The surface CO2 efflux was measured using the closed-chamber method. A total of 30 PVC collars with a diameter of 10.4 cm and a height of 10 cm were installed 5 cm deep in the soil around the three subsoil observatories. The organic layer of 15 collars was removed in order to be able to distinguish between mineral soil respiration and total soil respiration. Soil respiration was measured with the EGM-3 SRC-1 soil respiration chamber (PP Systems, USA) and the LI-6400-09 soil chamber (LI-COR, Inc., USA). The measurement system was changed due to technical problems with the EGM-3 system; however, a comparison between the two systems revealed only minor differences. Each collar was measured three times per sampling day from March 2014 to March 2016, with sampling ranging from once a month to once a week. Annual soil respiration was derived from the linear interpolation of measured CO2 fluxes from the collars. Furthermore, soil respiration was modelled by fitting an Arrhenius-type model (Eq. ), introduced by and using soil temperature data from 10 cm depth, and the measured CO2 fluxes as follows: 1F0=a×eE0T+273.2-T0×T-10283.2-T0, where F0 is soil respiration (µmol m-2 s-1), a, E0 and T0 are fitted model parameters, and T is the soil temperature at 10 cm depth (in degrees Celsius).

In addition to continuous CO2 concentration monitoring, two gas samples per depth and subsoil observatory were taken at the end of the stainless steel tubing from the suction cups with a syringe and filled into 12 mL evacuated gas vials (Labco Exetainer; Labco Limited, UK). The sampling started in May 2014, with an interval of between once a month and once a week. The CO2 concentration in the soil gas samples was analysed by gas chromatography (Agilent 7890A; Agilent Technologies, Inc., USA). The δ13C values of the CO2 samples were measured by an isotope ratio mass spectrometer (Delta Plus with a GP interface and GC box; Thermo Fisher Scientific, Germany) connected to a PAL autosampler (CTC Analytics AG, Switzerland). The 13C results are expressed in parts per thousand (ppt) relative to the international standard of Vienna Pee Dee Belemnite (VPDB).

Soil gas samples for radiocarbon analysis were taken in October and December 2014 in subsoil observatories 1 and 3. The CO2 was sampled using a self-made molecular sieve cartridge as described in . Briefly, each stainless steel cartridge was filled with 500 mg zeolite type 13X (40/60 mesh, charge 5634; IVA Analysetechnik GmbH & Co. KG, Germany), which is used as an adsorbent for CO2. The molecular sieve cartridges were connected to the installed gas samplers. The soil atmosphere of the corresponding depth was then pumped with an airflow of 7 mL min1 over a desiccant (Drierite; W. A. Hammond Drierite Co. Ltd, USA) to the molecular sieve cartridge for 40 min to trap the CO2 on the molecular sieve. Surface samples were taken from a respiration chamber . The atmospheric CO2 inside the chamber was removed prior to sampling by circulating an airflow of ≈ 1.5 L min-1 from the chamber through a column filled with soda lime until the equivalent of 2–3 chamber volumes had been passed over the soda lime. Thereafter, the airflow was run over a desiccant and the molecular sieve cartridge for 10 min to collect the CO2 sample.

In the laboratory, the adsorbed CO2 was released from the molecular sieve cartridge by heating the molecular sieve under a vacuum . The released CO2 was purified cryogenically and sealed in a glass tube. The radiocarbon (14C) analysis was directly performed on the CO2 with the gas ion source of the mini carbon dating system (MICADAS; Ionplus AG, Switzerland) at ETH Zurich . The 14C concentrations are reported as fraction modern carbon (F14C), whereby F14C values of less than one denote that the majority of the C was fixed before the nuclear bomb tests in the 1960s, while values greater than one indicate C fixation after the bomb tests.

This method is based on the assumption that molecular diffusion is the main gas transport in the soil atmosphere. Therefore, gas fluxes, e.g. CO2 fluxes in a soil profile, can be calculated from the CO2 concentration gradient and the effective gas diffusion coefficient in the specific soil layer of interest.

