Introduction

The emission of volcanic-hydrothermal fluids from fumaroles and soil diffuse degassing structures (DDS) are prevalent forms of thermal energy release in quiescent volcanoes1,2, and their monitoring is of primary importance in understanding volcanic activity3,4,5,6. The amount of CO2 emitted by volcanic DDS is thought to be, globally, a relevant contributor (likely the most important) to the CO2 budget from volcanic activity to the atmosphere7,8. However, the uncertainties in determining the amount of the volcanic diffuse CO2 emission are significant, as biological activity can also produce abundant CO2. In fact, over the last 20 years, the definition and characterization of the diffuse degassing processes has been based, with a few exceptions, only on CO2 flux measurements without differentiating between their possibly disparate deep- (i.e., volcanic-hydrothermal) or shallow (i.e., biogenic) sources. Coupling CO2 flux measurements with other parameters collected from the surface or within the soil in volcanic areas (e.g. 2,9,10), can be crucial to better decipher the actual fraction of gas emitted from magmatic-hydrothermal systems. This approach is of fundamental importance in cases where the statistical partitioning11 and subsequent removal from the total CO2 output of non-hydrothermal CO2 flux (of biogenic origin) is not easily applicable or ambiguous. Ultimately, a multi-parametric strategy circumvents over-interpretation in the extent and the amount of deep degassing estimated for active volcanoes worldwide.

In addition to monitoring of CO2 in volcanic areas, the determination of radon (222Rn) and thoron (220Rn)—two radiogenic nuclides produced within the crust by the radioactive decay of radium progenitors in the U-Th decay series (ref.12 and refs therein)—in the soil gas phase may help differentiating shallow and deep sources of gas9,13. Owing to the very different half-lives of 222Rn (3.82 d) and 220Rn (55.6 s), their ratio can be a proxy for the depth at which they are released. In absence of any preferential flow pathways, such as fractures and faults, radon gas diffuses and disperses slowly through the rock-soil pores, covering only very short distances from its source14. Consequently, 222Rn-220Rn activities detected in the subsurface are mostly related to the contribution of shallow gas production by U-Th-bearing minerals in the rock-soil matrix. However, in active volcanic areas and fault zones, the relatively fast advective transport of fluids along permeable structures may mobilize the radon gas produced in the crust for longer distances15,16. According to this scenario, the gas measured from volcanic soil may be interpreted as a mixture between two different contributions9: (1) shallow radon gas production (i.e., low 222Rn/220Rn ratio) within an undisturbed soil and (2) deep radon gas production (i.e., high 222Rn/220Rn ratio) with transport towards the surface in the presence of carrier gases (e.g., CO2).

Here, we report and discuss the results obtained by a multi-parametric survey, with the aim of unequivocally determining the sources of the gases measured from the soil of the Nisyros caldera (Aegean Arc, Greece; Fig. 1a, b), selected as a test site. The Nisyros caldera is one of the earliest volcanoes at which soil CO2 fluxes were measured17 and where detailed maps of the degassing structures exist18,19. A recent CO2 flux survey has documented that the soil CO2 emission is controlled by nine different DDS (Fig. 1c; ref.19), which correspond to the fracture network of the caldera and to the hydrothermal craters. From the 1st to the 9th of April 2019, we monitored emissions at 55 locations (Fig. 1c): (1) 32 sampling points located at the DDS 9 (samples A); (2) 16 sampling points located at the east of DDS 9 (samples B); (3) 7 sampling points randomly located at the hydrothermal craters (samples C).

Figure 1
figure 1

(a) Location of Nisyros and (b) extent of the caldera and of the CO2 flux survey of October 201819. The map was generated using the open source QGIS software (available at https://www.qgis.org/it/site/) using the Bing Aerial base map. (c) Probability map of the CO2 flux measured during October 2018 (redrawn after ref.19). The 9 diffuse degassing structures (DDS) are defined by solid line perimeters. DDS 7, 8, and 9 cover the southern part of the Lakki plain, while the DDS 1–6 extend over the hydrothermal area of the caldera (white circles indicate the fumarolic vents). Samples A, B, and C are reported as green, blue and red circles, respectively. Easting and northing coordinates refer to the WGS 84/UTM zone 35 S.

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Among these sites, we focus more specifically on samples A, which extend over a DDS located at the southwestern edge of the Lakki plain and adjacent to the Lofos dome (DDS 9 in Fig. 1c). In the samples A area, anomalous soil CO2 emission is related to a NW–SE lineament, which probably corresponds to the buried tip of a 2-km-long NW–SE fault cutting the Profitis Ilias dome18. This fault was active during the last seismic swarm recorded at Nisyros in 1996–199720. Due to sedimentary cover and the superposition of vegetated soils, there is no visible surface evidence of hydrothermal outgassing (e.g., argillic alteration, sulfur deposition or fumarolic vents).

