An Assessment of the Tipping Point Behavior for Shoreline Retreat: A PCR Model Application at Vung Tau Beach, Vietnam

Abstract

Storm waves and rising sea levels pose significant threats to low-lying coastal areas, particularly sandy beaches, which are especially vulnerable. The research on the long-time-scale changes in sandy coasts, especially the identification of tipping points in the shoreline-retreat rate, is limited. Vung Tau beach, characterized by its low terrain and rapid tourism-driven economic growth, was selected as a typical study area to quantify the shoreline retreat throughout the 21st century under various sea-level rise (SLR) scenarios, and to identify the existence of tipping points by investigating the projected annual change in shoreline retreat (m/yr). This study employs the Probabilistic Coastline Recession (PCR) model, a physics-based tool specifically designed for long-term coastline change assessments. The results indicate that shoreline retreat accelerates over time, particularly after a tipping point is reached around 2050 in the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios. Under the SSP5-8.5 scenario, the median retreat distance is projected to increase from 19 m in 2050 to 89 m by 2100, nearly a fourfold rise. In comparison, the retreat distances are smaller under the SSP1-2.6 and SSP2-4.5 scenarios, but the same accelerating trend is observed beyond 2050. These findings highlight the growing risks associated with sea-level rise, especially the rapid increase in exceedance probabilities for retreat distances by the end of the century. By 2100, the probability of losing the entire beach at Vung Tau is projected to be 22% under SSP5-8.5. The approach of identifying tipping points based on the PCR model presented here can be applied to other sandy coastal regions, providing critical references for timely planning and the implementation of adaptation measures.

1. Introduction

The low-elevation coastal zone (LECZ) is characterized by a high population density and a concentration of economic activities [1]. Nearly 1 billion people live within 10 km of the coastline, and the population living far away from the coast continues to decline [2]. Coastal zones generate approximately 65.12% of global economic output, occupying only about 18.43% of the land area [3]. The negative impacts of climate change on coastal zones, such as potential shoreline retreat, can significantly affect human life and property, socio-economic development, and surrounding ecosystems [4,5]. An analysis of global shoreline change data from 1984 to 2016 reveals that 24% of the world’s sandy shorelines are retreating at rates exceeding 0.5 m/yr [6]. The IPCC (Intergovernmental Panel on Climate Change) Sixth Assessment Report states, with high confidence, that most of the world’s sandy coasts will experience an increase in erosion throughout the 21st century [7]. By the end of the 21st century, 50% of sandy coastlines of the world are projected to face severe shoreline retreat under a high-emission scenario [7]. According to the U.S. Climate Resilience Toolkit (https://toolkit.climate.gov/) (accessed on 16 October 2023), coastal erosion in the US alone costs approximately USD 500 million in economic losses annually, with more than 300 km² of coastal wetlands lost each year [8,9]. Given these severe impacts, predicting future coastline changes is essential to provide valuable reference points for coastal zone management.

Several studies have been conducted to predict shoreline retreats in the context of climate change. Global coastal systems are subjected to a diverse array of wave regimes, tidal patterns, and sediment dynamics, which exhibit significant variability across different geographic locales [10]. Bruun [11] developed a conceptual model, known as the Bruun rule, to project long-term shoreline retreats due to sea-level rise. This method is widely used at the local, regional, and national scales, although various concerns have been raised about the quantitative accuracy of local-scale predictions derived from the Bruun rule [12]. Deviating from the Bruun Rule, Ranasinghe and Callaghan [13] introduced a physics-based model, the Probabilistic Coastline Recession Model (PCR) to provide probabilistic estimates of shoreline retreat driven by sea-level rise. The PCR model accounts for joint probabilities between key erosion variables such as wave height, period, and direction, as well as storm-event duration and the time intervals between events. The PCR model has been applied in many parts of the world, including Sri Lanka [14], Japan [15], and so on. However, all PCR model applications to date have focused on deriving projections of coastline position change and associated economic risk. In this study, for the first time, we use the PCR model to project the “tipping point” related to shoreline retreat. The PCR model specifically focuses on wave-induced effects, particularly under storm conditions. Moreover, the PCR model integrates considerations of sea-level rise, providing a more holistic view of coastal change dynamics.

