Optimization design of urban rainwater and flood drainage system based on SWMM

Xihan Cao

doi:10.1515/nleng-2025-0146

Article Open Access

Optimization design of urban rainwater and flood drainage system based on SWMM

Xihan Cao

Published/Copyright: August 21, 2025

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From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

As global climate change and urbanization accelerate, urban rainwater and flood drainage systems are facing increasingly severe challenges. Traditional drainage system design methods are no longer able to meet the complex needs of modern cities. To improve the overall performance of urban rainwater and flood drainage system, a coupling model of multiobjective optimization algorithm and rainstorm management model is constructed. This model has been used for comprehensive optimization of urban rainwater and flood drainage systems. In the comparative analysis of the proposed coupling model, the standard deviation of the total overflow of the nodes was 65 million yuan. Then, the empirical analysis of the urban stormwater drainage system proposed in the study shows that the total discharge of the drainage outlet of the study model is 4428.73 and 1386.49, respectively, with the increase in time in the recurrence period of 2 and 50-year rainfall. In addition, the research model achieved remarkable results in the reduction in peak flow and water depth, increasing the drainage efficiency by 15.7% on average. This research not only provides new theoretical basis and practical guidance for the optimization design of urban rainwater and flood drainage systems, but also has important significance for enhancing the ability of cities to respond to extreme climate events and reducing urban water-logging disasters.

Keywords: SWMM; drainage system; optimization algorithm; coupling model; empirical analysis

1 Introduction

In the process of urbanization, the urban rainwater and flood drainage is becoming increasingly prominent, especially in the context of high-density population and rapid urbanization [1,2]. The design and operation of urban rainwater and flood drainage systems are crucial for ensuring the normal operation of cities and the quality of life of residents [3]. However, due to factors such as the continuous expansion of urban scale and climate change, traditional urban rainwater and flood drainage systems often find it difficult to cope with the increasing pressure of rainwater and flood [4]. To effectively address urban storm-water drainage issues, a comprehensive and sustainable optimization design method must be adopted. Storm Water Management Model (SWMM) is used to simulate and analyze the urban rainwater and flood discharge [5]. It is widely used in fields such as hydrology, hydrogeology, and environmental engineering to predict and manage rainwater and flood problems in urban areas [6]. In addition, the SWMM can also simulate the drainage performance of urban drainage systems, including pipeline flow rate, pump station operation, sewage treatment, and other aspects [7]. Simulating the performance of drainage systems in different scenarios can provide decision support for urban planning and design, such as optimizing drainage system design, improving the operation and maintenance of drainage facilities, etc. [8]. Based on the SWMM, different design schemes can be simulated and evaluated to select the optimal solution. This study applies the SWMM to the optimization design of urban rainwater and flood drainage systems, aiming to improve the drainage and flood prevention performance of the drainage system, while reducing the construction and maintenance costs of infrastructure. Previous studies have comprehensively considered the multi-dimensional influence of stormwater drainage in the process of urbanization, and combined SWMM model with the optimal design of urban stormwater drainage system. The limitation of the definition lies in that the model may not be able to completely restore the real scene when simulating the stormwater situation under complex terrain and extreme climate conditions, and there are some idealized assumptions. Through the implementation of this research, it is hoped that new ideas and methods can be provided for the optimal design of urban rainwater and flood drainage systems.

2 Related works

Urban storm-water drainage system refers to the facilities and engineering used in the city to collect, transport, and discharge rainwater. Its purpose is to effectively discharge rainwater from the city during rainfall, to prevent problems such as water-logging and flooding and ensure the normal operation and safety of the city. Many experts have conducted relevant research on urban rainwater and flood drainage systems. Mohammadiun et al. proposed a method to explore the impact of bottleneck blockage on the resilience of urban rainwater drainage systems. Empirical analysis showed that bottleneck blockage had a significant impact on the resilience of urban rainwater drainage systems [9]. Hussain et al. built a SWMM simulation method to explore the impact of land use and climate change on the performance of rainwater drainage systems. The research results indicated that these two had a significant impact on the performance of rainwater drainage systems. With the process of urbanization, the increase in impermeable area results in an increase in runoff coefficient and an increased burden on drainage systems [10]. Shepley et al. proposed an evaluation method for the impact of the interaction between farmland drainage systems and groundwater on urban karst. The research results indicated that the interaction between agricultural drainage systems and groundwater had a significant impact on the formation and development of urban karst. Adopting this research method could effectively implement soil and water conservation measures, increase surface vegetation coverage, reduce soil erosion, and thus reduce negative impacts on groundwater [11]. Saata et al. conducted in-depth research on the impact of the interaction between agricultural drainage systems and groundwater on sediment in rainwater drainage systems. The agricultural drainage system indirectly affected the sediment in the rainwater drainage system by affecting the quality and flow of groundwater. These sediments could serve as adsorbents for organic pollutants in the natural environment, separating pollutants from water and reducing water pollution [12].

