In this research, the authors aim to evaluate the damage caused by floods in Vinh Phuc Province. The study incorporates the construction of hydro-hydraulic models and the development of damage functions for the main elements at risk. In order to ensure the accuracy of the calculated results, the hydro-hydraulic models and damage curves are verified for their reasonableness. The outcomes of this study give us an overview of flood damage in the research area. It indicates that the potential level of flood damage is a matter of significant concern, with an annual damage estimate of approximately 6.9 million USD. The research also reveals the distribution of damage by sector and by space. According to the research findings, the greatest damage was in Vinh Tuong District, where most of the damage was caused by flooding of agricultural land. In contrast, residential buildings in the area suffered relatively little damage compared to agricultural land. This information is crucial for decision-makers to implement effective and targeted mitigation measures.

  • Developing a hydrological and hydraulic model to flooding in Phan-Ca Lo basin. Mathematical models are effective tools for hazard assessment.

  • Establishing two specific damage functions for residential area and agricultural land of Vinh Phuc Province.

  • Assessing flood damage in Vinh Phuc Province through damage–frequency curve and the expected annual damage.

Flood is a natural disaster that frequently causes heavy damage to properties and the environment (McGrath et al. 2019; Zeleňáková et al. 2019). Climate change has led to an increase in the frequency and severity of flooding, resulting in a higher potential for damage (Kefi et al. 2018; Cea & Costabile 2022). Despite its significance, research on flood risk in developing countries still has limitations (Romali & Yusop 2021). Flood damage is often divided into direct/indirect and visible/invisible damage (Smith & Ward 1998; Jonkman et al. 2008; Velasco et al. 2016). Direct damage is primarily caused by the physical impact of the hazard, such as structural damage to buildings. Indirect damage includes the disruption of economic activities and the reduction of investment opportunities. Visible damage can be converted into monetary values, while invisible damage cannot be directly measured. Examples of invisible damage include loss of life and damage to cultural heritage. The assessment of indirect and invisible damage is still a significant challenge (Seifert et al. 2010; Meyer et al. 2013). To simplify and make calculations feasible, many studies often focus on the direct and visible damage.

The commonly accepted approach to flood hazard assessment is simulation via mathematical models (de Moel et al. 2015; Kefi et al. 2018; Tran & Nguyen 2024). In particular, flood simulation is often applied by hydraulic models. The foundation of hydraulic models is the use of physical equations that simulate 1D/2D flow, such as the Saint–Venant equation system. The advantage of these models is that they provide detailed results on depth, velocity, and inundation period (de Moel et al. 2015). The levels of hazard can be presented by hazard maps (Tingsanchali & Karim 2010; Binh et al. 2019; Vojtek et al. 2023). Information about the spatial distribution of the key affected factors enables an intuitive overview of hazards. However, the application of hydraulic models requires a large amount of work, including data collection, model establishment, model calibration and validation. The accuracy of the simulation model is an extremely important issue. However, due to the data limitation, many previous studies often only mentioned lightly flood simulation inherited the flood simulation results or did not mention the issue of model calibration and verification. Budiyono et al. (2015) calculated the damage to Jakarta, Indonesia. The study only focused on damage curves, while the flood maps used in the study were reported by village managers. Zeleňáková et al. (2019) modelled the flood risk in Kružlov village, Slovakia using the Hec Ras model and GIS platform. This research showed us the potential result of the hydraulic model, but the model validation process was skipped. In addition to the calibration and validation of the model, the determination of the input boundary in the hydraulic model is a critical factor in the resulting calculations. To the best of the authors' knowledge, this aspect has not been adequately addressed in previous research. Overcoming these limitations is feasible in this study.

Assessing vulnerability is a challenging process because the vulnerability has multiple dimensions. Several studies assess vulnerability by individual proxy indicators or composite indicators (Stathatou et al. 2016; Mansir et al. 2021). However, the availability and uniformity of data related to vulnerability assessment indicators in different areas are some of the major limitations of the method. Assessing a relationship between the level of damage and flood factors is a globally accepted concept (Lang et al. 2010; Martínez-Gomariz et al. 2020). The factors, affecting damage, can vary depending on the sectors being evaluated. Some previous studies have developed damage curves of sectors with different flood depths (Notaro et al. 2014; Shrestha et al. 2021). Some authors combine flooding depth with other factors such as flow velocity (Lazzarin et al. 2022) or flooding period (Thieken et al. 2005) to establish a correlation with the extent of damage. Most authors developed the damage function based on survey data. Therefore, application is limited to specific areas. Furthermore, very few studies have data to verify the accuracy of the established damage functions (Seifert et al. 2010). This is also the remaining gap in previous research. To overcome this gap, the damage curves need to be verified with independent damage data from the locality to check their reasonableness.