A tipping point refers to the critical moment when noticeable and irreversible changes begin to occur. In climate change research, IPCC [7] proposed the concept of a “climate tipping point” and defined it as the key threshold at which global or regional climate shifts from one stable state to another, with these events being irreversible. The tipping points in environmental systems are critical thresholds beyond which a small perturbation can cause a sudden and dramatic shift to a new state. These transitions are abrupt and can trigger cascading feedback loops that accelerate the change. For example, the melting of the Greenland and West Antarctic ice sheets will cause the sea level to rise by up to 5.3 m, and change the Earth’s albedo, further amplifying atmospheric warming [16]. In this context, we define the tipping point for shoreline retreat in a similar but slightly modified manner. The tipping point for shoreline retreat is here assumed to have been reached when the annual rate of retreat begins to increase monotonically, indicating a transition to a new state of increased erosion. If the recession rate accelerates, and the recovery is stationary, this would leave a beach in a progressively more vulnerable state for future storm impacts. This in turn would increase the recession rate again.

This study focuses on Vung Tau beach in Vietnam, using the PCR model to quantify shoreline retreat in the 21st century under various sea-level rise scenarios. A framework for identifying tipping points, based on probabilistic shoreline change predictions, is proposed. This framework can be applied to similar coastal areas, offering critical information for timely adaptation planning.

2. Study Area and Data Collection

2.1. Study Area

The study area is in Vung Tau, Vietnam, located on the northern edge of the Mekong Delta (107°7′3″–10°21′59″) (Figure 1). The shoreline of the study area is nearly 11 km long. Waves reaching the Vung Tau coast are affected by two monsoons: the northeast monsoon in winter and the southwest monsoon in summer. During the northeast monsoon season from October to April, the waves predominantly come from the northeast direction, with wave heights in the range of 2.0 to 5.0 m being dominant. In the southwest monsoon season from May to September, the waves come from the southwest and west, with wave heights in the range of 0.0 to 2.0 m being predominant [17]. Sediment transport along the Vung Tau coast mainly occurs during the relatively quiescent southwest monsoon, which promotes seasonal deposition on the inner shelf. However, an energetic northeast monsoon resuspends fine-grained sediment on the seafloor [18]. The tide regime in Vung Tau is characterized as a mixed semidiurnal tide, with a tidal range of 3–4 m [19]. Tropical depression systems and strong monsoon activity occur mainly from October to February [20]. The average shoreline-retreat rate in the study area is approximately 0.5 m/year ± 0.2 m/year [21]. Vung Tau has developed rapidly and is the leading oil and natural gas production base in Vietnam. It has one of the highest per capita incomes in the country, and aims to become a national maritime economic center by 2030 [22]. However, the coastal terrain of Vung Tau beach is extremely low, an average of 3–4 m above sea level [23], making it highly susceptible to severe economic losses from storm-induced erosion.

2.2. Data

2.2.1. Wave Climate

Wave data serve as a fundamental dataset for identifying storm events. Given the scarcity of existing wave data spanning long time periods, our study uses ERA5 hourly reanalysis data from 1940 to present [25], with a horizontal resolution of 0.5°. To ensure the timeliness of wave data, the selected time series spans from 1 January 1993 to 31 December 2022. The wave rose is shown in Figure 2. The dominant angle of wave incidence is NE, with more than 25% of significant wave heights being greater than 2 m.

