Classifying Headland-Bay Beaches and Dynamic Coastal Stabilization

Abstract

In this paper, a framework is developed for classifying bay types using stability and a sediment supply source. The framework is used to classify a total of 212 headland-bay beaches in Southeast Asia. The results show that static bays, bays with no sediment supply, and dynamic bays (with a sediment supply), account for 36% and 64%, respectively, while stable bays, bays that can maintain their long-term shoreline stability, and unstable bays (changing their shape over time), account for 69% and 31%, respectively. The results reveal the importance of dynamic bays. The dynamic parabolic bay shape and bay characteristic equations have been verified to bridge the knowledge gap of coastal stabilization and management in dynamic bays. The verification of bay characteristic equations shows an efficiency index of more than 78%. The bay characteristic equation shows that dynamic bays are highly sensitive to low sediment supply and become less sensitive when the sediment supply increases. Knowledge of the coastal stabilization concept successfully implemented for static unstable bays has been extended in this study and applied to stabilize dynamic unstable bays using the verified equations. Sediment control and the combined method are developed in this study, and a case study is presented on the stabilization of a dynamic unstable bay.

1. Introduction

Headlands or headland-bay beaches (HBBs) are present in approximately half of the world’s coastlines [1,2,3]. HBBs are common features in shorelines experiencing predominant waves with at least one natural or artificial fixed point, leading to the diffraction of incoming waves [4]. In most cases, HBBs are asymmetric in shape, characterized by a shadow curved zone, gentle transition, and/or relatively straight tangential segment at the downdrift end [5]. An example of a HBB is shown in Figure 1. Hsu et al. [5] classified HBBs by dividing their planform stability into three types: static equilibrium bay (SEB), dynamic equilibrium bay (DEB), and unstable bay (UB). In a SEB, the predominant waves break simultaneously around its entire periphery; hence, the net longshore sediment transport produced by longshore currents is almost non-existent, and no additional sediment is required to maintain its stability. On the other hand, a DEB requires a sediment supply to maintain its stability. If the sediment supply ceases, the shoreline will recede toward the shoreline of the SEB as a limit. An UB cannot maintain its stability [5,6,7]. The classification can be used to explain the existing condition of a HBB and preservation measures that should be implemented. The measures aim to maintain the HBB stability of stable bays or stabilize unstable bays.

Klein et al. [3] classified HBBs in Santa Catarina into three types using the Parabolic Bay Shape Equation (PBSE): SEB, close to SEB and DEB (or UB). A close to SEB is one with a sediment supply and can be fitted almost perfectly with the PBSE. The PBSE can be used to successfully classify SEBs by considering only one parameter, namely wave obliquity. However, the PBSE cannot be used to classify DEBs because wave obliquity, as well as sediment supply, are their main parameters. The study classified DEBs and UBs together because DEBs may become UBs when the sediment supply changes. It is necessary to develop a method for classifying DEBs and UBs separately to determine the actual condition of the bays with specific measures. The present study extends the research of Klein et al. [3] to develop a practical method for classifying HBB types. A qualitative framework for HBB classification is developed in this research, providing systematic steps.

Recently, equations involving a relationship between sediment supply and HBB have been developed using experimental data [8,9], but not verified with field data. The present study verifies the equations with field data to obtain tools for computing the bay planform and its characteristics. The verified equations can be used to compute the effects of a sediment supply change and stabilizing dynamic unstable bays. The coastal areas in Southeast Asia (SEA) under study in this paper have been subjected to shoreline erosion for decades [10,11,12,13]. The sediment supply from rivers to SEA beaches has been reduced, causing shoreline erosion [11]. The beaches become unstable and need more sediment supply to maintain stability. This paper demonstrates a method for coastal stabilization and the management of dynamic UBs in SEA using the verified equations.

Accordingly, the present study aims to develop a systematic framework for bay classification, verifying equations for computing the dynamic bay planform and characteristics using field bays in SEA. Finally, a conceptual method is proposed to apply the verified equation for coastal stabilization and management.

2. Materials and Methods

2.1. Study Area

The study area covers the coastlines of five countries in SEA: Cambodia, Malaysia, Myanmar, Thailand, and Vietnam, which are subject to a persistent northeast and southwest monsoon climate [14]. The northeast and southwest monsoons influence the coastal processes in the Andaman Sea and the Gulf of Thailand, respectively [15]. The monsoons generate waves in a predominant direction, creating equilibrium bays. The average tidal range in SEA is 2 m (micro-tides), and the tidal heights are not sufficiently high enough to generate strong currents [16]. The tidal range can be classified as wave-dominated beaches using the criteria proposed by Short [17]. One assumption of the PBSE (used to develop the equation verified in the present study) is that a bay is in a micro-tidal environment [5,18]. The HBBs are selected under the following criteria: (1) the bay must be sandy; (2) it must only have one sediment supply source in the upcoast area; (3) no sheltering must exist, such as rocks or islands within the embayment; (4) the upcoast diffraction point or upcoast control point (UCP) must be visible; (5) no shadows, clouds or vegetation cover must appear on the satellite images of the selected area; and (6) its size must be between 300 m and 10 km. The first three criteria are defined to follow the assumption of the verified equations in the present study and to not select bays with a complex planform. The fourth and fifth criteria are designed to include only bays that can be analyzed using satellite images. The final criterion is intended to exclude very small or large HBBs, which may have different processes to average-sized bays. A total of 212 bays were included in the present study, as shown in Figure 2.

