## 3 Methods  
### Sampling and Analysis  
To characterize the hydrogeochemistry of groundwater in the study area, 15 of the most representative springs with different geochemical features were selected (e.g., from low to high mineralization, the presence and/or absence of free gases and bubbling) from among approximately 80 springs measured in previous studies [39]. Water samples were collected during two surveys performed in October 2018 and January 2019. In each sampling campaign, chemical-physical parameters (temperature, pH, and electrical conductivity) were also measured on-site through the multiparametric probe WTW Multi 3620 IDS. The collected samples for several analyses (including major and trace elements, stable isotope of water, dissolved and free gases, and noble gas isotope ratio) were kept at low temperatures in ice-filled fridge boxes to avoid alterations of components prior to the laboratory analyses. Samples for the determination of major (anions and cations) and trace element concentrations were analyzed at the Geochemistry Laboratory of Earth Sciences Department of Sapienza University (Rome, Italy). Samples for analysis of the stable isotopes (\(\delta\)18O-H\({}_{2}\)O and \(\delta\)D-H\({}_{2}\)O), gaseous contents, and isotopic ratios were sent to the geochemistry laboratories of the National Institute of Geophysics and Volcanology of Palermo. Samples for the major and trace element analyses were filtered in situ through a 0.45 \(\upmu\)m filter into polyethylene bottles. In addition, waters collected for trace element analysis were acidified with added concentrated ultrapure HNO\({}_{3}\) to prevent the precipitation of metals. Samples for the analyses of stable isotopes and dissolved gases were collected in glass bottles. Gas samples were collected in Pyrex bottles with vacuum valves at both ends, taking care to prevent air contamination. For the determination of major ions, samples were analyzed by ion chromatography. Waters with a high electrical conductivity (greater than 800 \(\upmu\)S/cm) were diluted with ultrapure water before inserting them into the chromatograph. To determine the anionic content (F\({}^{-}\), Cl\({}^{-}\), SO\({}_{4}\)\({}^{2-}\), and NO\({}_{3}\)\({}^{-}\)), a Dionex ICS 5000 chromatograph was used, while the cationic content (Ca\({}^{2+}\), Mg\({}^{2+}\), Na\({}^{+}\), and K\({}^{+}\)) was determined by a Dionex ICS 1100 chromatograph. The analytical error associated with these instruments is less than 5%, as also testified by the cation-anion balance checked on each sample [69]. The software Dionex Chromeleon, connected to both chromatographs, allowed us to know the concentrations of each major ion of the sampled waters in terms of ppm (mg/L). Alkalinity was measured by titration with 0.05 N HCl on site. Analysis of the trace elements was carried out using an ICP-MS spectrometer (X Series 2 Thermo Fisher Scientific Waltham, MA, USA). Ultrapure water (Millipore, Milli-Q, 16 M\(\Omega\) cm) was used to prepare blanks, standard solutions, and sample dilutions, and an internal standard, Rh, was added to correct the ICP-MS instrumental drift. The analytical accuracy of this method ranges between 2% and 5% [21; 70]. Measurement of the stable isotopes of water (\(\delta^{18}\)O and \(\delta\)D) was carried out on samples collected in the first campaign (October 2018) to improve the hydrogeochemical model and to understand the mixing processes between the waters of the regional karst system and those of deep origin. These analyses were performed at the Istituto Nazionale di Geofisica e Vulcanologia of Palermo, Sicily, Italy. The isotopic ratio of oxygen was measured using a Thermo Delta V Plus mass spectrometer coupled to a GasBench II, exploiting the equilibration technique between H\({}_{2}\)O and CO\({}_{2}\)[71]. For the determination of the hydrogen isotopic ratio, a Delta Plus XP mass spectrometer coupled with a TC/EA reactor was utilized. The isotopic values for the waters are expressed in \(\delta\)% vs V-SMOW (Vienna Standard Mean Oceanic Water).