2.2.2. Beach Profile and Median Sediment Diameter

The beach profile is a key dataset reflecting coastal topography and is used for the calculation and verification of erosion volume in the subsequent application of a PCR model. Figure 3 shows the average beach profile of the coastal topography of Vung Tau, which was obtained from the Southern Institute of Water Resources Research, Vietnam [26]. Beach profiles were collected from the berm at the landward boundary, extending outward to a depth of 15–20 m, with measurements taken at intervals of 1 km between them. Most of the subaerial beach have berms. For areas without berms, we extended the profiling to the point where the beach gradient became less dynamic and transitioned into the backshore, which could be marked by dunes or other coastal defenses. The beach profile data indicate that areas with a water depth shallower than 10 m with respect to the mean sea level (MSL) is located within 1500 m of the shoreline. The data are utilized to calculate both the height and slope of the beach. We calculated the shoreline retreat based on the average beach profile, thereby representing the overall shoreline change in the study area. The median sediment diameter is around 0.2 mm [26].

2.2.3. Relative Sea-Level Rise

Relative sea-level rise data are the basic data for computing the future shoreline retreat. Here, we use the regional sea-level rise data including vertical land motions projected by IPCC AR6 for Vung Tau [27] for the period from 1 January 2023 to 31 December 2100. The regional SLR came from tide-gauge and satellite-altimetry observations. The baseline for the SLR curve is based on the period from 1995 to 2014. The selected scenarios include SSP1-2.6, SSP2-4.5, and SSP5-8.5, which respectively correspond to the low, medium, and very high scenarios for future greenhouse gas emissions (Figure 4). We used the median value of sea-level rise in three scenarios. The first half of the scenario is the Shared Socioeconomic Pathway (SSP) and the second half is the Representative Concentration Pathway (RCP). The assumptions of the sea-level rise (SLR) scenarios, as sourced from the IPCC’s Sixth Assessment Report (AR6), are shown in

Table 1. Main characteristics of the three SLR scenarios.

SLR-Scenarios	Socio-Economic Pathways	Radiative Forcing	Description
SSP1-2.6	Sustainability—taking the green road	2.6 W m−2	“Stringent mitigation” scenario
SSP2-4.5	Middle of the road	4.5 W m−2	Intermediate scenario
SSP5-8.5	Fossil-fuel development	8.5 W m−2	Very high warming scenario

. We assume the mean sea level (MSL) as a reference for the shoreline, which provides a more stable benchmark for long-term coastal analysis.

3. Application of the PCR Model at Vung Tau Beach

The PCR model integrates probabilistic extreme-value functions and joint probability models (JPM) to simulate future storm events over the next 100 years, based on the distribution characteristics of historical storm events. The model calculates shoreline-retreat distances under SLR scenarios using a structural erosion model, and the results are validated through high-precision physical erosion models. The simulation runs 10,000 cycles until the probability of shoreline retreat converges to 1% [14]. The scheme of the PCR model is shown in Figure 5. The basic steps for applying the PCR model at Vung Tau, similar to previous applications elsewhere, are as follows:

• Using historical storm-event data, apply generalized extreme value (GEV) distribution functions and linear relations to analyze the relationships between the maximum significant wave height during the storms (H_s), mean peak period (T_p), storm-event duration (Dur), and average wave direction (Dir).
• Apply the JPM storm generator presented by Callaghan et al. [29] to randomly generate storm events from 2023 to 2100.
• Use relative sea-level rise data from the IPCC Sixth Assessment Report (Section 2.2.3) to determine the amount of sea-level rise during each storm in the synthetic storm-event time series.
• Apply the structural erosion model by Mendoza and Jiménez [30] to calculate the shoreline-retreat distances.
• Record the shoreline position after each storm for each year of the simulation, subtract the final position (averaged over the last 3 simulation years) from the initial shoreline position to estimate shoreline retreat.
• Repeat Steps 1–5 until the calculated low exceedance probability of retreat converges at 0.01.
• Use the 2023–2100 time series of shoreline-retreat positions under different scenarios to identify the tipping point.

These steps are elaborated in the next sections.