The conventional approach to flood risk assessment encompasses hazard assessment, exposure assessment, vulnerability assessment, and their integration to form a comprehensive risk assessment (Kron 2005; Foudi et al. 2015; Luu et al. 2020). Hazard assessment involves evaluating flood characteristics, such as water depth corresponding certain frequency. The outcome of this step typically includes inundation maps that depict water depth and flooded areas. Exposure assessment involves defining the elements at risk within the flooded area, which can include residential, non-residential, agricultural, and other uses, as well as people. However, each element possesses its own susceptibility to flooding, necessitating an evaluation of their vulnerability in the subsequent step. The final stage in this process involves risk assessment, which integrates the three preceding components. Risk results can be expressed qualitatively (risk classification) or quantitatively (usually converting the level of damage in terms of money).

Damage assessment provides a foundation for establishing damage mitigation solutions. However, accurately assessing the level of damage caused by floods is still limited. The primary objective of this research endeavour is to gain a more comprehensive understanding of the flood damage situation in Vinh Phuc Province. This study encompasses a broader scope beyond merely assessing damage from a particular flood or frequency. Instead, it presents an approach that offers an overview of damage across space and frequency. To achieve this, the study develops integrated hydrological and hydraulic models to simulate flood hazards in the study area. It is imperative to validate these models to ensure the reliability of the calculated results. Leveraging the advantages of mathematical models, the study meticulously determines the flood hazard corresponding to design flood frequencies in detail. Furthermore, the study develops damage functions for some of the main elements at risk. The damage curves elucidate the specificity of the area through field surveys and data collection from localities. All of the aforementioned contents collectively aim to address existing research gaps and provide a more accurate method of damage assessment.

Vinh Phuc Province is located in the Red River Delta region of the Northern midlands and mountains, with coordinates from 21°35′15″N to 21°08′55″N (on the Red River in Dai Tu commune, Yen Lac District); from 105°20′25″E to 105°47′15″E. In recent years, the level of flood damage has become increasingly serious. The main cause is the phenomenon of prolonged heavy rain in a large area combined with the draining system not draining in time, plus the typical low-lying terrain of Vinh Yen City (Nguyen 2018). According to reported data, some typical major floods, such as in 2020 and 2022, have caused thousands of billions of Vietnam Dong (VND) in damage in Vinh Phuc Province (Vinh Phuc Province 2020, 2023). Therefore, assessing flood damage becomes urgent in Vinh Phuc Province.

The research area is the Phan-Ca Lo river basin in Vinh Phuc Province. The river system includes two main rivers: the Ca Lo river and the Phan river. The scope of the study shown in Figure 1. The integrated hydro-hydraulic simulation is carried out on the entire Phan-Ca Lo river system (sub-basins with solid red borders). Meanwhile, due to limited data conditions, the damage calculation only applies to the area located in Vinh Phuc Province (green area).
Figure 1

Study area.

The approach of our study is shown in the diagram in Figure 2. The research content can be divided into four main steps including (1) collecting, analysing, and processing data, (2) applying hydro-hydraulic models to identify hazards and elements at risk, (3) a survey to construct a damage function, (4) and evaluating the damage for the research area.
Figure 2

The methodology flow chart.

Figure 2

The methodology flow chart.

Close modal

In the first step, various types of data on the research area are collected. They include many types of data such as hydrometeorological data, topography, structures affecting flood drainage, land use, and damage information. These data are analysed and processed as input for subsequent assessment steps. Based on topographic data from the 1/10,000 scale map, the study area was divided into nine sub-basins, as shown in Figure 1. The contribution flows to the river Phan – Ca Lo system were estimated from rainfall on these sub-basins. These flows were used as the boundaries for the hydraulic model. The areas of sub-basins are shown in Table 1. Additionally, the researchers gathered river cross-sections to establish hydraulic models.

Table 1

Phan-Ca Lo river sub-basins, Vinh Phuc Province

IDSub-basinF (km2)
Ca Lo Basin 227.34 
Phan Basin 282.89 
LV01 79.16 
LV02 130.02 
LV03 54.29 
LV04 94.74 
LV05 58.56 
LV06 49.50 
LV07 44.99 
IDSub-basinF (km2)
Ca Lo Basin 227.34 
Phan Basin 282.89 
LV01 79.16 
LV02 130.02 
LV03 54.29 
LV04 94.74 
LV05 58.56 
LV06 49.50 
LV07 44.99 
Table 2

Summary of information and data collected through questionnaire surveys

Data categoriesCollected information/data
Residential buildings Flood depth 
Flood damage (building damaged, asset damaged, etc.) 
Building area 
Estimate total value of residential building 
Agriculture Flood depth 
% productivity deduction 
Data categoriesCollected information/data
Residential buildings Flood depth 
Flood damage (building damaged, asset damaged, etc.) 
Building area 
Estimate total value of residential building 
Agriculture Flood depth 
% productivity deduction 

