Abstract

Urban flooding has emerged as a significant issue in rapidly expanding cities like Thu Duc City, Vietnam, exacerbated by the dual pressures of urbanization and climate change. This study employs an integrated 1D-2D hydrodynamic model to assess flood risks and hazards, incorporating probabilistic analyses of rainfall and tidal levels. Simulations across varying recurrence intervals produce detailed flood hazard maps that identify vulnerable areas and quantify flood depths. Key findings indicate that central areas, including Thu Duc market and Tam Binh Ward, are highly prone to flooding, with depths exceeding 1.5 meters in severe scenarios. The flood hazard maps reveal consistent flooding patterns, with both flood depths and affected areas increasing over time. Economic assessments estimate average annual flood losses at 21,622 billion Vietnamese dong (VND), underscoring the substantial economic consequences of flooding in the region. This study uniquely integrates multi-factor boundary conditions, combining rainfall and tidal influences for a more comprehensive risk assessment than traditional single-factor approaches. The findings highlight the urgency of enhancing drainage infrastructure and implementing targeted flood management strategies, such as retention basins and improved urban planning. These results offer critical insights for urban planners and policymakers aiming to mitigate flood risks and enhance resilience in rapidly urbanizing areas.

1 Introduction

The risk of flooding is defined as the potential occurrence of a serious disaster (Di Baldassarre et al. 2009), which can be represented as a function of both severity and the probability of flooding. Regarding risk, according to a study (Crichton 1999), it is the likelihood of experiencing losses and depends on three factors: hazard, vulnerability, and exposure. If any of these risk factors increases, then the overall risk also increases (Barredo and Engelen 2010).

In the construction of flood risk maps, hydrodynamic models are the most commonly used tools (Karmakar et al. 2022). There are many factors that affect the reliability of risk assessment. In addition to the sophistication of the model, the appropriateness of the boundary conditions applied to the model is also important. Although urban flooding is the result of the simultaneous impact of multiple factors (such as rainfall, tides, river overflow, storm surge, etc.), in most studies, the probability of flooding is calculated based on the probability of a single selected factor. On the other hand, studies by Barredo and Engelen (2010), Apel et al. (2009), and Karmakar et al. (2010) focus on assessing the probability of river overflow. There have also been efforts to develop flood risk and hazard maps under the combined influence of two factors such as upstream flow and coastal tide levels (Moftakhari et al. 2019; FEMA 2015). However, rainfall, a critical factor in urban flooding, was not accounted for in the aforementioned study.

The purpose of this paper is to introduce a new calculation of flood risks and hazards in Thu Duc City. Thu Duc is a new city established by combining three districts including Thu Duc, District 2, and District 9. Thu Duc is directly below and located in the east of Ho Chi Minh (HCM) City (Figure 1).

Figure 1 Thu Duc City in the east of HCM City.

Thu Duc is a municipal city (sub-city) under the administration of HCM City, Vietnam. The city was founded by the Standing Committee of the National Assembly on December 9, 2020 from the districts of 2, 9, and Thu Duc District (The Saigon Times 2020). Thu Duc City shares the same climate as HCM City. Situated in the tropical monsoon zone near the equator, the city experiences consistently high temperatures throughout the year. The climate is characterized by two distinct seasons: the rainy season and the dry season, both of which significantly shape the local landscape and environment. Average temperatures typically hover around 30°C, accompanied by abundant sunshine. From May to November, the rainy season delivers regular afternoon downpours, usually lasting a few hours. (Asian Development Bank 2010).

Thu Duc is being built to become a smart city with a high quality of life. However, many areas of the city are frequently flooded. According to the report from the Thu Duc City People's Committee at the workshop "Current situation and solutions to reduce flooding in Thu Duc City" on May 31, 2024, there are currently 24 flooded areas in the city, typically in the Thu Duc market area, which is often heavily flooded every time it rains. To calculate and simulate flooding in these scenarios, an integrated hydrodynamic model was used. The model was built using F28 software including 1D submodels for flow in the rivers, in the sewers, and on the roads, and 2D submodels for shallow water and overland flow (Le et al. 2023). All flood factors are grouped into two factors: rainfall in the area (R), represented by rainfall at Phuoc Long A rain gauge station, and water levels at the outlet of the drainage system (H), represented by the water level at the Phu An hydrological station. The probability of flooding in the area is determined by the combination of rainfall at the Phuoc Long A station and water levels at the Phu An station, as established by the R-H method developed by Le and Hoa (2024).

