2.1 Instrumentation

The concentration of δ¹³C and δ¹⁸O values of CO₂ were measured with an OA-ICOS, as described in detail by Baer et al. (2002) and Jost et al. (2006). In this study, we used an OA-ICOS, (LGR CCIA 36-d) manufactured by Los Gatos Research Ltd in San Francisco, USA. The LGR CCIA 36-d measures CO₂ concentration and δ¹³C and δ¹⁸O values at a frequency up to 1 Hz. The operational CO₂ concentration range was 400 to 25 000 ppm. The operating temperature range was +10–+35 ^∘C, and the sample temperature range (gas temperature) was between −20 and 50 ^∘C. The recommended inlet pressure was < 0.0689 MPa. The multiport inlet unit (MIU), an optional design that comes along with LGR CCIA 36-d, had a manifold of eight digitally controlled inlet ports and one outlet port. It presented the user with an option of measuring eight different CO₂ samples at the desired time interval. Three standard gases with distinct δ¹³C and δ¹⁸O values were used for calibration in this study (see Table S1 in the Supplement). The standard gases used in this study were analysed for absolute concentration and respective δ¹³C and δ¹⁸O values. δ values are expressed based on Vienna Pee Dee Belemnite (VPDB) CO₂ scale and were determined by high precision IRMS analysis.

Figure 1Set-up made for calibration of OA-ICOS (LGR CCIA 36-d). I (1, 2) represents CO₂ standards, CO₂ mix denotes gas standards mixed in equal molar proportion, I3 represents synthetic air, MFC (1, 2) denotes mass flow controller, F (1, 2) represents PTFE filter, V (1, 2, 3) denotes pressure-reducing valves, V4 shows three-way ball valve, V (5, 6) stands for pressure controller valve with safety bypass, P (1–7) denotes steel pipes, and P (8–11) represents Teflon tubing.

Download

2.2 Calibration set-up and protocol

We developed a two-step calibration procedure to (a) correct for concentration-dependent errors in isotopic data measurements and (b) correct for deviations in measured δ values from absolute values due to the offset (other than concentration-dependent error) introduced by the laser spectrometer. Also, we used Allan variance curves for determining the time interval to average the data (Nelson et al., 2008) in order to achieve the highest precision that can be offered by the LGR CCIA 36-d (Allan et al., 1997).

The first part of our calibration methodology was developed to correct for the concentration-dependent error observed in preliminary studies for δ¹³C and δ¹⁸O values measured using OA-ICOS. Such a calibration protocol was used in addition to the routine three-point calibration performed with in-house CO₂ gas standards of known δ¹³C and δ¹⁸O values. We developed a CO₂ dilution set-up (see Fig. 1) in which each of the three CO₂ standard gases was diluted with synthetic CO₂-free air (synthetic air) to different CO₂ concentrations. By applying a dilution series, we identified the deviation of the measured (OA-ICOS) from the absolute (IRMS) δ¹³C and δ¹⁸O values depending on CO₂ concentration (see Fig. 4). The δ¹³C and δ¹⁸O values of our in-house calibration gas standards were measured via cryoextraction and dual-inlet IRMS. δ¹³C and δ¹⁸O of the standard gases (see Table S1) across a wide range of CO₂ concentrations are measured using OA-ICOS. The deviation of the measured δ¹³C, and δ¹⁸O from absolute values with respect to changing CO₂ concentrations was mathematically modelled and later used for data correction (see Fig. 5). A standard three-point calibration was then applied to correcting for concentration-dependent errors (see Fig. 7). The standards used covered a wide range of δ¹³C and δ¹⁸O values, including the values observed in the field of application.