In the second step, the Mike family models are set up to develop a flood hazard map. It includes the hydrological model MIKE-NAM was established to convert rainfall to runoff (Kumar et al. 2019), the Mike 11 HD model (DHI 2020) for main channel flow simulation, and the Mike 21 FM model (DHI 2016) for flood plain overland flow simulation. Because there are currently no flow measurement data in the basin. The study calibrates and validates hydrological models using a similar basin Ngoc Thanh (F = 22.37 km2). The micro-tuning of this set is carried out to calculate contribution flow from sub-basins. Using this approach, some studies have been successfully applied in Vietnam (Tran 2016; Tran et al. 2021). In this study, the Mike Flood model is used for the Phan-Ca Lo river system. The model's scope was extended until the confluence of the Cau river, as shown in Figure 3. The Phan-Ca Lo river system was simulated with 5 main river branches, 13 channels, and a total length of 287 km. The model had 13 upstream boundaries, as shown in Figure 1. However, due to the small control basin area, the flow at these locations, considered as close boundaries, was insignificant. We assumed all rainfall transferring to discharge as lateral boundaries. The nine lateral boundaries were calculated using the MIKE-NAM model, as mentioned earlier. The downstream boundary of the model was the water level at the Luong Phuc Station. The floodplain area's topography was simulated using a triangular mesh in the Mike 2D model, while structural systems, such as roads and dikes, were also included to ensure accuracy. The model is also validated by observed data at Manh Tan Station. The study conducted simulations of the past major and design floods to determine the level of inundation corresponding to these floods using the validated model. Integrating the extent of flooding with collected land-use data, the study can determine the elements at risk in the research area.
Figure 3

Survey location of subjects at risk: (a) residential area and (b) agriculture land.

Figure 3

Survey location of subjects at risk: (a) residential area and (b) agriculture land.

Close modal

In the third step, a survey is performed to gather damage information. The accuracy of the damage results depends greatly on the quality of the collected damage data (Shrestha et al. 2021). Therefore, in this study, damage statistics were gathered through survey questionnaires. With limited time and budget, the research only focused on agricultural land and residential areas, which were the main damaged sectors based on past statistics. This study had 20 agricultural land and 15 residential area samples. The survey locations were distributed throughout the study area to ensure representativeness, as shown in Figure 3. The information was collected corresponding to the most recent major flood in 2022. There was the historical flood that occurred recently in the basin, so the collected information from local people ensures accuracy.

Based on the survey data, a damage function could be developed for each object. Combining the element at risk and flood depth with the damage curves, the study can assess the damage of each subject in the research area. The equation to estimate the damage for each object is determined by the following formula:
(1)
where D is the damage value of the target (VND). E is the maximum unit value of the object (VND/m2). For agricultural land, this value is taken according to the market price of agricultural products at the time of the flood. For residential buildings, the values of each object and the items inside are very different. This is consistent with what has been found in a previous report by JRC (Huizinga et al. 2017). In the study, this value is calculated from the average value of the investigated subjects. V is the damage factor (–) value is determined from the damage curve. A is the object area (m2).

Due to a shortage of investigation samples, the damage curves had a large uncertainty, which can affect the reliability of the results. To address this issue, the research collected independent damage information for all sectors in Vinh Phuc Province caused by a recent flood event. This information was the damaged statistical information was summarized by the local government.

At the end of this process, the study conducted damage assessments corresponding to design flood frequencies to construct damage-probability curves (DPC) and expected annual damage (EAD). DPC represents the relationship between the level of damage associated with a specific flood frequency, while EAD represents the average level of damage over a long period (Foudi et al. 2015). The study also created damage maps corresponding to design frequencies, which allow for prioritization based on the location. This information will be useful for decision-makers in terms of socio-economic development and mitigation measures.

Validate hydrological and hydraulic models

The reliability of simulation results plays a very important role in determining the extent of damage. According to Notaro et al. (2014) the uncertainty of the model is larger than the uncertainty of the damage function. For that reason, the MIKE-NAM model for the Ngoc Thanh basin was calibrated and validated with observed data from two major floods occurring in the basin. The first flood event was from 01:00 on 23 July 1971 to 11:00 p.m. on 24 July 1971 and the second flood event was from 01:00 on 3 October 1978 to 1:00 p.m. on 5 October 1978. The results of model calibration and verification are shown in Figure 4 and Table 3.
Table 3

The calibration and validation result for the hydrological model

StationCharacteristicCalibrationValidation
Qmax (m3/s)Qmax (m3/s)
Ngoc Thanh Calculate 134 131 
Observer 122 118 
Peak error 12.0 12.7 
NASH (%) 91.6 91.8 
StationCharacteristicCalibrationValidation
Qmax (m3/s)Qmax (m3/s)
Ngoc Thanh Calculate 134 131 
Observer 122 118 
Peak error 12.0 12.7 
NASH (%) 91.6 91.8 
Figure 4

Calculated and actually measured discharge flow path at Ngoc Thanh Station during flood: (a) July 1971; (b) October 1978.

Figure 4

Calculated and actually measured discharge flow path at Ngoc Thanh Station during flood: (a) July 1971; (b) October 1978.