In order to account for temperature and pressure dependencies of the CO2 sensors, the CO2 concentrations were corrected with a compensation algorithm for the GMP221 (S1) provided by the manufacturer (Niklas Piiroinen, Vaisala Oyj, Finland, personal communication, 2014). For the flux calculation, CO2 volume concentrations were converted to CO2 mole concentrations (Eq. ) as follows: 2C=Cv×pR×T, where C is the CO2 mole concentration (µmol m-3), Cv is the CO2 volume fraction (µmol mol-1), p is the atmospheric pressure in Pascal (Pa), R is the universal gas constant (8.3144 J K-1 mol-1) and T is the soil temperature in kelvin (K) measured by temperature sensors at the corresponding soil depths. The CO2 flux of a soil layer was calculated using Fick's first law (Eq. ) as follows: 3F=-Ds×dCdz, where F is the diffusive CO2 flux (µmol m-2 s-1), Ds is the effective diffusivity in the soil atmosphere (m2 s-1) determined as described below, C is the CO2 concentration (µmol m-3) and z is the depth (metres). The equation is based on the assumption that (1) molecular diffusion is the dominating transport process in the soil atmosphere and other transport mechanisms – i.e. convective CO2 transport due to air pressure gradients or diffusion in the soil, and convective transport with soil water – are negligible, and (2) gas transport is 1D e.g.. The effective diffusivity Ds was calculated with Eq. () as follows: 4Ds=D0×τ, where D0 is the CO2 diffusivity in free air. The pressure and temperature effect on D0 were taken into account by the following: 5D0=Da0×p0p×TT01.75, where Da0 is a reference value of D0 at standard conditions (1.47×10-5 m2 s-1 at T0 293.15 K and p0 1.013×105 Pa) . The dimensionless tortuosity factor τ at each depth was modelled as a function of the air-filled pore space ε for each soil depth. The model was derived from a power function fit from laboratory diffusion experiments (see above) on the undisturbed soil cores.

To account for the non-uniform vertical distribution of the soil water content in the soil profile, Ds was estimated as the harmonic average between the two measurement depths as follows: 6Ds=Δz1+Δz2Δz1Dsz1+Δz2Dsz2, where Δz1,2 (metres) is the thickness of the corresponding soil layer, and Dsz1,2 is the effective diffusivity of the respective soil layer. Finally, assuming a constant flux between measured CO2 at depth zi and zi+1, the CO2 flux (Fi) was calculated by combining Eqs. ()–() as follows: 7Fi=Δzi+Δzi+1ΔziDszi+Δzi+1Dszi+1×Ci+1-Cizi+1-zi, where Fi is the CO2 flux (µmol m-2 s-1) at the upper boundary (zi) between depth zi and zi+1 (metres). To calculate soil respiration (F0) at the surface with the gradient method, a CO2 concentration of 400 µmol mol-1 at the soil surface and a constant Ds for the first 10 cm were assumed.

The CO2 production (Pi) in a soil layer was calculated as the difference between the flux (Fi) leaving the specific soil layer at the upper boundary (zi) and the input flux (Fi+1) at the lower boundary (zi+1) of the specific soil layer. Therefore, Pi had the unit of a flux (µmol m-2 s-1) a similar approach was done by, for example,. 8Pi=Fi-Fi+1.

Total soil respiration was calculated as the sum of CO2 production in all soil layers. Equation () is based on the assumption of a steady-state diffusion. Steady-state conditions for CO2 concentration and volumetric water content were mostly given, except during a few heavy rain events where steady-state conditions were not met due to changing water contents in the profiles. Most soils exhibit increasing CO2 concentrations with increasing soil depth. Therefore, CO2 production is mostly positive with upward CO2 fluxes. However, if the CO2 concentration in a soil layer is greater than in the layers below, the calculated CO2 production in the layers below can become negative (downward directed). Hence, in the present study, no CO2 production was assumed when the calculated CO2 production in a soil layer was negative. This approach was based on the assumption that there are no relevant CO2 sinks in the soil profile. Furthermore, negative CO2 production is considered as CO2 storage, which will be released if the CO2 concentration gradient or diffusion conditions change. In OB1, negative CO2 production values were calculated in the first year at 30–50 cm depth (331 out of 365 d) and at 50–90 cm depth (359 out of 365 d). In the second year, negative values also occurred in OB1 at 30–50 cm depth (8 out of 308 d) and at 50–90 cm depth (182 out of 308 d).

To determine the contribution of the labelled leaf litter to CO2 in the soil atmosphere, we used the isotopic mixing equation (Eq. ) as follows: 9L=1-δ13CM-δ13CLδ13CB-δ13CL, where δ13CM is the isotopic signature of the gas sample, δ13CL is the isotopic signature of the labelled leaf litter (1241 ‰ for OB1 and 1880 ‰ for OB2 and OB3), and δ13CB is the average isotopic signature of the soil atmosphere for each observatory and depth before the labelled leaf litter was applied, assuming there was no change.