Standard gases were released to a mass flow controller (ANALYT-MTC, series 358, MFC1) after passing through a pressure controller valve (see Fig. 1) with safety bypass (TESCOM, D43376-AR-00-X1-S, version 5). A Swagelok filter, (Stainless Steel All-Welded In-Line Filter; Swagelok, SS-4FWS-05, F1) was installed at the inlet of the flow controller (ANALYT-MTC, series 358, MFC1). Synthetic air was released and passed to another flow controller (ANALYT-MTC, series 358, MFC2) through a Swagelok filter (F2 in Fig. 1). CO₂ and synthetic air leaving the flow controllers (MFC1 and MFC2 respectively) were then mixed and drawn through a Teflon tube (P8) with a 6.35 mm outer diameter (OD), which was kept in a gas thermostat unit (see Fig. 1). The thermostat unit contained (a) a thermostat-controlled water bath (Kottermann, 3082) and (b) an Isotherm flask containing liquid nitrogen. The water bath was used to raise the temperature above room temperature and also to bring the temperature down to +5 ^∘C by placing ice packs in the water bath. To reach low temperatures (−20 ^∘C), we immersed the tubes in the isotherm flask filled with liquid N₂. Leaving the thermostat unit, the gas was directed to the multiport inlet unit of the OA-ICOS. By using the thermostat unit, we introduced a shift in the reference gas temperature, and the aim was to test the temperature sensitivity of the OA-ICOS in measuring δ¹³C and δ¹⁸O values. The third CO₂ standard gas (which is used for validation) was produced by mixing the other two gas standards in equal molar proportions in a 10 L volume plastic bag with an inner aluminum foil coating and welded seams (CO₂ mix: Linde PLASTIGAS^®) under 0.03 MPa pressure by diluting to the required concentration using synthetic air. The mixture was then temperature adjusted and delivered to the MIU by using a 6.35 mm (OD) Teflon tube (P10). From the multiport inlet unit, calibration gases were delivered into the OA-ICOS for measurement using a 6.35 mm OD Teflon tube (P9) at a pressure <0.0689 MPa, with a flow rate of 500 mL min⁻¹. The gas leaving the OA-ICOS through the exhaust was fed back to the 6.35 mm (OD) Teflon tube (P8) by using a Swagelok pipe tee (Stainless Steel Pipe Fitting, Male Tee, 6.35 mm OD, Male NPT), intersecting the P8 line before entering the thermostat unit. Thus, the gas fed was looped in the system until steady values were reported by the OA-ICOS based on CO₂ (ppm), δ¹³C, and δ¹⁸O measurements. CO₂ gas standards were measured at 27 different CO₂ concentration levels ranging between 400 and 25 000 ppm. Every hour before sampling, synthetic air gas was flushed through the system to remove CO₂ to avoid memory effects. The calibration gases were measured in a sequence, one after the other, four times. During each round of measurement, every calibration gas was diluted to different concentrations of CO₂ (400–25 000 ppm), and the respective isotopic signature and concentration were determined. For each measurement of δ¹³C and δ¹⁸O at a given concentration, the first 50 readings were omitted to avoid possible memory effects of the laser spectrometer, and the subsequent readings for the next 256 s were taken and averaged to get maximum precision for δ¹³C and δ¹⁸O measurements. When switching between different calibration gases at the multiport inlet unit, synthetic air was purged through the systems for 30 s to avoid cross contamination.

2.3 Experimental sites

In situ experiments were conducted to measure δ¹³C, δ¹⁸O, and concentrations of soil CO₂ in two different soil types (calcareous and acidic soil). The measurements in a calcareous soil were conducted during June 2014 in cropland cultivated with wheat (Triticum aestivum) in Neuried, a small village in the upper Rhine Valley in Germany, situated at 48^∘26^′55.5${}^{\prime \prime }$ N, 7^∘47^′20.7${}^{\prime \prime }$ E, 150 m a.s.l. The soil type described as calcareous Fluvic Gleysol IUSS Working Group WRB (2015) developed on gravel deposits in the upper Rhine Valley. Soil depth was medium to deep, with high contents of coarse material (>2 mm) up to 30 %–50 %. Mean soil organic carbon (SOC) content was 1.2 %–2 %, and SOC stock ranged between 50 and 90 t ha⁻¹. The average pH was found to be 8.6. The study site receives an annual rainfall of 810 mm and has a mean annual temperature of 12.1 ^∘C.

In situ measurements in an acidic soil were conducted by the end of July 2014 in the model ecosystem facility (MODOEK) of the Swiss Federal Research Institute WSL in Birmensdorf, Switzerland (47^∘21^′48${}^{\prime \prime }$ N, 8^∘27^′23${}^{\prime \prime }$ E; 545 m a.s.l.). The MODOEK facility comprises 16 model ecosystems, split below ground into two lysimeters with an area of 3 m² and a depth of 150 cm. The lysimeters used for the present study were filled with acidic (Haplic Alisol) forest soil IUSS (2014) and planted with young beech trees (Arend et al., 2016). The soil pH was 4.0, with a total SOC content of 0.8 % (Kuster et al., 2013).

2.4 Experimental set-up

The OA-ICOS was connected to gas-permeable, hydrophobic membrane tubes (Accurel^® tubing, 8 mm outer diameter) of 2 m length, placed horizontally in the soil at different depths. Tubes were laid in six different depths (4, 8, 12, 17, 35, and 80 cm) for calcareous soil and three depths (10, 30, and 60 cm) for acidic soil.

