Impact of Different Design Rainfall Pattern Peak Factors on Urban Flooding

Abstract

In order to investigate the influence of different design rainfall peaks on urban flooding characteristics based on the MIKE hydrodynamic model, the inundation process scenarios were extrapolated for different recurrence periods and three single- and double-peak rainfall types in Zhoukou city as an example, and the equivalent values of total inundation and inundation area were compared and analysed. The results show that bimodal rainfall has a higher risk of inundation than unimodal rainfall for the same rainfall ephemeris and return period. For unimodal rainfall, when the return period is less than 20 years, the more advanced the rainfall peak, the more severe the design rainfall inundation. When the return period is greater than 20 years, the further back the rainfall peak, the more severe the inundation of the design rainfall. The difference between the risk of inundation due to single- and double-peaked rainfall decreases as the return period increases.

1. Introduction

In the context of global climate change and rapid urbanisation, urban flooding due to heavy rainfall is a frequent occurrence [1]. And as people and property continue to congregate in built-up areas, the damage caused by flooding under a storm of the same magnitude is greater than ever [2]. For example, in July 2021, the city of Zhengzhou was hit by a once-in-a-millennium rainstorm, resulting in direct losses of 40.9 billion yuan and 380 deaths and disappearances, and on 22 May 2020, Guangzhou was hit by a very heavy rainstorm that caused extensive flooding throughout the city, resulting in direct economic losses of over 10 billion yuan and 4 deaths. On 21 July 2012, a very heavy rainstorm in Beijing caused flooding and secondary disasters, resulting in 79 deaths. As can be seen, heavy rainfall flooding has seriously threatened peoples’ normal lives and caused serious casualties and property damage to society [3].

The main mature models for urban flooding include SWMM, SOBEK, MIKE urban, and others [4]. The different models have their own advantages and disadvantages in terms of hydraulic simulation. In comparison, the MIKE URBAN model has the advantages of high technical integration, a wide range of data interfaces, simplicity, and accuracy in modelling and operation [5]. For example, Liu Xingpo et al. [6] evaluated the modelling efficiency and effectiveness of flow timeline models, such as EPA SWMM and MIKE urban, and found that MIKE Urban could automatically import pipe network data and the batch input of model parameters. The model structure was similar to that of the inferred equation method and was more effective under the condition of using user-defined time area curves. Huang Linyu et al. [7] used MIKE FLOOD as a platform to build a storm water flooding model to assess the drainage capacity of the current storm water pipe network in Pudong New Area, Shanghai, and to provide a basis for countermeasures for relevant authorities. Ren Meifang et al. [8] carried out a simulation of waterlogging in Jinan city based on the MIKE urban model and analysed the causes of waterlogging in the Lixia District interchange area. Tang Ming et al. [9] used the MIKE coupled model to simulate the storm waterlogging in the Qingshan Lake drainage area of Nanchang City and determined the composite rain-type method. Chen An-Li et al. [10] assessed the risk level of flooding in Fuzhou city using MIKE coupled coordination model and drew up a table on risk level. Tian Fuchang et al. [11] used the MIKE FLOOD coupled model to simulate the extent of regional inundation and the overflow process.

