Construction and application of sponge city resilience evaluation system: a case study in Xi’an, China

Urban vulnerability is evident when highly complex flood risks overlap with diverse cities, and it is important to enhance the resilience of cities to flood shocks. In this study, a sponge city resilience assessment system is established considering engineering, environmental and social indicators, and the grey relational analysis method (GRA) is used to quantify sponge city resilience. At the same time, a multi-objective optimization model is established based on the three dimensions of water ecological environment, drainage safety, and waterlogging safety. The optimal configuration of grey-green infrastructure is weighed by combining the ideal point method, aiming to ensure that cities effectively reduce flood risk through the optimal configuration scheme. Taking the Xiaozhai area in Xi’an as the study area, the evaluation results show that the grey relational degree (GRD) of the resilience indexes of the original scheme is between 0.390 and 0.661 under the seven different return periods, while the optimization scheme ranges from 0.648 to 0.765, with the best sponge city resilience at a return period of 2a. Compared with the original scheme, the optimized sponge city resilience level increases from level II to nearly level I in the low return period and from level IV to level II in the high return period, indicating that city’s ability to cope with waterlogging and pollution is enhanced significantly. Besides, the main factor affecting the sponge city resilience is the runoff control rate, followed by pollutant load reduction rate, which can provide a methodological framework for the assessment and improvement of sponge city resilience.


