# Development of a Multiscenario Planning Approach for Urban Drainage Systems
## 1 Introduction  
Planning robust urban drainage systems (UDSs) to anticipate future climatic conditions is essential for regional communities to mitigate the effects of potential severe flooding. However, accounting for uncertain future conditions in UDS planning is a complex task, and engineers or designers often face difficult decisions. The traditional approach to UDS planning generally focuses on a single future condition (e.g., the most probable rainfall scenario) that is perceived to be the most likely to occur; this is known as the single-scenario-based optimization approach. However, this approach does not ensure system robustness to satisfy performance requirements under various future conditions. For example, the lowest cost UDS design obtained with a single rainfall scenario with a 50-year return period, although conservative, redundant, and involving high economic investment, would fail in several years when unanticipated future events unfold, for example, transition of a spatial and temporal rainfall pattern of a region and construction of a large apartment complex. Considerable effort has been devoted to considering scenario(s) in the water resources engineering domain such as the following: evolution of land use and impact assessment [1; 2; 3; 4; 5; 6; 7; 8; 9; 10], water distribution system (WDS) design [11; 12], watershed management [13; 14], water resources management in natural river basins [15], and UDS design [16; 17; 18; 19]. The focus of these studies was to obtain the most feasiblesolution for the most probable scenario. In previous studies, although solutions for individual scenario(s) have been effectively presented, most of these studies have not provided compromise solutions or integrated policies for scenario-planning-based models. However, an alternative way to overcome the limitations of these studies is to simultaneously consider a wide range of multiple probable future scenarios, i.e., the multi-scenario planning approach. In the field of WDS, [PERSON] and [PERSON] [20; 21] demonstrated the effect of considering the multi-scenario approach by highlighting the vulnerability of the single-scenario solution under different future scenarios because of the solution's bias to the single scenario considered. Specifically, [PERSON] and [PERSON] [20] introduced the concept of regret cost (RC), which quantifies over-design and under-design investments of a design solution in different future scenarios. The compromise solution across multiple scenarios was finally obtained by limiting the RC and comparing the optimal solutions of individual scenarios and the compromise solution under different scenarios. In the water resources engineering domain, one of the research groups in the UDS domain, [PERSON] et al. [22], introduced a multi-scenario-based design approach, i.e., a two-phase design method in which the individual scenario optimal solution was sought in the first phase and the compromise solution was determined in the second phase, based on the identification of common elements and the calculation of RC. However, the aforementioned study contained several significant limitations which included: (1) RC was calculated at a system-wide level; (2) variation of temporal rainfall distribution was disallowed; and (3) flooding was disallowed (the so-called \"fail-safe\" design) which hindered verification of the system's hydraulic performance in expelling flood-level volumes of water in the proposed model. In addition, various temporal and spatial distributions of rainfall were not incorporated in the scenarios considered. In summary, a compromise solution from the aforementioned model did not effectively respond or adaptive to recent climatic change conditions, which lead to considerable uncertainties regarding the operation of the UDS. Multi-scenario-based UDS planning that considers both spatial and temporal rainfall patterns is required to ensure stable UDS performance.