Seasonal Environmental Controls on Soil CO₂ Dynamics at a High CO₂ Flux Sites (Piton de la Fournaise and Mayotte Volcanoes)

Abstract

Environmental parameters drive seasonal soil CO₂ efflux toward the atmosphere. However, their influence is not fully understood in contexts of high CO₂ fluxes where CO₂ accumulates in the subsurface. A prime example are volcanoes subject to continuous CO₂ diffuse degassing rising from deep magmatic reservoirs, through the subsurface and up to the atmosphere. For many of these volcanoes where soil CO₂ is monitored, a seasonal influence of the atmosphere and water table is observed but not characterized. Here, we compare variations of air temperature, atmospheric pressure, rainfall and water table level with near-surface soil CO₂ concentration by performing a time-lagged detrended cross-correlation analysis on years-long time series from the volcanoes of Piton de la Fournaise and Mayotte. At Piton de la Fournaise, soil CO₂ variations correlate best with air temperature variations (0.81) and water table variations (0.74). In Mayotte, soil CO₂ variations correlate best with atmospheric pressure variations (−0.95). We propose that at Piton de la Fournaise, the thick vadose zone and high permeability favor CO₂ transfer by thermal convection. Additionally, energy transfer is decoupled from mass transfer. Slow heat transfer from the atmosphere down to the accumulated CO₂ layers in the subsurface results in a delayed influence of air temperature and of the water table level on the thermal gradient between the subsurface and the atmosphere, and consequently on the efficiency of the CO₂ transfer. In Mayotte, we propose that the thin vadose zone and the presence of a network of large fractures favor CO₂ transfer by barometric pumping.

Plain Language Summary

The soil is a major reservoir of gaseous CO₂ at the scale of the planet. This soil CO₂ is mobile and can escape to the atmosphere and contribute to global warming. It thus important to understand what controls its mobility. In contexts of high soil CO₂ contents, environmental parameters can drive soil CO₂ transfers toward the atmosphere, but their influence is still poorly understood at timescales beyond a few days. To address this issue, we studied how air temperature, atmospheric pressure, rainfall, and water table level affect soil CO₂ efflux in volcanic environments where the soil CO₂ content is naturally high due to magmatic degassing. Our study sites are the volcanoes of Piton de la Fournaise and Mayotte. We performed a time-lagged detrended cross-correlation analysis which compares the similarity between different time series. We find that air temperature, atmospheric pressure and water table level variations can cause soil CO₂ to move toward the surface. The magnitude of their influence and the type of transfers depend on the geological properties of the study sites. We also find that these influences can occur with significant delays of over a hundred days.

Key Points

• Air temperature, atmospheric pressure, and water table level influence soil CO₂ concentrations at a seasonal scale

• The decoupling of heat and mass transfer in the subsurface induces a delayed response of soil CO₂ concentrations to environmental forcing

• CO₂ mass transport at high flux is driven by thermal convection or barometric pumping depending on site properties

1 Introduction

The understanding of transport and accumulation of CO₂ in and between the different terrestrial reservoirs is crucial in the context of global change. Soils are one of the largest gaseous CO₂ reservoirs (Baldini et al., 2018). However, two main aspects of the carbon geochemical cycle are rarely addressed regarding soil CO₂ efflux toward the atmosphere. First, very often, only the first centimeters of the soil are considered. Yet, for the past 20 years, the scientific community has evidenced a major role of the subsurface in soil CO₂ transport and accumulation and it is necessary to take into account at least the first few meters (Gross & Harrison, 2019; Harrison et al., 2011; Jobbágy & Jackson, 2000). Second, the abiotic CO₂ production processes tend to be overlooked in studies addressing global carbon budgets. It is indeed often considered that soil CO₂ efflux is equivalent to soil respiration, while in many geological settings, inorganic carbon represents the main source (Mörner & Etiope, 2002; Rey, 2015). Diffuse magmatic CO₂ can also interact with the carbon cycle in the biosphere (Beulig et al., 2015; Holdaway et al., 2018). As a result, the response of soil CO₂ to variations of environmental parameters is well constrained in contexts where CO₂ is organic and remains confined to the first meter of the soil, but remains poorly understood otherwise, making it impossible to anticipate how global change will affect soil CO₂ efflux. Volcanic settings are ideally suited to address these limitations with their soils naturally affected by high fluxes of deep sourced magmatic CO₂. Indeed, CO₂ is one of the most abundant volatiles in magmas in all volcanic settings and has the particularity of exsolving at depths >10 km (Di Muro et al., 2016; Edmonds & Woods, 2018). The deep exsolved CO₂ rises toward the surface through the entire rock column and can be measured as a diffuse gaseous component in soils at a regional scale (e.g., Chiodini et al., 1999; James et al., 1999; Viveiros et al., 2012). Environmental parameters affect the transport of this magmatic CO₂ in soils by modifying the gas properties (e.g., density, Rinaldi et al., 2012) or the properties of the physical environment (e.g., permeability, Viveiros et al., 2014). Additionally, biogenic CO₂ in soils contribute to the total CO₂ budget in soils (e.g., Liuzzo et al., 2015) while also reacting to environmental forcing (e.g., Nakadai et al., 2002).

Given that the total budget of the magmatic CO₂ diffuse degassing can be equivalent or higher to the emissions during eruptive events (Caliro et al., 2005; Chiodini et al., 2000; Werner et al., 2019) it represents the long term CO₂ contribution to the soils and then to the atmosphere in volcanic settings. Therefore, at volcanoes all over the world, these fluxes are monitored to track deep transfers of magma, providing years-long large datasets of CO₂ concentrations and/or fluxes in diverse soils settings. In all monitoring sites, it has been evidenced that variations of air temperature, atmospheric pressure, wind, rainfall, humidity and water level induce substantial modifications of soil CO₂ concentrations and fluxes (Boudoire et al., 2017a; Camarda et al., 2019; Carapezza et al., 2002; Granieri et al., 2003; Laiolo et al., 2016; Lewicki et al., 2007; Liuzzo et al., 2013, 2015, 2013; Padilla et al., 2014; Padrón et al., 2008; Pérez et al., 2006; Rinaldi et al., 2012; Rogie et al., 2001; Salazar et al., 2004; Scudero et al., 2022; Viveiros et al., 2014, 2008; Werner et al., 2019). The volcanology community studies these correlations between environmental parameters and soil CO₂ concentration and fluxes in order to isolate the variations due to magmatic activity. Most of these studies provide empirical mathematical corrections, but very few address directly the physical transport processes responsible for the observed variability. Among those studies, most are focused on short-term effects, from a few hours to a few days. Yet, a seasonal periodicity is described on all monitoring sites and attributed to environmental influences. The understanding of this seasonal component is critical for long-term monitoring of volcanic hazard, but also to constrain the response of soil CO₂ transport to climate change, which is the aim of this paper.