3.1. Storm Identification and Statistical Analysis

Storms waves can lead to offshore sediment transport that crosses the depth of closure, causing the non-return of sediment to the beach, which is a key process in shoreline retreat. In the PCR model framework, storm events are identified using ERA5 wave data. This study uses the peak over threshold (POT) method to identify the time when Hs is higher than a certain threshold and records the storm duration. This threshold is based on percentiles: 90th, 95th, and 97th. After sensitivity-testing, the 95th percentile significant wave height is used as the cut-off threshold for storm events, which are recorded when the storm duration exceeds 24 h.

At Vung Tau Beach, 154 storms were observed over a 30-year period (1993–2022), averaging about 5 storms per year, as shown in Figure 6. Four variables showing the characteristics of storm events were extracted accordingly, including H_s (2.25–3.47 m), Dir (56.98–74.20°), T_p (6.56–10.95 s), and Dur (25–98 h).

The statistical analysis of storm events was conducted following the approach of Dastgheib et al. [14]. The maximum significant wave height and storm duration were fitted with the generalized extreme value (GEV) distribution, as shown in Figure 7a,b.

The correlation between different storm characteristics was analyzed. Based on previous studies [15], the maximum significant wave height during storms was used as the main parameter and its correlation with other variables was analyzed. Figure 8a shows that there is no correlation between the maximum significant wave height and the average wave direction during the storm. Figure 8b shows a correlation between the maximum significant wave height and storm duration. The greater the maximum significant wave height, the longer the storm duration. To further analyze the relationship between storm duration and maximum significant wave height, a joint cumulative distribution function (CDF) was fitted by the “Clayton” copula method (Figure 9). Figure 10 shows the linear relationship between the maximum significant wave height and the average wave peak period during the storm period. The correlation is stronger at low peak periods.

3.2. Storm-Event Generation

Based on the storm characteristics identified from 1993 to 2022 and their correlations, the storm events were randomly generated in a 78-year time series (2023–2100), including recovery intervals. Each storm event is defined by its maximum significant wave height, mean storm duration, mean peak wave period, mean wave direction, and storm interval. Since storm events from 1993 to 2022 mainly occurred from November to March of the following year, less stormy periods were concentrated from April to October. This leads us to derive and apply seasonal values for the rate parameter of the Poisson distribution used to model storm recurrence.

3.3. Erosion Model and Beach Recovery

An erosion model is used to calculate storm erosion volumes and to convert these volumes into shoreline-retreat distance. We applied the structural shoreline-retreat model by Mendoza and Jimenez, which requires the following as input: storm characteristics (H_s, T_p, and Dur) and beach morphology (median particle size and beach slope) [14]. Jiménez et al. [31,32] identified the D₀ parameter as the best predictor of beach profile change. However, to quantitatively predict beach profile changes in sediment volume, the beach slope must be included as an additional variable, leading to the J parameter [28], which is used to predict the amount of erosion caused by storms, and its calculation is as follows.

$$J={|D_{0,e}-D_0|}^{0.5}\times m,\hspace{1em}with D_0=H/T\times W_s$$

(1)

where, J is the erosion volume, D_0,e is the equilibrium Dean parameter value (2.5 for deep-water waves), D₀ is the Dean parameter, indicating the type of beach profile change, H is the significant wave height, T is the mean wave period, W_s is the sediment fall velocity, and m is the average profile slope.

Due to the absence of pre- and post-storm erosion data, we calibrated Mendoza and Jimenez’s structural erosion functions using 1D XBeach models in surfbeat mode with standard settings, to estimate calibration coefficients for the study area [33]. The C1 and C2 values are determined by linear fitting of ΔV and J × dt, where dt represents storm duration and is calculated as follows.

$$△V=C1\times J\times dt+C2$$

(2)

The formula for converting coastal erosion into shoreline retreat is as follows.

$$△X=△V/(B+d-SLR)$$

(3)

where ΔX is the shoreline retreat (m), ΔV is the erosion amount (m²), B is the berm height (m), d is the depth where beach profile erosion begins (m), and SLR is the sea-level rise (m).

