Urban flooding risk assessment based on FAHP–EWM combination weighting: a case study of Beijing

Abstract Urban flooding is a long-standing problem that greatly hinders the development of the city. As a means of flood risk management, risk assessment plays a significant role in reducing flood risk. In this article, a multi-criteria decision analysis (MCDA) model for assessing urban flood risk is proposed, and the assessment results can provide a more scientific basis for urban disaster management. The model innovatively uses the fuzzy analytic hierarchy process (FAHP) and entropy weight method (EWM) subjective and objective combination weighting methods to determine the weight, with risk, exposure, vulnerability and emergency capability as the criterion layers, and 13 representative elements such as rainfall and altitude as the index layers. Taking Beijing as the research area, the flood risk distribution map was made to provide relevant basis for the management department. The evaluation results are further compared with historical flood disaster information to verify the accuracy of the model. The results show that the accuracy of the analytic hierarchy process (AHP) and AHP–EWM methods is 62.07% and 66.38%, while the accuracy of the FAHP–EWM method can reach 75.68%. In this study area, the models and methods we proposed are more reasonable and effective.


Introduction
Urban flooding refers to continuous rainfall or heavy rainfall in a short period of time, resulting in urban water accumulation exceeding urban drainage capacity and causing urban water accumulation (Peng and Zhang 2022).Due to extreme weather, rapid urbanization and climate change, urban areas are facing global flood risk challenges with increasing risks to human life, health, property and the environment (Hallegatte et al. 2013;Wang et al. 2021).According to statistics, the current global losses caused by various natural disasters, the proportion of rainstorms and flood realistic.AHP-EWM and other subjective and objective combination weighting methods have also been adopted by many scholars, but the accuracy of flood risk assessment is not very high.This article proposes a subjective and objective weight determination method combining fuzzy analytic hierarchy process (FAHP) and EWM and compares this method with AHP and AHP-EWM methods in flood risk assessment.
At present, there is no unified standard for flood disaster risk assessment in the research based on the MCDA method.Different researchers select different evaluation indicators to construct the system framework according to the characteristics of the study area and the availability of data.However, the existing risk assessment system related to flood disasters only considers the risk of disaster-causing factors of urban floods (Roy et al. 2021), attaches importance to the resilience of infrastructure and objective factors such as meteorology and topography (Wang et al. 2017;Zhang et al. 2018;Tehrany et al. 2019), and ignores the prevention and control awareness, emergency treatment and post-disaster recovery subjective factors of the government and citizens.Therefore, when constructing the urban flood risk assessment system, this article fully considers the complexity of urban carriers and the role of human doors in mitigating disaster preparedness risks and comprehensively considers various factors such as risk, exposure, vulnerability and urban emergency capacity, making the evaluation results more standardized and scientific.
In this study, taking Beijing as an example, according to the risk formation theory of natural disasters, the urban flooding risk assessment is divided into four criteria layers: hazard, exposure, vulnerability and urban emergency capacity, and 13 risk assessment indicators are selected to construct a flood risk assessment system.A flood risk assessment model based on FAHP-EWM combination weighting has been established.Based on the GIS platform, the flood disaster risk is visualized to quickly obtain the scope and risk level of flood disaster.This study comprehensively considers the influence of various factors on urban flood disasters, making the evaluation more scientific and standardized.The research results can provide scientific basis for flood control, disaster assessment and disaster reduction.

The study area
This study was conducted in six major urban areas of Beijing, China: Dongcheng District, Xicheng District, Haidian District, Chaoyang District, Shijingshan District, and Fengtai District (see Figure 1).Beijing is located in the northwest of the North China Plain.As the capital, municipality and national central city of China, it is the centre of China's political, cultural, scientific, educational and international exchanges, and the decision-making and management centre of China's economy and finance.Once a serious urban flood problem occurs, the consequences are very serious.Geographically, Beijing is located between 115 20 0 E and 117 30 0 E, and between 39 28 0 N and 41 05 0 N.The overall altitude shows a trend of high in the northwest and low in the southeast.The west, north and northeast directions of Beijing are surrounded by mountains, and the southeast direction is a plain that gently inclines to the Bohai Sea.
Beijing has a typical continental monsoon climate with four distinct seasons.In summer, the temperature is higher and the rain is more concentrated.The average annual precipitation in Beijing is about 626 mm, and the summer rainfall intensity is large, accounting for 75% of the annual precipitation.Under the combined influence of climatic conditions and underlying surface characteristics, the study area is a flood-prone area, and Beijing is also one of the key flood control cities in China.
On July 21-22, 2012, Beijing suffered the strongest rainstorm and flood disaster in 61 years, resulting in 10,660 houses collapsing, 1.602 million people affected, and economic losses of 11.64 billion Yuan.On the night of August 16, 2020, a short-term heavy rainfall event occurred in Beijing, with a maximum precipitation of 96.2 mm, resulting in serious water accumulation in the low-lying areas of urban interchange facilities.The attack of the heavy rainstorm had a serious impact on the lives and social production of Beijing residents.