Two main processes control the transfer of gaseous CO₂ from mantle depth to the earth surface passing through soils: advection and diffusion. Both have been identified and described in volcanic settings at short time-scales (<10 days). Usually soil CO₂ transport is attributed to a combination of advection and diffusion, with advection being dominant at high fluxes and diffusion at lower fluxes (Camarda et al., 2007; Capasso et al., 2001; Lewicki et al., 2003; Rinaldi et al., 2012; Viveiros et al., 2014). Variations of air temperature and atmospheric pressure can affect advective transport through variations of the density of the fluid, the pressure gradient or the temperature gradient. Laiolo et al. (2016) and Camarda et al. (2019) proposed driving mechanisms for the seasonal periodicity of soil CO₂ emissions on Stromboli volcano and Vulcano island respectively. Laiolo et al. (2016) shows a negative correlation between air temperature and soil CO₂ flux and argue that higher emissions occur during fall-winter because fluid convection is promoted by the higher soil-air temperature gradient. Conversely, during summer, this gradient is reversed and near-surface convection is inhibited. This advective transport mechanism relies on the thermal gradient between the surface and the depth. It is otherwise known as thermally induced convection, thermal convective venting or thermal convection (Ganot et al., 2014; Levintal et al., 2020; Nachshon et al., 2011). Camarda et al. (2019) shows a negative correlation between atmospheric pressure and soil CO₂ emissions at a seasonal scale, which similarly relies on the seasonal atmospheric pressure gradient. However, neither Laiolo et al. (2016) or Camarda et al. (2019) include in their analysis a possible delay between the environmental forcing and the system's response. Scudero et al. (2022), on the basis of wave-transform analysis of time series on Etna volcano, identify a delayed influence of meteorological variables on the annual variations of CO₂ emissions at a seasonal scale. They propose that the phase synchronicity and the delay between environmental forcing and soil CO₂ response is controlled by local factors (i.e., exposure, elevation, local permeability at the site, etc.).

Additionally, a possible role of the hydrogeological system on soil CO₂ emissions is inferred in several studies but poorly constrained. Modeling shows that variations of the water table level and flow may impact gas transfers to the surface (Viveiros et al., 2014). Yet, the influence of the water table level is only alleged in two soil CO₂ monitoring sites at Fogo and Furnas volcanos in the Azores (Viveiros et al., 2008), where authors use the soil water content as a proxy. The role of rainfall has also been observed at short-term scales where a link between increase of soil CO₂ emissions and the rainy season is suggested (e.g., Boudoire et al., 2017a).

The soil CO₂ monitoring network of the Observatoire Volcanologique du Piton de la Fournaise (OVPF-IPGP) is a very interesting natural laboratory for the study of environmental effects on soil CO₂ emissions in tropical environments. The network consists of five permanent monitoring stations which record the hourly dynamic concentration of CO₂ in soils as well as environmental parameters: four for observations at the Piton de la Fournaise volcano, on the island of La Réunion and one for observations at the island of Mayotte. The oldest station dates back to 2013. All stations are located in different soil settings in terms of elevation, vegetation and geological basement, and with different background levels of soil CO₂ concentrations. The tropical climate of La Réunion and Mayotte induce high rainfall, making them ideal settings for the study of the role of hydrogeological parameters in soil CO₂ emissions. For this study, we used all five stations of Piton de la Fournaise and Mayotte and compared the environmental time series with the soil CO₂ concentration time series in order to better understand their effect. We focus on the seasonal timescale and for the first time, we use water table level data.

In volcanology studies, mathematical corrections of environmental effects on soil CO₂ time series use one or more of the following methods: moving average filters, multivariate linear regressions and Fourier transform based filters (Boudoire et al., 2017a; Granieri et al., 2003; Gurrieri et al., 2021; Laiolo et al., 2016; Oliveira et al., 2018; Rinaldi et al., 2012; Viveiros et al., 2008, 2014). Multivariate linear regressions have the advantage of analyzing the correlation between CO₂ and multiple environmental parameters simultaneously. Fourier transform based filters are efficient for correcting periodic influences, but these methods do not account for possible delays between forcing and response nor for the non-stationarity of time series. To address these issues, new methods involving continuous-time filters and wavelet transform filters have been recently explored (Lewicki et al., 2017; Oliveira et al., 2018; Scudero et al., 2022), but a compromise has to be made between frequency resolution and the correction for non-stationarity. Detrended Cross-Correlation Analysis (DCCA) is another method for analyzing the relation between non-stationary time series which is growing in use (Horvatic et al., 2011; Kristoufek, 2014; Podobnik & Stanley, 2008; Vassoler & Zebende, 2012; Zebende, 2011), and to our knowledge, it has not been applied to the study of soil CO₂ time series yet. We chose to apply a variation of this method, Detrended time-Lagged Cross-Correlation Analysis (Shen, 2015). Detrending the data filters the large anomalies due to volcanic emissions thus retaining only the periodical signal due to the influence of environmental parameters. Adding a time-lagged parameter allows for the computation of the delays between environmental forcing and system response.

From these cross-correlations, we are able to decipher the main drivers and means of soil CO₂ transfer in terms of environmental parameters, soil characteristics and physical transport processes involved. We propose a conceptual model for the soil CO₂ transfers at piton de la Fournaise and Mayotte which brings a new light on the understanding of soil CO₂ transfers at a seasonal scale and their consequences in a context of climate change.