Introduction
With the rapid urbanization process, the phenomenon of the urban rain island effect is becoming more and more obvious; once there is continuous rainstorm weather, it will directly lead to regional waterlogging in the city (Jacobson 2011;Le Floch et al. 2022), and urban water pollution incidents occur frequently (He et al. 2008). It can be seen that the vulnerability of cities to future disasters is increasing proportionally (Ribeiro and Goncalves 2019). While traditional emergency management plans mainly respond to disasters passively, ignoring the adaptability of urban systems themselves (Geis 2000), resilience theory has been applied to urban management in various countries as a new research perspective, China proposed to build resilient cities in the 14th Five-Year Plan, and UNISDR (2014) proposed a resilience scoring system to assess the resilience level of cities. At the same time, international organizations also provided relevant support for the construction of resilient cities. The 100 resilient cities plan proposed by the Rockefeller Foundation in 2013 aimed to provide technical and financial support for cities to develop and implement resilience plans to enhance their ability of withstanding external shocks or resilience (Spaans and Waterhout 2017).
Resilience, which means "returning to its original state" and is also often translated as "elasticity." Walker et al. (2004) pointed out that the concept of "elasticity" tends to give researchers an inertia of thinking about returning to the original state, which cannot fully cover the characteristics of the long-term adaptability of cities that they emphasize. Holling (1973) first applied the concept of resilience to the field of ecology, describing it as the ability of an ecosystem to return to a stable state after being disturbed. Meerow et al. (2016) argued that resilience refers to the ability of an entire urban system to maintain or rapidly restore desired functions in the face of disaster disruptions, as well as the ability to adapt to rapid transformation in response to current and future changes. However, how a static landscape environment can be sustainable in the midst of fickle disturbances and changes, the resilience theory proposed by Ahern (2011) provided new perspectives and approaches to the hybrid paradox of sustainability and stability.
At this stage, the understanding of sponge city resilience and indicators is still a scarce in nature, and there is a lack of systematic and effective quantitative framework for sponge city resilience evaluation and faces the problem of unsound sponge city construction indicators. Therefore, how to scientifically select appropriate indicators to quantify sponge city resilience is its core problem, and the establishment of a reasonable indicator system helps to accurately convert resilience theory into practice. Recently, Zhao et al. (2021) established an urban ecological resilience evaluation system based on the DPSIR framework and assessed the resilience of urban ecological networks using the ecological network analysis model. Based on a grey correlation method model of coefficient of variation, Long et al. (2022) constructed a VPOSR framework system to evaluate the carrying capacity of urban water environment from five aspects: vitality, pressure, organization, state, and resilience. Lu et al. (2022) used PSO-BP neural networks to quantify sponge city resilience in four subsystems: economy, society, environment, and technology, and selected indicators such as urban per capita GDP, urbanization rate, and per capita local financial expenditure on science and technology to analyze their comprehensive resilience. Mou et al. (2021) aimed to build five subsystem models, namely economy-environment-population-resource-technology, to assess the sustainability and resilience of cities under future threats. In previous studies, it is worth noting that the selection of resilience evaluation indicators tends to focus on macro-dimensional considerations, while the consideration of microscale indicators needs to be further strengthened. In this study, resilience indicators are selected for flood prevention and control, covering engineering, environmental, and social dimensions, which fully reflect the dynamic changes of the contribution of each system to resilience under different recurrence period conditions. Simultaneously, a reasonable selection of evaluation methods will help us to more accurately evaluate the performance of sponge facilities under flood impact, the bearing strength of each drainage system, and the resilience of the sponge city system restored to the best state. Therefore, this study uses the grey relational analysis (GRA) method of grey system theory proposed by Deng (1993) to extensively evaluate the resilience of sponge cities and identify the strong correlation factors affecting the resilience level.
Low impact development (LID) is effective in urban flood control. Many studies have been devoted to confirming the great potential of the combination of LID practices in spatial strategies for flood mitigation and improved urban drainage system performance (Kumar et al. 2022;Tansar et al. 2022). However, low impact development (LID) has limited hydrological capacity to respond to extreme events (Qiao et al. 2020), while Casal-Campos et al. (2018 noted that grey infrastructure lacks robustness in terms of sustainability due to imbalances in economic, environmental, and social benefits, and overcame these limitations by implementing hybrid solutions combining green retrofits and grey rehabilitations. Alves et al. (2018) proposed that combining sustainable green infrastructure with traditional grey infrastructure is the best way to ensure resilience before extreme events occur. It can be seen that the coupling of grey-green infrastructure is the most promising way to achieve urban resilience development and can effectively improve the stability and reliability of urban flood control management (Chen et al. 2021;Wang et al. 2022). At present, the exploration of the optimal layout of grey-green infrastructure under multi-goal orientation has also become a hot issue. By using the multiobjective optimization method, the differences in the optimal combination layout under the guidance of different benefits, flood risk, water quantity, and quality goals were weighed and compared (Li et al. 2019;Yao et al. 2022). Wang et al. (2021) considered two types of resilience in urban hydrology: technical and operational resilience, and evaluation system resilience based on life-cycle cost optimization coupled with grey-green infrastructure. Dong et al. (2017) focused on the role of different grey-green infrastructures in enhancing the resilience of urban drainage systems and considered the uncertainties of urbanization and climate change. The relationship between system resilience and the cost of LID infrastructures was compared. Relatively speaking, few studies have combined urban flooding with the general framework of sponge city resilience, and lack the analysis of urban subsystems under flood disasters and the comparison of resilience improvement under optimal configuration schemes. This research aims to fill this gap by innovatively proposing a sponge city resilience assessment framework system to improve the construction of sponge city, effectively focusing on solving the problem of flood prevention and flood control, and measuring the resilience improvement of the optimal allocation scheme under urban flood disasters through microscale indicators of engineering, environment, and society. Its main contributions are as follows: (1) To weigh the optimal allocation scheme of greygreen infrastructure with the goal of water ecological environment, drainage safety, and waterlogging prevention safety; (2) to establish a sponge city resilience assessment system based on grey relational analysis method to measure resilience improvement level of the optimal allocation scheme; (3) to explore the correlation of various resilience indicators and identifying the key factors affecting the resilience of sponge cities; (4) to propose some targeted suggestions of sponge city resilience improvement.

Study area
Xi'an is located in central Shaanxi Province, China, with an average annual precipitation of 583.7 mm. The season distribution of rainfall is very uneven, mostly concentrated in May to October, of which the rainfall from July to September accounts for 55.6% of the annual rainfall, with heavy rainfall occurring time to time. The research area (i.e., Xiaozhai area) is located in the Yanta District of Xi'an City, which is the largest urban core area in the downtown area of Xi'an. The total area of the research area is 30.12 km 2 , as shown in Fig. 1.

Sponge city resilience assessment system
In this paper, sponge city resilience is used to represent the ability of sponge cities to cope with flood disasters and runoff pollution. The assessment results can be used as the basis for the establishment of subsequent sponge facilities and the improvement of the sponge storage functions of cities. The overall framework is shown in Fig. 2. The right side of the figure represents the process of seeking the optimal configuration scheme of grey-green infrastructure by establishing a multi-objective optimization model. The left side shows the construction and evaluation of the sponge city resilience assessment framework system, based on which the correlation between the indicators of the three subsystems (engineering, environment, and society) and resilience is explored, and the resilience level improvement evaluation of the optimal configuration scheme is carried out. The indicator selection results are shown at the bottom of the figure.

