Hydrodynamic Analysis-Based Modeling of Coastal Abrasion Prevention (Case Study: Pulau Baai Port, Bengkulu)

Abstract

Pulau Baai Port, located strategically in the Indian Ocean and considered a vital maritime hub in Indonesia, grapples with persistent challenges related to abrasion and sedimentation, which negatively impact its maritime infrastructure. One of the affected components is the exposed gas pipeline installation along the port’s coastline. The sedimentation rate along Pulau Baai’s coastline is alarming, ranging from 600,000 to 800,000 m³/year, resulting in coastal abrasion at a rate of up to 20 m/year. This study focuses on three scenarios using MIKE 21, including a baseline without alternatives, shore protection alternatives, and jetty protection alternatives. A comprehensive dataset, incorporating bathymetric maps, wave patterns, current data, and sediment characteristics, supports the analysis of coastal dynamics, emphasizing the urgency for intervention. The research introduces the novelty of analyzing coastal abrasion through the exposure of underground pipelines, establishing a relationship between impacting factors such as wave height, tides, sedimentation, and coastal abrasion. Mitigation alternatives, particularly alternative model-2 with jetty protection, are recommended based on a thorough evaluation of the model performance and actual measurements. The results show that Pulau Baai’s sediment, primarily sandy, experiences substantial abrasion and coastline changes, notably in alternatives-2 and -3. The study anticipates potential sedimentation in certain sections of the subsea exposed pipelines in the absence of shore protection. The outcomes of this research provide a foundational guide for informed decision making and strategies to ensure the sustainable functionality of maritime infrastructure in Pulau Baai and similar coastal regions.

1. Introduction

As one of the crucial ports facilitating the maritime transportation of commodities in the Bengkulu Province, Indonesia, Pulau Baai Port is situated approximately 20 km from the city center of South Bengkulu [1,2,3]. This port also plays an instrumental role in supporting oil and gas explorations, with vital pipeline installations tracing its shoreline [4]. Consequently, it is imperative to minimize any disturbances that have the potential to harm the pipeline infrastructure along the Pulau Baai Port coastline. Pulau Baai Port directly faces the Indian Ocean, characterized by intense hydrodynamics and ocean waves, which significantly impact its coastline [5,6,7]. These ocean waves are more than mere natural forces; they generate substantial wave energy, resulting in significant sediment transport from the shoreline, often surpassing sediment deposition and causing sediment reduction and loss [8,9]. This predicament is exacerbated by the constant presence of western and eastern monsoon winds, which introduce siltation and sedimentation, leading to the erosion of local beaches [10,11,12].

The sedimentation rate along the coastline of Pulau Baai port reaches staggering proportions, with estimates ranging from 600,000 to 800,000 m³/year, while coastal abrasion steadily encroaches at a rate of up to 20 m/year [3,13,14,15,16]. The most severe siltation occurs at the port’s entrance channel, and if left unchecked, it could have severe consequences, including disruptions to economic sectors and the potential exposure of existing pipeline installations along its shoreline [17,18,19]. This is due to the main access to the port being hindered by siltation or erosion along the coast [20,21].

The sediment transport occurring in coastal areas is a crucial physical process leading to erosion and deposition, and this has been the focus of study for several authors employing a modeling approach [22,23]. Utilizing a comprehensive sediment transport model with a specific focus on the most affected port areas, the MIKE 21 modeling tool was employed to assess the impacts of waves, wind, and tidal surges on the coastal abrasion reality of Pulau Baai Port. The Spectral Wind-Wave Model (SW) and Hydrodynamic Model (HD) modules were utilized [11,24,25]. The calibrated and verified MIKE 21/3 FM Coupled Model was then applied to quantify the morphological changes in the shoreline due to sediment transport over the next 10 years. The results of the shoreline morphological changes from the simulated period are used as a reference to formulate effective and efficient alternatives for implementation at the study site. In the planning of appropriate alternatives, MIKE 21 was also used to simulate the effects of waves and tidal floods on currents and erosion dynamics, taking into account the planned construction of alternatives. This modeling was conducted using three different scenarios: a scenario without using alternatives, a scenario using shore protection alternatives, and a scenario using jetty protection alternatives.

A comprehensive dataset, including bathymetric maps, wave patterns, current data, and sediment characteristics, was compiled to support this research. These components provide essential elements for a comprehensive analysis of coastal dynamics at Pulau Baai Port, emphasizing the urgent need for proactive interventions. The primary aim of this research was to gain insights that will enable informed decision making when selecting optimal solutions to mitigate dredging challenges. The results of this model-based investigation will serve as a foundation for strategies guiding efforts to ensure the sustainable functionality of maritime infrastructure in the surveyed research area.