Beach recovery during storms is modeled with a constant beach recovery rate. Coastal profiles tend to seek an equilibrium state in response to prevailing wave conditions. After an erosion event, the beach profile will attempt to recover through wave-driven sediment transport and aeolian processes to adjust to the new climate, that is, beach recovery. Assuming that, without SLR, the present rate of a 0.5 m/yr retreat [21] would continue into the future, the probability of a 0.5 m/yr shoreline retreat is taken to be 50% without SLR, implying that the processes of enhanced erosion or accretion are equally likely. Over a simulation period of 78 years (without SLR), this rate suggests a potential shoreline retreat of approximately 39 m with a 50% probability of exceedance. The beach recovery rate is subsequently determined as 0.0292 m/yr using a trial-and-error approach, based on this fixed retreat value. Since the distance from the shoreline to the edge of the main road is 130 m, we assume that retreat exceeding 130 m is not possible at this location.

3.4. Tipping Point

The shoreline position after each storm is recorded annually. Following Dastgheib [15], the final shoreline position is calculated using the average of the last 3 years of the simulation, and the 78-year shoreline retreat is obtained by subtracting the initial shoreline position. Each year is divided into a storm period and a less stormy period. The storm period occurs from November to April, and the rest of year is the less stormy period. The shoreline position after the less stormy period is taken as the final shoreline position for the year. The study uses the shoreline position in 2023 as a baseline, and hence the initial shoreline position in the starting year (2023) is set to 0. To identify tipping points, the annual shoreline position changes were plotted for each climate scenario, analyzing the years when shoreline-retreat rates began to increase noticeably and monotonically, indicating a transition to a new state characterized by increased erosion.

4. Shoreline Projection for Vung Tau Beach

The PCR-model-computed retreat curves for 2050, 2080, and 2100 for the study site are shown in Figure 11. The gray rectangle indicates the maximum allowed retreat distance (130 m) due to the road’s proximity to the beach.

In the same sea-level rise scenario, as time progresses, the shoreline-retreat distance continues to increase (Figure 11). In the SSP5-8.5 scenario, the retreat distance with a 50% exceedance probability in 2100 will be nearly four times that of 2050, retreating from 19 m to 89 m. In the SSP1-2.6 and SSP2-4.5 scenarios, the shoreline retreat has almost the same multiplier relationship as time progresses for the same exceedance probabilities. The 1% exceedance probability retreat will double in the SSP5-8.5 scenario, from 94 m to 217 m. However, due to the blocking effect of the road, the maximum retreat distance can only reach 130 m.

The exceedance probabilities for the same distance of shoreline retreat also continue to increase in time (Figure 11). In the SSP1-2.6 scenario, the exceedance probability of a 130 m shoreline retreat in 2080 is 3.5%, and in the SSP2-4.5 and SSP5-8.5 scenarios, it is 4.0% and 4.7%, respectively. Therefore, the intervals of the exceedance probability changes for the 2080 time horizon are 0.5% and 0.7% for SSP1-2.6–SSP2-4.5, and SSP2-4.5–SSP5-8.5, respectively. By 2100, the exceedance probabilities of the shoreline retreating 130 m under the SSP1-2.6 and SSP2-4.5 scenarios are 14.3% and 16.8%, respectively; in the SSP5-8.5 scenario, the shoreline will retreat to the edge of the road with a 22.0% exceedance probability in 2100, potentially causing the beach to disappear. Therefore, for the 2100 time horizon, the interval of exceedance probability changes for the three scenarios are 2.5% and 5.2%, significantly larger than for 2080.

