The study location is within the Laval catchment, part of the IRSTEA Draix Bléone Experimental Observatory and the Réseau des Bassins Versants network, located near the town of Draix, Alpes-de-Haute-Provence, France. The small catchment (0.86 km2) is heavily instrumented, with continuous monitoring of rainfall, river water discharge, river solid load transport, total dissolved fluxes and physical erosion rates over the last 4 decades (Cras et al., 2007; Mathys et al., 2003). These measurements provide hydrodynamic and geomorphic context for any studies of oxidative weathering. The lithology of the catchment is composed of black Jurassic marine marls (from the Bajocian to the Callovo-Oxfordian stages), which contain inorganic carbon and organic matter (Graz et al., 2012). Sulfide minerals are widespread as disseminated pyrite and veins which outcrop in the catchment (Cras et al., 2007). The rock-strength, climate and geomorphic setting combine to produce a badland-type morphology with very steep and dissected slopes.

Erosion rates are very high, with sediment export fluxes of 11 200 t km-2 yr-1 on average during the period 1985 to 2005 AD (with a minimum of 4400 t km-2 yr-1 in 1989 and a maximum of 21 100 t km-2 yr-1 in 1992) (Graz et al., 2012; Mathys et al., 2003). Assuming a regolith bulk density of ∼ 1 to 1.5 t m-3 (Mathys and Klotz, 2008; Oostwoud Wijdenes and Ergenzinger, 1998), this equates to a physical erosion rate of ∼ 7 to 10 mm yr-1 on average, but that can reach maximum values of 14 to 20 mm yr-1. These features limit the development of soils, and bare rock outcrops represent 68 % of the catchment surface area (i.e. 0.58 km2) (Cras et al., 2007; Mathys et al., 2003). As a result, it is easy to find regolith and rock surfaces that are devoid of soils and roots, and where sedimentary rocks are directly exposed to the oxygen-rich atmosphere. These are key parts of the landscape contributing to weathering, solute production (Cras et al., 2007) and sediment production (Graz et al., 2012; Mathys et al., 2003; Oostwoud Wijdenes and Ergenzinger, 1998). Bare rock outcrops are characterized by the development of weathered marls and regolith. Regolith typically extends to at least ∼ 20 cm with the following characteristics: (i) the upper ∼ 3 cm is loose detrital cover composed of millimetre-to-centimetre-sized fragments of marls, (ii) from ∼ 3 to ∼ 10 cm is the loosened upper regolith which is somewhat fragmented, (iii) from ∼ 10 to 20 cm is the compact lower regolith which retains the marl structure but not its cohesion, and (iv) at depths more than ∼ 20 cm is the marl bedrock (unweathered marl) (Maquaire et al., 2002; Mathys and Klotz, 2008; Oostwoud Wijdenes and Ergenzinger, 1998). Lateral variation in the regolith thickness exists with larger thicknesses on crests, intermediate in gullies and minimal in talwegs (Maquaire et al., 2002). Marl bedrock porosity ranges between 0.17 and 0.23 (Traveletti et al., 2012).

In order to measure the flux of CO2 produced by oxidative weathering of sedimentary rocks and accumulate enough CO2 to perform stable carbon isotope and radiocarbon measurements, we use accumulation chambers (e.g. Billett et al., 2006; Hardie et al., 2005). These have been extensively used to measure soil respiration (e.g. Hahn et al., 2006; Hardie et al., 2005) and CO2 evasion by streams and rivers (e.g. Billett et al., 2006; Borges et al., 2004), but have not yet been used to examine rock–atmosphere interactions. Because most fine-grained sedimentary rocks have a degree of competency, accumulation chambers can be made by directly drilling into the rock. Here we use a rock drill to make 40 cm long chambers with an inner diameter of 29 mm. Our aim was to minimize the volume of the chamber while maximizing the surface of exchange with the surrounding rock.