The novelty of this research lies in the analysis of coastal abrasion evident in Pulau Baai Port, demonstrated by the exposure of underground pipelines to the open air. The relationships between impacting factors such as wave height, tides, sedimentation, and coastal abrasion were examined to anticipate recurring incidents in locations with similar conditions to Pulau Baai Port’s coastline. Simulation results from evaluated mitigation alternatives using the three scenarios were compared with actual measurements to assess the model’s performance. The recommended alternative choices can be tailored based on the effectiveness and efficiency conditions of coastal areas facing similar issues.

2. Materials and Methods

In Figure 1, a flowchart outlines the study methodology tailored to assess sediment transport conditions at the study site, considering the influence of wave direction [26]. The ultimate objective is to identify the most suitable protection alternatives to mitigate the occurring abrasion. The evaluation of this methodology encompasses the following sequential steps:

Step 1.

Methodological assessment based on the literature and field research.

Step 2.

Preparation of input parameters for the numerical model, including bathymetry, wave boundary conditions, tidal variations, wind, currents, and relevant data [10].

Step 3.

Establishment of a 2D numerical model to simulate the hydrodynamics occurring at the study location.

Step 4.

Numerical modelling of alternative shore protection strategies considering the prevailing hydrodynamic conditions and changes in coastal morphology [27,28].

Step 5.

Comparative analysis of alternatives-1, -2, and -3 with respect to the coastal conditions of the port, within a specified temporal constraint of 10 years.

2.1. Study Area

The research was conducted along the shoreline of Pulau Baai Port with coordinates ranging from a longitude of 102°16′00″ to 102°18′30″ east and latitude of 03°53′00″ to 03°55′30″ south, covering an outer water area of 2183.47 ha and an inner water area of 1000 ha [2,3,13]. As can be observed in Figure 2, it is evident that there has been a noticeable change in the coastline conditions at the study location from 2019 to 2022 (Figure 2A–D). Figure 2A shows that in 2019, a significant portion of the coastal land area was still present at the research site. However, in 2020 and 2021, as depicted in Figure 2B,C, it is apparent that the coastal land has begun to erode due to ongoing erosion, reaching its most severe condition, as indicated in Figure 2D. In this last image, the extent of coastal land has become severely limited, and it is on the verge of transforming into a fully aquatic region. These changes are attributed to the impact of strong waves, causing coastal erosion and abrasion [28,29]. This phenomenon has consequences for the submerged pipeline installations within the shoreline, leading to exposure to the external environment [27,30,31], as depicted in Figure 3. The image was captured during a site survey to assess the condition of existing pipeline installations.

From this inspection, it is evident that the pipelines are significantly exposed from the shoreline, revealing the entire pipeline structure. Given the challenges observed at the port, a study on abrasion and wave dynamics will be conducted to obtain parameters for determining suitable alternatives for shore protection to be implemented at the study site. This study aims to address issues related to coastal morphology similar to those found at Pulau Baai Port, Bengkulu, Indonesia.

2.2. Sampling and Data Collection

Sampling procedures were conducted using topographic, bathymetric, and metocean measurement methods. Bathymetric measurements were carried out to acquire data on the seabed surface profiles, employing a Single Beam Echo Sounder, an instrument utilizing sound waves for reflection off the water bottom [32,33]. The bathymetric survey was divided into three distinct areas, as depicted in Figure 4. This survey specifically targeted areas along the coastline that suffered severe erosion and locations frequented by ships, rather than covering the entire coastal region. Area-1, which encompasses the outermost zone measuring 1500 m × 930 m, featured survey lanes set at intervals of 100 m × 100 m. Moving to Area-2, which covered the outer region near the shoreline, it spanned a total area of 543,300 m². In this area, the survey lanes were designed with a 10 m spacing along the main lane perpendicular to the shoreline and a 20 m spacing along lanes intersecting the main lane. Area-3 consisted of the bay/pool area with dimensions of 171 m × 156 m, and its lanes were configured with a 10 m spacing along the main lane perpendicular to the shoreline and a 20 m spacing along lanes intersecting the main lane.

The survey findings for these three areas provided seabed depth data. In Area-1, the seabed depth ranged from 3.55 m to 14 m below the Low Water Spring (LWS). Area-2 showed seabed depths ranging from 0 to 4.75 m below the LWS, while in Area-3, depths ranged from 5.25 m to 9.75 m below the LWS. The maximum seabed depth was recorded at the jetty head in Area-3, measuring 8.95 m below the LWS.