2 Methodology

2.1 Hydrodynamic model

A hydrodynamic model is a useful tool in flood research. It allows for simulating scenarios to obtain data for analysis. Due to the flow diversity, the drainage system's mathematical model will be an integrated one. The F28 software is used to build the mathematical model. The submodels involved in the integrated model include a 1D submodel for river/canal flow, a 1D submodel for flow in sewers and on roads, and a 2D submodel for shallow and overland flow (Le et al. 2023). The flow on the roads can also be modeled using a 2D submodel and the calculation results will be more accurate. However, this approach will lead to a huge number of 2D elements, which is not suitable for large-scale calculations.

The1D submodel flow is solved using1D Saint-Venant equations:

(1)

(2)

Where:

η	=	water level (m),
A	=	cross-section area (m2),
g	=	acceleration due to gravity,
Q	=	flow rate (m3/s),
s and t	=	longitudal distance in the direction of flow and time,
ql and Va	=	lateral inflow along the river (m2/s) and its velocity component along river axis (m/s), and
	=	conveyance factor (m3/s)

In which:

R	=	hydraulic radius (m), and
n	=	Manning’s roughness coefficient.

In the 2D submodel, flow is solved using 2D Saint-Venant equations (Lai 2010). If you consider the surface inflow, see Equation 3:

(3)

(4)

Where:

	=	water level,
	=	gradient operator in Cartesian coordinates,
	=	vector of the flow rate per unit width,
	=	depth-averaged velocity vector,
	=	water depth,
	=	stress tensor, and
	=	vector of external forces.

In which:

	=	depth averaged effective stress, and
	=	bed shear stress.

And:

AH	=	eddy viscosity,
ρ	=	specific mass of water, and
i and j	=	axis index and have a value of 1 or 2, where 1 denotes the x-axis and 2 denotes the y-axis. When i has the value 1, j will have the value 2, and when i has the value 2, j will have the value 1, and
qv and vx, vy	=	inflow per unit surface (m/s), and its two components of velocity (m/s).

The 1D submodel for flow in sewers and on roads is an integrated model of two 1D submodels: one for flow in the pipes, and one for flow on the roads. These flows are also solved using Equations 1 and 2. All equations are solved using the finite volume method in which the 2D submodel mesh is unstructured with quadrilateral elements.

Submodels are connected to each other by supernodes, and overflow links to form a unified model. A supernode, which is a common node among several submodels, combines their volumes and calculates water levels using the mass conservation equation. Overflow links connect two submodels by flow over spillways. Overflow links typically link 2D submodels of floodplains to 1D submodels of rivers, canals, or roads. Momentum transfer is calculated to ensure the model's overall accuracy. In the study by Le et al. (2023), two types of links, supernode and overflow, which integrate the 1D and 2D submodels in the F28 software, are presented in detail. Since the 1D sewer flow submodel and the 1D road flow submodel are always coupled, these two submodels will be described as one object. These two submodels are connected at the manholes by overflow links.

The drainage system model of Thu Duc City is established within the city's boundaries. The drainage system in the study area consists of pipes with diameters ranging from 0.4 m to 1.0 m. In several roads surrounding Thu Duc Market, the drainage systems have pipe diameters of less than 0.1 m. These systems were constructed long ago and now exhibit limited water drainage capacity. The Thu Duc City model is then integrated into the Saigon-Dong Nai river system model (SG-DN) to address boundary conditions. The SG-DN model is also an integrated 1D-2D model, where rivers and canals are simulated using the 1D submodel, and estuaries and flood-prone areas are simulated using the 2D submodel. After integration, the resulting model can still be considered the SG-DN model, with the difference being that the Thu Duc City area is modeled in detail. Integrating the Thu Duc City model into the SG-DN model is carried out in the same manner as integrating the submodels. Inheriting the SG-DN model reduces the effort required to input the computational grid data of the submodels but also minimizes the steps needed to calibrate the model on a large scale.