As the root cause of flooding, heavy rainfall has an important influence on flooding in addition to the amount and intensity of rainfall, i.e., the type of rainfall. The rain pattern, as a concept describing the storm process, expresses the process of distribution of storm intensity on a time scale and is directly related to the maximum extent and depth of waterlogging. Therefore, it is significant to study and analyse the impact of different design storm rainfall patterns on urban flooding. For example, Chen Qing et al. [12] used the P&C method and the Chicago method to derive the rainfall pattern of short-duration storms based on drainage and flood control planning, and found that the results were basically consistent. Li Pinliang et al. [13] applied the MIKE urban model to simulate the pressure-bearing operation and pipe point overflow of a district drainage network in Chengdu under different rainfall patterns and intensities, and to improve urban flooding by setting up storage ponds and increasing the pipe diameter. Liu, Sakura et al. [14] statistically analysed the rainfall rain pattern characteristics in Hangzhou. Zhao Lina et al. [15] used the fuzzy identification method to classify the rainfall process in Beijing by rain type and to explore its impact on urban flooding. However, most scholars have only explored the effects of a single rainfall type on urban flooding. For example, Cao Jingfu et al. [16] evaluated the effect of different unimodal rainfall patterns on the total amount of waterlogging. Lei Xiangdong et al. [17] studied the effect of LID measures on urban stormwater runoff pollution processes using a typical Chicago rain pattern. Hou Jingming et al. [18] designed a single-peak type rainfall with different peak ratios to simulate and analyse the waterlogging situation in Xixian New Area. Wang Di [19] used typical field rainfall process lines to generate bimodal design rainfall and to analyse the risk of internal flooding in the current area. Ceng Guoping [20] compared the runoff processes under four design rainfall patterns, and the results showed that the rainfall pattern had a significant effect on the peak flood flow. Cao Jingfu et al. compared the effects of different short duration storm rainfall types on the amount of urban flooding and peak present time, and suggested to focus on single-peak type I rainfall. Tang et al. compared the same magnification ratio amplification method with the same frequency amplification method used to design rain patterns for the inundation process in Nanchang City and found that the simulated water levels of rivers and lakes obtained differed greatly. Cheng Dan et al. [21] used the same frequency analysis method with the Huff rain pattern to derive the 24 h design storm in Wuhan and found that the rain pattern based on the same frequency method resulted in a lower proportion of compliant networks and more severe waterlogging. In addition to the several commonly used design rainfall patterns, many scholars have also studied the impact of different rainfall characteristics on urban flooding. When comparing the flooding results of Xiamen Island under a different design rainfall, Liu Jiahong et al. [22] found that the flooding characteristics were strongly influenced by the location of the rainfall peaks, and the total peak amount of water accumulation and the area of water accumulation increased with the increase in the rainfall peak coefficient. Krvavica et al. [23] found that the choice of design storm and rainfall duration had a significant effect on the flood simulation results. Pan et al. [24] demonstrated that the peak flows simulated in the SWMM (storm water management model) for the Triangle, Huff and Chicago rainfall types differed significantly and underestimated the peak flows.

However, rainfall processes are often not simply a single process and different rain patterns cause different levels of inundation and disaster risk. Therefore, this paper is based on the MIKE model, which is a numerical simulation from the perspective of the impact of different rain patterns on waterlogging. The main studies are: 1. The systematic comparative analysis of urban flooding processes under different design storm rainfall pattern; 2. The effect of peak pattern and peak ratio on inundation area and inundation depth for different design rainfall patterns at the same return period; and 3. The analysis of the characteristics of urban flooding in response to rainfall rain patterns to provide a reference for early warning and forecasting of urban flooding, disaster prevention and control.

2. Materials and Methods

2.1. Overview of the Study Area

Zhoukou is located in the East Henan Plain, southeast of Henan Province. The geographical coordinates are 33°03′–34°20′ north latitude and 114°05′–115°39′ east longitude, 135 km wide from north to south and 140 km long from east to west [25]. See Figure 1 for a map of Zhoukou’s location. Zhoukou is part of the Yellow and Huai Plain and has an overall flat landscape. However, due to external forces, especially the alluvial accumulation of the Yellow River flooding, ridge and depression microlandscapes have developed extensively, changing the monolithic shape of the plain landforms. The spatial characteristics of rainfall in Zhoukou are significant, mainly in the form of gradually decreasing average annual rainfall from south to north. According to the analysis of the multi-year average rainfall data of Zhoukou City from 1966 to 2020, it can be seen that the multi-year average rainfall of Zhoukou City is 759.7 mm, with the maximum of 1238.8 mm, which occurred in 2003, and the minimum is 423.7 mm, which occurred in 1966. Rainfall mostly occurs in the form of heavy rainfall. Rainfall patterns produce fast flow rates, which tend to cause high peak flows of rainwater runoff and generate high pressure on drainage systems, making them susceptible to natural disasters, such as flooding, waterlogging and erosion [26].

2.2. Lower Bedding Surface Conditions

The central urban area of Zhoukou City extends from the south to the Ningluo Expressway, from the east to the Dagang Expressway and from the northwest to the Shangzhou Expressway, which is actually an area enclosed by three expressways, with a total area of about 271 km², the current urban construction land area is about 70 km², and the rest is mainly agricultural land and village construction land. Based on the collected 1:1000 topographic maps, elevation data, such as contour lines and elevation points in the central city of Zhoukou, as well as boundary data of roads, buildings, water systems, distribution of flood control projects, green areas, land use and other elements, are extracted to generate high-precision DEM data that distinguish between types of ground cover. The intensity of rainfall and subsurface conditions are the two main factors that affect urban surface runoff. To investigate the subsurface conditions in the study area, a combination of field surveys, large-scale topographic maps, and high-resolution remote sensing images was used. The analysis included a comprehensive examination of the types of water bodies, grass, woods, bare soil, roads, squares, roofs, and paving in small areas. Based on this analysis, the subsurface in the central city of Zhoukou was classified into five major categories, namely building land, green land, river land, transport land, and agriculture and forestry (see Figure 2).

