## 3 Results and Analysis
### Functionality at Sector Scale and Community Scale  
For a flood intensity ranging from 0 m to 8 m with an increment of 1 m, the sustainable functionality of each sector immediately following the hazard is estimated based on individual building fragilities, as shown in Figure 6.  
Our findings align with the depth-damage curve delineated by [7], which correlates the flood depth experienced by structures with the percentage loss in structural value due to flood damages. The analysis reveals a pronounced decline in functionality across all four sectors, approaching zero when flood levels hit the 8 m mark. Notably, the business sector exhibits the steepest reduction in operational capacity, while the residential sector demonstrates a relatively gradual descent post-flooding. This observed homogeneity in resilience among the various supporting building sectors may be attributed to a shared vulnerability profile among individual structures. Figure 6 illustrates this phenomenon,  
Figure 6: Exceedance probability results for each sector: (**a**) R.S. ; (**b**) B.S. ; (**c**) E.S. ; and (**d**) P.S. where a 50% probability of retained functionality corresponds to flood depths of 3 m, 1.5 m, 1.5 m, and 2 m for the R.S., B.S., E.S., and P.S. building sectors, respectively. With the optimized community-level resilience model, the overall community functionality defined in Equation (4) is assessed using matrix \(A\). The result is plotted in Figure 7.  
The community functionality decreases with an increase in the measured intensity of flood depth (m), reaching 0.87, which is the threshold of proper functionality, as discussed in Section 2. When the flood intensity is at this threshold, the flood depth reaches 1.57 m, as listed in Table 4.  
At this intensity of threshold, the residual functionalities for R.S., B.S., E.S., and P.S. drop to 0.80, 0.50, 0.55, and 0.67, respectively. The main purpose of this study is to provide a methodology for assessing flood resilience at the community level. The hypothetical community consisting of wood frame buildings is case-specific. Further study should be performed to estimate flood resilience more accurately based on more comprehensive data, providing more reliable results. Figure 8 shows the relative contribution of each community supporting the building sector to community-level residual functionality immediately after a flood disaster. It can be observed that residential buildings have the most important impact on community-level functionality, while the other three sectors seem relatively less impacted during flood scenarios, and the variation in the functionality of residential buildings is bigger than in the other three sectors. Also, it is found that the community-level functionality loss is attributed mostly to the loss of the residential building sector, specifically when the community-level \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scale** & **Flood Depth (m)** & **Loss** & **Residual Functionality** \\ \hline Community & & 0.13 & 0.87 \\ \hline R.S. & & 0.20 & 0.80 \\ \hline B.S. & \multirow{2}{*}{\(1.57\)} & 0.50 & 0.50 \\ \cline{1-1} \cline{3-3} E.S. & & 0.45 & 0.55 \\ \cline{1-1} \cline{3-3} P.S. & & 0.33 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The loss and residual functionality at the threshold (15% population dislocation) derived from Monte Carlo Simulations. Figure 7: Community-level functionality as a function of flood intensity (m). functionality decreases below 90% of the original level. However, when community-level functionality is lower than 90% of the normal level, the functionality of the education sector is the highest among these four sectors. Figure 9 illustrates the sensitivity analysis findings. It is important to note that the disparity between the scenarios where the functional loss of one sector leads to the complete functional loss of other sectors and the scenarios that do consider these interdependencies is more significant.