## 3 Case Study  
The Aidoughmoush Dam is located in the city of Maneh, Azerbaijan Province, Iran. As shown in Figure 3, the dam was constructed on the Aidoughmoush River in the Caspian catchment. The primary purpose of the dam is to supply irrigation water for the region, of which \(15\times 10^{3}\) ha is cultivated land. The maximum and minimum storage volumes for this dam are \(145.7\times 10^{6}\) m\({}^{3}\) and \(8.9\times 10^{6}\) m\({}^{3}\), respectively.  
The objective function involves minimizing the irrigation deficit  
\[Minimize(OF)=\sum_{t=1}^{T\sum^{2}}\left(\frac{D_{t}-R_{t}}{D_{max}}\right) \tag{15}\]  
where \(D\) is the demand, \(R\) is the quantity of released water, and \(D_{max}\) is the maximum demand.  
The continuity equation for this reservoir is based on the equation  
\[S_{t+1}=S_{t}+I_{t}-loss_{t}-R_{t}-Sp_{t} \tag{16}\]  
where \(S_{t+1}\) is the storage at time \(t+1\); \(I_{t}\) is the inflow to the reservoir; \(loss_{t}\) represents the total losses, such as evaporation, and \(Sp_{t}\) is the dam overflow.  
The loss is computed based on the equation  
\[Loss_{t}=A_{t}\times EV_{t} \tag{17}\]  
where \(A_{t}\) is the area of the reservoir and \(EV\) is the value of evaporation.  
Additionally, the value of dam overflow is computed based on the equation  
\[Sp_{t}=\left[\begin{array}{c}0\gets if(S_{t})\leq S_{max}\\ \left.St(S_{t})_{maxmax}\right.\end{array}\right] \tag{18}\]  
In addition, the following constraints should be considered for the stored and released quantities of water.  
\[0\leq R_{t}\leq D_{t}\;St_{max_{min}} \tag{19}\]  
Furthermore, if the constraints are not satisfied, penalty functions should be added to the objective function as follows:  
\[P_{1,t}=\left[\begin{array}{c}0\gets if(S_{t+1}>S_{\min})\\ \dfrac{\left(S_{\min}-S_{t+1}\right)^{2}}{S_{\max}}\leftarrow\textit{ otherwise}\end{array}\right] \tag{20}\]  
\[P_{2,t}=\left[\begin{array}{c}0\gets if(S_{t+1})<S_{\max}\\ \dfrac{\left(S_{t+1}-S_{\max}\right)^{2}}{S_{\max}}\leftarrow\textit{ otherwise}\end{array}\right] \tag{21}\]  
Figure 3: Location of the Aydougmoush Dam.  
\[P_{3,t}=\left[\begin{array}{c}0\gets if(R_{t})<D_{t}\\ \frac{\left(R_{t}-D_{t}\right)^{2}}{D_{\max}}\gets otherwise\end{array}\right] \tag{22}\]  
The following steps are used for reservoir optimization:  
Step 1: First, scenario A\({}_{1}\)B and the HAD-CM3 model are used to simulate climate change based on the LARS-WG5 model.  
Step 2: The model is evaluated based on the predicted maximum and minimum temperatures and precipitation for the base period (1980-1999).  
Step 3: Then, the climate change model is used to calculate the temperatures and precipitation in the future period.  
Step 4: Next, the IHACRES model uses the computed temperatures and precipitation from Steps 2 and 3 to estimate runoff.  
Step 5: The computed runoff from the previous step is used as inflow into the reservoir, and reservoir operation based on the shark algorithm begins.  
Step 5: Additionally, the following indices are considered to evaluate the water supply for the base and future periods based on the shark algorithm.  
* Reliability index  
The reliability index reflects the ratio of water demand to the quantity of released water for one operation period [29; 39].  
\[\alpha_{V}=\frac{\sum\limits_{t=1}^{T}R_{t}}{\sum\limits_{t=1}^{T}D_{t}}\times 100 \tag{23}\]
* Vulnerability index  
The vulnerability index reflects the maximum probability of failure in an operation period [29; 39]:  
\[\lambda=Max_{t=1}^{T}\left(\frac{D_{t}-R_{t}}{D_{t}}\right) \tag{24}\]  
where \(\lambda\) is the vulnerability index.  
* Resiliency index  
The resiliency index reflects the ability of a system to avoid failure [29]:  
\[\gamma_{i}=\frac{f_{si}}{F_{i}} \tag{25}\]  
where \(\gamma_{i}\) is the resiliency index, \(f_{si}\) is the number of failure series in the operation period, and \(F_{i}\) is the number of the failure periods.