2 Soil CO₂ Monitoring Stations: Data and Setting

Piton de la Fournaise is the youngest (>430 ky ago, Gillot et al., 1994) and only active volcano of the island of La Réunion, which is part of the Mascarene volcanic archipelago (Figure 1). Its magmas originate from the mantle. During their multistep ascent to the surface, these magmas release their primary volatile budget progressively (Boudoire et al., 2017b; Di Muro et al., 2016). The CO₂ released from different parts of the volcano's plumbing system is transported to the surface through several preferential pathways constituted by deep faults (Boudoire et al., 2017b; Liuzzo et al., 2015; Michon et al., 2015). The soil CO₂ monitoring stations are located on top of these structures. This monitoring of soil CO₂ variations was initiated in 2013 with the installation of PNRN and PCRN stations (Table 1, Figure 1). Then, stations BLEN and GITN were installed in 2015 and 2018, respectively. All stations are located on the western flank of the volcano within 14 km or less of each other, at high elevations (>1,000 m), with normal annual temperatures from 6.4 to 20.8°C. The sites are characterized by substantial normal annual rainfall, from 2020 to 5190 mm. The stations are installed on thin soils (<0.5–1 m thick) formed on basaltic lavas which are highly permeable (∼10⁻² to 10⁻⁴ m², Bourhane et al., 2015; Folio, 2001; Join et al., 2005). As a result, water can infiltrate deeply and quickly, and aquifers are unconfined. At PNRN station, located at 700 m from the borehole.

Figure 1

(a) Location of the islands of La Réunion and Mayotte (Map data ©2022 Google); Location of the soil CO₂ monitoring stations (b) along the magma paths at Piton de la Fournaise; (c) close to gas seeps areas (green stars) on Petite Terre in Mayotte. Bathymetry from Ifremer Geo-Ocean (2022).

Table 1. General Characteristics of the Soil CO₂ Monitoring Stations at Piton de La Fournaise

Station	Installation date	Latitude (°)	Longitude (°)	Elevation (m)	Land use	Normal annual temperature (°C) ^a	Normal annual rainfall (mm) ^a
PNRN	2013	−21.13690	55.62450	1,045	Urban area	12.6–20.8	4,571
PCRN	2013	−21.20830	55.57210	1,554	Pasture lands	9–18.6	2020
BLEN	2015	−21.16430	55.56150	1,655	Pasture lands	9–18.6	2020
GITN	2018	−21.21805	55.68417	2,240	Highland vegetation	6.4–15.8	5,190
UDMN	2020	−12.79992	45.28612	17	Urban area	n.a.	n.a.

• ^a Météo-France (2022).

Forage Bras Creux with available water level data (online data repository: https://donnees.eaureunion.fr/), the vadose zone is ∼110 m thick. At GITN, PCRN and BLEN, there is no available data for the thickness of the vadose zone at the precise location of the stations. However, hydrogeological modeling indicates a very thick vadose zone of ∼600 m at GITN (Folio, 2001; Join et al., 2005). The hydrogeological system of Piton de la Fournaise comprises an interconnected hydrogeologic network of regional scale with waters flowing from the inner to the outer part of the edifice. This main water body in the edifice is drained by high flow springs in deeply cut valleys. In the Bras de la Plaine valley located at the West of BLEN and PCRN stations, at distances of respectively ∼2 and ∼4 km, several of these high flow springs emerge at altitudes comprised between 1,100 m elevation at the top of the valley and 680 m further down (e.g., source des Hirondelles spring at 940 m elevation with a median flow of 160 l/s, BSS ID: 12291X0007/HY, Office de l'eau online data repository: https://donnees.eaureunion.fr/). The elevation of these high flow springs can be considered equivalent to the water table level of the main aquifer system. Therefore, the vadose zone underneath BLEN and PCRN stations is large of several hundred meters. However, several springs with lower flows also emerge closer to the stations, indicating the presence of superficial aquifers of smaller significance above the main water body (e.g., source Samary at an elevation of 1,534 m with a median flow of 2 L/s, Office de l'eau online data repository: https://donnees.eaureunion.fr/). Indeed, preferential pathways or isolated circulations can result from local discontinuities such as permeable paleo-valleys and less permeable paleo-soils (Dumont et al., 2021).

Mayotte, part of the Comoros volcanic archipelago, is composed of two main islands, Grande Terre and Petite Terre, and does not have a single main volcanic edifice (Figure 1). In 2018, seismic and volcanic activity resumed at the eastern submarine feet of Mayotte, producing the rapid construction of a huge submarine edifice at 3.5 km bsl and 50 km east of the shore of Petite Terre (Berthod et al., 2021; Cesca et al., 2020; Feuillet et al., 2021; Lemoine et al., 2020). The activity declined until 2021. This seismic and volcanic activity is tied to a long (∼N110°) volcanic chain crossing the eastern flank of Mayotte and whose subaerial expression is the island of Petite Terre (<0.15 My, Debeuf, 2009; Nehlig et al., 2013). Gas seeps are identified below sea level at the new volcanic edifice, in the area called horseshoe where most of the seismicity is recorded, and at Petite Terre. On land, CO₂ escapes by bubbling through fractures in the lagoon of the Airport beach. Prolonging the airport beach, is a thick ash sequence (tens of meters) with a bulk rock permeability of ∼10⁻⁵ to 10⁻⁶ m² (Guilbert et al., 2008), lower than in La Réunion. Yet, on top of this ash sequence, there are high CO₂ concentrations in the soil with a magmatic geochemical signature (Liuzzo et al., 2021) indicating that the degassing at the beach is prolonged diffusely through the soil. We infer that the fracture network which is visible at the beach is continued in the ash sequence. This is where the UDMN soil CO₂ monitoring station of Mayotte was installed in 2020 (Table 1, Figure 1). The station is located at an elevation of 17 m, therefore the vadose zone is only 17 m thick or less. Like in La Réunion, Mayotte's climate is tropical, hot and humid (mean annual rainfall >1,500 mm).