The SWMM can simulate and predict various rainwater runoff management measures. Its effectiveness and benefits in practical environments provide scientific basis for decision-makers. Some domestic and foreign researchers have made outstanding achievements in the SWMM. Jin-Mei et al. proposed a rainfall control scheme for urban roads in spillway ground on the SWMM for urban rainwater and flood drainage systems. The research results indicated that the SWMM could accurately simulate the operation of urban rainwater and flood drainage systems, providing a reliable tool for optimizing design. The accuracy and reliability of the model were verified through comparison and analysis with actual data [13]. Arjenaki et al. developed a SWMM-based low impact development (LID) modeling method for the design and impact of urban runoff collection networks. The SWMM could accurately simulate the operation of urban runoff collection networks, providing a reliable tool for optimizing design. Through parameter settings and model construction, the problems and challenges of the system were identified [14]. For the evaluation of urban permeable surface infiltration methods, Parnas et al. combined SWMM and the hydrological rainfall-runoff model for evaluation. The research results indicated that the SWMM could accurately simulate urban surface runoff and infiltration processes, providing strong support for the evaluation of permeable surface infiltration methods. Through parameter settings and model construction, the effects were compared. Meanwhile, combined with the hydrological rainfall-runoff model, the advantages and disadvantages of different infiltration methods were evaluated and compared [15]. Randall et al. used the SWMM to simulate and compare on-site observations on the evaporation and flow issues of lined permeable pavement. Comparing the simulation results of the SWMM with on-site observations, the model could accurately simulate the evaporation and flow processes of the lined permeable pavement [16].

In summary, numerous domestic and foreign scholars have conducted extensive research and analysis on the optimization of urban rainwater and flood drainage systems based on the SWMM. There have been significant breakthroughs in the improvement and application of the SWMM. In this study, based on the SWMM, the urban rainwater and flood drainage system has been optimized, which has strong potential application value.

3 Optimal design of urban rainwater and flood drainage system based on SWMM

3.1 Construction of urban drainage system based on SWMM

SWMM is a dynamic precipitation runoff simulation model primarily applied to simulate a single precipitation event or long-term water quantity and quality simulation in a city. This model can simulate runoff, water quality, hydrology, and hydraulic conditions, track and simulate the water quality and quantity of runoff, as well as the flow rate, depth, and quality of water in each pipeline and river. Figure 1 displays the schematic diagram of the SWMM.

Figure 1

Schematic diagram of SWMM.

The infiltration model is an important component of the SWMM, used to calculate the water infiltration from the surface into the soil after rainfall [17]. In the SWMM, three infiltration models are available for selection: Horton model, Green-Ampt model, and SCS-CN model [18]. The Horton model is an empirical formula ground on rich soil infiltration experimental data, which is suitable for describing the changes in infiltration rate during long-term rainfall processes [19]. This model assumes that the infiltration rate decreases exponentially over time until it reaches the minimum. The infiltration rate is shown in Eq. (1).

(1) f p = f c + ( f 0 − f c ) e − α t ,

where f c signifies the stable infiltration rate. f 0 signifies the initial infiltration rate. α signifies the attenuation coefficient of infiltration. t represents the infiltration time. According to the definition of permeability coefficient, the permeability coefficient is shown in Eq. (2).

(2) f = ( S max − S ) T ,

where T represents a constant related to soil type and soil moisture content. The Green-Ampt model takes into account the influence of soil moisture content, which describes rapid infiltration and high soil moisture content [20]. In the Green-Ampt model, the cumulative infiltration depth of rainfall is shown in Eq. (3).

(3) h = 16 × t × ( 1 − θ 0 ) A ,

where t represents the rainfall time. A represents the catchment area. θ 0 represents the initial moisture content. The SCS-CN model describes the infiltration process under different soil textures and surface cover conditions [21]. In the SCS-CN model, the total runoff is shown in Eq. (4).