Establishment of SWMM model
Generalization of the study area The study area is divided into 268 sub-catchments. The drainage network system is The land use consists of roads, industrial land, residential land, commercial land, and green space squares, which are divided into the pavement, roof, and green space according to modeling requirements.

Rainfall design
In this paper, the rainfall selects the Chicago rainfall patterns to generate a designed rainfall process of different sessions. The rainstorm intensity for Xi'an is specified as formula (1), and a total of 6 rainfall scenarios are set up during the design rainfall return period, namely, 1a, 2a, 5a, 10a, 20a, and 50a, with a rainfall duration of 2 h and a time step of 1 min. ratio of the annual rainfall in Xi'an is calculated as shown in Fig. S1, from which a rainfall depth of 17.4 mm is used for the case of 80% volume capture ratio of the annual rainfall (i.e., equivalent to a return period of 1.331a).

Model calibration and validation
Since the outlets are in a bustling street, it is difficult to measure the actual discharge flow process under the actual conditions. To overcome the problem that the measured data of the rainwater pipe network cannot meet the requirements, the model parameter calibration method based on the runoff coefficient is adopted (Xing 2009). That is, the simulated runoff coefficient obtained by the design field rainfall is compared with the actual integrated runoff coefficient in the research area, and the peak time is used as the calculation basis for the simulation value of the runoff coefficient, and then the parameters were iterated. The range of runoff coefficients of the underlying surface is shown in Table S1. The degree of dispersion of the two sets of data is analyzed by the coefficient of variation C (V) (Ψ), and the calculation is shown in where C (V) (Ψ) is the coefficient of variation between the simulated and actual integrated runoff coefficient; ∆Ψ and Ψ are the difference and the mean between the simulated and actual integrated runoff coefficients, respectively. The SWMM model is used to simulate the 2h design rainfall with a return period of 5a and 10a. The simulated integrated runoff coefficients compared to the actual values are shown in Table S2. The integrated runoff coefficients of the two designed rainfalls meet the requirements of 0.6 to 0.8 in urban densely built-up areas (MOHURD 2021). Meantime, the coefficients of variation of the simulated and actual integrated runoff coefficients under different return periods are − 3.80% and 4.78%, and the average value of the absolute value of the coefficients of variation is less than 5%, which means that the model has good reliability and can meet the simulation requirements.
Through the collection of relevant waterlogging data in the research area, heavy rain occurred in Xi'an City on July 24, 2016, with a 1h rainfall of 66.6 mm and a return period of more than 50 years. The pipe sections and points where ponding is more likely to occur in the statistical study area are shown in Fig. 3(a). The model parameters are verified using the return period 50a rainfall as the model input condition, and the simulation results are shown in Fig. 3(b). It can be found that the measured water accumulation point is consistent with the simulation results of the model, and there is a small amount of water accumulation in other areas of the model, so the model has strong rationality.

