## 2 Materials and Methods  
### Monitoring Data  
The monitoring data used in the present work were: \({}^{220}\)Rn (thoron) activity concentration, fumarolic tremor, background seismicity, ground deformation, CO\({}_{2}\) air concentration flux and the temperature and pressure of the hydrothermal system (Figure 1).  
The \({}^{220}\)Rn activity concentration (Bq/m\({}^{3}\)) monitoring was carried out by continuous measurements in the soil gas of Campi Flegrei caldera, at Monte Olibano and Monte Sant'Angelo sites. Monte Olibano (OLB) is inside a disused railway tunnel into the central area of the caldera; while Monte Sant'Angelo (MSA) is outside the Department of Physics '[PERSON]' of the University of Naples \"Federico II\" [27]. The \({}^{220}\)Rn measurements were performed by electrostatic collection of the ionized descendants of the gas (\({}^{216}\)Po, \({}^{212}\)Po and \({}^{212}\)Bi) on a Silicon detector inside a cylindrical metallic chamber [28]. The monitor used was the RaMonA\({}^{\text{\textregistered}}\) system, able to distinguish and observe weak signals, e.g., from the \({}^{220}\)Rn, in the presence of a lot of background noise due to \({}^{220}\)Rn [29]. The complete alpha spectrum of \({}^{220}\)Rn and \({}^{222}\)Rn was analyzed by FORTAS\({}^{\text{\textregistered}}\) software, which allows the adequate discrimination of thoron and radon progeny by deconvolution fitting processes with high accuracy [30]. The soil gas was 1 L/min pumped gas from a depth of 0.80 m to the inlet of the metallic chamber. This air inlet position allowed relatively constant environmental processes. The time interval of detected and processed data was 1 h, but the daily average of the data was used in the analysis. The same methodology was also used to monitor the \({}^{222}\)Rn, using \({}^{218}\)Po and \({}^{214}\)Po descendants [1]. The device also monitored temperature, relative humidity and pressure inside the detection chamber and in the surface soil of the measurement site. The detailed description of the entire process of \({}^{220}\)Rn monitoring can be found in [29; 30].  
The fumarolic tremor measures seismic changes in ground vibration, in m/s, in real time (real-time seismic amplitude measurement-RSAM). A characteristic RSAAM value was computed daily by assuming as representative the minimum value registered during the night, corresponding to the time of the day when anthropogenic noise is lowest (lower than during daylight hours). It was monitored by a 3-component seismometer located at the Pisciarelli fumarole. Analytical methodologies and uncertainties are described in [31; 32; 33]. The background seismicity refers to the cumulative distribution of Campi Flegrei seismicity, which simply corresponds to the sum of the days in which at least one earthquake occurred. The reference station for Campi Flegrei seismicity is located close to the Pisciarelli hydrothermal area where the post-2000 seismicity focuses. A full description of the Campi Flegrei seismic network is reported in [23; 32]. Ground deformation data (cm) represent the maximum vertical displacement acquired by the GPS network, which provided measurements of the 3D time changes in stations operating at Campi Flegrei. A full description of the GPS network is reported in [32; 33]. The CO\({}_{2}\) concentration flux (umol/mol) from Pisciarelli vent was monitored by systematic sampling. The analytical methods and their uncertainties are available in [19; 34]. The trend of CO\({}_{2}\) flux, used in this work, was computed by applying the EMD method (see Section 2.2). The temperature and pressure of the hydrothermal system was estimated by applying a gas-equilibria approach applied to the hottest fumaroles of Campi Flegrei. The details are in [35].