## 3 Materials and Methods  
Fourteen water samples, coming from Capodacqua di Spigno Spring, were analysed by the Isotope Geochemistry Laboratory of the University of Parma (Italy), using the IRMS (isotope-ratio mass spectrometry--Finnigan Delta Plus equipment) continuous flow-equilibration method with CO\({}_{2}\) for \(\delta^{18}\)O and H\({}^{2}\) for \(\delta^{2}\)H. Regarding the isotopic composition of rainfall water, no sampling was performed in the rainfall gauge stations considered in this study. Isotopic abundance ratios are expressed as parts per million of their deviations, as given by the Vienna Standard Mean Ocean Water (VSMOW) Equation (1):  
\[\delta\ =\ \frac{\left(\text{R}_{\text{sample}}-\text{R}_{\text{SMOW}}\right)}{ \text{R}_{\text{SMOW}}}\ \times\ 10^{3} \tag{1}\]  
where R = \({}^{2}\)H/\({}^{1}\)H for hydrogen and \({}^{18}\)O/\({}^{16}\)O for oxygen, the ratio of the heavy to light isotope and R\({}_{\text{SMOW}}\) is the isotopic ratio of the standard (Standard Mean Ocean Water) [1]. Results, shown in Table 1, are expressed as per million deviations from the internationally accepted standard VSMOW according to Equation (1). The analytical error is \(\pm 0.2\%\) for \(\delta^{18}\)O and \(\pm 1\%\) for \(\delta^{2}\)H.  
Figure 2: Geological framework and hydrographic network, based on [PERSON] et al., 2019 [15]. During the same days, that groundwater samples were taken, and discharge measurements were carried out along the river near Capodacqua di Spigno Spring, by the current-meter. The main equipment applied to measure the stream flow velocity is a SEBA horizontal axis current-meter F1. The SEBA current-meter has been used according to EN ISO 748:2007 requirements. This activity consisted mainly of measuring the excess flow rate of the spring in a discharge channel. In order to measure water velocity, we used the \"Three-Point Method\" described by the National Environmental Monitoring Standards (NEMS) [18]. Velocities were measured at 0.2, 0.6, and 0.8 of the depth below the surface. Knowing the flow rate exploited by the local water management company, it was therefore possible to reconstruct discharge supplied by Capodacqua di Spigno Spring (Table 2). In this regard, Figure 3 shows the graph that compares the trend of monthly rainfalls, the exploited flow rates (in grey) and the delivered flow rates by the spring (in blue), calculated as the addition of the outflowing discharges, measured in the river section, and flow rates exploited by the local water supply agency. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Date** & \(\mathbf{\delta^{18}O}\) **(\%\({}_{\circ}\) VSMOW)** & \(\mathbf{\delta^{2}H}\) **(\%\({}_{\circ}\) VSMOW)** \\ \hline
26 April 2018 & \(-\)7.2 & \(-\)40.1 \\
25 May 2018 & \(-\)7.2 & \(-\)40.4 \\
27 June 2018 & \(-\)7.3 & \(-\)41.0 \\
30 July 2018 & \(-\)7.3 & \(-\)41.1 \\
29 August 2018 & \(-\)7.3 & \(-\)40.9 \\
01 October 2018 & \(-\)7.4 & \(-\)41.2 \\
08 November 2018 & \(-\)6.9 & \(-\)37.9 \\
18 December 2018 & \(-\)6.8 & \(-\)37.6 \\
18 January 2019 & \(-\)7.1 & \(-\)39.8 \\
19 February 2019 & \(-\)7.2 & \(-\)40.3 \\
20 March 2019 & \(-\)7.3 & \(-\)40.6 \\
30 April 2019 & \(-\)7.2 & \(-\)40.1 \\
29 May 2019 & \(-\)6.7 & \(-\)37.2 \\
26 June 2019 & \(-\)7.4 & \(-\)41.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Isotope composition of spring water samples collected from May 2018 to June 2019.