Multi-objective optimization method
Multi-objective optimal configuration of green infrastructure Four types of the most commonly used green infrastructures are adopted, including rain gardens (RG), sunken green belts (SG), permeable pavements (PP), and green roofs (GR). The specific parameter values are shown in Table S3. Comprehensively considering the observed parameters such as the land use and the distribution area of the building, the total area of LID practices shall not exceed 20% of the research area, and four types of LID practices are laid out in all sub-catchments at 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18%, and 20% of the area ratio, respectively, a total of 40 schemes. The size of LID practices is selected as the decision variable. Due to the large number of types of green infrastructure, "sponge equivalent" is used as a unified measurement method. The control effects (i.e., runoff control, pollution reduction, cost, landscape effect) of the specified unit quantity in different green infrastructures are used as the benchmark, and the corresponding effects of other facilities have comparable quantitative values compared with them. Since higher runoff control rate, pollutant load reduction rate, and landscape effect mean better, while lower cost means better, four objective functions are: where 1 is the runoff control rate for RG per unit area ratio; 1 is the pollutant load reduction rate for RG per unit area ratio; N i , N i , N i , andN i are the runoff control equivalents, pollution reduction equivalents, cost equivalents, and landscape effect equivalents of the i th LID practices, respectively ( N 1 =N 1 =N 1 =N 1 =1);x 1 ,x 2 ,x 3 , x 4 are area proportions of the RG, SG, PP, and GR, respectively. The area layout requirements of the 80% annual runoff control rate, the 40%  where ′ represents the additional runoff control rate required for an annual runoff control rate of 80% in the original scheme; ′ represents the additional pollutant load reduction rate required for an annual runoff pollutant load reduction rate of 40% in the original scheme.
Multi-objective optimal configuration of grey infrastructure It is difficult to cope with heavy rainfall events by setting LID practices only, and improving the storage capacity is still the main way to solve urban waterlogging. As studied by Duan et al. (2016), LID facilities can play a global role in flood control, while storage tanks can play a local role in controlling flood risk. Therefore, conduit transformations (CT; i.e., pipe diameter expansion) and additional storage tank (ST) volume are considered to improve the performance of the rainwater system based on the optimal scheme of green infrastructure. The growth of pollutants does not change when rainfall intensity is constant, so only the effect of pipe diameter on water volume regulation is considered. The design return period of the current rainwater system is less than once every 2 years in the study area, so, based on the current pipe diameter of the rainwater pipe network, enlarging the pipe diameter of the rainwater system from 5 to 100% in turn, with steps of 5%, with 100 mm as a grade, 100 mm is counted when the expanded pipe diameter is less than 100 mm. A multi-objective optimization model is constructed based on the 20 kinds of pipe diameter expansion ratio schemes as the decision-making variables, with the node overflow rate, conduit overload rate, node overload rate, and cost as the objective functions, and the pipe diameter expansion scale of 0-100% as constraint conditions. Pipeline costs mainly include material costs and construction costs; most of the research on the optimization of rainwater pipe networks has expressed the cost function as a unit price model, and the cost is only related to pipe diameter and burial depth. The cost formula for the fitted pipe unit price model is as follows (Jin 1990): (4) where C is the cost per unit length of the pipeline (CNY/100 m); D is the pipe diameter (mm); H is the average buried depth of the pipeline (m); F is the total cost of pipe network construction; L i is the length of the i th pipe.
By optimizing the volume of ST, the runoff control effect of rainwater can be effectively improved and the drainage pressure of the pipeline can be reduced. Therefore, based on expanding pipe diameter, a rectangular storage tank with an effective water depth of 10 m is designed, and the volume of the storage tank is changed by changing the area of the model storage unit. A volume standard of 200-700 m 3 /ha of the hardened area is used to design the 11 scenarios with a step size of 50 as the decision variables. The overflow, runoff control rate, and cost are used as the objective functions, and the standard range of 200-700 m 3 /ha hardened area for the volume of the ST is used as the constraint. The volume of storage is evenly distributed to ST in the study area, and it is arranged in front of the severe waterlogging node (i.e., the node with a waterlogging duration exceeding 0.5 h and overflow exceeding 1000 m 3 ) and outlets. The hardened area of each outlet is as follows (i.e., V is the total volume of the ST): Outlet PFK1: The catchment area is 10.78 km 2 , and the volume of ST is 0.42 V. Outlet PFK2: The catchment area is 7.63 km 2 , and the volume of ST is 0.3 V. Outlet PFK3: The catchment area is 7.23 km 2 , and the volume of ST is 0.28 V.
Optimal selection method of grey-green infrastructure This study constructs a multi-objective optimization model based on water ecological environment objectives, drainage safety objectives, and waterlogging prevention safety objectives. Ideal point method is used to determine the optimal configuration scheme of grey-green facilities under different rainfall scales, aiming to transform the multi-objective problem into a single objective problem that is easy to solve Zhu et al. 2022). By constructing an evaluation function, the value of each objective function is approximated to its optimal value as much as possible. The optimal value is regarded as the ideal point of the multi-objective optimization range when all objective functions reach the optimal value (minimizing the distance between each objective function and the ideal point); the ideal point at this time is taken as the optimal solution. Its function is constructed as where p is the number of objective functions; i is the weight; f i (x) is the i th objective function; f * i is the ideal point for the i th objective function.
In this study, the weights of the objective function are calculated based on the global sensitivity analysis method (Luan et al. 2017), and the original data is normalized to obtain the normalized matrix C = c ij m×n , and the influence of each index on the variation degree of evaluation result is separated by the variance decomposition formula. The global sensitivity is used to measure the influence degree, and then normalized according to the index weight sensitivity to obtain the index weigh finally: where S T ij is the sensitivity of the j th index weight of the i th evaluation object; S T j is the global sensitivity of each index;W j is the j th index weigh.