Stations used to measure soil CO₂ concentrations and environmental parameters (P, T, RH, wind speed and direction) are described in detail in Boudoire et al. (2017a) and summarized here. Data are acquired on hourly basis and transmitted in real time at the Observatoire Volcanologique du Piton de la Fournaise (OVPF/IPGP). The stations were designed by the Istituto Nazionale di Geofisica e Vulcanologia (INGV) Sezione di Palermo (Gurrieri et al., 2008). For the measurement of soil CO₂ concentration, a 50 cm long probe is inserted into the soil and connected by a Teflon pipe to a Gascard NG dual-wavelength nondispersive infrared gas analyzer (CO₂ gas measurement range 0%–10%). The molar fraction of CO₂ is measured in a soil-air gas mixture pumped at 0.8 L/min and are automatically corrected for air temperature and atmospheric pressure effects on gas molecular density (Gurrieri and Valenza (1988)). In this study, we focus on raw concentration data, without converting them in flux units.

Our study spans the period lasting from August 2013 to September 2021(Bénard et al., 2023). At PNRN, average daily soil CO₂ concentration was the lowest 0.08% ± 0.04% (full range from 0.03% to 0.43%). The highest concentrations were measured at BLEN, average daily soil CO₂ concentration was 0.82 ± 0.32% (full range from 0.22% to 2.42%). The maximum recorded concentration is lower when approaching the volcano, even if the average daily concentrations are similar on BLEN, PCRN and GITN stations. At PCRN, average daily soil CO₂ concentration was 0.63% ± 0.24% (full range from 0.10% to 1.20%). At GITN, average daily soil CO₂ concentration was 0.76% ± 0.21% (full range from 0.11% to 1.27%). The highest concentrations in our data set are recorded in Mayotte. At UDMN, average daily soil CO₂ concentration was 2.34% ± 0.88% (full range from 1.10% to 4.88%). Spurious data (<10 days) related to technical malfunction was removed from the datasets. There are larger data gaps (months) when the equipment failed to acquire data.

Air temperature and atmospheric pressure are measured hourly by meteorological stations located at a height of 2 m at each site. Temperature is measured by Mela® sensors PK-ME with a precision of ±0.2 K. Pressure is measured by STS® sensors ATM. ECO with a precision of ±0.375 psi.

Soil CO₂ concentrations, air temperature and atmospheric pressure data are available on the IPGP online data repository at https://dataverse.ipgp.fr/privateurl.xhtml?token=c93d13c3-e998-428d-877a-1ab70773e5ad (a permanent DOI will be generated if the article is accepted).

Rainfall daily time series were obtained from the French national meteorological service Météo France online repository (https://publitheque.meteo.fr/). For PNRN, GITN and UDMN we used data from the Plaine des Palmistes (ID 97406220), the Bellecombe-Jacob (ID 97419380) and the Pamandzi (ID 98508001) Météo France stations, respectively, all located within 800 m of the stations. For PCRN and BLEN, we used data from the Plaine des Cafres (ID 97422440) Météo France station, at distances of 120 m and 5 km from the stations, respectively.

For Piton de la Fournaise, water table level daily time series were obtained from the Office de l'eau online data repository (https://donnees.eaureunion.fr/). We selected the borehole Forage Petite Plaine (Figure 1, BSS ID: 12292X0041/F) for comparison with soil CO₂ concentrations for the stations PCRN and BLEN. This unexploited borehole is the closest to these soil CO₂ stations with water table level data available for the study period. The borehole is located 7 km away from PCRN and 4 km away from BLEN. This borehole appears to be connected to the Plaine des Cafres aquifer system (Aunay et al., 2012).

For comparison with the soil CO₂ station PNRN, we selected the unexploited borehole Forage Bras Creux (BSS ID: 12276X0071/FORAGE) located only 700 m away. For GITN, there is no available water table level data so this parameter was not considered. For Mayotte, water table level daily time series were obtained from the national groundwater data online repository ADES (BRGM data). We selected the borehole Piézomètre de Labattoir 4 (BSS ID: 12308X0086/PZ4) for comparison with soil CO₂ concentrations for the station UDMN, which is located at a distance of 1.7 km. At distances of several kilometers from the soil CO₂ stations, water table level measurements can be considered representative only of water table level variations at the scale of the entire interconnected aquifer system. To obtain this general trend and remove variations due to local events, before performing the cross-correlation analysis, we applied a Gaussian filter with the scipy. ndimage.gaussian_filter1d function in python, with the standard deviation for Gaussian kernel parameter equal to 10.

3 Cross-Correlation Analysis Method

Our approach relies on the DCCA method (Podobnik & Stanley, 2008; Zebende, 2011). With this method, two time series are divided in overlapping windows of a defined time scale. For each window, the time series are detrended to correct for non-stationarity and their correlation coefficient is computed. For two non-stationary time series {x_i} and {y_i} of equal length N, with i = 1, 2, …, N, two integrated series and are computed, where and are the mean of the each time series and with k = 1, 2, …, N. These two integrated time series are divided into N−n overlapping windows, each containing n + 1 values, the variable n corresponding to the time scale. A least-square linear regression is then applied to each window of each series, giving the trends and with i ≤ k ≤ i + n. The covariance of the residuals is then computed for each window by:

(1)

The detrended covariance function is obtained by averaging the covariance of the residuals over all N − n overlapping windows:

(2)

The detrended variance functions F_DFA(n,R) and F_DFA(n,R′) are also computed based on the Detrended Fluctuation Analysis (DFA) method (Peng et al., 1994), and obtained by:

(3)

(4)

Finally, the DCCA coefficient ρ(n,R,R′) is obtained by:

(5)

In this study, we use a variation of the DCCA method developed by Shen (2015), the time-lagged DCCA method, to correlate soil CO₂ time series with environmental time series. The method introduces the additional variable τ, defining the delay, to the computation of the DCCA coefficient. The independent time series {y_i} is integrated considering τ as in with k + τ = 1, 2, …, N. The two integrated series R_k and are divided into N − n − |τ| overlapping windows, each containing n + 1 values. The local trends are computed with i = 1,2,…, N − n − τ when τ ≥ 0, and with i = −τ + 1, …, N − n when τ < 0. Equations 1-5, are modified as such:

(6)

(7)

(8)

(9)

(10)

(11)

We compute the time-lagged DCCA coefficients ρ_j(τ,R,R′) for all delays τ in the interval [−l;l], where l is the maximum delay, between soil CO₂ {x_i} and each j environmental time series {}, {}, …, {} where i = 1,2,…, N and j = 1, 2,…, m. For each environmental time series, the resulting estimated delay corresponds to the positive delay value τ at which the absolute value of the cross-correlation coefficient |ρ_j(τ,R,R′)| is the highest.

