## 4 Discussion  
There are only a few contributions in the literature on modelling hydropower generation as a function of meteorological and hydrological variables in the context of adequacy analyses. This paper attempts to fill this gap in the literature by providing tools for modelling water availability for power generation using statistical methods. The results obtained suggest that the Monte Carlo approaches applied may be suitable for simulating hourly values of water availability for hydropower generation. Indeed, by creating synthetic precipitation profiles, hourly synthetic profiles of direct runoff can be obtained, considering either the intensity of the precipitation or its accumulated amount. These simulated hourly profiles can thus be used as input for conducting adequacy analyses. In fact, simulations of hourly profiles of water availability can be used as input to hydropower generation models, thereby simulating hourly profiles of hydropower generation for adequacy analyses by researchers and transmission system operators. In addition, this approach can be used to simulate several years of hydropower plant operation, so that different possible scenarios can be considered in each simulated year with an acceptable computational effort. In this way, both researchers and transmission system operators can understand the limits within which a given hydropower plant can elastically provide its availability to meet energy demand in a given region characterized by a specific climate, thus improving the adequacy level of the market area in which the power plants are located. Furthermore, the method proposed here can be applied to hydropower plants with reservoirs of any size and flow rate. For plants that belong to low- extent catchments, the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{(a)} \\ \hline  & \multicolumn{3}{c}{\(\mathbf{e_{mean}(\%)}\)} & \multicolumn{6}{c}{\(\mathbf{e_{STD}(\%)}\)} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 5.9 & 6.4 & 1.6 & 2.5 & 8.1 & 7.7 & 30.5 & 16.6 \\ Median & 5.7 & 6.3 & 1.4 & 2.5 & 6.3 & 7.0 & 24.1 & 15.6 \\ STD & 1.6 & 1.2 & 1.0 & 1.2 & 6.7 & 5.3 & 26.7 & 9.9 \\ \hline  & \multicolumn{6}{c}{(b)} \\ \hline  & \multicolumn{3}{c}{\(\mathbf{e_{mean}(\%)}\)} & \multicolumn{6}{c}{\(\mathbf{e_{STD}(\%)}\)} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 2.4 & 3.2 & 2.2 & 3.1 & 21.3 & 12.3 & 26.4 & 36.2 \\ Median & 2.3 & 3.1 & 2.3 & 2.8 & 13.8 & 7.4 & 24.6 & 28.4 \\ STD & 1.4 & 1.0 & 1.1 & 1.6 & 24.1 & 12.5 & 21.7 & 30.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: (a) Mean, median, and standard deviation (STD) of the errors on the mean (\(\mathbf{e_{mean}}\)) and standard deviation (\(\mathbf{e_{STD}}\)) evaluated in the case of synthetic soil moisture daily profiles, for the Paterno case study, using twenty years of data for each individual season. (b) Mean, median, and standard deviation (STD) of the errors on the mean (\(\mathbf{e_{mean}}\)) and standard deviation (\(\mathbf{e_{STD}}\)) evaluated in the case of synthetic soil moisture daily profiles, for the Busachi case study, using twenty years of data for each individual season. Rational Method is well-suited, while for plants that belong to extensive catchments, the NRCS method can be chosen. Regarding the results of the linear regressions presented in Section 3, the strong positive correlation found for both sites in winter can be explained by the fact that winter is modelled for the months of December, January, and February and the greater amount of precipitation that accumulates in the soil in December and January meets higher radiation intensity and temperatures in February. Indeed, more water is available to the soil for evapotranspiration due to the late winter precipitation, and more ET\({}_{0}\) is available due to the higher irradiance and temperatures.