Table 1. Planned boundary coordinates for the bathymetric survey area.

Point Area	Boundary Point	Easting	Northing
Area-1	1	197,610.10	9,568,924.32
	2	198,699.66	9,569,885.73
	3	199,379.46	9,569,251.95
	4	198,204.89	9,568,207.89
Area-2	1	198,392.11	9,568,323.29
	2	198,505.32	9,568,304.53
	3	198,757.12	9,568,449.05
	4	198,866.37	9,568,481.43
	5	198,892.78	9,568,373.67
	6	199,008.25	9,568,310.85
	7	199,084.41	9,568,307.13
	8	199,190.73	9,568,354.56
	9	199,421.73	9,568,515.30
	10	199,744.38	9,568,913.65
	11	199,376.74	9,569,239.29
Area-3	1	199,129.72	9,568,040.02
	2	199,275.90	9,568,104.75
	3	199,347.36	9,567,954.81
	4	199,206.58	9,567,886.56

presents the data pattern of the bathymetric measurement coordinates for each area. In Area-1 and Area-3, 4 boundary points were utilized, whereas Area-2 had a total of 11 boundary points, owing to the survey’s adherence to the coastline’s shape in that area.

On the other side, the metocean method was performed to obtain tide, wind, wave, and current data at Pulau Baai Port. The wave and current observation survey employed an Acoustic Doppler Current Profiling (ADCP) instrument, with data collected at hourly intervals for 17 min over a period of 30 days. ADCPs employ the Doppler shift in echoes from pulsed signals within directed acoustic diverging beams to estimate flow velocities, making them suitable for deployment in diverse environments like oceans, rivers, and estuaries for extended durations (several months) to assess flow variability across a broad spectrum of time scales, typically sampling at a few hertz [34]. Tidal observations were conducted using a Valeport Tide Master instrument over the same 30-day period. Wind data samples were taken from a meteorological station installed at an elevation of 10 Mean Sea Levels (MSLs) within the study area. In addition, secondary wind and wave data were also obtained from global ECMWF data for calibration purposes.

Table 2. Coordinates of sampling locations for each data measurement.

Point Name	Coordinates
	Latitude	Longitude
ADCP	3°53′41.90″ S	102°16′52.20″ E
Tide	3°54′8.14″ S	102°17′28.65″ E
Wind	3°53′30.50″ S	102°18′0.39″ E

displays the coordinates of the sampling locations for each type of data measurement.

The classification of tidal types is determined based on the Formzahl number divided according to the following criteria [35,36]:

• Semi-Diurnal Tide: If the Formzahl (F) value is 0.00 < F ≤ 0.25;
• Mixed Tide, Prevailing Semi-Diurnal: If the Formzahl (F) value is 0.25 < F ≤ 1.5;
• Mixed Tide, Prevailing Diurnal: If the Formzahl (F) value is 1.5 < F ≤ 3.0;
• Diurnal Tide: If the Formzahl (F) value is F > 3.0.

This value can be calculated using the following Equation (1):

$$F=\frac{(K1+O1)}{(M2+S2)}$$

(1)

Here, F represents the Formzahl number; K1 stands for the main luni–solar diurnal constituent; O1 is the principal lunar diurnal constituent; M2 represents the principal lunar constituent; and S2 refers to the principal solar constituent [35].

2.3. Hydrodynamic Model

This research utilizeds the MIKE 21/3 coupled FM model, which includes the MIKE 21 Hydrodynamic Model (HD) and Spectral Wave (SW) and Sediment Transport (ST) modules to simulate hydrodynamics, wave characteristics, and sediment transport [24,37]. The MIKE 21 module simulates variations in water elevation and discharge to consider the response functions of forces in rivers, lakes, estuaries, and coastal areas. It employs a numerical solution to the full, time-dependent, and nonlinear depth-averaged Navier–Stokes equations, based on the conservation of mass and momentum [25,37]. Depth and water velocity were computed in a 2-dimensional grid using simplified equations, as outlined in Equations (2)–(4) below.

$$\frac{\partial \zeta }{\partial t}+\frac{\partial p}{\partial x}+\frac{\partial q}{\partial y}=\frac{\partial d}{\partial t}$$