The rock powder left inside the chamber after its drilling was blown away using a compressed-air gun in order to minimize the presence of potentially reactive dust. Then, after measuring the dimensions of the chamber, its entrance is fitted with a small PVC tube (∼ 3 cm diameter, ∼ 3 cm long), which allows a tight seal with an inserted rubber stopper containing two holes. Two Pyrex^® tubes (ID = 3.4 mm and OD = 5 mm; one of 12 cm long and one of 7 cm long) are inserted through the rubber stopper. The differential length is to improve airflow in the chamber while in operation. The sections of the Pyrex^® tubes sticking out of the chamber are fitted with Tygon^® tubing (E-3603; Saint-Gobin, France). To isolate the accumulation chamber from the atmosphere as well as possible, the Tygon^® tubing is sealed with WeLock^® clips (Scandinavia Direct Ltd, UK) and silicone sealant (Unibond^® Outdoor) is placed around the entrance of the chamber (the 3 cm diameter PVC tubing and the rubber stopper) (Fig. 1). The newly installed chamber is left for ∼ 2 days to allow the sealant to fully dry. Here we acknowledge that a perfect seal is impossible, due to the natural rock fracturing around the chamber. Table 1 summarizes the dimensions of an example chamber drilled and sealed in the field on 13 December 2016.

Drilling introduces an oxygen-rich atmosphere in the chamber and surrounding marl regolith and bedrock (similar to outcropping marls exposed to the atmosphere). If gaseous O2 is consumed (e.g. by Reaction R1), this would create a gradient in the partial pressure of O2 (pO2) whereby the atmosphere surrounding the rock and chamber is of higher pO2. Given the natural porosity and permeability of the shale bedrock, any diffusion of O2 is likely to be into the chamber. This should act continuously to fuel the chamber with oxygen. In contrast, if CO2 is produced inside the chamber (by Reactions R1 and R2) then the partial pressure of CO2 (pCO2) will exceed that of the atmosphere. The result is that for chambers where oxidative weathering is occurring, the ingress of “contamination” by atmospheric CO2 should be minimal, and there should be a supply of O2 for reactions. These inferences can be tested using a pO2 probe and by trapping CO2 and measuring its isotope composition.

In this example we aimed to measure oxidation of sedimentary rocks and intended to minimize the role of CO2 produced by root respiration. Therefore, the chambers were drilled on cleared rock surface, devoid of visible roots. The rock powder produced when drilling the chambers was collected, freeze-dried and ground in the laboratory to fine powder for measurement of its organic and inorganic carbon content and its isotopic composition.

A closed-loop CO2 sampling system similar to the molecular sieve sampling system (MS3) described in Hardie et al. (2005) was used for CO2 flux measurements and CO2 sampling (Fig. 1). The system incorporated the following components: an air filter; a water trap (cartridge filled with magnesium perchlorate); a portable infrared gas analyser (IRGA) equipped with an internal air pump, calibrated to a pCO2 range of 0 to 5000 ppmv and installed with an pO2 probe (EGM-5, PP Systems, USA); a CO2 scrub (cartridge filled with soda lime); a bypass; and a set of WeLock^® clips that allow the air flow to be diverted through the bypass or the CO2 scrubber cartridge. Optionally a zeolite molecular sieve sampling cartridge can be inserted in the line (see Sect. 2.4).