Technical details of the measurement set-up are shown in Fig. 2. Both ends of the membrane tubes were extended vertically upwards, reaching the soil top by connecting them to gas impermeable Synflex^® tubing (8 mm OD) using Swagelok tube fitting union (Swagelok: SS-8M0-6, 8 mm tube OD). One end of the tubing system was connected to a solenoid switching valve (Bibus: MX-758.8E3C3KK), by using a stainless-steel reducing union (Swagelok: SS-8M0-6-6M), to the outlet of the LGR CCIA 36-d by using 6.35 mm (OD) Teflon tubing. The other end was connected via the multiport inlet unit to the gas inlet of the LGR CCIA 36-d.

This way, a loop was created in which the soil CO₂ drawn into the OA-ICOS was circulated back through the tubes and in and out of the OA-ICOS and measured until a steady state was reached. We experienced no drop in cavity pressure while maintaining a closed loop (see Fig. S2). Each depth was selected and continuously measured for 6 min at specified time intervals by switching to defined depths at the multiport inlet unit and also at the solenoid valve.

Figure 2Installation made for soil air CO₂ (ppm), δ¹³C-CO₂ and δ¹⁸O−CO₂ measurements using off-axis integrated cavity output spectrometer (OA-ICOS). Hydrophobic membrane tubing was installed horizontally in soil at different depths. MIU: multiport inlet unit.

Download

Figure 3Allan deviation curve for δ¹³C (a) and δ¹⁸O (b) measurements by OA-ICOS CO₂ carbon isotope analyser (LGR CCIA-36d).

Download

3.1 Instrument calibration and correction

The highest level of precision obtained for δ¹³C and δ¹⁸O measurements at the maximum measuring frequency (1 Hz) was determined by using Allan deviation curves (see Fig. 3). The maximum precision of 0.022 ‰ for δ¹³C was obtained when the data were averaged over 256 s, and the maximum for δ¹⁸O, 0.077 ‰, was obtained for the same averaging interval as for δ¹³C.

Figure 4Variability observed in (a) δ¹³C and (b) δ¹⁸O measurements using OA-ICOS before calibration. δ¹³C and δ¹⁸O measured using OA-ICOS for heavy standard and light standard are shown as red and blue circles respectively. Actual δ¹³C and δ¹⁸O values reported after measuring by IRMS for heavy standard and light standard are shown as red and blue dashed lines respectively.

Download

To correct for CO₂ concentration-dependent errors in raw δ¹³C and δ¹⁸O data, we analysed data obtained from the OA-ICOS to determine the sensitivity of δ¹³C and δ¹⁸O measurements against changing concentrations of CO₂. We observed a specific pattern of deviance in the measured isotopic data from the absolute values (both for δ¹³C and δ¹⁸O) across CO₂ concentration ranging from 25 000 to 400 ppm (see Fig. 4). Uncalibrated δ¹³C and δ¹⁸O measurements showed a standard deviation of 6.44 ‰ and 6.80 ‰ respectively, when measured under changing CO₂ concentrations.

Table 1Correction factor models are fitted for Diff-δ¹³C, DF (degrees of freedom), AIC_C (Akaike information criterion), and [CO₂] CO₂ concentration in ppm.

Download Print Version | Download XLSX

Table 2Correction factor models are fitted for Diff-δ¹⁸O, DF (degrees of freedom), AIC_C (Akaike information criterion), and [CO₂] CO₂ concentration in ppm.

Download Print Version | Download XLSX

Figure 5Mathematical models for concentration dependent drift in OA-ICOS measurements of stable isotopes of carbon (a) and oxygen (b) in CO₂ from IRMS measurements. Blue circles show Diff-δ¹³C (a) and Diff-δ¹⁸O (b) data points, and lines represent different mathematical models fitted on the measured data.

Download

Figure 6Corrected (a, c) δ¹³C and (b, d) δ¹⁸O measurements by OA-ICOS CO₂ carbon isotope analyser. δ¹³C and δ¹⁸O measured for heavy standard and light standard are shown as red and blue circles respectively. Actual δ¹³C and δ¹⁸O values reported after measuring by IRMS are shown as black dashed lines, and 95 % confidence intervals are shown as coloured dashed lines, respectively.