(2)

$$\frac{\partial p}{\partial t}+\frac{\partial }{\partial x}\left(\frac{p^2}{h}\right)+\frac{\partial }{\partial y}\left(\frac{pq}{h}\right)+gh\frac{\partial \zeta }{\partial x}+\frac{gp\sqrt{p^2{+q}^2}}{C^2{h}^2}-\frac{1}{{\rho }_w}\left[\frac{\partial }{\partial x}\left({h\tau }_{xx}\right)+\frac{\partial }{\partial y}\left({h\tau }_{xy}\right)\right]-\Omega q-{fVV}_x+\frac{h}{{\rho }_w}\frac{\partial }{\partial x}\left(P_a\right)=0$$

(3)

$$\frac{\partial q}{\partial t}+\frac{\partial }{\partial y}\left(\frac{q^2}{h}\right)+\frac{\partial }{\partial x}\left(\frac{pq}{h}\right)+gh\frac{\partial \zeta }{\partial y}+\frac{gq\sqrt{p^2+q^2}}{C^2{h}^2}-\frac{1}{{\rho }_w}\left[\frac{\partial }{\partial y}\left({h\tau }_{yy}\right)+\frac{\partial }{\partial x}\left({h\tau }_{xy}\right)\right]+\Omega p-{fVV}_y+\frac{h}{{\rho }_w}\frac{\partial }{\partial y}\left(p_a\right)=0$$

(4)

where h(x,y,t) represents the water depth (m); ζ(x,y,t) signifies the time-varying water depth (m); (x,y,t) denotes the surface elevation (m); p,q(x,y,t) stand for flux density in the x, y directions (m³/s/m); C(x,y) is Chezy’s resistance (m¹/²/s); g is the acceleration due to gravity (m/s²); f(V) represents the wind friction factor; V,Vx,Vy(x,y,t) are wind velocity and components in the x, y directions (m/s); Ω(x,y,t) denotes the Coriolis parameter, latitude-dependent (s⁻¹); pa(x,y,t) indicates atmospheric pressure (kg/m/s²); ρw is the density of water (kg/m³); x,y are spatial coordinates in meters; t signifies time (s); and xx,xy,yy represent the effective shear stress components [38]. The stability in the MIKE model developed by DHI is controlled by the Courant Number or CFL Number, where the formula used is as follows [39]:

$$C_R=C_x\frac{∆t}{∆x}+C_y\frac{∆t}{∆y}$$

(5)

where C_x and C_y represent velocities; Δt denotes the time interval; and Δ_x and Δ_y are spatial increments, and the tidal wave velocity is derived from the following equation:

$$C=\sqrt{gh}$$

(6)

where g represents gravity, and h denotes water depth. The model can be considered stable when the CFL Number value is <1.

For the MIKE 21 SW module, a spectral wave model is employed to simulate wave transformations [40]. The MIKE 21 SW encompasses directional decoupling and full spectral formulations where parameterization is performed within the frequency range by incorporating the zeroth and first-moment wave-action spectrum as parameters [41]. The wave-action balance equation is formulated in Cartesian or spherical coordinates using Equation (7) below.

$$\frac{E}{\sigma }=\frac{\partial N}{\partial t}+\mathit{\nabla }\left(\overline{v}N\right)=\frac{S}{{\sigma }^{\prime \prime }}$$

(7)

where N(x,σ,θ,t) is the wave-action density; t is time; x = (x,y) is the Cartesian coordinate, and $\overline{v}$ (Cx,Cy,Cσ,Cθ) is the group velocity in four-dimensional phase space x, σ, and θ; S is the source term for the energy balance equation; and ∇ is the four-dimensional differential operator in the x, σ, and θ space. In this study, the full spectral formulation was chosen [42].

2.4. Data Calibration and Validation

The convergence level between observational data and modeling results was calculated using statistical parameters [31,37]. In this study, the Root Mean Square Error (RMSE) was employed to assess the model performance or prediction, utilizing the following equation:

$$RMSE=\sqrt{\frac{1}{n}\sum {(y_i-x_i)}^2}$$

(8)

where x_i is the observational data; Y_i is the modeling result; and n is the total number of data points.

2.5. Model Setup

In the SW simulations, a fully spectral and instationary formulation was applied with logarithmic spectral discretization, distinguishing wind-sea and swell at an 8 s frequency [38]. The average water level (0.36 m) over the domain was initialized from tidal variations at boundaries. Wind forcing utilized ECMWF database data, and open boundary waves were modeled with ECMWF database information. Conditions, including diffraction, wave breaking, and bottom friction, were set to default. Energy transfer considered quadruplet wave–wave interactions due to varying depths. White capping for wind-dominated waves followed the MIKE21 recommendations.

