2.1. Rainstorminduced Flood Risk Assessment Method
The flood risk assessment method based on the index system has the advantages of easy data acquisition and simple modeling and has been widely used in urban flood risk assessment research (Shadmehri Toosi et al. 2019). In the paper, based on the regional disaster system theory and the natural disaster risk assessment principles, the urban flood risk evaluation index system is constructed by considering the flood risk influence factors from two aspects of disaster hazard and vulnerability (Arnell &Gosling 2016, Mukhopadhyay et al. 2016, Schumann &Andreadis 2016), as shown in Table 1, in which how to obtain the data of submergence depth is very important.
Table 1
Urban flood risk evaluation index system
Criterion layer

Index layer

Scheme layer

Hazard

Disaster causing factor

Submergence depth / mm

Disaster inducing environment

Elevation / m

Slope / (°)

River network density / (km/km2)

Runoff coefficient

Vulnerability

Disaster bearing body

Population density / (people/km2)

GDP density / (ten thousand RMB/km2)

The proportion of the elderly population / %

Disaster prevention and mitigation capability

GDP per capita / ten thousand RMB

Years of education / a

Road network density / (km/km2)

This paper draws on the active submergence algorithm and uses the idea of risk field to construct the urban rainstorm submergence algorithm. The basic idea of the algorithm is that the rainstorms in local areas of the city cause water to accumulate in lowlying areas, which in turn overflows and spreads outward when the water is full, that is, submergence. All lowlying waterlogging points are risk sources, and the water level of the risk source is compared with the elevation of the adjacent outer ring grid to determine whether the ponding water spreads outward. This is the gradual submergence process of accumulated water along the terrain from high to low. In this process, it is also necessary to determine whether the ponding areas where multiple risk sources may spread have intersected. The specific steps of the algorithm are as follows:
(1) Elevation attribute. On the basis of grid division 100 m × 100 m, the Digital Elevation Model (DEM) data is read to obtain the elevation value of each raster, which is marked and numbered by matrix as the attribute value of DEM raster.
(2) Determine the location of waterlogging points. These locations are the depressions prone to flood or obtained from actual surveys to further determine the raster number of risk sources and their waterlogging level, which are also used as DEM raster attributes.
(3) Waterlogging diffusion. Starting from a waterlogging point risk source, the waterlogging diffusion is carried out in turn to judge whether the waterlogging level is greater than the elevation value of the eight grids in the adjacent outer circle. If it is more than, the waterlogging will spread to this grid, which has connectivity with the risk source, and the water depth value of the flooding point will be assigned to the grid waterlogging elevation. The flood spreads outward in a circle until the waterlogging level is less than the elevation value of the outer circle or reaches the boundary.
(4) Repeat step (3) to get the diffusion range of all risk sources. When a grid participates in the diffusion of two or more nodes, its elevation each time is calculated as the original elevation.
(5) Multirisk source problem. After the diffusion of all risk sources is completed, it is judged whether there is a grid involved in the diffusion process of multiple risk source waterlogging points nodes. If there is, this grid is considered to be affected by the risk source with the highest waterlogging level, and the diffusion results in these grids is updated. Until all grids are judged, the diffusion is finished.
(6) Submergence depth. Each grid waterlogging level minus its elevation value is the rainstorm submergence depth of the grid, and finally the submergence result in the study area is obtained.
However, the influence factors involved in flood risk and the flood risk process are uncertain and ambiguous. Fuzzy comprehensive evaluation method can solve these problems very well and is suitable for risk evaluation with fuzzy and uncertain characteristics (Cai et al. 2019, Lai et al. 2020, Sarica et al. 2021, Zadeh 1965). After collecting all factor data in Table 1 and referring to the research results of Huang andLi (2021) and Abdalla et al. (2014), the fuzzy comprehensive evaluation is used to assess urban rainstorminduced flood risk in the study area, the specific process is shown in Fig. 1.
2.2. Floodinduced Water Pollution Risk Assessment Method
Urban flood is generally caused by shortterm extreme heavy rainfall, which is sudden, and the discharge of enterprise risk substances induced by it is also sudden (Yang et al. 2018), then the floodinduced water environment pollution disaster is a sudden environmental risk event. The environmental risk system consists of three elements: risk source, receptor, and pathway (Cao et al. 2019, Liu et al. 2018). The risk field can characterize the hazard mode and scale of enterprise risk sources, and the tolerance of risk receptors to hazard from risk sources can be characterized by receptor vulnerability (Cao et al. 2019, Zhou et al. 2020b). This paper refers to and revises the gridbased environmental risk analysis method in the Recommended Methods for Risk Assessment of Environmental Incidents in Administrative Areas (MEP 2018b), and combines the ideas and methods of the environmental risk field evaluation method to evaluate the risk of water pollution due to flood in the study area (Xing et al. 2016). This paper only conducts risk assessment for water environment pollution and assumes that the water environment pollutants leak instantaneously. The evaluation process is shown in Fig. 2, and the specific steps are as follows:
