1. Introduction
The eastern coastline of Da Nang City, Vietnam, has undergone a critical shift in its morphological regime. While exhibiting a predominant trend of accretion prior to 2015, the period since 2016 has been characterized by dominant erosion, with an established average annual retreat rate of −0.39 m/year (Luc et al., 2025). The severity of this issue is highlighted by extreme events, such as the −42.98 m of localized shoreline retreat observed at the My Khe beach segment during the 2024–2025 Northeast (NE) monsoon season relative to the preceding summer period (Luc et al., 2025).
This erosional process is strongly correlated with the formation of a mega-cusp beach morphology, in which pronounced erosion is concentrated in the concave sections of the cusp features (Luc et al., 2024; Tanaka et al., 2018; Tinh et al., 2018), demonstrating that erosion at My Khe Beach exhibits seasonal variability. Specifically, the coastline experiences significant erosion during the NE monsoon (October to April), with measured retreat ranging from 27.9 to 76.2 m between 2021 and 2023. Conversely, accretion dominates during the Southwest (SW) monsoon (May to September). These distinct morphological outcomes are driven by the varying wave conditions throughout the year (Anh et al., 2025). The high-energy NE monsoon is characterized by nearshore waves from the ENE and NE directions, generating significant wave heights (Hs) of 1.5–2 m. This drives high-intensity longshore currents, reaching velocities of up to 0.45 m/s, which dramatically exacerbates sediment transport and erosion. In contrast, the SW monsoon is characterized by lower-energy waves (Hs ≈ 1 m) from the ESE and SE, which approach the shore obliquely. This results in reduced longshore current dynamics (V < 0.2 m/s) and a relatively stable accreting shoreline with minimal morphological changes.
My Khe Beach is geographically positioned along the Da Nang coastline, located between the mouths of the Han River to the north (≈ 27 km) and the Thu Bon River to the south (≈ 25 km) (Fig. 1(a)). The mouth of the Han River is hydrodynamically shielded from My Khe Beach by the Son Tra mountain range, resulting in minimal influence on local current and wave regimes (Anh et al., 2025). Conversely, the Thu Bon River has a documented history of regional sediment transport. A persistent deficit in the sediment supply from the Thu Bon River was identified as a major contributor to severe erosion along the adjacent Cua Dai coastline between 1994 and 2015 (Nagasawa et al., 2018). Although this erosional trend is projected to advance northward toward Da Nang, the large distance suggests that its long-term impact on My Khe Beach is currently minor. Therefore, the observed short-term, high-intensity seasonal erosion at My Khe is likely governed by local hydrodynamic factors rather than by large-scale regional sediment deficits.
Coastal evolution is fundamentally driven by a combination of dynamic factors including waves, tides, wind, and longshore currents. Wave energy, characterized by height, period, and direction, is directly correlated with the intensity of coastal erosion; higher energy leads to a stronger erosional impact (Short, 2012). Furthermore, wind can generate wave shear stress that affects nearshore areas (Fagherazzi & Wiberg, 2009). The most significant erosional risk occurs when high-wave action coincides with elevated water levels from high tides and strong winds, which facilitate offshore wave overtopping and sediment removal (Desplanque & Mossman, 2004; Lyddon et al., 2019; Rulent et al., 2021; Wolf, 2009). Tides and their generated currents also play a significant role, accounting for approximately half of the energy influencing coastlines and shaping longshore and cross-shore sediment movement (Short, 2012).
Coastal erosion studies have employed various analytical techniques to investigate these complex processes. These include mathematical and physical models (Lefebvre et al., 2014; Quang et al., 2023; Trung et al., 2014), spatial analysis tools such as the Digital Shoreline Analysis System (DSAS) (Quang et al., 2021; Trang et al., 2023), and empirical orthogonal function (EOF) analysis (Winant et al., 1975; Lemke et al., 2014). The choice of method depends on the available data, with the EOF being particularly effective decomposing shoreline changes into principal spatial and temporal modes of variability.
Despite the clear seasonal signal and severity of the mega-cusp formation at My Khe Beach, a process-based investigation linking hydrodynamic forcing directly to the observed morphological changes is required. This study applied an integrated approach that combines multi-temporal satellite and high-resolution unmanned aerial vehicle (UAV)-based shoreline monitoring with EOF analysis. The objective of this study was to thoroughly investigate the dominant processes and determine the formation mechanisms of both beach cusps and mega-cusps at My Khe Beach in Da Nang, Vietnam.