Before each CO2 flux measurement, the Tygon^® tubes exiting the chamber were fitted with auto-shutoff Quick Couplings^™ (Colder Products Company, USA), and the CO2 contained within the sampling system was removed using the CO2 scrubber cartridge. When no CO2 is left in the sampling system (as indicated by the IRGA), the air flow is diverted through the bypass, and the system connected to the chamber (Fig. 2). The use of the auto-shutoff couplings prevents atmospheric contamination at the moment of connection to the chamber. Then, pCO2 in the chamber is lowered to near-atmospheric pCO2 by guiding the air flow through the CO2 scrubber cartridge. We let the CO2 accumulate in the chamber for several minutes (typically 10 min) by guiding the air flow through the bypass (Fig. 2). This operation can be repeated several times to provide multiple measurements of CO2 flux over a period of hours (Fig. 3). The CO2 evolution in the chamber typically shows a curvature, the curve flattening with time and higher concentration (Fig. 3). In order to calculate the CO2 flux, we first convert the pCO2 measurements into the mass of carbon contained in the chamber: m=pCO2106⋅V⋅A, where m is the mass of carbon in the chamber (mgC), pCO2 is the concentration of CO2 in the chamber in ppm (cm3 m-3), and V is the total volume (cm3), i.e. the sum of the volume of the chamber (VCh) and the volume of the CO2 sampling system (VL) when air flows through the bypass. Factor A converts centimetres cubed of CO2 into milligrams of carbon, depending on temperature and pressure following the ideal gas law: A=P⋅MCR⋅T⋅10-3, where P is the pressure (Pa) as measured by the IRGA, MC is the molar mass of carbon (g mol-1), R is the gas constant (m3 Pa K-1 mol-1) and T is the temperature (K) in the chamber. Then the rate (q, in mgC min-1) at which carbon accumulates in the chamber is calculated using an exponential model (described below; Pirk et al., 2016) and converted into a flux of carbon (Q in mgC m-2 day-1) emitted to the atmosphere under the form of CO2 using Q=1440q/S, where 1440 converts mgC min-1 into mgC day-1, and S (m2) is the inner surface area of the chamber exchanging with the surrounding rock. To calculate the rate of accumulation of carbon (q) in the chamber we use the exponential model described by Pirk et al. (2016): dmtdt=q-λmt-m0, where dmtdt is the carbon mass change in the chamber with time. Parameter m0 is the mass of carbon in the chamber at the beginning of the CO2 accumulation and that should be close to the mass of carbon in the chamber at atmospheric pCO2. The constant λ (in units of time, here in min-1) describes the sum of all processes which are proportional to the carbon mass difference Δmt=mt-m0 and is responsible for the curvature of the carbon mass accumulation evolution (Fig. 3). The model does not a priori assume any process to be responsible for the curvature (Pirk et al., 2016). In the case of the measurement of CO2 flux in soils, the curvature (λ) relates to leakages, diffusivity from soil CO2 into the chamber headspace and photosynthesis (Kutzbach et al., 2007). In the case of our chambers drilled in rock, since it is assumed that there is no possibility of photosynthesis, λ likely relates to the diffusivity of carbon from the rock to the chamber headspace and to the chamber leakiness. Equation (7) is solved by fitting the following function to the data (Fig. 3b): mt=qλ1-exp-λt+m0. Several parameters lead to uncertainties in the flux calculations. They are all related to the conversion of pCO2 to mass of carbon (Table 1): (i) the volume of the chamber (VCh), (ii) the surface area of exchange with the surrounding rock (S), (iii) the volume of the closed-loop system when air flows through the bypass (VL was determined to be 127.8±0.5 cm3 through an experiment of successive CO2 dilution in a known volume), and (iv) the temperature in the chamber was assumed to range from 0 to 20 ∘C over the course of the experiment. We estimated the relative uncertainty on the measured flux using a Monte Carlo simulation of error propagation using the ranges listed above and in Table 1. The resulting relative uncertainty on the measured flux was estimated to be within ±2.5 %. An additional relative uncertainty linked to the rate of CO2 accumulation in the chamber (parameter q obtained through fitting the exponential model to the data) ranges between 0.5 and 1.0 %. Altogether, the final relative uncertainty determined with our Monte Carlo simulation of error propagation was found to be within ±3 %. In the case that the relative standard deviation on multiple flux measurements is higher than 3 %, we adopt the standard deviation as the uncertainty.

CO2 evading the rock accumulates in the chamber and can be sampled using a zeolite molecular sieve trap (Garnett et al., 2009; Garnett and Hardie, 2009; Hardie et al., 2005). Zeolites have a high affinity for polar molecules such as H2O and CO2, and are widely used to separate CO2 from air at ambient temperature and pressure. The gas trapped by the zeolite sieve can be extracted in the laboratory at high temperature for CO2 purification and isotope analysis (Garnett and Murray, 2013; Hardie et al., 2005). The type of zeolite (13X) and the design of the cartridge containing the zeolite are described by Hardie et al. (2005) and Garnett et al. (2009). In our study the CO2 was sampled “actively” – i.e. using the CO2 sampling system coupled to the pump incorporated in the IRGA to force the air through the zeolite molecular sieve cartridge (Fig. 1) following Hardie et al. (2005). Two approaches can be used. The first involves connection of the line to the chamber for the duration of trapping, which was used on 27 March 2017. Each removal of CO2 onto the trap can be controlled to return the chamber to ambient atmospheric pCO2, allowing for a subsequent measurement of CO2 flux (Fig. 3). The second approach allows pCO2 to accumulate in the chamber, before attaching the scrubbed line and sampling the CO2, which we tested on 30 March 2017. The benefit of the latter method is that it allows the gas line and IRGA to be used for other tasks while in the field, but may be more susceptible to atmospheric inputs during the connection of lines.