Close modal
Figure 5

Calculated and measured water level profile at Manh Tan Station for flood: (a) November 2008; (b) June 2022.

Figure 5

Calculated and measured water level profile at Manh Tan Station for flood: (a) November 2008; (b) June 2022.

Close modal

The set of parameters is reliable and accurate in simulating runoff for the study area. This is demonstrated by the fact that the simulation results match the observed data with a Nash-Sutcliffe Efficiency Index (NASH coefficient) above 90% at both the calibrated and the calibrated steps. The calculated flood peak value is also only slightly higher than the actual measured value, providing a safety margin. The values of the parameters are shown in Table 4. In this set of parameters, the parameters CQOF, and CK1,2 are the most important. The parameter CQOF is the overland flow runoff coefficient. Therefore, it greatly affects the total flow volume. This parameter is very important because it determines the amount of excess water to form runoff and the amount of water infiltration. In basins with flat terrain, composed of coarse sand, the CQOF value is relatively small. In basins where soil permeability is poor such as clay and boulders, its value will be very huge. Meanwhile, the CK1,2 is the time constants for routing overland flow. They are very important parameters, affecting the maximum discharge and the shape of the hydrograph. Based on the set of parameters of the Ngoc Thanh basin, the study conducted micro-adjustments to suit the conditions of each sub-basin to calculate the boundaries for hydraulic models.

Table 4

The set of parameter of the Ngoc Thanh hydrological model

IDParameterValueUnitRangeNote
Umax  mm 10–20 Maximum water content in surface storage 
Lmax  mm 100–300 Maximum water content in root zone storage 
CQOF  – 0.1–1 Overland flow runoff coefficient 
CQIF  – 200–1,000 Time constant for interflow 
CK1,2  hour 3–48 Time constants for routing overland flow 
TOF  – 0–0.99 Root zone threshold value for overland flow 
TIF  – 0–0.99 Root zone threshold value for inter flow 
TG  – 0–0.99 Root zone threshold value for ground water recharge 
CKBF  hour 1,000–4,000 Time constant for routing baseflow 
IDParameterValueUnitRangeNote
Umax  mm 10–20 Maximum water content in surface storage 
Lmax  mm 100–300 Maximum water content in root zone storage 
CQOF  – 0.1–1 Overland flow runoff coefficient 
CQIF  – 200–1,000 Time constant for interflow 
CK1,2  hour 3–48 Time constants for routing overland flow 
TOF  – 0–0.99 Root zone threshold value for overland flow 
TIF  – 0–0.99 Root zone threshold value for inter flow 
TG  – 0–0.99 Root zone threshold value for ground water recharge 
CKBF  hour 1,000–4,000 Time constant for routing baseflow 

The hydraulic model also was validated in this study. For hydraulic models, the main parameter of the model is the roughness coefficient. A trial-and-error process is used to find the appropriate roughness coefficient. Roughness coefficient values vary according to land cover. The reference value of the roughness coefficient through technical documents (Chow 1959; Brunner 2020). The study compared the calculated water level data from the model with observed data from the Manh Tan Station during two heavy flood events. The calibration process used heavy rains from 1 to 10 November 2008 and the flood from 23 May to 8 June 2022, was used to validate the model. The calculation results show that the error of maximum water level between calculation and measurement is, respectively, 0.20 and 0.21 m (Table 5), and the calculated and observed flood peaks appear at the same time and the hydrographs have the same shape (Figure 5). The study also compared the model calculation results with the survey flood marks of the 2022 historic flood at Ca Lo bridge. The results show that the water level between calculation and actual measurement is 8.72 and 8.84 m, respectively. From the results, it is clear that the model is also reliable in simulating flowing steps.

Flood damage curves

Using survey data from investigation samples, the study developed the correlation functions between the level of damage and the inundation depth. The vertical axis in the chart represents the percentage of damage, ranging from 0 (no damage) to 1 (complete damage). The horizontal axis represents the inundation depth. Due to the large dispersion in the survey data, which is likely due to information about flooding extent being collected from people's memories, the results are approximate and have more fluctuations. Additionally, the study is limited in its ability to differentiate between different types of residential areas and agricultural land, which can lead to variations in investigation results for the same flooding depth. Although the data collected are limited in depth, most flood depths were not higher than 3 m. However, the damage level of sectors also reached 60% when the water level reached 3 m. Therefore, the damage level needs to be extrapolated with the depth greater than 3 m. Notaro et al. (2014) applied four types of curves including linear, polynomial-2ord, exponential, and power to construct the damage function. The results show that the polynomial-2ord type gives the most reasonable results. In this study, we apply the polynomial-2ord line form to the study area. The results of the damage function are shown in Figure 6(a) and 6(b) and the following equations:
(2)
(3)
Figure 6

Damage curve for residential building (a) and agriculture (b).

Figure 6

Damage curve for residential building (a) and agriculture (b).