The SW results informed the HD runs. Higher-order time and space discretization (CFL 0.8) and an initial level (0.36 m) based on the mean sea level variation were employed. Coriolis forces, tidal components, and turbulence (Smagorinsky formulation, eddy viscosity 0.28) were applied. Bed resistance used Manning’s number (50 [m^1/3/s]) and a linearly varying wind friction factor.

The SW and HD results were extracted for a smaller area with a finer mesh. In analyzing the hydrodynamics’ effect on sediment transport, the MIKE21 HD and ST were run jointly. ST feedback recalculated currents and surface elevations. Models in the MIKE21 ST, combining wave and current effects, examined waves’ influence on sediment transport. The sediment transport rate variation was simulated with a grain size of 0.105 mm, porosity of 0.4, and relative density of 2.645. The time step (300 s) recorded sediment transport rates and morphology every 5 min. Morphological model conditions included zero sediment flux gradient and bed level change at boundaries. Higher-order schemes were applied for space and time discretization. Bed resistance remained at the calibrated value (50 m^1/3/s), updating every 5 min.

3. Result and Discussions

3.1. Wave Model

The input for the wave model employs a nesting model or a combination of models, integrating a larger area (denoted in red) with a smaller area (denoted in yellow) characterized by a higher grid resolution [43], as depicted in Figure 5. Simultaneously, Figure 6 presents bathymetric data obtained from surveys and global bathymetric data, which constitute essential inputs for the wave model.

Graphical representations in Figure 7 show the data results for wave height (Hs), wave period (Ts), and wind speed spanning in Figure 8, where all the data were from 2012 to 2022. Subsequently, based on the depicted graph, a wave rose was generated using the ADCP survey method. The model’s validity was assessed through a comparison with the wave rose derived from the ECMWF wave model data, as illustrated in Figure 9. The findings reveal a similarity between the wave rose data from the model and the survey data at the same location and during the same month. Hence, it can be inferred that ECMWF data are well suited for incorporation as input for the wave model, which will be coupled with the sediment model to capture the abrasion processes occurring in the study area.

3.2. Current Model

The current, wave, and sediment models were coupled to obtain patterns of currents, waves, and abrasion areas at Pulau Baai Port, particularly at a point of severe coastal abrasion where an installed pipeline is located. In this modeling, previously analyzed wave data, the National Digital Elevation Model (DEMNAS), and field sediment sample data were utilized. Each sediment sample underwent laboratory testing, certified to meet national standards (accredited by KAN). Tests were conducted in the laboratory for each sediment sample. The laboratory results indicate that sediment in the study area is sand with a specific gravity value of 2.645 and grain size of 0.1050. One current verification point and one tidal verification point were conducted to obtain the most accurate current model. Tidal verification results are presented in a diagram in Figure 10. From the data, it can be observed that the amplitude of the tidal model is slightly smaller relative to the observational amplitude, while the tidal phase in the field and model are the same. The graph shows that the tidal model values closely approximate the field tidal values. The RMSE value for a tidal point is 0.07 m.

Shifting to the validation process for a single point of the current, the verification was conducted by considering both the direction and speed of the current. The simulated results for both components of the velocity exhibit patterns that align remarkably well with the observed data. This alignment is consistent with the expectations derived from the simulation outcomes. The overall patterns of the current speed and direction in the model closely resemble the observed values, showcasing a high degree of fidelity with an RMSE value of 0.05 m/s. The graphical representation of the velocity, comparing observational and modelled current speeds, is depicted in Figure 11. This graphical representation provides visual insight into the degree of agreement between the observed and simulated current velocities at the specified point. The primary reason for the greater dominant current survey velocity compared to the model’s is the larger amplitude of the dominant tide survey in contrast to the tide model’s amplitude. Moreover, differences in the wind parameters employed in the model input, as opposed to the actual wind parameters at the current survey location, could also contribute to these variations.

3.3. Coastal Abrasion

The simulation model encompasses three distinct alternatives. Alternative-1 employs shore protection extending over a length of 1200 m represented as a horizontal red line in Figure 12, while alternative-2 incorporates jetty protection spanning 650 m with the planning location indicated by a vertical red line in Figure 13. In contrast, alternative-3 represents a scenario with no shore protection. The integration of the current, wave, and sediment models allows for an assessment of the magnitude of abrasion within the study area over 5 and 10 years. These alternatives and their respective configurations are visually depicted in Figure 12 and Figure 13.