The CO2 was also sampled “passively”, when the zeolite molecular sieve is connected to the chamber for several months following the procedure described in Garnett et al. (2009) (Fig. 4). This approach has the benefit of providing an integrative view of CO2 production over longer periods of time. A passive trap was installed on 15 December 2017 (2 days after the chamber was constructed) and removed on 26 March 2017 (101 days after its installation) for chamber H6. Based on previous work (Garnett et al., 2009; Garnett and Hardie, 2009; Garnett and Hartley, 2010), it is expected that the passive trap method can lead to a fractionation of the stable carbon isotope composition (δ13C) of 4.2±0.3 ‰ associated with the diffusion of CO2 from the chamber to the zeolite trap. In addition, a sample of local atmospheric CO2 was also collected by actively circulating the atmosphere sampled at ∼ 3 m elevation above the valley floor through a zeolite molecular sieve.

After sample collection the zeolite molecular sieves were sealed with WeLock^® clips on either end before being disconnected from the sampling system (active or passive) and returned to the NERC Radiocarbon Facility (East Kilbride, UK) for CO2 recovery. The CO2 collected was desorbed from the zeolite by heating (425 ∘C) and cryogenically purified (Garnett and Murray, 2013). One aliquot of the recovered CO2 was used for stable carbon isotope composition (δ13C) measurement using isotope ratio mass spectrometry (IRMS; Thermo Fisher Delta V; results expressed relative to the Vienna Pee Dee Belemnite (VPDB) standard). A further aliquot was converted to graphite and analysed for 14C / 12C ratio using accelerator mass spectrometry at the Scottish Universities Environmental Research Centre (SUERC). Radiocarbon measurements were, following convention, corrected for isotopic fractionation using the measured sample IRMS δ13C values, and reported in the form of the fraction modern, Fm (ASN/AON in Stuiver and Polach, 1977; corresponding to 14aN in Mook and van der Plicht, 1999, or F14C in Reimer et al., 2004; Table 2).

As the chamber was drilled away from the obvious influence of root respiration, the CO2 emitted from the rock should originate from (i) the oxidation of the organic carbon contained within the rock mass following Reaction (R1), and/or from (ii) the dissolution of the carbonate minerals by sulfuric acid following Reaction (R2). Some of the CO2 collected in active or passive zeolite molecular sieves might also originate from atmospheric CO2, i.e. the ambient air (see discussion below). To correct for possible atmospheric contamination, and partition the sources of CO2, we solve the following isotope mass balance system: fAtm+fRockOC+fCarb=1fAtm⋅δ13CAtm+fRockOC⋅δ13CRockOC+fCarb⋅δ13CCarb=δ13CChamberfAtm⋅FmAtm+fRockOC⋅FmRockOC+fCarb⋅FmCarb=FmChamber where fAtm is the mass fraction of CO2 originating from the atmosphere, fRockOC is that originating from the oxidation of the rock-derived organic carbon, and fCarb is that originating from carbonate dissolution by sulfuric acid. Subscript “Chamber” stands for the CO2 sampled from the chambers (i.e. trapped in the zeolite molecular sieves). The terms δ13C and Fm stand for the stable carbon isotope and radiocarbon compositions of the three possible sources of CO2 listed above and of the CO2 sampled in the chamber.

Table 3 shows the δ13C and Fm values of the three possible sources of CO2 involved in the isotope mass balance. These values were measured in the laboratory. The δ13CAtm and FmAtm values were measured from the atmospheric CO2 sample actively trapped in a zeolite molecular sieve (see Sect. 2.4). The stable carbon isotope composition of the rock-derived organic carbon (δ13CRockOC) was obtained by IRMS after inorganic carbon removal from the powdered rock samples by HCl fumigation, followed by closed-tube combustion to produce CO2. The stable carbon isotope composition of the carbonates (δ13CCarb) was obtained after dissolution of the carbonates of the powdered rock samples by phosphoric acid in vacuumed vessels following standard procedures at NERC Radiocarbon Facility. Since the rock-derived organic carbon and carbonates were formed millions of years ago they do not contain radiocarbon any longer, and their fraction modern (FmRockOC and FmCarb) levels should be close to the AMS background as confirmed by our measurements (Table 3). Consequently, when solving the isotope mass balance, FmRockOC and FmCarb were set to 0.

