Abstract

Located in the southeast of Hue city in Thua Thien Hue province, Thuan An estuary plays a crucial role as a waterway and flood drainage pathway for the Huong River. Importantly, the morphology of the Thuan An estuary has been subjected to continuous change during monsoon seasons with the process of sediments in the estuary and erosion along the northern and southern coasts. Remarkably, the process of sediments directly impacts flood drainage and navigation along the waterway, as well as the sustainable development of Thua Thien Hue marine economy. Therefore, the goal of this study is to insightfully provide hydrodynamic regimes using a Delft3D model combined with ArcGIS software. The results showed that the estuary is wave-dominated lowland coasts. The coastal barrier is formed from sand that is transported along the shoreline by wave-driven longshore currents. During the northeast monsoon, river flow is significantly small, tidal currents combine with longshore currents by waves to form a strong longshore current with direction from northeast to southwest. Whereas, during the southwest monsoon, the sandbar extending from the southern side expands northward, leading to sedimentation accumulation at the river mouth channel. Specifically, a sandbar is formed at the river mouth with an accumulation of up to about 0.8 m.

1 Introduction

Coastal areas and estuaries have significant importance in the socio-economic development strategy and problems related to the security of the central coastal provinces of Vietnam, spanning from Nghe An to Binh Thuan. However, the hydrodynamic regime in this region is affected by various factors: rivers, seas, and human activities interact, establishing a dynamic equilibrium. Therefore, a variation originating from one or more above-mentioned components could lead to subsequent changes in other components, creating a new balance. Physical factors, such as waves and currents under the wind forces, or human factors like embankment or irrigation works upstream, affect this new balance. Several publications focus on analyzing the coastal hydrodynamic processes based on applying hydro-dynamical models (Besio et al. 2003; Hu et al. 2009; Borsje et al. 2013; Parsapour-Moghaddam et al. 2018; Balaji et al. 2022). Studies relating directly to Thua Thien Hue, Vietnam include Hung et al. (2024), Hung et al (2020), Hung (2019), Lam et al. (2003), Lam et al. (2007), Lam et al (2009). Other related publications, including Le et al. (2023) and Bui et al. (2024), use satellite images and field trips in the analysis of the ecosystem and flood problems. Generally, results from the previous studies focus on flood events and non-upgraded measured data, especially when related to negative weather events like tropical storms. Meanwhile, Thua Thien Hue province is often faced with multiple natural hazards (e.g., tropical cyclones, floods, and landslides) which cause great damage to both people and property. For instance, in 2020, natural disasters killed 41 people, left 11 missing, and caused damages totaling VND 2,273 billion. Typhoons were also recorded in Ketsana in 2009, and Damrey in 2017 (VDDMA 2021). Studies implemented for this region include Hung et al. (2024), Hung et al. (2020), Hung (2019), Lam et al. (2009). However, in recent years, the impact of climate change and rising sea levels has intensified, prompting an increase in human socio-economic activities both upstream in the rivers and within coastal estuaries (Pang et al. 2023; Griggs et al. 2021). This heightened activity has made the process of accretion and erosion more complex in terms of scale and intensity, resulting in significant economic and social consequences. Consequently, it becomes imperative to study and assess the hydrodynamic regime, including waves, water levels, and currents, within these coastal estuary areas.

Thua Thien Hue province is covered by the mainland and the territorial sea towards the East Sea. The mainland of Thua Thien Hue has the following geographical coordinates:

• Northernmost point: 16^º44'30'' north latitude; 107^º23'48'' east longitude;
• Southernmost point: 15^º59'30'' north latitude; 107^º41'52'' east longitude at the southernmost mountain peak;
• Westernmost point: 16^º22'45'' north latitude; 107^º00'56'' east longitude; and
• Easternmost point: 16^º13'18'' north latitude; 108^º12'57'' east longitude.