Measurements of different parameters were performed during a wet season. We selected H2S-free sites to avoid the prolonged exposure of the RAD7 radon detector to sulfur-bearing gas species. The sampling strategy adopted for each site consisted of measurements of the soil CO2 flux (in g m−2 d−1), determination of the carbon isotopic composition in the CO2 efflux from the ground (δ13CCO2 in ‰ vs. V-PDB), as well as measurements of soil temperature (T in °C), CO2 concentration (CCO2 in vol%) and 222Rn (radon) and 220Rn (thoron) activities (in kBq m−3) at 80 cm of soil depth (Table 1). In addition, we measured the soil permeability (k in m2; see “Methods”), which displayed medium-to-high values. Finally, we sampled and analyzed the δ13CCO2 of the main fumaroles, and specific laboratory experiments were designed to characterize Rn exhalation from soils and rocks in the area of interest (see “Methods”).

Table 1 Gas measurements at Nisyros caldera at the surface or at 80 cm of soil depth.
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The aim of the study is to clearly characterize the deep degassing signal coming from the magmatic-hydrothermal system as recorded by gases present in and emanating from the soil. In order to achieve this objective, we employ an approach based on the carbon isotopic signature in the CO2 efflux to quantitatively subdivide the measured CO2 fluxes (measCO2 flux) into a fraction of magmatic-hydrothermal origin (deepCO2 flux) and a fraction derived from shallow biogenic production (bioCO2 flux) active in the soil. To simplify data interpretation, we apply Principal Component Analysis (PCA) on the entire multi-parametric data set.

Results and discussion

Results from our multi-parametric survey are listed in Table 1 and are summarized in the boxplots of Fig. 2, which describe the statistics of the data. In the following subsections, we briefly discuss the significance of each measured parameter in terms of its shallow versus deep origin, and we perform a multivariate analysis.

Figure 2
figure 2

Boxplots and tables of the geochemical parameters (CO2 flux, δ13CCO2,e, CCO2, T, 222Rn, 220Rn, and 222Rn/220Rn ratio) measured at Nisyros caldera, summarizing the descriptive statistic of the data. Boxplots of the computed variables deepCO2 flux and bioCO2 flux are also shown. Samples A, B and C are marked with green, blue and red colors, respectively.

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Measured parameters

Soil temperature and CO2 concentration

Values of soil T and CCO2 range over large intervals (from 12.9 to 81.3 °C and from 0.4 to 52%, respectively; Table 1; Fig. 2), noting the different processes controlling each of these variables. Such processes were investigated applying the graphical statistical approach (GSA11, see “Methods”), that entails analyzing the distribution of the data in log-probability plots, where a normal population delineates a straight line, while n normal overlapping populations define curves characterized by n−1 inflection points. Both T and CCO2 data define curves characterized by one inflection point (Fig. 3), indicating the overlapping of background (population I in Fig. 3) and anomalous values (population II in Fig. 3).

Figure 3
figure 3

Probability plots of (a) soil temperatures and (b) soil CO2 concentrations at 80 cm depth. Both the plots define the overlapping of 0.7 population I (background) and 0.3 population II (anomaly). The anomalies refer to all the samples C (hydrothermal craters) and to some of the samples A (DDS 9).

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The means of the background T and CCO2 populations (population I) were estimated at 17.6 °C ± 0.4 °C and 6.0% ± 1%, respectively, while the means of the anomalous T and CCO2 populations (population II) at 44.9 °C ± 5.1 °C and 32.3% ± 4.6%, respectively (for details on the calculations see “Methods”). It is worth noting that in both cases (T and CCO2) the anomalous values represent 30% of the measurements. This coincidence is not surprising, because both the anomalies are generated by the subsurface condensation of vapors rising from the hydrothermal system located at depth in the Lakki plain (ref. 19 and refs therein). In detail, the anomalously high temperatures reflect the latent heat of condensation, while the high CCO2 are caused by the CO2 contents of the original hydrothermal vapors.

Diffuse CO2 fluxes from biogenic and deep carbon sources

During each CO2 flux measurement with the accumulation chamber (AC; see “Methods”), we collected two samples of gas at different CO2 concentration to analyze both δ13CCO2 and CCO2 in laboratory (see “Methods”). Each couple of δ13CCO2 − CCO2 (δ13CCO2,I − CCO2,I, δ13CCO2,II − CCO2,II; Table S1) plotted in the δ13CCO2 versus 1/CCO2 diagram (Fig. 4), defines a mixing line between the CO2 present in the chamber at the time of the first measurement, and the CO2 entering the chamber during the interval of time between the two measurements (i.e., the soil CO2 efflux). The isotopic composition of each CO2 efflux (δ13CCO2,e, the gas entering the AC) has been computed as the intercept at 1/CO2 = 0 (i.e., pure CO2) of the straight line determined by the corresponding couple δ13CCO2,I − CCO2,I, δ13CCO2,II − CCO2,II.