For all five monitored soil CO₂ stations of Piton de la Fournaise and Mayotte, a seasonal trend is visible on the soil CO₂ concentration time series (Figure 2). This periodical behavior can be quantified by performing Fourier Transform analyses on the interpolated daily averaged time series. The main amplitude peak is at a period of ∼366 days, corresponding to an annual periodicity (Figure 3), although for stations UDMN and GTIN, the peak maximums are poorly constrained due to the shortness of the time series. The maximum peak amplitudes are very high for stations PCRN, BLEN, and UDMN (>1,400), lower for station GITN (907) and the lowest for station PNRN (43). For comparison, soil CO₂ monitoring station GFUR1 at Furnas volcano (Azores) displays a peak amplitude of ∼58 at an annual periodicity (Viveiros et al., 2014).

Figure 2

Time series of daily averaged soil CO₂ concentration (%), temperature (°C), atmospheric pressure (hPa), water table level (m a.s.l.) and rainfall (mm) at soil CO₂ monitoring stations of PNRN, PCRN, BLEN, GITN (Piton de la Fournaise) and UDMN (Mayotte).

Figure 2 (continued)

Time series of daily averaged soil CO₂ concentration (%), temperature (°C), atmospheric pressure (hPa), water table level (m a.s.l.) and rainfall (mm) at soil CO₂ monitoring stations of PNRN, PCRN, BLEN, GITN (Piton de la Fournaise) and UDMN (Mayotte).

Figure 2 (continued)

Time series of daily averaged soil CO₂ concentration (%), temperature (°C), atmospheric pressure (hPa), water table level (m a.s.l.) and rainfall (mm) at soil CO₂ monitoring stations of PNRN, PCRN, BLEN, GITN (Piton de la Fournaise) and UDMN (Mayotte).

Figure 2 (continued)

Time series of daily averaged soil CO₂ concentration (%), temperature (°C), atmospheric pressure (hPa), water table level (m a.s.l.) and rainfall (mm) at soil CO₂ monitoring stations of PNRN, PCRN, BLEN, GITN (Piton de la Fournaise) and UDMN (Mayotte).

Figure 2 (continued)

Time series of daily averaged soil CO₂ concentration (%), temperature (°C), atmospheric pressure (hPa), water table level (m a.s.l.) and rainfall (mm) at soil CO₂ monitoring stations of PNRN, PCRN, BLEN, GITN (Piton de la Fournaise) and UDMN (Mayotte).

Figure 3

Amplitude spectrum of the soil CO₂ concentrations time series at stations PNRN, PCRN, BLEN, GITN, and UDMN. All stations display a peak at ∼366 days, corresponding to an annual periodicity.

This observed annual periodicity allows us to consider that variations of soil CO₂ concentrations can be mainly explained by the variations of environmental parameters whose timeseries display the same periodicity. However, because our study sites are located in volcanic environments, deep recharges of magma will occur occasionally. The fresh magma will then lose its gas which will result in an increase of the CO₂ flux at the surface of the water table, which can in turn influence the near-surface soil CO₂ timeseries, resulting in non-stationary series. The detrended cross-correlation analysis we propose is meant to correct this non-stationarity and to isolate the periodical signal due to environmental influences, which is the object of this study. However, this approach can only be successful when the amplitude periodicity is sufficiently high. At PNRN station, where soil CO₂ concentrations are the lower by one order of magnitude compared to other stations, two strong positives CO₂ anomalies affect the periodicity of the signal, resulting in a low periodicity compared to the other stations. Soil CO₂ concentrations are two to five times higher before March 2014 (mean soil CO₂ concentration = 0.33%) and starting from 2020 (mean soil CO₂ concentration = 0.13%) compared to the period from 2015 to 2020 (mean soil CO₂ concentration = 0.06%), which we interpret as magma degassing events. For this reason, we only selected the period from March 2014 to 2020 for the correlation analysis at PNRN station.

The seasonal trend is the most marked for the following environmental parameters: air temperature, water table level, atmospheric pressure and rainfall (Figure 2). These parameters were thus selected for the cross-correlation analysis approach. In order to focus on the seasonal timescale, we suppressed the shorter periodicities in the time series. Before averaging them to a daily time-step, we applied a 1.5 days-low pass filter by fast Fourier transform analysis (FFT) to the hourly time series of soil CO₂. For the purpose of the computation, all gaps in the data were filled by linear interpolation irrespective of their duration.

After preprocessing the data, we calculated the delays and correlations between soil CO₂ and air temperature, water table level, atmospheric pressure and rainfall time series by performing a time-lagged DCCA, following the procedure in paragraph 3. For Piton de la Fournaise stations, in order to better constrain the annual periodicity of soil CO₂ time series, we used a time scale n of 366 days, corresponding to 1 year. We computed the time-lagged DCCA coefficients for all delays τ in the interval [−l;l] with l = 366, assuming that the delay should not exceed the timescale. For the Mayotte station with a shorter time series of length N = 598, considering that i = 1,2,…, N − n − τ when τ ≥ 0 and i = −τ + 1, …, N − n when τ < 0, using a time scale of n = 366 days only allows for the correlation computation on a limited number of i days and τ delays. We thus chose to use a time scale and a maximum delay of n = l = 183, which corresponds to a half a period.

4 Results

The results of the cross-correlation analysis are presented in Table 2 and Figure 4. The correlation coefficients versus delays display a periodic behavior with a 1-year period (Figure 3). Therefore, for each station and each parameter, we chose to retain the maximum absolute value of the correlation coefficients for the first peak and corresponding delay. For all stations, high correlations coefficients are obtained with the time-lagged DCCA method (Table 2) between soil CO₂ concentrations and air temperature (from |0.72| to |0.90|), atmospheric pressure (from |0.60| to |0.95|) and water table level (from |0.70| to |0.85|). The correlation with rainfall is lower (from |0.41| to |0.71|). Temperature is the environmental parameter having the highest correlation coefficient values (positive) for Piton de la Fournaise stations, while for Mayotte it is atmospheric pressure (negative).

