## 2 Methodologies
### Further Physical Considerations of General Utility  
The amount of water that the soil can hold in the unsaturated zone depends on the porosity of the soil, which in turn depends on the soil texture. In fact, porosity is defined as the ratio of pore volume to total soil volume [34]; thus, once the texture of the soil is known, its porosity value can also be known [47]. It follows from the above definition that porosity is related to the amount of water contained in the soil. In fact, the soil is saturated when all the water fills the pore space, so denoting \(\theta_{\rm ST}\) as the volumetric water content (VWC) of the soil at saturation (unsaturated zone), \(\theta_{\rm ST}\) coincides with porosity. As a consequence, field capacity and the permanent wilting point are specific fractions of \(\theta_{\rm ST}\), and thus of porosity [33; 47]; the value of this fraction, depends on the soil texture.  
The ET at first member of (2) (Section 2.1) is actual evapotranspiration, that is, it is also related to the amount of water in the soil. In fact, given the type of land cover and soil texture, evapotranspiration increases (decreases) as SMC increases (decreases), all other atmospheric variables being equal. However, the evapotranspiration evaluated through the equations in Section 2.2 does not consider the amount of water in the soil. Due to this, it is therefore necessary to estimate the actual evapotranspiration, ET\({}_{0,\rm ACT}\), by tying potential ET\({}_{0}\) to the VMC. For this purpose, the following function is introduced here:  
\[\frac{\rm ET_{0,ACT}}{\rm ET_{0}}=\min\left\{\max\left[\frac{\theta-\theta_{ \rm WP}}{\theta_{\rm FC}-\theta_{\rm WP}},0\right],1\right\}(\rm dimensionless) \tag{14}\]  
where the first member is the ratio of the actual (ET\({}_{0,\rm ACT}\)) to potential evapotranspiration (ET\({}_{0}\)), and at second member \(\theta\) is the VMC; \(\theta_{\rm FC}\) is the VMC corresponding to the field capacity and \(\theta_{\rm WP}\) is that corresponding to the wilting point. Knowing ET\({}_{0}\) from Equation (3) and evaluating the ratio in (14), for daily values of \(\theta\), it is possible to obtain the values of ET\({}_{0,\rm ACT}\).  
Some hydrological considerations are worth drawing attention to:  
Figure 1: Map showing the geographical locations of the two Italian case studies Paterño (Sicily) and Busachi (Sardinia).  
* If the hydrological cycle was annual (rather than seasonal), then it would be possible to estimate approximately ET (2) as the difference between precipitation and runoff, being that SMC has annual cycles;
* From the perspective of hydropower generation, field capacity is useful water, being that more water causes both surface runoff and groundwater recharge;
* Since ET\({}_{0}\) is here calculated for grassland, the stomatal control of leaves does not come into play in the relationship between ET\({}_{0}\) and actual evapotranspiration (34). This physical aspect of grassland implies that the relationship between ET\({}_{0,\text{ATC}}\) and ET\({}_{0}\) is largely given by the water content of the soil;
* In applying the methodologies described in this section some assumptions were implicitly made: over the several years of simulations conducted, human land use does not change, and no mining of groundwater is carried out.