The goal of identifying tipping points is to detect the time when shoreline retreat accelerates noticeably, providing a reference timeframe for informed coastal-zone management. For this purpose, here the annual change in the median shoreline retreat (referred to as P50 hereafter) is used as a diagnostic. The parameter P50 is calculated using the PCR model that simulates the potential retreat distances from 2023 to 2100 through 10,000 iterations. This results in 10,000 retreat values for each year, from which the distance at which there is a 50% probability of shoreline retreat is determined. The P50 fitted curve in Figure 12 indicates a sharp increase in the shoreline-retreat rate at the beginning of the simulation period across all three scenarios, attributed to the assumption of a zero value in the 3-year averaging method. The increased retreat rate at this time does not indicate a tipping point. The shoreline-retreat rate stabilizes around 2030.

Figure 12 illustrates that the tipping point for shoreline retreat is around 2050 across the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios. Notably, after 2050, the median estimated shoreline-retreat rate (P50, Figure 12) increases noticeably faster than it does in the period before 2050.

The P50 shoreline retreat shows a non-linear upward trend from 2030 to 2100 under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios. The 2030–2100 period has been segmented into three phases based on the temporal breakpoints at 2050 and 2080, corresponding to the periods 2030–2050, 2051–2080, and 2081–2100. Analysis of the average annual rate of change in P50 under different scenarios reveals that during 2030–2050 (Figure 13), the rates are relatively consistent, averaging around 0.77 m/yr. From 2051 to 2080, there is a gradual increase in the average annual change rate over time, increasing with higher emission scenarios, reaching a maximum of approximately 1.09 m/yr under SSP5-8.5. From 2081 to 2100, a significant increase in the average annual change rate of is observed, particularly under the SSP5-8.5 scenario, reaching 1.72 m/yr. This suggests that the impact of climate change on shoreline retreat becomes more pronounced toward the end of the 21st century.

5. Discussion

This study used the PCR model to predict the shoreline retreat at Vung Tau beach, Vietnam, under three sea-level rise (SLR) scenarios: SSP1-2.6, SSP2-4.5, and SSP5-8.5. The results indicate that the impact of SLR and storm events on shoreline retreat becomes increasingly pronounced with advancing years. This study is the first to apply the PCR model to the coastal environment of Vietnam. The PCR model, a physics-based tool for risk-informed coastal zone management, was utilized to project the probabilistic retreat of sandy beaches in response to climate change drivers. The median retreat distances projected by the PCR model for the end of the 21st century under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios were found to be 75 m, 80 m, and 89 m, respectively. A plethora of studies, encompassing those conducted in Japan [15], as well as comprehensive global analyses [13], underscore the limitations of conventional models such as the Bruun rule in fully accounting for the spectrum of uncertainties inherent to climate-related impacts, particularly within the context of high-emission scenarios. Notably, empirical evidence has demonstrated the significance of the probabilistic framework employed by the PCR model in elucidating the “deep uncertainties” inherent in predictive modeling. These uncertainties arise from the pronounced variability in storm patterns and the rates of sea-level rise (SLR), as highlighted by Thiéblemont et al. [34]. Additionally, the PCR model provides a more detailed analysis of the temporal evolution of shoreline retreat, which delves deeper into the implications of retreat timing, particularly the tipping point.

A critical finding is the identification of a tipping point in 2050 for shoreline retreat across the considered scenarios. This tipping point signifies a critical threshold beyond which the shoreline retreat is expected to accelerate, potentially leading to significant coastal erosion and loss of coastal habitats. This finding aligns with Barnard et al. [35], which presents a multidisciplinary case study from Santa Barbara, California (USA). Their study found that tipping points for beaches and wetlands could be reached with just 0.25 m or less of sea-level rise, projected to occur around 2050. This is similar to the finding at Vung Tau, indicating mid-century will be a critical time for coastal ecosystems worldwide adapting to climate change. Upon reaching a tipping point, the shoreline retreat shifts from a state of equilibrium to a new state of increased erosion, exerting a profound threat to the ecosystems bordering the shore. Research [35] indicates that even a relatively modest increase in sea levels can precipitate a critical threshold for shoreline retreat: a significant reduction in the width of ecologically vital intertidal zones due to sea-level rise, leading to the loss of ecosystem functions and services.