The SG-DN model uses discharge boundary conditions at the upstream nodes of the 1D submodel based on observed data, and water level boundaries imposed at the 2D sea boundary nodes calculated according to the correlation with the water level at the nearby Vung Tau station. Rainfall over Thu Duc City will be imposed according to the scenarios of the combination of (R-H) in which the rain will accrue when the water level at Phu An station is equal to the water level in the combination.

2.2 Steps to create flood hazard maps and calculate flood risk

The flood risk assessment is conducted through an eight-step process, as follows:

1. Use isoprobability curves of (R-H) combinations, for each return period to determine the rainfall (R) at the Phuoc Long A rain gauge station, and water level (H) at the Phu An hydrological station of four (R-H) combinations.
2. Create a hydrodynamic model of the drainage system of Thu Duc City.
3. Run the model to obtain water level results at the Phu An station over a period of several days, and determine the time when the water level at Phu An station is equal to the water level in the (R-H) combinations.
4. Create flood hazard maps.
5. Run the model to simulate the flood scenarios. In each scenario, rainfalls will be imposed at the time defined in Step 3.
6. For each return period, determine the maximum flood depth among scenarios.
7. Based on maximum flood depth, create flood hazard maps for different return periods.
8. Determine flood risk: Flood damage is assessed using flood hazard maps and maps of vulnerable objects.

Studies have assessed risks from many different perspectives, including economic losses and environmental and social risks. This paper uses a quantitative economic risk assessment method, based on a damage cost schedule for flooding in HCM City established by Haskoning (FIM 2013), to estimate direct tangible flood damage costs. Haskoning's study identified 10 main assets in HCM City (including Thu Duc City) susceptible to flood damage, with damage per square meter determined for different flood levels. In Thu Duc City, significant damage is only observed in urban and rural residential areas. Agricultural land, despite its large area, does not suffer flood damage. Other damages are negligible due to the small, affected areas.

Thus, flood damage for each return period is calculated by multiplying the flooded area by the damage function value corresponding to each type of flooded object and flood depth. The average annual damage (EAD) is calculated using the formula by Olsen et al. (2015).

(5)

Where:

N	=	number of return period intervals,
Di	=	damage corresponding to the 𝑖-th return period (billion VND), and
Ti	=	return period (year).

3 Results and Discussion

3.1 Integrated model of Thu Duc City drainage system

The drainage system model of Thu Duc City, integrated into the SG-DN river model, has been developed according to the method presented in Section 2.1. The calculation grids of the following submodels are shown in Figure 2:

• 1D submodel for river/canal flow,
• 1D submodel for the sewer/road system, and
• 2D submodel for surface runoff in the Thu Duc City area.

Figure 2 Calculated mesh of the submodel.

The parameters of the submodels in the integrated SG-DN model are as follows:

• 1D river submodel: Includes 1,114 branches with 968 nodes, 9,770 cross-sections, and 8,656 calculated segments. The section lengths range from 41 m to 636 m, with the shortest sections located in the Thu Duc City area.
• 1D sewer and road submodel: Includes 4,499 sewer branches with 3,625 nodes, 39,150 cross-sections, and 34,651 segments. The section lengths are approximately 30–40 m.
• 2D submodel: The 2D model covers the grid up to the riverbank and road edges. This submodel has 134,802 quadrilateral elements with 151,106 nodes. The edge lengths of the quadrilateral elements are equivalent to the segment sizes of the 1D models.

The drainage system data was referenced from the HCM City Department of Construction. The terrain elevation data in the 1D road submodel, and the 2D model were referenced from the 1/2,000 scale map published by the Ministry of Natural Resources and Environment.