Selection of evaluation indicators
Given the problem of sponge city resilience assessment, 10 index factors are mainly considered from the aspects of engineering, environment, and society. At the engineering level, the relevant factors of sponge city drainage design and underlying surface were mainly considered. The environmental level is selected according to relevant national policies such as the Measures for Performance Evaluation and Assessment of Sponge City Construction. At the social level, indicators of the impact of urban waterlogging and runoff pollution on human life are considered, and a weight determination solution based on the global sensitivity analysis method is used to establish the index system for sponge city resilience evaluation, with the index system shown in Table 1.

Evaluation methods for indicators
The grey relational analysis method (GRA) was introduced to assess the resilience level of sponge cities under flooding. Its core idea is to determine whether the relationship is close by determining the geometric similarity of the curve geometry of the reference sequence and the original sequence, and the more similar the curves are, the higher the correlation between the corresponding sequences. In this study, the optimal values in the index data column of the evaluated object are used as the reference sequence V 0k , and the measured values of each T i is maximum overload hours under the return period of the i th years, T 50a is maximum overload hours of a return period of 50 years without LID practices indicator are the original sequences V ik . Since indicators C2, C8, C9 and C10 are cost-type indicators (the smaller the sample value, the better the indicator), while the remaining indicators are the benefit-type indicators (the larger the sample value, the better the indicator), the data is normalized in the process and the GRD is calculated, which is expressed as follows: where , 100, 100… 100};min i min k Δ ik ,max i max k Δ ik is two-level minimum and maximum differences, respectively; is the discriminant coefficient, ∈ [0,1]. Generally used = 0.5; w i is the weight of the i th indicator; ik is a grey correlation coefficient. The range of GRD is (0, 1). The higher the grey correlation between the correlation sequences, the closer the indicators of sponge city resilience in the region are to the optimal values, and the better the regional sponge city resilience (Huang et al. 2019).

Grades of evaluation indicators
According to the score of GRD, the resilience of the sponge city is divided into five grades, and the classification criteria of each evaluation level of sponge city resilience are as follows: level I (extremely strong ability to cope with waterlogging and pollution) ∈ [0.8, 1]; level II (strong ability to cope with waterlogging and pollution) ∈ [0.6, 0.8); level III (average ability to cope with waterlogging and pollution) ∈ [0.4, 0.6); level IV (poor ability to cope with waterlogging and pollution) ∈ [0.2, 0.4); level V (very poor ability to cope with waterlogging and pollution) ∈ [0, 0.2). The classification criteria for each resilience indicator are shown in Table 2.

Scheme optimization under water ecological environment objectives
According to the analysis of the regulation effect of water quality and water quantity of LID practices under the different proportions of layout schemes, it can be seen that LID practices have a relatively obvious reduction effect on low return period, and the runoff control rate and pollutant load reduction rate are approximately a straight line when the rainfall is 17.4 mm, as shown in Fig. S2. Therefore, the runoff control and pollutant reduction capabilities of SG, PP, and GR can be converted into RG runoff control and pollutant load reduction capabilities in the form of an equivalent. According to the simulation results, the proportion of area required to meet the total annual runoff control rate of 80% and the pollutant load reduction rate of 40% for each type of facility to be laid out separately can be calculated, as shown in Table 3. Taking the RG as a research unit (equivalent is 1), the runoff control capacity of 1% SG is equivalent to that of 0.75% RG, so the runoff control equivalent of SG is 0.75. Life cycle cost analysis (LCC) is used to obtain the present value cost Xu et al. 2019). The initial cost, operation and maintenance cost (O and M), and salvage value are shown in Table 3. The cost equivalents of RG, SG, PP, and GR are 1, 0.09, 0.26, 0.22, respectively. The landscape effect scoring criteria for different LID practices are as follows: RG (excellence, 4 points), SG (medium, 2 points), PP (medium, 2 points), and GR (good, 3 points). In summary, the landscape effect equivalents of RG, SG, PP, and GR are 1, 0.5, 0.5, and 0.75, respectively.
Applying the global sensitivity analysis to the empowerment, the global sensitivities of the annual runoff control rate, pollutant reduction rate, cost and landscape effect are calculated according to formula (8), which are 9.04, 12.18, 32.75, and 8.59, respectively. It can be seen that the global sensitivity of the cost index is high, which has a greater impact on the degree of variation of the evaluation results. According to formula (9), the weights are calculated as follows: annual runoff control rate (0.15), annual pollutant load reduction rate (0.19), cost (0.52), and landscape effect (0.14). The ideal point f * = (−20.2, −15.6, 5.55, −22.5) T for the multi-objective optimization domain of four functions is obtained from formula (7), and the total objective function is found: For this quaternion quadratic equation, the genetic algorithm function of MATLAB software is used to solve the equation, and the possible solutions in the Pareto leading edge solution set are screened. The results of the four LID layout ratios are taken: x 1 = 4.1778%, x 2 = 10.8222%, x 3 = 7.4814%, x 4 = 2.5186%. The min∅(f (x)) obtains the minimum value, that is, the value of the ideal point corresponding to the distance of each objective function is the smallest.

