## 4 Results and Discussion
Table 3 presents a sensitivity analysis of the shark algorithm in the base and future periods. The optimal population size for the shark algorithm, which is based on minimization the objective function in the base period, is 30, and M is also 30 in this period. M is the number of points investigated in a local search by sharks. Additionally, the value of \(\alpha\) is 0.78 for the base period. In the future period, the optimal population size for the shark algorithm is 50, the best value M value is 30, and the value of \(\alpha\) is 0.68. Table 4 shows the results for 10 random runs of the shark algorithm for the base and future periods. The average solution for the base period was less than that for the future period. Moreover, the global solution of the problem was obtained using Lingo software (Lingo, 2010) and a nonlinear programming method. Results indicated that the average solution of the shark algorithm for the base and future periods was 0.99% of the global solution. Furthermore, the coefficients of variation were small for both periods. This finding suggests that the shark algorithm provides high-quality solutions. Evapotranspiration associated with each crop should be calculated to compute the irrigation demand. Therefore, evapotranspiration was computed based on the crop coefficient and reference crop evapotranspiration. However, the necessary data were not available for the future period; thus, the reference crop evapotranspiration was computed based on another method. First, a regression relationship between the temperature and reference crop evapotranspiration was obtained for the base period. Then, this equation was used to compute the reference crop evapotranspiration for the future period based on the simulated temperatures for the future period. Next, the following equation was used to calculate crop evapotranspiration by  
\[ET_{C}=K_{C_{t}}\times ET_{0} \tag{26}\]  
where \(ET_{C}\) is evapotranspiration, \(K_{C_{t}}\) is the crop coefficient, and \(ET_{0}\) is the reference crop evapotranspiration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **R2** & **RMSE (106 m3)** & **MBE (106 m3)** \\ \hline Calibration & 0.96 & 3 & 1 \\ Verification & 0.92 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical analysis for predicted runoffs in the base period. Figure 9: Predicted runoffs for the future and base periods. Subsequently, effective rainfall was computed based on the equation  
\[ \begin{split} P_{e}&=\frac{P_{t}}{125\times(125-0.2P_{t} )}\gets P_{t}\leq 250\text{ mm}\\ P_{e}&=125+0.1\times P_{t}\gets P_{t}\geq 250 \text{ mm}\end{split}  \tag{27}\]  
where \(P_{e}\) is effective rainfall and \(P_{t}\) is rainfall. Equation (27) is taken from the Soil Conservation Service. Next, the net volume of water was computed based on the equation  
\[WR_{t}=ET_{C}-P_{e} \tag{28}\]  
Then, the volume of the demand was calculated based on the equation  
\[V_{t}=\frac{WR_{t}\times 10\times A}{1000000} \tag{29}\]  
where \(V_{t}\) is the volume of the demand and \(A\) is the cultivated area. Water demand for the future was computed based on Equation (29). In this equation, the effective rainfall is computed based on Equation (27) and generated rainfall by climate change models and scenarios. Evapotranspiration, based on Equation (26), was then computed. The reference crop evapotranspiration was based on Penman-Monteith, and the crop coefficient was calculated based on mean relative humidity, wind speed, and information about the growth periods of crops. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Run** & **Base Period** & **Future Period** \\ \hline
1 & 1.455 & 1.529 \\
2 & 1.457 & 1.525 \\
3 & 1.455 & 1.525 \\
4 & 1.455 & 1.525 \\
5 & 1.455 & 1.525 \\
6 & 1.455 & 1.525 \\
7 & 1.455 & 1.525 \\
8 & 1.455 & 1.525 \\
9 & 1.455 & 1.525 \\
10 & 1.455 & 1.525 \\ Average solution & 1.455 & 1.525 \\ Variation coefficient & 0.0006 & 0.0008 \\ Global solution & 1.454 & \\ \hline \hline \end{tabular}
\end{table}