2.2. General Methodological Remarks

2.2.1. Types of Headland-Bay Beaches

The degree of stability in a HBB can be used to define the measures that should be implemented. For example, in the case of a natural HBB identified as a SEB, the “do nothing” option should be adopted to preserve its stability. A DEB can improve its stability by introducing an artificial UCP to convert it from dynamic to static [5].

Klein et al. [3] classified 90 HBBs in Santa Catarina, Brazil. The PBSE was used to classify bay type. If the predicted planform from the PBSE was landward of the existing shoreline, the HBB would be DEB or UB. DEBs and UBs could not be classified separately using the PBSE. Moreover, this method may not be applicable for use with all HBBs. Ingleses Beach is an example of a DEB with a shoreline position almost perfectly matching the predicted planform. This bay has a sediment supply from sand bypassing a natural headland.

Tasaduak et al. [10] classified HBBs in Thailand using satellite images taken at different time intervals to analyze the long-term shoreline change. A bay is said to be at the equilibrium state if its periphery has remained almost unchanged. The SEB and DEB were classified using the available sediment supply source. This study showed that rivers can also be sediment supply sources for bays.

The framework developed in this present study employs a practical method for HBB classification with the purpose of obtaining a systematic method for classifying DEBs and UBs separately. This method can be used to classify bay types using long-term shoreline stability and the availability of a sediment supply source. Dynamic bay sub-types can be classified for sediment supply sources using the method proposed in the present study. A conceptual flowchart for selecting measures with respect to the type of bay is also developed in the present study.

2.2.2. Bay Planform Equations

Several empirical equations have been proposed to determine the shoreline planform of a headland-bay beach at an equilibrium state, such as logarithmic spiral [19], PBSE [18], and hyperbolic-tangent [20]. These equations can be used to determine only the planform of SEB. The PBSE is the most widely used equation [21] because (1) only the PBSE has the coordinate origin that coincides with the physical process of the HBBs. (2) Beach stability issues can be addressed. (3) It provides an explicit relationship between beach alignment and incoming waves [5]. The PBSE was developed by Hsu and Evans [18] using reanalyzed experimental models from Vichetpan [22] and Ho [23] and prototype headland-bay beaches in Australia. It is a second polynomial equation based on two primary parameters: wave obliquity (β) and control line length (R₀), representing the distance between the upcoast diffraction point or UCP to the nearest straight downcoast beach or downcoast control point (DCP). The characteristics of the PBSE are shown in Figure 3. The PBSE is a function of β only, indicating that the shape of the SEB depends mainly on wave obliquity.

Recently, Tan and Chiew [24] modified the PBSE using only experimental data to obtain an equation for DEBs. The source of sediment in an unlimited amount at the updrift end was supplied for the experiment. Therefore, this equation cannot be used to determine the effects of a sediment supply change.

Tasaduak and Weesakul [9] proposed an equation to determine the dynamic equilibrium planform (DEP). It was derived by modifying the PBSE using experimental data with a wide range of wave obliquity (20–60°) and sediment supply ratio (SSR, 0.055–0.268). A new parameter, namely SSR, was introduced into the C coefficients of PBSE, representing the difference between the sediment supply into the bay (Q_r) and potential longshore sediment transport (Q_lt). When the SSR approaches zero and infinite value, this equation will approach those of Hsu and Evan [18] and Tan and Chiew [24], respectively. It is chosen for use in the present study because of its flexibility, as previously explained, despite it not yet being verified with field bays.

Elshinnawy et al. [25] derived an equation following that of Tan and Chiew with an additional parameter to include the effect of sediment supply to the bay resulting in the bay planform not being parallel with the wave crest of incident waves. This equation was verified with only five DEBs in Brazil. The verified bays have a wave obliquity of around 50°. The predicted planform can match well with the field. The equation assumes that the DCP of the DEB is at the same location as the SEB, rendering it invalid as the DCP moves shoreward while supplying sediment to the bay.

The present study verifies the equation of Tasaduak and Weesakul [9] with field bays. The objective of bay planform verification is to obtain an equation to determine the DEP in the field, and the results of SSR will be used for bay planform analysis.

2.2.3. Bay Characteristic Equations

Silvester and Hsu [6,7] proposed empirical equations to determine the maximum indentation distance ratio (a/R₀) and its location (${\theta }_c$). The definitions of a and θ_c are shown in Figure 3, where a is the greatest indentation distance compared to the control line at θ_c to the wave crest line. The equations were developed using the same dataset as the PBSE. The equations provide a swifter method for determining bay stability when a static equilibrium planform is not essential [3,18]. The equation for determining a/R₀ was verified by Klein et al. [3] using SEBs in Brazil. The study shows that the a/R₀ equation has a coefficient of determination (R²) = 0.4164. However, the defined DCP did not follow the assumption of Silvester and Hsu [6,7].

Tasaduak [8] proposed an equation to determine a/R₀ and ${\theta }_c$ based on that of Tasaduak and Weesakul [9]. This equation can be used to compute the a/R₀ and ${\theta }_c$ of both SEBs and DEBs. The equation has an implicit function of β, ${\theta }_c$, and SSR. When β and SSR are known, a/R₀ and ${\theta }_c$ can be determined by trial and error. The equations can be verified with field data to identify the practical maximum erosion of SEB and DEB.

