## 3 Materials and Methods
### Parameter Determination and Model Verification  
#### 3.3.1 Calculation of Model Parameters  
The key model parameters included the catchment area, infiltration rate, and pipeline length. The catchment area and pipeline length were read by SWMM automatically, while the characteristic width was calculated using the following equation:  
\[\text{Width }=K\times\sqrt{S_{Area}} \tag{3}\]  
where \(S_{Area}\) is the area of the catchment, m\({}^{2}\), and \(K\) is a parameter, generally between 0.2 and 5. The characteristic width represents the average width of the catchment, serving as a basis for estimating the runoff volume generated from the catchment. The value of \(K\) is selected based on the specific attributes of the catchment and can be adjusted to better align with its actual conditions. In this study, \(K\) was assigned a value of 1, a commonly used default when the catchment's shape is not well-defined or when detailed geometric information is unavailable. This approach simplifies the hydrological modeling process by providing a representative width for irregularly shaped catchments, facilitating practical application in modeling scenarios.  
Considering the impact of rainfall duration on soil infiltration, the Horton model was employed to calculate the soil permeability:  
\[f_{p}=f_{c}+(f_{0}-f_{c})e^{-kt} \tag{4}\]  
where \(f_{p}\) is the soil infiltration rate at \(t\) time, mm/h;\(f_{0}\) is the initial infiltration rate, mm/h; \(f_{c}\) is the stable infiltration rate, mm/h; \(t\) is the time, h; \(k\) is an empirical parameter, indicating the decreasing coefficient of infiltration capacity with time, 1/h.  
The Manning coefficient, also known as the runoff roughness coefficient, reflects the influence of pipe channels and surface roughness on water flow. This coefficient can be determined using the weighting method based on the underlying surface conditions [34; 35]:  
\[N\text{-imperv}=\frac{\sum_{i=1}^{n}N\text{area}_{i}\times M_{i}}{\sum_{i=1}^{ n}N\text{area}_{i}} \tag{5}\]  
\[N\text{-perv}=\frac{\sum_{j=1}^{n}area_{j}\times M_{j}}{\sum_{j=1}^{m}area_{j}} \tag{6}\]  
where \(N\)-imperv is the Manning coefficient for the impervious area; \(N\)-perv is the Manning coefficient for the pervious area; \(n\) is the number of impermeable underlying surfaces in the catchment; \(Narea_{i}\) is the area of impermeable underlying surface in the \(i\)th catchment, m\({}^{2}\); \(M_{i}\) is the Manning coefficient of impermeable underlying surface in the \(i\)th catchment; \(m\) is the number of permeable underlying surfaces in the catchment; \(area_{j}\) is the area of permeable underlying surface in the \(j\)th catchment, m\({}^{2}\); and \(M_{j}\) is the Manning coefficient of permeable underlying surface in the \(j\)th catchment.  
The Manning coefficient varies depending on the type of underlying surface, with each surface type associated with a specific Manning value. The majority of the impermeable surfaces examined were asphalt roads, rigid pavements, plastic tracks, concrete grounds and structures. In contrast, green spaces, bare soil, and green belts were categorized as permeable areas. Based on the SWMM application handbook [35; 36], the initial Manning coefficient for impermeable surfaces was 0.015, while for permeable surfaces, it was 0.18.