# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## Materials and Methods
### Precipitation Data  
Hydrological modeling performance was conducted through the study of six single precipitation events, examined in pairs with similar characteristics. The selected events occurred from 2010 to 2017, mostly during the growing season (spring and summertime). The precipitation was spatially and temporally varying, thus hourly data were collected by sixteen rain gauges across the Humber River Watershed, which thereafter were used to calculate--via gauge weighting--the mean areal precipitation in each of the sub-basins, through the Thiessen polygons methodology. The characteristics that made the examined events significant, studying them in pairs, were: (a) high precipitation intensity in all the sub-basins, higher than 10 mm/h, with values even equal to 25 mm/h, under dry antecedent moisture conditions (AMC Type I); (b) double hydrological peak in a short period, also under dry AMC; and (c) various antecedent moisture conditions, specifically normal (Type II) to wet (Type III) AMC in the predominantly rural sub-basins, whereas dry AMC (Type I) in the urban--for the most part--sub-basins. In all the aforementioned categories, the total amount of precipitated water was greater in the second studied event of each pair. The hydrometric features of the six studied rainfall events examined in pairs, along with the observed peak discharges, are indicated in Table 2. Especially for the events of normal to wet AMC at agricultural lands, an adjustment to some of the considered AMC types was assumed, which is one of the factors that determine the curve number (_CN_), so that there is uniformity in the respective sub-basins of the particular rain events. The limits of rainfall values of the previous five days that specify the type of AMC per season are defined in Section 2.3. Figure 2: (a) Land uses and (b) soil groups of Humber River Basin. Base maps reprinted from Agriculture and Agri-Food Canada under Open Government License—Canada, vers. 2.0 ([[https://open.canada.ca/en/open-government-licence-canada](https://open.canada.ca/en/open-government-licence-canada)]([https://open.canada.ca/en/open-government-licence-canada](https://open.canada.ca/en/open-government-licence-canada)), accessed on 11 May 2020). Another important factor for the hydrometric analysis of the examined events is the time difference \(\Delta t\) (h) between the time of the observed peak discharge and the time of the peak precipitation intensity for every monitored sub-basin, which is shown in Table 3. Considering that \(\Delta t\) is equal to the travel time of the peak rainfall from the basin's inlet to reach the outlet, expressed by the corresponding flow hydrograph, then \(\Delta t\) (h) is given by the equation:  
\[\Delta t=\frac{L\times 1000}{V\times 3600} \tag{1}\]  
where \(L\) (km) is the length of the longest flow path of the sub-basin and \(V\) (m/s) is the average velocity. Examining the sub-basin W800 of the first pair of events having high precipitation intensity, regarding the 28-30 May 2013 event, during five days before the storm, the AMC were equal to 3.5 mm, followed by 11.8 mm of rainwater during only 19 h of the precipitation event, which implied that the ground was already saturated before the peak rain intensity. Then, in 1 h, 10.7 mm of rain fell, which was the peak precipitation, and the peak discharge came after 6 h, which is quite reasonable. The resulting average velocity of the peak rain should have been equal to 2.5 m/s, very realistic due to the saturated terrain. On the other hand, concerning the same sub-basin of the 3-10 July 2013 severe rain event, during five days before the storm, the AMC was equal to 0.2 mm. Afterward, during 111 h of the rain event, only 18.8 mm of precipitated water occurred, which signified that there were very dry conditions before the peak rain intensity. Since then, in 4 h fell 58.1 mm of rain, while the 17.9 mm fell only in 1 h, which in total explained the observed peak discharge occurring 13 h after the peak rain intensity.