Construction of risk assessment model
Although the concept of risk has been widely used by researchers, there is no unified definition (Aven 2016;Mishra and Sinha 2020).The fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC) pointed out that risk is the result of the interaction of three factors: hazard, exposure and vulnerability (IPCC 2014).Based on the factor theory of natural disaster risk formation and taking into account the city's ability to cope with flood disasters, this study established a risk assessment model with four criteria layers: hazard (H), exposure (E), vulnerability (V), and emergency (R).Urban flood risk can be expressed as: Urban flood risk ¼ f ðH, E, V, RÞ Because different indicators have different effects on flood risk and the weights given are different, this article redefines urban flood risk as a combination of different assessment indicators and their weights, as shown in Equation (2). where

Evaluation indicators
Flood risk assessment is an interdisciplinary issue of natural and social sciences, involving the assessment of complex systems such as nature, society and economy (Ali et al. 2016).
After consulting a number of experts and reading and referring to the research on urban flood risk assessment, according to the principle of flood risk assessment combined with the characteristics of the study area, 13 representative evaluation Indicators were selected.Table 1 summarizes the indicator selection and data sources.Rainfall is the main cause of urban floods (Chen et al. 2015;Wang et al. 2015).Rainstorms can increase urban rainfall rapidly and cause serious urban water accumulation.Therefore, rainfall, rainstorm proportion and storm rainfall are selected as disaster-causing factors to evaluate the hazard of the study area.Altitude and slope have an impact on the direction and speed of water flow, while drainage network and vegetation coverage affect the infiltration of rainwater.Therefore, altitude, slope, normalized differnce vegetation index (NDVI) and drainage density are selected to evaluate the exposure of hazard-pregnant environment.In areas with dense population, roads and buildings, the damage and impact caused by flood disasters are more serious, and the losses are greater.Population density, road density, land use/land cover (LULC) and gross domestic product (GDP) are selected for vulnerability assessment of hazard-affected bodies.Education status determines whether people can quickly make the right response when the disaster comes, and the level of medical care determines the speed of rescue.Therefore, the education status and medical level are selected to evaluate the urban emergency capacity.

Research framework
The method framework proposed in this article is shown in Figure 2, which is mainly divided into three stages: (a) selection and treatment of flood risk assessment indicators; (b) the indicator weight is determined based on FAHP and EWM combination weighting; and (c) flood risk pattern analysis based on GIS.

Weight determination method
2.3.1.Fuzzy comprehensive evaluation method FAHP is a qualitative and quantitative system analysis method proposed by Professor T. L. Saaty in the 1970s.It mainly judges the importance of each indicator based on the experience of experts, so as to obtain the subjective weight method.This method takes into account the ambiguity between indicators and can control the subjective factors of expert scoring to the minimum to improve the reliability of the evaluation results.Therefore, we use FAHP to allocate the subjective weight of urban flood risk-related indicators.The weight of each indicator is determined by the opinions of 10 experts, the literature review (Zhang et al. 2020;Mahmoud and Gan 2018) and field experience.The detailed steps are as follows: (1) Constructing judgement matrix For the system that needs to be decided, the relationship between the factors is analysed, and then the hierarchical structure of the target layer, criterion layer and indicator layer of the system is established in turn (Ni et al. 2017).The n indicators m1, m2, m3, … , mn of the same level and the same membership relationship are compared in pairs, and each expert is allowed to score them according to the 1-9 scale method.The score value corresponds to Table 2.
The judgement matrix H nÂn of each indicator layer is obtained.
where a ij is the importance scale of m i 、m j relative to the upper factor.a ii ¼ 1, a ij ¼ 1=a ji : (2) Convert to fuzzy complementary judgement matrix According to scale conversion formula (Equation 4), the judgement matrix is converted into a fuzzy complementary judgement matrix B nÂn .
(3) Construct a fuzzy matrix judgement matrix According to Equations ( 6) and ( 7), the fuzzy complementary judgement matrix is further transformed into a fuzzy matrix judgement matrix R nÂn : where r ij is the importance scale of m i and m j relative to the upper factors; Calculate weight According to weight calculation formula (Equation 9), the weight of each indicator layer is calculated: Because the fuzzy judgement matrix is consistent, it does not need to be tested for consistency and can reflect the subjective thinking of decision makers.