(1) Grid division. Considering the size of the study area, the create fishnet function of ArcGIS is used to divide it into grids of 500 m × 500 m, which are marked and numbered with a matrix. The risk at \((x, y)\) in the matrix is determined by the risk field strength and risk receptor vulnerability that may occur there.
(2) Water environment risk field strength calculation. The strength of a grid water environmental risk field is related to the nature and amount of risk substances discharged, and the distance between the grid and the risk source (Xing et al. 2016, Zhou et al. 2020a, Zhou et al. 2020b). The flood risk level is determined to quantify the impact of flood on the enterprise risk source, and then the gridbased environmental risk analysis method is introduced to calculate the risk field strength of the water environmental risk source (Xing et al. 2016), which can be expressed as:
$${E}_{x,y}=\left\{\begin{array}{c}{\sum }_{i=1}^{n}{P}_{i}{Q}_{i}{P}_{x,y}, 0\le {l}_{i}<2\\ {\sum }_{i=1}^{n}\left(1\frac{{l}_{i}}{20}\right){P}_{i}{Q}_{i}{P}_{x,y}, 2\le {l}_{i}\le 20\\ 0, 20\le {l}_{i}\end{array}\right.$$
1
where \({E}_{x,y}\) is the floodinduced water environment risk field strength of a grid; \({Q}_{i}\) is the ratio of the maximum environmental risk substances existing amount to the \(i\)th risk source critical amount; \({P}_{x,y}\) is the probability of the risk field appearing in a certain grid, generally 10 − 6/a; \({l}_{i}\) is the distance between the grid center point and the risk source, the unit is km, and the maximum influence distance is set to 10 km; \(n\) is the risk source number; \({P}_{i}\) is the occurrence probability of the floodinduced sudden water environmental events at risk sources (AlvarezGalvez 2016, Khakzad &Van Gelder 2018). The risk itself is an uncertainty event, so the formation of environmental risk field also has a certain probability, that is, when the enterprise risk source is submerged, water environment pollution event will not necessarily occur. Whether the enterprise has risk material leakage, on the one hand, it should consider the submergence depth of the enterprise involved, on the other hand, it is also related to the enterprise's own water environment risk prevention and control capabilities, thus calculating the possibility of the enterprise risk material leakage from the two perspectives of disaster causing factors and prevention and control capabilities, as shown in the Fig. 3. This conditional probability is mainly based on Bayes' theorem, which is determined by the following formula:
$${P}_{i}=P\left({A}_{j}/B\right)=\frac{P\left({A}_{j}\right)P\left(B/{A}_{j}\right)}{\sum _{j=1}^{n}P\left({A}_{j}\right)P\left(B/{A}_{j}\right)}$$
2
where \(P\left({A}_{j}\right)P\left(B/{A}_{j}\right)\) is the total probability formula, which can deduce the probability value of the relevant states. \(B\) is the flood risk level, \({A}_{j}\) refers to all the possible causes of event \(B\), \(P\left({A}_{j}\right)\) refers to the prior probabilities derived from priori data, and \(j\) represents a specific variable.
The water pollution environmental risk field is affected by the external environment, the location of the risk sources, its own properties and the propagation medium, and is characterized by uneven intensity. The direction of water flow will flow from high to low, and affect the surrounding grid only when the grid where the risk source is located is higher than the surrounding grid. In order to accurately determine the influence scope of the risk source, the regional growth method is introduced to search from the first circle grid closest to the risk source and compare the elevation value of the 8 surrounding grids with the those of the risk source (Zhou et al. 2020a, Zhou et al. 2020b). If it is less than, this grid around the risk source is considered as the affected grid. Repeat the above steps and stop the search once the elevation value is greater than the last comparison grid value or the 10 km boundary is reached. Then the risk field strength of each risk source in each grid is calculated according to formula (5). If the same grid is affected by multiple risk sources, the sum of the field strength of these risk sources on that grid is the risk field strength of that grid.
The floodinduced water environment risk field strength of each grid is standardized for comparison, and the formula is as follows:
$${E}_{x,y}=\frac{{E}_{x,y}{E}_{min}}{{E}_{max}{E}_{min}}\times 100$$
3
where \({E}_{x,y}\) is the floodinduced water environment risk field strength of a grid, multiplied by 100 to make all risk field strengths fall within [1,100], so as to be consistent with the subsequent vulnerability; \({E}_{max}\) is the maximum water environment risk field strength in the whole area; \({E}_{min}\) is the minimum water environment risk field strength in the whole area.
(3) Water environmental risk receptor vulnerability calculation. Referring to the research results of Zhou et al. (2020a) and Cao et al. (2019), the sensitivities of different grids in the study area are determined mainly by considering the levels of rivers, lakes, and reservoirs and the functional area of water bodies. The method for calculating the vulnerability of water environmental risk receptors is shown in Table 2.
Table 2
Determination method of water environmental risk receptor vulnerability
Target