2.3. Materials

2.3.1. Satellite Images

Satellite images are publicly available to provide a solution for shoreline change over the past three decades [26] and have been used to analyze shoreline change [12,26,27,28,29]. Luijendijk et al. [12] detected global sandy shorelines using Google Earth satellite images between 1984 and 2016. The study showed that analysis of the composite images can significantly decrease the effect of tides on the detected shoreline positions. Moreover, Vieira da Silva et al. [30] indicated that waves are the main parameter for HBBs with sediment bypass, while tides play a secondary role. The present study follows the study from Luijendijk et al. [12], which successfully detected the shoreline change. A time series of Google Earth satellite images was collected for this present study to minimize the tidal effect on shoreline detection even though tides are not the main driver in SEA. Satellite images from 1984, 1992, 2000, 2008, and 2016 are used to analyze long-term shoreline stability.

2.3.2. Field Sediment Supply Ratio

Field SSR data were collected to verify the bay planform equation. The SSR field data of four bays with stable shorelines in Thailand were collected by Tasaduak et al. [10], all of which only have a sediment supply from the river. These bays are Klong Ban Klaeng, Khao Laem Riw, Patong, and Nang, with SSRs of 0.051, 0.0981, 0.159, and 0.155, respectively. The quantity of sediment supply was computed using regional analysis, indicating an empirical relationship between the catchment area and rate of sediment transport in the river. The longshore sediment transport was computed using the CERC formula [31] under deep water wave conditions.

2.4. Approach

2.4.1. Development of Headland-Bay Beach Classification Framework

The present study extends the research conducted by Klein et al. [3] to propose a practical method for HBB classification. The qualitative framework was developed based on two main concepts, namely long-term shoreline stability and the availability of a sediment supply source in the present study. First, a bay can be classified into two types: stable and unstable, using the shoreline stability concept. A bay is considered to be stable if its shoreline does not change over a period of 20–30 years or beyond [5]. If a shoreline change occurs, the bay is said to be unstable. It should be noted that stable and equilibrium states are different. A bay is at the equilibrium state when the incoming sediment supply equals the outgoing sediment transport. A bay must maintain its equilibrium state for at least 20 years to be considered stable. Dynamic bays become stable only if their sediment supply does not change for more than 20–30 years. Static bays are always stable if they are SEBs because they receive no sediment. Stability of the bay shoreline in the long term can be analyzed using Google Earth satellite images at different time intervals.

Secondly, the availability of a sediment supply source can be used to classify HBBs into two main types: static and dynamic. If no sediment supply source is found in the bay, it is considered to be static. For bays with a sediment supply or dynamic bays, there are two possible types of sediment supply sources, namely upcoast bypassing [25,29] and rivers [10,11,32]. The sediment supply source can be identified in the satellite images. A bay is considered to have a sediment supply from a river, provided the river is within the upcoast part of the bay. A sediment supply from upcoast bypassing can be addressed by checking possible sediment supply sources such as available rivers or DEBs adjacently outside the bay upcoast.

The HBBs can be categorized into six types, the first three of which belong to the stable bay group: (1) static stable bay (SSB), (2) dynamic stable bay (DSB) from sediment bypass (DSBB), and (3) DSB from a river (DSBR). The last three types belong to the unstable bay group: (4) static unstable bay (SUB), (5) dynamic unstable bay (DUB) from sediment bypass (DUBB), and (6) DUB from a river (DUBR). The framework for HBB classification in the present study is illustrated in Figure 4 and consists of the following systematic steps.

(1) Check whether the bay is a HBB: A headland must exist at the upcoast of the bay for a HBB to be assumed. If it is a HBB, the classification will continue as set out in step 2.1. If not, step 2.2 should be followed.

(2.1) Collect satellite images: Satellite images over a long period of time must be collected. The present study collected a time series of Google Earth satellite images covering 32 years (1984, 1992, 2000, 2008, and 2016) for each selected HBB in SEA.

(2.2) Stop classifying the bay type: The classification needs to be stopped since it is not a HBB.

(3) Delineate the shoreline from the satellite images: The shoreline in each period needs to be delineated to analyze the changes.

(4) Compare the time series of the shoreline: The shoreline in each image is compared. If the shorelines of a bay are in the same position (no change in shoreline), the bay is considered to be stable. If the bay contains one shoreline that does not match the others (a change in shoreline), the bay is unstable.

(5) Address the sediment supply source: the sediment supply source in the bay is identified.

2.4.2. Verification of Bay Planform Equation

Verification of the bay planform was conducted to prove that the equation from Tasaduak and Weesakul [9] can be used in the field. The equation is expressed as Equation (1) with its C coefficients shown in Equations (2)–(4). The definition of Equation (1) is shown in Figure 3. Equation (1) will be called dynamic parabolic bay equation (DPBSE) throughout this paper. The DPBSE was verified with DSBs classified in the present study. Two methods of verification, i.e., comparing field planform and field SSR, were used. An optimal SSR that can fit DPBSE to the field planform best was used in the verification process with the field planform. For comparison with the field SSR, the field planform was verified with DEP computed using field SSR. A total of 4 bays in Thailand (Klong Ban Klaeng, Khao Laem Riw, Patong and Nang) were used in the verification with field SSR. The accuracy of DPBSE was measured using 3 indicators: Efficiency Index (EI), Relative Root Mean Squared Error (RRMSE), and Coefficient of determination (R²).

$$\frac{R}{R_0}=C_0+C_1 \left(\frac{\beta }{\theta }\right)+C_2 {\left(\frac{\beta }{\theta }\right)}^2$$