Figure 4
figure 4

δ13CCO2 versus 1/CO2 plot. The concentration of CO2 is expressed as ppm by volume (i.e., pure CO2 corresponds to 1/CO2 = 0). The isotopic composition of the CO2 efflux (δ13CCO2,e; see the violet circles) was computed as the y intercept at x = 0 of the straight lines connecting the first (δ13CCO2,I − CCO2,I) and second (δ13CCO2,II − CCO2,II) samples. See the text for further explanation.

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The δ13CCO2,e of the measured gas was used to assess the relative contributions of the bioCO2 flux active in the soil and the deepCO2 flux coming from the hydrothermal system to the measCO2 flux. The multi-step computation begins by partitioning the statistical distribution of the δ13CCO2,e values, applying the GSA approach11,21 (see “Methods”). Values of δ13CCO2,e plotted in the probability diagram (Fig. 5), define three distinct populations. About 30% of the samples belong to the biogenic CO2 population with the lighter values of δ13CCO2,e (δ13CCO2, bio = − 27.2 ± 1.4‰), typical of the biogenic carbon produced in the soil. About 26% of the samples belong to the deep CO2 population with the heavier values of δ13CCO2,e (δ13CCO2,deep = − 1 ± 0.7‰). The remaining 44% of the samples consist of a mixed population with values of δ13CCO2,e (− 17 ± 9‰) intermediate between the biogenic and deep CO2 populations.

Figure 5
figure 5

Probability plot of the carbon isotopic composition of the soil CO2 efflux and fumarolic CO2. The green and the red fields indicate the mean carbon isotopic composition ± 1σ of both biogenic and deep CO2 populations.

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The mean δ13CCO2 value of the deep CO2 population (δ13CCO2,deep = − 1 ± 0.7‰), mostly defined by the δ13CCO2 of the fumarolic fluids and by the δ13CCO2,e of samples C, is significantly heavier than that of the typical magmatic CO2 (MORB δ13CCO2 ≈ − 4 to – 8‰ (ref. 22 and refs therein)). This divergence may result from a variety of mutually inclusive processes, such as (1) release of crustal CO2 from the subducted carbonate, (2) fractionation within the hydrothermal system (e.g., boiling, fluid-rock interaction, precipitation of carbonate minerals), (3) thermal and/or metamorphic decarbonation of the limestone (Aegean limestone δ13C = − 0.5 to 2.5‰23,24) basement of Nisyros (as was suggested also for Santorini volcano10,25).

We therefore conclude that the deepCO2 flux (1) is equals to the measCO2 flux (i.e., bioCO2 flux = 0) for the samples with δ13CCO2,e > − 1.7 ‰ (i.e., heavier than the mean δ13CCO2,deep − 1σ), and (2) is equals to 0 (i.e., bioCO2 flux = measCO2 flux) for samples with δ13CCO2,e < − 25.8 ‰ (i.e., lighter than the mean δ13CCO2, bio + 1σ). For the samples with intermediate values of δ13CCO2,e, we computed the fractions of the deep (Y) and biogenic (1–Y) CO2, using the following carbon isotopic mass balance:

$$\delta^{13} {\text{C}}_{{\text{CO2, e}}} = \delta^{13} {\text{C}}_{{{\text{CO2}},deep}} \times Y + \delta^{13} {\text{C}}_{{{\text{CO2}},bio}} \times \left( {1{-}Y} \right);$$
(1)

Through Eq. (1), we have derived the deepCO2 flux (deepCO2 flux = measCO2 flux × Y) and the bioCO2 flux (bioCO2 flux = measCO2 flux × (1–Y)).

Results show a relatively high bioCO2 flux estimated for both the samples A and B (Table 1 and Fig. 2), with a mean of 17.6 g m−2 d−1 and 24.5 g m−2 d−1, respectively. In particular, the CO2 diffusively emitted from the sites of samples B derives mostly from biogenic activity, indicative of a minimal deepCO2 contribution (Fig. 2). The mean value of bioCO2 flux of samples B, i.e. 24.5 g m−2 d−1 (95% confidence interval of 13.3–35.7 g m−2 d−1), is up to one order of magnitude higher than the mean of the biogenic fluxes estimated for the same area in October 2018 and in 1999–2001 (~ 4 g m−2 d−1 and 8 g m−2 d−1, respectively; ref.18,19,21). The environmental factors (e.g., air–soil temperature and humidity, rain, wind speed) can affect the biogenic soil CO2 emission26,27,28,29,30 by favoring soil respiration processes (i.e., roots, microbial and fauna respiration, and decomposition of organic matter31). Indeed, the bioCO2 flux increase is clearly related to the wet meteorological conditions encountered before and during the survey, which promoted growth of vegetation in the Lakki plain. In previous surveys (1999–200118 and 201819), this area was instead characterized by a few shrubs growing in bare soils, due to the very dry summer.