Download

The dependency of δ¹³C and δ¹⁸O values on the CO₂ concentration was compensated by using a non-linear model. The deviations (Diff-δ) of the measured delta values (δ_(OA-ICOS)) from the absolute value of the standard gas (δ_(IRMS)) at different concentrations of CO₂ were calculated (Diff-$\mathit{\delta }={\mathit{\delta }}_{\text{(OA-ICOS)}}-{\mathit{\delta }}_{\text{(IRMS)}}$). Several mathematical models were then fitted to Diff-δ as a function of changing CO₂ concentration (see Fig. 5). The mathematical model with the best fit for Diff-δ data was selected using the corrected Akaike information criterion (AIC_C; Glatting et al., 2007; Hurvich and Tsai, 1989; Yamaoka et al., 1978). The non-linear model fits applied for Diff-δ¹³C and Diff-δ¹⁸O measurements are given in Tables 1 and 2, respectively. For Diff-δ¹³C, a three-parameter exponential model fitted best with r²=0.99 (see Table 3 for the values of the parameters; see Fig. S3a for model residuals), and a three-parameter power function model (see Table 2) with r²=0.99 showed the best fit for Diff-δ¹⁸O (see Table 3 for the values of the parameters; see Fig. S3b for model residuals). The best fit was then introduced into the measured isotopic data (δ¹³C and δ¹⁸O) and corrected for concentration-dependent errors (see Fig. 6). After correction, the standard deviation of δ¹³C was reduced to 0.08 ‰, and the deviation of δ¹⁸O to 0.09 ‰, for all measurements across the whole CO₂ concentration range.

Figure 7Three-point calibration lines for (a) δ¹³C and (b) δ¹⁸O measurements using OA-ICOS with 95 % confidence interval.

Download

After correcting the measured δ¹³C and δ¹⁸O values for the CO₂ concentration-dependent deviations, a three-point calibration (Sturm et al., 2012) was made by generating linear regressions with the concentration-corrected δ¹³C and δ¹⁸O values against absolute δ¹³C and δ¹⁸O values (see Fig. 7; see Fig. S4 for linear regression residuals). Using the linear regression lines, we were able to measure the validation gas standard, with standard deviations of 0.0826 ‰ for δ¹³C and 0.0941 ‰ for δ¹⁸O.

Table 3Parameter values for correction factor model fit for Diff-δ¹³C and Diff-δ¹⁸O.

Download Print Version | Download XLSX

For the LGR CCIA 36-d, we found that routine calibration (correction for concentration-dependent error plus three-point calibration) was necessary for obtaining the required accuracy, in particular under fluctuating CO₂ concentrations. The LGR CCIA-36d offers an option for calibration against a single standard, a feature which was already in place in a predecessor model (CCIA DLT-100; Guillon et al., 2012). This internal calibration is sufficient when LGR CCIA-36d is operated only under stable CO₂ concentrations. To correct for the concentration dependency, we introduced mathematical model fits, which corrected for the deviation pattern found for both δ¹³C and δ¹⁸O. We assume that these deviations are instrument specific and that the fitting parameters need to be adjusted for every single device. Experiments conducted to investigate the influence of external temperature fluctuations on OA-ICOS measurements did not show any significant changes in the temperature inside the optical cavity of the OA-ICOS (see Fig. S1). The previous version of the Los Gatos CCIA was strongly influenced by temperature fluctuations during sampling (Guillon et al., 2012). The lack of temperature dependency as observed here with the most recent model can be mostly due to the heavy insulation provided with the system, which was not found in the older models.

Guillon et al. (2012) found a linear correlation between CO₂ concentration and respective stable isotope signatures with a previous version of the Los Gatos CCIA CO₂ stable isotope analyser. In our experiments with the OA-ICOS, the best fitting correlations between CO₂ concentration and δ¹³C and δ¹⁸O measurements were exponential and power functions, respectively. We assume that measurement accuracy is influenced by the number of CO₂ molecules present inside the laser cavity of the particular laser spectrometer, as we observed large standard deviation in isotopic measurements at lower CO₂ concentrations. This behaviour of an OA-ICOS can be expected, as it functions by sweeping the laser along an absorption spectrum, measuring the energy transmitted after passing through the sample. Therefore, energy transmitted is proportional to the gas concentration in the cavity. The laser absorbance is then determined by normalising against a reference signal, finally calculating the concentration of the sample measured by integrating the whole spectrum of absorbance (O'Keefe et al., 1999).

Figure 8Depth profile of (a) δ¹³C, (b) carbon content, (c) δ¹³C of soil carbonate, and (d) δ¹⁸O of soil carbonate in calcareous soil.