Entropy weight method
Entropy is a concept used to measure the degree of confusion in thermodynamics.In information theory, information entropy is used to evaluate the order of indicators.
According to the definition of information entropy, entropy can be used to describe the degree of difference in data indicators.The smaller the information entropy, the greater the difference degree of the indicator, the more information provided by the indicator, the greater the impact on the comprehensive evaluation results, that is, the greater the corresponding weight value.EWM relies on the information itself and is an objective weighting method.The calculation steps of EWM are as follows.
(1) Standardization Because the units of data corresponding to different indicators are not uniform, it is easy to cause the indicators with higher values to be too prominent in the process of comprehensive evaluation and analysis, which relatively weakens the role of indicators with lower values.The Min-Max normalization method used in this article can unify the data of different dimensions into 'pure data' and simplify the calculation.
For n samples with m indicators, the value of the jth indicator of the ith sample is expressed as The standardized formula for positive indicator is: The standardized formula for negative indicator is: where X ij is the original data of the indicator; X 0 ij is the value of each indicator after standardization; maxX j , minX j are the maximum and minimum values of the indicator j, respectively.
(2) Calculate the weight of the ith sample under the jth indicator.
(3) Find the jth indicator information entropy.
where d ¼ 1 ln n > 0, H j > 0: (4) Calculate the weight of each indicator EWM is used to determine the objective weight, so as to reduce the subjective influence of experts and fully mine the information carried by the original data.However, the weight value may not be consistent with the actual importance of the corresponding indicators.In order to construct the judgement matrix, it is necessary to quantify LULC, education level and medical level in GIS (Zeng and Huang 2018).The elements of the matrix are judged by the grid value.The entropy weight results are 0.0633 (rainfall), 0.1068 (rainstorm proportion), 0.0829 (storm rainfall), 0.1028 (altitude), 0.1038 (slope), 0.0976 (NDVI), 0.0542 (drainage density), 0.0004 (population density), 0.1034 (road density), 0.0316 (LULC), 0.0482 (GDP), 0.1000 (education status), 0.1050 (medical level).
This study combines the subjective weight x 1 with the objective weight l 1 to obtain the combined weight k 1 , which is defined as: The change of a and b changes the combination weight.In order to find the best comprehensive weight vector, it is necessary to find the optimal weight distribution coefficient.The minimum standard deviation is used to determine the optimal weight distribution coefficient to minimize the standard deviation of the weight vector.Enumeration calculation and the results are shown in Figure 3.
According to Figure 3, the subjective weight ratio a is 0.613 when the minimum variance is obtained, so b is 0.387.

Hazard of disastrous factors
Disaster-causing factors are the first step in analysing disaster risk and the direct cause of disasters.Urban floods are mostly caused by rainfall.The more rainfall in a region, the more rainstorms, and the more water on the ground, the greater the potential danger and the greater the possibility of flood disaster.

Rainfall:
The most direct factor affecting urban floods is rainfall.Long-term rainfall will greatly increase the risk of urban floods.With the impact of human factors and climate change on the global environment, urban flooding has become more frequent, intense and uncertain.The rainfall data in the study area used the annual average rainfall from 2010 to 2020.The results are shown in Figure 4(a).