Thuan An estuary in Thua Thien Hue province is one of two estuaries connecting the Tam Giang-Cau Hai lagoon system with the East Sea. Because a traffic intersection connects the coastal region and the Huong River basin, Thuan An estuary is important in the ancient capital of Hue in terms of strategy, trade, and economics. Therefore, understanding the hydrodynamic characteristics of this region is crucial for effective management and planning. By comprehending the behavior of waves, water levels, and currents, authorities and stakeholders can develop appropriate strategies to mitigate the impacts of coastal erosion, ensure the sustainable development of coastal areas, and safeguard the socio-economic well-being of the local communities. Figure 1 shows the study area.

Figure 1 The study area.

2 Materials and methods

2.1 Materials

Topographical data, including bathymetry data, for this study and a 1:5,000 scale map for the Thuan An estuary was surveyed by the authors in 2023, as well as 1:50,000 to 1:10,000 scale topographic maps for coastal areas published by Ministry of Natural Resources and Environment of Viet Nam. The authors used an AWAC instrument (Acoustic Wave and Current Profiler) manufactured by Nortek to measure the currents and waves (Figure 2 (a)). At a scale of 1:5,000, the topography was created based on GPS technology combined with an ODOM single-beam echo sounder and RTK machine. Sediment samples were collected and analyzed to define parameters (e.g., grain composition and distribution, average grain diameter D50, and specific gravity) (Figure 2 (b)).

Figure 2 Field trips in Thua Thien Hue (a) for measuring the currents and waves, and (b) collecting the samples

Figure 3 (a) illustrates a coastal seabed topographic map at a scale of 1:50,000 for the coastal area of Thua Thien Hue province to 50 m deep sea.

Figure 3 (a) Coastal and offshore topographic map; and (b) grid mesh for the study.

Figure 4 shows the location of a monitoring station for water levels, waves, and current data from April 9 to April 14, 2023.

Figure 4 Monitoring station.

2.2 Model setup

In this study, a Delft3D model is used for calculating hydrodynamic characteristics in the Thuan An estuary (Deltares 2011). As a component of Delft3D, the FLOW model is a comprehensive hydrodynamic and transport simulation program. It is specifically designed to simulate three-dimensional hydrodynamics and transport processes. Furthermore, the FLOW model is capable of simulating various aspects of hydrodynamics, including water flow patterns, water levels, and velocities. It considers factors such as tides, wind, and density-driven flows to provide accurate representations of real-world conditions. By combining hydrodynamic and sediment transport simulations, the FLOW model provides a comprehensive tool for studying and understanding the complex interactions between water and sediment in coastal and estuarine systems.

Generally, governing equations in the FLOW model are based on the Reynolds-Averaged Navier-Stocks equations and the continuity equation. According to Broomans (2003), the momentum equations are shown in both  and  directions (σ-coordinates).

(1)

(2)

Where F’’_x and F’’_y represent the horizontal viscosity terms.

(3)

(4)

Where the Reynolds stresses τ_xx, τ_xy, and τ_yy  are satisfied using the Boussinesq approach.

(5)

With .

Where:

qin and qout	=	local sources and sinks of water per unit of volume (1/s), respectively,
P	=	non-local source term of precipitation,
E	=	non-local kink term due to evaporation,
dσ	=	total derivative from σ-coordinates in the vertical,
H = d + ζ	=	total water depth,
d and ζ	=	depth below this plane, and water level above a reference plane, respectively,
, , , ,	=	Reynolds’ time-averaged components in σ-coordinates,
x, y, σ	=	direction in σ-coordinates,
ρo	=	standard density,
p, f, and h	=	pressure, Coriolis, and water level, respectively,
τxx, τxy, and τyy	=	Reynolds stresses,
v th and v tv	=	horizontal and vertical turbulent viscosity,
Gηη and Gξξ​	=	conversion factors from curvilinear coordinates to linear coordinates,
ξ and η	=	othogonal curvilinear coordinate system on horizontal, and
Q	=	contributions per unit area due to the discharge or withdrawal of water, precipitation and evaporation.

Additional details for these equations are described in Deltares (2011).