According to the analysis of the current situation of the urban built-up area in Zhoukou city, the lower mat surface is highly hardened, while the indicators for green space and square land are significantly low, accounting for only about 4% of the total urban land ratio, which is less than 5 square meters per capita. This is far below the indicators that account for 10 square meters per capita. Figure 2 shows the current situation of the central urban area of Zhoukou city.

2.3. Rainfall Data

The Chicago rain pattern method is a distribution of the frequency of the storm intensity formula. The amount of rain in any calendar hour in the derived design storm rain pattern is equal to the design rainfall, and the calculated flood flow is relatively stable and easy to use. It is only necessary to calculate the rainfall crest factor r from rainfall data, and the value of r can be estimated in areas where information is scarce, with less reliance on storm data. The Chicago rainfall pattern is more suitable for extrapolating to urban areas, where a design rainfall calendar of around 3 h is most accurate.

Therefore, the rainfall boundary conditions for the model input use the Chicago rain type of the storm intensity equation plus the rain crest factor to derive the design storm process line [27].

Storm intensity equation:

$$i=\frac{q}{t}=\frac{A\ast (1+C\ast \mathrm{Lg}\mathrm{T})}{167\ast (t+b{)}^n}$$

(1)

Upward band:

$$i_a=\frac{A\left[\frac{\left(1-n\right)t_a}{1-r}+b\right]}{{\left(\frac{t_a}{1-r}+b\right)}^{n+1}}$$

(2)

Descending section:

$$i_b=\frac{A\left[\frac{\left(1-n\right)t_b}{r}+b\right]}{{\left(\frac{t_b}{r}+b\right)}^{n+1}}$$

(3)

where i is the storm intensity, mm/min; t is the rainfall calendar time, min; t is the recurrence period, a; A is the rain force parameter; c is the rain force variation parameter; n is the storm attenuation index; b is the rainfall calendar time correction factor for all local empirical parameters in the storm intensity equation; and r is the peak coefficient (dimensionless), i.e., the ratio of peak present time to storm calendar time, r ∈ (0,1).

The revised formula for storm intensity in the central city of Zhoukou was also obtained based on the announcement of the revised storm intensity in the central city of Zhoukou.

$$i=\frac{q}{t}=\frac{3032.247(1+0.828\mathrm{LgT})}{167\ast (t+21.405{)}^{0.755}}$$

(4)

The values of the local empirical parameters A, n and b in the equation for storm intensity in the central city of Zhoukou under different return periods can be obtained by combining Equations (1) and (4), and the corresponding design storm rain patterns can be deduced by substituting Equations (2) and (3).

In summary, in order to characterise the different rain patterns and to study the influence of different peak patterns and the location of the rain peaks on the inundation area and inundation depth of the city, rain peak coefficients of r = 0.25 and r = 0.75 for single-peaked rainfall and r = 0.5 for double-peaked rainfall were chosen. Eighteen design rainfall events were calculated for six different recurrence periods (T = 1, 5, 10, 20, 50, 100a), and a rainfall calendar of 3 h was chosen. The frequency curve of the design rainfall is shown in Figure 3.

2.4. Model Construction

MIKE was developed independently by DHI Water & Environment & Health [28] and integrates the one-dimensional model MIKE URBAN or MIKE 11 with the two-dimensional model MIKE 21 [29], which is a dynamically coupled model system that can simultaneously simulate drainage networks, open channels, drainage channels, various hydraulic structures and two-dimensional slope flows, and can be used for the simulation of watershed flooding and urban flooding [30].