Rainstorm proportion:
Rainstorm proportion refers to the proportion of the frequency of rainstorm in all rainfall frequencies.The higher the proportion of urban rainstorm, the more the number of short-term heavy rainfall, the more the accumulation of water, and the greater the possibility of flood.The rainstorm proportion data in this article comes from the 'China long and short-duration rainstorm rainfall characteristic dataset' (Kong 2018).The data of nine meteorological stations in and around the study area are selected for interpolation analysis to visualize the rainstorm proportion data.The results are shown in Figure 4(b).

Storm rainfall:
Storm rainfall refers to the rainfall generated by rainstorm.Rainstorm is the most important factor in urban flood disasters.High-intensity rainfall in a short period of

Environmental exposure of disaster
The disaster environment is the external environment, which is composed of natural and social aspects (Du et al. 2017).In places such as flat terrain and underpasses, rainwater collection is more likely to occur, drainage is not smooth, water accumulation is formed, and floods are induced.During the rainy season, the river flow increases, the denser the water system is, and the areas closer to the river network are more prone to flooding.Vegetation has a strong effect on soil and water conservation.The higher the vegetation coverage, the stronger the soil water storage capacity and the lower the risk of flood disaster.

Altitude:
Altitude is one of the important factors that directly affect urban floods (Hoque et al. 2019).It affects the direction of surface runoff, and water flows from high to low-lying areas.Therefore, urban floods are more likely to occur in lower and flatter areas.This article uses the 2020 NASA data and the ArcGIS 10.7 version to extract the digital elevation model (DEM) data of the study area.The results are shown in Figure 5(a).

Slope:
Slope will affect the velocity and flow of water.The larger the slope, the larger the surface runoff, and it is not easy to form dead water.The low slope has a large amount of water seepage, which has little effect on surface runoff and is prone to flooding.Urban flood risk increases with the decrease of slope.The slope data in this article were extracted from DEM by GIS, and the results are shown in Figure 5(b).

NDVI:
NDVI is usually used to represent the vegetation coverage.When the value is close to 0, it means no vegetation, and the closer it is to 1, the greater the vegetation coverage.The areas with high vegetation coverage have strong water retention capacity and low urban flood risk.This article uses vegetation cover data for 2020, and the results are shown in Figure 5(c).

Drainage density:
The density of river network is another important parameter affecting flood risk.The increase of rainfall in the rainy season causes the river water level to rise sharply, which is prone to flooding.Therefore, areas with high river network density are more prone to flooding than areas with low river network density.The river data used in this article are from OpenStreetMap data from 2022.The river network density refers to the ratio of river length to basin area.The results are shown in Figure 5(d).

Vulnerability of hazard-affected body
The hazard-affected body is the object of flood disaster.The vulnerability of disasteraffected bodies can be qualitatively reflected by factors such as economic conditions and population density (Huang and She 2020).When disasters occur in places with dense population, high per capita GDP, and more buildings, economic losses and casualties will be relatively large, and the risk will be higher.

Population density:
It is the primary task to protect human life and safety when flood disaster comes.As an important part of the carrier, population density is used to reflect the vulnerability of the disaster-affected body.In areas with dense population distribution, the loss of personnel caused by flood disasters will be more serious, and the vulnerability will be higher.The population distribution of Beijing is derived from the GPW v4 dataset.In order to improve the accuracy of the data, we revised the GPW v4 dataset based on the seventh census public data, and the results are shown in Figure 6(a).

Road density:
Once road congestion and other problems occur in places with developed road traffic, the impact on economic activities will be more serious.Road congestion and serious road water accumulation will lead to victims' inability to escape and rescuers' inability to rescue.Therefore, the denser the road, the higher the vulnerability of the disaster-affected body.The road data in this study comes from the OpenStreetMap website.The road density is the length of the road per square kilometre.The results are shown in Figure 6(b).

Land use/land cover:
The change of land use type and the increase of impervious surface aggravate the occurrence of urban flooding events.Land use and land cover (LULC) data are derived from the global cover product of the GLC_FCS30-2020 Fine Classification System (Zhang et al. 2021).The main land use and land cover types in the study area are cultivated land, forest land, grassland, impervious surface, water body and other six types.Different land use and land cover types have different degrees of damage, among which the impervious surface has the weakest seepage capacity and the highest economic value.The results are shown in Figure 6(c).disasters, helps people make correct decisions and reduces losses in the face of disasters.The education level improves people's ability to cope with the impact of urban flood disasters, and people with high education levels have higher disaster response ability.Through the data of the seventh national census, the education situation was analysed according to the number of illiterate people in each urban area.The results are shown in Figure 7(a).

