. The continuous accumulation of swells at the time when both swell and water level (“Total water level” in Figures 13, 18) are highest will increase the total water level in the coastal area, as shown in Figure 18. These results are in line with results reported by Hoeke et al. (2013), Andrade et al. (2013), Cheriton et al. (2016), Wandres et al. (2020), Dhoop and Thompson (2021), Cheriton et al. (2024). The numerical results showed that at P4, even though the surge height is higher than at P2 (0.6 m at P4 and 0.4 m at P2) while the swell height is lower, less than 0.1 m (0.52 m at P2 and 0.03 m at P4) due to the shallow effect (Figure 4c). The surge heights at peak astronomical tides are 0.57 m at P3 and 0.42 m at P2; however, the swell height is around 0.52 m at P2, higher than 0.33 m at P3 at the peak total water level. In addition, at P3, mangrove cover may be the reason for the lack of reports of abnormal rises in water levels.