# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## Materials and Methods
### Precipitation Data
Under these circumstances, the average velocity of the precipitated water should have been equal to 1.1 m/s. Noticing the second pair of events with the two hydrological peaks, during the 7-15 April 2013 rain event, the interest was focused on the second peak of precipitation intensity which was higher than the first one in all the sub-basins by a factor of 0.42 to 1.26. The raise was not proportional to the peak runoff; specifically, the sub-basins W1460 and W1030 showed a decrease in the peak discharge at the second peak compared to the first one. Moreover, the second peak discharge was higher than the first one in the rest four sub-basins by a factor of 0.26 to 0.50. Generally, in all the watersheds, the time of the first peak discharge was quite delayed in relation to the time of the first peak precipitation height because the precipitated water between the two mentioned times was significant. Indicatively, regarding the sub-basin W1460, the time of the first peak discharge occurred 31 h after the time of first peak precipitation, while in the meantime 21 mm of rain fell. In this case, the resulting average velocity of the peak rain should have been very low and equal to 0.28 m/s. Concerning the 30 April-7 May 2017 rain event, although the first peak precipitation was higher than the second one in nearly all the sub-basins except for W1030, nevertheless, the second peak discharge was higher than the first one in most of the sub-basins, in addition to W1030 and W900. However, in the latter one, the differences were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Event**} & \multicolumn{6}{c}{\(\Delta t\) (h) = Time of Observed Peak Q – Time of Max P} \\ \cline{2-7}  & **W1460** & **W790** & **W800** & **W900** & **W1030** & **W1020** \\ \hline
28–30 May 2013 & 18 & 10 & 6 & 10 & 2 & 14 \\
3–10 July 2013 & 14 & 11 & 13 & 11 & 3 & 15 \\
7–15 April 2013 & 31 & 29 & 34 & 32 & 23 & 29 \\ (1 st and 2 nd peak) & 13 & 10 & 13 & 10 & 2 & 12 \\
30 April–7 May 2017 & 13 & 14 & 18 & 28 & 1 & 13 \\ (1 st and 2 nd peak) & 27 & 28 & 29 & 13 & 15 & 25 \\
26–30 June 2010 & 17 & 11 & 5 & 13 & 1 & 2 \\
22–25 June 2017 & 7 & 2 & 6 & 9 & \(-\)4 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time difference between the time of the observed peak discharge and the time of the peak precipitation intensity for the six studied precipitation events. very small, almost indistinguishable. The above observation in most of the sub-basins was because lots of millimeters of rain fell between the second peak precipitation and the second peak discharge. In particular, regarding the sub-basins W1460, W790, and W800, the second peak precipitation intensity was equal to 3.2 mm, 2.6 mm, and 2.6 mm correspondingly, whereas the second peak discharge came after 27 h, 28 h, and 29 h, respectively, after quite enough additional precipitated water to the corresponding sub-basins equal to 35.3 mm, 35 mm, and 32.9 mm. The developed average velocities were particularly low. Regarding the third pair of events, having normal to wet AMC at the agricultural lands, first of all, the AMC of the sub-basin W1020 of the 26-30 June 2010 event were very close to the upper limit of the dry conditions--and thus were considered as Type I. The same was supposed for the 22-25 June 2017 event. For the latter event, the AMC of the sub-basin W790 were very close to the upper limit of normal conditions, and hence were assumed to be Type II. Moreover, the AMC of the sub-basin W900 were very close to the lower limit of normal conditions, and therefore were regarded as Type II. The above considerations were applied for the uniformity of the initial conditions. Within a more thorough observation of the third pair of events with the 5 days' AMC classified as normal (Type II), in regard to the sub-basin W790 of the 26-30 June 2010 event, the 5 days' AMC were recorded as equal to 46.5 mm. After that, at a period of 35 h of the rain event, 18.2 mm of water fell, which did not classify the event as a sudden one, but mostly as one of longer duration.