## 3 Results
### Monte Carlo Approaches
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & & & & & & & \\ \hline \multicolumn{8}{c}{**Rational method**} \\ \hline  & \multicolumn{4}{c}{**e\({}_{\text{mean}}\)(\%)**} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 2.4 & 3.9 & 4.3 & 2.6 & 2.9 & 4.1 & 4.2 & 2.7 \\ Median & 1.5 & 3.2 & 3.3 & 2.3 & 2.1 & 3.5 & 3.3 & 2.3 \\ STD & 2.3 & 2.8 & 3.3 & 1.7 & 2.6 & 3.1 & 3.5 & 2.1 \\ \hline \multicolumn{8}{c}{**NRCS method**} \\ \hline  & \multicolumn{4}{c}{**e\({}_{\text{mean}}\)(\%)**} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 1.6 & 0.5 & 0.2 & 2.3 & 41.2 & 42.6 & 47.8 & 38.1 \\ Median & 0.8 & 0.4 & 0.1 & 1.9 & 42.7 & 43.3 & 49.2 & 38.5 \\ STD & 1.8 & 0.4 & 0.2 & 1.5 & 7.3 & 7.5 & 6.8 & 6.3 \\ \hline \multicolumn{8}{c}{**Rational method**} \\ \hline  & \multicolumn{4}{c}{**e\({}_{\text{mean}}\)(\%)**} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 2.6 & 4.7 & 5.8 & 3.2 & 3.5 & 5.6 & 5.8 & 3.3 \\ Median & 2.2 & 2.5 & 4.5 & 2.8 & 2.7 & 3.0 & 4.2 & 3.1 \\ STD & 2.2 & 8.3 & 4.3 & 2.4 & 3.0 & 13.9 & 5.1 & 2.7 \\ \hline \multicolumn{8}{c}{**NRCS method**} \\ \hline  & \multicolumn{4}{c}{**e\({}_{\text{mean}}\)(\%)**} \\ \hline  & **Win** & **Spr** & **Sum** & **Aut** & **Win** & **Spr** & **Sum** & **Aut** \\ \hline Mean & 0.6 & 1.1 & 0.7 & 1.3 & 44.4 & 44.8 & 47.8 & 42.6 \\ Median & 0.5 & 0.6 & 0.1 & 1.1 & 44.8 & 44.3 & 47.3 & 42.5 \\ STD & 0.4 & 2.0 & 2.9 & 0.8 & 5.3 & 10.7 & 10.3 & 5.5 \\ \hline \end{tabular}
\end{table} 
Table 4: (a) Mean, median, and standard deviation (STD) of the errors on the mean (e\({}_{\text{mean}}\)) and standard deviation (e\({}_{\text{STD}}\)) evaluated in the case of synthetic runoff profiles, for the Paterno case study. (b) Mean, median, and standard deviation (STD) of the errors on the mean (e\({}_{\text{mean}}\)) and standard deviation (e\({}_{\text{STD}}\)) evaluated in the case of synthetic runoff profiles, for the Busachi case study. The synthetic profiles of the direct runoff evaluated by the Rational method show error statistics very close in magnitude to those obtained for precipitation, with two exceptions for Busachi, i.e., the STD of the error on the mean and standard deviation in spring. In contrast, in the case of the NRCS method, the synthetic direct runoff error statistics provided better results on the mean than the synthetic precipitation, in both case studies. However, the error statistics on standard deviation give results that are an order of magnitude greater than the respective statistics of the synthetic precipitation profiles, and then of the synthetic runoff profiles (Rational method). This fact could be due to the nonlinear nature of the link between precipitation and direct runoff expressed by the NRCS equation. Regarding the synthetic generation of daily SMC profiles, the historical daily values of the specific seasons of the specific year are considered as data base. This implies that the synthetic generation algorithm is applied on significantly less data than hourly precipitation data. Table 5a,b shows the results obtained. The error statistics on the mean reveal little deviation between the historical and simulated averages, for both locations, comparable even with the statistics obtained in the case of precipitation; on the other hand, the error statistics on the standard deviation are higher than those on the mean, even by an order of magnitude, as in summer in Patermo, and winter, spring, autumn in Busachi. These statistics of the error on the standard deviation may or not be considered acceptable depending on the objectives of a given research work: for the purposes of this paper, the percentage values of these statistics are considered acceptable. Furthermore, it is desired to understand whether, by considering more data for generating synthetic profiles of SMC, results in lower percentage errors on the standard deviation than in the previous case.