Scheme optimization under drainage safety objectives
To enable the study area to meet the drainage safety objectives, the rainwater system performance should be improved by expanding the pipe diameter based on the preferred scheme in the "Scheme optimization under water ecological environment objectives" section with the rainwater system design return period 5a as the rainfall condition. The SWMM model is used to simulate 20 grey-green infrastructures. The overflow and overload of nodes and conduits in the study area are shown in Table 4. It can be seen that 20 pipe diameter expansion schemes have alleviated the overflow and overloading of nodes, overloading of conduits. With the increase of pipe diameter, the number of overflow nodes decreases gradually. When the pipe diameter is enlarged by more than 55%, no overflow is generated at the study area nodes. When amplification ratio of the pipe diameter exceeds 40%, the number of pipe overloads is no longer significantly reduced, and the decreasing trend of the number of node overloads gradually slows down, which may be due to excessive runoff being diverted downstream by the upstream conduit, and excessive downstream flow still causes the pipeline to be overloaded. It is worth noting that the change of node overload rate is from 81.84 -29.35% -1.99%. Almost all nodes are in an overload state when the research area is in the original scheme. The increase in pipe diameter significantly reduces the overload rate of nodes. It is observed that the combination of LID and drainage system is very effective, which can give full play to the role of LID in controlling urban rainwater runoff, absorbing early rainfall, and the excess rainfall is discharged by the drainage system, which is consistent with the findings of Cheng et al. (2022). According to the simulation results, the node overflow rate, conduit overload rate, node overload rate, and cost data of 20 pipe diameter enlargement proportional schemes are normalized and fitted with polynomials. The global sensitivities of node  (8). It can be seen that the global sensitivity of the conduit overload rate is high and has a great impact on the variation degree of evaluation results. The four sub-target weights are calculated by the formula (9) as follows: node overflow rate (0.25), pipe section overload rate (0.29), node overload rate (0.22), and cost (0.24). A total objective function is shown in the formula (13). The optimal amplification ratio of the pipe diameter is: x = 0.45; at this time, min∅(f (x)) is the value of the ideal point corresponding to the distance of each objective function, which is the smallest: where x is the expansion ratio of pipe diameter.

Scheme optimization under waterlogging prevention safety objectives
To enable the study area to meet waterlogging prevention safety goals, ST is considered to be added based on the "Scheme optimization under drainage safety objectives" section drainage safety optimization scheme based on the return period of the waterlogging control design 50a. The results of surface runoff under the grey-green infrastructure combination scheme are further analyzed (Table 5). Since the LID layout ratio and the pipe diameter are the same for the 11 schemes of ST, the initial LID storage, final storage, infiltration loss, and surface runoff simulation results are equal. Results for the same return period reveal the reduction rate of the overflow is from 40.34-48.1% after adding 11 schemes, and the reduction rate of flooding loss is from 72.78-97.57% compared with the scheme LID + CT. It can be seen that the addition of ST can effectively store rainwater to delay its rapid discharge and reduce its overflow. Meanwhile, the runoff control rate of LID practices achieves 60.69% compared to the original scheme. This is because green infrastructure reduces the amount of stormwater entering the network by changing the subsurface conditions to enhance infiltration and evaporation, resulting in lower peak flows and runoff. External outflow shows a significant increase with the expansion of pipe diameter based on green infrastructure, which is caused by the grey pipe network being able to quickly collect runoff and discharge it through the rainwater pipe network. It is clear that the combined grey-green infrastructure can well alleviate the pressure on the drainage system and successfully shift from an urban drainage-based stormwater management strategy to a rainwater retention and sustainable use strategy that facilitates urban development. And it is expected to improve the resilience of stormwater systems. The overflow and runoff control rate refers to the simulation results of 11 storage volume schemes, and the unit cost of ST is estimated at 1200 CNY/m 2 using the technical guide (MOHURD 2015). The total objective function is as follows: where x is the volume of ST (m 3 /100 m 2 hardening area). The optimal volume setting standard of ST is x = 3.5. At this time, the min∅(f (x)) to obtain the minimum value, that is, when the volume of ST is 350 m 3 /ha, the objective function has been approximated to the corresponding ideal optimal value to the greatest extent. The optimal scheme is 4.1778% RG + 10.8222% SG + 7.4814% PP + 2.5186% GR + 45% CT + 350m 3 /ha ST.