3.3.1. Results of the Current Velocity Simulation with Alternative Model

In alternatives-1, -2, and -3, the dominant current direction is toward the northeast. This is attributed to the dominant wave approach angle, forming an angle with the shore protection, resulting in the occurrence of longshore currents, as illustrated in Figure 14. However, in alternative-1, the area inside the shore protection exhibits predominantly calm current speeds, with a maximum speed along the pipeline route of 0.07 m/s, whereas in the jetty area, it reaches 0.12 m/s. Meanwhile, in alternative-2, which employs jetty protection, the maximum current speed is 0.71 m/s, and alternative-3 has a maximum current speed of 0.76 m/s. In the overall channel area of the alternatives, the dominant current direction is southeast, entering the bay. This is influenced by the dominant wave direction originating from the northwest, pushing water masses into the bay. A comprehensive overview of the statistical values for current speeds is provided in

Table 3. Current velocity statistic values.

Location	Statistics	Current Velocity (m/s)
		Alt-1	Alt-2	Alt-3
Pipeline	Average	0.01	0.18	0.20
	Max	0.07	0.71	0.76
	min	0.00	0.00	0.00
Jetty	Average	0.01	0.01	0.02
	Max	0.12	0.06	0.14
	min	0.00	0.00	0.00
Tide	Average	0.02	0.00	0.18
	Max	0.08	0.05	0.61
	min	0.00	0.00	0.00

.

3.3.2. Results of Morphological Changes from the Results of Sedimentation Modelling for Each Alternative

Figure 15 presents the morphological changes observed over 5 and 10 years in each alternative within the pipeline area. In the analysis of Figure 15A,B, it is clear that the implementation of alternative-1 effectively prevents erosion in the pipeline area, shielding provided by the shore protection. Contrarily, Figure 15C,D reveals that the use of jetty protection fails to halt erosion in the pipeline area, primarily due to the influence of dominant currents induced by waves. These currents transport sand or sediment toward the bay, resulting in sedimentation or siltation in the bay area. Notably, erosion levels in the channel and pipeline area range from 1 to 3.2 m. Similarly, the outcomes in alternative-3, as depicted in Figure 15E,F, indicate more severe erosion extending toward the jetty location, emphasizing the absence of any protective measures.

The bathymetric and coastline conditions over 5 and 10 years in alternative-1 show no significant changes due to the protection provided by the shore protection, effectively mitigating coastal erosion, as depicted in Figure 16A,B. In alternative-2, as shown in Figure 16C,D, the bathymetric and coastline conditions in the channel area exhibit no significant changes, indicating a stable or equilibrium condition. However, outside the planned jetty protection area, erosion occurs, transforming the area into open water. In this alternative, the most substantial erosion occurs on the eastern coastline, resulting in a notable change in the coastline. The bathymetric simulation results for alternative-3 in Figure 16E,F reveal changes in bathymetry after 5 and 10 years in the jetty area, pipeline area, and channel area due to severe erosion in the absence of shore protection. This leads to changes in the coastline and the conversion of affected areas into open water. An overlay of the coastline change models at the study location over a 10-year period was conducted to observe the differences in changes for each alternative, as depicted in Figure 17. In the figure, the green line stands for the coastline condition for alternative-1, the red line represents the coastline for alternative-2, and the yellow line symbolizes the coastline condition for alternative-3. From the overlay results, the most significant coastline changes occur on the eastern side for alternatives-2 and -3.

3.4. Alternative Wave Models

After obtaining the bathymetric change model over a 10-year period from the erosion model, wave modelling was conducted to assess the impact of the bathymetric changes on wave conditions. Monthly wave roses were generated to analyze the wave height and dominant wave directions for each month. Furthermore, wave recurrence periods were calculated for 2, 5, 10, 25, 50, and 100 years. In alternative-1, using shore protection as one of the mitigation alternatives, wave heights along the pipeline route remained consistently low, owing to the protection provided by the shore protection measures. In contrast, alternative-2 with jetty protection and alternatives-3 with no protection exhibited significant wave heights in the channel and pipeline areas due to their open nature, dominated by swell waves characterized by long periods. Consequently, significant wave breaking was observed predominantly in areas near the shore. Furthermore, in alternatives-2 and -3, the dominant wave direction in the channel and pipeline areas was from the northwest. Across all alternatives, wave heights at the jetty area remained relatively low, facilitating jetty operations for 100% of each month or approximately 94% annually in the case of alternative-3. Figure 18, Figure 19 and Figure 20 present the results of the simulation model, wave roses, and wave recurrence periods for alternatives-1, -2, and -3.

