## 2 Materials and Methods
### Reference Evaptranspiration Model  
The reference evapotranspiration is an important notion in hydrological and agricultural applications, able to describe the evaporative demand of the atmosphere [15]. It only depends on the weather data and it can be defined as the evapotranspiration under standard conditions of a hypothetical grass reference crop according to FAO irrigation and drainage study No. 56 [15].  
In this study, daily reference evapotranspiration, ET\({}_{0}\), was computed by using daily weather data retrieved from ground sensors at AWS sites and, alternately, by using bias-corrected reanalysis data and spatially interpolated data from ground sensors by cross-validation.  
ET\({}_{0}\) (mm day\({}^{-1}\)) is computed with the FAO Penman-Monteith equation, as follows:  
\[\text{ET}_{0}=\frac{1}{\lambda}\frac{\Delta(\text{R}_{\text{n}}-\text{G})+ \gamma\frac{900}{\text{T}+2\gamma 3}\text{WS\text{-}VPD}}{\Delta+\gamma(1+0.34\text{-WS})} \tag{1}\]  
where:  
* \(\lambda\) is the latent heat of vaporization;
* \(\Delta\) is the slope of the vapor pressure curve (kPa \({}^{\circ}\)C\({}^{-1}\));
* \(\gamma\) is the psychometric constant (kPa \({}^{\circ}\)C\({}^{-1}\));
* T is the daily mean air temperature at 2 m height (\({}^{\circ}\)C) computed as the average between the daily maximum (T\({}_{\text{max}}\)) and minimum (T\({}_{\text{min}}\)) air temperature at 2 m height at the highest available temporal resolution of data;
* WS is the wind speed at 2 m height above ground (m s\({}^{-1}\)) computed from the wind speed at 10 m above the ground by multiplying for a factor of about 0.75 given by the logarithmic equation of the wind speed profile [15];
* VPD is the daily vapor pressure deficit (kPa), computed as function of T\({}_{\text{max}}\) and T\({}_{\text{min}}\) and relative humidity, RH. If available, dew point temperature (T\({}_{\text{dew}}\)) is used for computing VPD, instead of RH);
* R\({}_{\text{n}}\) is the net radiation at the crop surface (MJ m\({}^{-2}\) day\({}^{-1}\)) and G is the soil heat flux density (MJ m\({}^{-2}\) day\({}^{-1}\)). The net radiation (R\({}_{\text{n}}\)) was calculated as the difference between the incoming net shortwave radiation and the outgoing net long-wave radiation. The incoming net shortwave radiation is a fraction of the incoming shortwave solar radiation (RS), computed for the reference crop by setting the albedo equal to 0.23.  
Table 3 reports monthly statistics averaged over years 2008-2018 for daily ET\({}_{0}\), computed with ground-based weather data at the 18 AWSs.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Station** & **April** & **May** & **June** & **July** & **August** & **September** \\ \hline
**ID** & **Mean** & **cv** & **Mean** & **cv** & **Mean** & **cv** & **Mean** & **cv** & **Mean** & **cv** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 3: Monthly statistics for Food and Agriculture Organization of the United Nations (FAO) Penman–Monteith reference evapotranspiration, ET\({}_{0}\) (mm day\({}^{-1}\)), averaged over years 2008–2018.  
The mean daily ET\({}_{0}\) values over the region are 2.78 mm day\({}^{-1}\) in April, 3.51 mm day\({}^{-1}\) in May, 4.55 mm day\({}^{-1}\) in June, 4.94 mm day\({}^{-1}\) in July, 4.00 mm day\({}^{-1}\) in August and 2.80 mm day\({}^{-1}\) in September. The minimum mean value over a month of daily ET\({}_{0}\) is registered in September, 2.21 mm day\({}^{-1}\) and the maximum in July, 5.54 mm day\({}^{-1}\). The mean coefficient of variation is minimum in July, 0.17 and maximum in April, 0.32.