The submodels are interconnected to form an integrated model. This model includes supernode links between the 1D river submodel and the 2D submodel, between the 1D sewer submodel and the 1D river submodel, or the 2D submodel at the sewer mouths. There are also overflow links between the 1D river submodel and the 2D submodel at the riverbanks, between the 1D road submodel and the 2D submodel at the curbs, and between the 1D road submodel and the 1D sewer submodel at the manholes. The computational grid of the integrated model is shown in Figure 3. Integrating the hydraulic model of Thu Duc City into the overall downstream SG-DN river model will address the boundary condition issues of the Thu Duc City hydraulic model. Furthermore, this integration will allow for the consideration of bidirectional hydraulic interactions between the water bodies in Thu Duc City and the downstream SG-DN river area. However, this integration also makes the model more complex and significantly increases the computational run time. The model has been calibrated before use to ensure the reliability of the calculation results. The criterion for evaluating the calibration results is the agreement between the calculated flow and water level results and the measurement data, particularly when applying 1D models to rivers and canals. For the 1D sewer and road submodel, the calibration was conducted using flood monitoring data during rainfall events in the area.

Figure 3 Mesh of the 1D-2D integrated model of Thu Duc City, and the location of monitoring stations.

Calibrate 1D model for river

The model has been implemented based on data from 10 monitoring periods conducted by various studies and projects. The calibration parameters include the roughness coefficient of the 1D river/canal model and the roughness coefficient of the 2D estuary model. Figure 4 and Figure 5 show comparisons of some of the calculation results. This monitoring was carried out in March 2015 on the SG-DN River. Table 1 presents the results of evaluating the effectiveness of the model calibration using the Nash-Sutcliffe coefficient for this monitoring period.

Table 1 Nash-Sutcliffe coefficient for calculation results of discharge and water levels in March 2015.

Nash-Sutcliffe coefficient	Phu Cuong Station	Nha Be Station	Phu An Station	Cat Lai Station	Bien Hoa Station
Discharge Q	0.94	0.93	0.93	0.84	0.71
Water levels H	0.98	0.94	0.78	0.87	0.72

Figure 4 Water level at hydrological stations on Sai Gon–Dong Nai River in March 2015 (symbols – observed data; lines – calculated results).

Figure 5 Discharge at hydrological stations on Sai Gon–Dong Nai River in March 2015 (symbols – observed data; lines – calculated results).

The high Nash-Sutcliffe coefficient indicates that the model has been very well-calibrated. The calibration results show that the Manning’s roughness coefficient of the 1D submodel river/channels ranges from n = 0.016 to 0.06, depending on the river branch. For the 2D submodel, the Manning’s roughness coefficient is determined to be in the range of n = 0.015 to 0.018, depending on the region.

Calibration of the 1D submodel for sewers and roads

The 1D submodel for sewers and roads has been calibrated using reference data from the Ho Chi Minh City Urban Drainage Company, observed during four rain events on the following dates: June 2, 2022, June 22, 2022, August 15, 2022, and September 6, 2022. The adjustment parameters include the Manning’s roughness coefficients of the 1D sewer model, the 1D road model, and the 2D model for areas affected by rain and tidal flooding. Figure 6 shows flooding on the roads during the rain on the afternoon of June 22, 2022.

Figure 6 Flood levels calculated during the afternoon rain on June 22, 2022 (color scale unit: meters).

Table 2 Comparison of calculations and flood measurements during the afternoon rain on June 22, 2022, on roads in Thu Duc City.

No.	Road name	Flood range in road			Flood depth (m)
		From	To		Monitoring	Calculated	Error
1	Quoc Huong	Le Van Mien		Street No.65	0.20	0.27	0.07
2	Nguyen Van Huong	In front of Hoang Anh Gia Lai building			0.20	0.21	0.01
3	To Ngoc Van	Railway	Pham Van Dong		0.30	0.64	0.34
4	Dang Thi Ranh	Duong Van Cam	To Ngoc Van		0.20	0.34	0.14
5	Ho Van Tu	Kha Van Can	Alley 45		0.20	0.28	0.08
6	Kha Van Can	Duong Van Cam	Thu Duc Post Office		0.20	0.25	0.05
7	Vo Van Ngan	Dang Van Bi	Thu Duc Market		0.20	0.37	0.17
8	Duong Van Cam	Alley 17	House No. 49		0.20	0.63	0.43
9	National Road No.13	Gia Dinh Shoes	Hiep Binh Junction		0.10	0.00	-0.10
10	Hiep Binh	Street No. 1	Hiep Binh Secondary School		0.10	0.16	0.06
11	Do Xuan Hop	In front of Phuoc Binh Ward People's Committee			0.15	0.25	0.10

Calibration has determined that the Manning’s roughness coefficient of sewers is n = 0.013, of roads is n = 0.022, and of 2D flooded areas is between n = 0.016 and n = 0.500, depending on the location.