The highest waves observed in model-1 (Figure 18) reached 1.26 m and were located in the northeast region of the coast. In this first alternative, the area where ships dock is shielded from the impact of high waves from the north, due to the installed shore protection, and is exposed only to wave energy from the bay. This alternative shows the most effective mitigation measures in attenuating incoming waves and minimizing the risk of coastal erosion. Additionally, the presence of shore protection ensures that docked ships are still unaffected by wave surges, as the wave heights in the bay range only from 0.1 to 0.2 m. However, this alternative proves less cost-effective due to the substantial budget required for the construction of shore protection spanning 1200 m.

Meanwhile, for the wave heights in alternative-2, which employs a 650 m long jetty protection, as depicted in Figure 19, it is evident that the wave heights are also around 1.2 m–1.3 m. The distinguishing feature of this alternative from model-1 lies in the dispersion of wave heights reaching into the bay area. Nevertheless, due to the presence of jetty protection, as indicated by the vertical yellow line in the Port area and along the west coast, the installations of gas pipelines and ship berths remain unaffected by these waves. With the mitigation scheme of model-2, the wave heights in that area range only from 0.3 to 0.54 m. However, model-2 has its drawback, as it may lead to suspended sediment transport at the southern end of the jetty protection due to incoming waves. To address this issue, the initially planned length of the jetty protection, which was 650 m, is optimized to 420 m.

On the other hand, alternative-3, which involves no protective alternatives (Figure 20), exhibits a uniform distribution of wave heights at 1.2 m–1.3 m, impacting the gas pipeline installations along the coastal edge of Pulau Baai Port. The absence of protective measures exacerbates erosion, as there is nothing to impede wave energy from eroding the coastal edge and exposing the buried pipelines.

Based on the annual extreme wave model data, recurrence periods were calculated using statistical concepts, particularly focusing on the 100-year cycle [44,45]. The primary objective was to estimate the most critical scenarios for the design, especially regarding the structural capacity to mitigate wave impacts. Recurrence period calculations were performed using the Weibull method [7,46] with k values of 0.75, 1, 1.4, and 2, and the Gumbel method, with respective to RMSE values of 0.021 m, 0.042 m, 0.041 m, 0.051 m, and 0.033 m. Among these methods, the Weibull method with k = 0.75 yielded the smallest RMSE value of 0.021 m, with a 90% confidence level and a 5% probability of exceeding the upper limit.

Table 4. Alternate wave re-periods 1, 2 and 3 at the point of the pipeline installation site.

Return Period		ALT1			ALT2	ALT3
	E	SE	S	SW	NW	NW
2-years
Hs (m)	0.02	0.06	0.10	0.11	1.23	1.25
Ts (s)	1.50	1.73	1.95	1.96	13.26	13.49
5-years
Hs	0.07	0.14	0.15	0.19	1.40	1.42
Ts (s)	1.78	2.17	2.18	2.42	15.05	15.26
10-years
Hs	0.12	0.22	0.19	0.27	1.56	1.58
Ts (s)	2.04	2.59	2.41	2.85	16.76	16.97
25-years
Hs	0.19	0.33	0.25	0.38	1.80	1.81
Ts (s)	2.44	3.22	2.74	3.50	19.33	19.52
50-years
Hs	0.25	0.43	0.30	0.48	1.99	2.01
Ts (s)	2.77	3.75	3.02	4.04	21.45	21.64
100-years
Hs	0.31	0.53	0.35	0.58	2.20	2.22
Ts (s)	3.12	4.30	3.32	4.61	23.71	23.89

and

Table 5. Alternate Wave Re-Periods-1, 2 and 3 at jetty location points.