2.4.1. One-Dimensional River Hydrodynamic Model

The MIKE 11 model is a key component of the MIKE FLOOD flood simulation component developed by the Danish company DHI. Based on urban water systems and hydrological information, MIKE 11 can construct a one-dimensional river network model for urban river water simulation, which has the advantages of saving labour, accurate calculations and visualisation of the results. The computational principle is one-dimensional hydrodynamics, including the continuous and kinematic equations, which are discretized using the finite difference method in a six-point central Abbott–Ionescu format and the discrete equations are solved using the catch-up method [31]. The expressions are as follows:

Continuous equation:

$$\frac{\partial Q}{\partial x}+\frac{\partial A}{\partial t}=q$$

(5)

Momentum equation:

$$\frac{\partial Q}{\partial t}+\frac{\partial (\alpha \frac{Q^2}{A})}{\partial x}+gA\frac{\partial h}{\partial x}+\frac{gQ\left|Q\right|}{C^{2}AR}=0$$

(6)

where x and t are the coordinates of the calculation point in space and time, respectively; A is the area of the overflow section; Q is the overflow flow; h is the water level; q is the side inlet flow; C is the Xie Cai coefficient; R is the hydraulic radius; α is the momentum correction factor; and g is the acceleration of gravity.

The study area in the central city of Zhoukou includes a total of 11 rivers: Shahe, Yinghe, Shainhe, Jialu, Yunliao, Jadong Dry Drainage, Liusha, Happiness, Wuchonggou, Jiaotong Dry Drainage and Yangzhu Dry Drainage.

2.4.2. Two-Dimensional Hydrodynamic Model

The two-dimensional hydrodynamic model used in this paper is based on the Navier–Stokes mean equation for the continuum of integration along the water depth and the momentum equation.

Continuity equation:

$$\frac{\partial h}{\partial t}+\frac{\partial h\overline{u}}{\partial x}+\frac{\partial h\overline{v}}{\partial y}=hS$$

(7)

Momentum equation in the x-direction:

$$\begin{gathered} \frac{\partial h\overline{u}}{\partial t}+\frac{\partial h\overline{u^2}}{\partial x}+\frac{\partial h\overline{{vu}^2}}{\partial y}=f\overline{v}h-gh\frac{\partial \eta }{\partial x}-\frac{h}{{\rho }_0}\frac{\partial P_a}{\partial x}-\frac{g{h}^2}{{2\rho }_0}\frac{\partial \rho }{\partial x}+\frac{{\tau }_{sx}}{{\rho }_0}-\frac{{\tau }_{bx}}{{\rho }_0}- \\ \frac{1}{{\rho }_0}\left(\frac{\partial S_{xx}}{\partial x}+\frac{\partial S_{xy}}{\partial x}\right)+\frac{\partial }{\partial x}\left(h{T}_{xx}\right)+\frac{\partial }{\partial x}\left(h{T}_{xy}\right)+h{u}_{s}S \end{gathered}$$

(8)

The equation of momentum in the y-direction:

$$\begin{gathered} \frac{\partial h\overline{v}}{\partial t}+\frac{\partial h\overline{uv}}{\partial x}+\frac{\partial h\overline{v^2}}{\partial y}=-f\overline{u}h-gh\frac{\partial \eta }{\partial y}-\frac{h}{{\rho }_0}\frac{\partial P_a}{\partial y}-\frac{g{h}^2}{{2\rho }_0}\frac{\partial \rho }{\partial y}+\frac{{\tau }_{sy}}{{\rho }_0}-\frac{{\tau }_{by}}{{\rho }_0}- \\ \frac{1}{{\rho }_0}\left(\frac{\partial S_{yx}}{\partial y}+\frac{\partial S_{yy}}{\partial x}\right)+\frac{\partial }{\partial x}\left(h{T}_{xy}\right)+\frac{\partial }{\partial y}\left(h{T}_{yy}\right)+h{v}_{s}S \end{gathered}$$

(9)

where t is time; x, y and z are Cartesian coordinates; h = $\eta$ + d is the total water depth; $\eta$ is the water level; d is the hydrostatic depth; u and v are the components of the flow velocity in the x- and y-directions, respectively; g is the acceleration of gravity; f is the Koch force term $f=2\mathsf{\Omega }\sin \phi$ ($\mathsf{\Omega }=0.729\times {10}^{-4}{\mathrm{s}}^{-1}$ is the angular velocity of the Earth’s rotation, $\phi$ is the local latitude); $f\overline{u}$ and $f\overline{v}$ are the acceleration due to the Earth’s rotation; $P_a$ is the barometric pressure term; ${\rho }_0$ is the density of seawater at normal conditions; $\rho$ is the density of water; $S_{xx}$, $S_{xy}$, $S_{yx}$ and $S_{yy}$ are the wave radiation stress term; $T_{xx}$, $T_{xy}$, $T_{yx}$ and $T_{yy}$ are the horizontal viscous stress term; ${\tau }_{sx}$ and ${\tau }_{sy}$ are the surface wind stress term; S is the source-sink term; and $u_s$ and $v_s$ are the source-sink current velocity.

