## 5 Results  
A new soil CO\({}_{2}\) flux survey was performed in the Mt. Amiata area in the summer of 2019 to expand the previously investigated area and delimit the degassing areas. Starting from the previously surveyed area, the new soil CO\({}_{2}\) flux survey was extended toward the south and south-east, now completely covering Bagnore and Piancastagnaio geothermal fields and a portion of the Paglia River Valley. There were 738 new soil CO\({}_{2}\) flux measurements collected over an area of about 60 km\({}^{2}\). The survey was performed using the same technique defined in the previous work with the same instrument under dry and stable weather conditions. The measurements were collected over a regular grid with a spacing of 250 m to maintain consistency with the previous general survey and integrate all data. [PERSON] et al. [16] concluded that the selected grid spacing was the best choice for a regional survey like this, considering the wide area under investigation, and showed that the grid spacing used was sufficiently accurate and adequate to reveal and highlightthe main degassing areas and structures, although small-scale degassing structures were not detected. The southeastern sector of the new survey, characterized by the presence of cultivated fields and pastures, was successfully covered with a regular grid of soil CO\({}_{2}\) flux measurements, while the presence of steep and impervious morphology prevented covering the southern part of the surveyed area with an equally spaced grid of soil CO\({}_{2}\) flux measurements (Figure 2). Because this work aims to estimate the total soil CO\({}_{2}\) flux over the Mt. Amiata area and that the two surveys were both made during the summer season under the same weather conditions, the whole soil CO\({}_{2}\) flux dataset was treated as a single dataset comprising 3208 measurements spanning over an area of 280 km\({}^{2}\) with a coverage of about 12 measures per km\({}^{2}\). A few measurements were discarded from the analytical treatment when the regression coefficient (R\({}^{2}\)) of the exponential regression of the fitting curve to the measured concentration in the chamber within the time exceeded 0.85. Soil CO\({}_{2}\) flux values in the Mt. Amiata area range from 0.43 up to 296.41 umol m\({}^{-2}\) s\({}^{-1}\) (1.6-1127 g m\({}^{-2}\) d\({}^{-1}\)) (Table 1 and Figure 3). The dataset was analyzed through the GSA method, and data were plotted on the log-normal probability plot ([PERSON], 1997). Even though the log-normal probability plot of soil CO\({}_{2}\) flux data in the Mt. Amiata area (Figure 4) does not show a clear polymodal statistical distribution, the partitioning of the flux data was performed as described by [PERSON] ([PERSON], 1997) and [PERSON] et al. (2006). Two inflection points were observed that identify three overlapping log-normal populations: i.e., population A (inflection point at 0.77 log\({}_{10}\)CO\({}_{2}\), umol m\({}^{-2}\) s\({}^{-1}\)), population C (inflection point at 1.55 log\({}_{10}\)CO\({}_{2}\), umol m\({}^{-2}\) s\({}^{-1}\)), and a third population (population B) made up of a mixture of populations A and C.  
Figure 2: Measurement points for the first A and second B surveys. The summary statistics for populations A, B, and C are shown in Table 2. [PERSON]'s \(t\) estimator [50] was used to calculate the mean flux, standard deviation, 95% confidence interval, and threshold of the log-normal populations identified with the procedure proposed by [PERSON] [48]. Population A is defined by a mean of 4.9 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\) (18.6 g m\({}^{-2}\) d\({}^{-1}\)) and a threshold of 10.41 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\) (39.6 g m\({}^{-2}\) d\({}^{-1}\)) and represents 20% of the dataset. Population A denotes the pure biological background population. Population C represents 6% of the dataset and is defined by a mean of 49.75 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\) (189.2 g m\({}^{-2}\) d\({}^{-1}\)) and a threshold of 32.6 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\) (123.9 g m\({}^{-2}\) d\({}^{-1}\)).