(1)

where R₀ is the control line or length of the line joining the upcoast diffraction point or UCP to the near straight downcoast beach or downcoast control point (DCP). β is an angle between the incident wave crest and the control line. R is the radii measured from the UCP to the bay periphery at angle θ to the wave crest line.

$$C_0=\left(-0.00062+0.00041e^{-4SSR}\right){\beta }^2+\left(0.0338-0.024e^{-3.6SSR}\right)\beta -0.7154+0.6572e^{-4.4SSR}$$

(2)

$$C_1=\left(0.0014-0.0012e^{-7.5SSR}\right){\beta }^2+\left(-0.0703+0.0759e^{-8SSR}\right)\beta +2.4824-1.7015e^{-7.5SSR}$$

(3)

$$C_2=\left(-0.00072+0.000704e^{-12SSR}\right){\beta }^2+\left(0.032-0.048e^{-15SSR}\right)\beta -0.6227+0.904e^{-15SSR}$$

(4)

2.4.3. Verification of Bay Characteristic Equations

The present study verifies bay characteristic equations to check their performance in the field. Two equations from Silvester and Hsu [6,7] and one from Tasaduak [8] are expressed in Equations (5)–(7), respectively. The definitions of these equations are shown in Figure 3. These equations were analyzed using both the SSBs and DSBs classified in the present study. Three performance indicators (EI, RRMSE, and R²) were used to evaluate the model performance.

$$\frac{a}{R_0}=0.014\beta -0.000094{\beta }^2$$

(5)

$${\theta }_c=63+1.04\beta$$

(6)

where a is the greatest indentation distance compared to the control line at θ_c to the wave crest line.

$$\frac{a}{R_0}=\mathit{cos}\left(\frac{\beta \pi }{180}\right)\left[C_0+C_1\left(\frac{\beta }{{\theta }_c}\right)+C_2{\left(\frac{\beta }{{\theta }_c}\right)}^2\right]\left[\mathit{sin}\left(\frac{{\theta }_c\pi }{180}\right)-\mathit{cos}\left(\frac{{\theta }_c\pi }{180}\right)\mathit{tan}\left(\frac{\beta \pi }{180}\right)\right]$$

(7)

3. Results

3.1. Types of Headland-Bay Beaches in Southeast Asia

The classification results for 212 bays in SEA are presented in

Table 1. Classification of headland-bay beach stability.

Type		Number of Bays			Percentage
		Stable	Unstable	Total	Stable (%)	Unstable (%)
Static		49	28	77	63.64	36.36
Dynamic	Bypass	46	22	68	67.65	32.35
	River	51	16	67	76.12	23.88
	All	97	38	135	71.85	28.15
Total		146	66	212	68.87	31.13

(Further details of HBB classification for each country are shown in the Appendix A,

Table A1. Stability of headland-bay beaches in each country.

Country	Type		Number of Bays			Percentage
			Stable	Unstable	Total	Stable (%)	Unstable (%)
Cambodia	Static		1	5	6	16.67	83.33
	Dynamic	Bypass	6	0	6	100.00	0.00
		River	5	2	7	71.43	28.57
		All	11	2	13	84.62	15.38
	Total		12	7	19	63.16	36.84
Malaysia	Static		2	6	8	25.00	75.00
	Dynamic	Bypass	9	8	17	52.94	47.06
		River	7	8	15	46.67	53.33
		All	16	16	32	50.00	50.00
	Total		18	22	40	45.00	55.00
Myanmar	Static		20	4	24	83.33	16.67
	Dynamic	Bypass	17	1	18	94.44	5.56
		River	30	2	32	93.75	6.25
		All	47	3	50	94.00	6.00
	Total		67	7	74	90.54	9.46
Thailand	Static		12	7	19	63.16	36.84
	Dynamic	Bypass	6	12	18	33.33	66.67
		River	3	2	5	60.00	40.00
		All	9	14	23	39.13	60.87
	Total		21	21	42	50.00	50.00
Vietnam	Static		14	6	20	70.00	30.00
	Dynamic	Bypass	8	1	9	88.89	11.11
		River	6	2	8	75.00	25.00
		All	14	3	17	82.35	17.65
	Total		28	9	37	75.68	24.32
All	Static		49	28	77	63.64	36.36
	Dynamic	Bypass	46	22	68	67.65	32.35
		River	51	16	67	76.12	23.88
		All	97	38	135	71.85	28.15
	Total		146	66	212	68.87	31.13

). The locations of HBBs with respect to their stability are illustrated in Figure 5. The results show that the number of dynamic HBBs (135 bays) is approximately double that of static HBBs (77 bays). One-third of the dynamic bays are unstable. There are fewer UBs than stable bays, equating to one-third of the total. There are more dynamic UBs than static. All SUBs become unstable with the construction of coastal structures or beach nourishment. The dynamic bays have almost equal numbers of both sediment supply types. In contrast, dynamic bays with sediment bypass seem to be more unstable.

3.2. Verification of Dynamic Parabolic Bay Shape Equation (DPBSE)

The DPBSE has been verified using both the field bay planform with 97 DSBs and field SSR. Examples of field bay planform and field SSR verification are shown in Figure 6a,b, respectively. The equation verified with the field planform shows high model performance in most bays. The range of performance indicators, EI, RRMSE, and R² are 94.71–99.99%, 0.11–5.42%, and 0.99–1.00, respectively. The average performance of the indicators, EI, RRMSE, and R² is 99.12%, 1.23%, and 0.99. The results of the field SSR verification with four bays in Thailand are shown in

Table 2. Verification results of the DPBSE with field SSR.