The construction of the MIKE 21 model consisted mainly of the construction of the base terrain and the processing of the sub-base data. Topography is one of the most important factors influencing urban flooding, and the construction of the base topography is key to determining the extent of urban inundation. The base topography only reflects the undulation of the ground surface in the absence of man-made buildings and does not reflect the particular urban area catchment characteristics in urban terrain where a large number of man-made buildings have been constructed. It was therefore necessary to process the subsurface data, mainly by processing the relevant layers in Arcgis and converting the format to ASCII text for importing into MIKE Zero for the construction of a two-dimensional surface diffuse flow model.

The calculation grid is divided within MIKE 21 based on the collected base topographic information of the central city of Zhoukou, including various water-blocking structures, such as buildings, roads, bridges, embankments, etc. Depending on the application requirements, MIKE 21 can divide the calculation area into a rectangular grid, or an irregular triangular grid. The 2D hydrodynamic model of the central city of Zhoukou uses a rectangular grid with a grid size of 2 m × 2 m. Buildings, such as bridges, dykes and roadbeds, within the area can be generalised and simulated using the hydraulic buildings module of MIKE 21.

The simulated area is about 145.75 km². The model uses a rectangular grid with a grid number of 3.64 × 10⁷ and a grid size of 4 m².

2.4.3. One-Dimensional Pipe Network Model

The MIKE urban model is mainly used to simulate urban drainage systems and is divided into two parts: rainfall runoff simulation and pipe network simulation. The results of the rainfall runoff simulation are the boundary conditions of the pipe network simulation. The model is based on the one-dimensional flow continuity equation and the flow dynamics equation, and the model is solved by the six-point implicit difference method [32]. The pipe network model consists of 11,029 inspection wells and 11 pumping stations.

2.4.4. Lower Bedding Surface Generalisation

The parameters that affect the results of the pipe network model mainly concern impermeability, i.e., the runoff coefficient for each sub-catchment. Impermeability determines the amount of runoff from each sub-catchment, which in turn affects the amount of rainfall entering the inspection wells. The four main types of land use in urban areas include buildings, roads, water bodies and green spaces. Imperviousness needs to be determined based on the land use types within the study area, and in MIKE Urban, the average imperviousness of each sub-catchment is calculated using area-weighted averages based on the different land use types. According to the recommended values for imperviousness given in the Code for Outdoor Drainage Design, GB50014-2006 issued by the Ministry of Construction, the imperviousness values for different land use types for buildings, roads, water bodies and green spaces are shown in

Table 1. Table of site parameters.

Type of Land Use	Water Impermeability (%)
Architecture	90
Roads	80
Water bodies	0
Green spaces	35

.

3. Results and Discussion

3.1. Model Validation

After the flooding model was constructed, the model was validated based on the measured rainfall data from the Zhoukou station, combined with rainfall statistics (disaster statistics, records of waterlogged road sections and depth of waterlogging). Due to the limited information on the depth of ponding from measured rainfall, the main focus was to verify the flood prone point, and the depth of ponding at that point. Since July 2021, Zhoukou has suffered a serious flood situation with a triple overlap of historical local rainfall extremes, upstream reservoir releases, and confluence within multiple rivers from 17:00 on 21 July to 11:00 on 22 July. The maximum precipitation in Zhoukou reached 248.9 mm, with a maximum hourly rainfall intensity of 51.3 mm. There are 20 major waterlogged sites in Zhoukou (see Figure 4). A comparison of the measured maximum ponding depths with the modelled maximum ponding depths is shown in

Table 2. Comparison of measured maximum ponding depths with model simulated maximum ponding depths.

