## 3 Data and Methodology
### High-Intensity Rainfall-Runoff Model  
This study divides each rainfall event into n time intervals, and each time interval is the same time \(\Delta T\). Equation (2) for calculating the time interval follows:  
\[n=T/\Delta T \tag{2}\]  
Figure 2: The map of 889 sub-basins in NYC.  
where \(n\) is the number of time intervals in the rainfall period, \(T\) is the total duration of the rainfall period, and \(\Delta T\) is the duration of the time interval.  
The time \(t_{k}\) from the beginning of the rainfall event to the \(k\)th interval \(\Delta T\) is expressed using Equation (3):  
\[t_{k}=k\cdot\Delta T,\ k=1,2,3\ldots n \tag{3}\]  
This rainfall model mainly considers rainfall, the infiltration rate of different soils, and the drainage capacity of stormwater management systems in NYC. Therefore, the calculation equation of the runoff volume at time \(t\) in this study is  
\[V_{t_{k}}=V_{t_{k-1}}+R_{k}-I_{k}-D_{k} \tag{4}\]  
where \(V_{t_{k}}\) and \(V_{t_{k-1}}\) are the runoff volume after the time interval \(t_{k}\) and \(t_{k-1}\), \(R_{k}\) is the rainfall volume during time (\(t_{k}\), \(t_{k-1}\)), \(I_{k}\) is the infiltrated volume during time (\(t_{k}\), \(t_{k-1}\)), and \(D_{k}\) is the volume of water drained through the sewer system during the time (\(t_{k}\), \(t_{k-1}\)). The infiltration volume was determined by the average infiltration rate and area of the soil. The infiltration rate depends on the soil conditions. Based on infiltration capacity, [PERSON] and [PERSON] proposed that the soil can be divided into four general conditions: good, medium, poor, and impervious [36]. The infiltration rate of different land conditions is shown in Table 1.  
The infiltrated volume during time (\(t_{k}\), \(t_{k-1}\)) is expressed as Equation (5):  
\[I_{k}=\Delta T\cdot\left(A_{b}f_{b}+A_{t}f_{t}+A_{g}f_{g}\right) \tag{5}\]  
where \(f_{b}\), \(f_{t}\), and \(f_{g}\) are the average infiltration rates for bare soil, tree canopy, and grass, and \(A_{b}\), \(A_{t}\), and \(A_{g}\) are the areas for bare soil, tree canopy, and green area in a sub-basin. Bare soil has more runoff and a poor infiltration condition, so \(f_{b}\) = 0.035 cm/h (from Table 1). Tree canopy is in good condition, so \(f_{t}\) = 5.24 cm/h (from Table 1). The grass is in moderate condition, so \(f_{g}\) = 0.63 cm/h was considered (Table 1). The rainfall volume and the volume of water drained through the sewer system during the time (\(t_{k}\), \(t_{k-1}\)) are calculated as follows:  
\[D_{k} =d\cdot\Delta T \tag{6}\] \[R_{k} =r\cdot\Delta T \tag{7}\]  
where \(r\) is the average rainfall intensity during \(\Delta T\), and \(d\) is the discharge rate of the drainage system of NYC. In the _Stormwater Management Design Manual of New York_, the stormwater system in New York is designed to deal with a 10 year rainfall [37]. According to the data provided by NOAA, \(d\) is 36.322 mm/h [38]. However, these data were produced for large scale flood analysis and might not provide the precise information required for complex urban flood analysis. The horizontal accuracy of the rainfall data may reach up to 5 km (3.11 miles) and significant sampling errors could also occur due to longer duration periods. After the runoff volume was obtained, the submerged depth can be queried in the database of the corresponding sub-basin.