## 4 Comparison between Calculation Models and Full-Scale Measurements
### Reverberation Time along the Street
Comparison between Iterative Model Combining the Radiosity Method and Image Source Method (IMCRI) and the Existing Hybrid Model of Image Source Model (ISM) and Acoustic Radiosity Model (ARM)  
An existing hybrid model (EHM) of ISM and ARM was developed to reveal the improvement by modeling image patches (specular reflections after diffuse reflections) in the IMCRI. The difference in the reflection modeling scheme between the IMCRI and EHM is described in Section 2. Other implementations in the EHM were the same as the IMCRI. Figure 8 shows the comparison between the IMCRI and EHM (SPL\({}_{\text{IMCRI}}\)-SPL\({}_{\text{EHM}}\) and RT\({}_{\text{IMCRI}}\)-RT\({}_{\text{EHM}}\)) with different building facade heights and scattering coefficients. As shown in Figure 8a, the differences between IMCRI and EHM were small (\(<\)1.5 dB and 0.3 s) in the street with low building facades (H = 5). However, in the street with high building facades (H = 45), significant differences of up to 5.5 dB and 1.7 s were found, as shown in Figure 8b. Because the modeling scheme mainly affects the high-order reflected sound, the SPL difference between IMCRI and EHM varied with the distance from the source. No significant differences were found in the near-field (D = 5) in both streets because it was dominated by the direct sound and the specular reflected sound of the ground. However, there were considerable differences in the far-field (D = 50) when the scattering coefficient increased. The maximum difference was approximately 1.5 and 5.5 dB in two streets with different building facade height. On the contrary, the RT difference between IMCRI and EHM was independent of the distance because it was mainly determined by the late reflected sound. The RT difference between EHM and IMCRI was significantly larger in streets with high building facades. In general, this result shows that the reflection modeling scheme has significant influences on SPL and RT simulations in streets with high building facades, which is common in modern cities. By considering the full sound energy transfer path, the IMCRI can significantly improve the simulation accuracy of SPL in the far-field and RT in the whole street. Because more sound transfer paths were calculated in the IMCRI, the time cost of the IMCRI was larger than EHM in most cases, as shown in Table 2. As described in Section 2, an auto-termination process was used in the IMCRI to decide whether a sufficient number of paths were calculated and to stop the whole calculation process. In the street with high building facades (W = 16; H= 35), more iterations were needed due to the strong influence of scattering sound energy from the building facades. In this case, the IMCRI required a calculation time that was greater than that of the EHM by an approximate factor of 2.5-7. In streets with a low, flat building facade (W = 15; H = 6), only a small part of the sound energy was scattered by the building facade. The termination condition could be achieved with a few iterations. Therefore, the time cost of the IMCRI was similar to that of the EHM and was even less when the scattering coefficient was very low. The results in Figure 8 and Table 2 show that a good balance between model accuracy and time cost was achieved by the auto-determination process in the IMCRI. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time Cost/s**} & \multicolumn{3}{c}{**Street 1: W = 15; H = 6**} & \multicolumn{3}{c}{**Street 6: W = 16; H = 35**} \\ \cline{2-7}  & **S = 0.05** & **S = 0.5** & **S = 0.95** & **S = 0.05** & **S = 0.5** & **S = 0.95** \\ \hline EHM & 53 & 97 & 102 & 1827 & 2258 & 2576 \\ IMCRI & 44 & 96 & 153 & 5016 & 15891 & 14491 \\ Ratio (IMCRI/EHM) & 0.8 & 1.0 & 1.5 & 2.7 & 7.0 & 5.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The time cost of existing hybrid model (EHM) and the IMCRI W, H, and S are street width, building facade height and the scattering coefficient of the building facade, respectively. Figure 8: The comparison between the IMCRI and EHM in two streets.