Comprehensive evaluation of sponge city resilience
Combined with the AHP-entropy method (Zhong et al. 2022), the final weight w i of the 10 indicators is determined, and obtained sponge city resilience evaluation values with different return periods under the optimization scheme, as shown in Table 6. The resilience of the sponge city shows a slight upward trend with the increase of the return period, reaching the best state at the return period of 2a with GRD of 0.765, and then gradually decreases under the high return period, reaching the lowest at the return period of 50a with GRD of 0.648, which is related to the runoff control rate and peak flow reduction rate maintained at a high level. In addition, the pollutant load reduction rate at a return period of 2a increased by 18.89% over the rainfall scenario of 17.4 mm required to meet the annual runoff target, and there was no flooding and the fastest recovery time for overloads in the pipe section. We noticed that different return periods can affect the effectiveness of each subsystem in improving resilience of the sponge city. Under the high return period, cities need to be more resilient to flood disasters, and the resilience assessment method based on scenario simulation can help to scientifically formulate urban flood prevention and control measures in advance according to different rainstorm scenarios.

Correlation analysis of subsystem evaluation indicators
As can be seen from Fig. 4, the ground impermeability (C2) is the key index of the engineering subsystem, and the higher the correlation coefficient value, the stronger the correlation between this index and urban resilience, which illustrates that the increase of hardened pavement seriously restricts the city's ability to improve the response capacity of stormwater disasters. Soil infiltration capacity (C3) decreases sharply with the increase of the return period. The index is close to 0.4 under the return period of 50a, indicating that its influence on sponge city resilience under the high return period is decreasing. In the environmental subsystem, the GRD of pollutant load reduction rate (C6) increases from 0.38 to 0.66 at the return period of 1a to 50a, indicating that the index has a positive impact on the improvement of sponge city resilience. The runoff control rate (C4) and the peak flow reduction rate (C5) show a downward trend with the increase of the return period, showing that the problem of waterlogging caused by excessive runoff seriously restricted sponge city resilience. The most obvious indicator of social subsystem change is the conduit overload recovery time (C10), which decreases significantly with the increase of the return period, illustrating that sponge city resilience harms the high return period. Under the low return period, the correlation between the proportion  . 4 The variation trend of correlation of sponge city resilience evaluation index of subsystem (engineering, environment, society) in the return periods of 1a-50a of waterlogging volume (C8) and the proportion of waterlogging nodes (C9) is close to 1, it can be seen that the waterlogging problem is closely related to sponge city resilience.
The main factors affecting sponge city resilience can be discussed by GRA. The weighted correlation degree of the indexes is shown in Table 6. The relational degrees between the ten evaluation indexes and sponge city resilience are C4 > C6 > C8 > C9 > C5 > C7 > C10 > C3 > C2 > C1. Among them, the runoff control rate (C4) is highly correlated with sponge city resilience with a relational degree of 1.526, and its influence degree on sponge city resilience fluctuates between 28.7% and 30.6% under different return periods, as shown in Fig. 5. The next correlation with sponge resilience is pollutant load reduction rate (C6) and the proportion of waterlogging volume (C8), both of which increase slightly with the increase of the return period, showing that these three indicators can well evaluate the ability of cities to cope with waterlogging and pollution. Therefore, the overall enhancement of sponge city resilience cannot be achieved without mutual coordination among the subsystems. In the planning stage, the weaknesses of each subsystem of the system should be considered comprehensively according to the needs of different periods, aiming to provide specific guidance programs to enhance urban rain and flood disaster resilience.