Radon and thoron activities and exhalation rates

Given the short half-life (55.6 s) and low recoil range (30 nm) of 220Rn, the relatively high activity of 220Rn (and low 222Rn/220Rn ratio) in samples A and B (Fig. 2), measured with RAD7 (see “Methods”), suggests that the nuclides are recoiled in the soil matrix or, at least, at shallow levels (e.g., 32). Considering the medium-to-high permeability of the soil (Table 1) and a subsurface fluid flow timescale of ~ 5 min (i.e., five half-lives of 220Rn), it is reasonable to conclude that the radon gas measured traveled no further than a few tens of centimeters of depth by diffusion (~ 10–6 m2 s−133). On the other hand, the high activity of 222Rn of samples A (see the outliers of 222Rn and 222Rn/220Rn boxplots in Fig. 2) is indicative of a deep contribution by an advective gas-carrying fluid transport9,13,34,35,36,37,38,39,40. Consistent with this scenario, these samples display also relatively high deepCO2 flux (see also deepCO2 flux outliers of samples A in Fig. 2).

The 222Rn/220Rn ratios of the soil gas samples C are very high and define a separate data population (Fig. 2). The low levels of 220Rn of samples C (Fig. 2) are mostly related to a low number of free-state radon atoms residing and accumulating within the altered soil matrix. The persistent and intense circulation of hot, acidic hydrothermal fluids led to argillic alteration and secondary mineralization in this area of the caldera41. Accordingly, the soil structure alternates between porous- and sealed portions. The self-sealing of the pore volume between minerals increases the probability of radon recoil into the same or adjacent mineral grains rather than into the pore space42, therefore, it locally reduces the emanation of radon12,43. Conversely, most of the 222Rn activity measured in samples C is of deeper origin and related to the effect of an advective carrier gas (Fig. 2). The absence of correlation (R2 = 0.06) between 222Rn activity concentrations measured during the survey and the exhalation rate (E222) determined in laboratory (see “Methods”), and the extremely low values of E222 of both soils and rhyolitic-rhyodacitic rocks (Table 2), strengthen the hypothesis that a large amount of 222Rn reaches the surface by an advective transport mechanism controlled by deepCO2 fluxes. This is particularly evident for the samples C (Fig. 2), which, together with the outliers of samples A, show maximum deepCO2 fluxes (up to 208.6 g m−2 d−1) with respect to the entire data set.

Table 2 Soil and rock samples used for the determination of the 222Rn and 220Rn exhalation rates.
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Deep versus shallow degassing component and DDS definition

Despite careful inspection of the scatterplot matrix (Fig. S2), there is no straightforward way to interpret correlations between variables, in particular to distinguish whether they are controlled by deep or shallow degassing processes. To simplify the interpretation, we investigate which variable, or combination of variables, control the observed large (spatial) variability of the data. Thus, we performed a Principal Component Analysis (PCA, see “Methods”) on the different measured parameters (deepCO2 flux, bioCO2 flux, T, CCO2, 220Rn, and 222Rn/220Rn ratio). PCA aims at defining a set of linearly uncorrelated variables called principal components (PC), ranking them in terms of their overall control on the variance. Therefore, PCA, which is often used to reduce dimensionality in the data set by selecting those variables that mainly control the variance in the data, is here applied to summarize and simplify the relationships among the presented multivariate set of data. In our case, the firsts three PC cumulatively retain 90.9% of the total variance in the data. The eigenvectors matrix and the importance of components in Table 3a show that PC1 explains the 61.9% of the variance in the data set, and describes a dimension to which deepCO2 flux, CCO2, T, and 222Rn/220Rn ratio contribute almost equally. PC2 retains the 15.2% of the variance in the data set and delineates a dimension mainly correlated with bioCO2 flux. PC3 accounts for 13.8% of the variance in the data set, suggesting that most of the contribution is loaded by 220Rn and bioCO2 flux. The remaining PC (i.e., PC4, PC5, and PC6) explain only a minor part of the total variance in the data and, hence, are not further considered. Such results from PCA clearly indicate that the variance in the data is governed by two different degassing components: (1) PC1 is related to deeper sources and (2) PC2 and PC3 (i.e., the residual variance) are related to shallower processes. This is particularly evident upon inspection of the biplots (Fig. 6), displaying both the principal component scores (i.e., circles, triangles, and squares for samples A, B and C, respectively) and the loading vectors (i.e., purple arrows). PC1 places much weight on variables strongly controlled by magmatic-hydrothermal processes (i.e., deepCO2 flux, T, CCO2, and 222Rn/220Rn ratio). Their almost equal contribution on PC1 is documented by the length of each vector (Fig. 6), while their strong positive correlation is shown by the low angles between the vectors (Fig. 6). The shallow degassing component (represented by PC2 and PC3) depends on bioCO2 flux and 220Rn activity, which are quite positively correlated in PC2, and uncorrelated in PC3 (Fig. 6). The absence of a clear correlation attests to the independent origins of the two shallow signals: bioCO2 flux is controlled by soil biogenic processes, while 220Rn activity depends on the physical–chemical properties of the soil (e.g., Ra content in the mineral phase and porosity).