The WAVE module is based on the third-generation wave model SWAN (Simulating Waves Nearshore), which was developed at Delft University of Technology. Governing equations for this module can be found in Gil et al. (2006).

Grid mesh

Creating a model mesh file is a crucial step that directly impacts the accuracy of simulation model results. The process of mesh generation involves several important aspects, including selecting an appropriate modeling area, accurately representing terrain, currents, winds, and wave fields, defining open and hard boundaries (shorelines), and determining the spatial resolution while considering model stability.

In the case of the Thua Thien Hue province coastal area, the grid comprises 150,132 cells, covering the entire region. The grid size varies with a resolution of 15 m to 200 m (Figure 3 (b)).

Initial and boundary conditions

During the process of propagation from offshore to estuaries and coastal areas, waves undergo various processes such as the shallow water effect, wave refraction, wave diffraction, wave breaking, and so on. These processes lead to changes in wave characteristics as they approach the shore, including changes in wave direction, wave spectrum, and wave height. Therefore, the model scope needs to be appropriate to simulate the aforementioned wave processes. However, it is important to avoid selecting a model range that is too wide, as it may adversely affect the calculation speed due to limitations in computer configuration.

The initial conditions for the calculations consist of calm water surface conditions, with wave parameters set to zero. Additionally, the flow rate in the river is set to zero.

Boundary conditions: Three boundaries are considered, including the eastern deep-water boundary and two lateral boundaries. The deep-water boundary utilizes water level boundaries derived from a set of harmonic constants extracted from the global tidal model TPXO. Wind boundary conditions are determined based on various sources of wind data (e.g., wind data from meteorological stations, and wind data collected from meteorological stations located within the study area).

Global reanalysis wind data: Wind boundary conditions could be determined based on various sources of wind data (e.g., wind data from meteorological stations, or wind data collected from meteorological stations located within the study area.) However, it is extremely difficult to gather wind data at meteorological stations. As such, for this study, global reanalysis wind data obtained from the NCEP-NOAA is used. This dataset provided hourly wind data with a resolution of 0.2 x 0.2 degrees, covering the period from 1988 to the present.

Wind data measured during surveys: Wind data collected specifically for the implemented topics and projects within the study area.

Deep water wave boundary conditions: For deep water wave boundary conditions, wave data is extracted from the global wave model WaveWatchIII at coordinates 17°N,108°E. This dataset provides information about wave characteristics in deep water areas such as significant wave height, peak wave period, mean wave direction.

Furthermore, the output of a MIKE 11 model is directly used as input for the Delft3D model without the general description (e.g., how to setup, calibration) due to not main point in this study.

2.3 Model calibration

The study utilizes the Nash-Sutcliffe criterion (Nash and Sutcliffe 1970) to assess the agreement between the modeled and the measured data

(6)

Where:

	=	Measured value at time i,
	=	Calculated value at time i,
	=	Number of pairs of comparison points between actual measured data and calculated data, and
	=	Average measured value.

Table 1 shows the goodness-of-fit of the model using the NSE index.

Table 1 The goodness-of-fit

NSE value		The goodness of fit
NSE ≤ 0.40		Bad
0.40 < NSE ≤ 0.70		Average
0.70 < NSE ≤ 0.85		Good
0.85 < NSE ≤ 1.00		Excellent

Model performance was evaluated using error statistics such as root mean squared error (RMSE), which is frequently used to measure discrepancies between the values predicted by a model and the observed data. The formula for calculating model performance is presented as follows:

(7)

Where:

Oi, Mi	=	Observed and modeled values, respectively, and
N	=	Number of values.

3 Results and discussion

3.1 Calibration

Figures 5 and 6 show the results of modeled hydrodynamic characteristics using Delft3D from April 10, 2023 to April 15, 2023.

Figure 5 Simulated (model) and measured (obs) water level.

Figure 6 Modeled and measured speed and current direction.

