*2.4. Study Area and Data Description*

A real-world urban stormwater system located in Salt Lake City, UT, U.S., was selected as the case study, shown in Figure 3. This study case, with an area of 81-ha, is semi-arid, and has soil composed of four primary types: alluvial fan, artificial fill, silt and clay, and sand and gravel deposits. The soil surrounding the study area is classified as hydrologic soil groups B and C, with low infiltration capacity, which has a relatively poorly draining surface. Due to climate change and urbanization, the studied area has suffered from floods more frequently than 1990s, and the increase in the magnitude and duration of the storm events has pushed the resulting stormwater system out of service. This urban drainage network was represented by a rainfall-runoff SWMM model. SWMM is a state-of-art tool developed to help support local, state, and national stormwater management objectives to reduce runoff, discharge, and improve stormwater quality [63,64]. It has been widely used all over the world in similar type of investigations including stormwater runoff, combined and sanitary sewers, and other drainage systems [65–67]. Figure 3 shows the components of this SWMM model, which includes one rain gauge, 60 junctions, 61 conduits, two outfalls, and seven sub-catchments, while the groundwater interflow, water evaporation, snowmelt, and manhole hydraulic loss are neglected during the simulation [68].

**Figure 3.** Study area located in the northern Utah state (left-top sub-figure: 1 degree roughly means 106 kilometer), the U.S. and the topological view of the stormwater urban drainage system model plotted by the PCSWMM v.7.3. (major sub-figure, scale unit is kilometer).

For this study, we created 6 artificial precipitation series according to the Chicago distribution method in PCSWMM v.7.3, and then imported them as modeling inputs. The distribution for the synthetic rains is shown in Figure 4. These rainfalls with durations of 3 h, 12 h, to 48 h and return periods ranging from 2-year to 5-year almost contain all typical features and characteristics of real storms in the study area. Additionally, rainfall measurements for two real rainfall events were collected to test the clustering algorithm. These rain records from 5 May 2015 rainfall event and 8 July 2015 rainfall event are representative for the typical real storms under average climatic conditions in the study area. Compared with water depth generated by the artificially designed rainfall data, the time-series water depth produced by the real-world storms contains more non-stationarity and noise. Nevertheless, the obtained findings are subsequent validated with real rain records.

**Figure 4.** Distribution plots of artificially designed rainfalls with different return periods and rainfall duration.

#### **3. Results**