Improvement analysis of sponge city resilience
The grey relational degree of the optimization scheme from Fig. 6 is above 0.648, indicating that there is an obvious correlation between these influencing factors and sponge city resilience. According to the sponge city resilience level division standard in Table 2, it can be seen that, compared with the original scheme in the study area, sponge city resilience of the optimization scheme is still level II under the 1a, 1.331a (i.e., 17.4 mm) return period, but it is close to level I. Sponge city resilience is increased from level III to level II under the rainfall of 2a, 5a, 10a, and 20a, and from level IV to level II under a rainfall return period of 50a. This result shows that the ability of the study area to cope with waterlogging and pollution can be effectively improved by combining the grey-green infrastructure. Sponge city's resilience gradually declines with the increase of the rainfall return period, but the selected optimization scheme can still cope with the city's waterlogging and pollution well under the 50a return period and can meet the requirements of water ecological environment and water safety.
According to the analysis of the correlation of each resilience index, we can improve the resilience level of sponge cities from the following four aspects: Firstly, combining waterlogging control with rainwater utilization enhances the recycling of water resources. Secondly, it is also possible to effectively control runoff by strengthening the combined deployment of grey-green infrastructure to enhance the resilience of urban subsystems to flood disasters. Thirdly, paying more attention to reducing pollution load emission at the source is one of the most direct and effective measures to alleviate the resilience of sponge cities, which is consistent with the study of Chai and Zhou (2022). In addition, safe and sustainable cities need government departments to strengthen the management mechanism of resilience construction from the management level, and it is inseparable from the public's support and promotion of resilience construction.

Conclusions
Finding ways to effectively assess and respond to future uncertain shocks is essential for urban stormwater management and urban ecological construction. In this study, the sponge resilience evaluation index system constructed is helpful to explore the methods and paths of evaluating and enhancing the resilience of sponge cities and quantitatively evaluates the optimal configuration scheme under a multiobjective optimization model for grey-green infrastructure based on this system. This paper reports the findings of a case study in the Xiaozhai area of Xi'an.
The runoff control rate increases by 42.43% after the deployment of LID facilities, which indicates LID has a good effect on alleviating runoff. With the combination of grey-green infrastructure, the node overload rate is reduced from 81.84 -29.35 -1.99%, and the conduit overload rate is from 39.85 -12.13 -0%. It can be seen that increasing the pipe diameter can alleviate the node and conduit overload situation and increase the external outflow. If the sponge city construction process needs to reduce flooding loss, priority should be given to the increasing volume of the storage tank. Under different optimization objective functions, the possible solutions of Pareto's frontier solution set are screened, and the optimal scheme of 4.18%RG + 10.82%SG + 7.48% PP + 2.52%GR + 45%CT + 350m 3 /ha ST as the optimal scheme of the study area. Sponge city resilience is evaluated and shows a slight upward trend with the increase of the return period, and then shows a downward trend under the high return period based on this optimization scheme. Sponge city resilience is optimal at a return period of 2a, with a grey relational degree of 0.765. Compared with the original scheme, sponge city resilience has been greatly improved after optimization and increased from level II to near level I under the low return period. It is upgraded from level IV to level II under the high return period, which shows that the ability to cope with waterlogging and pollution is strong, and it can meet the requirements of water ecological environment, drainage safety, and flood prevention safety goals. It can be seen that the combination of green and grey infrastructure can not only effectively reduce runoff and alleviate waterlogging but also provide further potential in enhancing system resilience.
Ten indicators were widely selected to construct a sponge resilience assessment system in the fields of engineering, environment, and society, and from the perspective of the correlation between the evaluation indicators of each subsystem and sponge city resilience, C4 > C6 > C8 > C9 > C 5 > C7 > C10 > C3 > C2 > C1 under low return period. The strongest correlation is the runoff control rate (C4), followed by the pollutant load reduction rate (C6). This means that managers should pay more attention to the investment in runoff control and pollution control, not only to reduce the discharge of pollutants from the source but also to use greygreen facilities to transfer runoff and highlight the improvement of the water environment. The quantitative method of the sponge city resilience system and the multi-objective optimal configuration framework proposed by this institute can be applied to the quantitative assessment of urban capacity to cope with waterlogging and pollutants and can be used as the establishment basis for subsequent sponge function improvement.
There are also some limitations in this study. The indicators of sponge cities still need to be systematically improved, and the influence of hydrometeorological, geographical, and economic factors can be considered. This study does not analyze the coupling synergistic effect between the indicators, and it needs to be further clarified whether the dynamic interaction between the influencing factors in urban development will have corresponding positive and negative effects on the resilience of sponge cities. In addition, multi-objective optimization problems based on system resilience in different dimensions can also be studied in depth in the future.