Table 3 Principal Component Analysis (PCA) of deepCO2 flux, bioCO2 flux, CCO2, T, 222Rn/220Rn ratio, and 220Rn activity. (a) refers to the PCA performed using the whole data set; (b) refers to the PCA performed using the data of samples A (Table 1). “Propor. Variance” indicates the amount of the variation represented by the different eigenvalues. “Cum. Prop.” indicates the proportion of variance cumulatively retained by the eigenvalues.
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Figure 6
figure 6

Biplot of PC1 versus PC2 and PC1 versus PC3 for the data acquired on April 2019. The markers represent the scores of samples A, B, and C on the PC1, PC2, and PC3 extracted from Principal Component Analysis. The purple arrows indicate the PC loading vectors. The length of the vector from the origin reflects the variance of the variable. The correlation between two variables is given by the angle between two vectors; the smaller is the angle, the greater is the correlation65. For each group of samples, 80% bivariate ellipses of the scores are drawn.

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PC1, PC2, and PC3 displayed in Fig. 6 satisfactorily reproduce the geochemical differences observed among samples A, B and C. Samples with large positive scores on PC1 are highly influenced by a deep degassing process, whereas those with negative scores are weakly dependent on hydrothermal system dynamics. The analysis indicates that samples C are most affected by the deep component (Fig. 6), in agreement with the very active hydrothermal circulation of fluids in this portion of the caldera, whereas samples B are mostly affected by the shallow soil activity. Consequently, their scores are located in a narrow portion of the negative PC1 dimension, while they have significantly higher scores on PC2 and PC3 (Fig. 6). On the other hand, samples A appear to reflect contributions from both deep and shallow degassing components. A consistent part of the scores overlaps in the region of shallow degassing defined by the scores of samples B, while the remaining scores of samples A spread over the PC1 dimension and approach the values of samples C (Fig. 6). The overall distribution of the samples A, intermediate between those of samples B and C, is distinguished by the shape and orientation of the green ellipses.

The distinction between a deep and a shallow degassing component becomes particularly clear from analysis of PCA results performed using only samples A (Table 3b; Fig. 7). Notably, 94.6% of the variance in the data can be explained by PC1 (60.7%), PC2 (19.3%) and PC3 (14.5%). PC1 is almost entirely controlled by deepCO2 flux, CCO2, T, and 222Rn/220Rn ratio (Table 3b), to which they contribute almost equally, and they are near-perfectly positively correlated (Fig. 7). PC2 and PC3 are strongly controlled by bioCO2 flux and 220Rn (with an almost equal contribution; Table 3b), and they are negatively correlated (Fig. 7).

Figure 7
figure 7

Biplot of PC1 versus PC2 for the samples A data acquired on April 2019. The numbers associated to the green circles (namely, the scores of PC1 and PC2) correspond to the number of samples A in Table 1. The very low angles between the deepCO2 flux, T, CCO2, and 222Rn/220Rn ratio loading vectors indicate a strong positive correlation between these variables, which together define the deep degassing component PC1.

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The data sets of the four variables defining the deep degassing component were processed to construct deepCO2 flux, CCO2, T, and 222Rn/220Rn ratio 2D maps of the DDS extending over the site from which samples A were taken, by a sequential Gaussian simulation (sGs, see “Methods”). These maps are compared to the CO2 flux map in order to understand differences in the estimation of the degassing from DDS (spatial distribution and quantitative estimation of the gas output) deriving from the multi-parametric approach.