Close modal

The study in question also compared the outcomes it found with damage functions from other research conducted in areas with comparable conditions, such as the average damage function for the Asian region developed by the Joint Research Centre (JRC) (Huizinga et al. 2017). Upon comparing the two damage curves perceived, in terms of visible trends, the study's damage function was lower than the JRC 2017 damage curve for both residential buildings and agricultural land. As the flooding depth increased, this difference became more pronounced. However, analysis showed that this difference was approximately 10%.

To verify the reliability of the constructed damage function, the study compared the level of damage with statistical data for each local administrative unit for the historical flood in 2022. The level of damage for sectors at the district level is depicted in Figure 7. The results demonstrated that the calculated damage value was highly consistent with local statistics, with the coefficient of correlation R2 for residential buildings and agricultural land both approximately equal to 1. The calculation results showed that the approach yielded values that were highly consistent with local statistical data. This not only validated the reliability of the constructed damage function but also attested to the accuracy of the input data sources. Based on these damage functions, the level and spatial distribution of damage for specific floods or design floods can be determined specifically.
Figure 7

The comparison between statistical and calculated damage for residential building (a) and agriculture (b).

Figure 7

The comparison between statistical and calculated damage for residential building (a) and agriculture (b).

Close modal

Damage-probability curve and EAD

According to Penning-Rowsell et al. (2005), a minimum of five flood events are necessary to construct the damage–frequency curve. Therefore, flood frequencies of 20, 10, 5, 2, 1, 0.5, and 0.1% are calculated. A flood frequency of 20% is considered a frequent flood in the region, while a flood event with a frequency of 0.1% is deemed an extremely rare occurrence. Figure 8 displays the damage–frequency curve for the study area. The vertical axis represents the level of damage, while the horizontal axis represents the frequency of occurrence. The area enclosed by the damage–frequency curve and the horizontal axis represents the EAD. EAD is a crucial index that demonstrates the potential damage experienced by the study area on an annual basis. Although the study area does not encompass the entire Vinh Phuc Province, it encompasses the most crucial regions with dense populations and agricultural land. Therefore, the calculations generally reflect the level of damage in the province.
Table 5

The calibration and validation result for the hydraulic model

StationCharacteristicCalibrationValidation
Zmax (m)Zmax (m)
Manh Tan Calculate 8.01 7.89 
Observer 7.81 7.68 
Peak error 0.20 0.21 
NASH (%) 97 92 
StationCharacteristicCalibrationValidation
Zmax (m)Zmax (m)
Manh Tan Calculate 8.01 7.89 
Observer 7.81 7.68 
Peak error 0.20 0.21 
NASH (%) 97 92 
Figure 8

The damage–frequency curve for the research area.

Figure 8

The damage–frequency curve for the research area.

Close modal
Figure 9 and Table 6 present the spatial distribution flood damage corresponding to a frequency of 5%. The 5% frequency is selected to present because it is the design flood for mixed urban and agricultural area. The result shows that the most damage of residential building occurs in Vinh Yen City and Yen Lac District. It is interesting to note that Vinh Yen, the central city of the province, and Yen Lac District is the area where that has been converted from agricultural land to industrial use. Although the value of residential building damage is not big compared to agricultural land in these locations, the indirect damage in terms of economic disruption and socio-political impacts is very concerning. In this study, this indirect damage is not considered. However, when comparing the residential building damage in these regions with other areas, it is possible to qualitatively assess the indirect damage that may occur. In addition, Vinh Tuong District, which is primarily an agricultural area, indicates the highest level of damage to agricultural land, but less damage to residential buildings than other areas. The high terrain areas of Tam Duong and Phuc Yen districts make them less prone to flooding and result in a lower level of damage. From the short review above, key findings emerge to determine the level and the distribution damage. The damage level in different areas is useful information for the workload of mitigation plans as well as for deciding on priority options between regions. Damage information by object determines appropriate prevention solutions taking into account the unique characteristics of each region.
Table 6

Statistics on damage level by administrative unit (USD)

DistrictResidential areaAgricultural landTotal
Binh Xuyen 26,658 3,497,250 3,523,868 
Phuc Yen 24,386 1,606,041 1,630,427 
Tam Duong 7,507 285,087 292,635 
Vinh Tuong 157,881 4,884,708 5,042,590 
Vinh Yen 27,389 890,158 917,546 
Yen Lac 84,317 3,850,627 3,934,904 
DistrictResidential areaAgricultural landTotal
Binh Xuyen 26,658 3,497,250 3,523,868 
Phuc Yen 24,386 1,606,041 1,630,427 
Tam Duong 7,507 285,087 292,635 
Vinh Tuong 157,881 4,884,708 5,042,590 
Vinh Yen 27,389 890,158 917,546 
Yen Lac 84,317 3,850,627 3,934,904 
Figure 9

Spatial damage distribution map in 5% flood event.

Figure 9

Spatial damage distribution map in 5% flood event.