2. Study Area and Methodology
2.1 Study Area
The study area was My Khe Beach, a vital segment of the eastern coastline of Da Nang City, Vietnam (Fig. 1 (a) and (b)). This coastal stretch is regionally renowned for its extensive, gently sloping, and visually appealing sandy shore. However, My Khe Beach has experienced a dramatic shift in stability, undergoing severe and sustained erosion over the past decade (Fig. 2).
2.2 Research Methods
2.2.1. Shoreline change analysis using satellite and UAV imagery
This study employed a multi-scale integrated methodology that combines remote sensing analysis, hydrodynamic modeling, and statistical methods, transitioning from a broad-scale regional context to detailed local process monitoring.
Long-term regional shoreline evolution using satellite imagery: To establish the context of regional coastal evolution, we analyzed longterm shoreline changes using a historical archive of satellite imagery. Over 385 shoreline positions were extracted from Landsat (5, 7, 8, 9) and Sentinel-2 missions from 1988 to 2025. The analysis spanned an 18.5 km stretch of the Da Nang coastline. Shoreline positions were determined at 10 m transects, with My Khe Beach corresponding to transects located between x = 5000 m and x = 7700 m (Fig. 3 (a), (b)). Linear regression rate (LRR) analysis was applied to quantify the magnitude and direction of long-term erosion or accretion trends across four distinct temporal periods (1988–1995, 1996–2005–2006–2015, and 2016–2025). Furthermore, high-frequency monthly shoreline variations were analyzed to reveal the dominant seasonal patterns corresponding to the NE monsoon (October–April) and SW monsoon (May–September). This historical analysis provided an essential baseline for interpreting the current accelerated erosion observed at My Khe Beach.
High-resolution monitoring using UAV technology: To facilitate detailed process-based morphological analysis, 57 high-resolution UAV surveys were systematically conducted at My Khe Beach between March 2022 and July 2025 (Fig. 4). Each survey covered a 2.70 km stretch of coastline, generating data along 545 cross-shore transects spaced at 5 m intervals. This high spatial resolution is critical, enabling the precise detection and characterization of morphological features ranging from standard beach cusps (scale ≈ 10 m) up to mega-cusp scales (scale ≈ 100–1000 m). For each UAV survey, specific beach cusp characteristics were systematically quantified to track morphological changes, including
Cusp spacing (λ): The distance between adjacent cusp horns.
Embayment amplitude (D): The maximum distance between the cusp horn and trough.
Shape parameter (a = D/λ): A dimensionless measure of the cusp’s sharpness or development.
Cusp abundance: The number of cusps features present within the study area.
This high-frequency, high-resolution dataset provides the necessary details for applying advanced statistical analyses and directly correlating morphological changes with hydrodynamic forcing.
2.2.2 EOF analysis of shoreline variability
The EOF technique was employed to identify and decompose the dominant spatio-temporal modes of shoreline variability at My Khe Beach. This method, classically applied in coastal studies to separate morphological signals (Winant et al., 1975), enables the distinction between large-scale seasonal changes and higher-order oscillations related to rhythmic features.
An EOF analysis was applied to a high-resolution, UAV-derived shoreline dataset covering the period 2022–2025 to clarify the mechanisms responsible for the development of cusp and mega-cusp features at My Khe Beach. The EOF method decomposes the normalized shoreline anomaly into orthogonal spatial eigenfunctions (en (x)) and their corresponding temporal coefficients (cn (t)).
The measured shoreline position y(x, t) is first separated into the spatial mean y̅(x) and temporal anomaly y′(x, t):
where x denotes the alongshore coordinate, and t is the time. The anomaly term y′(x, t) is normalized and arranged into a data matrix for the EOF decomposition. The variability is then expressed as a linear combination of the principal modes, resulting in the spatial eigenfunctions en (x) and temporal coefficients cn (t )that satisfy
Each EOF mode represents an independent pattern of spatial variability and its associated temporal evolution. The spatial eigenfunction en (x) describes the characteristic alongshore pattern of the n-th mode, and the temporal coefficient cn (t)indicates when and how strongly this pattern is expressed.
To examine the higher-order modes independently, the first mode can be removed from the signal. The residual signal is calculated as follows:
Multiple modes can also be combined to reconstruct specific components of the residual signal:
The contribution rate Rn associated with the n-th EOF mode is quantified to evaluate its relative importance within the total shoreline variability. The contribution rate is computed from the corresponding eigenvalue λn as
This decomposition provides an objective data-driven framework for identifying the dominant patterns of shoreline variability and their temporal evolution without imposing a priori assumptions about the physical processes responsible for each mode.