Waterlogged Spots	Measured Water Depth /cm	Simulated Water Depth /cm	Difference /cm
1	61	64	3
2	42	43	1
3	54	57	3
4	32	30	−2
5	81	78	−3
6	81	83	2
7	62	58	−4
8	43	44	1
9	39	42	3
10	40	42	2
11	41	39	−2
12	42	42	0
13	61	57	−4
14	58	62	4
15	42	41	−1
16	59	62	3
17	43	40	−3
18	34	37	3
19	32	33	1
20	32	37	5

. As can be seen from Table 2, The difference between the measured and modelled values at 20 waterlogged locations is within 5 cm. If the number of samples measured is large enough, the accuracy of the validated model will be higher and the results more accurate.

3.2. Analysis of Changes in Total Inundation

In this study, 18 design rainfall events were used for the model simulations and the inundation grids and inundation depths of the inundated areas were counted. The process of total inundation variation for each rainfall type under different return periods was calculated by superimposition (Figure 5), with bimodal rainfall having a more severe impact on inundation than unimodal rainfall. For two unimodal rainfall events, a unimodal rainfall with a rainfall crest factor of 0.25 results in more inundation when the return period is less than 20 years. For example, at a rainfall return period of 5 years, a single-peaked rainfall with a rainfall crest factor of 0.25 would produce a maximum peak inundation of 159,400 cubic metres, while a single-peaked rainfall with a rainfall crest factor of 0.75 would produce a peak inundation of 152,800 cubic metres. However, when the return period is higher than 20 years, a single-peaked rainfall with a rainfall crest factor of 0.75 produces a higher peak inundation than a single-peaked rainfall with a rainfall crest factor of 0.25. In addition, as the intensity of precipitation increases, the difference between the peak inundation volumes due to different rainfall types decreases. For example, at a return period of 100 years, as can be seen from

Table 3. Comparison of peak water accumulation at different recurrence periods.

Return Period	V(r = 0.5)–V(r = 0.25)/m³	V(r = 0.5)–V(r = 0.75)/m³	V(r = 0.25)–V(r = 0.75)/m³
1	5900	12,500	6600
5	5210	10,532	5322
10	4276	8432	4156
20	4100	1936	2164
50	3603	1860	−1743
100	2596	1044	−1552

, a single-peaked rainfall type with a rainfall crest factor of 0.75 only results in 1552 m³ more peak inundation than a single-peaked rainfall type with a rainfall crest factor of 0.25.

The reason for these results is that the bimodal rainfall has two rain peaks, which will occur as time progresses. Therefore, for the same return period, the depth of ponding is greater than for a single-peak rainfall. As the recurrence period increases, the amount of rainfall increases and the rate at which water accumulates in the drains increases accordingly, and the difference in depth between the two decreases. For the same return period, when the return period is small, e.g., 1a, 5a or 10a, the more advanced the rainfall peak, the greater the depth of ponding. Due to the intensity of the rainfall at the beginning, the drainage pipes do not have time to drain, and the rainwater collects quickly at the surface. When the recurrence period is large, such as 50a or 100a, and the rainfall is all relatively heavy, the rainfall in front of the rain peak will first accumulate, after which the rainfall behind the rain peak will start to accumulate and then reach its peak. Therefore, the further back the rain crest is at this point, the greater the depth of standing water caused. However, for large recurrence periods when the drainage capacity of the pipes is not up to the required level, the total rainfall is the same and the difference in water accumulation caused between the different rain peaks is gradually decreasing.

As a result, different types of rainfall have different effects on the amount of inundation and the risk of inundation. Of these rainfall types, bimodal rainfall can result in the greatest amount of inundation and the highest risk of internal flooding. For unimodal rainfall, when the rainfall return period is less than 20 years, rainfall with more advanced peaks will result in more severe inundation. When the rainfall return period is higher than 20 years, the further back the rainfall peak, the more severe the inundation. At the same time, the difference in peak inundation from different types of rainfall decreases as the recurrence period increases.

When addressing urban flooding, it is advisable to prioritize the identification of bimodal rainfall patterns, as they often result in pronounced waterlogging. In the case of single-peaked storms characterized by short recurrence periods, particular attention should be given to storms exhibiting early peak occurrence times. Conversely, for single-peak storm events with extended recurrence periods, the severity of waterlogging intensifies with later peak occurrences, necessitating proactive measures to mitigate the associated risks well in advance.