Name	Field	Performance Indicator
	SSR	EI (%)	RRMSE (%)	R2
Khlong Ban Klaeng River Mouth	0.051	99.94	0.15	0.99
Khao Laem Riw	0.091	98.69	2.12	0.99
Nang	0.159	96.89	2.86	0.99
Patong	0.155	98.76	1.36	0.99
	Avg.	98.57	1.37	0.99

. A high R² is shown in the verification with the field bay planform.

3.3. Stable Bays in Southeast Asia

This section studies the characteristics of the SSB and DSB. A total of 146 stable bays in SEA were measured and analyzed in this study. All parameters except the SSR were measured directly from the satellite images. The SSR was obtained by fitting the DSBs with the DPBSE using the optimum SSR value. The average values of bay characteristics are summarized in

Table 3. Average characteristics of stable bays in Southeast Asia.

Type	Basic Characteristics				Erosion Characteristics
	R0 (km)	β (deg)	θmax (deg)	SSR	a (km)	a/R0	θc (deg)	A (km2)
SSB	1.51	39.23	118.52	-	0.57	0.38	99.38	1.07
DSBB	1.93	33.31	116.56	0.21	0.57	0.30	81.67	1.60
DSBR	3.25	35.42	117.91	0.18	0.92	0.31	86.28	3.09

(Further details of which can be found in the Appendix A,

Table A2. Characteristics of stable bays in Southeast Asia.

Country	Type		R0 (km)	β (deg)	θmax (deg)	SSR	a (km)	a/R0	θc (deg)	A (km2)
Cambodia	SSB	range	1.59	37.66	125.00	-	0.64	0.40	102.00	0.86
		mean	1.59	37.66	125.00	-	0.64	0.40	102.00	0.86
		SD	-	-	-	-	-	-	-	-
	DSBB	range	0.79–9.97	24.35–46.00	75.00–133.00	0.03–0.88	0.16–2.56	0.20–0.37	62.00–98.00	0.09–17.36
		mean	2.69	29.61	99.33	0.24	0.71	0.27	77.83	3.17
		SD	3.59	8.20	22.29	0.33	0.91	0.06	12.84	6.95
	DSBR	range	0.96–4.28	37.2–56.57	112.50–172.00	0.01–0.36	0.45–1.81	0.29–0.47	81.00–110.00	0.35–6.83
		mean	2.09	46.20	139.60	0.15	0.81	0.38	99.40	1.92
		SD	1.30	7.79	28.34	0.17	0.57	0.07	11.22	2.76
Malaysia	SSB	range	0.37–0.45	42.65–45.94	129.50–132.00	-	0.16–0.20	0.43–0.44	106.67–109.94	0.05–0.08
		mean	0.41	44.30	130.75	-	0.18	0.44	108.31	0.07
		SD	0.06	2.33	1.77	-	0.03	0.01	2.31	0.02
	DSBB	range	0.54–1.39	23.15–50.26	80.00–158.50	0.07–0.81	0.12–0.39	0.18–0.4	53.00–106.00	0.05–0.32
		mean	0.81	33.65	128.06	0.28	0.22	0.28	76.9	0.14
		SD	0.26	11.19	28.31	0.26	0.09	0.09	20.42	0.10
	DSBR	range	0.32–6.13	28.61–51.23	60.00–171.50	0.02–0.91	0.10–2.26	0.23–0.41	60.00–103.84	0.02–10.98
		mean	3.03	40.00	128.07	0.22	1.04	0.34	90.33	3.64
		SD	2.12	8.26	36.26	0.31	0.81	0.07	15.9	3.98
Myanmar	SSB	range	0.61–3.84	13.00–56.18	93.00–172.00	-	0.23–1.20	0.24–0.48	82.00–119.43	0.12–5.04
		mean	1.47	36.50	121.45	-	0.51	0.36	99.08	0.90
		SD	0.84	10.53	23.51	-	0.26	0.07	10.41	1.22
	DSBB	range	0.26–6.5	12.08–48.52	74.50–165.00	0.02–0.50	0.08–1.97	0.19–0.47	43–117	0.02–3.98
		mean	1.72	31.81	116.85	0.17	0.51	0.30	81.85	0.82
		SD	1.71	10.04	22.14	0.13	0.50	0.07	19.23	1.19
	DSBR	range	0.63–9.80	7.80–65.08	78.00–148.00	0.02–0.95	0.19–2.04	0.09–0.41	53.57–111.83	0.07–10.89
		mean	3.07	34.35	113.15	0.16	0.82	0.30	84.07	2.45
		SD	2.20	13.69	17.57	0.19	0.51	0.09	17.22	2.84
Thailand	SSB	range	0.39–3.93	21–56.31	84.00–149.50	-	0.12–1.75	0.22–0.54	71.00–119.55	0.04–5.14
		mean	1.55	35.52	111.67	-	0.56	0.35	90.95	1.16
		SD	1.20	12.30	17.27	-	0.51	0.10	15.89	1.73
	DSBB	range	0.60–4.99	32.59–50.80	110.00–151.50	0.07–0.35	0.21–1.73	0.27–0.45	77.12–112.48	0.12–6.26
		mean	2.13	42.00	122.50	0.20	0.77	0.34	93.12	1.76
		SD	1.72	7.70	15.84	0.13	0.66	0.07	14.06	2.40
	DSBR	range	0.46–2.34	16.83–36.53	90.00–137.00	0.05–1.19	0.15–0.28	0.12–0.33	85.31–137	0.05–0.48
		mean	1.15	29.05	113.17	0.45	0.21	0.25	104.02	0.21
		SD	1.04	10.67	23.51	0.64	0.06	0.12	28.65	0.24
Vietnam	SSB	range	0.64–4.01	30.63–57.13	90.00–154.50	-	0.27–1.66	0.36–0.47	89.5–116.34	0.15–5.50
		mean	1.69	45.7	118.00	-	0.71	0.43	105.59	1.39
		SD	1.12	8.26	17.37	-	0.43	0.04	8	1.73
	DSBB	range	9.97	25.79	76.00	0.07	2.57	0.26	76.00	17.75
		mean	9.97	25.79	76.00	0.07	2.57	0.26	76.00	17.75
		SD	-	-	-	-	-	-	-	-
	DSBR	range	1.02–9.06	14.45–51.67	67–154.5	0.03–0.37	0.26–2.3	0.15–0.49	49–116.75	0.27–12.74
		mean	4.69	32.77	116.19	0.12	1.3	0.29	80.05	5.38
		SD	2.51	13.31	25.12	0.10	0.66	0.09	20.33	4.24
All	SSB	range	0.37–4.01	13.00–57.13	84.00–172.00	-	0.12–1.75	0.22–0.54	71.00–119.55	0.04–5.50
		mean	1.51	39.23	118.52	-	0.57	0.38	99.38	1.07
		SD	1.00	10.82	19.78	-	0.39	0.08	12.28	1.47
	DSBB	range	0.26–9.97	12.08–50.80	74.50–165.00	0.02–0.88	0.08–2.57	0.18–0.47	43.00–117.00	0.02–17.75
		mean	1.93	33.31	116.56	0.21	0.57	0.30	81.67	1.60
		SD	2.33	10.10	24.51	0.20	0.65	0.07	17.90	3.97
	DSBR	range	0.32–9.8	7.80–65.08	60.00–172.00	0.01–1.19	0.10–2.30	0.09–0.49	49.00–137.00	0.02–12.74
		mean	3.25	35.42	117.91	0.18	0.92	0.31	86.28	3.09
		SD	2.30	12.85	23.91	0.23	0.62	0.09	18.63	3.48