3. Long-Term and Wide-Area Shoreline Change Using Satellite Images
3.1 Based on Monthly Averaged Shoreline Position Data
The LRR analysis (Figs. 5 and 6) revealed four distinct phases in the long-term evolution of the Da Nang coastline. During 1988–1995, the coast experienced a predominantly accretional trend, with an average rate of 0.66 m/year and local maxima reaching 2.52 m/year, whereas erosion was limited to approximately 15% of the transects. In the subsequent period (1996–2005), the shoreline remained overall stable (0.0 m/year); however, erosion with an average rate of −0.97 m/year dominated nearly half of the shoreline, particularly between Son Tra Mountain and Sao Mai Beach, whereas other sections exhibited accretion at approximately 0.93 m/year. From 2006 to 2015, accretion prevailed along nearly 81% of transects, with an average rate of 0.89 m/year, whereas localized erosion was most pronounced at Man Thai Beach (up to −1.67 m/year). In contrast, the 2016–2025 period marked a shift toward net erosion, averaging −0.39 m/year and affecting approximately 69% of the coastline, with severe erosion hotspots observed at Non Nuoc, Sao Bien, and My Khe Beach, where retreat rates reached up to −2.31 m/year.
The analysis confirmed a fundamental reversal of the coastal regime in the most recent decade, shifting from a stable/accreting state (1988–2015) to a predominantly erosional state (2016–2025).
The erosion observed at My Khe Beach is critical for understanding regional coastal processes. Although previous studies have suggested that sediment deficit-driven erosion originating at Cua Dai (Thu Bon River mouth) may propagate northward toward Da Nang (Nagasawa et al., 2018), recent LRR results for My Khe Beach do not support this propagation hypothesis. Instead, erosion at My Khe occurs in distinct, moderate stages, aligning with observations from other geographically isolated coastal segments, such as the Cua Lo coastline, located approximately 50 km south of Cua Dai (Quang et al., 2021). This distinction indicates that the erosion mechanism governing My Khe Beach is fundamentally different from the progressive sediment-starved retreat documented at Cua Dai Beach. This difference suggests that local and seasonal hydrodynamic forces, rather than a regional sediment budget deficit, are the primary drivers of the change in the My Khe shoreline.
3.2 Based on Instantaneous Shoreline Position (Non-Averaged)
An analysis of the instantaneous (non-averaged) monthly shoreline positions along transects x = 5000 m to x = 7700 m (Fig. 7) revealed a clear seasonal pattern in beach dynamics. The shoreline generally advances seaward during the first half of the year, typically reaching its maximum extent in June–August, followed by landward retreat from October to January.
May–September, corresponding to the late dry season and the onset of the SW monsoon, exhibits a progressive accretional trend. This phase is characterized by a weaker NE wind influence and the dominance of southeast (SE) wave directions, resulting in low wave energy conditions. These conditions favor onshore sediment transport and beach accretion.
Conversely, the wet and storm season, which is dominated by the NE monsoon (November–February), drives significant erosion. The most pronounced shoreline retreat is consistently observed from October to November, which coincided with the peak occurrence of tropical cyclones and strong NE monsoon events. The resultant high-energy waves approaching from the east and northeast induce intense offshore sediment transport and visible beach scarping, leading to a significant narrowing of the active beach face.
The magnitude of this shoreline fluctuation is not uniform throughout the study area. The central section (x ≈ 5000–6000 m) exhibits the largest seasonal amplitude (~50–60 m). This indicates that the central beach is the zone that is most responsive to monsoonal and wave forcing. Toward the southern sector (x ≈ 7000–7700 m), the amplitude decreases (~30 m), implying a comparatively more stable shoreline and potentially decreased direct exposure to the highest-energy NE waves.
Overall, the annual accretion-erosion cycle at My Khe Beach is a typical, annual recurrent response of an open sandy coast facing eastward, governed by the interaction of monsoonal wind regimes, prevailing wave direction, and tropical cyclone activity. This predictable cyclical pattern provides essential high-frequency insights for developing effective coastal management and seasonal shoreline protection strategies.
