# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## 3 Results  
Regarding the HEC-HMS hydrological model, a sensitivity analysis was performed including eight parameters, by changing one parameter at a time. Each new parameter test was applied after checking the result from the comparison of the modeled and recorded hourly discharges. In the calibration process of the six studied events examined in pairs, it was found that specific equations were more suitable to calculate the time of concentration (\(T_{c}\)) at each sub-basin, since the \(T_{c}\) was very sensitive, producing great time shifts and variance of the maximum modeled runoff. In particular, the Simas-Hawkins formula fit best to the rural sub-watersheds (W1460, W790), the Johnstone-Cross equation matched most to the rural sub-basin with fairly urbanized areas (W800) and to semi-urban and semi-rural sub-basin (W1020), the Williams formula was applied properly to the rural sub-basin with some urban development at its outlet (W900), and the Carter equation was more appropriate for completely urban sub-basins (W1030 and the ungauged W1180). At the calibration procedure, the Nash-Sutcliffe efficiency (NSE) coefficient [65] was used in all studied sub-basins in order to measure the efficiency of the model, which is given by the following equation:  
\[R^{2}=1-\frac{\sum_{i=1}^{n}(Q_{sim,i}-Q_{obs,i})^{2}}{\sum_{i=1}^{n}\left(Q_ {obs,i}-\overline{Q_{obs}}\right)^{2}} \tag{6}\]  
where \(Q_{sim,i}\) (m\({}^{3}\)/s) is the simulated flow values at time interval \(i\), \(Q_{obs,i}\) (m\({}^{3}\)/s) is the observed flow values at time interval \(i\), \(\overline{Q_{obs}}\) (m\({}^{3}\)/s) is the mean observed flow value, and \(n\) is the number of time-steps. Concerning the HBV-light hydrological model, the analysis of fifteen parameters, by changing one at a time, was performed to investigate the model response. During the calibration procedure, it was noticed that the snowfall correction factor (_SFCF_) was a sensitive parameter in the rural sub-basins, generating a higher fluctuation of peak modeled discharge. Specifically, the rural sub-basins (W1460, W790) responded better with lower values of _SFCF_, thus the selected calibrated value was equal to 0.7; the rural sub-basins with enough urbanized regions (W800, W900) fit better with a slightly raised value of _SFCF_ equal to 0.9, thus a minor correction in the snowfall was assumed; the urban and semi-urban sub-basins (W1030, W1020) worked well with the factor equal to 1, therefore no correction to snowfall was needed. Moreover, the threshold air temperature (_TT_) below which precipitation was simulated as being snow rather than rain fit better at \(-0.5\)\({}^{\circ}\)C for the rural sub-basins and agricultural ones with some urban development, whereas for the urban and semi-urban sub-basins, _TT_ was set equal to 0 \({}^{\circ}\)C. The degree-hour factor (_CFMAX_) was calibrated close to its upper proposed value for all the sub-basins, specifically equal to 0.15 mm/h \({}^{\circ}\)C. Additionally, no seasonal variability was assumed in degree-hour, therefore the factor _SP_ was equal to 1. The three parameters of the soil moisture routine were applied per vegetation class. The maximum water content of the soil box (_FC_) was expected to be greater in the rural areas (forests, crops) than in the urban regions. On the other hand, the threshold value for actual evaporation reaching potential evaporation (_LP_) was supposed to be small in natural/vegetated zones, where actual evaporation was high. On the contrary, in built-up territories, the _LP_ was supposed to be higher because of the lower levels of actual evaporation. Moreover, increasing the _BETA_ parameter increased the runoff. The remaining twelve parameters of the snow, the response, and the routing routine were considered to be applied uniformly to all the land use zoning of each sub-basin. In particular, the parameters that concern the response routine showed neither trend between the studied sub-basins nor amongst the different rain events.