2.1 Case study

Tam Ky City, one of two cities situated in Quang Nam Province, serves as the administrative-economic center, with a total urban area of about 11 km² (depicted by the black line in Figure 1). The drainage system of the city comprises an extensive pipeline network of 57 km, with more than 530 manholes connected to 7-km canals and 7 detention ponds. The drainage system discharges directly into the Tam Ky River and Ban Thach River through six outlets (as shown in Figure 1). A key limitation of the city's drainage system is that the bottom elevation of its six outlets ranges from −1.32 m to −0.28 m, while the flood water level in the Ban Thach River can reach from +1.7 m to +2.7 m, corresponding to Alarm Level I and III respectively.

In Tam Ky City, inundation is a recurring issue that can be attributed to several factors. The primary reason behind is the concentration of flow from catchments of the Ban Thach and Tam Ky river basins due to heavy rain in these areas. Subsequently, the concentrated flow interacts with the discharge from the spillway operation from Phu Ninh reservoir and high tidal levels at Hoi An and Cua Lo. To effectively represent flow progress in the river basin, a hydraulic model was developed with its boundary extending to the North of the study area, as shown in Figure 1, covering a catchment area of more than 1000 km² (the red line). Figure 1 also displays the location of meteo-hydrological stations, including six meteorological stations (Thang Binh, Tam Ky, Ky Phu, Phu Ninh, Xuan Binh, and Nui Thanh), a hydrologic station (Ky Phu), a tidal water level station (Hoi An), observed discharge at Phu Ninh reservoir and flood marks obtained from two flood events (2013 and 2021).

According to data from the Vietnam General Department of Meteorology and Hydrology, the central region is highly susceptible to typhoons and tropical typhoons, accounting for nearly 70% of all typhoons affecting Vietnam. These weather events, along with tropical depressions and cold air, often result in heavy rain, leading to severe inundation in the region. The average annual rainfall of the entire basin ranges from 3000 to 4000 mm. Rainfall distribution varies across seasons, with 65%–75% of the annual rainfall concentrated in the season from September to December. Observations from meteo-hydrological stations in Tam Ky City (the red circle in Figure 1) recorded a total rainfall of 531.4 mm over a 3-day period from 22 to 24 October 2021. During this period, the highest total rainfall in 24 h was 503.2 mm, and the heaviest rainfall in 1 h and 15 min was 61 and 23.4 mm, respectively. Figure 2 presents recent urban inundation events occurred in Tam Ky City.

2.2 Hydraulic model

Forecasting urban inundation has emerged as a significant trend in recent times (Chen et al., 2022; Eldho et al., 2018). However, this task is complex as it is affected not only by such triggers as urban rainfall or river flood water levels (Bisht et al., 2016; Chen et al., 2022), but also by the characteristics of the drainage system and urban topography (Eldho et al., 2018). In this study, a hydraulic model was developed by integrating water body and urban data, effectively connecting the river basin and urban hydrological systems. This coupling was achieved by combining 1D processes, which encompass river channels and pipe systems, with 2D processes which involve overflow from rivers, urban manholes, and other components (DHI, 2014a, 2014b). The MIKE Flood model provided river channel water level, which served as tidal conditions for the MIKE Urban model representing the urban drainage system, while the MIKE-Urban model calculated the inundation volume for all manholes and outlets within the city (DHI, 2014c, 2014d). During normal conditions, all urban runoff is discharged to the river through the pipe system and outlets when the river water level is lower than the outlet elevation. However, when the river water level rises above the outlet elevation, interactions occur between urban runoff and river water, potentially resulting in blockages of the stormwater conveying system and manholes. As a consequence, urban inundation occurs. This hydraulic model was carefully calibrated and validated using actual inundation events. Subsequently, it can be employed to predict urban inundation through data forecasting of rainfall and tide. The general flowchart diagram of this study is illustrated in Figure 3.

3.1 Data for hydraulic model setup

The data used to set up the hydraulic model was collected from various reliable and available data sources, as described in Table 1 and Figure 4. In particular, the water level observation in the drainage system was measured directly by water level sensors located at Tran Quy Cap and Ton Duc Thang roads (indicated by two blue points in Figure 1b) on 7 and 8 October, 2022.