The occurrence of beach cusps on My Khe Beach exhibited pronounced seasonality and scale-dependent morphodynamics (Fig. 8). During the SW monsoon season (May–August), regular small-scale cusps developed with a mean frequency of 4.1 ± 0.9 cusps day−1 and typical spacing of 8.5 ± 2.1 m, associated with lower wave energy conditions (Hs = 0.38 ± 0.26 m). In contrast, the high-energy NE monsoon (October–April) caused a morphological transition to a mega beach cusp, which intensifies in December and January. These mega-cusps exhibited significantly larger dimensions, with spacing ranging from 200 to 500 m and occasionally reaching up to 691.1 m (Fig. 9), and average amplitudes of approximately 15 m (maximum: 57.6 m). The development of the mega-morphology was accompanied by significant shoreline erosion, which was particularly evident from late 2024 to early 2025 period (Luc et al., 2025). Wave reanalysis data (2013–2025) indicated that significant wave heights during the NE monsoon (Hs = 1.15 ± 0.65 m) exceeded the cusp-initiation threshold (Hs > 0.8 m) for 64.6% of the time. This contrasts sharply with the SW monsoon, where the threshold exceeds only 5.3% of the time, which is an approximate ninefold difference in the potential erosive wave energy that dictates the dual-scale cusp morphology.
This pronounced seasonality directly reflects the monsoon-driven modulation of the nearshore wave climate. The abrupt transitions in April–May and September–October, coinciding with monsoon reversals, suggest threshold-dependent cusp field development that requires sustained wave heights above 0.8 m and directional stability within ±20° for at least 48 h.
The observed dynamics at My Khe Beach presented a strong seasonal contrast characteristic of monsoon-influenced coasts. The elevated wave energy of the NE monsoon facilitates sustained swash-driven self-organization (Coco et al., 1999). The consistent northeasterly wave approach (78.6° ± 19.3°) promotes edge-wave coherence, which is theorized to govern cusp spacing (λ ∝ g·Tp2/π; Guza & Inman (1975)). The observed mean spacing of 8.5 m closely aligns with the theoretical prediction for a typical wave period Tp = 7.4 s. In contrast, during the SW monsoon, reduced wave energy (threshold exceedance <6%) and greater directional variability (±27.8°) disrupt edge-wave patterns and inhibit cusp formation. These results align with global observations showing enhanced cusp activity under moderate and directionally stable wave conditions (Masselink et al., 2004), but they emphasize the strong seasonal contrast characteristic of monsoon-influenced coasts.
A study by Son et al. (2025) at My Khe Beach also indicated that the formation process of beach cusps in this area is highly complex and influenced by multiple factors. However, research has confirmed that the cusp morphology at My Khe exhibits a distinct seasonal cycle, developing strongly during the NE monsoon (from October to March) and gradually weakening before almost disappearing during the SW monsoon (from May to September). The spacing between the cusp crests ranges from 100 to 300 m, which is significantly larger than that predicted by edge-wave harmonic models (Son et al., 2025).
4. Shoreline Change from 2022 to 2025
4.1 Seasonal Shoreline Variability and the Formation of Mega-Cusps
Shoreline variability at My Khe Beach, analyzed using high-resolution UAV-derived shoreline data (2022 and 2025) combined with simulated nearshore wave parameters and sea-level records (Son Tra tide gauge) revealed pronounced seasonal coupling between hydrodynamic forcing and shoreline morphology (Fig. 10).
The analysis confirmed the dominance of mega-cusp morphology at the study site, substantially exceeding typical cusp scales between 10 and 50 m (Todd Holland, 1998):
Mean cusp spacing (λ): 222 m (Range: 40 to 587.3 m).
Mean embayment amplitude (D): 12.7 m (Range: 2 to 47.5 m).
The mean shape parameter (a = D/λ): 0.0556, which is within the typical global range of 0.03–0.10 (Masselink & Pattiaratchi, 1998).
Critically, the coefficient of variation (CV = 36%) for the amplitude was significantly higher than that for the cusp spacing (CV = 25%), indicating that the amplitude is a more dynamic parameter, demonstrating a faster and more sensitive response to fluctuations in the incident wave energy.
During the NE monsoon (October–March), both the significant wave height (Hs) and peak wave period (Tp) exhibit pronounced increases, indicating energetic, long-period swells generated by monsoon-driven systems. Correspondingly, the shoreline exhibits strong alongshore fluctuations and rhythmic undulations, suggesting the development of well-defined beach cusps. The computed power spectral density (PSD) of the incident wave field (Fig. 10(d)) showed intensified energy between 0.08 and 0.12 Hz during these energetic periods, while the PSD of shoreline (Fig. 10(e)) exhibited concurrent spectral peaks at spatial wavenumbers of 0.02–0.05 m−1. These peaks correspond to rhythmic features spaced approximately 20–50 m apart. This spectral coherence highlights a clear morphodynamic linkage between offshore hydrodynamics and beach self-organization.