The map of the NW–SE alignment of the DDS highlighted during the previous campaign (Fig. 8a), shows the spatial distribution of the CO2 fluxes measured in October 201819. The maps of T (Fig. 8e) and CCO2 (Fig. 8f) in this region are very well correlated, and the spatial distribution of the anomaly is in concordance with the 2018 CO2 flux alignment. The new map of CO2 fluxes recorded in April 2019 (Fig. 8c) follows the general trend of outgassing from NW towards SE but, at the same time, illustrates a large extension of the DDS. Furthermore, the total CO2 output of the DDS in April 2019 is estimated at 4.54 t d−1, while the same area in October 2018, when the bioCO2 flux was very low, emitted 1.80 t d−1. Our new deepCO2 flux data from April 2019 (Fig. 8d) provide an estimation of the total output of CO2 (1.82 t d−1) very close to that found on October 2018, thereby excluding the possibility of any change in hydrothermal-volcanic CO2 emission. This conclusion is also supported by the absence of any manifestations (e.g., earthquakes, ground deformations, gravimetry changes, and increase of fumarolic activity) of volcanic unrest recorded after October 2018, that instead occurred at Nisyros after the seismic crisis of the 1996–199718,20,44,45,46,47,48. Nevertheless, the October 2018 map of CO2 flux was constructed using more points (i.e., 124) than those collected in the April 2019 survey. To facilitate comparison between the two data sets, we used the October 2018 data set to randomly draw a set of measurements (i.e., 32) identical of those from the April 2019 data set, following their spatial distribution as closely as possible (Fig. 8b). Obviously, the DDS loses detail on a graphical representation, but the new estimation for the CO2 output of October 2018 is still less than the half of April 2019 (i.e., 2.13 t d−1 versus 4.54 t d−1), and hence the discrepancy in CO2 fluxes between the two dates cannot be explained by a difference in sampling density.

Figure 8
figure 8

E-type maps constructed by a pointwise linear average of 200 sequential Gaussian simulations of different attributes over the area covered by samples A. The black circles represent the sampling sites. The maps show: (a) the CO2 flux measured during October 201819. (b) the CO2 flux measured during October 2018, produced using 32 points sampled from the original data set. (c) the CO2 flux measured on April 2019. (d) the deepCO2 flux. (e) T. (f) CCO2. (g) 222Rn/220Rn ratio. (h) PC1 scores. The maps were created with the software Surfer, version 11.0.642 (https://www.goldensoftware.com/products/surfer). Easting and northing coordinates refer to the WGS 84/UTM zone 35 S.

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Therefore, the CO2 flux measurements alone would lead to the erroneous conclusion that the increased extent and total CO2 output from the DDS resulted from magmatic-hydrothermal activity. Instead, because the biogenic CO2 production strongly increased in this area in April 2019, accounting for about 60% (~ 2.72 t d−1) of the total CO2 daily output, the total CO2 flux also increased, despite the fact that the intensity of the volcanic activity was similar at the time of the two surveys. This behavior can be quantified with estimates of the deepCO2 flux, which more faithfully tracks the extent of the DDS (Fig. 8d) and its total CO2 output. Importantly, the deepCO2 flux map pairs with the anomaly defined by the 222Rn/220Rn ratio map (Fig. 8g), suggesting again the advective transport of 222Rn by deepCO2. More generally, the extent of the DDS defined by the variables linked to the deep degassing (deepCO2 flux, T, CCO2, and 222Rn/220Rn ratio) are very well correlated with each other (Fig. 8d–g). The map of the PC1 scores (Fig. 8h), i.e. the deep degassing component returned from PCA, integrates all information from deepCO2 flux, T, CCO2, and 222Rn/220Rn ratio maps, thereby most accurately reflecting the distribution of magmatic-hydrothermal outgassing relative to shallow background gases. The importance of the multi-parametric approach is underlined by the capacity to better define the spatial distribution of DDS.

Concluding remarks

The multi-parametric approach presented in this study has important ramifications for a better understanding of the degassing behavior of magmatic-hydrothermal systems. Correct interpretation of diffuse CO2 fluxes from the soil is not a trivial task in active volcanic areas, especially when measurements are conducted in different periods of the year affected by seasonality and/or in humid and vegetated areas. The Nisyros caldera represents an ideal test site in which seasonal variations may result in changes in biogenic gas production with respect to the magmatic-hydrothermal CO2 emissions. We demonstrate that the biological processes contribute up to 60% of the total CO2 output, thus causing potential misinterpretation of surveillance measurements of CO2 fluxes if they were to be attributed to volcanic-hydrothermal activity alone. The analysis of different soil gas parameters (δ13CCO2, CCO2, T, and 222Rn/220Rn ratio) permits the classification and interpretation of the different contributors to the observed hydrothermal gas emission. Through a Principal Component Analysis, we identify three main components. The component that predominantly controls the variance (PC1) is correlated to a deep degassing process, which is closely associated with hydrothermal system dynamics (i.e., deepCO2 flux, T, CCO2, and 222Rn/220Rn ratio); the other significant components (PC2 and PC3) are instead related to shallow degassing processes (i.e., bioCO2 flux and 220Rn). Hence, the main result from the PCA is to integrate all indicators of deep gas sources into one component not affected by shallow, non-hydrothermal processes (e.g., seasonal/biological effect on gas production).