Return Period	Alt1								Alt2								Alt3
	N	NE	E	SE	S	SW	W	NW	N	NE	E	SE	S	SW	W	NW	N	NE	E	SE	S	SW	W	NW
1-year
Hs (m)	0.09	0.05	0.03	0.03	0.08	0.14	0.12	0.09	0.24	0.02	0.01	0.01	0.01	0.11	0.17	0.26	0.48	0.02	0.01	0.02	0.03	0.12	0.19	0.33
Ts (s)	1.85	1.66	1.52	1.56	1.80	2.16	2.06	1.88	2.72	1.46	1.44	1.43	1.44	2.01	2.30	2.83	4.07	1.47	1.45	1.50	1.52	2.06	2.45	3.20
5-years
Hs (m)	0.19	0.16	0.08	0.11	0.19	0.21	0.16	0.20	0.29	0.05	0.05	0.04	0.05	0.21	0.28	0.35	0.57	0.07	0.06	0.09	0.10	0.21	0.28	0.45
Ts (s)	2.44	2.26	1.83	1.97	2.43	2.55	2.29	2.48	2.98	1.68	1.66	1.61	1.64	2.54	2.91	3.35	4.54	1.77	1.69	1.88	1.95	2.56	2.93	3.90
10-years
Hs (m)	0.29	0.26	0.13	0.18	0.30	0.28	0.20	0.30	0.33	0.09	0.09	0.07	0.08	0.30	0.38	0.44	0.65	0.12	0.10	0.16	0.18	0.30	0.36	0.57
Ts (s)	2.99	2.82	2.12	2.35	3.02	2.91	2.51	3.06	3.22	1.88	1.86	1.79	1.83	3.04	3.49	3.84	4.99	2.05	1.92	2.24	2.36	3.03	3.38	4.56
25-years
Hs (m)	0.44	0.41	0.21	0.28	0.46	0.38	0.26	0.46	0.40	0.15	0.14	0.12	0.13	0.43	0.54	0.58	0.77	0.20	0.16	0.25	0.29	0.43	0.48	0.75
Ts (s)	3.82	3.66	2.57	2.93	3.92	3.46	2.84	3.92	3.59	2.19	2.16	2.04	2.11	3.79	4.37	4.59	5.65	2.47	2.26	2.78	2.98	3.75	4.06	5.55
50-years
Hs (m)	0.56	0.53	0.28	0.36	0.59	0.46	0.31	0.58	0.45	0.19	0.19	0.16	0.17	0.54	0.67	0.69	0.87	0.26	0.21	0.33	0.38	0.53	0.58	0.90
Ts (s)	4.51	4.35	2.93	3.40	4.65	3.92	3.11	4.63	3.89	2.44	2.42	2.26	2.35	4.41	5.09	5.21	6.20	2.81	2.54	3.23	3.48	4.34	4.63	6.37
100-years
Hs (m)	0.69	0.67	0.35	0.46	0.73	0.54	0.36	0.72	0.51	0.24	0.24	0.20	0.22	0.66	0.81	0.80	0.97	0.32	0.26	0.42	0.48	0.65	0.69	1.05
Ts (s)	5.23	5.09	3.32	3.91	5.44	4.40	3.40	5.39	4.21	2.71	2.68	2.48	2.60	5.07	5.86	5.86	6.79	3.18	2.83	3.71	4.02	4.97	5.23	7.24

present the statistical results of the recurrence periods for each wave direction.

4. Conclusions

In summary, Pulau Baai’s sediment is predominantly sandy, with sedimentation and erosion primarily influenced by longshore currents induced by wave direction. Substantial abrasion and significant coastline changes occur, particularly in alternatives-2 and -3, driven by longshore currents leading to transport. Simulation for alternative-3 in the jetty area experiences erosion, transforming the region into open water over approximately two years of model simulation. Depth alteration or erosion in the channel and pipeline route within alternatives 2 and 3 ranges from 1 to 3.2 m. Unlike alternative-1, which closes all wave access and has shore protection in the middle of the coastline area, the erosion depth value in alternatives-2 and -3 is influenced by the wave height that spreads evenly at the jetty point and pipe installation because the beach in the central area is not blocked by any building protection.

The most suitable mitigation alternative for issues in Baai Island Port is to use alternative model-2 with jetty protection. This alternative, initially planned at 650 m and optimized to 420 m, is suggested to prevent erosion in the jetty area where the ship rests. Potential sedimentation is anticipated in certain sections of the existing subsea pipeline route. After ten years of erosion, a significant increase in wave height (Hs) within Pulau Baai’s waters is observed: 0.22 m for alternative-1 and 1.32 m for alternatives-2 and -3, representing an elevation of approximately 1.1 m from existing conditions. Given substantial waves in the Pulau Baai area, there is a considerable risk of vessels colliding with exposed pipelines in the absence of shore protection. This is due to the lack of obstacles diverting the incoming wave direction, pushing vessels into the area impacted by abrasion.

Wave heights for alternatives-1, -2, and -3 at the jetty are relatively low, allowing year-round operational capabilities for alternatives-1 and -2 due to dominant wave heights remaining below 0.5 m. In alternative-1, wave heights along the pipeline route are kept low due to the presence of shore protection. Conversely, alternatives-2 and -3 exhibit higher wave heights, allowing for the consideration of a 100-year wave height with a magnitude of 2.2 m from the northwest direction.

Reviewing cost effectiveness and mitigation effectiveness for abrasion issues, alternative-2 is a suitable protection to be applied in the coastal area of Baai Island Port. The results of this research on mitigation alternatives for abrasion are expected to be applicable to locations with similar morphological conditions and issues along the Baai Island Port coastline.