# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## Materials and Methods
### Hydrological Model HEC-HMS, Setup, and Methods
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Author**} & **Formula** & **Notes** & **References** \\ \hline Simas–Hawkins & \(T_{\text{C}}=0.0085\frac{A^{(5.94)}+(\frac{100}{200}-10)^{0.313}}{L^{(3.94)}+( \frac{5.915}{5.92})}\) & Data of 168 basins in USA & [47; 48] \\ Johnstone–Cross & \(T_{\text{C}}=0.4623\frac{10.5}{575}\) & Data of 19 rural basins in USA & [49] \\ Williams & \(T_{\text{C}}=\frac{0.605-L}{(1005)^{L^{2}}+A^{0.21}}\) & Specially recommended to rural basins & [50] \\ Carter & \(T_{\text{C}}=0.0977\frac{10.6}{575}\) & Data of an urban basin in USA & [51] \\  & & (A \(<\) 20.72 km\({}^{2}\), \(<\) 0.005) & [51] \\ \hline \hline \end{tabular} Notes: Simas–Hawkins is in English units, where \(A\) (\(\hat{\text{n}}^{2}\)) is the watershed area, \(L\) (ft) is the longest flowpath, and \(S\) (ft/ft) is the slope of the longest flowpath. Johnstone–Cross, [PERSON] and [PERSON] formulas are in S.I. units, where \(L\) (km) is the longest flowpath, \(S\) (m/m) is the slope of the longest flowpath, and \(A\) (km\({}^{2}\)) is the watershed area.  
\end{table} 
Table 5: List of formulas used for the estimation of the time of concentration (h). The parameters regarding the exponential recession baseflow method are the initial discharge per area, the recession constant, and the ratio-to-peak. The recession constant expresses the decay of the baseflow rate among two rain events, determined as the proportion of baseflow at the time being to the specific baseflow which occurred the previous day [38]. The recession constant may take values among 0.3, relating to small basins, and 0.8, regarding large basins [52]. The ratio-to-peak was the preferred process of resetting the baseflow to its initial value throughout a rain event, which will occur at the time that the present baseflow was divided by the highest baseflow decreases at the determined value [38]. The parameters that concern the Muskingum routing method are the Muskingum \(K\) (h) expressing the time that the flood wave travels along the channel [38], and the Muskingum \(X\), a dimensionless weighting factor among influx and outflux, ranging from 0 in the case of maximum attenuation in which the flood wave's shape is flattening to 0.5 in case that there is no attenuation of the rainwater proceeding through the channel [39]. The number of sub-reaches of the channel should also be introduced [38], a parameter that does not cause considerable differences on the flow hydrograph at the exit of the sub-basin, whether the routing system of the channel consists of one reach, or either two or three sub-reaches [53]. The channels from the outlets of the sub-basins W1460, W790, W800, and W900 were routed to the exit of the sub-basin W1020. The corresponding routing channels were named R1580, R1590, R1600, and R1610. In addition, the water channels from the exits of the sub-basins W1030 and W1020 were directed to the outlet of the sub-basin W1180, named R1620 and R590, respectively, while there is no gauging station at this sub-basin's exit. We assumed that the movement of rainwater through totally agricultural lands with high levels of infiltration may lead to maximum attenuation, corresponding to a Muskingum \(X\) equal to 0, whereas in totally urban areas it was considered that there was equal weight among influx and outflux, and the flood wave propagated into the reach uniformly, without attenuation, therefore the Muskingum \(X\) was equal to 0.5. The length of the channels, their slopes, as well as the resulting Muskingum \(X\) parameter per each channel, are displayed in Table 6.  
The output hydrograph at the exit of the sub-basin W1020 results from the water precipitated at the particular sub-basin, as well as the rainwater routed through the channels R1580, R1590, R1600 and R1610. In addition, the flow hydrograph at the outlet of the ungauged sub-basin W1180 was derived from the rain fallen to the specific sub-basin added to the rain directed via the reaches' channels R1620 and R590.