Table 2. Correlation Coefficients and Delays Obtained With the Time-Lagged Detrended Cross-Correlation Analysis Method

Station	Environmental parameter	Time-lagged DCCA coefficient	Delay (days)
PNRN	Air temperature	0.75	61
	Water table level	0.75	15
	Atmospheric pressure	−0.60	57
	Rainfall	0.60	57
PCRN	Air temperature	0.90	164
	Water table level	0.77	109
	Atmospheric pressure	−0.89	164
	Rainfall	0.70	148
BLEN	Air temperature	0.72	88
	Water table level	0.70	23
	Atmospheric pressure	−0.62	99
	Rainfall	0.48	79
GITN	Air temperature	0.85	53
	Atmospheric pressure	−0.72	67
	Rainfall	0.41	19
UDMN	Air temperature	0.84	35
	Water table level	0.85	6
	Atmospheric pressure	−0.95	21
	Rainfall	0.71	38

Figure 4

Correlation coefficients versus delays (lags in days) obtained with the time-lagged detrended cross-correlation analysis method. Soil CO₂ concentration time series are compared with air temperature (red), water table level (blue), atmospheric pressure (orange) and rainfall (light blue) time series for the four soil CO₂ monitoring stations at Piton de la Fournaise volcano: (a) PNRN, (b) PCRN, (c) BLEN, and (d) GITN. For each environmental parameter, the maximum correlation coefficient and corresponding delay are marked.

For stations at Piton de la Fournaise and Mayotte, Figure 4 shows the correlation coefficients against the delays (in days) for soil CO₂ concentration versus environmental parameters. For all stations, the resulting curves show a periodicity of 366 days with synchronized phases for the correlation of soil CO₂ with air temperature and rainfall and an inverse phase for atmospheric pressure. A periodicity of 366 days is also observed for the correlation of soil CO₂ with the water table level. For Piton de la Fournaise stations, it is out of phase compared to the other parameters, with a peak appearing earlier, while in Mayotte, it has a phase shift similar to that of air temperature and rainfall.

The delays at which the different phases occur is very different between stations span a wide range. Delays are the largest for station PCRN (119–171 days) and the smallest for station UDMN (6–38 days).

5 Discussion

The observed periodicity implies that the soil has a buffering ability, and thus that CO₂ is accumulating in the soil and subsurface. Indeed, studies of deep CO₂ leakage in soils show that in permeable environments, gaseous CO₂ coming from the depths has the ability of accumulating in soils in the unsaturated zone, and because CO₂ has a higher density than air, a “ponding” phenomenon is observed where CO₂ concentration is the highest above the unconfined water table (de Lary et al., 2012; Oldenburg & Unger, 2003). In these models, dissolution is considered negligible. It has been demonstrated that in surface waters, through the water column, CO₂ flow dominates over dispersion, as CO₂ solubility is low at low air pressures (Oldenburg & Lewicki, 2006). This reasoning can be applied for unconfined aquifers, where ground air pressure is low as well. At Piton de la Fournaise and Mayotte, there is magmatic CO₂ rising from the mantle into the unconfined aquifers. Also considering the range of permeabilities in both sites, a ponding phenomenon is likely to occur and will thus be integrated in our conceptual model (Figure 5). The significantly lower CO₂ concentrations values at station PNRN compared to the other stations (by one order of magnitude) indicates that the superficial biotic contribution from the soil layer constitutes a more significant part of the CO₂ content, and thus that the CO₂ source is partly superficial.

Figure 5

CO₂ transfer from the depth to the surface (a) by barometric pumping in Mayotte (b) by thermal convection and with concurrent heat transfer at Piton de la Fournaise.

Each environmental parameter is inferred to have a distinct effect on soil CO₂ as they rely on different physical properties. Consequently, they should induce responses at different times. Therefore, correlations between near-surface soil CO₂ concentrations and environmental parameters displaying phase synchronicity can be considered spurious and attributed to the interdependence of the environmental parameters. For instance, for all stations, the correlation between near-surface soil CO₂ concentration and rainfall and the correlation between near-surface soil CO₂ and air temperature and atmospheric pressure display a phase synchronicity. Since the correlation coefficient for rainfall is significantly lower compared to the other two parameters (Table 2, Figure 4), we deduce that this correlation is spurious and due to the interdependence of rainfall, air temperature and atmospheric pressure. Additionally, the correlation between rainfall and near-surface soil CO₂ concentration is expected to be negative as rainfall should decrease the permeability of the soil and obstruct the pathway to the surface (Granieri et al., 2003; Viveiros et al., 2008).

Similarly, in Mayotte, the correlation between near-surface soil CO₂ and the water table level, and the correlation between near-surface soil CO₂ and temperature and atmospheric pressure show a phase synchronicity, suggesting that only one of these parameters is driving CO₂ mass transfer from the subsurface to the near-surface soil. At Piton de la Fournaise however, the correlation between near-surface soil CO₂ and the water table level, and the correlation between near-surface soil CO₂ and temperature and atmospheric pressure show a phase difference, suggesting that both the water table level and either air temperature or atmospheric pressure influence near-surface soil CO₂ concentrations.

Changes in air temperature and in atmospheric pressure can generate CO₂ transfers in the subsurface through advection or diffusion. Advection can result either from a thermal gradient between the atmosphere and the subsurface, which generates thermal convection, or from a pressure gradient, which generates barometric pumping. Both mechanism are expected to be greater than diffusion in highly fractured environments, such as volcanic settings (Ahlers et al., 1999; Ganot et al., 2014; Nachshon et al., 2011; Nilson et al., 1991). Site properties can favor either one of these two mass transport processes.