). The results show both basic and erosion characteristics. The average R₀ for SSBs is 1.51 and 1.93 and 3.25 for DSBBs and DSBRs, respectively. The wave obliquity of SSBs is 39.23, slightly greater than that of the DSBs, while the SSR is almost equal. The erosion characteristics show the same value of a for SSBs and DSBBs. The computed A value is highest for the DSBR.

3.4. Performance of Bay Characteristic Equations

Equations (5)–(7), used for computing the bay characteristics, have been verified in the present study. The verification results are shown in

Table 4. Verification results of bay characteristic models.

Type		Efficiency Index (EI, %)		Relative Root Mean Squared Error (RRMSE, %)		Coeff. of Determination (R2)
		Equations (5) and (6)	Equation (7)	Equations (5) and (6)	Equation (7)	Equations (5) and (6)	Equation (7)
SEB	a/R0	99.92	99.60	0.55	0.56	0.99	0.99
	θc	99.64	99.65	0.53	0.52	0.93	0.93
DEB	a/R0	-	89.73	-	1.16	-	0.82
	θc	-	77.80	-	1.05	-	0.79

and Figure 7. These equations show high accuracy for computing static bays. The range of performance indicators, EI, RRMSE, and R², for verifying static bays are 99.60–99.92%, 0.52–0.56%, and 0.93–0.99, respectively. Only Equation (7) was verified with DSBs. Equation (7) uses an EI, RRMSE, and R² of 89.73, 1.16, and 0.82 for verifying a/R₀, respectively. These indicators show lower accuracy (EI = 77.80%, RRMSE = 1.05, and R² = 0.79) when verifying Equation (7) with θ_c.

4. Discussion

4.1. Headland-Bay Beach Classification Framework

The results show that this qualitative framework can be used to classify DSBs and UBs separately. The framework can be improved by constructing quantitative indicators. In the case of static bays, the method proposed by Klein et al. [3] can also be used to determine the stability of the bays. A SEB is always a SSB if no new coastal structure or beach nourishment is implemented in the area, as illustrated in Figure 8. For dynamic bays, it is not applicable to determine their stability using one satellite image since the sediment supply may change over time. A composite of satellite images obtained over more than 20 years can be used to clarify the difference between DEBs and DSBs. Dynamic bays experiencing no sediment supply change become DEBs. When the sediment supply changes, a shoreline change occurs, and the DEBs become DUBs. DEBs may be considered to be DSBs when they are at the equilibrium state for more than 20 years. This means that the shorelines of DEBs may change over time, but those of DSBs will not.

Dynamic bays tend to be in the same region, as shown in Figure 5. Reducing sediment supply in the upper part of a region may cause erosion to multiple bays in other parts. The construction of coastal structures to protect a dynamic bay may not be appropriate since this will cause erosion in the downcoast region, as can be observed by comparing the dynamic bays in Myanmar and other countries. The dynamic bays in Myanmar are natural and can maintain stability because the sediment supply does not change. The situation for dynamic bays is different in Malaysia and Thailand, where many coastal structures have been constructed in the bays. A regional coastal stabilization and management system should be implemented for regions with multiple dynamic bays.

