# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## 3 Results
For the 4-10 July 2013 event, the index was very good for all the sub-basins. In Figures 3 and 4, the rainfall distribution as well as the observed and modeled hydrographs, the latter resulting from both hydrological models, are displayed at the outlet of the six gauged sub-basins, regarding the events 28-30 May 2013 and 4-10 July 2013, respectively. In Table 11, the calibration of the Muskingum \(K\) (h) parameter at the channels R1580, R1590, R1600, and R1610 of the HEC-HMS hydrological model due to the severe storm of 4-10 July 2013 was performed, concerning the resulting peak discharge at the exit of the sub-basin W1020, by using the Nash-Sutcliffe index. The assumed number of sub-reaches per each channel, without causing any discrete changes at the output hydrograph, were set to three for the channels R1580, R1590, and R1610, whereas one was considered for the channel R1600. The best-applied values for Muskingum \(K\) at the channels R1580, R1590, R1600, and R1610 at the outlet of the sub-basin W1020 were 4.5 h, 3 h, 1.1 h, and 2 h, respectively, and produced a Nash-Sutcliffe coefficient equal to 0.897. Figure 3: Precipitation, observed and modeled discharge of the 28-30 May 2013 rain event at the six gauged stations. Concerning the events of the 7-15 April 2013 and 30 April-7 May 2017 with the two hydrological peaks, the detailed chosen parameter values that better verified the observed flow hydrographs at the exit of the six gauged sub-basins, as well as the resulting Nash-Sutcliffe indices for each sub-basin, per hydrological model, are indicated in Tables 12 and 13. Observing Table 12, regarding the HEC-HMS hydrological model, the calibrated values of the ratio \(R/(T_{c}+R)\), compared with the reference values of Table 4, were increased by 9.9%, 4.6%, 53.8%, and 1.2% in the sub-basins W1460, W790, W1030, and W1020, respectively, whereas there was a reduction by 8.3% and 6.5% in the sub-basins W800 and W900, respectively. The calibration of the CN showed that the reference values of dry conditions fitted well at most of the sub-basins, except for the applied value at the urban sub-watershed W1030. In this case, it was decreased by 19.8% in comparison to the calculated reference value. Concerning the % imperviousness, in addition to the sub-basin W1020 where there was a small reduction of 9.5% compared to the reference value, in the sub-basin W1030 there was a significant decrease of 50%, while in the remaining \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Outlet of Sub-Basin** & \(T_{c}\) **(h)** & \(\frac{R}{T_{c}+R}\) & \(R\) **(h)** & \(\infty\) **(\(D\))** & **\(\infty\)** & **Initial** & **Decisrange** & **Recession** & **Ratio to** & **7–15 April** & **30 April-7** \\
**Sub-Basin** & & & & & **Impervious** & **per Area** & **Constant** & **Peak** & **2013** & **May 2017** \\ \hline W1460 & 14.07 & 0.7 & 32.83 & 38 & 24 & 0.012 & 0.8 & 0.475 & 0.647 & 0.858 \\ W790 & 8.67 & 0.65 & 16.09 & 63 & 22 & 0.0035 & 0.8 & 0.1 & 0.696 & 0.924 \\ W800 & 14.15 & 0.5 & 14.15 & 61 & 27 & 0.003 & 0.8 & 0.3 & 0.682 & 0.818 \\ W900 & 11.77 & 0.525 & 13.01 & 64 & 55 & 0.003 & 0.8 & 0.1 & 0.646 & 0.935 \\ W1030 & 4.03 & 0.175 & 0.85 & 65 & 36.5 & 0.002 & 0.3 & 0.275 & 0.611 & 0.516 \\ W1020 & 18.04 & 0.375 & 10.83 & 70 & 38 & 0.01 & 0.8 & 0.025 & 0.767 & 0.714 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: HEC-HMS model verification via parameter calibration for the events of 7–15 April 2013 and 30 April–7 May 2017. Figure 4: Precipitation, observed and modeled discharge of the 4–10 July 2013 rain event at the six gauged stations. sub-watershers, there was a considerable increase in comparison to the initial values. This increase was important so that the model was verified. This is explained because the studied events have two hydrological peaks, thus by the time of the second peak precipitation intensity, the soil was saturated enough, and therefore less water was infiltrated, hence the % imperviousness was higher than the initially calculated values.