Download

Figure 9Time course of the evolution of soil gas CO₂ (ppm), δ¹³C, and δ¹⁸O in calcareous (a, c, e) and acidic (b, d, f) soils. Data collected continuously over a 12 h time frame for the calcareous soil and a 14 h time window with intermittent data collection for the acidic soil.

Download

Figure 10Daily average data of soil CO₂ (ppm), δ¹³C, and δ¹⁸O in calcareous (a, b, c) and acidic (d, e, f) soils across soil depth profiles.

Download

3.2 Variation in soil CO₂ concentration, carbon, and oxygen isotope values

Figures 9 and 10 show the CO₂ concentration and the δ¹³C and δ¹⁸O measurements of soil CO₂ in the calcareous as well as in the acidic soil across the soil profile with a sub-daily resolution and as averages for the day, respectively. We observed an increase in the CO₂ concentration across the soil depth profile for both the calcareous and the acidic soil. Moreover, there were rather contrasting δ¹³C values across the profile for the two soil types. In the calcareous soil, CO₂ was relatively enriched in ¹³C in the surface soil (4 cm) as compared to the 8 cm depth. Below 8 cm down to 80 cm depth, we found an increase in δ¹³C values. At 80 cm depth, the δ¹³C in soil CO₂ ranged between −7.15 ‰ and −3.35 ‰ (see Fig. 9), with a daily average of $-\mathrm{6.19}\pm \mathrm{1.45}$ ‰ (see Fig. 10), hence being clearly above atmospheric values ($\approx -\mathrm{8.0}$ ‰). For δ¹⁸O values of calcareous soil, the depth profile showed no specific pattern, except for the δ¹⁸O values at 80 cm depth, which were found to be less negative than the values at the other depths. The δ¹⁸O value in the top 4 cm was found to be slightly more enriched that the 8 cm depth, and between 8–35 cm, δ¹⁸O values showed little variation relative to each other. For the sub-daily measurements, we observed a sharp decline in δ¹⁸O values at around 02:00 CET, which is also observed but less pronounced for the δ¹³C signal. We assume that the reason for such aberrant values is a technical issue rather than a biological process. It could be due to the fact that the internal pump in the OA-ICOS was not taking an adequate amount of gas into the optical cavity, thereby creating a negative pressure inside the cavity resulting in the observed aberrant values. The patterns observed for the δ¹³C values of CO₂ in the calcareous soil with ¹³C enrichment in deeper soil layers can be explained by a substantial contribution of CO₂ from abiotic origin to total soil CO₂ release as a result of carbonate weathering and subsequent outgassing from soil water (Schindlbacher et al., 2015). According to Cerling (1984), the distinct oxygen and carbon isotopic composition of soil carbonate depends primarily on the isotopic signature of meteoric water and on the proportion of C₄ biomass present at the time of carbonate formation (Cerling, 1984) but also on numerous other factors that determine the ¹³C value of soil CO₂. CO₂ released as a result from carbonates in calcareous soil site have a distinct δ¹³C value of −9.3 (mean value across soil profile 0–80 cm depth; Fig. 8c), while CO₂ released during biological respiratory processes has δ¹³C values around −24 ‰, as observed in the acidic soil (Fig. 10e). The δ¹³C values of soil CO₂ observed in the deepest soil layer in the calcareous soil site most likely indicate the presence of carbonate sources of a pedogenic and geologic origin. Even though the contribution of CO₂ from abiotic sources to soil CO₂ is often considered to be low, several studies have reported significant proportions ranging between (10 %–60 %), emanating from abiotic sources (Emmerich, 2003; Plestenjak et al., 2012; Ramnarine et al., 2012; Serrano-Ortiz et al., 2010; Stevenson and Verburg, 2006; Tamir et al., 2011). Bowen and Beerling (2004) showed that isotope effects associated with soil organic matter (SOM) decomposition can cause a strong gradient in δ values of soil organic matter with depth but are not always reflected in the δ¹³C values of soil CO₂. We have measured soil samples for bulk soil δ¹³C, carbonate δ¹³C, and δ¹⁸O values and have also determined the percentage of total carbon in the soil across a depth profile of (0–80 cm; see Fig. 8). We observed an increase in δ¹³C values for bulk soil in deeper soil layers (see Fig. 8a, c). Moreover, the carbonate δ¹³C values also got more positive in the 60–80 cm layer. Since total organic carbon content decreases with depth, it can be assumed that the CO₂ derived from carbonate weathering, having less negative δ¹³C values, more strongly contributed to the soil CO₂ (especially since we see an increase in soil CO₂ concentration with depth). This is accordance with the laser-based measurements which showed a strong increase in the δ¹³C of soil CO₂ in the deepest soil layer, leading us to the hypothesis that this signal indicates a strong contribution of carbonate-derived CO₂. Water content, soil CO₂ concentration, and the presence of organic acids or any other source of H⁺ are the major factors influencing carbonate weathering, and variations in soil CO₂ partial pressure, moisture, temperature, and pH can cause degassing of CO₂ which contributes to the soil CO₂ efflux (Schindlbacher et al., 2015; Zamanian et al., 2016). CaCO₃ solubility in pure H₂O at 25 ^∘C is 0.013 g L⁻¹, but in weak acids like carbonic acid, the solubility is increased up to 5 fold (Zamanian et al., 2016). The production of carbonic acid due to CO₂ dissolution will convert carbonate to bicarbonates, resulting in exchange of carbon atoms between carbonates and dissolved CO₂.We assume that at our study site, the topsoil is decarbonated due to intensive agriculture for a longer period, thus the soil CO₂ there originates primarily from autotrophic and heterotrophic respiratory activity. In contrast to the deeper soil layers, where the carbonate content is high, CO₂ from carbonate weathering is assumed to be a dominating source of soil CO₂. Also, outgassing of CO₂ from the large groundwater body underneath the calcareous Gleysol might contribute to the inorganic CO₂ sources in the deeper soil, as we found the groundwater table to be 1–2 m below the soil surface. Relative ¹³C enrichment of the CO₂ in the topsoil (4 cm) compared to that at 8 cm depth is probably due to the invasive diffusion of atmospheric CO₂, which has a δ¹³C value close to −8 ‰ (e.g. Levin et al., 1995). The δ¹⁸O patterns for CO₂ between 4 and 35 cm might reflect the δ¹⁸O of soil water with stronger evaporative enrichment at the top and ¹⁸O depletion towards deeper soil layers. In comparison, the strong ¹⁸O enrichment of soil CO₂ towards 80 cm in the calcareous Gleysol very likely reflects the ¹⁸O values of groundwater lending further support to the high contribution of CO₂ originating from the outgassing of groundwater. We, however, need then to assume that the oxygen in the CO₂ is not in full equilibrium with the precipitation-influenced soil water. Since mainly microbial carbonic anhydrase mediates the fast equilibrium between CO₂, and water in the soil and the microbial activity is low in deeper soil layers (Schmidt et al., 2011), we speculate that in deep layers with a significant contribution of groundwater derived CO₂ to the CO₂ pool, a lack of full equilibration with soil water might be the reason for the observed δ¹⁸O values.