The CO2 fluxes and productions for each layer and isotopologue of CO2 (12CO2 and 13CO2) were calculated using the isotopic signature of the soil atmosphere and Eqs. ()–(). To account for different effective diffusivities of 12CO2 and 13CO2, the effective diffusivity Ds for 13CO2 was adjusted, according to , as follows: 10Ds=12Ds=1.0044×13Ds, where it is assumed that Ds is equivalent to 12Ds due to the fact that about 99 % of total CO2 is 12CO2.

To determine the contribution of the labelled leaf litter to the CO2 production in a soil layer and accounting for diffusion effects, the isotopic signature of CO2 production (δ13P-CO2) in each soil layer was calculated with Eq. () as follows: 11δ13P-CO2=13P-CO2Rst×12P-CO2-1×1000, where Rst is the isotopic ratio of the VPDB reference standard, while 13P-CO2 and 12P-CO2 are the CO2 production for each isotopologue of the respective soil layer. Afterwards, Eq. () was used to calculate the amount of labelled leaf litter to total CO2 production, where δ13CB was substituted with the average isotopic signature of CO2 production (Eq. ) before the labelling, and δ13CM was substituted with the isotopic signature of CO2 production. The litter-derived CO2 production was calculated by multiplying the amount of labelled leaf litter (L) with the total CO2 production of the respective soil layer.

The isotopic signature of soil CO2 (δ13CO2) in the observatories before the start of the labelling experiment ranged from -25.4 ‰ to -21.8 ‰, with no significant differences between soil depths (Fig. a). The labelling experiment was conducted to assess the fate of fresh litter added on top of the organic layer into different C fractions (e.g. SOC and DOC), including soil CO2. A total of 6 d after the application of the 13C-labelled leaf litter, CO2 was already enriched in litter-derived C down to 90 cm depth in all the observatories. The isotopic signature ranged from 70 ‰ at 10 cm depth to -19 ‰ at 90 cm depth (Fig. b). Thus, the maximum contribution of litter-derived C to total CO2 was 5 % at 10 cm depth 6 d after the litter replacement (Fig. c). At 90 cm, the maximum amount of litter-derived CO2 was 0.6 % 2 weeks after the beginning of the labelling experiment (Fig. c). In addition, minor peaks with up to 0.8 % of CO2 derived from the labelled litter were observed at all depths after rain events within the first 6 months of litter application. The average contribution of litter-derived CO2 decreased with time and reached a range of 2.5 % to 0.2 % at 10 cm depth from January 2015 to July 2016. The total amount of labelled litter-derived C to the CO2 production below 10 cm was 291 mg C m-2 (±127) (Fig. ), which accounted for 0.12 % of the total CO2 production below 10 cm depth.

Assuming that diffusion is the main transport process of CO2 in the soil atmosphere, the CO2 flux between two soil layers can be calculated for each C isotope separately. As mentioned, a positive flux indicates the release of CO2 from mineralisation or root respiration in the respective soil layer. A negative flux, in turn, represents the downward diffusion of CO2 from the layer above. Due to the high 13C enrichment in the applied litter, negative 13CO2 fluxes can indicate a downward diffusion of litter-derived CO2 from the soil layer above (Fig. ). On average for the three observatories, 20 out of 41 samplings had negative 13CO2 fluxes below 90 cm depth, indicating a downward movement of labelled litter-derived CO2. Furthermore, OB2 and OB3 had positive 13CO2 fluxes between 10 and 90 cm, indicating a transport of labelled litter-derived C down the soil profile as dissolved organic carbon (DOC) and mineralisation of this DOC. Meanwhile, the observed 13C enrichment in CO2 in OB1 below 30 cm depth might also be influenced by diffusion of labelled litter-derived 13CO2 from the soil layer above (10 to 30 cm).

The radiocarbon content of the bulk SOC decreased strongly with increasing soil depth from close to atmospheric values (F14C 0.99) at 10 cm to an apparent age of about 3460 years before the present (F14C 0.65) at 110 cm depth (Fig. ; grey triangles). In contrast, the 14C concentrations of the CO2 in the soil atmosphere were relatively constant throughout the soil profile and for both samplings, with values in the range of 1.03–1.07 F14C and, thus, they derive mainly from the post-bomb period (Fig. ; black dots). This indicates a young source of CO2 production. Consequently, old subsoil SOC was not detected as a significant source of CO2 production.