Medical level:
During the flood, if timely treatment can be provided to the injured residents in the nearest hospital, the casualties caused by the disaster can be effectively reduced.The more medical rescue points, the stronger the ability to cope with flood disasters, and the smaller the loss.Through the open source software Baidu Map Crawler, the medical facility points are obtained.After manually excluding hospitals such as beauty hospitals, stomatological hospitals, pet hospitals, etc., the nuclear density tool is used to analyse the medical rescue points.The results are shown in Figure 7(b).

Hazard, exposure, vulnerable, urban emergency capacity coverage map
After normalizing the evaluation indicators, the FAHP-EWM method is used to determine the weights, and the corresponding weights are assigned to different indicators to obtain the hazard coverage map, sensitive coverage map, fragile coverage map and disaster prevention and mitigation capacity coverage map of the study area (Figure 8).
Figure 8(a) is the hazard coverage map of urban disaster-causing factors, showing the distribution of the possibility of flood disasters, which is determined by the three Indicators of rainfall, rainstorm proportion and rainstorm rainfall.The risk degree of the study area shows an increasing trend from west to east, mainly because the number of rainstorms in the eastern region is higher, and the amount of rainstorms is higher, which creates a prerequisite for the occurrence of flood disasters.Figure 8(c) is the vulnerability coverage map of the hazard-affected body, which shows the degree of vulnerability or damage in the study area, which is determined by the four indicators of population density, road density, LULC and GDP.The highvulnerability areas in the study area are mainly concentrated in the city centre.There are many buildings in the city centre, the proportion of impervious surface is high, and the rainwater infiltration is slow.At the same time, high GDP and high population density also lead to high vulnerability.
Figure 8(d) is the urban emergency capacity coverage map, reflecting the city's own ability to cope with disasters, determined by the level of education and the density of medical facilities.The central urban area of the study area has dense medical facilities, high education level and high ability to cope with disasters.

Flood risk map
GIS is used to generate a flood risk map of Beijing, as shown in Figure 9.According to the natural discontinuity classification method, the flood risk is divided into five categories, and the proportion of each level in the study area is 9.67% (very low), 22.5% (low), 32.65% (moderate), 28.19% (high) and 6.98% (very high).The very high-risk areas are mainly distributed in Dongcheng District and Xicheng District; the high-and moderate-risk areas are mainly concentrated in Chaoyang District and Haidian District.Low risk and very low risk are mainly distributed in the suburbs of Shijingshan District and Fengtai District.
The medium and above risks are mainly concentrated in the east and west areas.This is mainly because the lower altitude and slope improve the environment of flood development, and a large number of impervious surfaces hinder the water seepage capacity of the surface.In addition, the economic prosperity of the region also leads to higher vulnerability.The combination of various factors leads to high risks in the eastern and western urban areas.

Validation
Due to the long-term impact of floods, Beijing's waterlogging points are endless.This article collects 116 waterlogging points in Beijing from 2011 to 2022, mainly from government reports and news information, and uses waterlogging points to verify risk zoning (Figure 10).
From the collected disaster information of Beijing, most of the waterlogging points are concentrated in the city centre and distributed along the urban roads, which is consistent with the waterlogging risk map generated by the model.
According to detailed statistics, 25 of the 116 waterlogging points are distributed in very high-risk areas, 63 in high-risk areas, 20 in moderate-risk areas, 6 in low-risk areas, and 2 in very low-risk areas (see Table 4).75.86% of the waterlogging points are distributed in high-and very high-risk areas.The consistency between flood risk map and waterlogging points is relatively high, indicating the superiority of the selected indicators and weighting methods.

Method comparison
In order to reflect the accuracy of the weighting method used in this article, only the FAHP-EWM weighting method is changed to compare the reliability of the model while keeping the criterion layer and the indicator layer unchanged.The flood risk map generated by the AHP and AHP-EWM weighting methods is shown in Figure 11.
Among them, 66.38% of the waterlogging points in the AHP-EWM risk map are distributed in high-risk and very high-risk areas; in the AHP risk map, 62.07% of the waterlogging points are distributed in high-and very high-risk areas, and 12.07% of the waterlogging points are distributed in low-and very low-risk areas.In the FAHP-EWM weighting method, 75.86% of the waterlogging points are located in the very high-risk area and the high-risk area, and only 1.7% of the waterlogging points are located in the very low-risk area.The statistical distribution of waterlogging points in the three methods is shown in Figure 12.It can be seen that the FAHP-EWM method proposed in this article is obviously superior to the AHP and AHP-EWM combination weighting methods and can be used for rapid and reliable assessment of urban flood risk.