In contrast, during the SW monsoon (May–September), the wave energy and Hs remain low and stable, resulting in smoother and more uniform shoreline configurations with minimal cusp activity. The PSD during this period is dominated by low-frequency, short-period wave energy, which is insufficient to drive rhythmic shoreline development.
Notably, extreme cusp formation events are associated with short-lived, high-energy bursts, particularly in early November 2023 and January 2024, when Hs exceeded 4–5 m and Tp reached >12 s. These episodes were inferred to be the direct drivers of the largest and most widely spaced mega-beach cusps observed in the later satellite data (late 2024 to early 2025).
Overall, the results demonstrate that the cuspated shoreline formation at My Khe is primarily driven by high-energy long-period waves associated with the NE monsoon. The temporal alignment between the wave and shoreline spectra provides strong evidence of morphodynamic feedback linking the incident wave energy, alongshore sediment transport gradients, and rhythmic shoreline evolution within the swash zone.
4.2 Wave Data Analysis and Shoreline Response
Based on shoreline data extracted from 57 UAV surveys, the spatial characteristics of the beach cusps were quantitatively defined, including mean spacing λ = 232.2 m (range: 124.6–358.8 m), mean embayment amplitude D = 12.8 m (range: 4.6–23.2 m), and the characteristic shape parameter a = D/λ ≈ 0.056. These morphological parameters were correlated with simulated nearshore wave conditions from the validated hydrodynamic model (Anh et al., 2025) to evaluate the shoreline morphological response to wave forcing.
The relationship between embayment amplitude and cusp spacing (λ) follows a robust power-law form D = 0.049λ1.016 (R2 = 0.437). The near-unity exponent (1.016 ≈ 1.0) confirms that beach cusps at My Khe exhibit geometric self-similarity across multiple spatial scales, maintaining a consistent shape parameter of a ≈ 0.05 regardless of absolute size (Fig. 11). The strong correlation between D and λ (r = 0.630) indicates that larger cusps have proportionally deeper embayments, consistent with both edge wave theory (Guza & Inman, 1975) and self-organization models (Werner & Fink, 1993). The shape parameter also correlates strongly with the embayment amplitude (r = 0.653), suggesting that the cusp geometry is primarily controlled by amplitude variations rather than spacing adjustments.
To analyze the influence of incident wave parameters on the formation and development of cusps, we established a correlation matrix comprising 12 variables using the Pearson correlation coefficient (r). The results were visualized using a heatmap with a color scale ranging from −1 (blue) to +1 (red), accompanied by numerical values in each cell to facilitate the identification of strongly correlated variable pairs (Fig. 12).
Specifically, the embayment amplitude exhibited a moderate yet statistically significant sensitivity to the integrated wave energy conditions. The correlation with the 7-day cumulative wave power (P7d) reached r = 0.385, whereas the correlation with the maximum wave height over 7 days was r = 0.391. Although modest, these values indicated that the amplitude responded to sustained wave forcing rather than to instantaneous wave conditions. This was further evidenced by the progressive increase in correlation from 3-day P3d (r = 0.259) to 5-day P5d (r = 0.320), and finally 7-day P7d (r = 0.385). This trend suggests a characteristic morphological response timescale of 5–7 days, reflecting gradual cross-shore sediment redistribution during prolonged energetic periods. Meanwhile, the spacing between the beach cusp crests also exhibited a significant correlation with the cumulative wave power, increasing progressively from P3d (r = 0.246) to P5d (r = 0.302), and reaching P7d (r = 0.377).
In contrast, the relationship between the amplitude and instantaneous wave parameters (Hs: r = 0.274; Tp: r = 0.101) was considerably weaker than that observed with the cumulative metrics. This confirmed that short-term wave measurements are inadequate for describing the complex large-scale cusp morphology. This finding strongly supports the interpretation of cusps as morphodynamic equilibrium features that respond to sustained forcing rather than instantaneous wave conditions (Coco et al., 1999, 2003; Masselink et al., 2004).