3.2 Combinations of rainfall at Phuoc Long A station and water level at Phu An station

Using the isoprobability curves of combinations of (R-H) as created in (Le and Hoa 2024), the rainfall at Phuoc Long A station, and the water level at the Phu An station for 40 combinations are determined and presented in Table 3. The location of these combinations on isoprobability curves is shown in Figure 7.

Table 3 Combinations of rainfall at Phuoc Long A station (R), and water level at Phu An station (H) for different return periods.

H (cm)	R (mm)
	Rainfall duration (60 min)				Rainfall duration (90 min)				Rainfall duration (120 min)
	2 y	3 y	5 y	10 y	2 y	3 y	5 y	10 y	2 y	3 y	5 y	10 y
174	-	-	-	0	-	-	-	-	-	-	-	-
171	-	-	0	-	-	-	-	-	-	-	-	-
168	-	0	-	-	-	-	-	-	-	-	-	-
166	0	-	-	-	-	-	-	-	-	-	-	-
140	17	21	26	32	25	33	45	59	30	40	56	75
80	22	28	36	43	42	58	80	92	51	68	86	101
0	25	32	40	47	48	70	88	98	60	77	93	108

Figure 7 Isoprobability curves of combinations of rainfall at Phuoc Long A station—water level of Phu An station (R-H), (grey small points = observed events; red points = working points).

3.3 Flood risk and hazards in Thu Duc City

For each flood return period, there are three curves corresponding to different rain durations. On each curve, four combination points (R-H) are selected, including one with the maximum water level, and one with the maximum rainfall, to serve as boundary conditions for the inundation simulation. This results in 12 flooding scenarios for each return period. The maximum value from these simulations determines the flood level for each period. These flood levels are then mapped to show the flood risk for the corresponding return period. Figure 8 presents the flood hazards in Thu Duc City for return periods of 2, 3, 5, and 10 years.

Figure 8 Distribution of flood hazard in Thu Duc City by return periods.

The simulation results of the numerical model show that the flood distribution aligns with the terrain and geomorphological characteristics of the area. Based on simulations over four return periods, flood locations on the map remain consistent, with variations only in flood depth and area. Thu Duc City, which accounts for nearly 50% of the city's area, has the highest flood risk. The central areas often experience flood depths ranging from 0.5 m to over 1.5 m, highlighting the need for special attention to flood management in low-lying urban areas.

The flooded area increases periodically from a return period of 2 years to a return period of 10 years (Table 4). These flooded areas are characterized by low, sunken terrain, agricultural areas, or aquaculture ponds. During rainy periods, water accumulates in these areas, causing flooding in adjacent urban regions. Additionally, the backflow of water onto the road surface due to some sewer lines also creates water storage basins.

Table 4 Flood depth and inundated area in Thu Duc City by return periods.

Flood Depth (m)	Inundated Area (ha)
	T = 2 years	T = 3 years	T = 5 years	T = 10 years
≥ 1.50	7.4	10.0	19.6	30.5
≥ 1.00	663.1	792.5	959.8	1,180.1
≥ 0.50	4,444.9	4,871.8	5,353.8	5,926.9
≥ 0.30	6,075.8	6,492.1	7,008.9	7,556.9
≥ 0.20	6,858.7	7,316.1	7,868.3	8,401.8
≥ 0.10	7,870.5	8,341.1	8,857.2	9,397.3

The northeast area of Thu Duc City experiences flooding from Nguyen Tri Phuong Street, through Suoi Cai, to the University of Economics and Law Street (Linh Xuan Ward) and Suoi Cai, Van Han Street (Linh Trung Ward). The depth of flooding increases with frequency. Although this area has high terrain and is less affected by high tides, it still faces urban flooding risks due to steep terrain, high urbanization density, and debris in the Suoi Cai section, which obstructs the drainage process and leads to flooding.