As can be seen in Figure 5, in the case of water level, there is a strong agreement between the calculated results from the model and measured data at the monitoring station, in terms of both the magnitude and phase of tidal water level fluctuations. The NSE index, reaching 0.88, indicates a good fit between the model and the measurements. Furthermore, in the case of waves (Figure 7), the calculated results of wave height, wave direction, and wave period demonstrate a positive correlation in both phase and magnitude when compared to the actual measured results. The RMSE index for water level, current, and waves between calculated and actual measured results are 0.07, 0.1, 0.11, respectively. With these results, it can be stated that the numerical model effectively captures and describes the behavior of currents, waves, and water levels with a reasonable level of accuracy at the Thuan An estuary.

Figure 7   (a) Modeled (Hs­_tt) and measured (Hs­_td) significant wave height; (b) modeled (Tp_tt) and measured (Tp­_td) wave period; and (c) modeled (MWD_tt) and measured (MWD_td) mean wave direction.

The calibration results of the model at Thuan An demonstrates promising outcomes. For wave characteristics (Figure 7), the calculated results of wave height, wave direction, and wave period exhibit a satisfactory level of agreement with the actual measured values. This suggests that the model accurately captures the characteristics of the waves at the monitoring station. For current characteristics (Figure 6), the model successfully replicates the current velocity and direction observed in the actual measurements, with a minimal difference in magnitude. This indicates that the model reliably represents the flow dynamics in the area. Considering the overall calibration results, the model has been effectively adjusted to ensure its reliability. Consequently, the set of calibrated parameters will be utilized for subsequent simulation calculations. This calibration process enhances confidence in the model's ability to accurately simulate the studied system and provides a solid foundation for future analyses and predictions. It is specially noted that the results are also extracted at 3 locations, as shown in Figure 11, where points P1 and P3 are present for the north and south bank of Thuan An estuary, respectively, and point P2 presents for the river estuary. The purpose of this is to define the parameter changes related to wave and current regimes.

3.2 Wave regimes

To evaluate the hydrodynamic regime of the Thuan An estuary, the year 2017 was chosen as the simulation period to assess and analyze the hydrodynamic processes occurring within the estuary. The wave calculations for the Thuan An estuary are depicted in Figure 8. The dominant wave direction in this area is northeast, with wave heights ranging from 0.3 m to 2.5 m along the coast. During the southwest monsoon period, wave heights typically range from 0.3 m to 1.2 m. In contrast, during the northeast monsoon period, the wave heights are significantly higher, ranging from 0.5 m to 2.5 m (as shown in Figure 9). Consequently, there is a substantial disparity in coastal wave heights within the Thuan An estuary area between the two seasons in any given year. During the northeast monsoon period, the wave heights are 1.2 to 2 times higher than those observed during the southwest monsoon period.

Figure 8 Waves in Thuan An estuary during (a) southwest, and (b) northeast monsoons.

Figure 9 Wave height in 2017.

3.3 Current regimes

The calculation results for the current field in the Thuan An estuary area are presented in Figure 10 (a–b). The current coastal velocity within the estuary predominantly falls within the range of 0.03 m/s to 0.43 m/s, with the flow direction alternating between northwest-southeast and southeast-northwest.

Figure 10 Currents in Thuan An estuary during (a) southwest, and (b) northeast monsoons.

The extracted calculation results are obtained at three specific locations, as indicated in Figures 11 to 13. Points P1 and P3 represent the north bank area and the south bank area of the Thuan An estuary, respectively. It is observed that the flow velocity at the south bank tends to be higher than that at the north bank. During the southwest monsoon period that occurs from April to September, the current velocity can reach up to 0.2 m/s. In contrast, during the northeast monsoon, the flow velocity is generally higher compared to the southwest monsoon, ranging from 0.1 m/s to 0.43 m/s. Consequently, the flow velocity during the northeast monsoon surpasses that of the southwest monsoon. At point P2, which represents the river mouth area, the flow velocity is predominantly in the north-south direction, with speeds ranging from 0.1 m/s to 0.55 m/s. These results are consistent with previous studies on a large scale. For example, as stated by Lam et al. (2009), the author showed that the current direction shifts from northwest to southwest during the peak of the northeast monsoon, which produces strong surface currents along the coast (Lam et al. 2009; Inman and Harris 1966). However, in the context of negative climate conditions (e.g., tropical storms and floods), the findings are clearly present in the hydrodynamic regime for this study.

