# Hydrological Analysis of Extreme Rain Events in a Medium-Sized Basin
## Materials and Methods
### Hydrological Model HBV-Light, Setup and Methods  
The HBV-light model developed by the University of Zurich, a conceptual semi-distributed model capable of simulating the runoff of a basin comprised of several sub-watersheds [54], such as the Humber River basin, was the other one of the two models applied to calibrate the six single examined events. The initial model, Hydrologiska Byrans Vattenbalansavdelning (HBV) was primarily developed by the Swedish Meteorological and Hydrological Institute (SMHI) [55; 56]. Although the HBV-light model is a relatively recent version, the research community already uses it widely for flood forecasting, and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Channel** & **Length (km)** & **Slope (m/m)** & **Muskingum \(X\)** & **Routed to Exit** \\  & & & **of Sub-Basin** \\ \hline R1580 & 75.522179 & 0.001905 & 0.3 & W1020 \\ R1590 & 51.146611 & 0.00185 & 0.3 & W1020 \\ R1600 & 19.12083 & 0.001358 & 0.425 & W1020 \\ R1610 & 24.819795 & 0.00226 & 0.25 & W1020 \\ R1620 & 7.358818 & 0.002319 & 0.45 & W1180 \\ R590 & 12.12955 & 0.003117 & 0.45 & W1180 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Characteristics of the channels routed at the exit of the sub-basins W1020 and W1180. producing valid output results [57; 58; 59; 60; 61; 62]. The HBV-light version uses a warming-up period so that the initial state values progress to their proper values based on the meteorological data and parameter calibration [54; 63]. The warming-up period of the model for each one of the six studied rainfall events was one year, which is considered to be satisfactory and is shown in Table 7.  
A hydrological basin, in addition to potentially including various sub-basins, may also be divided into several elevation zones with mean altitudes representing area fractions of different vegetation classes. The simulation of basin discharge results by using precipitation, air temperature, and potential evaporation as input data [54], which in our case study were on an hourly time-step. Observed runoff was compared with the simulated runoff during model calibration. The unit of runoff was millimeters per hour. The simulation was performed in an hourly time-step. Three vegetation classes were considered per sub-basin which concerned forests/wetlands, croplands, and urban uses expressed as fractions of the sub-basin's area for each elevation zone. The fractions of the vegetation classes per sub-basin are shown in Table 8. As the sub-basins W1460, W790, W800, and W900 end up in sub-basin W1020, as the generated runoff to the latter sub-basin resulted from the addition of the previous four to the current one, being rescaled with the use of the relative contribution of the absolute areas for each of the sub-basins. The six studied sub-basins were divided into two to four elevation zones. The mean areal precipitation calculated through the Thiessen polygons methodology for each gauged sub-basin was applied to the elevation of the centroid of the sub-basin. Temperature data at the hourly time-step were also available from the network of sixteen meteorological gauges across the total hydrological basin. The average temperature of the stations closer to the centroid of each sub-basin was also applied at the centroid's elevation. Due to several altitude zones, an increase in precipitation (_PCALT_) by 10%/100m as well as a lapse rate of air temperature falling due to increasing altitude (_TCALT_) by 0.6 \({}^{\circ}\)C/100 m were considered, as proposed by [PERSON] [63]. Potential evaporation data were provided by field measurements conducted by [PERSON] et al. [64] at a naturalized/vegetated field and a residential/industrial region of the Greater Toronto Area, at a monthly time-step being converted into hourly data. As expected, the potential evaporation is lower in the urban area than in the rural one. The model uses four routines for the hydrological simulation of each sub-basin: (a) the Snow Routine, characterizing snowfall accumulation and snowmell; (b) the Soil Moisture