To quantify the wave conditions necessary for beach cusp formation, we applied a percentile-based threshold analysis, following the methodology of Masselink and Pattiaratchi (2001) and Stockdon et al. (2006). Beach cusps were classified as “well-developed” when N_cusp ≥ 3, resulting in 46 days (76.7%) with clear cusp presence and 14 days (23.3%) without. Wave conditions differed significantly between these groups: the cusp-present group exhibited mean Hs = 1.023 ± 0.458 m and P7d = 75,557 ± 64,408 W·day/m, whereas the cusp-absent group showed substantially lower values (Hs = 0.576 ± 0.380 m; P7d = 22,576 ± 30,599 W·day/m).
The threshold was determined by averaging the 10th percentile of the cusp-present distribution and the 90th percentile of the cusp-absent distribution, yielding Hs_threshold = 0.810 m and P7d_threshold = 29,466 W·day/m (Fig. 13). To evaluate threshold reliability, we calculated the accuracy, sensitivity, and specificity metrics (Fawcett, 2006). The P7d threshold demonstrated superior predictive performance, with 71.7% accuracy, 67.4% sensitivity, and 85.7% specificity, outperforming the Hs threshold alone (60.0% accuracy). Combined criteria using the OR logic (Hs ≥ 0.810 m OR P7d ≥ 29,466 W·day/m) achieved 70.0% accuracy with 71.7% sensitivity, suggesting that either instantaneous wave height or sustained wave power can trigger cusp formation. These results confirmed that 7-day cumulative wave power provides a more robust predictor of cusp presence than instantaneous wave height, consistent with the morphodynamic equilibrium framework.
Overall, the results indicate that the mega beach cusps at My Khe have self-similar features controlled primarily by sustained wave forcing over 5–7 days. The 7-day cumulative wave power is a more reliable predictor of cusp presence than instantaneous wave height, and the identified thresholds (Hs ≳ 0.8 m; P7d ≳ 3.0×104 W·day/m) provide practical criteria for anticipating cusp formation. These findings highlight cusps as self-organized morphodynamic features driven by sustained antecedent wave conditions.
4.3 EOF Analysis
We applied EOF decomposition was applied to isolate coherent, large-scale shoreline variability patterns from the 3.5-year UAV dataset (March 2022 to July 2025) across the 2.7 km length of My Khe Beach. Preprocessing, including linear detrending and spatial smoothing (using a 250-m window), was implemented to effectively reduce high-frequency noise while preserving the characteristic mega-cusp wavelengths (>200 m). The EOF decomposition revealed that the three dominant modes captured 87.9% of the total variance, with Mode 1 accounting for 81.1%, Mode 2 for 4.2%, and Mode 3 for 2.6% (Fig. 14).
Mode 1 represented the dominant beach-scale seasonal response to a monsoonal wave climate. The spatial function e1 (x) was remarkably uniform (≈ −0.04 to −0.05) along the entire beach, indicating coherent seasonal behavior driven by regional forcing rather than local effects. The temporal coefficient c1 (t) exhibited clear seasonal oscillation with amplitudes of ± 400–500 m: positive values (shoreline retreat) during the NE monsoon (October–April) when wave energy is high, and negative values (shoreline advance) during the SE monsoon (May–September) with lower wave energy (Fig. 15). This consistency confirmed that Mode 1 explained the primary source of shoreline variability at My Khe, aligning with the established monsoon climate of Central Vietnam.
After removing Mode 1, the residual ỹ revealed spatial undulations with dominant wavelengths of 394–640 m (mean: 407 ± 38 m), representing approximately 14%–23% of the beach length (Fig. 16). These wavelengths are characteristic of the mega-cusp features documented on sandy beaches worldwide. The spatial functions e2 (x) and e3 (x) displayed multiple alongshore oscillations, with e3 (x) showing a strong peak at x ≈ 400 m. Unlike Mode 1, the temporal coefficients c2 (t ) and c3 (t) lacked clear seasonal periodicity, instead showing sporadic variations during both monsoon seasons. This indicated that the mega-cusps at My Khe are transient superimposed phenomena rather than persistent features of the shoreline.
Despite the lack of strict temporal periodicity, the intensity of the mega-cusps exhibited a clear seasonal modulation. The root mean square (RMS) of Mode 2 + 3 varied dramatically, ranging from a minimum of 0.23 m (during the SE monsoon) to a maximum of 9.51 m (during the energetic NE monsoon), with a mean of 3.14 m (Fig. 17). This suggested that high-energy NE monsoon wave conditions are necessary for mega-cusp formation and maintenance, whereas lower-energy SE monsoon conditions facilitate shoreline smoothing. Spatial analysis of the RMS identifies three distinct hotspots with enhanced mega-cusp activity (RMS > 5 m), located at x ≈ 300–500 m, 700–900 m, and 2400–2700 m These localized variations warrant further investigation as they are potentially related to local bathymetric irregularities and wave refraction patterns that focus wave energy.