Figure 11 Current rise in the Thuan An estuary.

Figure 12 Current speed in the north (P1), and south (P3) banks of the Thuan An estuary.

Figure 13 Current speed at point P2 in the Thuan An estuary.

3.4 Accretion and erosion causes and regimes

The results of seabed topographic variation in the Thuan An estuary for two specific months, June and November, are depicted in Figure 14. Based on the calculations, it is observed that during the monsoon period, when the waves are low and the river flow is minimal, the seabed topography in the Thuan An estuary experiences very little change, remaining nearly unchanged. However, during the northeast monsoon period, significant changes occur. A sandbar forms, obstructing the river mouth and resulting in sedimentation levels of 0.8 m. This alteration in the seabed topography has implications for flood drainage and the navigation of boats, affecting both the entry and exit of vessels. Several studies about the morphological changes of the Thuan An estuary show that the shoals at the entrance to the inlet pose difficulties for boat navigation and flood evacuation. Furthermore, an analysis of longshore sediment transport from 1970–2004 showed a large sediment transport in a northwest direction (Lam et al. 2009). Generally, sedimentation strongly depends on the wind regime over this study. In other words, these findings highlight the dynamic nature of the Thuan An estuary, where the monsoon seasons play a crucial role in shaping the seabed topography and influencing the hydrological conditions.

Figure 14 Seabed topography variation in the Thuan An estuary during (a) southwest, and (b) northeast monsoons.

Obviously, the development of coastal urban areas in Vietnam is currently experiencing a significant and growing trend. As a country with an extensive coastline along the East Sea, Vietnam possesses abundant coastal resources and potential for economic growth and tourism. However, the rapid development of coastal urban areas also presents challenges and considerations. It is crucial to ensure sustainable development practices to protect and preserve the fragile coastal ecosystems, manage coastal erosion, and address potential environmental impacts. Adequate infrastructure, such as coastal protection systems, waste management facilities, and efficient transportation networks, must be established to support the growing population and economic activities with the purpose of building better urban areas and cities for a net-zero carbon future. This requires a deep understanding of the hydrodynamic regimes in the estuaries in Vietnam generally, and Thuan An, particularly. The findings in this study provide a reliable scientific background for effective measures in the present, near-, and far-future. It is also noteworthy that the Thuan An estuary varies strongly during the Northeast monsoon season, with the flow of sand and mud mainly from the south bank into the estuary. Therefore, to stabilize the Thuan An estuary, it is necessary to continuously implement scientific research and engineering solutions to limit the amount of sand and mud moving from the south bank causing sedimentation and negative effects on the shipping channel entering the estuary. Besides that, early warning systems and floodplain zoning classification are important to minimize the effects of heavy rain-flood events on the accretion and erosion processes in the estuary.

4 Conclusions

The Thuan An estuary exhibits seasonal variations in waterway channels and coastal beaches. This is a lowland coastal area, predominantly influenced by waves. The coastal barrier is formed through the transport of sand along the coast by longshore sand transport driven by waves. During the northeast monsoon season, the river flow is minimal, and the combination of tidal currents and longshore currents, induced by waves, creates a robust longshore current flowing from the northeast to the southwest. In the southwest monsoon season, the sandbar on the southern side expands towards the north, leading to sedimentation in the river mouth channel.

The results showed that during the northeast monsoon period significant changes are observed in the Thuan An estuary. The formation of a sandbar obstructing the river mouth results in an accumulation of about 0.8 m of sediment. In the near-future, several effective measures for flood drainage and navigation stability in the Thuan An estuary, using the state-of-the-art technologies, are expected to be deeply discussed.

Acknowledgements

This study is funded by the Ministry of Agriculture and rural development research project "Study measures to stable estuaries in central coast for social economic development and disaster prevention, application for Thuan An estuary, Thua Thien Hue province”.

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