A total of 3 months after the installation of the chamber H6, CO2 fluxes were measured alongside a series of zeolite-trapping events on 27 March 2017 (Fig. 3). If the chamber was perfectly isolated from the atmosphere, then we might expect the rate of carbon accumulation (dmtdt) to be constant. However, the rate of carbon accumulation decreases with time, which indicates that the chamber is not perfectly sealed, as expected. This has some important implications. First, the leak rate depends on the pCO2 gradient between the chamber and the atmosphere. Since this gradient is positive in the chamber (Fig. 2) (pCO2chamber>pCO2atmosphere), then CO2 likely diffuses from the chamber to the atmosphere. This has the advantage that it naturally minimizes any atmospheric CO2 contamination. Conversely, since the CO2 production is linked to the consumption of O2, then the O2 gradient is expected to be negative (pCO2chamber<pO2atmosphere), and thus atmospheric O2 naturally diffuses inside the chamber. This means that the chamber can be closed for months and still contain gaseous O2. Our measurements of O2 using the EGM-5 O2 probe suggest that the chamber had a similar pO2 as that contained in the ambient atmosphere of the catchment (the chamber value was 96 to 99 % of the atmosphere pO2).

The fluxes of CO2 measured in this chamber on 27 March 2017 decreased from 1384±42 to 684±21 mgC m-2 day-1 with the number of times we extracted the CO2 from the chamber (Fig. 3). The flux becomes approximately constant after three CO2 extractions during zeolite trapping, with an average of 705±15 mgC m-2 day-1 (1sd, n=4) for the last four flux measurements that are indistinguishable from each other within 2σ (Fig. 3). This observation might be explained by the fact that over time (days to months), CO2 accumulates not only in the chamber, but also in the regolith- or rock-connected pores surrounding the chamber in the lower compact regolith (Maquaire et al., 2002). Weathering reactions are likely to occur not only at the chamber–rock interface, but also into the rock mass over several centimetres as the weathered regolith extends to depths of up to 20 cm (Maquaire et al., 2002; Mathys and Klotz, 2008; Oostwoud Wijdenes and Ergenzinger, 1998).

When CO2 is first extracted from the chamber, the CO2 stored in the surrounding pores quickly refills the chamber. It appears that after three extractions this CO2 is depleted, meaning that the more constant values correspond to the actual flux of CO2 through the surface area of the chamber. We would therefore recommend that flux measurements are made on such a chamber following ∼ 3 to 4 removals of CO2, or adapted to less or more removals based on the results obtained after a series of flux measurements.

It has to be noted that the mass of carbon (mC) recovered on the zeolite molecular sieve during the period of passive trapping (Δt) cannot be directly and simply used to inform the flux of carbon through the chamber. This is because the rate of carbon trapping (mC / Δt) follows the first Fick's law (Bertoni et al., 2004) and hence depends on the partial pressure of CO2 in the chamber rather than on the flux itself. It is thus not trivial to assess the flux from the rate of carbon passive trapping (mC / Δt) as the flux itself may change through time. Similar reasons prevented the direct use of the amount of passively trapped CO2 to estimate flux rates in previous studies (Hartley et al., 2013). Nevertheless, the rate at which CO2 is trapped on the zeolite molecular sieve (mC / Δt) is still qualitatively informative about CO2 flux when compared to other sampling periods when CO2 is passively trapped (see the Appendix for further information).

To our knowledge, we report here the first attempt to directly measure the CO2 flux emitted during weathering of sedimentary rocks, and trap this CO2 to partition its sources using stable carbon isotopes and radiocarbon. We acknowledge that our chamber method has not been replicated, representing a limitation to our study. Nevertheless, our study is a field-based experiment, where many environmental parameters (e.g. temperature, precipitation, water content in the unsaturated zone) will have an impact on the weathering and erosion of the studied marls. Hence we expect that the CO2 flux we measured in March 2017 and its isotopic composition will be different from measurements carried out at another times of the year. Similarly, due to the marl geochemical heterogeneities (e.g. inorganic and organic carbon contents, as well as content in sulfide mineral), the CO2 flux and its isotopes could be expected to vary from one chamber to another. It is thus impossible to replicate the exact same results we present here. We propose that future work should aim to monitor numerous chambers over seasonal changes in environmental conditions.

While wary of these caveats, in the following sections we compare our results with other methods, to test the order of magnitudes of the CO2 flux we obtained using our cylindrical chambers against previously published estimates from other regions of the world. While this exercise is challenging due to major differences in the way the CO2 fluxes were estimated and in the surface area and timescales (local estimates at a fixed time vs. regional estimates averaged over months or years), it is informative to assess the reliability of our method.