3.2 Boundary conditions

The 11 discharge boundaries and three water level boundaries of the MIKE Flood model are presented in Figures 5 and 6. The data includes the observed water level at Hoi An station, tidal levels at Cua Lo and Ky Ha extracted from the East Sea model, and discharge boundaries obtained from a hydrological model (MIKE NAM model). These data are crucial for calibrating and validating corresponding inundation events occurred in October 2021 and November 2013. In addition, Figure 7 shows two independent rainfall events in October 2022, providing data for calibrating and validating the MIKE Urban model.

3.3 Data for model calibration and validation

To calibrate and validate the models in this study, the Nash-Sutcliffe coefficient was employed, as proposed by critical findings of Moriasi et al. (2007). First of all, the MIKE Flood model was calibrated for the inundation event in October 2021 by iteratively modifying bed friction resistance in both the river and floodplain until the simulated water surface elevation matched the observed water level and flood extent. After that, this model was validated using data from the inundation event in November 2013. In this way, the observed level on the river at Ky Phu hydrological station (see the red star symbol in Figure 1) was used to evaluate the simulation performance. Finally, the MIKE Urban model was calibrated and validated based on comparison of observed and simulated water levels at two manholes corresponding to two independent rainfall events occurred in September 2022 (see Figure 7a,b).

3.4 Data input for flood forecasting

The data used for urban inundation forecasting includes rainfall in the river-urban basin and tidal levels. In this study, we utilized rainfall predictions obtained from the Windy website (https://www.windy.com/) and the tidal level predictions from the East Sea model. These data were extracted 48 h before the expected landfall of Typhoon Nuru in Tam Ky City (from 25 to 26 September 2022). These data were analyzed to provide inputs for the hydraulic model.

The Windy website provides four rainfall prediction models, namely GFS 22 km, ECMWF 9 km, ICON 13 km, and METEOBLUE (see Figure 8a). After careful evaluation using rain gauges, it was determined that the GFS 22 km model demonstrated better correlation in terms of intensity, accumulation, and duration. Therefore, we decided to use the rainfall data from the GFS 22 km model for inundation forecasting (Figure 8a).

The prediction of tidal levels relies on the simulation results obtained from the MIKE 21/3 model (see Figure 8b) from the East Sea model. This model enables the simulation of tidal processes and wave propagation from offshore to the coastal area. The open boundaries of this model encompassed significant areas, including Taiwan, Luzon, Mindoro, Babalac, and Malacca straits.

4.1 Calibration and validation of the hydraulic model for river basin

The simulated and observed river water levels obtained at Ky Phu (Tam Ky) hydrological station for calibration and validation are presented in Figure 9a,b. The evaluation of model quality, as indicated by efficiency criteria, demonstrated a high level of agreement with the observed data. The Nash coefficients in the calibration and validation periods were 0.96 and 0.73, respectively.

In addition, the hydraulic simulation results in floodplains demonstrated a high level of accuracy. The error of the flood elevation at 16 flood marks on October 2021 and the water depth at seven observation marks on November 2013 between the simulation and field survey was quite small (see Appendices 1 and 2). It indicates that the MIKE Flood model of the river basin is stable and reliable for urban inundation forecasting.

4.2 Calibration and validation of the hydraulic model for urban area

Calibration and validation results for urban areas from MIKE Urban model also showed good results. The Nash indicators at gate 1 and gate 2 (two black circles in Figure 1b) were 0.74, 0.61, 0.78, and 0.72, respectively (Figure 10a–d). Overall, the results indicate that the hydraulic model is reliable for urban inundation forecasting.

4.3 Urban inundation forecasting

Figure 11b presents the urban inundation forecasting map generated 48 h before Typhoon Nuru landed in Tam Ky City on September 26, 2022. The map is the result of the coupled river-urban inundation modeling, combined with data forecasts of rainfall (Figure 8a) and tidal levels (Figure 8b). The map shows that seven major roads are inundated, with water depths ranging from 0.1 to 0.4 m, including Hung Vuong (0.4 m), Phan Chau Trinh (0.4 m), Nguyen Duc (0.3 m), Dien Bien Phu (0.3 m), Ly Thuong Kiet (0.15 m), Tra Thu Do (0.15 m), and Nguyen Thi Dinh (0.15 m). Figure 12 presents photos taken after the landfall of Typhoon Nuru in Tam Ky City. These photos serve as visual evidence, demonstrating that the predicted water depths at the inundation points, as noted in Figure 11b (corresponding to note 1, note 2, and note 3), align well with the actual conditions observed in reality.