(4) Q = P − S Δ t ,

where P represents the rainfall. S represents the surface water storage capacity. Δ t represents the interval of rainfall time. The surface runoff model simulates the process of runoff from precipitation to the formation of the watershed outlet section [22]. It describes how precipitation forms runoff through surface runoff and runoff processes. In the SWMM, the surface runoff model is mainly implemented through hydrological and hydraulic modules [23]. The hydrological module mainly simulates the processes of surface runoff production and convergence, including the production and convergence processes [24]. The runoff of the surface runoff model is shown in Eq. (5).

(5) Q = ( I − 0.2 S ) 2 ( I + 0.8 S ) ,

where I represents the rainfall. S represents the soil hydraulic conductivity. The soil hydraulic conductivity is shown in Eq. (6).

(6) S = 25.4 1,000 C N − 10 ,

where C N represents the number of numerical curves. The vector expression of the control flow equation is shown in Eq. (7).

(7) ∇ ⋅ u + ∂ ρ ∂ t = 0 ,

where ∇ ⋅ u represents the divergence of velocity field u , that is, the net rate of fluid outflow per unit volume, and ∂ ρ ∂ t represents the rate of change of fluid density ρ with time. The characteristics and scope of application of SWMM infiltration and surface runoff modules are displayed in Table 1.

Table 1

Characteristics and application range of SWMM infiltration and surface convergence modules

Module name	Calculation method	Method characteristics	Scope of application
Infiltration module	Horton equation	Assume that rainfall intensity is always greater than infiltration rate; infiltration rate changes with time. Soil storage capacity is not considered	It is suitable for small watershed and has few parameters to be determined
	Green-Ampt equation	The soil layer contains a rapidly changing dry and wet interface. Soil saturation and unsaturated infiltration were calculated separately. Infiltration varies with time	The requirements of soil parameters are high, but the parameters to be determined are few
	SCS-CN method	The CN of the underlying surface is different. The effect of initial water content on the flow-producing process is considered	It is suitable for calculation of large river basin and heavy rainstorm intensity
Surface convergence module	Nonlinear reservoir method	Assume that each sub catchment area is a rectangle of width W: there is a physical conceptual basis	The parameters are easy to determine and the calculation results are of high precision

In the SWMM, the research area is first divided to multiple sub catchment areas. After dividing sub catchment areas, the topology structure of the pipeline is constructed. By establishing the topology structure of the pipeline, the runoff direction and flow distribution of each sub catchment area can be clarified. Finally, based on the topology of the pipeline, the runoff from each sub catchment area is allocated to the nearest inspection wells.

3.2 Improved multiobjective optimization algorithm coupled with SWMM

In the SWMM drainage model, the cost and hydraulic performance of the pipeline network need to be considered simultaneously, which are two interrelated but mutually restrictive goals. Therefore, the study selects pipeline diameter and pipeline slope as optimization variables to construct a Multiobjective Optimization Problem (MOP) model. It is composed of multiple conflicting objectives. These goals are often not optimal simultaneously. Therefore, a balanced approach is applied to address these objectives [25]. The mathematical expression for MOP is shown in Eq. (8).

(8) minimize F ( x ) = ( f 1 ( x ) , f 2 ( x ) , … , f i ( x ) ) s . t . x ∈ X ,

where f i ( x ) signifies the i th objective function. x signifies the decision variable. X signifies the feasible domain of the decision variable. The objective in MOPs is multivariate, which means that there are multiple objective functions that need to be minimized or maximized. The solution to MOPs is usually a set of Pareto optimal solutions. This set of solutions is non-dominated on all objective functions, meaning that there are no other solutions that can simultaneously improve the performance of this set of solutions on all objectives. The Pareto optimal solution diagram is shown in Figure 2.

Figure 2

Pareto optimal solution diagram.

The Pareto optimal solution set is displayed in Eq. (9).

(9) P ∗ = { X ∗ } = { X ∈ Ω ¬ ∃ X ′ ∈ Ω , f j ( X ′ ) ≤ f j ( X ∗ ) ( j = 1 , 2 , … , r ) } ,

where X ∗ represents the optimal solution. Ω represents the solution space. f j represents the objective function. r represents the number of objective functions. The hypervolume metric is an indicator applied to evaluate the performance of multiobjective optimization algorithms. It evaluates the quality of the solution set by calculating its volume in the target space. The basic idea of the hypervolume metric is to obtain the metric value by calculating the area or volume between the Pareto front and a reference point. The hypervolume index of solution set S is shown in Eq. (10).