The unstable bays in this study were analyzed in more detail. UBs were classified into sub-types according to variations in shoreline position, namely retreat, accretion, and fluctuation. Examples of each sub-type are shown in Figure 9. The unstable bays in each sub-type are presented in

Table 5. Sub-types of unstable bays in SEA.

Type	SUB	DUBB	DUBR	Total
Accretion	10	15	6	31
Erosion	12	2	3	17
Fluctuation	2	2	5	9
Unclear	4	3	2	9
Total	28	22	16	66

. It should be noted that the unclear type refers to unstable bays whose satellite images have low resolution, making shorelines difficult to extract. As can be observed, the bays are mostly accretion. This is due to the construction of the coastal structures in the bays, as shown in

Table 6. Type of unstable bays with respect to shore protection measures.

Type	SUB	DUBB	DUBR	Total
Man-made	28	15	2	45
Natural	0	7	14	21
Total	28	22	16	66

. The DUBR has an equal number of sub-types because most are natural bays. The position of coastal structures in the SUBs makes them subject to erosion.

The classification results can assist in the implementation of proposed measures for maintaining the stability of specific bays. A conceptual flow chart of potential HBB measures is presented in Figure 10. An adequate sediment supply to the bay is required to maintain the stability of DEBs. In the case of unstable bays, stabilization is the key.

4.2. Dynamic Bay Planform Equation

The DPBSE potentially gives the same planform shape as in the field, even in the case of the field SSR due to the high EI and R², as shown in Figure 6. Tasaduak et al. [10] proposed a different set of C coefficients by fitting Equation (1) with bays in Thailand, although the accuracy of coefficients was not demonstrated. Moreover, there is a limitation in their coefficients, namely that the low value of the SSR is less than 0.15. The present study verifies DPBSE with SSR from 0.01 to 1.19. Tasaduak et al. [10] developed the coefficients using a bay wave obliquity between 26° and 56°, while the DPBSE was verified with a wave obliquity from 7.80° to 65.08°. This means the DPBSE is able to overcome the limitation encountered by Tasaduak et al. [10] and can be applied to a wider range of SSR and wave obliquity.

Elshinnawy et al. [25] proposed an equation to predict DEP with high prediction performance (R² = 0.99 and a root mean square error < 0.75% of the R₀). This indicates that both the DPBSE and their equation can be used to accurately determine the DEP. The results of their study were used to compute a SSR ranging from 0.176–0.446. The equation from Elshinnawy et al. [25] was verified using a wave obliquity ranging from 49.15–57.21°. Therefore, the DPBSE can be applied to a larger range of SSR and wave obliquity compared to their equation. The DPBSE is suitable for determining changes in dynamic bays caused by sediment supply and the preliminary design of dynamic unstable bays for coastal stabilization. An example of coastal stabilization using the DPBSE is presented in Section 4.6.

4.3. Characteristics of Stable Bays in Southeast Asia

DSBs are larger than SSBs according to the average computed value of R₀ and A. The a/R₀ of both DSBBs and DSBRs is smaller compared to SSBs. This implies that sediment supply is effective at reducing the erosion distance between DSBs and SSBs. DSBRs are larger than DSBBs. This is assumed to be because the direct sediment supply from the river makes the bay bigger. Bays with sediment bypass, indirect sediment supply, experience greater loss and are consequently smaller. The average wave obliquity (β) of SSBs, DSBBs, and DSBRs ranges from 20° to 55° according to the bay characteristic equations mentioned in Section 4.4. Only 14 out of 146 (or 212) bays have a wave obliquity outside the range. The maximum extent of the average bay (θ_max) is around 117°. The maximum bay extent mainly relates to the location and alignment of the UCP. The maximum indentation (θ_c) of DSBs is less than for SSBs, leading to a larger bay. Therefore, dynamic bays are likely to have larger bays of both types.

4.4. Bay Characteristic Equations

Equations (5) and (6) were developed using wave obliquity data ranging from 22.5–72° [6]. The range of wave obliquity for SSBs in SEA was from 13–57.13°. The verification results show that Equations (5) and (6) could still compute the bay characteristics outside the range of developed data. However, Equation (7) could not determine the bay characteristics interacting with wave angles, which were either too small (<20°) or too large (>55°), as indicated by the outliers in Figure 7c,d. Equation (7) exhibits high accuracy since it was developed using experimental data with wave angles ranging from 20–60° [9]. Therefore, the bay characteristics can be determined using these equations. These equations can be used for analyzing the location and erosion magnitude of the bay. Coastal management can be implemented using these equations, as demonstrated in Section 4.6.

4.5. Sensitivity Analysis

The sensitivity of the SSR in HBBs was tested using an equation proposed by Tasaduak [8], derived by integrating the area under the DPBSE as expressed in Equation (8). The dynamic bay area (A) exhibits a varying SSR and static A₀ when SSR = 0. The bay area (A) computed using Equation (8) is represented by the shaded area in Figure 3. The percentage of area change was defined according to the sensitivity of dynamic bays as 1-A/A₀, as shown by the results in Figure 11. The bay area was found to be very sensitive to the SSR since it has a linearly steep slope when the SSR is low (0–0.085). The bay area becomes less sensitive to the SSR if it has an exponential slope. In this case, the SSR ranges from 0.085–0.600. The SSR becomes non-sensitive to the bay area when it is greater than 0.600, indicating an almost horizontal slope. Lower wave obliquity also exhibits greater sensitivity to the bay area.

$$A=\frac{1}{2}{R}_0^2\left[C_0^2\theta +2C_0{C}_1\beta \ln \left|\theta \right|-\frac{2C_0{C}_2{\beta }^2}{\theta }-\frac{2C_1{C}_2{\beta }^3}{2{\theta }^2}-\frac{C_1^2{\beta }^2}{\theta }-\frac{C_2^2{\beta }^4}{3{\theta }^3}\right]\begin{array}{c}\theta ={\theta }_{max}\\ \theta =\beta \end{array}$$

(8)

The sensitivity of the dynamic bay area (A) compared to static (A₀) shows how the area changes according to varying sediment supply in terms of SSR. When used with DSBs, most are in the sensitive category, followed by very sensitive, as shown in

Table 7. Types of sensitivity.