Close modal

The current investigation has validated the effectiveness of a more comprehensive approach to damage assessment. The findings of this study indicate three key aspects. Firstly, the mathematical models are effective tools for hazard assessment. Secondly, the study has established two distinct damage functions, specifically for residential areas and agricultural lands in research area. Thirdly, the researchers have employed the damage–frequency curve and the EAD to assess the extent of flood damage in Vinh Phuc Province. The results of this study are more accurate than those of earlier investigations. Previous research has often skipped the model validate process, while the development of damage curves was typically without independent verification. These factors, along with the uncertainty associated with them, can significantly impact the accuracy of calculations. Therefore, the validation of both models and damage curves represents a significant advancement in this area of study.

For research area that regularly suffers from flooding, accuracy damage assessment is very necessary. This is the foundation for localities to prepare annual reserve budgets for natural disaster prevention. Moreover, when a damage mitigation solution is proposed, a new level of damage will be computed to compare with the current situation. The effectiveness of the solution can be quantified in monetary terms, making it convenient to compare costs and benefits of mitigation solutions. This provides a good starting point for discussion and further research.

Although mathematical models require a large amount of input data as well as high-quality personnel to conduct model set-up. The mathematical model shows many outstanding advantages. Firstly, the mathematical model gives detailed results in space and time. This is very important for assessing hazards and elements at risk. In this study, we only focus on flooding depth. However, factors, such as velocity or inundation period, can be determined. These can be researched more detailed in future studies. Another advantage of using mathematical models is their flexibility. The mathematical model gives quick results so hazard assessment after each flood or with different frequencies can be done quickly. If mitigation solutions are applied, the effectiveness of the solution can also be quickly determined quantitatively. The accuracy of the damage curve is of great concern. The damage information is often compiled after each flood event. This information can be collected from localities to verify to improve the appropriateness of the calculation results. Due to limited time and data, the study only focuses on two main sectors in Vinh Phuc Province, and the number of samples collected is limited and has not met the requirements of sampling technique. One other limitation of the study is that it did not take into account land-use changes over time. The study assumes that flooding occurs while agricultural land is under cultivation, so if flooding occurs after the harvest, the level of damage may not be as high as calculated.

In the future, the study will continue to investigate, collect more samples, and include other sectors such as roads and infrastructure to provide a more comprehensive view of flood damage in Vinh Phuc Province. Additionally, the detailed information in commune level needs to be done. This would be more helpful information in minimizing damage in the study area.

The current study presents a comprehensive examination of the damage inflicted by flooding on residential buildings and agricultural land in the Phan-Ca Lo river basin of Vinh Phuc Province. Employing a simulation technique that integrates mathematical models with field investigations, the study relies on these key factors to conduct its research. The research result shows that mathematical models are effective tools for hazard assessment. The mathematical models give fast, detailed results and are adaptable to many scenarios. The study also assesses the vulnerability of elements at risk using damage functions. The accuracy of the damage functions is validated with independent local data sources. This reliability of the results is crucial for the study's findings.