(10) H V ( S ) = 1 N ∑ i = 1 N ( ∑ j = 1 N d ( f 1 ( x i ) , f 1 ( x j ) ) ) ( ∑ k = 1 N d ( f 2 ( x i ) , f 2 ( x k ) ) ) ,

where N signifies the individuals in the solution set S. d ( f 1 ( x i ) , f 1 ( x j ) ) and d ( f 2 ( x i ) , f 2 ( x k ) ) represent the Euclidean distances of individuals in the solution set on the first and second objectives in the target space, respectively. The Non-dominated Sorting Genetic Algorithm-II is a multiobjective optimization method ground on dominance. Non-dominated sorting utilizes the concept of Pareto optimal solution to classify individuals in the population. Individuals with higher non-dominated states are ranked higher, allowing them to select the more outstanding individuals and have a greater chance of entering the next iteration. The crowding degree comparison operator uses crowding degree to measure the distribution of individuals in the population, thereby maintaining the distribution and diversity of the solution population. The crowding degree F is shown in Eq. (11).

(11) F = max ( max ( f i ( X ) ) − f i ( X ) ) ( max ( f i ( X ) ) + min ( f i ( X ) ) − 2 ⁎ f i ( X ) ) ,

where f i ( X ) signifies the value of the i th objective function. max ( f i ( X ) ) and min ( f i ( X ) ) represent the maximum and minimum values of the i in the population. The flow chart of improved multiobjective optimization algorithm coupled with rainstorm management model is shown in Figure 3.

Figure 3

The flow chart of improved multiobjective optimization algorithm coupled with rainstorm management model.

From Figure 3, after generating the initial population, for each individual, the study extracts relevant information by running SWMM simulations. This study focuses on parameters such as node burial depth and pipeline diameter, which are used to calculate pipeline costs. At the same time, the overload time of each node is extracted to determine the overall overload time. In addition, data such as node overflow and burial depth are extracted to evaluate constraint conditions. Finally, it is evaluated based on the individual’s objective function and constraints.

3.3 Optimization design of urban rainwater and flood drainage system based on coupling model

LID is a storm water management technique that controls storm water runoff and pollution through decentralized and small-scale source control, bringing development closer to natural hydrological cycles. Cost investment is an important consideration when choosing the scale of LID measures. Therefore, when formulating the LID deployment plan, various factors should be comprehensively considered, including technical feasibility, environmental impact, economic benefits, etc., to determine the optimal scale and configuration. Concave green space is a LID technology that utilizes open spaces to receive and store rainwater [26,27]. This green space utilizes open spaces, such as green spaces and roads, to naturally infiltrate rainwater and reduce runoff discharge. The cost of concave green space is as shown in Eq. (12).

(12) P = S × ( H × p + p 1 + p 2 ) ,

where S represents the green space area. H represents the depth of depression. p represents the unit price. p 1 represents the cost of soil improvement. p 2 represents the other expenses. Green roof is a LID technique that involves planting vegetation on the roof. Planting plants on the roof, green roofs can reduce rainwater runoff, improve urban microclimate, increase green area, and reduce heat island effects. The cost for green roofs is shown in Eq. (13).

(13) P ' = C × Y ,

where C represents the construction cost of a green roof. Y represents the lifespan of a green roof. Permeable pavement is a ground paved with permeable materials, which has good permeability performance. This paving design can allow rainwater to naturally penetrate underground, and reduce surface runoff, thus reducing flooding. It also helps to supplement groundwater and maintain ecological balance. According to different construction methods, permeable pavement has two types: fully permeable and semi-permeable. The study conducts experiments using semi-permeable pavement. Figure 4 displays the schematic diagram of the semi-permeable pavement structure.

Figure 4

Semi-permeable pavement structure diagram.

Semi-permeable pavement lays a layer of impermeable material on top of permeable material, allowing rainwater to partially penetrate underground and partially flow toward drainage pipes, which is suitable for areas with poor drainage. The cost of penetration pavement is shown in Eq. (14).

(14) P ″ = p 4 + p 5 + p 6

where p 4 represents the material cost. p 5 represents the construction cost. p 6 represents the maintenance cost. Among them, the material cost includes expenses for permeable materials, drainage materials, etc. Construction cost includes labor costs, machinery costs, etc. Maintenance cost includes daily cleaning, maintenance, and other expenses. The cost objective function of the research plan is shown in Eq. (15).