Methods

Field survey and laboratory analysis

Diffuse CO2 flux and isotopic compositions of the CO2 efflux

Following ref.11, the diffuse emission of CO2 from the soil was measured with the accumulation chamber (AC) methodology, employing an instrument developed at the Università di Perugia and described in detail in ref.19. The gas line from the infrared sensor (IR) to the AC, was modified by inserting a T-connector with a pierceable septum which permits direct sampling of the gas phase2,10,49 (see Fig. 2 in ref.2). During each flux measurement, two samples of gas were collected using a syringe equipped with a shut-off valve and then stored in a 12 mL-evacuated-vial (Labco Exetainer) for further analysis of δ13CCO2 and CO2 concentration. The first sample was taken at the beginning of the AC measurement when the CO2 concentration was relatively low, while the second sample was taken later when the CO2 concentration increased (see samples CCO2,I and CCO2,II, respectively, in Table S1). The carbon isotopes of CO2 (δ13CCO2,I and δ13CCO2,II, Table S1) were determined within a week of the sampling at the laboratories of INGV Osservatorio Vesuviano. The samples were analyzed using a continuous flow isotope ratio mass spectrometer (Thermo-Finnigan Delta XP) interfaced with a Gasbench II device that was equipped with an autosampler (δ13CCO2 standard error ± 0.1‰). For each sample, CO2 concentrations were determined both in the field (using the IR of the AC) and in laboratory together with the isotopic analysis. The determined concentrations were found to be in good accord, demonstrating the accuracy of the two techniques (Fig. S1).

Isotopic composition of the fumarolic CO2

During the survey, the main fumaroles of Lakki plain were sampled and analyzed (Table S2) to have an independent measurement of δ13CCO2 of deep origin involved in the diffuse degassing process. The used sampling and analytical methods employed are extensively described in ref.50.

222Rn-220Rn activity, soil pressure–temperature and CO2-H2S concentration

Soil gas measurements of 222Rn (radon, with half-life of 3.82 days) and 220Rn (thoron, with half-life of 55.6 s) nuclides at Nisyros caldera were performed using the RAD7 monitoring system (Durridge Company Inc., USA). The setup is equipped with a solid-state ion-implanted planar silicon detector, a pump with a flow rate of 1 L min−1, a gas-drying unit filled with a desiccant (CaSO4 with 3% CoCl2, as indicator) and an inlet filter (pore size 1 µm) for the fine dust particles. The factory-calibrated detector operates in a sensitivity range of 4–80,000 Bq m-3, with an accuracy of 5%. The soil gas measurement was carried out in “sniff mode” by determining 222Rn and 220Rn concentrations from the energy windows of 5.40–6.40 and 6.40–7.40 MeV, thus detecting the total counts (at 6.00 MeV) of alpha particles from the 3.04-min 218Po decay (222Rn daughter) and the total counts (at 6.78 MeV) of alpha particles from the 0.145-s 216Po (220Rn daughter). A stainless-steel gas probe (manufactured by RADON v.o.s. Inc.) was inserted into the soil at depth of 80 cm with the aid of a hammer and then connected to the inlet of the RAD7 via vinyl tubing. A small cylindrical cavity was created just below the probe head by the extrusion of a lost tip. The volume of the cavity (about 5.6 cm3) was large enough to enable soil gas collection using the RAD7 built-in pump. After a purging time of 10 min, the alpha particles were collected by a measurement cycle of 15 min. When the terrain is very humid, the water content in RAD7 gradually increases, even if a desiccant is employed. The radon activity concentration was progressively underestimated because of neutralization processes affecting radon daughters during electrostatic collection. The radon signal was, therefore, corrected according to the methodological approach reported in ref.51.

Soil gas permeability was also obtained by using PRM3 permeameter52. The instrument draws air from the same hollow probe used for radon measurement. The permeameter is equipped with a pump and a vacuum gauge that reads the negative pressure (ΔP), induced by soil gas extraction through the terrain. Intrinsic permeability is calculated according to a modified version of Darcy’s equation where the air flow (Q) is replaced by a linear equation of the form: Q = (m × ΔP + c), where m and c are the slope and the intercept of the instrument calibration curve, respectively.

Soil temperature and CO2-H2S concentration were measured with a K-type thermocouple and a Dräger X-am 7000 analyzer (Drägerwerk AG & Co. KGaA Inc., Germany), respectively. This latter instrument is equipped with an infrared sensor (full-scale 100% in volume, sensibility of 0.2%) for CO2 measurement, and with an electrochemical cell (full-scale 500 ppm, sensibility of 0.5 ppm) for H2S measurement. Since H2S was used to select sampling points with very low sulfur concentrations and generally close to 0%, its value is not reported in this study.

