# Development of a Multiscenario Planning Approach for Urban Drainage Systems
## 3 Application Results
### Scenario-Optimal Planning Solution for Individual Scenarios (Phase I)  
In Phase I, the S-city drainage network was independently designed using the scenario-optimal planning model (Equations (1)-(7)) for all future scenarios (i.e., S1 to S6). Table 1 summarizes certain statistics of the optimized dimensions of pipes and manholes and the cost components of the scenario-optimal solutions. The penalty cost was computed using Equation (5), considering the total system flooding volume in the solutions. The six scenario-optimal designs (D1 to D6) were obtained for the corresponding future scenarios (S1 to S6).  
While D6 (obtained from S6 in the third quartile of the Huff distribution with a high inflow at the southeastern corner) has the lowest system material cost, the largest investment was required to handle S5 in the same Huff distribution with a high inflow at midtown (D5 was obtained here). The system material cost for D5 was approximately 75% of that of D6. However, regarding the total cost, including the penalty cost (i.e., the system material cost and penalty cost), D3 incurred the lowest cost, whereas D1 was the most expensive. In addition, the total cost for D3 was approximately 83% of that of D1. Thus, the lowest cost D3 scenario-optimal solution leads to potentially small flooding volumes.  
Figure 6 shows the hydrogen of the network flooding (system performance) in the scenario-optimal solution under six scenarios (Figure 6a in the second quartile rainfall and Figure 6b in the third). High nodal inflows were transited from north to south in scenarios S1 to S3, as shown in Figure 6a and in S4 to S6, as shown in Figure 6b. Low penalty costs for D3 and D5 were supported by the lowest peaks in the flooding hydrographs in Figure 6a,b, respectively. Therefore, it was confirmed that directing more inflow to the outlet (i.e., development near the outlet, D3) and investing more in pipes and manholes (D5) would result in a less severe failure of the UDS.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Planning/Scenario \({}^{\text{a}}\)**} & **D1/S1** & **D2/S2** & **D3/S3** & **D4/S4** & **D5/S5** & **D6/S6** \\ \hline \multirow{3}{*}{Pipe} & Cost (\$M) & 1.466 & 1.462 & 1.318 & 1.372 & 1.823 & 1.357 \\ \cline{2-7}  & Max. size (m) & 2.13 & 1.83 & 1.83 & 1.83 & 2.13 & 1.83 \\ \cline{2-7}  & Min. size (m) & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 \\ \hline \multirow{3}{*}{Manhole} & Cost (\$M) & 0.205 & 0.190 & 0.203 & 0.195 & 0.194 & 0.162 \\ \cline{2-7}  & Max. depth (m) & 4.0 & 4.0 & 4.0 & 3.6 & 3.6 & 3.6 \\ \cline{2-7}  & Min. depth (m) & 1.5 & 1.5 & 1.5 & 1.8 & 1.8 & 1.5 \\ \hline Penalty & Cost (\$M) & 0.601 & 0.507 & 0.372 & 0.609 & 0.127 & 0.382 \\ \hline \multicolumn{2}{c}{System material cost (\$M)} & 1.671 & 1.652 & 1.521 & 1.567 & 2.017 & 1.519 \\ \hline \multicolumn{2}{c}{Total cost (\$M)} & 2.272 & 2.159 & 1.893 & 2.176 & 2.144 & 1.901 \\ \hline \multicolumn{2}{c}{\({}^{\text{a}}\) Scenario-optimal planning (P1 to P6) was the optimal solution corresponding to each scenario (S1 to S6).} \\ \end{tabular}
\end{table}
Table 1: Scenario-optimal designs for multiple future scenarios.