(15) F 1 = min ( S P + S 1 P ′ + S 2 P ″ ) ,

where S 1 signifies the total area of the green roof. S 2 signifies the total area of permeable pavement. The goal of the LID deployment plan is to enhance the infiltration, regulation, and utilization of rainwater runoff through strategies such as source control and decentralized treatment, promoting a virtuous water cycle in the city. To evaluate the hydraulic performance of the scheme, the total amount of runoff is used as the evaluation indicator. The function expression is shown in Eq. (16).

(16) F 2 = min V ,

where V represents the total amount of runoff. The optimized model solution flowchart is shown in Figure 5.

Figure 5

Flowchart of urban rainwater drainage system based on coupled model.

In Figure 5, the system flow of this study takes the following steps: First, the initial population is generated to cover the possible solution space, while avoiding premature convergence to the local optimal solution. Each individual is then simulated by SWMM, which accurately reflects the effects of stormwater management measures in different sub catchments, thus extracting the specific area of various types of green infrastructure under each scenario. After obtaining the simulation results, the study further calculated the implementation cost of each scheme and extracted the corresponding total runoff. Then, the scheme was evaluated according to two objective functions: total runoff and cost. Next through genetic operations such as selection, crossover, and variation, new populations are generated to simulate mechanisms such as natural selection, gene recombination, and gene mutation in the process of biological evolution, so that new populations can introduce new variations and diversity on the basis of retaining the original good genes. Finally, the process repeats until a preset number of iterations is reached.

4 Analysis of optimal design results based on the SWMM

4.1 Optimization result comparative analysis of the coupled model

The runoff coefficient reflects the surface runoff generated and the design, construction, and operation status of urban drainage systems. Point total overflow refers to the amount of water that overflows at a node under certain rainfall conditions. If the total overflow is large, it indicates that the drainage capacity is insufficient. It is necessary to increase drainage facilities or strengthen the maintenance and repair of pipeline networks, which also increases the total cost of infrastructure. The relationship between the runoff coefficient, total node overflow, and total cost of infrastructure of the research model is shown in Figure 6.

Figure 6

Relationship between runoff coefficient, total node overflow, and total cost of infrastructure. (a) Simulated runoff coefficient and (b) Q–E curve.

Figure 6(a) shows the simulated runoff coefficient of the research scheme. According to Figure 6(a), when the total cost of infrastructure increased, the cost of runoff coefficient was lower. The results indicate that while increasing infrastructure investment, the cost of runoff coefficient is effectively controlled. Figure 6(b) displays the runoff coefficient of the research scheme. In Figure 6 (b), when the total cost of infrastructure increased, the cost of total node overflow was lower. In the infrastructure construction, reasonable planning and design can reduce the cost of runoff coefficient, thereby achieving more efficient water resource management and utilization. The total cost of the designed infrastructure and the standard deviation of the total overflow of nodes vary with the number of iterations, as shown in Figure 7.

Figure 7

The total cost of the infrastructure and the standard deviation of the total node overflow with the number of iterations.

From Figure 7, the standard deviation of the total overflow of nodes in this research scheme tended to stabilize when the genetic algebra was 20, which was 3.58 m³. The total infrastructure cost in this research plan tended to stabilize when the genetic algebra was 30. The standard deviation of the total node overflow at this time was 65 million yuan. These data indicate that genetic algebra exerts a crucial function in the convergence and stability of scheme optimization. The objective function varies with the number of iterations, as shown in Figure 8.

Figure 8

The objective function changes with the number of iterations. (a) Study of the total cost of infrastructure for the total overflow of scheme cost and (b) runoff coefficient diagram of the study scheme.

Figure 8(a) shows the total infrastructure cost of node total overflow. In Figure 8(a), with the increase in genetic algebra, the total infrastructure cost of node total overflow showed a downward trend, ultimately reducing by 68 million yuan. This optimization effect is mainly attributed to the effective control of the total amount of water-logging by the plan. Figure 8(b) displays the runoff coefficient of the research scheme. From Figure 8(b), with the increase in genetic algebra, the runoff coefficient showed a gradually decreasing trend, ultimately decreasing by 0.008. This significant change further confirms the effectiveness of the research plan in reducing runoff coefficient and optimizing rainwater discharge.

4.2 Empirical analysis of new urban rainwater and flood drainage system

To verify the stability of the research model, the rainfall event in August 2021 in District A of a certain city is selected for validation. The Nash Coefficient (ENS) is selected as the evaluation index to simulate the load of outlet flow. The ENS coefficient is an important indicator for evaluating model performance. A large value usually means that the model has higher optimization during the simulation process. More accurate predictions are guaranteed. The load simulation results of outlet flow are shown in Figure 9.

Figure 9

Load simulation diagram of outlet flow.