The method described in this study will facilitate a model-based study to assess the damage that can be employed as a management tool for river basin management. In this study, the damage–frequency curve and the EAD due to flooding in the study area were calculated. The EAD in this area is 6.9 million USD, with the majority of the damage being attributed to agricultural land. Nevertheless, our research provides a detailed spatial and sector distribution of damage in this area. This information is particularly noteworthy and should receive attention from policymakers and the local people.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Binh
L. T. H.
,
Umamahesh
N. V.
&
Rathnam
E. V.
2019
High-resolution flood hazard mapping based on nonstationary frequency analysis: Case study of Ho Chi Minh City, Vietnam
.
Hydrological Sciences Journal
64
(
3
),
318
335
.
https://doi.org/10.1080/02626667.2019.1581363
.
Brunner
G. W.
2020
HEC RAS 6.0 Users Manual
.
Budiyono
Y.
,
Aerts
J.
,
Brinkman
J. J.
,
Marfai
M. A.
&
Ward
P.
2015
Flood risk assessment for delta mega-cities: A case study of Jakarta
.
Natural Hazards
75
(
1
),
389
413
.
https://doi.org/10.1007/s11069-014-1327-9
.
Cea
L.
&
Costabile
P.
2022
Flood risk in urban areas: Modelling, management and adaptation to climate change: A review
.
Hydrology
9
(
3
).
MDPI. https://doi.org/10.3390/hydrology9030050.
Chow
V. T.
1959
Open-Channel Hydraulic
.
International Student Edition, Kogakusha Company, LTD
,
Tokyo
.
de Moel
H.
,
Jongman
B.
,
Kreibich
H.
,
Merz
B.
,
Penning-Rowsell
E.
&
Ward
P. J.
2015
Flood risk assessments at different spatial scales
.
Mitigation and Adaptation Strategies for Global Change
20
(
6
),
865
890
.
https://doi.org/10.1007/s11027-015-9654-z
.
DHI
2016
MIKE 21 Flow Model User Manual
.
DHI
2020
Mike 11 User Manual
.
Foudi
S.
,
Osés-Eraso
N.
&
Tamayo
I.
2015
Integrated spatial flood risk assessment: The case of Zaragoza
.
Land Use Policy
42
,
278
292
.
https://doi.org/10.1016/j.landusepol.2014.08.002
.
Huizinga
J.
,
De Moel
H.
&
Szewczyk
W.
2017
Methodology and the Database with Guidelines
.
https://doi.org/10.2760/16510
Jonkman
S. N.
,
Bočkarjova
M.
,
Kok
M.
&
Bernardini
P.
2008
Integrated hydrodynamic and economic modelling of flood damage in the Netherlands
.
Ecological Economics
66
(
1
),
77
90
.
https://doi.org/10.1016/j.ecolecon.2007.12.022
.
Kefi
M.
,
Mishra
B. K.
,
Kumar
P.
,
Masago
Y.
&
Fukushi
K.
2018
Assessment of tangible direct flood damage using a spatial analysis approach under the effects of climate change: Case study in an urban watershed in Hanoi, Vietnam
.
ISPRS International Journal of Geo-Information
7
(
1
).
https://doi.org/10.3390/ijgi7010029.
Kron
W.
2005
Flood risk = hazard values vulnerability
.
Water International
30
(
1
),
58
68
.
https://doi.org/10.1080/02508060508691837
.
Kumar
P.
,
Lohani
A. K.
&
Nema
A. K.
2019
Rainfall runoff modeling using MIKE 11 NAM model
.
Current World Environment
14
(
1
),
27
36
.
https://doi.org/10.12944/cwe.14.1.05
.
Lang
M.
,
Pobanz
K.
,
Renard
B.
,
Renouf
E.
&
Sauquet
E.
2010
Exptrapolation des courves de tarage par modélisation hydraulique, avec application à l'analyse fréquentielle des crues
.
Hydrological Sciences Journal
55
(
6
),
883
898
.
https://doi.org/10.1080/02626667.2010.504186
.
Lazzarin
T.
,
Viero
D. P.
,
Molinari
D.
,
Ballio
F.
&
Defina
A.
2022
Flood damage functions based on a single physics- and data-based impact parameter that jointly accounts for water depth and velocity
.
Journal of Hydrology
607
.
https://doi.org/10.1016/j.jhydrol.2022.127485.
Luu
C.
,
Tran
H. X.
,
Pham
B. T.
,
Al-Ansari
N.
,
Tran
T. Q.
,
Duong
N. Q.
,
Dao
N. H.
,
Nguyen
L. P.
,
Nguyen
H. D.
,
Ta
H. T.
,
Le
H. V.
&
von Meding
J.
2020
Framework of spatial flood risk assessment for a case study in Quang Binh Province
.
Vietnam. Sustainability (Switzerland)
12
(
7
).
https://doi.org/10.3390/su12073058.
Mansir
I.
,
Bouchaou
L.
,
Chebli
B.
,
Ait Brahim
Y.
&
Choukr-Allah
R.
2021
A specific indicator approach for the assessment of water resource vulnerability in arid areas: The case of the Souss-Massa Region (Morocco)
.
Hydrological Sciences Journal
66
(
7
),
1151
1168
.
https://doi.org/10.1080/02626667.2021.1924379
.
Martínez-Gomariz
E.
,
Forero-Ortiz
E.
,
Guerrero-Hidalga
M.
,
Castán
S.
&
Gómez
M.
2020
Flood depth-damage curves for Spanish urban areas
.
Sustainability (Switzerland)
12
(
7
).
https://doi.org/10.3390/su12072666.
McGrath
H.
,
Kotsollaris
M.
,
Stefanakis
E.
&
Nastev
M.
2019
Flood damage calculations via a RESTful API
.
International Journal of Disaster Risk Reduction