222Rn-220Rn exhalation rate in laboratory

In order to determine the exhalation rate of 222Rn-220Rn in laboratory, several rock and soil samples from Nisyros caldera were also collected: (1) a rhyolitic pumice belonging to the Upper Pumice succession (sample UP), one of the caldera-forming Plinian eruptive cycles53,54, (2) a rhyodacitic lava (sample RD) from the post-caldera domes (in particular, the small dome of Lofos), following the Upper Pumice eruption55,56, (3) the soil from site A7 (sample SA7), (4) the soil from site A24 (sample SA24), and (5) the soil from site C2 (sample SC2). The closed-loop experimental setup is described in ref.57,58 and briefly consists of a stainless-steel accumulation chamber (5.1 L) connected via vinyl tubing to a gas-drying unit and to the RAD7. The accumulation chamber is immersed into a refrigerating thermostatic bath and kept at the constant temperature of 30 °C to avoid the oscillation of the radon activity concentration under the effect of thermal gradients. The detection limit of the experimental apparatus is equal to 0.01 and 6 Bq h−1 for 222Rn and 220Rn, respectively, provided that the activity concentration was corrected for the humidity and temperature measured by the radon detector (see ref.57,58). The duration of one single measurement was 24 h and 222Rn-220Rn mass exhalation rates were calculated for pre-dried samples (in an oven for 24 h) through the following equations:

$$E_{222} = \left( {m + \lambda_{222} \times C_{222} } \right) \times V$$
(2)

and

$$E_{220} = \lambda_{220} \times V_{0} \times \frac{{C_{222} }}{{e^{{({-}\lambda_{220} \times \frac{{V_{1} }}{Q})}} }}$$
(3)

where E222-E220 (Bq m−2 h−1), C222-C220 (Bq m-3), and λ222-λ220 (h−1) are mass exhalation rates, activity concentrations and decay constants of 222Rn and 220Rn, respectively. V, V0, and V1 (m3) are the free total volume of the system, the volume of the accumulation chamber and the volume of the vinyl tubing, respectively. Q (m3 h−1) is the pump capacity and m (Bq m-3 h−1) is the initial slope of the 222Rn growth curve.

Statistical analysis

Graphical statistical approach (GSA)

The polymodal distribution of the data results from the presence of more populations of data within the same distribution. In soil gas measurements, the occurrence of two or more populations can be related to the presence of multiple geochemical processes/sources controlling the observed variable. The GSA11 aims to identify and define each population of data in such a polymodal distribution. The approach consists of plotting the data on a probability plot, where a normal population plots on a straight line, whereas a polymodal distribution of n normal populations defines a curve with n−1 inflection points. Using a graphical procedure59,60, it is possible to subdivide such complex statistical distributions into individual normal populations and compute the fraction, the mean and the standard deviation of each of them. Since the computed means for the soil T and CCO2 refer to the logarithm of the T and CCO2 values, the mean values of such variables were then estimated using a Monte Carlo simulation procedure.

Principal component analysis (PCA)

PCA is a dimension reduction technique that allows the derivation of a low-dimensional set of components from a large n × p data matrix61. Strictly speaking, with a small number of principal components one can summarize most of the information of the original data set, composed by a large number of variables p and observations n. The principal components (PC) are a set of linearly uncorrelated variables, ranked in terms of their overall control on the variance. Along the first principal component (PC1) direction the data vary the most, and so on with a progressive decreasing in the variability of the data for the remaining principal components. Hence, the first three PC (in our case) collectively explain most of the variance in the set of data. PCA was performed initially on the whole data set (composed by deepCO2 flux, bioCO2 flux, T, CCO2, 222Rn/220Rn ratio, and 220Rn activity) and secondly only on samples A data. PCA was performed using the function prcomp of the package stats63 of the R statistical software63 on scaled variables. Results are then visualized using the package factoextra64.

Sequential Gaussian simulation (sGs)

In order to visualize the spatial distribution of different attributes (i.e., the variables considered in the PCA) over the area of samples A, we produced 2D E-type maps using the conditional sequential Gaussian simulation (sGs). The stochastic simulations were performed using the algorithm of sgsim code62, and considering as attributes deepCO2 flux, T, CCO2, 222Rn/220Rn ratio, and PC1 scores. The variables were simulated at each unsampled location defined by a regular grid of 107 × 226 cells of 2 m × 2 m (covering the samples A area), to reproduce the statistical and spatial distribution of each attribute (i.e., the semivariogram of the normal scores of the variable). The values are randomly drawn from a Gaussian conditional cumulative distribution function, which depends on the original data and on the data previously simulated21. The simulations were run in order to produce 200 equiprobable realizations for each data set. The E-type maps of the variables considered were derived through a pointwise linear average of all the realizations.