Conclusions
This article proposes an urban flood risk assessment model based on the FAHP-EWM combined weighting method.In the Multi-Criteria Decision Making (MCDM) framework, 13 indicators are selected to establish the indicator system based on the criteria of risk, exposure, vulnerability and disaster prevention and mitigation ability, and the risk coverage map and flood risk map of the criterion layer are generated.With the support of GIS, the visualization of risk coverage map and flood risk map is   realized, and the flood risk is divided into five grades according to the natural discontinuity point classification method.The flood risk assessment map generated in this study can provide valuable flood risk information for relevant departments and decision makers and assist in scientific disaster relief and early warning.
The FAHP-EWM combined weight method proposed in this article can balance the subjective and objective, and then improve the scientificity and rationality of the weight results.The proposed flood risk assessment model is applied in Beijing.The evaluation results show that 35.17% of the areas are at moderate or above risk, among which Dongcheng District and Xicheng District, with lower altitude and higher economic development, account for the highest proportion.The experimental comparative analysis results further confirm that the accuracy of FAHP-EWM weighting method is significantly better than that of AHP-EWM and AHP weighting methods in our current research area.
The research results of this article can provide valuable information for urban flood risk management, flood control and disaster reduction planning in the study area and other areas with similar conditions.In addition, when applying this method to other cities, it is necessary to properly consider the local natural environment and human environment and choose the indicators.At the same time, our research also has some limitations.For example, the selection of indicators can include more information about the uniqueness of the city, and the model can be applied to other regions for accuracy verification.
time makes urban water unable to discharge, resulting in large-scale floods.The more rainstorm rainfall, the more prone to floods.This article uses the public data 'China rainstorm dataset'(He et al. 2022) to analyse the rainstorm rainfall data from 2015 to 2019.The results are shown in Figure4(c).

Figure 7 .
Figure 7. Urban emergency capability indicator data processing results.Education status (a); medical level (b).

Figure 8
Figure8(b)  shows the exposure coverage of urban disaster-pregnant environment, which shows the ability of environment to flood disaster, and is determined by the four Indicators of altitude, slope, NDVI and river network density.The low-exposure area of the study area is mainly concentrated in the western mountainous area.The mountainous area has high altitude and high slope, which is conducive to the flow of rainwater and makes it difficult to form stagnant water.At the same time, the mountainous area has rich vegetation, strong soil water absorption capacity and poor ability to breed disasters.Figure8(c) is the vulnerability coverage map of the hazard-affected body, which shows the degree of vulnerability or damage in the study area, which is determined by the four indicators of population density, road density, LULC and GDP.The highvulnerability areas in the study area are mainly concentrated in the city centre.There are many buildings in the city centre, the proportion of impervious surface is high, and the rainwater infiltration is slow.At the same time, high GDP and high population density also lead to high vulnerability.Figure8(d) is the urban emergency capacity coverage map, reflecting the city's own ability to cope with disasters, determined by the level of education and the

Figure 8 .
Figure 8. Criteria layer risk coverage diagram.The hazard coverage map (a); the exposure coverage map (b); the vulnerability coverage map (c); the urban emergency capacity coverage map (d).

Figure 9 .
Figure 9. Flood risk map of Beijing.

Figure 12 .
Figure 12.The number of waterlogging points in different risk areas of FAHP-EWM, AHP and AHP-EWM.
UFR is urban flood risk; a, b, c, k are the weights of hazard factors, exposure factors, vulnerability factors, urban emergency capacity factors, respectively; H i , E j , V k , R m are the secondary indicators of hazard, exposure, vulnerability, urban emergency capacity, respectively; W h , W e , W v , W u are the weights of the secondary indicators.

Table 1 .
Summarizes the indicator selection and data sources.

Table 4 .
Distribution of waterlogging points.