Index

Description

Weight

Score

Water environmental risk
receptor vulnerability index

River, lake, reservoir grade

Grids through which grade 1 rivers, lakes, reservoirs, etc.

1/3

100

Grids through which grade 2 rivers, lakes, reservoirs, etc.

80

Grids through which grade 3 rivers, lakes, reservoirs, etc.

60

Grids through which grade 4 rivers, lakes, reservoirs, etc.

40

Grids through which grade 5 rivers, lakes, reservoirs, etc.

20

Water functional area

Grids through which class I water quality in rivers, lakes, reservoirs, etc.

1/3

100

Grids through which class II water quality in rivers, lakes, reservoirs, etc.

80

Grids through which class III water quality in rivers, lakes, reservoirs, etc.

60

Grids through which class IV water quality in rivers, lakes, reservoirs, etc.

40

Grids through which class V and inferior class V water quality in rivers, lakes, reservoirs, etc.

20

River, lake, reservoir buffer zone

Grids through which 1 km buffer zone of rivers, lakes, reservoirs, etc.

1/3

100

Grids through which 3 km buffer zone of rivers, lakes, reservoirs, etc.

75

Grids through which 5 km buffer zone of rivers, lakes, reservoirs, etc.

50

Grids through which 10 km buffer zone of rivers, lakes, reservoirs, etc.

25

(4) Calculation of floodinduced water pollution risk index. The following formula (4) is used to calculate the floodinduced water pollution risk index in each grid.
$${R}_{x,y}=\sqrt{{R}_{x,y}\times {V}_{x,y}}$$
4
where \({R}_{x,y}\) is the floodinduced water pollution environmental risk index at \((x, y)\); \({E}_{x,y}\) is the floodinduced water environment risk field strength at\((x, y)\); \({V}_{x,y}\) is the vulnerability index of water environmental risk receptor at \((x, y)\). According to the grid environmental risk index value, the floodinduced water pollution risk is divided into four levels: very high risk (\({R}_{x,y}\) > 80), high risk (60 < \({R}_{x,y}\) ≤ 80), moderate risk (30 < R ≤ 60), and low risk (R ≤ 30).