35
.
https://doi.org/10.1016/j.ijdrr.2019.101071.
Meyer
V.
,
Becker
N.
,
Markantonis
V.
,
Schwarze
R.
,
Van Den Bergh
J. C. J. M.
,
Bouwer
L. M.
,
Bubeck
P.
,
Ciavola
P.
,
Genovese
E.
,
Green
C.
,
Hallegatte
S.
,
Kreibich
H.
,
Lequeux
Q.
,
Logar
I.
,
Papyrakis
E.
,
Pfurtscheller
C.
,
Poussin
J.
,
Przyluski
V.
,
Thieken
A. H.
&
Viavattene
C.
2013
Review article: Assessing the costs of natural hazards-state of the art and knowledge gaps
.
Natural Hazards and Earth System Science
13
(
5
),
1351
1373
.
https://doi.org/10.5194/nhess-13-1351-2013
.
Nguyen
D. T.
2018
Scientific Research Facility on Flood Prevention Planning Based on Risk Analysis
.
Thuy Loi University, Hanoi
.
Notaro
V.
,
De Marchis
M.
,
Fontanazza
C. M.
,
La Loggia
G.
,
Puleo
V.
&
Freni
G.
2014
The effect of damage functions on urban flood damage appraisal
.
Procedia Engineering
70
,
1251
1260
.
https://doi.org/10.1016/j.proeng.2014.02.138
.
Penning-Rowsell
E.
,
Johnson
C.
,
Tunstall
S.
,
Tapsell
S.
,
Morris
J.
,
Chatterton
J.
&
Green
C.
2005
The Benefits of Flood and Coastal Risk Management: A Manual of Assessment Techniques 12
.
Middlesex University Press, London
.
Romali
N. S.
&
Yusop
Z.
2021
Flood damage and risk assessment for urban area in Malaysia
.
Hydrology Research
52
(
1
),
142
159
.
https://doi.org/10.2166/NH.2020.121
.
Seifert
I.
,
Kreibich
H.
,
Merz
B.
&
Thieken
A. H.
2010
Application et validation des FLEMOcs – un modèle d'estimation des dommages dus aux inondations dans le secteur commercial
.
Hydrological Sciences Journal
55
(
8
),
1315
1324
.
https://doi.org/10.1080/02626667.2010.536440
.
Shrestha
B. B.
,
Kawasaki
A.
&
Zin
W. W.
2021
Development of flood damage assessment method for residential areas considering various house types for Bago Region of Myanmar
.
International Journal of Disaster Risk Reduction
66
.
https://doi.org/10.1016/j.ijdrr.2021.102602.
Smith
K.
&
Ward
R.
1998
Floods: Physical Processes and Human Impacts
, 1st edn.
John Wiley, New York
.
Stathatou
P.
,
Kampragou
E.
,
Grigoropoulou
H.
,
Assimacopoulos
D.
,
Karavitis
C.
,
Porto
M. F. A.
,
Gironás
J.
,
Vanegas
M.
&
Reyna
S.
2016
Vulnerability of water systems: A comprehensive framework for its assessment and identification of adaptation strategies
.
Desalination and Water Treatment
57
(
5
),
2243
2255
.
https://doi.org/10.1080/19443994.2015.1012341
.
Thieken
A. H.
,
Müller
M.
,
Kreibich
H.
&
Merz
B.
2005
Flood damage and influencing factors: New insights from the August 2002 flood in Germany
.
Water Resources Research
41
(
12
),
1
16
.
https://doi.org/10.1029/2005WR004177
.
Tingsanchali
T.
&
Karim
F.
2010
Evaluation du danger d'inondation et zonage basé sur le risque dans une plaine d'inondation tropicale: Cas de la Rivière Yom, Thaïlande
.
Hydrological Sciences Journal
55
(
2
),
145
161
.
https://doi.org/10.1080/02626660903545987
.
Tran
2016
Developing a method to define main parameters of SCS – CN based on available data
. In
The Annual Conference of Thuyloi University
, pp.
495
497
.
Tran
C. K.
&
Nguyen
T. C.
2024
Consequence assessment of the La Giang dike breach in the Ca River system, Vietnam
.
Journal of Water and Climate Change
15
(
1
),
75
88
.
https://doi.org/10.2166/wcc.2023.380
.
Tran
C. K.
,
Nguyen
T. T.
&
Nguyen
T. N.
2021
Primarily results of a real-time flash flood warning system in Vietnam
.
Civil Engineering Journal (Iran)
7
(
4
).
https://doi.org/10.28991/cej-2021-03091687.
Velasco
M.
,
Cabello
À.
&
Russo
B.
2016
Flood damage assessment in urban areas. Application to the Raval district of Barcelona using synthetic depth damage curves
.
Urban Water Journal
13
(
4
),
426
440
.
https://doi.org/10.1080/1573062X.2014.994005
.
Vinh Phuc Province
.
2020
Summary Report of Natural Disaster Prevention, Disaster Control, Search and Rescue in 2020; Implementing Orientations and Tasks in 2021
.
Vinh Phuc Province
.
2023
Summary Report of Natural Disaster Prevention, Disaster Control, Search and Rescue in 2022; Implementing Orientations and Tasks in 2023
.
Vojtek
M.
,
Vojteková
J.
,
De Luca
D. L.
&
Petroselli
A.
2023
Combined basin-scale and decentralized flood risk assessment: A methodological approach for preliminary flood risk assessment
.
Hydrological Sciences Journal
68
(
3
),
355
378
.
https://doi.org/10.1080/02626667.2022.2157279
.
Zeleňáková
M.
,
Fijko
R.
,
Labant
S.
,
Weiss
E.
,
Markovič
G.
&
Weiss
R.
2019
Flood risk modelling of the Slatvinec stream in Kružlov village, Slovakia
.
Journal of Cleaner Production
212
,
109
118
.
https://doi.org/10.1016/j.jclepro.2018.12.008
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).