# Evaluation of Urban Transportation Resilience under Extreme Weather Events
## 3 Method
### Quantifying the Transportation Resilience in Different Subraes under EWEs  
The occurrence of EWEs may have varying degrees of impact on transportation resilience across subareas of the city. As the recovery process of transportation varies in each subarea, it is imperative to target the lowest resilience subarea to ensure it returns to its normal state, thereby reducing the impact of EWEs on that subarea. During the EWEs, when different subareas are affected, the transportation performance in each subarea is perturbed, and this perturbation continues for some time until the EWEs gradually cease. [PERSON] et al. [42] argued that, with the functionality recovery curve, there is a significant and sudden decrease in functionality due to an extreme event at time instant \(t_{0}\), followed by a gradual recovery of functionality, until the system is fully functional at time instant \(t_{2}\). Motivated by the resilience concept and resilience quantification framework [19], the transportation performance can also be depicted in a curve to illustrate the impacts of EWEs on urban transportation. The transportation performance curve can be analyzed in two phases, the disruption and recovery phases [43], as shown in Figure 5.  
As can be seen in Figure 5, the EWEs occur at \(t_{0}\), after which the transportation performance curve begins to show a downward tendency. Usually, it will drop to the threshold value where the transportation performance merely meets the lowest requirements, at which point the negative effects of EWEs are fully released. Subsequently, the transportation performance begins to recover gradually and returns to stability at \(t_{2}\). Among them, \(t_{0}\) indicates the time when the EWEs begin or the time when the transportation performance perturbation begins, \(t_{1}\) indicates the time when the perturbation reaches its lowest point, and \(t_{2}\) indicates the time when the perturbation ends. The disruption phase ranges from the time when the transportation performance perturbation begins to the time it reaches the lowest point. The slope of the disruption phase is denoted by \(k_{d}\), which is calculated as shown in Equation (5). The recovery phase ranges from the time when the perturbation reaches the lowest point to the time when the perturbation ends. The slope of the recovery phase is denoted by \(k_{r}\), which is calculated based on Equation (6).  
\[k_{d}=\frac{PI(t_{1})-PI(t_{0})}{t_{1}-t_{0}} \tag{5}\]  
\[k_{r}=\frac{PI(t_{2})-PI(t_{1})}{t_{2}-t_{1}} \tag{6}\]  
Figure 5: Curve showing transportation performance.  
Particularly, the normalized indicator PI (which ranges from [0, 1]) is used to measure the deviation of the transportation performance from its normal state at any moment under EWEs. The resilience index attempts to comprehensively represent resilience with one parameter, with the value varying between 0 and 1 [44]. It has been widely used for resilience analyses of various infrastructure systems. Thus, the normalized integrating PI over the time span of the EWEs yields the resilience (R) of the transportation, as shown in Equation (7).  
\[\text{R}=\int_{t_{0}}^{t_{2}}\frac{PI}{t_{2}-t_{0}}dt \tag{7}\]  
The value of R depends on the magnitude of the PI, and the duration of the impact of EWEs. This duration may exceed the time span of the EWEs and last for a considerable period of time. In this study, \(t_{0}\) is the moment when the PI value first drops below 0.95; \(t_{2}\) is the first point in time when the PI value remains at, at least, 95% during the next 24 h, which is to exclude the deviations of the PI from the specified values caused by factors including abnormal road congestion or changes in bus routes by public transportation groups.