The efficiency of thermally induced internal convection in porous media with heating from below is described by the Rayleigh-Darcy number Ra (Nield & Bejan, 2017):

(12)

where ρ₀ is the density, β is the thermal expansion coefficient, K is the permeability, H is the vertical dimension, ∆T is the temperature gradient, μ is the dynamic viscosity and α_m is the thermal diffusivity of the porous medium. Equation 12 shows that thermal convection increases with permeability, the depth of the vadose zone and the temperature gradient. In the case of natural soils, the geothermal gradient increases with depth, therefore the temperature gradient also depends on the depth of the vadose zone. In the case of fractured porous media, Mezon et al. (2018) showed that when the fracture network does not affect the thermal convection flow patterns, the output flux increases linearly with the fracture density and is described by an equivalent Rayleigh number Ra_eq, proportional to Ra. However, when the fracture network impacts the thermal convection flow patterns, the flow tends to be governed by a pressure drop. In fractured porous media, pressure transfers can be approached by the local seepage velocity described by Darcy's law in the matrix in Equation 13 and by the in-plate flow rate J in the fracture described in Equation 14 (Adler et al., 2013; Mourzenko et al., 2014):

(13)

(14)

where K_m is the permeability of the matrix, μ is the viscosity of the gas, ∇p is the total pressure gradient and ∇_sp is the pressure gradient in the fracture. The efficiency of barometric pumping will be controlled by these parameters, integrated on the length of the medium, hence the depth of the vadose zone. Mourzenko et al. (2014) demonstrate that barometric pumping is efficient in a limited set of conditions. The first one is that the fracture network must be connected. Additionally, an increase in the matrix porosity or in the fracture density results in a decrease in the barometric pumping efficiency.

At Piton de la Fournaise, the large permeabilities and estimated thicknesses of the vadose zone may result in very high Ra values, considered chaotic, and the equations describing porous system may thus not apply. In non-porous systems, such as karsts (Domínguez-Villar et al., 2013; Garcia-Anton et al., 2014; Luetscher et al., 2008; Mattey et al., 2021) and boreholes (Levintal et al., 2020), thermal convection and barometric pumping are also both observed, but at a seasonal scale, in all of these studies, thermal convection is the dominant transport mechanism.

In Mayotte, the bulk rock permeability is moderate but the rock formation is crosses by an interconnected network of large fractures. Additionally, the vadose zone is thin (<17 m). These site properties would theoretically create the ideal conditions for barometric pumping to occur. Barometric pumping is consistent with the results of our cross-correlation analysis, which show that the correlation between soil CO₂ concentrations and atmospheric pressure is significantly higher than those of other parameters (Table 2, Figure 4). For this reason, we advocate that in Mayotte, soil CO₂ mass transport from the subsurface to the near-surface soil at a seasonal scale occurs by barometric pumping and depends on variations of the atmospheric pressure, and that the other observed correlations play a less significant role. Low pressure air from the atmosphere propagates downwards through the fracture network and reaches the subsurface, where CO₂ accumulates and where the pressure is higher, which induces the motion of hot CO₂ rich air toward the surface (Figure 5a). The computed time for this CO₂ transfer is 21 days, from the variation of the atmospheric pressure to the variation of the near-surface soil concentration of CO₂. As the time series is very short for Mayotte (<2 years), the uncertainty on this delay remains significant and we would advise recomputing it after several years of monitoring.

At Piton de la Fournaise, where the rock permeability is very high, the vadose zone is also very deep, resulting in a large geothermal gradient between the accumulated CO₂ layers in the subsurface and the atmosphere. These site properties would theoretically favor thermal convection over barometric pumping. This is again consistent with the results of our cross-correlation analysis, which show that the correlation between near-surface soil CO₂ concentrations and air temperature is higher than those of other parameters (Table 2, Figure 4). For the four stations at piton de la Fournaise, we thus advocate that CO₂ mass transport from subsurface to near-surface at a seasonal scale occurs by thermal convection. Cold air from the atmosphere propagates downwards in the highly permeable and thick vadose zone and reaches the hotter subsurface, where CO₂ accumulates, which induces the motion of hot CO₂ rich air toward the surface (Figure 5b). However, our cross-correlation analysis also shows that the correlation between near-surface soil CO₂ concentrations and air temperature is positive, which contradicts our model. The observed delays also seem excessively large between the variation of air temperature and the resulting CO₂ efflux. To explain these discrepancies, we propose that there is a decoupling between heat transfer and CO₂ mass transfer.

Temperature can propagate in the ground by conduction with a wave-like behavior, with its velocity controlled by thermal diffusivity (Carslaw & Jaeger, 1959). Attenuation and delay between surface temperature and deep soil horizon temperatures thus increase with depth (Popiel et al., 2001; Schmidt et al., 2001; Smerdon et al., 2003, 2004; Tsilingiridis & Papakostas, 2014). At a depth of several meters, delays of a few to more than a hundred days can been observed (Ahlers et al., 1999; Smerdon et al., 2003, 2004). In contexts of very high permeability, in addition to conduction, heat can also be transmitted by water percolation and advective transport (Domínguez-Villar et al., 2013; Smerdon et al., 2006).

Although advective transport only affects a localized pathway constituted by empty spaces in the rock matrix (porosity and fractures), heat transfer affects the whole rock matrix, with significantly more inertia. We thus link the very large delays observed at Piton de la Fournaise (up to 164 at PCRN) to heat transfer through its very thick vadose zone from the surface down to the subsurface where CO₂ accumulates. The variations of this subsurface temperature displays the same periodicity as the variations of air temperature, but with a phase shift (Figure 5b). At any given time, the thermal gradient is given by the difference between this temperature in the subsurface and the temperature in the atmosphere, resulting in the same periodicity and a different phase shift. This thermal gradient powers the CO₂ mass transfer by thermal convection and is therefore proportional to the near-surface soil CO₂ concentration. Due to the phase shifts, the correlation between air temperature and the thermal gradient is positive, and so is the correlation between air temperature and near-surface soil CO₂ concentration.