In Figure 9, with the increase in time, the actual rainfall curve of District A in August 2021 showed two peaks. The simulated curve in this study closely matched the load of the actual outlet flow, without significant deviation. This result not only validates the effectiveness of the model, but also highlights its accuracy in traffic simulation. In addition, the ENS coefficient value of the model was greater than 0.7, indicating a higher model optimization. To verify the superiority of the research plan in the application of actual urban storm water drainage, comparative hydrological simulation experiments are conducted between the coupling model and traditional urban rainwater and flood drainage models such as InfoWorks CS model and SUSTAIN model. The experiment is conducted during the rainfall recurrence period of 2 years and 50 years. The total discharge of different models is compared, as shown in Figure 10.

Figure 10

Comparison diagram of total discharge flow process for different models. (a) P = 2a and (b) P = 50a.

Figure 10(a) shows the total discharge flow process of different models during the 2-year recurrence period of rainfall. According to Figure 10(a), the total discharge flow was 4428.73. Figure 10(b) shows the total discharge flow process of different models during the 50-year recurrence period of rainfall. According to Figure 10(b), the total discharge flow was 1386.49. Under these two conditions, comparative experiments are conducted on the main indicators of pollutants at the road outlet, including Suspended Solids (SS), Chemical Oxygen Demand (COD), Total Nitrogen (TN), and Total Phosphorus (TP). The pollution load reduction rates for different recurrence periods of each model are shown in Figure 11.

Figure 11

Comparison of pollution load reduction rates of different models in different recurrence periods. (a) P = 2a and (b) P = 50a.

Figure 11(a) shows the pollution load reduction rate during a 2-year recurrence period of rainfall. In Figure 11(a), the research model achieved significant reductions in SS, COD, TN, and TP loads. Among them, the reduction rate of SS load was relatively high, while the reduction rates of COD and TN load were also relatively stable. The reduction rate of TP load fluctuated, but overall it also showed a clear downward trend. Figure 11(b) shows the pollution load reduction rate during a 50-year recurrence period of rainfall. According to Figure 11(b), the SS, COD, TN, and TP loads of the research model all decreased. In terms of SS load, the reduction range of the study model was between 38.2 and 51.9%. In terms of COD load, the proportion of reduction ranges from 39.8 to 50.8%. For TN loads, the reduction rate ranged from 37.0 to 50.1%. In terms of TP load, the reduction was between 35.2 and 50.3%. This indicates that the research model has different effects on reducing pollution loads when dealing with different rainfall recurrence periods, but overall, they have achieved significant reductions.

5 Conclusion

Aiming at the frequent water-logging and poor drainage faced by urban rainwater and flood drainage systems, the SWMM was used to optimize the urban rainwater and flood drainage system. From the research results, the standard deviation of the total overflow rate of the research scheme tended to stabilize at a genetic algebra of 20, with a value of 3.58 m³. The standard deviation of the total cost of infrastructure tended to stabilize at a genetic algebra of 30, which was 65 million yuan. This indicated that genetic algebra had a significant impact on the convergence and stability of the optimization scheme. In the empirical analysis of the new urban rainwater and flood drainage system, the simulated curve closely matched the load of the actual outlet flow, without significant deviation. This result verified its effectiveness and accuracy. During the 2-year recurrence period of rain, the total discharge flow of the study model was 4428.73. Meanwhile, SS, COD, TN, and TP loads decreased by 51.8, 51.3, 50.2, and 51.1%, respectively. During the 50-year recurrence period of rainfall, the SS, COD, TN, and TP loads decreased by 51.9, 50.8, 50.1, and 50.3%, respectively. These data fully demonstrate the significant effect of this research plan in reducing pollutant loads. The limitation of this study is that the research area is still in the planning stage, and there is a lack of measured data to carefully calibrate and verify the model parameters. Therefore, further research needs to strengthen cooperation and communication with experts and practical operators in relevant fields to obtain more practical experience and feedback, and continuously optimize the model.

Funding information: Author states no funding involved.
Author contributions: Xihan Cao: conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing – original draft, and writing – review and editing. Author has accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: Author states no conflict of interest.
Data availability statement: All data generated or analyzed during this study are included in this published article.

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Received: 2024-09-24

Revised: 2024-11-05

Accepted: 2025-04-21

Published Online: 2025-08-21

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/nleng-2025-0146

Keywords for this article

SWMM; drainage system; optimization algorithm; coupling model; empirical analysis

Creative Commons

BY 4.0