The EOF analysis establishes a clear hierarchical structure of shoreline variability at My Khe: dominant seasonal oscillation (81% variance) that affects the entire beach uniformly, overlaid by transient mega-cusp features (~7% variance, λ ≈ 400 m) whose intensity is seasonally modulated. This behavior provides a crucial contrast to nearby coastal sites, such as Cua Dai Beach, where erosion has been shown to be a systematic, propagating phenomenon linked to progressive sediment deficits (Nagasawa et al., 2018; D. N. Quang et al., 2021). At My Khe, the lack of a propagating erosion signal and the dominance of the cyclical Mode 1 suggest that the erosion mechanism is best characterized as seasonal oscillation superimposed on a net erosion trend (−0.39 m/year), rather than spatially progressive sediment deficit. While short-term dynamics are dominated by reversible seasonal responses, a persistent decadal retreat indicates dynamic disequilibrium. This seasonal oscillation with transient rhythmic features may be a defining characteristic of wave-exposed embayed beaches in Central Vietnam, as similar patterns have been documented at Nha Trang Beach (Thanh et al., 2018; Tinh et al., 2021). A persistent wavelength scale of ~400 m likely emerges from the interactions between wave characteristics, beach morphology, and nearshore bathymetry, warranting further investigation through numerical modeling and wave data analysis.
This study utilized offshore wave reanalysis data (~25 km spatial resolution), which may not fully capture nearshore wave transformation processes (shoaling, refraction, and breaking) and site-specific bathymetric effects that are critical for shoreline dynamics. Despite this limitation, the strong correlations between 7-day cumulative wave power and cusp morphology (r = 0.385) suggest that offshore conditions reasonably represent dominant forcing mechanisms.
Future research incorporating nearshore wave modeling (e.g., SWAN) could propagate offshore waves to the nearshore zone and compare the simulated wave energy flux patterns with the EOF Mode spatial structures. If the modeled wave-focusing zones correspond to the mega-cusp hotspots identified in Modes 2 and 3 (~400 m wavelength), these modes would be validated as physically meaningful morphodynamic responses rather than statistical artifacts. Field measurements (acoustic Doppler current profilers and pressure sensors) would further strengthen model validation.
Although the EOF analysis identified the spatial patterns and seasonal modulation of mega-cusps, a critical question remains regarding their temporal stability: Do these erosion patterns migrate alongshore or remain fixed? To address this, we analyzed a high-frequency UAV time series (eight surveys over two months) during the peak NE monsoon period (December 2024–February 2025), when mega-cusps are most developed (Fig. 18).
Visual analysis revealed that, despite significant variations in cusp amplitude (growth-decay cycles associated with monsoon forcing), the alongshore positions of the cusp embayments and horns remained remarkably stationary. Six fixed cross-shore transects established at representative cusp features showed mean positional standard deviations of <5 m over the 2-month period, with no systematic migration detected. This stationarity confirms the “standing-wave” nature of the mega-cusp system, indicating control by persistent morphodynamic or geological templates, rather than freely migrating patterns.
Nearshore bar features were visible in the UAV imagery with wavelengths consistent with the mega-cusp spacing. Visual interpretation suggested predominantly in-phase coupling, where cusp embayments align with bar troughs/channels, and cusp horns align with bar crests. This configuration is characteristic of rip current-dominated circulation, where coupled bar-cusp cells reinforce both features (Castelle et al., 2007; MacMahan et al., 2006).
The combination of stationary bars and cusps in an in-phase configuration provides a mechanism for explaining the persistent erosion hotspots identified through EOF analysis: (1) fixed bar-channel geometry creates persistent circulation patterns, (2) rip currents at embayments cause localized erosion, (3) erosion zones are spatially locked to bar-channel positions, and (4) even as seasonal cusp amplitudes vary, hotspot locations remain fixed because the underlying morphodynamic template persists.
This standing-wave characteristic differs from that of beaches, where bars migrate freely and carry erosion patterns with them. At My Khe, a stationary template implies that erosion hotspots persist unless the template is modified. This has important coastal management implications: beach nourishment at hotspots will experience recurring erosion owing to persistent circulation forcing, requiring either modification of the bar-channel template or accommodation of persistent forcing in intervention designs.
