# The Sensitivity Analysis of Parameters in the 1D-2D Coupled Model for Urban Flooding
## 4 Results and Analysis
### Global Sensitivity Analysis  
The global sensitivity analysis of the nonlinear relationship between the 12 parameters of the coupled model and the total amount of water accumulated in Honggu Tan District was conducted using the Sobol method, and Figure 5 shows the parameter sensitivities calculated by the Sobol method under different return periods. From Figure 5a, it can be seen that the \(S_{1}\) values of Manning's coefficient of permeable water surface area (N-Perv) and minimum infiltration rate (Minrate) are significantly higher than the other parameters under different rainfall patterns, especially under the szzbl50a and Chicago50a rainfall patterns. [PERSON]'s coefficient of permeable surface area (N-Perv) had an \(S_{1}\) value of 0.755 in szzbl50a, which was much higher than the other rainfall patterns, indicating that it was the most sensitive to the total amount of ponded water. Minimum infiltration rate (Minrate) reached an \(S_{1}\) value of 0.684 for the cxzd50a rain pattern and 0.826 for the Chicago50a rain pattern, indicating that this parameter has a particularly significant effect on the total amount of standing water in these two rain patterns. In contrast, decay coefficient (Dc) is more moderately sensitive under the three rainfall patterns, with \(S_{1}\) values ranging from 0.0278 to 0.057, showing some influence but much less than the [PERSON]'s coefficient for the permeable surface area (N-Perv) and the minimum infiltration rate (Minrate). In addition, pipe roughness (Roughness) showed a strong sensitivity under the Chicago50a rain type, with an \(S_{1}\) value of 0.485, while it was significantly lower under the other rain types, indicating that the sensitivity of this parameter varies significantly between rain types. Comparing the values under the three rain patterns, it can be found that the sensitivity of Manning's coefficient of permeable surface area (N-Perv) and minimum infiltration rate (Minrate) is more prominent under cxzd50a and szzbl50a, indicating that they have a greater influence on the total amount of water accumulation. The sensitivity of minimum infiltration rate (Minrate) reached the highest value under the Chicago50a rainfall pattern, indicating that the contribution of Minrate to the total amount of standing water is significant under this rainfall pattern, followed by the Manning's coefficient of the permeable water surface area (N-Perv) and the stable infiltration rate (Fc), while the sensitivities of the other parameters, such as the Courant number (CFL) and the velocity diffusion coefficient (Vd), were less. From the results in Figure 5b, it can be seen that the Manning coefficient (N-Perv) and the minimum infiltration rate (Minrate) of the permeable water surface area are the most significant parameters contributing to the total amount of standing water. The \(S_{T}\) values of N-Perv are 0.644 and 0.065 for the szzbl50a and Chicago50a rain patterns, respectively, indicating its dominance in the global influence of the system. And the \(S_{T}\) values of Minrate exceed 0.5 in both cxzd50a and Chicago50a, indicating that its sensitivity is also not negligible. In contrast, the very low values of Courant number (CFL) and impervious area puddle storage (S-Imperv) indicate that their global influence on water volume is negligible. These types of parameters have low sensitivity and relatively insignificant contributions to the system. The remaining parameters, such as surface roughness (Friction) and pipe roughness (Roughness), exhibit moderate global sensitivity under some rainfall patterns but have a relatively small effect on the total amount of standing water. In the sensitivity analysis, \(S_{1}\) represents the first-order sensitivity of each parameter to the target output, i.e., the direct effect on the results when the parameter is varied individually. In contrast, \(S_{T}\) represents the global sensitivity, which includes the direct effect of the parameter and the interaction with other parameters.