Soil CO₂ concentration in the acidic soil showed a positive relationship with soil depth as CO₂ concentration increased along with increasing soil depth (Figs. 9 and 10). CO₂ concentrations were distinctly higher than in the calcareous soil, very likely due to the finer texture than in the gravel-rich calcareous soil. δ¹³C values amounted to approximately −26 ‰ in 30 and 60 cm depth, indicating the biotic origin from (autotrophic and heterotrophic) soil respiration (Schönwitz et al., 1986). In the topsoil, δ¹³C values did not strongly increase, pointing towards a less pronounced inward diffusion of CO₂ in the acidic soil site, most likely due to more extensive outward diffusion of soil CO₂, as indicated by the still very high CO₂ concentration at 10 cm creating a sharp gradient between soil and atmosphere. Moreover, the acidic soil was rather dense and contained no stones, strongly suggesting that gas diffusivity was rather small. δ¹⁸O depth patterns of soil CO₂ in the acidic soil most likely reflected δ¹⁸O values of soil water as CO₂ became increasingly ¹⁸O depleted from top to bottom. The δ¹⁸O of deeper soil layers CO₂ (30–60 cm) was close to the values expected when full oxygen exchange between soil water and CO₂ occurred (Kato et al., 2004). Assuming an ¹⁸O fractionation of 41 ‰ between CO₂ and water (Brenninkmeijer et al., 1983), this would result in an expected value for CO₂ of $\approx -\mathrm{10}\pm \mathrm{2}$ ‰ vs. VPDB CO₂. Corresponding results have been shown for δ¹⁸O of soil CO₂ using similar hydrophobic gas-permeable membrane tubes used when measuring δ¹⁸O of soil CO₂ and soil water in situ (Gangi et al., 2015).