In unconfined aquifers, such as at Piton de la Fournaise (Join et al., 2005), the carbon amount stored in the vadose zone can be controlled by its volume. Variations of the water table level changes the gas volume and can theoretically induce advective flow (Baldini et al., 2018). Although this process is rarely described in literature, Warrick (2001) states that these advective fluxes can be considered important only if the rate of rise or decline of the water-table is rapid, the permeability of the material is high and the water table is shallow. In the case of La Réunion, the permeability is high and the rise of the water table can be extremely rapid and large (∼10–20 m, Figure 2), due to the extremely high rainfall (3.2), but the vadose zone is very thick. Since CO₂ accumulates in the subsurface, its concentration increasing with depth down to the water table, the variation of the table level of 20 m at a depth of a hundred meters or more should not produce major changes close to the surface (de Lary et al., 2012; Oldenburg & Unger, 2003) but the level of the layers containing the most accumulated soil CO₂ would be raised. As a result, the conductive heat wave coming from the surface should reach CO₂ rich layers with a greater amplitude and a shorter delay (Popiel et al., 2001; Schmidt et al., 2001; Smerdon et al., 2003, 2004; Tsilingiridis & Papakostas, 2014). Depending on the phase shift, this process can increase the thermal gradient, and thus boost thermal convection. We tentatively explain the positive correlation between soil CO₂ concentration and water table level by this mechanism.

It should be noted that the UDMN station in Mayotte displays the highest CO₂ concentrations, more than twice that of Piton de la Fournaise stations, suggesting that the magnitude of the CO₂ flow could also play a part in the preferred driving mechanism for CO₂ transfer.

6 Conclusion

Our cross-correlation analysis of time series of soil CO₂ concentration and environmental parameters has successfully highlighted the environmental parameters driving different transport mechanisms of soil CO₂ toward the atmosphere at a seasonal scale in a context of high abiotic CO₂ flux.

At the four stations of Piton de la Fournaise, we observed a strong positive correlation between soil CO₂ and air temperature with a seasonal periodicity and delays of several tens to hundreds of days. These sites have particularly highly permeable units and thick vadose zones of up to several hundred meters. The geothermal gradient, which increases with depth, is thus high between the surface and the bottom of the vadose zone. From these correlations and site properties, we inferred that the thermal gradient powers the soil CO₂ transfers from the depth to the surface through thermal convection. These site properties also explain the observed delays between environmental forcing and CO₂ increase near the surface. Because of the high permeability, soil CO₂ accumulates in the vadose zone by ponding over the water table. Because of the thick vadose zone, heat conduction from the surface to the depth down to the accumulated CO₂ layer occurs with a large delay, which induces a shifted periodical variation of the thermal gradient and of the resulting rise of CO₂ generated by thermal convection. At these sites, we also observe a strong correlation between soil CO₂ and water table level. The depth of the vadose zone varies with the water table level, which in turn impacts the magnitude of the thermal gradient, thermal convection, and CO₂ efflux.

The study site of Mayotte has a lower permeability and a thinner vadose zone than all of the Piton de la Fournaise sites. It is located close to a large CO₂ bubbling field at sea, indicating that there is an interconnected fracture network. The soil CO₂ concentration at this site best correlate with the atmospheric pressure variations, with little delay. From these correlations and site properties, we inferred that the main soil CO₂ transport mechanism from the depth to the surface is barometric pumping.

The use of the Time-lagged DCCA method was decisive in determining the relations between soil CO₂ emissions and environmental parameters as it highlighted the large delays that are observed at a seasonal scale. The possibility of a delayed response due to CO₂ accumulation and the role of the water table level are rarely considered in the study of the long-term influence of environmental parameters on soil CO₂ variations, and yet, it is crucial to the understanding of the physical processes at stake. Our study is also the first to highlight the role of heat conduction in soil CO₂ transfers. Additionally, barometric pumping is more studied in relation to soil CO₂ transfers than thermal convection, which we demonstrated here can drive CO₂ transfers in contexts of high permeability and a thin vadose zone. This work calls attention to the need to account for potential consequences of global change on the air temperature and water table level in terms of CO₂ transport toward the surface in soils. Our work also gives way to a mathematical filtration of the influence of environmental parameters in volcanic environments in order to highlight magmatic contributions.

While our study successfully contributed to increase the knowledge about the long-term processes driving CO₂ transfers in soils, we found it particularly challenging due to the interdisciplinarity that the study of soils requires, being at the interface between the atmosphere, hydrosphere, biosphere and rocks. We found ourselves limited by the available knowledge about the site's precise hydrogeological characteristics (thickness of the vadose zone, permeability), and thus unable to verify our hypotheses numerically by modeling the soil CO₂ transfers. Future research should address these limitations by using geophysical data to estimate the thickness of the vadose zone and the permeability profiles. Additionally, the consequences of this diffuse degassing on the soil and on the biosphere should be studied, for example, from the evolution of the isotopic composition of soil CO₂.

Acknowledgments

The postdoctoral fellowship of B. Bénard is part of the Hatari Project INTERREG V Indian Ocean N° Synergie RE0023208, cofunded by the European Union, Région La Réunion, and Préfecture de La Réunion. The data used in this paper were acquired by soil CO₂ monitoring stations as part of the permanent instrumental network of Observatoire Volcanologique du Piton de la Fournaise–Institut de Physique du Globe de Paris (OVPF-IPGP). The operation and equipment are funded by Institut National des Sciences de l’Univers-Centre National de la Recherche Scientifique (INSU-CNRS), Ministère français de l'Enseignement supérieur, de la Recherche et de l'Innovation (MESRI), Préfecture de La Réunion, and Région La Réunion. Since June 2019, monitoring of Mayotte eruption was funded by Ministère de l’Enseignement Supérieur, de la Recherche et de l’Innovation (MESRI), Ministère de la Transition Ecologique (MTE) and Ministère des Outremers (MOM) with the support of Ministère de l’Intérieur (MI) and Ministère des Armées (MINARM) through the REVOSIMA (Réseau de surveillance volcanologique et sismologique de Mayotte). Data from Mayotte used in this paper have been acquired, processed and modeled in the framework of the REVOSIMA.

Open Research

Data Availability Statement

Soil CO₂ concentration, air temperature and atmospheric pressure data are available on the IPGP online data repository at https://doi.org/10.18715/IPGP.2023.ld8t37v7 (Bénard et al., 2023). Rainfall daily time series were obtained from the French national meteorological service Météo France online data repository (https://publitheque.meteo.fr/). Water table level daily time series were obtained from the Office de l'eau Réunion online data repository (https://donnees.eaureunion.fr/).