3.3. Inundation Extent Analysis

Figure 6 shows a map of the local inundation risk for each of the 5-year rainfall patterns. Comparing the differences in the distribution of inundation depths due to the different rainfall patterns, it can be seen that the bimodal rainfall pattern results in the greatest extent of inundation, followed by the unimodal rainfall pattern when r = 0.25, and the unimodal rainfall pattern when r = 0.75 results in the least extent of inundation.

Table 4. Peak inundated area and growth rate of inundated area between adjacent recurrence periods.

Reproduction Period/a	Peak Flooded Area/Million m²			Growth Rate/%
	r = 0.25	r = 0.50	r = 0.75	r = 0.25	r = 0.50	r = 0.75
1	1063.1	1124.8	1021.5	0	0	0
5	1367.3	1442.4	1346.6	28.53	28.12	31.66
10	1555.1	1621.2	1532.5	13.71	12.40	13.75
20	1674.5	1770.3	1623.4	7.63	9.17	5.92
50	1853.3	1923.4	1877.4	10.67	15.16	15.63
100	2001.1	2040.4	2023.3	8.01	6.09	7.75

presents the peak inundation area and growth rate of inundation area between adjacent return periods to visualize the differences in inundation area resulting from different rainfall patterns. The results show that the inundated area increases with the increase in the recurrence period. Floodwater initially covers low-lying areas, and gradually inundates higher areas around buildings due to the increasing rainfall intensity. By the 100-year rainfall, almost all of the areas excluding the ones covered by buildings are inundated, resulting in a slower growth trend of the inundated area. Additionally, there are differences in the peak inundation areas for the same rainfall return period due to different rainfall patterns. In all cases, the bimodal rainfall produced a higher area of inundation than the unimodal rainfall. For a return period of less than or equal to 20 years, the extent of inundation is greater for unimodal rainfall with a rainfall factor (r) of 0.25 compared to that of r = 0.75. Conversely, for a return period greater than 20 years, the extent of inundation is lower for r = 0.25 unimodal rainfall compared to that of r = 0.75.

It can be seen that the peak inundation area resulting from the design rainfall of the three rainfall types increases with the increase in the recurrence period, and the growth trend gradually becomes slower. The difference in the peak inundation area caused by the different rainfall types at the same return period is the same, with the bimodal rainfall producing the largest inundation area and the difference in inundation area between the two unimodal rainfall types following the same pattern as the peak inundation.

In addition to the Chicago method, the Huff method, the Pilgrim & Cordery method and the triangular method are also widely accepted as common methods for deriving urban design floods [33]. In contrast, the Chicago rain pattern peak occurrence time is determined by the peak position coefficient r, which is easy to calculate and highly flexible, and is therefore the most widely used. However, the method still has some limitations, and continuous improvement is needed to design storm rain patterns to meet the complex and variable situation of urban extreme precipitation in the context of climate change. In addition, studying the set of rain patterns for different types of disaster-causing precipitation based on the measured data and determining the most probable design rain pattern by combining the probability distribution of the occurrence of different rain patterns can be an important idea for urban design flood calculation.

4. Conclusions

Based on the MIKE model, this paper projected inundation scenarios for different design rainfall patterns and compared and analysed the total inundation and inundation extent. The main conclusions are as follows:

• Bimodal rainfall produces the highest peak inundation volume and the highest risk of inundation. For unimodal rainfall, when the rainfall return period is less than or equal to 20 years, a more forward rainfall peak leads to a more severe inundation situation, while for a return period greater than 20 years, a rainfall peak that is further back leads to a more severe inundation situation. As the return period increases, the difference between the peaks of inundation caused by different types of rainfall decreases.
• By extrapolating scenarios of the inundation process, the peak inundation area produced by the design rainfall of all three types increases with the increase in the return period, and the growth trend gradually becomes slower. The peak inundation areas resulting from different rainfall types vary with the same return period, with bimodal rainfall producing the largest inundation areas, and the difference in inundation areas between the two unimodal rainfall types following the same pattern as their peak inundation amounts.

This study can help to carry out more reasonable and effective flood control work, and has some application prospects. It has certain guiding significance for urban flood forecasting. It is recommended that when dealing with urban flooding, the first thing to consider is bimodal rainfall, which tends to produce severe waterlogging. For single-peaked storms with short recurrence periods, attention should be focused on storms with early peak occurrence times. For single-peak storm conditions with a long recurrence period, the later the peak of the storm occurs, the more severe the degree of waterlogging generated, which should be addressed well in advance.