Moreover, the clear identification of the 2050 tipping point across all SLR scenarios provides a benchmark for regional and local adaptation measures. This aligns with the concept of adaptation tipping points discussed in recent studies by Haasnoot et al. [36], which suggest that reaching a tipping point implies a shift in adaptation strategy, from incremental changes to transformative, long-term solutions such as managed retreat. This is particularly relevant for Vung Tau, where tourism and local livelihoods heavily depend on coastal stability, making it a potential case study for managed retreat strategies in developing countries. The recent work by Haasnoot et al. [37] on adaptation pathways underscores the importance of acting early, as the window of opportunity for flexible, low-cost measures is shrinking. Given that only around 25 years remain before the tipping point, this study’s results support calls for prioritizing measures with short-term actions that can be effectively implemented soon.

There are limitations to the study, particularly regarding the PCR model’s assumptions [13]. The model is limited to sandy coasts and assumes no changes in coastal profile shape, which simplifies the complex interactions between coastal geomorphology, hydrodynamics, and sediment transport. Moreover, the study focuses on SLR and storm wave interactions but does not consider other factors such as aeolian processes and ocean currents. Due to the absence of direct erosion data before and after storm events at our study site, we utilized the XBeach model to assist in validating the shoreline-retreat model in this study. Another approach is to digitize remote-sensing images from the past few years, and then compare or validate the derived data against future projections.

To address these limitations, future studies should aim to incorporate more complex coastal dynamics, e.g., aeolian transport and sediment supply from the lower shoreface. Under conditions of sufficient data, wave setup or wave runup could also serve as one of the main indicators for identifying storms. Socio-economic variables could also be incorporated into shoreline-retreat models, recognizing that human behavior and policy decisions will play a crucial role in determining the severity of future impacts [38,39].

Finally, future research should explore adaptation pathways for Vietnam and similar regions in greater detail. Studies like Haasnoot et al. [37] have proposed generic adaptation pathways that are flexible and can be adjusted to specific local contexts. Applying these frameworks to Vung Tau could offer tailored solutions that consider both short-term, low-regret strategies and long-term transformative changes such as managed retreat.

6. Conclusions

This study applies the Probabilistic Coastline Recession (PCR) model to project future shoreline retreat and the potential existence of shoreline-retreat tipping points at Vung Tau beach in Vietnam. Shoreline retreat is simulated from 2023 to 2100 under SLR scenarios for SSP1-2.6, SSP2-4.5, and SSP5-8.5. The erosion model was calibrated using the XBeach model and wave data available for the Vung Tau coast, providing a robust basis for the probabilistic predictions of shoreline change.

Under the same sea-level rise scenario, the distance of shoreline retreat increases over time. Under the highest-emission scenario (SSP5-8.5), the shoreline is projected to retreat nearly four times the distance projected in 2050 (19 m) by the year 2100, with a median retreat of up to 89 m. Under the SSP5-8.5 scenario, the probability of losing the entire beach in front of the road at Vung Tau (i.e., retreat of 130 m) is 22%.

The exceedance probability for the same retreat distance increases significantly over time, with the probability of a 130 m retreat rising from 3.5% in 2080 under the SSP1-2.6 scenario to 14.3% by 2100. Particularly under high-emission scenarios, this increase in the exceedance probability for the same retreat distance is more pronounced. In essence, the influence of sea-level rise becomes increasingly prominent as time progresses.

The study highlights a critical tipping point anticipated for around 2050, beyond which the rate of shoreline retreat is expected to significantly increase under all three SLR scenarios. This acceleration could lead to substantial coastal erosion and the loss of coastal habitats, underscoring the urgency for strategic planning and adaptive measures, confirming that mid-century is a critical period for coastal adaptation.

The study also emphasizes the importance proactive adaptation planning. The 2050 tipping point serves as a critical benchmark for regional and local coastal management and planning. The research findings advocate for a balanced approach to adaptation, combining short-term interventions with long-term structural adaptations to maximize coastal resilience.