In this study, a unique labelling approach was used to estimate the contribution of aboveground litter to CO2 production along a soil profile by applying stable isotope-enriched leaf litter to the soil surface. These results showed that litter-derived C did not significantly contribute to annual CO2 production below 10 cm depth. Leaf litter is decomposed and washed into the mineral soil as DOC. Within 1 year, only 0.13 % of total CO2 production between 10 and 90 cm originated from the labelled leaf litter. It should be considered that part of the measured 13CO2 may derives from the turnover of the microbial necromass, which could lead to an overestimation of the litter-derived CO2. However, the isotopic signature of the biomass at the study site ranges from -27 ‰ (10 cm) to -25.8 ‰ (90 cm; Sebastian Preußer and Ellen Kandeler, personal communication, 2020) which is lower than the isotopic signature of the soil atmosphere before the application of the labelled leaf litter. This indicates that the turnover of microbial biomass had no measurable effect on the isotopic signature of the soil atmosphere. Instead, it should be mentioned again that the determination of the CO2 production is based on the assumption of steady-state conditions in the soil. Sudden changes in the CO2 concentration or soil moisture, for example, after precipitation events can lead to a violation of this assumption, and the uncertainties in litter-derived CO2 production increase for these periods. A non-steady-state model might be better to describe such periods, but a non-steady-state model may also require a higher spatial and temporal resolution of measurements (water content, CO2 and 13CO2) at depths of 0–10 cm. Nevertheless, further research should address this point. However, in periods without major precipitation events (before the 13CO2 sampling) the contribution of litter-derived CO2 to total CO2 remained below 1 %. This indicates that, despite the uncertainties due to non-steady-state conditions, the mineralisation of DOC originating from the organic layer was a minor source of CO2 production in the soil profile below 10 cm. The average DOC flux in the subsoil observatories in the first year was estimated to be 20 g C m-2 yr-1 at 10 cm depth and 2 g C m-2 yr-1 at 50 cm depth, indicating a DOC input of 18 g C m-2 yr-1 into the 10 and 50 cm depth increments . An assumed complete mineralisation of this DOC would account for 11 % of CO2 production at this depth increment. Overall, most of the CO2 production between a depth of 10 and 90 cm must be derived from autotrophic respiration and heterotrophic respiration in the rhizosphere.

The very similar radiocarbon contents of soil CO2 produced at different depths, which were 1.06 F14C on average, revealed that ancient SOC components were not a major source of CO2 production. The results indicate that the CO2 originated mainly from young (several decades old) C sources, presumably mainly from root respiration, its exudates and DOC. Other studies have found similar results at a grassland site in California down to 230 cm depth and in temperate forests down to 100 cm . In addition, incubated root-free soil from three depths (15, 50 and 90 cm) and compared the radiocarbon signature of the respired CO2 with their results from the field. They found that CO2 from the short-term incubations had the same modern signature as the field measurements despite the high 14C age of the bulk SOC at 90 cm depth ∼1000 yr BP;. This supports the findings of the present experiment. Therefore, microbial respiration in temperate subsoils is mainly fed by relatively young C sources fixed less than 60 years ago.

A highly 13C-enriched CO2 source was introduced to the top of a soil profile. Shortly afterwards, an enrichment of 13C was measured in CO2 along the whole soil profile (Fig. b). However, this enrichment could not only be linked to the transport and mineralisation of litter-derived C along the soil profile (e.g. DOC in seepage water). The diffusion of 13CO2 down the soil profile also has to be taken into account. According to Fick's first law, 13CO2 diffuses into the soil profile following the 13CO2 gradient independently from the 12CO2. Thus, even though the total CO2 concentration increased with soil depth, meaning an upward diffusion of 12CO2, the 13CO2 gradient could be the opposite due to 13C-enriched leaf litter, leading to a downward diffusion of 13CO2. Consequently, this could lead to a misinterpretation of the pathways of subsoil 13CO2 in tracer experiments. Furthermore, this effect should also be taken into consideration when interpreting 14CO2 soil profile measurements as an indicator of the age of the mineralised SOC, as in other field studies e.g.. Downward diffusion of 14CO2 might be an important factor for explaining the observed 14CO2 profiles. If this downward diffusion is the case, the 14CO2 gradient should not have a continuous decrease with soil depth since the 14CO2 gradient is the driving factor for diffusion according to Eq. (). In fact, 14CO2 concentration at 30 cm depth in subsoil OB1 was greater than at 50 cm depth (Fig. ), which in turn led to a downward diffusion of 14CO2 from a depth of 30 to 50 cm. This might lead to a rejuvenation in the 14CO2 soil profile and to an underestimation of the mineralisation of old SOC in subsoils.