## 2 Methodologies
### Precipitation Data Assessment and Models for Water Availability in Hydropower Plants
\(\mathrm{I_{a}}\) and \(\mathrm{S}\) are related by the following empirical relationship [45]:  
\[\mathrm{I_{a}}=0.2\cdot\mathrm{S}(\mathrm{mm}) \tag{10}\]  
\(\mathrm{S}\), in turn, is evaluated by the following formula [31]:  
\[\mathrm{S}=\left(\frac{1000}{\mathrm{CN}}-10\right)\cdot 25.4(\mathrm{mm}) \tag{11}\]  
where \(\mathrm{CN}\) (dimensionless) is the runoff curve number, that is, a numerical coefficient that depends on the total precipitation (both duration and intensity), soil moisture status prior to precipitation, soil type, land cover type, and temperature. These meteorological and hydrological variables that influence the values of \(\mathrm{CN}\), and thus the resulting runoff, are called Antecedent Runoff Conditions (ARC) and are divided into three classes: ARC I (dry conditions), ARC II (average conditions), and ARC III (wetter conditions) [45; 46]. In this paper, it is assumed the ARC II class is valid. The values of \(\mathrm{CN}\) in the case of grassland and different types of soil texture take the following values [31]: \(\mathrm{CN}=39\) for sands, \(\mathrm{CN}=61\) for loans, \(\mathrm{CN}=74\) for clay loans, and \(\mathrm{CN}=80\) for clays. Monte Carlo Approaches for Synthetic Generation of Hourly Profiles of Precipitation and Runoff, and Daily Profiles of Soil Moisture Content  
Analyses of power generation from both programmable and non-programmable renewable sources requires stochastic modeling. In the case of hydropower generation, the generation of synthetic time series of meteorological and hydrological variables, for stochastic water availability assessments, go in this direction. In this paper, the Monte Carlo method is used to generate hourly synthetic profiles of precipitation and runoff, along with daily SMC profiles; the latter have a daily resolution since no hourly resolution is available for them in [29]. The Monte Carlo approach is chosen since it lends itself well to the stochastic simulations applied in this work, in which the number of variables makes the computational weight acceptable. In addition, ENTSO-E and several transmission system operators (including Italy's Terna) apply adequacy analyses using the Monte Carlo approach; however, they use the Monte Carlo method for the stochastic generation of availability profiles, whereas in this work Monte Carlo is used for the stochastic generation of time series of meteorological and hydrological quantities. Synthetic hourly precipitation profiles (mm/h) are evaluated by fitting a probability distribution over the twenty years of available data; specifically, a family of Pearson distributions is chosen, from which a single distribution identified through the mean, standard deviation, kurtosis, and skewness of the historical data series is selected. Random numbers are then extracted according to the distributions thus identified, and synthetic hourly precipitation series are obtained as output. This procedure is repeated using each year of historical data as a basis for each season; in this way, the inter-seasonal variability of precipitation trends is considered. Specifically, to simulate the inter-annual variability of precipitation trends, the algorithm implemented in this paper randomly chooses a single year from the twenty years of data, and the just described fitting and extraction procedure is applied to it. Once the synthetic hourly precipitation hourly profiles are obtained, at each Monte Carlo simulation, they are put as inputs into Equations (8) and (9), thus also obtaining synthetic direct runoff profiles. Regarding SMC data, they are expressed in saturation fractions (range from zero to one), with one indicating a soil completely saturated. Compared to the stochastic generation of hourly precipitation profiles, a different Monte Carlo algorithm is used for the generation of synthetic daily profiles of SMC. In fact, SMC synthetic profiles are generated through inverse and bootstrap methods together.