Bay Type	Type of Sensitivity
	Very Sensitive	Sensitive	Non-Sensitive
DSBB	16	27	3
DSBR	22	26	3
DSB	38	53	6

. This means that bays in SEA are sensitive to changes in sediment supply from rivers and bypasses. Changes in land use or development of the upcoast area of the bay must be restricted to avoid erosion.

4.6. Coastal Stabilization for Dynamic Bays

The coastal stabilization of static bays has been successfully implemented across the world and is referred to as the “headland control method” [33,34,35]. However, this method may not be appropriate for stabilizing dynamic bays. SEA contains many dynamic bays. Reducing the sediment supply of dynamic bays in the upper part of the region could decrease the sediment supply in the lower part and cause erosion, especially in sensitive and very sensitive bays. Therefore, a dynamic bay should be stabilized by controlling the amount of sediment supplied. The present study proposes a new method for stabilizing dynamic bays, referred to as the “sediment control method”. The idea is to constantly supply sediment to a bay, dynamically stabilizing its shoreline.

The DPBSE was used as a tool to determine the amount of sediment supply needed for maintaining bay stability. The sediment control method was used on Langkawi Bay (MY-DUBB8) in Malaysia, as shown in Figure 12. The upcoast area of the bay has been affected by land use change from forest to urban [36,37]. This may cause a reduction in the sediment supply to the bay, making it unstable. Langkawi Bay has a control line length of 0.58 km and wave obliquity of 46.84°. Its shorelines in 2008 and 2016 were fitted with the DPBSE to determine the SSR. More alternative shorelines can be determined by varying the SSR. The bay characteristics were computed using Equations (7) and (8). The characteristics of each alternative are shown in

Table 8. Bay characteristics for each alternative.

Alternative	SSR	a (km)	θc (deg)	A (km2)	1 − a/a0	1 − θc/θc0	1 − A/A0
Alternative 1 (SSB)	0.000	0.2693	112.08	0.1323	0.0000	0.0000	0.0000
Alternative 2 (shoreline in 2016)	0.100	0.2155	100.27	0.0990	0.2000	0.1054	0.2516
Alternative 3	0.200	0.1997	95.47	0.0895	0.2586	0.1482	0.3235
Alternative 4	0.400	0.1848	91.17	0.0807	0.3137	0.1866	0.3899
Alternative 5 (shoreline in 2008)	0.875	0.1783	89.40	0.0770	0.3380	0.2024	0.4182

. As can be observed, when the bay becomes a SSB, the shoreline and bay area in 2016 eroded by approximately 0.5 km and 0.3 km², respectively, while the location of the maximum indentation distance (θ_c) changes with the SSR. This means that the curved part of the planform varies with the SSR. The relationships between the characteristics of Langkawi Bay and SSR are shown in Figure 13. The results show that the bay is very sensitive to sediment supply when the SSR is low. The amount of sediment supply to the bay should be considered since it can become inefficient when the supply is too high. Therefore, both planform and bay characteristics need to be obtained. The best alternative for economists and stakeholders can be selected. As can be observed, this method is not only applicable for coastal stabilization, but also coastal management.

In addition to the headland and sediment control method, a combined method can be implemented by combining both. This would reduce the amount of constant sediment supply required for the bay in the future. The sediment control and combined method should be studied further in the field as an option for coastal stabilization.

5. Conclusions

A novel qualitative framework for HBB classification and analysis is proposed in this study, with the results indicating six types: SSB, DSBB, DSBR, SUB, DUBB, and DUBR. A total of 212 HBBs in SEA have been successfully classified using the framework. According to the findings, there are more stable than unstable bays, both static and dynamic. Moreover, there are twice as many dynamic as static bays. The framework can be widely used in other coastal areas of the world to classify and implement appropriate measures for each bay type for preservation purposes.

The bay characteristic equations for computing the maximum indentation distance or erosion and its location have been verified and could be helpful for supporting decision-making in coastal management planning. The classification of DSBs (DSBB, DSBR) from very sensitive to non-sensitive would be useful for implementing precautionary measures to avoid changes in the sediment budget upcoast or in the catchment of the bay. An analysis of bay characteristics shows that DSBs tend to be larger and subject to the same erosion as SSBs, indicating that an increased sediment supply to the equilibrium state can alleviate erosion.

The present study proposes a new method, namely sediment control using verified DPBSE, for dynamically stabilizing headland-bay beaches to bridge the current research gap. It can be combined with the existing headland control method, the so-called combined method. Dynamic coastal stabilization can be applied at specific, unstable local bays (DUBB, DUBR) using the present framework.

The framework uses qualitative indicators only. Quantitative indicators can be studied further to improve the framework. Bay classification can be extended for use in high tide areas to mitigate the tidal effect. The proposed sediment control and combined method can be improved by conducting experiments in the laboratory and field in a further study.