While this UAV-based visual analysis provides valuable qualitative evidence of bar-cusp coupling and system stationarity, a quantitative bathymetric time series would strengthen these findings by measuring bar relief changes and circulation cell geometry over seasonal cycles.
The observed stationarity suggests control by one or more persistent boundary conditions. The embayed beach configuration and Sơn Trà headland may create relatively fixed wave refraction patterns, whereas the predominantly shore-normal wave approach during the NE monsoon reduces alongshore forcing that would otherwise drive bar migration. Nearshore bars undergo seasonal cross-shore displacement (approximately 200–300 m) but appear to maintain consistent alongshore positions. However, a definitive identification of the controlling mechanism requires bathymetric time series, wave refraction modeling, and nearshore current measurements, which were not available in this study.
5. Conclusions
This study successfully monitored and analyzed the multi-scale morphodynamics and formation mechanisms of mega beach cusps at My Khe Beach, Da Nang, Vietnam, using an integrated approach combining long-term satellite imagery (1988–2025), high-resolution UAV surveys (2022–2025), and hydrodynamic modeling. The primary findings establishing the unique erosional mechanisms at My Khe Beach are summarized below:
Mega beach cusps develop primarily during the northeast monsoon (October–April), with a spacing of 200–500 m (mean: 232.2 m) and amplitudes of 2–48 m (mean: 12.7 m), which considerably exceed typical beach cusp scales. The cusps exhibit geometric self-similarity following the power-law relationship D = 0.0485 λ1.016 (R2 = 0.437) with a characteristic shape parameter a ≈ 0.05–0.06. The strong correlation between D and λ (r = 0.630) confirms that larger cusps have proportionally deeper embayments. The dominant wavelength of approximately 400 m corresponds to about 14%–23% of the beach length and remains relatively stable across monsoon seasons.
Mega-cusp formation at Non Nuoc Beach is fundamentally controlled by monsoonal wave climate variability. Northeast monsoon conditions generate significantly higher wave energy (Hs = 1.023 ± 0.458 m, P7d = 75,557 ± 64,408 W·day/m) compared with the southwest monsoon (Hs = 0.576 ± 0.380 m, P7d = 22,576 ± 30,599 W·day/m), representing a ninefold energy difference that drives pronounced seasonal morphological changes. Percentile-based threshold analysis identified critical conditions for cusp initiation: instantaneous wave heights exceeding 0.810 m or a 7-day cumulative wave power exceeding 29,466 W·day/m, under which high-energy waves from ENE-NE directions generate strong longshore currents that facilitate sediment redistribution and cusp development. This temporal integration of wave energy input indicates a characteristic morphological response timescale of 5–7 days, reflecting the time required for beach profile adjustment to approach equilibrium under the prevailing hydrodynamic conditions.
The shoreline dynamics exhibit pronounced seasonal cyclicity. During the northeast monsoon, the coast experiences significant erosion (27.9–76.2 m retreat, up to −42.98 m in 2024–2025) accompanied by mega-cusp development (RMS up to 9.51 m). In contrast, during the southwest monsoon (May–September), lower wave energy conditions facilitate shoreline recovery and the formation of small-scale regular cusps (spacing: 8.5 ± 2.1 m). EOF analysis showed that seasonal oscillation (Mode 1:81.1% variance) dominated shoreline variability, whereas mega-cusp features (Modes 2+3: ~7% variance) are transient phenomena with seasonally modulated intensity but no strict temporal periodicity.
The erosion mechanism at My Khe Beach reflects seasonal oscillations superimposed on a long-term retreat trend, indicating dynamic disequilibrium rather than equilibrium. This behavior is controlled by a monsoon-driven wave climate, which differs from the more severe progressive erosion observed near Cua Dai Beach. Three spatial hotspots with enhanced mega-cusp activity (RMS > 5 m) were identified at x ≈ 300–500 m, 700–900 m, and 2400–2700 m, likely influenced by local bathymetric irregularities and wave refraction patterns. Long-term trends indicate a shift from pre-2015 accretion to post-2015 net erosion (−0.39 m/year on average), with retreat rates locally reaching −2.31 m/year.
Time-series UAV analysis demonstrated that the mega-cusp locations remained stationary over multi-month timescales, confirming the standing-wave nature of the system controlled by persistent morphodynamic templates. The predominantly in-phase coupling between the cusps and nearshore bars, with embayments aligned with bar troughs, explains the persistence of erosion hotspots through spatially locked circulation patterns. Consequently, erosion hotspots persist unless the underlying morphodynamic template is modified, which has important implications for coastal management and intervention strategies.
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