## 2 Material and Methods  
### Resilience in Hydroelectricity Dam  
[PERSON] et al. (2003) defined the total loss of system in terms of time and functional level to express various attributes of resilience as a single value [15]. Since this definition expresses resilience as a single value, the comparative advantage of each scenario can be easily identified. In this study, the resilience of a hydropower reservoir using this analytical definition was applied [14]. It was defined based on engineering resilience, which is approached by focusing on the recovery time required to repair the damage done to the original properties [8]. Since the main purpose of the hydropower reservoir is to generate electricity, the components of robustness and rapidity were derived. Robustness was defined as the water level of the hydropower reservoir, and rapidity was defined as the time required to recover to an appropriate water level for power generation (Figure 1). The generation of electricity is determined by the effective head and the amount of outflow from the reservoir. Thus, it is necessary to keep the water level high to increase the effective head and the amount of outflow. However, since the water resources stored in the reservoir are limited and the effective head decreases when the outflow for generation is increased, it is essential to properly maintain them. Since the water level is determined by the inflow and outflow, the function of the power generation system is represented by the dam water level. Therefore, a resilience triangle was defined with the vertical axis as the dam water level as shown in Figure 1a. With this conceptual approach, area B surrounded by the dotted line in Figure 1 is defined as the resilience and area A is defined as the total loss. The equation of the hydropower resilience is as follows.  
\[R=\int_{t_{a}}^{t_{b}}W(t)-W_{lowest}dt\left\{\begin{array}{ll}W_{d}(t)&t_{0} <t<t_{a}\\ W_{r}(t)&t_{a}<t<t_{b}\end{array}\right. \tag{1}\]  
where, \(R\) is the resilience. \(t_{a}\) is the point at which recovery begins. \(t_{b}\) is the point at which recovery is complete. \(t_{0}\) is the point at which the loss occurred. \(W(t)\) is the water level function with time. \(W_{d}(t)\) is the function of operation. \(W_{r}(t)\) is the recovery function. \(W_{lowest}\) is the low water level of each reservoir.  
Figure 1: _Cont._  
Examples of applying this concept are shown in Figure 1b,c. Figure 1b shows an example of a different recovery time. \(T_{1}\), which has a faster recovery time at the same time interval, has greater resilience than \(T_{2}\) (\(R_{1}>R_{2}\)). This is because the case of \(T_{1}\) operates with a higher effective head, so the amount of power generation is higher. Figure 1c shows the case where the recovery time is the same, but the recovery function is different, and it can be said that \(F_{1}\) has greater resilience than \(F_{2}\) and \(F_{3}\) (\(R_{1}>R_{2}>R_{3}\)). In both examples, it can be said that the larger R is, the better the performance at the hydropower reservoir. Using this concept of resilience, it is possible to present a methodology for evaluating the power generation performance of reservoirs.