Based on satellite images, the areas of urban residential zones and agricultural or natural areas have been identified and are presented in Figure 9. Rural residential areas comprise the remaining areas of Thu Duc City outside the urban residential, agricultural or natural areas. By overlaying the damage-prone area map (Figure 9) onto the flood risk maps for different recurrence intervals (Figure 8), the flooded areas at various levels for each land type can be identified and are presented in Table 5.

Figure 9 Urban residential areas and agricultural or natural areas of Thu-Duc City.

Table 5 Flooded area corresponding to each flood recurrence interval (ha).

Inundation depth (m)	Subject suffering damage	Inundation area (ha)
		T = 2 years	T = 3 years	T = 5 years	T = 10 years
0 – 0.1	Urban residential areas	5,092.35	4,924.20	4,751.20	4,530.58
0.1 – 0.25		805.74	870.37	904.80	977.61
0.25 – 0.5		528.88	596.01	658.79	728.92
0.5 – 1		224.62	247.41	305.88	357.30
1 – 1.5		38.12	49.70	61.49	84.90
>1.5		5.84	7.85	13.38	16.24
0 – 0.1	Agricultural or natural areas	7,488.11	7,449.30	7,387.59	7,327.10
0.1 – 0.25		142.43	153.13	171.87	182.51
0.25 – 0.5		161.72	167.43	175.86	201.35
0.5 – 1		83.77	101.25	124.02	136.48
1 – 1.5		6.63	11.05	21.88	32.36
>1.5		0.91	1.46	2.89	6.67
0 – 0.1	Rural residential areas	2,508.63	2,460.27	2,350.25	2,258.84
0.1 – 0.25		404.99	405.84	445.82	458.76
0.25 – 0.5		166.41	200.88	244.18	274.10
0.5 – 1		66.64	76.54	91.95	116.39
1 – 1.5		5.43	8.46	17.17	37.11
>1.5		0.60	0.71	3.33	7.50

Flood damage for different land types has been calculated based on flooded areas for return periods of 2, 3, 5, and 10 years and damage cost schedule established by Haskoning (FIM 2013) as shown in Table 6. Using the formula in Equation 5, it is determined that Thu Duc City suffers an average of 21,622 billion VND in flood damages annually.

Table 6 Flood damage for the return period.

	Damage due to flooding (billion VND)
Flood depth (m)	T = 2 years	T = 3 years	T = 5 years	T = 10 years
Total damage (Di) (billion VND)	48,500.09	51,728.91	56,990.81	63,456.41

4 Conclusion

This study assessed flood risk in Thu Duc City using an integrated 1D-2D hydrodynamic model combined with probabilistic boundary conditions. The results identified key flood-prone areas, including the Thu Duc market, Tam Binh Ward, and Tang Nhon Phu A, where flood depths can exceed 1.5 meters in severe scenarios. The economic assessment revealed significant annual flood damage, averaging 21,622 billion VND, underscoring the substantial financial impact of recurring floods.

To enhance flood management strategies, the study recommends prioritizing infrastructure improvements, such as expanding key drainage channels and constructing retention basins in vulnerable areas. Additionally, findings support evidence-based urban planning and zoning policies to reduce exposure to flood risks in highly susceptible regions. Policymakers and urban planners can leverage these insights to develop targeted interventions, optimize resource allocation, and strengthen long-term resilience against urban flooding in Thu Duc City.

The study highlights key implications for urban planners, emphasizing the need to upgrade drainage infrastructure in flood-prone areas, adopt strategic zoning to avoid high-risk zones, and implement long-term resilience measures like retention basins. Policies enforcing flood-resilient designs and regular maintenance are also essential for effective flood management.

Although this study used a detailed numerical model and a multivariate combinatorial probability approach, some errors persist due to the problem's complexity. Certain factors, such as features obstructing 2D flow and limitations in rain gauge station data, were not fully considered. These challenges are the focus of ongoing refinement by the research team.

Acknowledgments

We acknowledge Ho Chi Minh City University of Technology (HCMUT), and VNU-HCM for supporting this study.

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