# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## Materials and Methods
### Hydrological Model HEC-HMS, Setup, and Methods
As with precipitation, so with AMC, the total millimeters of precipitated water in the precedent 5 days in each sub-basin are calculated via the Thiessen polygons methodology. Below are the equations for the CN related to dry conditions (AMC Type I) and wet conditions (AMC Type III), respectively [41]:  
\[CN_{I}=\frac{4.2\times CN_{II}}{10-(0.058\times CN_{II})} \tag{3}\]  
\[CN_{III}=\frac{23\times CN_{II}}{10+(0.13\times CN_{II})} \tag{4}\]  
For the dormant season, determined from mid-October to mid-April in Canada, AMC are characterized as Type I (dry) for the 5 previous days' precipitation less than 12.7 mm, Type II (normal) for prior precipitation ranging between 12.7 mm and 27.94 mm, whereas Type III (wet) for precedent precipitated water over 27.94 mm. On the other hand, for the growing season which extends to Canada for about five months, from late April to early October, AMC are referred to as dry for the former 5 days' rainfall under 35.56 mm, normal for a range between 35.56 mm and 53.34 mm, and wet for more than 53.34 mm [41]. Hence, the AMC ranges affecting the CN are remarkably different among dormant and growing seasons. The % imperviousness is another important parameter for hydrological modeling. High residencies are considered to have 65% impervious cover. Estate residencies have on average 25% imperviousness [37]. Golf courses are considered pervious. Roads, either gravel or paved, are assumed to be 100% impervious [42]. Industrial districts are 72% impervious [37]. Water bodies, forest wetland, treed wetlands, wetland, and wetland shrub have 0% imperviousness [43]. Both forests and trees are assumed to have 1% impervious cover [44]. Cropland is considered to be 3% impervious [43]. The total % imperviousness of each sub-basin was estimated by the sum of each % imperviousness of one land use multiplied by the area-weighted land use, as given below:  
\[\%Total\ Impervious=\frac{\sum_{i=1}^{n}(A_{i,\;LU}\times\% Impervious_{i})}{A_{ total}} \tag{5}\]  
The final estimated _CN_ as well as the % total imperviousness of every sub-basin are shown in Table 4.  
The parameters that concern the Clark Unit Hydrograph transform method [38] are the time of concentration (\(T_{c}\)) expressing the demanded time so that the precipitated water from the most remote place arrives at the basin's exit [45], and the storage coefficient (\(R\)) indicating the short-lived storage of excess rainfall in the hydrological catchment until it discharges to the exit [39]. Various studies have concluded that the ratio \(R/(T_{c}+R)\) of a watershed is steady, having a value range from 0.1 in the case of an urban catchment runoff to 0.7 in the case of a marshy and flat basin [46]. Thus, supposing that when the ratio is equal to 0.7 it corresponds to 0% urban territory, as well as when the ratio is equal to 0.1 it corresponds to 100% urban area, then the resulting ratios for each sub-basin are displayed in Table 4.  
Various empirical equations estimate \(T_{c}\), taking into account the watershed's geomorphological characteristics. The empirical formulas which were applied in this study are listed in Table 5, each one fitting better in sub-basins with specific characteristics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sub-Basin**} & \multicolumn{2}{c}{**Curve Number (CN)**} & \multicolumn{2}{c}{**\% Total**} & \multicolumn{2}{c}{**\% (Urban**} & \multirow{2}{*}{\(\frac{R}{T_{c}+R}\)} \\  & **Weighted CN\({}_{\text{II}}\)** & **CN\({}_{\text{I}}\) (Dry** & & & \\  & **(Normal Conditions)** & **Conditions)** & & & \\ \hline W1460 & 59 & 38 & 8 & 10.5 & 0.637 \\ W790 & 80 & 63 & 10 & 13.1 & 0.6214 \\ W800 & 79 & 61 & 19 & 25.8 & 0.5452 \\ W900 & 81 & 64 & 16 & 23.1 & 0.5614 \\ W1030 & 91 & 81 & 73 & 97.7 & 0.1138 \\ W1020 & 85 & 70 & 42 & 54.9 & 0.3706 \\ W1180 & 89 & 77 & 73 & 99.5 & 0.103 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the Humber sub-basins’ important variables.